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The degree of the Bernstein polynomials is computed from the length of $P$. + + +```python +def point_on_bezier_curve(P,x): + n = len(P) - 1 + b = all_bernstein(n, x) + c = 0. + for k in range(0, n+1): + c += b[k]*P[k] + return c +``` + +## Examples + +````{prf:example} +:label: bezier-curve-ex-1 + +```python +nt = 200 +ts = np.linspace(0., 1., nt) + +P = np.zeros((2, 2)) +P[:, 0] = [0., 1.] +P[:, 1] = [1., 0.] + +Q = np.zeros((nt, 2)) +for i,t in enumerate(ts): + Q[i,:] = point_on_bezier_curve(P,t) + +plt.plot(Q[:,0], Q[:,1], '-b') +plt.plot(P[:,0], P[:,1], '--ok', linewidth=0.7) + +for i in range(0, 2): + x,y = P[i,:] + plt.text(x+0.05,y+0.05,'$\mathbf{P}_{' + str(i) + '}$') + +plt.axis([-0.2, 1.2, -0.2, 1.2]) +``` + +![png](images/bezier/output_16_0.png) +```` + +````{prf:example} +:label: bezier-curve-ex-2 + +```python +nt = 200 +ts = np.linspace(0., 1., nt) + +P = np.zeros((3, 2)) +P[:, 0] = [1., 1., 0.] +P[:, 1] = [0., 1., 1.] + +Q = np.zeros((nt, 2)) +for i,t in enumerate(ts): + Q[i,:] = point_on_bezier_curve(P,t) + +plt.plot(Q[:,0], Q[:,1], '-b') +plt.plot(P[:,0], P[:,1], '--ok', linewidth=0.7) + +for i in range(0, 3): + x,y = P[i,:] + plt.text(x+0.05,y+0.05,'$\mathbf{P}_{' + str(i) + '}$') + +plt.axis([-0.2, 1.2, -0.2, 1.2]) +``` + +![png](images/bezier/output_17_0.png) +```` + +````{prf:example} +:label: bezier-curve-ex-3 + +```python +nt = 200 +ts = np.linspace(0., 1., nt) + +P = np.zeros((4, 2)) +P[:, 0] = [1., 1., 0., -1.] +P[:, 1] = [0., 1., 1., 0.] + +Q = np.zeros((nt, 2)) +for i,t in enumerate(ts): + Q[i,:] = point_on_bezier_curve(P,t) + +plt.plot(Q[:,0], Q[:,1], '-b') +plt.plot(P[:,0], P[:,1], '--ok', linewidth=0.7) + +for i in range(0, 3): + x,y = P[i,:] + plt.text(x+0.05,y+0.05,'$\mathbf{P}_{' + str(i) + '}$') +i = 3 +x,y = P[i,:] +plt.text(x-0.05,y+0.05,'$\mathbf{P}_{' + str(i) + '}$') + +plt.axis([-1.2, 1.2, -0.2, 1.2]) +``` + +![png](images/bezier/output_18_0.png) +```` + +````{prf:example} +:label: bezier-curve-ex-4 + +```python +nt = 200 +ts = np.linspace(0., 1., nt) + +P = np.zeros((4, 2)) +P[:, 0] = [1., 1., 0., -1.] +P[:, 1] = [0., 1., -0.5, 0.] + +Q = np.zeros((nt, 2)) +for i,t in enumerate(ts): + Q[i,:] = point_on_bezier_curve(P,t) + +plt.plot(Q[:,0], Q[:,1], '-b') +plt.plot(P[:,0], P[:,1], '--ok', linewidth=0.7) + +for i in range(0, 3): + x,y = P[i,:] + plt.text(x+0.05,y+0.05,'$\mathbf{P}_{' + str(i) + '}$') +i = 3 +x,y = P[i,:] +plt.text(x-0.05,y+0.05,'$\mathbf{P}_{' + str(i) + '}$') + +plt.axis([-1.2, 1.2, -0.7, 1.2]) +``` + +![png](images/bezier/output_19_0.png) +```` + +````{prf:example} +:label: bezier-curve-ex-5 + +```python +nt = 200 +ts = np.linspace(0., 1., nt) + +P = np.zeros((4, 2)) +P[:, 0] = [1., 0., 1., -1.] +P[:, 1] = [0., 1., 1., 0.] + +Q = np.zeros((nt, 2)) +for i,t in enumerate(ts): + Q[i,:] = point_on_bezier_curve(P,t) + +plt.plot(Q[:,0], Q[:,1], '-b') +plt.plot(P[:,0], P[:,1], '--ok', linewidth=0.7) + +for i in range(0, 3): + x,y = P[i,:] + plt.text(x+0.05,y+0.05,'$\mathbf{P}_{' + str(i) + '}$') +i = 3 +x,y = P[i,:] +plt.text(x-0.05,y+0.05,'$\mathbf{P}_{' + str(i) + '}$') + +plt.axis([-1.2, 1.2, -0.2, 1.2]) +``` + +![png](images/bezier/output_20_0.png) +```` + +## Derivatives of a Bezier curve + +Using the formulae \ref{eq:bernstein-der}, we have + +$$ +\begin{align} + \mathcal{C}^\prime(t) = \sum_{k=0}^n \mathbf{P}_k {B_k^n}^\prime(t) + = \sum_{k=0}^n n \mathbf{P}_k \left(B_{k-1}^{n-1}(x) - B_k^{n-1}(x) \right) +\end{align} +$$ + +by reordering the indices, we get \ref{eq:bezier-curve-der} + +$$ +\begin{align} + \mathcal{C}^\prime(t) &= \sum_{k=0}^{n-1} n \left( \mathbf{P}_{k+1} - \mathbf{P}_k \right) B_k^{n-1}(t) + \label{eq:bezier-curve-der} +\end{align} +$$ + +Therefor, we get the direct acces to the first order derivatives at the extremeties of a Bézier curve using the formulae \ref{eq:bezier-curve-der-1-ext} + +$$ +\begin{align} + \begin{cases} + \mathcal{C}^\prime(0) = n \left( \mathbf{P}_{1} - \mathbf{P}_0 \right) + \\ + \mathcal{C}^\prime(1) = n \left( \mathbf{P}_{n} - \mathbf{P}_{n-1} \right) + \end{cases} + \label{eq:bezier-curve-der-1-ext} +\end{align} +$$ + +Second derivatives can also be computed directly from the control points using the formulae \ref{eq:bezier-curve-der-2-ext} + +$$ +\begin{align} + \begin{cases} + \mathcal{C}^{\prime\prime}(0) = n(n-1) \left( \mathbf{P}_{0} - 2 \mathbf{P}_1 + \mathbf{P}_{2} \right) + \\ + \mathcal{C}^{\prime\prime}(1) = n(n-1) \left( \mathbf{P}_{n} - 2 \mathbf{P}_{n-1} + \mathbf{P}_{n-2} \right) + \end{cases} + \label{eq:bezier-curve-der-2-ext} +\end{align} +$$ + + +````{prf:definition} $r^{th}$ forward difference + + Let us consider a set of (control) points $\mathbf{P}$. + The $r^{th}$ forward difference of $\mathbf{P}$ is defined as +$$ + \begin{align} + \triangle^r \mathbf{P}_i := \triangle^{r-1} \mathbf{P}_{i+1} - \triangle^{r-1} \mathbf{P}_i + \end{align} +$$ + with +$$ + \begin{align} + \triangle \mathbf{P}_i = \triangle^1 \mathbf{P}_i := \mathbf{P}_{i+1} - \mathbf{P}_i + \end{align} +$$ +```` + +````{prf:proposition} High order dirivatives +$$ + \begin{align} + \mathcal{C}^{(r)}(t) = \frac{n!}{\left( n-r \right)!} \sum\limits_{i=0}^{n-r} \triangle^r \mathbf{P}_i B_i^{n-r}(t) + \label{eq:bezier-high-deriv} + \end{align} +$$ +```` + +Eqs (\ref{eq:bezier-curve-der-1-ext}) and (\ref{eq:bezier-curve-der-2-ext}) can be generelaized for high order derivatives. We have in fact the following result: + +```{prf:remark} +The derivatives of a Bézier curve at its extremeties up to order $r$ depend only on the first (or last) $r+1$ control points, and vice versa. +``` + +````{prf:proposition} + \label{prop:bezier-forward-difference} + $$\triangle^r \mathbf{P}_0 = \sum\limits_{i=0}^{r} \left( -1 \right)^{r-i} \binom{r}{i} \mathbf{P}_i $$ +```` + +## Integration of Bezier curves + +````{prf:proposition} +A primitive of A Bézier curve $\mathcal{C}(t) = \sum_{k=0}^n \mathbf{P}_k B_k^n(t)$ has the Bézier representation + +$$ +\begin{align} + \left( \int \mathcal{C} \right) (t) = \sum_{k=0}^{n+1} \mathbf{Q}_k B_k^{n+1}(t) + \label{eq:bezier-primitive} +\end{align} +$$ + +where + +$$ +\begin{align} + \mathbf{Q}_k := \mathbf{Q}_{k-1} + \frac{1}{n+1} \mathbf{P}_{k-1} + = \mathbf{Q}_{0} + \frac{1}{n+1} \left( \sum\limits_{i=0}^{k-1} \mathbf{P}_{i} \right) +\end{align} +$$ +```` + +Here, $\mathbf{Q}_{0}$ denotes an arbitrary integration constant. + +```{prf:remark} + Using Eq. (\ref{eq:bezier-primitive}), we have $\int_0^1 \mathcal{C}(t)~dt = \frac{1}{n+1}\left( \sum\limits_{i=0}^n \mathbf{P}_i \right)$. +``` + +## Properties of Bezier curves +Because of the *symmetry* of the Bernstein polynomials, we have + +- $\sum_{k=0}^n \mathbf{P}_k B_k^n = \sum_{k=0}^n \mathbf{P}_k B_{n-k}^n$ + +Thanks to the interpolation property, for $B_0^n$ and $B_n^n$, of the Bernstein polynomials at the endpoints, we get + +- $\mathcal{C}(0) = \mathbf{P}_0$ and $\mathcal{C}(1) = \mathbf{P}_n$ + +Using the partition unity property of the Bernstein polynomials, we get + +- any point $\mathcal{C}(t)$ is an *affine combination* of the control points + +Therefor, + +- Bézier curves are affinely invariant; *i.e.* the image curve $\Phi(\sum_{k=0}^n \mathbf{P}_k B_k^n)$ of a Bézier curve, by an affine mapping $\Phi$, is the Bézier curve having $\left( \Phi(\mathbf{P}_i) \right)_{0 \le i \le n}$ as control points. + +due to the partition unity of the Bernstein polynomials and their non-negativity, + +- any point $\mathcal{C}(t)$ is a *convex combination* of the control points + +finally, we get the *convex hull property*, + +- A Bézier curve lies in the convex hull of its control points + +## DeCasteljau Algorithm +In this section, we introduce the deCasteljau algorithm Algo. (\ref{algo:decasteljau}). The basic idea comes from the following remark; +using the reccurence formulae Eq. (\ref{eq:bernstein-rec}), we have + +$$ +\begin{align} + \mathcal{C}(t) &= \sum_{k=0}^n \mathbf{P}_k B_k^n(t) = \sum_{k=0}^n \mathbf{P}_k \left( (1-t) B_k^{n-1}(t) + t B_{k-1}^{n-1}(t) \right) \\ + &= \sum_{k=0}^{n-1} \mathbf{P}_k^1 B_k^{n-1}(t) \quad\quad\quad\quad\quad [\mathbf{P}_k^{1} := (1-t)\mathbf{P}_k + t \mathbf{P}_{k+1}] \\ + &= \sum_{k=0}^{n-2} \mathbf{P}_k^2 B_k^{n-2}(t) \quad\quad\quad\quad\quad [\mathbf{P}_k^{2} := (1-t)\mathbf{P}_k^1 + t \mathbf{P}_{k+1}^1] \\ + &= \ldots \\ + &= \sum_{k=0}^{0} \mathbf{P}_k^n B_k^{0}(t) \quad\quad\quad\quad\quad [\mathbf{P}_k^{n} := (1-t)\mathbf{P}_k^{n-1} + t \mathbf{P}_{k+1}^{n-1}] \\ + &= \mathbf{P}_0^n +\end{align} +$$ + +```{prf:algorithm} Evaluation of a Bézier curve, defined by its control points $\mathbf{P}$ at $x$ +:label: algo-decasteljau +**Input** $\mathbf{P}, x$ +**Output** $value$ + +$n \gets { len } \left( \mathbf{P} \right) - 1$ + +$\mathbf{Q} \gets \mathbf{P}$ + +For $j \gets 0$ : $n$ + + For $i \gets 0$ : $n-j$ + + $Q[i] \gets (1-x) Q[i] + x Q[i+1]$ + +Return $Q[0]$ +``` + +```python +def decasteljau(P, x): + n = len(P) - 1 + Q = P.copy() + x1 = 1.-x + for j in range(1, n+1): + for i in range(0, n-j+1): + Q[i] = x1*Q[i] + x*Q[i+1] + c = Q[0] + return c +``` + +## Conversion from monomial form +Let us consider a monomial representation of a curve + +$$ +\begin{align} +\mathcal{C}(t) = \sum_{k=0}^n \mathbf{Q}_k t^k +\end{align} +$$ + +Since + +$$ +\begin{align} + t^k &= \frac{1}{\binom{n}{k}} \binom{n}{k} t^k \left(1-t+t \right)^{n-k} + = \frac{1}{\binom{n}{k}} \left( \sum\limits_{i=0}^{n-k} \binom{n}{k} \binom{n-k}{n-k-i} t^{i+k} \left( 1-t \right)^{n-k-i} \right) \\ + &= \frac{1}{\binom{n}{k}} \left( \sum\limits_{i=0}^{n-k} \binom{k+i}{k} B_{k+i}^n(t) \right) + = \frac{1}{\binom{n}{k}} \left( \sum\limits_{j=0}^{n} \binom{j}{k} B_{j}^n(t) \right) +\end{align} +$$ + +we get, + +$$ +\begin{align} +\mathcal{C}(t) = \sum_{k=0}^n \mathbf{Q}_k t^k = \sum_{k=0}^n \mathbf{Q}_k \frac{1}{\binom{n}{k}} \left( \sum\limits_{j=0}^{n} \binom{j}{k} B_{j}^n(t) \right) +\end{align} +$$ + +hence, + +$$ +\begin{align} +\mathcal{C}(t) = \sum_{j=0}^n \left(\sum\limits_{k=0}^{n} \frac{\binom{j}{k}}{\binom{n}{k}} \mathbf{Q}_k \right) B_{j}^n(t) +\end{align} +$$ + +which is a Bézier curve of the form + +$$ +\begin{align} +\mathcal{C}(t) = \sum_{k=0}^n \mathbf{P}_k B_k^n(t) +\end{align} +$$ + +with + +$$ +\begin{align} +\mathbf{P}_k = \sum\limits_{k=0}^{n} \frac{\binom{j}{k}}{\binom{n}{k}} \mathbf{Q}_k +\end{align} +$$ + +```{prf:remark} + If $\mathbf{Q}_k = 0$ for all $k \geq 2$, then the control points are given by $\mathbf{P}_k = \mathbf{Q}_0 + k \mathbf{Q}_1$. +``` + +````{prf:proposition} Linear Precision + Conversly, if the $n+1$ control points $\mathbf{P}$ lie equidistantly on a line, then $\mathcal{C}$ is a linear polynomial, which can be written as $\mathcal{C}(t) = \left(1-t\right) \mathbf{P}_0 + t \mathbf{P}_n$. +```` + +## Conversion to monomial form +Given a Bézier curve $\mathcal{C}(t) = \sum_{k=0}^n \mathbf{P}_k B_k^n(t)$, we can derive its monomial representation using the Taylor expansion, + +$$ +\begin{align} + \mathcal{C}(t) &= \sum\limits_{k=0}^n \frac{1}{k!}\mathcal{C}^{(k)}(0) t^k \\ + &= \sum\limits_{k=0}^n \binom{n}{k} \triangle^k \mathbf{P}_0 t^k +\end{align} +$$ + +## Rational Bézier curves +We first introduce the notion of Rational Bernstein polynomials defined as, and $w_i > 0, \forall i \in \left[0, n \right]$ + +$$ +\begin{align} + R_k^n(t) := \frac{w_i B_k^n(t)}{\sum_{i=0}^n w_i B_i^n(t)} + \label{eq:rational-bernstein} +\end{align} +$$ + +````{prf:proposition} Properties of Rational Bernstein polynomials +- $R_k^n(x) \ge 0$, for all $k \in \left[0, n \right]$ and $x \in \left[ 0, 1 \right]$ \hfill [positivity] +- $\sum_{k=0}^n R_k^n(x) = 1$, for all $x \in \left[ 0, 1 \right]$ \hfill [partition of unity] +- $R_0^n(0) = R_n^n(1) = 1$ +- $R_k^n$ has exactly one maximum on the interval $\left[ 0, 1 \right]$, +- Bernstein polynomials are Rational Bernstein polynomials when all weights are equal +```` + +````{prf:definition} Rational Bézier curve + +$$ +\begin{align} + \mathcal{C}(t) = \sum_{k=0}^n \mathbf{P}_k R_k^n(t) + \label{eq:bezier-curve} +\end{align} +$$ + +where $R_k^n(t) := \frac{w_i B_k^n(t)}{\sum_{i=0}^n w_i B_i^n(t)}$ and $w_i > 0, \forall i \in \left[0, n \right]$ +```` + +### Example + +````{prf:example} +:label: bezier-curve-ex-7 + +```python +nt = 200 +ts = np.linspace(0., 1., nt) + +P = np.zeros((3, 2)) +P[:, 0] = [1., 1., 0.] +P[:, 1] = [0., 1., 1.] + +# weights +W = np.asarray([1., 1., 2.]) + +# weithed control points in 3D +Pw = np.zeros((3,3)) +for i in range(0, 3): + Pw[i,:2] = W[i]*P[i,:] + Pw[i,2] = W[i] + +Qw = np.zeros((nt, 3)) +for i,t in enumerate(ts): + Qw[i,:] = point_on_bezier_curve(Pw,t) + +Q = np.zeros((nt, 2)) +Q[:,0] = Qw[:,0]/Qw[:,2] +Q[:,1] = Qw[:,1]/Qw[:,2] + +plt.plot(Q[:,0], Q[:,1], '-b') +plt.plot(P[:,0], P[:,1], '--ok', linewidth=0.7) + +for i in range(0, 3): + x,y = P[i,:] + plt.text(x+0.05,y+0.05,'$\mathbf{P}_{' + str(i) + '}$') + +plt.axis([-0.2, 1.2, -0.2, 1.2]) +``` + +![png](images/bezier/output_25_0.png) +```` + +## Composite Bézier curve + +````{prf:example} +:label: bezier-curve-ex-6 + +```python +n = 2 + +nt = 200 +ts = np.linspace(0., 1., nt) + +# ... +P = np.zeros((3, 2)) +P[:, 0] = [1., 1., 0.] +P[:, 1] = [0., 1., 1.] + +Q = np.zeros((nt, 2)) +for i,t in enumerate(ts): + Q[i,:] = point_on_bezier_curve(P,t) + +plt.plot(Q[:,0], Q[:,1], '-r') +plt.plot(P[:,0], P[:,1], '--or', linewidth=0.7) +# ... + +# ... +P = np.zeros((3, 2)) +P[:, 0] = [0., -1., 0.] +P[:, 1] = [1., -1., -1.] + +Q = np.zeros((nt, 2)) +for i,t in enumerate(ts): + Q[i,:] = point_on_bezier_curve(P,t) + +plt.plot(Q[:,0], Q[:,1], '-b') +plt.plot(P[:,0], P[:,1], '--ob', linewidth=0.7) +# ... + +# ... +P = np.zeros((3, 2)) +P[:, 0] = [1., 1., 0.] +P[:, 1] = [0., -1., -1.] + +Q = np.zeros((nt, 2)) +for i,t in enumerate(ts): + Q[i,:] = point_on_bezier_curve(P,t) + +plt.plot(Q[:,0], Q[:,1], '-g') +plt.plot(P[:,0], P[:,1], '--og', linewidth=0.7) +# ... +``` + +![png](images/bezier/output_22_0.png) +```` diff --git a/_sources/chapter0/bezier.md b/_sources/chapter0/bezier.md new file mode 100644 index 0000000..e999a10 --- /dev/null +++ b/_sources/chapter0/bezier.md @@ -0,0 +1,74 @@ +# Bernstein polynomials + +Without loss of generality, we restrict to the case of the unit interval, namely $a=0$ and $b=1$. +In figure (Fig. \ref{fig:bernstein-polynomials}), we plot the first sixth Bernstein polynomials. + + +````{prf:definition} + +Fro $n \in \mathbb{N}$, the $n$-th degree Bernstein polynomials $B_{j,n}\,:\, [0,1] \longrightarrow \mathbb{R}$ are defined by + +$$ +B_{j,n}(x)=\frac{n!}{(n-j)!j!} x^j (1-x)^{n-j}, \quad x \in [0,1], \quad j=0, \ldots,n. +$$ +```` + +Bernstein polynomials exhibit interesting properties highlighted in the following proposition, + +```python +# needed imports +import numpy as np +import matplotlib.pyplot as plt +``` + +We first consider the evaluation of the Bernstein polynomials. + +## Evaluation of Bernstein polynomials + +The following function evaluates all Bernstein polynomials of degree $n$ at $x$ + +```python +def all_bernstein(n, x): + b = np.zeros(n+1) + b[0] = 1. + x1 = 1.-x + for j in range(1, n+1): + saved = 0. + for i in range(0, j): + tmp = b[i] + b[i] = saved + x1*tmp + saved = x*tmp + b[j] = saved + return b +``` + +## Bernstein polynomials properties + +````{prf:proposition} + +We have the following properties of Bernstein Polynomials, + +- Positivity: $B_{j,n}(x) \ge 0$, for all $x \in \left[ 0, 1 \right]$ and $0 \leq j \leq n$. +- Partition of unity: $\sum_{j=0}^n B_{j,n}(x) = 1$, for all $x \in \left[ 0, 1 \right]$. +- $B_{0,n}(0) = B_{n,n}(1) = 1$. +- $B_{j,n}$ has exactly one maximum on the interval $\left[ 0, 1 \right]$, at $\frac{j}{n}$. +- Symmetry: $B_{j,n}$ is symmetric with respect to $x = \frac{1}{2}$ for $j=0,\ldots,n$. +- Bernstein polynomials can be defined recursively using the formula + +$$ +\begin{align} + B_{j,n}(x) = (1-x) B_{j,n-1}(x) + x B_{k-1,n-1}(x), +\end{align} +$$ + + where we assume $B_{j,n}(x) = 0$ if $j < 0$ or $j > n$. + +- Bernstein derivatives can be computed using the formulae + +$$ +\begin{align} + {B_{j,n}}^\prime(x) = n \left(B_{j-1,n-1}(x) - B_{j,n-1}(x) \right). +\end{align} +$$ +using the same assumption as before. +```` diff --git a/_sources/chapter0/bsplines-curves.md b/_sources/chapter0/bsplines-curves.md new file mode 100644 index 0000000..07b808a --- /dev/null +++ b/_sources/chapter0/bsplines-curves.md @@ -0,0 +1,593 @@ +# B-Splines curves + +Let $(\mathbf{P}_i)_{ 0 \leqslant i \leqslant n}\in \mathbb{R}^d$ be a sequence of control points. Following the same approach as for Bézier curves, we define B-Splines curves as + +````{prf:definition} B-Spline curve +The B-spline curve in $\mathbb{R}^d$ associated to $T=(t_i)_{0\leqslant i \leqslant n + p + 1}$ and $(\mathbf{P}_i)_{ 0 \leqslant i \leqslant n}$ is defined by : + +$$ +\mathcal{C}(t) = \sum_{i=0}^n N_i^p(t) \textbf{P}_i +$$ + +```` + +```{prf:remark} + The use of open knot vector leads to an **interpolating curve** at the endpoints. +``` + +## Properties of B-Splines curves + +We have the following properties for a B-spline curve: + + +- If $n=p$, then $\mathcal{C}$ is a Bézier-curve, +- $\mathcal{C}$ is a piecewise polynomial curve, +- The curve interpolates its extremas if the associated multiplicity of the first and the last knot are maximum (*i.e.* equal to $p+1$), +- Invariance with respect to affine transformations, +- B-Spline curves are affinely invariant; *i.e.* the image curve $\Phi(\sum_{i=0}^n \mathbf{P}_i N_i^p)$ of a B-Spline curve, by an affine mapping $\Phi$, is the B-Spline curve having $\left( \Phi(\mathbf{P}_i) \right)_{0 \le i \le n}$ as control points and the same knot vector, +- strong convex-hull property: + if $t_j \leq t \leq t_{j+1}$, then $\mathcal{C}(t)$ is inside the convex-hull associated to the control points $\mathbf{P}_{j-p},\cdots,\mathbf{P}_{j}$, +- local modification : moving $\mathbf{P}_{j}$ affects $\mathcal{C}(t)$, only in the interval $[t_j,t_{j+p+1}]$, +- the control polygon is a linear approximation of the curve. We will see later that the control polygon converges to the curve under knot insertion and degree elevation (with different *speeds*). +- *Variation diminishing*: no plane intersects the curve more than the control polygon. + + +## Derivative of a B-spline curve +Using the derivative formula for *B-spline*, we can compute the derivative of a B-Spline curve: + +$$ +\begin{align} +\mathcal{C}^{\prime}(t) &= \sum_{i=0}^{n} \left( {N_{i}^{p}}^{\prime}(t) \mathbf{P}_i \right) +\\ + &= \sum_{i=0}^{n} \left( \frac{p}{t_{i+p}-t_{i}}N_{i}^{p-1}(t) \mathbf{P}_i - \frac{p}{t_{i+1+p}-t_{i+1}}N_{i+1}^{p-1}(t) \mathbf{P}_i \right) +\\ + &= \sum_{i=0}^{n} \frac{p}{t_{i+p}-t_{i}}N_{i}^{p-1}(t) \mathbf{P}_i - \sum_{i=1}^{n+1} \frac{p}{t_{i+p}-t_{i}}N_{i}^{p-1}(t) \mathbf{P}_{i-1} +\\ + &= \sum\limits_{i} {N_{i}^{p-1}}(t)\frac{p}{t_{i+p}-t_{i}} \left( \mathbf{P}_i - \mathbf{P}_{i-1} \right) +\\ + &= \sum\limits_{i} {N_{i}^{p-1}}(t) \frac{p}{t_{i+p}-t_{i}} \nabla \mathbf{P}_i +\end{align} +$$ + +where we introduced the **first backward difference** operator $\nabla \mathbf{P}_i := \mathbf{P}_i - \mathbf{P}_{i-1}$. + +````{prf:example} +:label: bsplines-curves-ex-1 + +we consider a quadratic B-Spline curve with the knot vector $T=\{000~\frac{2}{5}~\frac{3}{5}~111 \}$. + +We have $\mathcal{C}(t) = \sum_{i=0}^{4} {N_{i}^{2}}^{\prime}(t) \mathbf{P}_i $, then + +$$ +\mathcal{C}^{\prime}(t) = \sum\limits_{i} {N_{i}^{1}}(t) \mathbf{Q}_i +$$ + +where + +$$ +\mathbf{Q}_0 = 5 \{\mathbf{P}_{2} - \mathbf{P}_1\} ~~~~\mathbf{Q}_1 = \frac{10}{3} \{ \mathbf{P}_{3} - \mathbf{P}_2\} +$$ + +$$ +\mathbf{Q}_2 = \frac{10}{3} \{ \mathbf{P}_{4} - \mathbf{P}_3\}~~~~\mathbf{Q}_3 = 5 \{\mathbf{P}_{5} - \mathbf{P}_4\} +$$ + +the *B-splines* $\{ N_{i}^{1},~0 \leq i \leq 3\}$ are associated to the knot vector $T^{\ast}=\{00~\frac{2}{5}~\frac{3}{5}~11 \}$. +```` + +```python +# needed imports +import numpy as np +import matplotlib.pyplot as plt +``` + +```python +# importing bsplines utilities +from bsplines_utilities import find_span, all_bsplines, point_on_bspline_curve +``` + +## Examples + +````{prf:example} +:label: bsplines-curves-ex-2 + +```python +knots = [0., 0., 0., 1., 1., 1.] +degree = 2 +n = len(knots) - degree - 1 + +P = np.zeros((n, 2)) +P[:, 0] = [1., 1., 0.] +P[:, 1] = [0., 1., 1.] + +nx = 101 +xs = np.linspace(0., 1., nx) + +Q = np.zeros((nx, 2)) +for i,x in enumerate(xs): + Q[i,:] = point_on_bspline_curve(knots, P, x) + +plt.plot(Q[:,0], Q[:,1], '-b') +plt.plot(P[:,0], P[:,1], '--ok', linewidth=0.7) + +for i in range(0, n): + x,y = P[i,:] + plt.text(x+0.05,y+0.05,'$\mathbf{P}_{' + str(i) + '}$') + +plt.axis([-0.2, 1.2, -0.2, 1.2]) +``` + +![png](images/bsplines-curves/output_5_0.png) +```` + +````{prf:example} +:label: bsplines-curves-ex-3 + +```python +knots = [0., 0., 0., 0., 1., 1., 1., 1.] +degree = 3 +n = len(knots) - degree - 1 + +P = np.zeros((n, 2)) +P[:, 0] = [1., 1., 0., -1.] +P[:, 1] = [0., 1., 1., 0.] + +nx = 101 +xs = np.linspace(0., 1., nx) + +Q = np.zeros((nx, 2)) +for i,x in enumerate(xs): + Q[i,:] = point_on_bspline_curve(knots, P, x) + +plt.plot(Q[:,0], Q[:,1], '-b') +plt.plot(P[:,0], P[:,1], '--ok', linewidth=0.7) + +for i in range(0, n): + x,y = P[i,:] + plt.text(x+0.05,y+0.05,'$\mathbf{P}_{' + str(i) + '}$') + +plt.axis([-1.2, 1.2, -0.2, 1.2]) +``` + +![png](images/bsplines-curves/output_6_0.png) +```` + +````{prf:example} +:label: bsplines-curves-ex-4 + +```python +knots = [0., 0., 0., 0.25, 0.5, 0.75, 1., 1., 1.] +degree = 2 +n = len(knots) - degree - 1 + +P = np.zeros((n, 2)) +P[:, 0] = [0., 1., 1., -2., -1., -2.] +P[:, 1] = [.5, -1., 1., 1., 0., -1.] + +nx = 101 +xs = np.linspace(0., 1., nx) + +Q = np.zeros((nx, 2)) +for i,x in enumerate(xs): + Q[i,:] = point_on_bspline_curve(knots, P, x) + +plt.plot(Q[:,0], Q[:,1], '-b') +plt.plot(P[:,0], P[:,1], '--ok', linewidth=0.7) + +for i in range(0, n): + x,y = P[i,:] + plt.text(x+0.05,y+0.05,'$\mathbf{P}_{' + str(i) + '}$') + +plt.axis([-2.2, 1.3, -1.2, 1.4]) +``` + +![png](images/bsplines-curves/output_7_0.png) +```` + +````{prf:example} +:label: bsplines-curves-ex-5 + +```python +knots = [0., 0., 0., 0.25, 0.5, 0.5, 0.75, 1., 1., 1.] +degree = 2 +n = len(knots) - degree - 1 + +P = np.zeros((n, 2)) +P[:, 0] = [0., 1., 1., 0., -2., -1., -2.] +P[:, 1] = [.5, -1., 1., 2., 1., 0., -1.] + +nx = 101 +xs = np.linspace(0., 1., nx) + +Q = np.zeros((nx, 2)) +for i,x in enumerate(xs): + Q[i,:] = point_on_bspline_curve(knots, P, x) + +plt.plot(Q[:,0], Q[:,1], '-b') +plt.plot(P[:,0], P[:,1], '--ok', linewidth=0.7) + +for i in range(0, n): + x,y = P[i,:] + plt.text(x+0.05,y+0.05,'$\mathbf{P}_{' + str(i) + '}$') + +plt.axis([-2.2, 1.3, -1.2, 2.2]) +``` + +![png](images/bsplines-curves/output_8_0.png) +```` + +````{prf:example} +:label: bsplines-curves-ex-6 + +```python +knots = [0., 0., 0., 0.25, 0.5, 0.5, 0.75, 1., 1., 1.] +degree = 2 +n = len(knots) - degree - 1 + +P = np.zeros((n, 2)) +P[:, 0] = [0., 1., 1., 0., -2., -1., -2.] +P[:, 1] = [.5, -1., 1., 1., 1., 0., -1.] + +nx = 101 +xs = np.linspace(0., 1., nx) + +Q = np.zeros((nx, 2)) +for i,x in enumerate(xs): + Q[i,:] = point_on_bspline_curve(knots, P, x) + +plt.plot(Q[:,0], Q[:,1], '-b') +plt.plot(P[:,0], P[:,1], '--ok', linewidth=0.7) + +for i in range(0, n): + x,y = P[i,:] + plt.text(x+0.05,y+0.05,'$\mathbf{P}_{' + str(i) + '}$') + +plt.axis([-2.2, 1.3, -1.2, 1.2]) +``` + +![png](images/bsplines-curves/output_9_0.png) +```` + +````{prf:example} +:label: bsplines-curves-ex-7 + +```python +knots = [0., 0., 0., 0., 0., 0., 0., 1., 1., 1., 1., 1., 1., 1.] +degree = 6 +n = len(knots) - degree - 1 + +P = np.zeros((n, 2)) +P[:, 0] = [7., 6., 5., 4., 3., 2., 1.] +P[:, 1] = [0., 1., 1., -1., .5, -.5, 0.] + +nx = 101 +xs = np.linspace(0., 1., nx) + +Q = np.zeros((nx, 2)) +for i,x in enumerate(xs): + Q[i,:] = point_on_bspline_curve(knots, P, x) + +plt.plot(Q[:,0], Q[:,1], '-b') +plt.plot(P[:,0], P[:,1], '--ok', linewidth=0.7) + +for i in range(0, n): + x,y = P[i,:] + plt.text(x+0.05,y+0.05,'$\mathbf{P}_{' + str(i) + '}$') + +plt.axis([0.6, 7.4, -1.4, 1.4]) +``` + +![png](images/bsplines-curves/output_10_0.png) +```` + +````{prf:example} +:label: bsplines-curves-ex-8 + +```python + knots = [0., 0., 0., .2, .4, .6, .8, 1., 1., 1.] + degree = 2 + n = len(knots) - degree - 1 + + P = np.zeros((n, 2)) + P[:, 0] = [7., 6., 5., 4., 3., 2., 1.] + P[:, 1] = [0., 1., 1., -1., .5, -.5, 0.] + + nx = 101 + xs = np.linspace(0., 1., nx) + + Q = np.zeros((nx, 2)) + for i,x in enumerate(xs): + Q[i,:] = point_on_bspline_curve(knots, P, x) + + plt.plot(Q[:,0], Q[:,1], '-b') + plt.plot(P[:,0], P[:,1], '--ok', linewidth=0.7) + + for i in range(0, n): + x,y = P[i,:] + plt.text(x+0.05,y+0.05,'$\mathbf{P}_{' + str(i) + '}$') + + plt.axis([0.6, 7.4, -1.4, 1.4]) +``` + +![png](images/bsplines-curves/output_11_0.png) +```` + +## Rational B-Splines (NURBS) curves + +We recall that NURBS are defined as + +$$ + R_i^p(t) := \frac{w_i N_i^p(t)}{\sum_{j=0}^n w_j N_j^p(t)} +$$ + +where $w_i > 0, \forall i \in \left[0, n \right]$ are non-negative real numbers, called the weights. + +NURBS curves are then defined as + +$$ + \mathcal{C}(t) = \sum_{i=0}^n \mathbf{P}_i R_i^p(t) +$$ + +Notice that a NURBS curve in $\mathbb{R}^d$ can be described as a NURBS curve in $\mathbb{R}^{d+1}$ using the control points: + +$\textbf{P}^{\omega}_i = ( \omega_i \textbf{P}_i, \omega_i )$ + +This remark is used for the evaluation and also to extend most of the B-Splines fundamental geometric operations to NURBS curves. + +```{prf:remark} +Although there is a function **point_on_nurbs_curve** to evaluate NURBS curves, we make use of an explicit call to the spline version in this notebook. +``` + +### Examples + +````{prf:example} Quarter circle +:label: nurbs-curves-ex-1 + +```python +knots = [0., 0., 0., 1., 1., 1.] +degree = 2 +n = len(knots) - degree - 1 + +P = np.zeros((n, 2)) +P[:, 0] = [1., 1., 0.] +P[:, 1] = [0., 1., 1.] + +# weights +s2 = 1./np.sqrt(2) +W = np.zeros(n) +W[:] = [1., s2, 1.] + +# weithed control points in 3D +Pw = np.zeros((n,3)) +for i in range(0, n): + Pw[i,:2] = W[i]*P[i,:] + Pw[i,2] = W[i] + +nx = 200 +xs = np.linspace(0., 1., nx) + +Qw = np.zeros((nx, 3)) +for i,x in enumerate(xs): + Qw[i,:] = point_on_bspline_curve(knots, Pw, x) + +Q = np.zeros((nx, 2)) +Q[:,0] = Qw[:,0]/Qw[:,2] +Q[:,1] = Qw[:,1]/Qw[:,2] + +plt.plot(Q[:,0], Q[:,1], '-b') +plt.plot(P[:,0], P[:,1], '--ok', linewidth=0.7) + +for i in range(0, n): + x,y = P[i,:] + plt.text(x+0.05,y+0.05,'$\mathbf{P}_{' + str(i) + '}$') + +plt.axis([-0.2, 1.2, -0.2, 1.2]) +``` + +![png](images/bsplines-curves/output_15_0.png) +```` + +````{prf:example} Circular arc of $120°$ +:label: nurbs-curves-ex-2 + +```python +knots = [0., 0., 0., 1., 1., 1.] +degree = 2 +n = len(knots) - degree - 1 + +P = np.zeros((n, 2)) +a = np.cos(np.pi/6.) +P[:, 0] = [ a, 0., -a] +P[:, 1] = [.5, 2., .5] + +# weights +W = np.zeros(n) +W[:] = [1., 1./2., 1.] + +# weithed control points in 3D +Pw = np.zeros((n,3)) +for i in range(0, n): + Pw[i,:2] = W[i]*P[i,:] + Pw[i,2] = W[i] + +nx = 200 +xs = np.linspace(0., 1., nx) + +Qw = np.zeros((nx, 3)) +for i,x in enumerate(xs): + Qw[i,:] = point_on_bspline_curve(knots, Pw, x) + +Q = np.zeros((nx, 2)) +Q[:,0] = Qw[:,0]/Qw[:,2] +Q[:,1] = Qw[:,1]/Qw[:,2] + +plt.plot(Q[:,0], Q[:,1], '-b') +plt.plot(P[:,0], P[:,1], '--ok', linewidth=0.7) + +for i in range(0, n): + x,y = P[i,:] + plt.text(x+0.05,y+0.05,'$\mathbf{P}_{' + str(i) + '}$') + +plt.axis([-1.2, 1.2, .0, 2.2]) +``` + +![png](images/bsplines-curves/output_17_0.png) +```` + +````{prf:example} half circle +:label: nurbs-curves-ex-3 + +```python +knots = [0., 0., 0., 0., 1., 1., 1., 1.] +degree = 3 +n = len(knots) - degree - 1 + +P = np.zeros((n, 2)) +P[:, 0] = [1., 1., -1., -1.] +P[:, 1] = [0., 2., 2., 0.] + +# weights +W = np.zeros(n) +W[:] = [1., 1./3., 1./3., 1.] + +# weithed control points in 3D +Pw = np.zeros((n,3)) +for i in range(0, n): + Pw[i,:2] = W[i]*P[i,:] + Pw[i,2] = W[i] + +nx = 200 +xs = np.linspace(0., 1., nx) + +Qw = np.zeros((nx, 3)) +for i,x in enumerate(xs): + Qw[i,:] = point_on_bspline_curve(knots, Pw, x) + +Q = np.zeros((nx, 2)) +Q[:,0] = Qw[:,0]/Qw[:,2] +Q[:,1] = Qw[:,1]/Qw[:,2] + +plt.plot(Q[:,0], Q[:,1], '-b') +plt.plot(P[:,0], P[:,1], '--ok', linewidth=0.7) + +for i in range(0, n): + x,y = P[i,:] + plt.text(x+0.05,y+0.05,'$\mathbf{P}_{' + str(i) + '}$') + +plt.axis([-1.2, 1.2, -.2, 2.2]) +``` + +![png](images/bsplines-curves/output_19_0.png) +```` + +````{prf:example} Circle as 4 arcs +:label: nurbs-curves-ex-4 + +We already saw how to construct a circular arc (with angle = $\frac{\pi}{2}$, using Bézier curves. + +Constructing a circular arc can be done in different ways. In this example, we consider a B-Spline curve as a composite of 4 Bézier curves. + + +```python +knots = [0., 0., 0., .25, .25, .5, .5, .75, .75, 1., 1., 1.] +degree = 2 +n = len(knots) - degree - 1 + +P = np.zeros((n, 2)) +P[:, 0] = [1., 1., 0., -1., -1., -1., 0., 1., 1.] +P[:, 1] = [0., 1., 1., 1., 0., -1., -1., -1., 0.] + +# weights +s2 = 1./np.sqrt(2) +W = np.zeros(n) +W[:] = [1., s2, 1., s2, 1., s2, 1., s2, 1.] + +# weithed control points in 3D +Pw = np.zeros((n,3)) +for i in range(0, n): + Pw[i,:2] = W[i]*P[i,:] + Pw[i,2] = W[i] + +nx = 200 +xs = np.linspace(0., 1., nx) + +Qw = np.zeros((nx, 3)) +for i,x in enumerate(xs): + Qw[i,:] = point_on_bspline_curve(knots, Pw, x) + +Q = np.zeros((nx, 2)) +Q[:,0] = Qw[:,0]/Qw[:,2] +Q[:,1] = Qw[:,1]/Qw[:,2] + +plt.plot(Q[:,0], Q[:,1], '-b') +plt.plot(P[:,0], P[:,1], '--ok', linewidth=0.7) + +for i in range(1, n-1): + x,y = P[i,:] + plt.text(x+0.05,y+0.05,'$\mathbf{P}_{' + str(i) + '}$') + +# plot P_0 = P_8 +x,y = P[0,:] +plt.text(x+0.05,y+0.05,'$\mathbf{P}_0 = \mathbf{P}_8$') + +plt.axis([-1.2, 1.2, -1.2, 1.2]) +``` + +![png](images/bsplines-curves/output_21_0.png) +```` + +````{prf:example} Circle as 3 arcs +:label: nurbs-curves-ex-5 + +We already saw how to construct a circular arc (with angle = $120°$, using Bézier curves. + +In this example, we consider a B-Spline curve as a composite of 3 Bézier curves. + + +```python +knots = [0., 0., 0., 1./3., 1./3., 2./3., 2./3., 1., 1., 1.] +degree = 2 +n = len(knots) - degree - 1 + +P = np.zeros((n, 2)) +a = np.cos(np.pi/6.) +P[:, 0] = [ a, 0., -a, -2*a, 0., 2*a, a] +P[:, 1] = [.5, 2., .5, -1., -1., -1., .5] + +# weights +W = np.zeros(n) +W[:] = [1., 1./2., 1., 1./2., 1., 1./2., 1.] + +# weithed control points in 3D +Pw = np.zeros((n,3)) +for i in range(0, n): + Pw[i,:2] = W[i]*P[i,:] + Pw[i,2] = W[i] + +nx = 200 +xs = np.linspace(0., 1., nx) + +Qw = np.zeros((nx, 3)) +for i,x in enumerate(xs): + Qw[i,:] = point_on_bspline_curve(knots, Pw, x) + +Q = np.zeros((nx, 2)) +Q[:,0] = Qw[:,0]/Qw[:,2] +Q[:,1] = Qw[:,1]/Qw[:,2] + +plt.plot(Q[:,0], Q[:,1], '-b') +plt.plot(P[:,0], P[:,1], '--ok', linewidth=0.7) + +for i in range(1, n-1): + x,y = P[i,:] + plt.text(x+0.05,y+0.05,'$\mathbf{P}_{' + str(i) + '}$') + +# plot P_0 = P_6 +x,y = P[0,:] +plt.text(x+0.05,y+0.05,'$\mathbf{P}_0 = \mathbf{P}_8$') + +plt.axis([-2.2, 2.2, -1.2, 2.2]) +``` + +![png](images/bsplines-curves/output_23_0.png) +```` diff --git a/_sources/chapter0/bsplines-operations.md b/_sources/chapter0/bsplines-operations.md new file mode 100644 index 0000000..73751af --- /dev/null +++ b/_sources/chapter0/bsplines-operations.md @@ -0,0 +1,489 @@ +# Fundamental geometric operations for B-Splines + + +Having more control on a curve, adding new control points, can be done in two different ways: + +1. insert new knots + +2. elevate the polynomial degree + +In general, one way need to use both approaches. +For each strategy, we shall consider one algorithm. + +**Remark**: +In this notebook we only use B-Splines curves, but similar functions are also available for NURBS. + +```python +# needed imports +import numpy as np +import matplotlib.pyplot as plt +``` + +## Knot insertion + +Assuming an initial B-Spline curve defined by: + +* its degree $p$ +* knot vector $T=(t_i)_{0\leqslant i \leqslant n + p + 1}$ +* control points $(\mathbf{P}_i)_{ 0 \leqslant i \leqslant n}$ + +We are interested in the new B-Spline curve as the result of the insertion of the knot $t$, $m$ times (with a span $j$, i.e. $t_j \leqslant t < t_{j+1}$). + +After such operation, the degree is remain unchanged, while the knot vector is enriched by $t$, $m$ times. The aim is then to compute the new control points $(\mathbf{Q}_i)_{ 0 \leqslant i \leqslant n + m}$ + +For this purpose we use the DeBoor algorithm: + +$$ +\begin{align} + n &:= n+m + \\ + p &:= p + \\ + T &:= \{ t_0,.., t_j, \underbrace{t, ..., t}_{m}, t_{j+1},.., t_{n+k}\} + \\ + \textbf{Q}_i &:= \textbf{Q}_i^{m} +\end{align} +$$ + +where + +$$ +\begin{align} + \textbf{Q}_i^0 &= \textbf{P}_i + \\ + \textbf{Q}_i^r &= \alpha_i^r \textbf{Q}_i^{r-1} + (1-\alpha_i^r) \textbf{Q}_{i-1}^{r-1} +\end{align} +$$ + +with + +$$ +\begin{align} + \alpha_i^r &= + \left\{\begin{array}{cc} + 1 & i \leqslant j-p+r-1 \\ + \frac{t-t_i}{t_{i+p-r+1}-t_i} & j-p+r \leqslant i \leqslant j-m \\ + 0 & j-m+1 \leqslant i + \end{array}\right. +\end{align} +$$ + +The following python function implements the previous algorithm. + + +```python +# import the knot insertion function +from bsplines_utilities import insert_knot_bspline_curve +``` + +From now on, we shall also use the following function to plot curves and their control points: + + +```python +from bsplines_utilities import plot_curve +``` + +**Examples** + + +```python +def example_1(times=1): + knots = [0., 0., 0., 0., 1., 1., 1., 1.] + degree = 3 + n = len(knots) - degree - 1 + + P = np.zeros((n, 2)) + P[:, 0] = [1., 1., 0., -1.] + P[:, 1] = [0., 1., 1., 0.] + plot_curve(knots, degree, P, with_ctrl_pts=False) + + # we don't plot the first and last points + # they will be plotted later + for i in range(1, n-1): + x,y = P[i,:] + plt.text(x+0.05,y+0.05,'$\mathbf{P}_{' + str(i) + '}$') + + t = 0.5 + knots, degree, P = insert_knot_bspline_curve(knots, degree, P, t, times=times) + plot_curve(knots, degree, P, color='r', label='Q', with_ctrl_pts=False) + + # we don't plot the first and last points + # they will be plotted later + n = len(knots) - degree - 1 + for i in range(1, n-1): + x,y = P[i,:] + plt.text(x+0.05,y+0.05,'$\mathbf{Q}_{' + str(i) + '}$') + + # plot endpoints + for i in [0, n-1]: + x = P[i,0] ; y = P[i,1] + if i == 0: + Pi = '\mathbf{P}_{' + str(i) + '}' + elif i == n-1: + Pi = '\mathbf{P}_{' + str(i-1) + '}' + + Qi = '\mathbf{Q}_{' + str(i) + '}' + text = '${Pi} = {Qi}$'.format(Pi=Pi, Qi=Qi) + plt.text(x+0.05,y+0.05,text) +``` + + +```python +example_1(times=1) +``` + + + +![png](images/bsplines-operations/output_9_0.png) + + + + +```python +example_1(times=2) +``` + + + +![png](images/bsplines-operations/output_10_0.png) + + + + +```python +example_1(times=3) +``` + + + +![png](images/bsplines-operations/output_11_0.png) + + + + +```python +def example_2a(nt = 3): + knots = [0., 0., 0., 0., 1., 1., 1., 1.] + degree = 3 + n = len(knots) - degree - 1 + + P = np.zeros((n, 2)) + P[:, 0] = [1., 1., 0., -1.] + P[:, 1] = [0., 1., 1., 0.] + plot_curve(knots, degree, P, with_ctrl_pts=False) + + # we don't plot the first and last points + # they will be plotted later + for i in range(1, n-1): + x,y = P[i,:] + plt.text(x+0.05,y+0.05,'$\mathbf{P}_{' + str(i) + '}$') + + ts = np.linspace(0., 1., nt+2)[1:-1] + for t in ts: + knots, degree, P = insert_knot_bspline_curve(knots, degree, P, t, times=1) + + plot_curve(knots, degree, P, color='r', label='Q', with_ctrl_pts=False) + + # we don't plot the first and last points + # they will be plotted later + n = len(knots) - degree - 1 + for i in range(1, n-1): + x,y = P[i,:] + plt.text(x+0.05,y+0.05,'$\mathbf{Q}_{' + str(i) + '}$') + + # plot endpoints + for i in [0, n-1]: + x = P[i,0] ; y = P[i,1] + if i == 0: + Pi = '\mathbf{P}_{' + str(i) + '}' + elif i == n-1: + Pi = '\mathbf{P}_{' + str(i-1) + '}' + + Qi = '\mathbf{Q}_{' + str(i) + '}' + text = '${Pi} = {Qi}$'.format(Pi=Pi, Qi=Qi) + plt.text(x+0.05,y+0.05,text) +``` + + +```python +# curve after inserting [0.25 0.5 0.75] +example_2a(nt=3) +``` + + + +![png](images/bsplines-operations/output_13_0.png) + + + + +```python +# curve after inserting [0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9] +example_2a(nt=9) +``` + + + +![png](images/bsplines-operations/output_14_0.png) + + + +## Order elevation + +There are also many algorithms for degree elevation of a B-Spline curve. In the sequel, we will be using the one developped by Huand, Hu and Martin (2005). + +The previous algorithm is implemented by the following function + + +```python +# import the degree elevation function +from bsplines_utilities import elevate_degree_bspline_curve +``` + +**Example 1.** + + +```python +def example_1(m=1): + knots = [0., 0., 0., 0., 0.5, 1., 1., 1., 1.] + degree = 3 + n = len(knots) - degree - 1 + + P = np.zeros((n, 2)) + P[:, 0] = [1., 1., .5, -.5, -1.] + P[:, 1] = [0., .5, 1., .5, 0.] + + plot_curve(knots, degree, P, with_ctrl_pts=False) + + # we don't plot the first and last points + # they will be plotted later + for i in range(1, n-1): + x,y = P[i,:] + plt.text(x+0.05,y+0.05,'$\mathbf{P}_{' + str(i) + '}$') + + knots, degree, P = elevate_degree_bspline_curve(knots, degree, P, m=1) + plot_curve(knots, degree, P, color='r', label='Q', with_ctrl_pts=False) + + # we don't plot the first and last points + # they will be plotted later + n = len(knots) - degree - 1 + for i in range(1, n-1): + x,y = P[i,:] + plt.text(x+0.05,y+0.05,'$\mathbf{Q}_{' + str(i) + '}$') + + # plot endpoints + for i in [0, n-1]: + x = P[i,0] ; y = P[i,1] + if i == 0: + Pi = '\mathbf{P}_{' + str(i) + '}' + elif i == n-1: + Pi = '\mathbf{P}_{' + str(i-1) + '}' + + Qi = '\mathbf{Q}_{' + str(i) + '}' + text = '${Pi} = {Qi}$'.format(Pi=Pi, Qi=Qi) + plt.text(x+0.05,y+0.05,text) + +example_1() +``` + + + +![png](images/bsplines-operations/output_18_0.png) + + + +**Example 2.** + + +```python +def example_2(m=1): + knots = [0., 0., 0., 0., 0.5, 0.5, 1., 1., 1., 1.] + degree = 3 + n = len(knots) - degree - 1 + n_initial = n + + P = np.zeros((n, 2)) + P[:, 0] = [260., 100., 260., 420., 580., 420.] + P[:, 1] = [100., 260., 420., 420., 260., 100.] + plot_curve(knots, degree, P, with_ctrl_pts=False) + + # we don't plot the first and last points + # they will be plotted later + for i in range(1, n-1): + x,y = P[i,:] + plt.text(x+0.05,y+0.05,'$\mathbf{P}_{' + str(i) + '}$') + + knots, degree, P = elevate_degree_bspline_curve(knots, degree, P, m=m) + plot_curve(knots, degree, P, color='r', label='Q', with_ctrl_pts=False) + + # we don't plot the first and last points + # they will be plotted later + n = len(knots) - degree - 1 + for i in range(1, n-1): + x,y = P[i,:] + plt.text(x+0.05,y+0.05,'$\mathbf{Q}_{' + str(i) + '}$') + + # plot endpoints + for i in [0, n-1]: + x = P[i,0] ; y = P[i,1] + if i == 0: + Pi = '\mathbf{P}_{' + str(i) + '}' + elif i == n-1: + Pi = '\mathbf{P}_{' + str(n_initial-1) + '}' + + Qi = '\mathbf{Q}_{' + str(i) + '}' + text = '${Pi} = {Qi}$'.format(Pi=Pi, Qi=Qi) + plt.text(x+0.05,y+0.05,text) +``` + + +```python +example_2(m=1) +``` + + + +![png](images/bsplines-operations/output_21_0.png) + + + + +```python +example_2(m=2) +``` + + + +![png](images/bsplines-operations/output_22_0.png) + + + + +```python +example_2(m=4) +``` + + + +![png](images/bsplines-operations/output_23_0.png) + + + + +```python +example_2(m=8) +``` + + + +![png](images/bsplines-operations/output_24_0.png) + + + +## Translation + +Since B-Spline curves are invariant under affine transformations, whan translating a curve with a given displacement, the new curve has the same knot vector while the control points are obtained by applying the same translation to the initial ones. + +The following function implements this utility + + +```python +# import the translation of a B-Spline curve +from bsplines_utilities import translate_bspline_curve +``` + + +```python +def example_1(): + knots = [0., 0., 0., 0., 1., 1., 1., 1.] + degree = 3 + n = len(knots) - degree - 1 + + P = np.zeros((n, 2)) + P[:, 0] = [1., 1., 0., -1.] + P[:, 1] = [0., 1., 1., 0.] + plot_curve(knots, degree, P) + + knots, P = translate_bspline_curve(knots, P, [1., 1.5]) + plot_curve(knots, degree, P, color='r', label='Q') + +example_1() +``` + + + +![png](images/bsplines-operations/output_27_0.png) + + + +## Rotation + +Rotating a B-Spline curve with an angle $\theta$ is done by applying it on the control points, as for the translation algorithm. + +The following function implements this utility. + + +```python +# import the rotation of a B-Spline curve +from bsplines_utilities import rotate_bspline_curve +``` + + +```python +def example_1(): + knots = [0., 0., 0., 0., 1., 1., 1., 1.] + degree = 3 + n = len(knots) - degree - 1 + + P = np.zeros((n, 2)) + P[:, 0] = [1., 1., 0., -1.] + P[:, 1] = [0., 1., 1., 0.] + plot_curve(knots, degree, P) + + knots, P = rotate_bspline_curve(knots, P, np.pi/3., center=[-1.,0.]) + plot_curve(knots, degree, P, color='r', label='Q') + +example_1() +``` + + + +![png](images/bsplines-operations/output_30_0.png) + + + +## Homothetic transformation + +The following function implements a hmothetic transformation for B-Spline curves. + + +```python +# import the homothetic transformation of a B-Spline curve +from bsplines_utilities import homothetic_bspline_curve +``` + + +```python +def example_1(): + knots = [0., 0., 0., 0., 1., 1., 1., 1.] + degree = 3 + n = len(knots) - degree - 1 + + P = np.zeros((n, 2)) + P[:, 0] = [1., 1., 0., -1.] + P[:, 1] = [0., 1., 1., 0.] + plot_curve(knots, degree, P) + + knots, P = homothetic_bspline_curve(knots, P, 0.5, center=[0.,0.]) + plot_curve(knots, degree, P, color='r', label='Q') + +example_1() +``` + + + +![png](images/bsplines-operations/output_33_0.png) + + + + diff --git a/_sources/chapter0/bsplines-surfaces.md b/_sources/chapter0/bsplines-surfaces.md new file mode 100644 index 0000000..c945976 --- /dev/null +++ b/_sources/chapter0/bsplines-surfaces.md @@ -0,0 +1,255 @@ +# B-Splines surfaces + +The B-spline surface in $\mathbb{R}^d$ associated to knots $(T_u, T_v)$ where $T_u=(u_i)_{0\leqslant i \leqslant n_u + p_u + 1}$ and $T_v=(v_i)_{0\leqslant i \leqslant n_v + p_v + 1}$, and control points $(\mathbf{P}_{ij})_{ 0 \leqslant i \leqslant n_u, 0 \leqslant j \leqslant n_v}$ is defined by : + +$$ +\mathcal{C}(u,v) = \sum_{i=0}^{n_u} \sum_{j=0}^{n_v} N_i^{p_u}(u) N_j^{p_v}(v) \textbf{P}_{i,j} +$$ + +```python +# needed imports +import numpy as np +import matplotlib.pyplot as plt + +from mpl_toolkits.mplot3d import Axes3D +from matplotlib import cm +``` + + +```python +# importing bsplines utilities +from bsplines_utilities import find_span, all_bsplines, point_on_nurbs_surface, point_on_bspline_surface, insert_knot_bspline_surface, insert_knot_nurbs_surface +``` + +**Example 1**: + +In this first example, we consider a surface that approximate the function $(u,v) \mapsto \sin(\pi u) \sin(\pi v)$ + + +```python +def example_1(): + Tu = [0., 0., 0., 1., 1., 1.] + pu = 2 + nu = len(Tu) - pu - 1 + + Tv = [0., 0., 0., 1., 1., 1.] + pv = 2 + nv = len(Tv) - pv - 1 + + P = np.zeros((nu, nv,1)) + + gridu = np.linspace(0., 1., nu) + gridv = np.linspace(0., 1., nv) + + for i,u in enumerate(gridu): + for j,v in enumerate(gridv): + P[i, j, 0] = np.sin(np.pi*u)*np.sin(np.pi*v) + + nx = 101 + xs = np.linspace(0., 1., nx) + + ny = 101 + ys = np.linspace(0., 1., ny) + + Q = np.zeros((nx, ny, 1)) + for i,x in enumerate(xs): + for j,y in enumerate(ys): + Q[i,j,:] = point_on_bspline_surface(Tu, Tv, P, x, y) + + fig = plt.figure() + ax = fig.gca(projection='3d') + + X, Y = np.meshgrid(xs, ys) + Z = Q[:,:,0] + + # Plot the surface. + surf = ax.plot_surface(X, Y, Z, cmap=cm.coolwarm, + linewidth=0, antialiased=False) + + # Add a color bar which maps values to colors. + fig.colorbar(surf, shrink=0.5, aspect=5) + +example_1() +``` + + + +![png](images/bsplines-surfaces/output_5_0.png) + + + +**Example 2**: + +This example shows the construction of a square in 2D. +The B-Spline surface is created using the function **make_square** + + +```python +def make_square(origin=(0,0), length=1.): + Tu = [0., 0., 1., 1.] + Tv = [0., 0., 1., 1.] + pu = 1 + pv = 1 + nu = len(Tu) - pu - 1 + nv = len(Tv) - pv - 1 + gridu = np.unique(Tu) + gridv = np.unique(Tv) + + origin = np.asarray(origin) + + P = np.asarray([[[0.,0.],[0.,1.]],[[1.,0.],[1.,1.]]]) + for i in range(0, 2): + for j in range(0, 2): + P[i,j,:] = origin + P[i,j,:]*length + + return (Tu, Tv), (pu, pv), P +``` + + +```python +def plot_surface(knots, degrees, P, weights=None, Nu=101, Nv=101, color='b'): + Tu, Tv = knots + pu, pv = degrees + + nu = len(Tu) - pu - 1 + nv = len(Tv) - pv - 1 + gridu = np.unique(Tu) + gridv = np.unique(Tv) + + us = np.linspace(0., 1., Nu) + vs = np.linspace(0., 1., Nv) + + # ... + Q = np.zeros((Nv, 2)) + if weights is None: + for i,u in enumerate(gridu): + for j,v in enumerate(vs): + Q[j,:] = point_on_bspline_surface(Tu, Tv, P, u, v) + + plt.plot(Q[:,0], Q[:,1], '-'+color) + + else: + for i,u in enumerate(gridu): + for j,v in enumerate(vs): + Q[j,:] = point_on_nurbs_surface(Tu, Tv, P, weights, u, v) + + plt.plot(Q[:,0], Q[:,1], '-'+color) + # ... + + # ... + Q = np.zeros((Nu, 2)) + if weights is None: + for j,v in enumerate(gridv): + for i,u in enumerate(us): + Q[i,:] = point_on_bspline_surface(Tu, Tv, P, u, v) + + plt.plot(Q[:,0], Q[:,1], '-'+color) + + else: + for j,v in enumerate(gridv): + for i,u in enumerate(us): + Q[i,:] = point_on_nurbs_surface(Tu, Tv, P, weights, u, v) + + plt.plot(Q[:,0], Q[:,1], '-'+color) + # ... +# ... + +``` + + +```python +def example_2(): + knots, degrees, P = make_square(origin=(0,0), + length=1.) + + t = 0.5 + Tu, Tv, pu, pv, P = insert_knot_bspline_surface(*knots, *degrees, P, t, + times=1, + axis=None) + + plot_surface((Tu, Tv), (pu, pv), P, + weights=None, + Nu=101, Nv=101, + color='b') + +example_2() +``` + + + +![png](images/bsplines-surfaces/output_9_0.png) + + + +**Example 3**: + +The following example shows how to create and plots a circle using NURBS. + +We shall need the following function: + + +```python +def make_circle(center=(0.,0.), radius=1.): + Tu = [0., 0., 0., 1, 1., 1.] + Tv = [0., 0., 0., 1, 1., 1.] + pu = 2 + pv = 2 + nu = len(Tu) - pu - 1 + nv = len(Tv) - pv - 1 + gridu = np.unique(Tu) + gridv = np.unique(Tv) + + + s = 1./np.sqrt(2) + P = np.zeros((nu,nv,2)) + P[0,0,:] = np.asarray([-s , -s ]) + P[1,0,:] = np.asarray([-2*s , 0. ]) + P[2,0,:] = np.asarray([-s , s ]) + P[0,1,:] = np.asarray([0. , -2*s ]) + P[1,1,:] = np.asarray([0. , 0.0 ]) + P[2,1,:] = np.asarray([0. , 2*s ]) + P[0,2,:] = np.asarray([s , -s ]) + P[1,2,:] = np.asarray([2*s , 0. ]) + P[2,2,:] = np.asarray([s , s ]) + + P *= radius + P[:,:,0] += center[0] + P[:,:,1] += center[1] + + W = np.zeros((3,3)) + W[0,0] = 1. + W[1,0] = s + W[2,0] = 1. + W[0,1] = s + W[1,1] = 1. + W[2,1] = s + W[0,2] = 1. + W[1,2] = s + W[2,2] = 1. + + return (Tu, Tv), (pu, pv), P, W + +``` + + +```python +def example_3(): + knots, degrees, P, W = make_circle(center=(0.,0.), radius=1.) + + t = 0.5 + Tu, Tv, pu, pv, P, W = insert_knot_nurbs_surface(*knots, *degrees, P, W, t, + times=1, + axis=None) + + plot_surface((Tu, Tv), (pu, pv), P, + weights=W, + Nu=101, Nv=101, + color='b') + +example_3() +``` + + + +![png](images/bsplines-surfaces/output_12_0.png) + diff --git a/_sources/chapter0/bsplines.md b/_sources/chapter0/bsplines.md new file mode 100644 index 0000000..f5d01fe --- /dev/null +++ b/_sources/chapter0/bsplines.md @@ -0,0 +1,529 @@ +# B-Splines + +Given a subdivision $\{x_0 < x_1 < \cdots < x_r\}$ of the interval $I = [x_0, x_r]$, the \textbf{Schoenberg space} is the space of piecewise polynomials of degree $p$, on the interval $I$ and given regularities $\{k_1, k_2, \cdots, k_{r-1}\}$ at the internal points $\{x_1, x_2, \cdots, x_{r-1}\}$. + +Given $m$ and $p$ as natural numbers, let us consider a sequence of non decreasing real numbers $T=\{t_i\}_{0\leqslant i \leqslant m}$. $T$ is called **knots sequence**. From a knots sequence, we can generate a B-splines family using the reccurence formula \ref{eq:bspline-reccurence}. + +````{prf:definition} B-Splines using Cox-DeBoor Formula +:label: def-bspline +The j-th B-spline of degree $p$ is defined by the recurrence relation: + +$$ +\begin{align} + N_j^p = \frac{t-t_j}{t_{j+p}-t_{j}} N_j^{p-1} + \frac{t_{j+p+1}-t}{t_{j+p+1}-t_{j+1}} N_{j+1}^{p-1}, + \label{eq:bspline-reccurence} +\end{align} +$$ + +where + +$$ +N_j^0(t) = \chi_{ \left[ t_j, t_{j+1} \right[ }(t) +$$ + +for $0 \leq j \leq m-p-1$. +```` + +```{prf:remark} + When working with Bernstein polynomials, we introduced the convention $B_i^n=0$ for all $i<0$ or $i>n$. For B-Splines, we have a similar convetion $N_j^p=0$ if $j<0$ or $j>n$. In addition, we also assume $\frac{0}{0} = 0$, when using the formula \ref{eq:bspline-reccurence} and $N_j^0 = 0$ if $t_j = t_{j+1}$. +``` + +```python +# needed imports +import numpy as np +from numpy import empty +import matplotlib.pyplot as plt +``` + +````{prf:example} +:label: bsplines-ex-1 + +We consider a linear B-Spline with the knot vector $T = [0, 1, 2]$ + + +```python +def N1_0(t): + if t >= 0 and t< 1: return t + if t >= 1 and t< 2: return 2-t + return 0. + +xs = np.linspace(0., 2., 200) +plt.plot(xs, [N1_0(x) for x in xs], label='$N_0^1$') +plt.legend() +``` +![png](images/bsplines/output_5_1.png) +```` + +````{prf:example} +:label: bsplines-ex-2 + +We consider a linear B-Spline with the knot vector $T = [0, 0, 1]$ + +```python +def N1_0(t): + if t >= 0 and t< 1: return 1-t + return 0. + +xs = np.linspace(0., 1., 200) +plt.plot(xs, [N1_0(x) for x in xs], label='$N_0^1$') +plt.legend() +``` +![png](images/bsplines/output_7_1.png) +```` + +````{prf:example} +:label: bsplines-ex-3 + +We consider a linear B-Spline with the knot vector $T = [0, 1, 1]$ + +```python +def N1_0(t): + if t >= 0 and t< 1: return t + return 0. + +xs = np.linspace(0., 1., 201)[:-1] +plt.plot(xs, [N1_0(x) for x in xs], label='$N_0^1$') +plt.legend() +``` + +![png](images/bsplines/output_9_1.png) +```` + +````{prf:example} +:label: bsplines-ex-4 + +We consider linear B-Splines with the knot vector $T = [0, 0, 1, 1]$ + +```python +def N1_0(t): + if t >= 0 and t< 1: return 1-t + return 0. + +def N1_1(t): + if t >= 0 and t< 1: return t + return 0. + +xs = np.linspace(0., 1., 201)[:-1] +plt.plot(xs, [N1_0(x) for x in xs], label='$N_0^1$') +plt.plot(xs, [N1_1(x) for x in xs], label='$N_1^1$') +plt.legend() +``` + +![png](images/bsplines/output_11_1.png) +```` + +````{prf:example} +:label: bsplines-ex-5 + +We consider linear B-Splines with the knot vector $T = [0, 0, 1, 2]$ + +```python +def N1_0(t): + if t >= 0 and t< 1: return 1-t + return 0. + +def N1_1(t): + if t >= 0 and t< 1: return t + if t >= 1 and t< 2: return 2-t + return 0. + +xs = np.linspace(0., 2., 201)[:-1] +plt.plot(xs, [N1_0(x) for x in xs], label='$N_0^1$') +plt.plot(xs, [N1_1(x) for x in xs], label='$N_1^1$') +plt.legend() +``` + +![png](images/bsplines/output_13_1.png) +```` + +````{prf:example} +:label: bsplines-ex-6 + +We consider a quadratic B-Spline with the knot vector $T = [0, 0, 1, 1]$ + +```python +def N2_0(t): + if t >= 0 and t< 1: return 2*t*(1-t) + return 0. + +xs = np.linspace(0., 1., 201)[:-1] +plt.plot(xs, [N2_0(x) for x in xs], label='$N_0^2$') +plt.legend() +``` + +![png](images/bsplines/output_15_1.png) +```` + +````{prf:example} +:label: bsplines-ex-7 + +We consider a quadratic B-Spline with the knot vector $T = [0, 0, 1, 2]$ + + +```python +T = [0, 0, 1, 2] +def N2_0(t): + if t >= 0 and t< 1: return 2*t-3./2.*t**2 + if t >= 1 and t< 2: return 0.5*(2-t)**2 + return 0. + +xs = np.linspace(0., 2., 200) +plt.plot(xs, [N2_0(x) for x in xs], label='$N_0^2$') +plt.legend() +``` + +![png](images/bsplines/output_17_1.png) +```` + +````{prf:example} +:label: bsplines-ex-8 + +We consider linear B-Splines with the knot vector $T = [0, 0, 1, 2, 3, 3]$ + +```python +def N1_0(t): + if t >= 0 and t< 1: return 1-t + return 0. + +def N1_1(t): + if t >= 0 and t< 1: return t + if t >= 1 and t< 2: return 2-t + return 0. + +def N1_2(t): + if t >= 1 and t< 2: return t-1 + if t >= 2 and t< 3: return 3-t + return 0. + +def N1_3(t): + if t >= 2 and t< 3: return t-2 + return 0. + + +xs = np.linspace(0., 3., 201)[:-1] +plt.plot(xs, [N1_0(x) for x in xs], label='$N_0^1$') +plt.plot(xs, [N1_1(x) for x in xs], label='$N_1^1$') +plt.plot(xs, [N1_2(x) for x in xs], label='$N_2^1$') +plt.plot(xs, [N1_3(x) for x in xs], label='$N_3^1$') +plt.legend() +``` + +![png](images/bsplines/output_19_1.png) +```` + +````{prf:example} +:label: bsplines-ex-9 + +We consider quadratic B-Splines with the knot vector $T = [0, 0, 0, 1, 1, 1]$ + +```python +def N2_0(t): + if t >= 0 and t< 1: return (1-t)**2 + return 0. + +def N2_1(t): + if t >= 0 and t< 1: return 2*t*(1-t) + return 0. + +def N2_2(t): + if t >= 0 and t< 1: return t**2 + return 0. + +xs = np.linspace(0., 1., 201)[:-1] +plt.plot(xs, [N2_0(x) for x in xs], label='$N_0^2$') +plt.plot(xs, [N2_1(x) for x in xs], label='$N_1^2$') +plt.plot(xs, [N2_2(x) for x in xs], label='$N_2^2$') +plt.legend() +``` + +![png](images/bsplines/output_21_1.png) +```` + +## B-Splines properties + +B-Splines have many interesting properties that are listed below. In general, most of the proofs are done by induction on the B-Spline degree. + +````{prf:proposition} + B-splines are piecewise polynomial of degree $p$ +```` + +```{prf:remark} + The B-splines functions associated to open knots sequences without internal knots, \textit{i.e.} the length of the knots sequence is exactly $2p+2$, are the Bernstein polynomials of degree$p$. +``` + +````{prf:proposition} compact support + $N_j^p(t) = 0$ for all $t \notin [t_j, t_{j+p+1})$. +```` + +````{prf:proposition} + \label{prop:non-vanishing-bsplines} + If $t \in~ [ t_j,t_{j+1} ) $, then only the \textit{B-splines} $\{ N_{j-p}^p,\cdots,N_{j}^p \}$ are non vanishing at $t$. +```` + + +````{prf:proposition} non-negativity + $N_j^p(t) \ge 0, \quad \forall t \in [ t_j, t_{j+p+1} ) $ +```` + +````{prf:proposition} Partition of unity + $\sum N_i^{p}(t) = 1, \forall t \in \mathbb{R}$ +```` + +```{prf:remark} +The previous sum $\sum N_i^{p}(t)$ has a meaning since for every $t \in \mathbb{R}$, only $p+1$ B-Splines are non-vanishing. +``` + +```{prf:remark} + For the sake of simplicity, we shall avoid using summation indices on linear expansion of B-Splines. +``` + +````{prf:lemma} +$$ + \begin{align} + \sum a_j N_j^p = \sum \left(\frac{t_{j+p}-t}{t_{j+p}-t_{j}}a_{j-1} + \frac{t-t_j}{t_{j+p}-t_{j}} a_j\right) N_j^{p-1} + \end{align} +$$ +```` + +````{prf:proposition} Marsden's idenity +$$ + \begin{align} + \left( x-y \right)^p = \sum\limits_{j} \rho_j^p(y) N_j^p(x) + \label{eq:marsden-spline} + \end{align} +$$ + +where + +$$ + \begin{align} + \rho_j^p(y) = \prod\limits_{i=j+1}^{j+p} (t_{i} -y) + \end{align} +$$ +```` + +Thanks to Marsden's identity and the proposition \ref{prop:non-vanishing-bsplines}, we now are able to prove the local linear independence of the B-Splines basis functions. + +````{prf:proposition} Local linear independence + On each interval $[t_j, t_{j+1})$, the B-Splines are lineary independent. +```` + +```{prf:remark} + We will see in the Approximation theory part, that the B-Splines family has also a global linear independence property. +``` + +````{prf:proposition} Derivatives of B-Splines +The derivative of B-Splines can be computed reccursivly by deriving the formula \ref{eq:bspline-reccurence}, which gives + +$$ +\begin{align} + {N_j^p}^\prime = \frac{p}{t_{j+p}-t_{j}} N_j^{p-1} - \frac{p}{t_{j+p+1}-t_{j+1}} N_{j+1}^{p-1} + \label{eq:bspline-ders-reccurence} +\end{align} +$$ + +```` + +## Evaluation of B-Splines + +Given a knot sequence $T=\{t_i\}_{0\leqslant i \leqslant n + p}$, we are interested in the algorithmic evaluation of B-Splines of degree $p$. + +```{warning} +Add evaluation diagram +``` + +For a given real point $x$, it is done in two steps: + +1. find the knot span index $j$, such that $x \in~ ] t_j,t_{j+1} [ $ +2. evaluate all non-vanishing B-Splines $N_{j-p}^p, \cdots, N_j^p$ + +The first point is achieved by the function implemented by the following function: + +```python +def find_span( knots, degree, x ): + # Knot index at left/right boundary + low = degree + high = 0 + high = len(knots)-1-degree + + # Check if point is exactly on left/right boundary, or outside domain + if x <= knots[low ]: returnVal = low + elif x >= knots[high]: returnVal = high-1 + else: + # Perform binary search + span = (low+high)//2 + while x < knots[span] or x >= knots[span+1]: + if x < knots[span]: + high = span + else: + low = span + span = (low+high)//2 + returnVal = span + + return returnVal +``` + +The second point is implemented by the following function, that returns all non-vanishing B-Splines at $x$ + + +```python +def all_bsplines( knots, degree, x, span ): + left = empty( degree , dtype=float ) + right = empty( degree , dtype=float ) + values = empty( degree+1, dtype=float ) + + values[0] = 1.0 + for j in range(0,degree): + left [j] = x - knots[span-j] + right[j] = knots[span+1+j] - x + saved = 0.0 + for r in range(0,j+1): + temp = values[r] / (right[r] + left[j-r]) + values[r] = saved + right[r] * temp + saved = left[j-r] * temp + values[j+1] = saved + + return values +``` + +The following function plots all B-Splines given a knot vector and a polynomial degree. + + +```python +def plot_splines(knots, degree, nx=100): + xmin = knots[degree] + xmax = knots[-degree-1] + + # grid points for evaluation + xs = np.linspace(xmin,xmax,nx) + + # this is the number of the BSplines in the Schoenberg space + N = len(knots) - degree - 1 + + ys = np.zeros((N,nx), dtype=np.double) + for ix,x in enumerate(xs): + span = find_span( knots, degree, x ) + b = all_bsplines( knots, degree, x, span ) + ys[span-degree:span+1, ix] = b[:] + + for i in range(0,N): + plt.plot(xs,ys[i,:], label='$N_{}$'.format(i+1)) + plt.legend(loc=9, ncol=4) +``` + +## Knots vector families + +There are two kind of **knots vectors**, called **clamped** and **unclamped**. Both families contains **uniform** and **non-uniform** sequences. + +The following are examples of such knots vectors + +### Clamped knots (open knots vector) + +#### uniform + +````{prf:example} +:label: bsplines-ex-10 + +```python +T = np.array([0, 0, 0, 1, 2, 3, 4, 5, 5, 5]) + +plot_splines(T, degree=2, nx=100) +``` + +![png](images/bsplines/output_30_0.png) +```` + +````{prf:example} +:label: bsplines-ex-11 + +```python +T = [-0.2, -0.2, 0.0, 0.2, 0.4, 0.6, 0.8, 0.8] + +plot_splines(T, degree=2, nx=100) +``` + +![png](images/bsplines/output_31_0.png) +```` + +#### non-uniform + +````{prf:example} +:label: bsplines-ex-12 + +```python +T = [0, 0, 0, 1, 3, 4, 5, 5, 5] + +plot_splines(T, degree=2, nx=100) +``` + +![png](images/bsplines/output_33_0.png) +```` + + +````{prf:example} +:label: bsplines-ex-13 + +```python +T = [-0.2, -0.2, 0.4, 0.6, 0.8, 0.8] + +plot_splines(T, degree=2, nx=100) +``` + +![png](images/bsplines/output_34_0.png) +```` + +### Unclamped knots + +#### uniform + +````{prf:example} +:label: bsplines-ex-14 + +```python +T = [0, 1, 2, 3, 4, 5, 6, 7, 8] + +plot_splines(T, degree=2, nx=100) +``` + +![png](images/bsplines/output_36_0.png) +```` + + +````{prf:example} +:label: bsplines-ex-15 + +```python +T = [-0.2, 0.0, 0.2, 0.4, 0.6, 0.8, 1.0] + +plot_splines(T, degree=2, nx=100) +``` + +![png](images/bsplines/output_37_0.png) +```` + +#### non-uniform + + +````{prf:example} +:label: bsplines-ex-16 + +```python +T = [0, 0, 3, 4, 7, 8, 9] + +plot_splines(T, degree=2, nx=100) +``` + +![png](images/bsplines/output_39_0.png) +```` + +````{prf:example} +:label: bsplines-ex-17 + +```python +T = [-0.2, 0.2, 0.4, 0.6, 1.0, 2.0, 2.5] + +plot_splines(T, degree=2, nx=100) +``` + +![png](images/bsplines/output_40_0.png) +```` diff --git a/_sources/chapter0/cad.md b/_sources/chapter0/cad.md new file mode 100644 index 0000000..843df56 --- /dev/null +++ b/_sources/chapter0/cad.md @@ -0,0 +1,3 @@ +# Computer Aided Design + +TODO diff --git a/_sources/chapter0/data-structure.md b/_sources/chapter0/data-structure.md new file mode 100644 index 0000000..6a15a16 --- /dev/null +++ b/_sources/chapter0/data-structure.md @@ -0,0 +1,146 @@ +# Data Structure + +In the sequel, we shall use **StencilMatrix** and **StencilVector** from the **psydac** library. + +For the moment, we are only interested about having an appropriate data structure to store our computations. +Once the assembly is done, we will convert the matrix into a scipy sparse matrix, while the vector will be converted to numpy array. + +We will see later how one can impose boundary conditions. + +# 1D Case + + +```python +import numpy as np + +from psydac.fem.splines import SplineSpace +from psydac.fem.tensor import TensorFemSpace +from psydac.linalg.stencil import StencilMatrix +from psydac.linalg.stencil import StencilVector +from psydac.ddm.cart import DomainDecomposition +``` + + +```python +from gallery_section_03 import assemble_stiffness_1d +from gallery_section_03 import assemble_vector_1d +``` + + +```python +xmin = 0. ; xmax = 1. +nelements = 8 +degree = 3 +grid = np.linspace( xmin, xmax, num=nelements+1 ) +V = SplineSpace(degree=degree, grid=grid) +dd = DomainDecomposition(ncells=[V.ncells], periods=[False]) +V = TensorFemSpace(dd, V) +``` + + +```python +stiffness = StencilMatrix(V.vector_space, V.vector_space) +``` + + +```python +stiffness = assemble_stiffness_1d( V, matrix=stiffness ) +``` + + +```python +stiffness = stiffness.tosparse() +``` + + +```python +f = lambda x: 2. +``` + + +```python +rhs = StencilVector(V.vector_space) +``` + + +```python +rhs = assemble_vector_1d( f, V, rhs=rhs ) +``` + + +```python +rhs = rhs.toarray() +``` + +## 2D Case + + +```python +from gallery_section_03 import assemble_stiffness_2d +from gallery_section_03 import assemble_vector_2d +``` + + +```python +x1min = 0. ; x1max = 1. +x2min = 0. ; x2max = 1. +nelements1 = 8 +nelements2 = 8 +degree1 = 3 +degree2 = 3 +grid1 = np.linspace( x1min, x1max, num=nelements1+1 ) +grid2 = np.linspace( x2min, x2max, num=nelements2+1 ) + +V1 = SplineSpace(degree=degree1, grid=grid1) +V2 = SplineSpace(degree=degree2, grid=grid2) + +dd = DomainDecomposition(ncells=[V1.ncells, V2.ncells], periods=[False, False]) +V = TensorFemSpace(dd, V1, V2) +``` + + +```python +stiffness = StencilMatrix(V.vector_space, V.vector_space) +``` + + +```python +stiffness = assemble_stiffness_2d( V, matrix=stiffness ) +``` + + +```python +stiffness = stiffness.tosparse() +``` + + +```python +# convert the sparse matrix to dense +stiffness = stiffness.toarray() +``` + + +```python +f = lambda x,y: 2. +``` + + +```python +rhs = StencilVector(V.vector_space) +``` + + +```python +rhs = assemble_vector_2d( f, V, rhs=rhs ) +``` + +### Matrix profile + + +```python +import matplotlib.pyplot as plt + +plt.spy(stiffness) +``` + +![png](images/data-structure/output_24_1.png) diff --git a/_sources/chapter0/fem.md b/_sources/chapter0/fem.md new file mode 100644 index 0000000..b0e99ed --- /dev/null +++ b/_sources/chapter0/fem.md @@ -0,0 +1,209 @@ +# Introduction to B-Splines FEM + +Let $\Omega \subset \mathbb{R}^d$ be a computational domain that is the image of a logical domain $\mathcal{P}$, *i.e.* a unit line (in *1d*), square (in *2d*) or a cube (in *3d*) with a **mapping** function + +$$ +\Omega = \mathcal{G} (\mathcal{P}) +$$ + +We consider the Poisson problem with Homogeneous Dirichlet boundary conditions: + +$$ + \mbox{Find} ~ u \in H^1_0(\Omega), ~ \mbox{such that} +$$ +$$ + - \nabla^2 u = f, ~~ \Omega +$$ + +Using a Galerkin-Rietz method, we introduce a discrete finite elements space $\mathcal{V}_h = \mathbf{span}\{ \phi_j, 1 \leq j \leq n_V \}$ for trial and test functions. Here the index $j$ is a multi-index. For example, in $2D$, we have $j = (j_1, j_2)$ + +Let $u_h \in \mathcal{V}_h$ such that $u_h = \sum_{j=1}^{n_V} u_j \phi_j$. Then the weak formulation for the Poisson equation writes + +$$ + \sum_{j=1}^{n} u_j \int_{\Omega} \nabla \phi_j \cdot \nabla \phi_i = \int_{\Omega} f \phi_i, \quad \forall 1 \leq i \leq n +$$ + +which can be written in a matrix form + +$$ + M U = F +$$ + +where $U$ denotes the coefficients $(u_j, ~ 1 \leq j \leq n)$ and $F$ is a vector consisting of the terms $\int_{\Omega} f \phi_i$ for $1 \leq i \leq n$. Finally, the matrix $M$ is called the **stiffness** matrix and its entries are defined as + +$$ + M_{ij} = \int_{\Omega} \nabla \phi_j \cdot \nabla \phi_i +$$ + +We will denote our basis function by $b_i$ and $b_j$ rather than $\phi_i$ and $\phi_j$. In this case, in order to solve the Poisson problem, one needs to + +1. Assemble the matrix $M$ of entries +$$ + M_{ij} = \int_{\Omega} \nabla b_j \cdot \nabla b_i +$$ +2. Assemble the right hand side $F$ of entries +$$ + F_{i} = \int_{\Omega} f b_i +$$ +3. Solve the linear system +$$ + M U = F +$$ + +Since at the end, we need to compute the $L^2$-norm of the error $u-u_h$, we need also to evaluate (discretize) the following (scalar) expression: + +$$ +\| e_h \|_{L^2}^2 := \| u-u_h \|_{L^2}^2 = \int_{\Omega} (u-u_h)^2 +$$ + + +## Discretization of the Poisson problem + +Now let's go back to a matrix entry $M_{ij}$, we have +$$ +M_{ij} = \sum_e \int_{Q_e} \nabla b_i \cdot \nabla b_j +$$ +We know that every basis function $b_i$ is a polynomial over the element $Q_i$. We can then use one of the Gauss quadrature formulae. + +**Note**: +In the case of *B-splines* we will avoid having to evaluate on the boundary of our element (B-Splines are only defined on the right, if we don't do so, evaluating derivatives may lead to wrong results). Hence we will use the Gauss-Legendre formula. + +**Note**: +In general, the quadrature formulae are given on the interval $[-1, 1]$. We therefor need to remap these points for every element, in out partition. + +Let's assume now that our quadrature points have been remapped, and let's call them $\xi_k$, $\omega_k$ will denote the associated weight to $\xi_k$. +In this case $M_{ij}$ can be written as + +$$ +M_{ij} = \sum_e \sum_k \omega_k \nabla b_i(\xi_k) \cdot \nabla b_j( \xi_k) +$$ + +Now let's go back to a rhs entry $F_{i}$, we have +$$ +F_{i} = \sum_e \int_{Q_e} f b_i +$$ +We know that every basis function $b_i$ is a polynomial over the element $Q_i$. We can then use one of the Gauss quadrature formulae. + +Since our quadrature points have been remapped ( points : $\xi_k$, weights : $\omega_k$ ). + +In this case $F_{i}$ can be written as + +$$ +F_{i} = \sum_e \sum_k \omega_k b_i(\xi_k) f( \xi_k) +$$ + +Now let's go back to a norm $e_h$, we have +$$ +\| e_h \|_{L^2}^2 = \sum_e \int_{Q_e} (u-u_h)^2 +$$ + +which leads to + +$$ +\| e_h \|_{L^2}^2 = \sum_e \sum_k \omega_k (u(\xi_k) - u_h( \xi_k))^2 +$$ + +The missing part here, is how to evaluate the discrete field $u_h$. This will be covered in the next part. + + +## Expressions + +When using a Finite Elements method, one needs to compute the following kind of expressions: + +* **bilinear form**. Example : $\int_{\Omega} \phi_i \phi_j ~ d\Omega$ +* **linear form**. Example : $\int_{\Omega} f \phi_i ~ d\Omega$ +* **functional**, i.e. integral of a scalar (vector) expression. Example : $\int_{\Omega} (u-u_h)^2$ + +A general formal definition of a variational form $a$ is given by Eq. \ref{eq:var-form-def}, as real-valued \textit{multi-linear} map on the product of a sequence of function spaces $\{V_j\}_{j=1}^\rho$ : + +\begin{align} + a = + \begin{cases} + V_\rho \times \ldots \times V_2 \times V_1 \times \mathcal{P} \rightarrow \mathbb{R} + \\ + a(v_\rho, \dots, v_1; w_1, \dots, w_\nu, c_1, \dots, c_\eta) + \end{cases} + \label{eq:var-form-def} +\end{align} + +where $\rho$ is the arity of the variational form, and the special cases $\rho=0,1,2$ yield to the notions of \emph{functional}, \emph{linear form} and \emph{bilinear form}, respectively. +Each of the spaces $V_j$ may be a scalar/vector function space, or a product of other function spaces. +$\mathcal{P}$ is the space of all parameters (which can be empty), containing either functions or constants (with respect to differential operators). +A function parameter is referred to as a \emph{field} and is an element of a function space, therefore it may be represented by its coefficients over a given basis. +The general definition of the space of parameters is given as $\mathcal{P} := \left( W_1 \times \ldots \times W_\nu \right) \times \mathbb{R}^\eta$ where $\left( W_i \right)_{1 \le i \le \nu}$ can be scalar or vector function spaces and $\eta$ is the number of (real) constants. +We shall refer to the parameters as \textit{free variables}, as they will not appear in the signature of the variational form, and are defined as global variables (or local to the current scope). + +In the sequel, we shall see how the different expressions can be evaluated. We will developp the different needed algorithms, that we will use in the next chapters. + +Since, we will end up by computing an integral over the domain, we will need the following procedures + +* Assembly over the domain: this will loop over the elements of the domain. In each element, we shall call a kernel procedure that performs the computation over one single element. +* depending on the multi-linear map (expression) to evaluate, we shall have three kinds of kernels: + - a kernel for computing expressions with arity of 2 + - a kernel for computing expressions with arity of 1 + - a kernel for computing expressions with arity of 0 +* we shall not discuss for the moment the data structure used to store the results of the kernels + + +## Notations + +In the sequel, we shall use the following arguments + +* n_elements_d (d=1,2,3) number of elements of the grid in each direction +* an element will always refer to a grid element, which considered as the a tuple +* k_d (d=1,2,3) will denote the number of quadrature points in each direction, with respect to current element +* The operator $\texttt{coeff}$ will denote the local coefficients of a field over the current element +* The operator $\texttt{value}$ will denote the values of a field over the current element + + +## Assembly procedures + +The generic form of the assembly procedure is described next. In general, it is splitted in 3 parts: + +* Pre-process: select the needed data, related to the current element. +* Process: call the kernel for computations on the given element +* Post-process: + +### Pre-process + +For each function space (both $V_i$ and $W_i$) involved in the expression, we need to get the basis functions over the current element, as well as their spans. + +The following examples are not general, since we consider only one function space. + + +## Evaluation of a discrete field on a given element + +When a free-variable is used in the expression, one needs to evaluate it on the quadrature points. In what follows, we describe the evaluation of a discrete field, with respect to a given element + +![title](images/algorithms/eval_field_1d.png) +![title](images/algorithms/eval_field_2d.png) + +## Kernel for an expression with arity = 1 + +![title](images/algorithms/kernel_arity1_1d.png) +![title](images/algorithms/kernel_arity1_2d.png) + +### Computing contributions of test basis functions (1D) + +![title](images/algorithms/contribution_arity1_1d_ex1.png) +![title](images/algorithms/contribution_arity1_1d_ex2.png) + +### Computing contributions of test basis functions (2D) + +![title](images/algorithms/contribution_arity1_2d_ex1.png) +![title](images/algorithms/contribution_arity1_2d_ex2.png) + +## Kernel for an expression with arity = 2 + +![title](images/algorithms/kernel_arity2_1d.png) +![title](images/algorithms/kernel_arity2_2d.png) + +### Computing contributions between test and trial basis functions (1D) + +![title](images/algorithms/contribution_arity2_1d_ex1.png) +![title](images/algorithms/contribution_arity2_1d_ex2.png) + +### Computing contributions between test and trial basis functions (2D) + +![title](images/algorithms/contribution_arity2_2d_ex1.png) +![title](images/algorithms/contribution_arity2_2d_ex2.png) diff --git a/_sources/chapter0/howto.md b/_sources/chapter0/howto.md new file mode 100644 index 0000000..62df7f4 --- /dev/null +++ b/_sources/chapter0/howto.md @@ -0,0 +1,2 @@ +# What to expect from IGA-Python + diff --git a/_sources/chapter0/iga.md b/_sources/chapter0/iga.md new file mode 100644 index 0000000..1ffca4b --- /dev/null +++ b/_sources/chapter0/iga.md @@ -0,0 +1,3 @@ +# Isogeometric Analysis + +TODO diff --git a/_sources/chapter0/performance-acceleration.md b/_sources/chapter0/performance-acceleration.md new file mode 100644 index 0000000..0b03c46 --- /dev/null +++ b/_sources/chapter0/performance-acceleration.md @@ -0,0 +1,316 @@ +# Performance and Acceleration + +In this section, we shall see how to accelerate our Python code assembly and get native speed. +We will be using [Numba](https://numba.pydata.org/) and [Pyccel](https://github.com/pyccel/pyccel). + +The **StencilMatrix** format are based on a negative indexing, which we provide through a syntactic-sugar approach by overiding the **__getitem__** and **__setitem__** methods. The entries are in fact stored in the the private attribute **\_data** which is a *numpy.NdArray*. We therefor use a shift by adding **p** as described in the **StencilMatrix** method + +```python +class StencilMatrix( object ): + ... + def _shift_index( index, shift ): + if isinstance( index, slice ): + start = None if index.start is None else index.start + shift + stop = None if index.stop is None else index.stop + shift + return slice(start, stop, index.step) + else: + return index + shift +``` + +In order to use a Python accelerator, we will first need to pass the *NdArray* as argument to the assembly function and not the **StencilMatrix** object. + +Since this will be *ugly* it is highly recommanded that one creates an *interface* function that will be calling the *core* assembly function. It is the later one that we will accelerate using Numba or Pyccel. + + +```python +from psydac.fem.splines import SplineSpace +from psydac.fem.tensor import TensorFemSpace +from psydac.linalg.stencil import StencilMatrix +from psydac.linalg.stencil import StencilVector +from psydac.ddm.cart import DomainDecomposition +``` + +## 1D Case + +### Pure Python + +The novelties here are + +* we add Python Typing Syntax to our function +* we use the matrix as **inout** argument, in the spirit of Fortran. This means that we shall have a procedure and not a function. +* we shift the access to memory when storing the Matrix entries + + +```python +def assemble_stiffness_1d_pure(nk1: 'int', + p1: 'int', + nq1: 'int', + spans_1: 'int[:]', + basis_1: 'double[:,:,:,:]', + weights_1: 'double[:,:]', + points_1: 'double[:,:]', + matrix: 'double[:,:]'): + """ + assembling the stiffness matrix using stencil forms + """ + + # ... build matrices + for ie1 in range(0, nk1): + i_span_1 = spans_1[ie1] + for il_1 in range(0, p1+1): + for jl_1 in range(0, p1+1): + i1 = i_span_1 - p1 + il_1 + j1 = i_span_1 - p1 + jl_1 + + v = 0.0 + for g1 in range(0, nq1): + bi_0 = basis_1[ie1, il_1, 0, g1] + bi_x = basis_1[ie1, il_1, 1, g1] + + bj_0 = basis_1[ie1, jl_1, 0, g1] + bj_x = basis_1[ie1, jl_1, 1, g1] + + wvol = weights_1[ie1, g1] + + v += (bi_x * bj_x) * wvol + + # we shift the test index by p1 + matrix[i1, p1+j1-i1] += v + # ... + + # NOTE: we will not return the matrix. + # explainations will come later + #return matrix +``` + +#### Timing using pure Python + + +```python +import numpy as np + +xmin = 0. ; xmax = 1. +nelements = 400 +degree = 3 +grid = np.linspace( xmin, xmax, num=nelements+1 ) +V = SplineSpace(degree=degree, grid=grid) +dd = DomainDecomposition(ncells=[V.ncells], periods=[False]) +V = TensorFemSpace(dd, V) + +M = StencilMatrix(V.vector_space, V.vector_space) + +# Sizes +[s1] = V.vector_space.starts +[e1] = V.vector_space.ends +[p1] = V.vector_space.pads + +# Quadrature data +nk1 = V.quad_grids()[0].num_elements +nq1 = V.quad_grids()[0].num_quad_pts +spans_1 = V.quad_grids()[0].spans +basis_1 = V.quad_grids()[0].basis +points_1 = V.quad_grids()[0].points +weights_1 = V.quad_grids()[0].weights + +%timeit assemble_stiffness_1d_pure( nk1, p1, nq1, spans_1, basis_1, weights_1, points_1, M._data ) +``` + + 13.2 ms ± 126 µs per loop (mean ± std. dev. of 7 runs, 100 loops each) + + +### Using Pyccel + + +```python +from pyccel.epyccel import epyccel +``` + + +```python +assemble_stiffness_1d_pyccel = epyccel(assemble_stiffness_1d_pure) +``` + +#### Timing + + +```python +import numpy as np + +xmin = 0. ; xmax = 1. +nelements = 400 +degree = 3 +grid = np.linspace( xmin, xmax, num=nelements+1 ) +V = SplineSpace(degree=degree, grid=grid) +dd = DomainDecomposition(ncells=[V.ncells], periods=[False]) +V = TensorFemSpace(dd, V) + +M = StencilMatrix(V.vector_space, V.vector_space) + +# Sizes +[s1] = V.vector_space.starts +[e1] = V.vector_space.ends +[p1] = V.vector_space.pads + +# Quadrature data +nk1 = V.quad_grids()[0].num_elements +nq1 = V.quad_grids()[0].num_quad_pts +spans_1 = V.quad_grids()[0].spans +basis_1 = V.quad_grids()[0].basis +points_1 = V.quad_grids()[0].points +weights_1 = V.quad_grids()[0].weights + +%timeit assemble_stiffness_1d_pyccel( nk1, p1, nq1, spans_1, basis_1, weights_1, points_1, M._data ) +``` + + 12.2 µs ± 139 ns per loop (mean ± std. dev. of 7 runs, 100,000 loops each) + + +## 2D case + +### Pure Python + + +```python +def assemble_stiffness_2d_pure(nk1: 'int', nk2: 'int', + p1: 'int', p2: 'int', + nq1: 'int', nq2: 'int', + spans_1: 'int[:]', spans_2: 'int[:]', + basis_1: 'double[:,:,:,:]', basis_2: 'double[:,:,:,:]', + weights_1: 'double[:,:]', weights_2: 'double[:,:]', + points_1: 'double[:,:]', points_2: 'double[:,:]', + matrix: 'double[:,:,:,:]'): + """ + assembling the stiffness matrix using stencil forms + """ + + # ... build matrices + for ie1 in range(0, nk1): + i_span_1 = spans_1[ie1] + for ie2 in range(0, nk2): + i_span_2 = spans_2[ie2] + # evaluation dependant uniquement de l'element + + for il_1 in range(0, p1+1): + for il_2 in range(0, p2+1): + for jl_1 in range(0, p1+1): + for jl_2 in range(0, p2+1): + i1 = i_span_1 - p1 + il_1 + j1 = i_span_1 - p1 + jl_1 + + i2 = i_span_2 - p2 + il_2 + j2 = i_span_2 - p2 + jl_2 + + v = 0.0 + for g1 in range(0, nq1): + for g2 in range(0, nq2): + bi_0 = basis_1[ie1, il_1, 0, g1] * basis_2[ie2, il_2, 0, g2] + bi_x = basis_1[ie1, il_1, 1, g1] * basis_2[ie2, il_2, 0, g2] + bi_y = basis_1[ie1, il_1, 0, g1] * basis_2[ie2, il_2, 1, g2] + + bj_0 = basis_1[ie1, jl_1, 0, g1] * basis_2[ie2, jl_2, 0, g2] + bj_x = basis_1[ie1, jl_1, 1, g1] * basis_2[ie2, jl_2, 0, g2] + bj_y = basis_1[ie1, jl_1, 0, g1] * basis_2[ie2, jl_2, 1, g2] + + wvol = weights_1[ie1, g1] * weights_2[ie2, g2] + + v += (bi_x * bj_x + bi_y * bj_y) * wvol + + matrix[i1, i2, p1+j1-i1, p2+j2-i2] += v + # ... +``` + +#### Timing + + +```python +# create the spline space for each direction +x1min = 0. ; x1max = 1. +nelements1 = 32 +degree1 = 3 +grid1 = np.linspace( x1min, x1max, num=nelements1+1 ) +V1 = SplineSpace(degree=degree1, grid=grid1) + +x2min = 0. ; x2max = 1. +nelements2 = 32 +degree2 = 3 +grid2 = np.linspace( x2min, x2max, num=nelements2+1 ) +V2 = SplineSpace(degree=degree2, grid=grid2) + +# create the tensor space +dd = DomainDecomposition(ncells=[V1.ncells, V2.ncells], periods=[False, False]) +V = TensorFemSpace(dd, V1, V2) + +M = StencilMatrix(V.vector_space, V.vector_space) + +# Sizes +[s1, s2] = V.vector_space.starts +[e1, e2] = V.vector_space.ends +[p1, p2] = V.vector_space.pads + +# Quadrature data +[ nk1, nk2] = [g.num_elements for g in V.quad_grids()] +[ nq1, nq2] = [g.num_quad_pts for g in V.quad_grids()] +[ spans_1, spans_2] = [g.spans for g in V.quad_grids()] +[ basis_1, basis_2] = [g.basis for g in V.quad_grids()] +[ points_1, points_2] = [g.points for g in V.quad_grids()] +[weights_1, weights_2] = [g.weights for g in V.quad_grids()] + +%timeit assemble_stiffness_2d_pure( nk1, nk2, p1, p2, nq1, nq2, spans_1, spans_2, basis_1, basis_2, weights_1, weights_2, points_1, points_2, M._data ) +``` + + 5.97 s ± 491 ms per loop (mean ± std. dev. of 7 runs, 1 loop each) + + +### Using Pyccel + + +```python +assemble_stiffness_2d_pyccel = epyccel(assemble_stiffness_2d_pure) +``` + +#### Timing + + +```python +# create the spline space for each direction +x1min = 0. ; x1max = 1. +nelements1 = 32 +degree1 = 3 +grid1 = np.linspace( x1min, x1max, num=nelements1+1 ) +V1 = SplineSpace(degree=degree1, grid=grid1) + +x2min = 0. ; x2max = 1. +nelements2 = 32 +degree2 = 3 +grid2 = np.linspace( x2min, x2max, num=nelements2+1 ) +V2 = SplineSpace(degree=degree2, grid=grid2) + +# create the tensor space +dd = DomainDecomposition(ncells=[V1.ncells, V2.ncells], periods=[False, False]) +V = TensorFemSpace(dd, V1, V2) + +M = StencilMatrix(V.vector_space, V.vector_space) + +# Sizes +[s1, s2] = V.vector_space.starts +[e1, e2] = V.vector_space.ends +[p1, p2] = V.vector_space.pads + +# Quadrature data +[ nk1, nk2] = [g.num_elements for g in V.quad_grids()] +[ nq1, nq2] = [g.num_quad_pts for g in V.quad_grids()] +[ spans_1, spans_2] = [g.spans for g in V.quad_grids()] +[ basis_1, basis_2] = [g.basis for g in V.quad_grids()] +[ points_1, points_2] = [g.points for g in V.quad_grids()] +[weights_1, weights_2] = [g.weights for g in V.quad_grids()] + +%timeit assemble_stiffness_2d_pyccel( nk1, nk2, p1, p2, nq1, nq2, spans_1, spans_2, basis_1, basis_2, weights_1, weights_2, points_1, points_2, M._data ) +``` + + 3.56 ms ± 127 µs per loop (mean ± std. dev. of 7 runs, 100 loops each) + + +## Exercises + +1. Write the accelerated version of the rhs assembly produce using Pyccel and Numba and compute their timing. +2. Perform a benchmark between Pyccel and Numba while varying the B-Spline degree. diff --git a/_sources/chapter0/poisson-1d.md b/_sources/chapter0/poisson-1d.md new file mode 100644 index 0000000..426fde2 --- /dev/null +++ b/_sources/chapter0/poisson-1d.md @@ -0,0 +1,303 @@ +# B-splines FEM solver for Poisson equation (1D) + +Following the previous [section](http://nbviewer.jupyter.org/github/ratnania/IGA-Python/blob/main/lessons/Chapter1/01_introduction_fem.ipynb), we implement here a B-Splines FEM for the Poisson problem in 1D, with homogeneous boundary conditions. + +Appropriate data-structures for matrices and vectors, involved when assembling a bilinear and linear form, will be discussed in the next section. + +We consider the following Poisson problem in 1D: +$$ +-u^{\prime \prime} = f, \quad (0,1) +\\ +u(0) = 0 ~~ \mbox{and} ~~ u(1) = 0 +$$ + +Using the algorithms developped in section 1., for assembly a bilinear form and a linear form, we see that we need to assemble + +* The Stiffness matrix +* The right hand side (rhs) + + +```python +# needed imports +from numpy import zeros, ones, linspace, zeros_like, asarray +from matplotlib.pyplot import plot, show +%matplotlib inline +``` + + +```python +# ... assembling the stiffness matrix using stencil forms +def assemble_stiffness(nelements, degree, spans, basis, weights, points, matrix): + + # ... sizes + ne1 = nelements + p1 = degree + spans_1 = spans + basis_1 = basis + weights_1 = weights + points_1 = points + + k1 = weights.shape[1] + # ... + + # ... build matrices + for ie1 in range(0, ne1): + i_span_1 = spans_1[ie1] + for il_1 in range(0, p1+1): + for jl_1 in range(0, p1+1): + i1 = i_span_1 - p1 + il_1 + j1 = i_span_1 - p1 + jl_1 + + v = 0.0 + for g1 in range(0, k1): + bi_0 = basis_1[ie1, il_1, 0, g1] + bi_x = basis_1[ie1, il_1, 1, g1] + + bj_0 = basis_1[ie1, jl_1, 0, g1] + bj_x = basis_1[ie1, jl_1, 1, g1] + + wvol = weights_1[ie1, g1] + + v += (bi_x * bj_x) * wvol + + matrix[i1, j1] += v + # ... + + return matrix +# ... +``` + + +```python +# ... Assembly procedure for the rhs +def assemble_vector(f, nelements, degree, spans, basis, weights, points, rhs): + + # ... sizes + ne1 = nelements + p1 = degree + spans_1 = spans + basis_1 = basis + weights_1 = weights + points_1 = points + + k1 = weights.shape[1] + # ... + + # ... build rhs + for ie1 in range(0, ne1): + i_span_1 = spans_1[ie1] + for il_1 in range(0, p1+1): + i1 = i_span_1 - p1 + il_1 + + v = 0.0 + for g1 in range(0, k1): + bi_0 = basis_1[ie1, il_1, 0, g1] + bi_x = basis_1[ie1, il_1, 1, g1] + + x1 = points_1[ie1, g1] + wvol = weights_1[ie1, g1] + + v += bi_0 * f(x1) * wvol + + rhs[i1] += v + # ... + + # ... + return rhs + # ... +# ... +``` + +--- +**Note**: +We added the function **f** as an argument of the *assemble_rhs* function. In general, we will avoid calling a function over the quadrature points for performance reasons. + +--- + +We will need the following imports from the **psydac** library. + + +```python +# nedded imports +from psydac.core.bsplines import elements_spans # computes the span for each element +from psydac.core.bsplines import make_knots # create a knot sequence from a grid +from psydac.core.bsplines import quadrature_grid # create a quadrature rule over the whole 1d grid +from psydac.core.bsplines import basis_ders_on_quad_grid # evaluates all bsplines and their derivatives on the quad grid +from psydac.utilities.quadratures import gauss_legendre # computes gauss legendre quadrature points & weights +from utilities.plot import plot_field_1d # plot a solution for 1d problems +``` + +Now, let's create a B-spline Finite Element Space $V$ over a grid of $32$ elements, and using **cubic** *B-splines*. + +A B-Spline space is defined here through a grid, we then call the function **make_knots** to create an open knot sequence. We finally, compute the spans for every element, to avoid doing it for each quadrature point on the current element, in the assembly procedure. + + +```python +p = 3 # spline degree +ne = 32 # number of elements + +grid = linspace(0., 1., ne+1) +knots = make_knots(grid, p, periodic=False) +spans = elements_spans(knots, p) +``` + + +```python +nelements = len(grid) - 1 +nbasis = len(knots) - p - 1 + +# we need the value a B-Spline and its first derivative +nderiv = 1 + +# create the gauss-legendre rule, on [-1, 1] +u, w = gauss_legendre( p ) + +# for each element on the grid, we create a local quadrature grid +points, weights = quadrature_grid( grid, u, w ) + +# for each element and a quadrature points, +# we compute the non-vanishing B-Splines +basis = basis_ders_on_quad_grid( knots, p, points, nderiv, normalization=False ) +``` + +Assembling the **Stiffness** matrix is then done using + + +```python +stiffness = zeros((nbasis, nbasis)) +stiffness = assemble_stiffness(nelements, p, spans, basis, weights, points, matrix=stiffness) +``` + +### Analytical solution + +In finite elements, one of the first tests we do is to check polynomial solutions of with a degree that smaller or equal to the one we chose for our discretization. +Here, we take the analytical solution $u(x) = x(1-x)$ which leads to the rhs $f(x) = - \partial_{xx} u(x) = 2$. + + +```python +f = lambda x: 2. +rhs = zeros(nbasis) +rhs = assemble_vector(f, nelements, p, spans, basis, weights, points, rhs=rhs) +``` + +In order to apply the homogeneous Dirichlet boundary conditions, we only have to remove the first and the last splines, since their values at the boundary is $1$. Due to the partition of unity, the remaining splines are $0$ on the boundary. + + +```python +# apply homogeneous dirichlet boundary conditions +rhs = rhs[1:-1] +stiffness = stiffness[1:-1, 1:-1] +``` + +We use a **cg** solver from **scipy** to solve the linear system. + + +```python +from scipy.sparse.linalg import cg +u, info = cg( stiffness, rhs, rtol=1e-6, maxiter=5000 ) +``` + +Now, we need to add the first and last control points, which are equal to **0**, then proceed to the plot. + + +```python +u = [0.] + list(u) + [0.] +u = asarray(u) +plot_field_1d(knots, p, u, nx=401) +``` + + + +![png](images/poisson-1d/output_20_0.png) + + + +## The Spline Space class + +Since we will be calling over and over the block-lines [5] and [6], we created a class called **SplineSpace** that you can import from **psydac** library. + +### Matrix profile + +Let's check the profile of our matrix. + +```python +import matplotlib.pyplot as plt + +plt.spy(stiffness) +``` + +![png](images/poisson-1d/output_23_1.png) + + +As expected, it is a sparse matrix and it has a typical profile (band one). + +### Next step + +In fact, we are not done yet! +The problem now, is that the data structure we are using for the matrix (here as a dense matrix) will consume too much memory, and is not taken into account the locality! + +Since on each element, there are exactly $p+1$ consecutive non-vanishing *B-splines*, we know that on each element there are at most $2p+1$ non zeros entries (in every direction). This means that we will need to set entries as the following, in $1D$: + +```python +M[i1, j1 - i1] += v_s +``` + +in $2D$: + +```python +M[i1, i2, j1 - i1, j2 - i2] += v_s +``` + +and in $3D$: + + +```python +M[i1, i2, i3, j1 - i1, j2 - i2, j3 - i3] += v_s +``` + +Unfortunatly, this can not be represented as a **numpy.ndarray**, because of the negative indexing! +Moreover, if our aim is to write a parallel code, other consideration must be taken into account. + +More details will be found in the next [section](http://nbviewer.jupyter.org/github/ratnania/IGA-Python/blob/main/lessons/Chapter1/03_data_structure.ipynb). + + +## Exercises + +### Exercise 1. + +1. Implement a 1D Poisson solver using non homogeneous Dirichlet boundary conditions. + +2. Implement a 2D Poisson solver using homogeneous and non homogeneous Dirichlet boundary conditions. + +### Exercise 2. + +We consider the Heat equation in 1D + +$$ +\partial_t u = \nabla^2 u +$$ + +with homogeneous boundary conditions. + +1. Write an explicit FEM solver. What do you notice about the dependency of the CFL with respect to the degree? what about the regularity? + +2. Write an implicit FEM solver. + +### Exercise 3. + +We consider a unidirectional flow in the velocity/pressure formulation + +$$ +\partial u_x = - \frac{1}{\rho} \partial_x p + \nu \partial_{yy}^2 u_x + g_x +$$ + +where the unknown $u_x$ is a function of $y$ only. + +We will consider $\partial_x p = -2$ and $g_x = 0.4$. The boundary conditions are given by $u_x(y=0) = u_x(y=h) = 0$. + +1. Write an explicit and implicit time schemes and solvers. + +2. Find numerical CFL in the case of explicit time scheme. + +3. Find the steady state. + diff --git a/_sources/chapter0/poisson-2d.md b/_sources/chapter0/poisson-2d.md new file mode 100644 index 0000000..c5f3bca --- /dev/null +++ b/_sources/chapter0/poisson-2d.md @@ -0,0 +1,185 @@ +# B-splines FEM solver for Poisson equation (2D) + +In this section, we show hoa to use **simplines** to solve a 2D Poisson problem with homogeneous boundary conditions +$$ +- \nabla^2 u = f, \Omega, +\\ +u = 0, \partial \Omega +$$ +where the computation domain $\Omega$ is the unit square. + + +```python +# needed imports +from numpy import zeros, ones, linspace, zeros_like, asarray +import numpy as np +from matplotlib.pyplot import plot, show +import matplotlib.pyplot as plt + +%matplotlib inline +``` + + +```python +from psydac.fem.splines import SplineSpace +from psydac.fem.tensor import TensorFemSpace +from psydac.linalg.stencil import StencilMatrix +from psydac.linalg.stencil import StencilVector +from psydac.ddm.cart import DomainDecomposition +``` + + +```python +from gallery_section_04 import assemble_stiffness_2d +from gallery_section_04 import assemble_vector_2d +``` + +## Create the Finite Elements Space + +In 2D, our Spline function space is defined as + +$$ +\mathcal{V}_h := \texttt{span}\{ B_{i_1}^{p_1} B_{i_2}^{p_1}, ~ 1 \le i_1 \le n_1, ~ 1 \le i_2 \le n_2\} +$$ + +which is basicaly +$$ +\mathcal{V}_h = \mathcal{V}_h^1 \otimes \mathcal{V}_h^2 +$$ +where +$$ +\mathcal{V}_h^1 := \texttt{span}\{ B_{i_1}^{p_1}, ~ 1 \le i_1 \le n_1\} +$$ +and +$$ +\mathcal{V}_h^2 := \texttt{span}\{ B_{i_2}^{p_2}, ~ 1 \le i_2 \le n_2\} +$$ + +```python +# create the spline space for each direction +x1min = 0. ; x1max = 1. +nelements1 = 1 +degree1 = 2 +grid1 = np.linspace( x1min, x1max, num=nelements1+1 ) +V1 = SplineSpace(degree=degree1, grid=grid1) + +x2min = 0. ; x2max = 1. +nelements2 = 1 +degree2 = 2 +grid2 = np.linspace( x2min, x2max, num=nelements2+1 ) +V2 = SplineSpace(degree=degree2, grid=grid2) +``` + +```python +dd = DomainDecomposition(ncells=[V1.ncells, V2.ncells], periods=[False, False]) +# create the tensor space +V = TensorFemSpace(dd, V1, V2) +``` + +## Assemble the Stiffness Matrix + +The stiffness matrix entries are defined as + +$$ +M_{\textbf{i}, \textbf{j}} := \int_{\Omega} \nabla B_{\textbf{i}} \cdot \nabla B_{\textbf{j}} +$$ + +where +$$ +B_{\textbf{i}}(x_1,x_2) := B_{i_1}(x_1)B_{i_2}(x_2), \quad \textbf{i} := (i_1,i_2) +$$ +and +$$ +B_{\textbf{j}}(x_1,x_2) := B_{j_1}(x_1)B_{j_2}(x_2), \quad \textbf{j} := (j_1,j_2) +$$ + + +```python +stiffness = StencilMatrix(V.vector_space, V.vector_space) +stiffness = assemble_stiffness_2d( V, matrix=stiffness ) +``` + +## Assemble the rhs + +The right hand side entries are defined as + +$$ +F_{\textbf{i}} := \int_{\Omega} f B_{\textbf{i}} ~d\Omega +$$ + + +```python +rhs = StencilVector(V.vector_space) + +f = lambda x,y: 2*x*(1 - x) + 2*y*(1 - y) +rhs = assemble_vector_2d( f, V, rhs=rhs ) +``` + +## Imposing boundary conditions + + +```python +s1, s2 = V.vector_space.starts +e1, e2 = V.vector_space.ends + +# ... needed for iterative solvers +# left bc at x=0. +stiffness[s1,:,:,:] = 0. +rhs[s1,:] = 0. +# right bc at x=1. +stiffness[e1,:,:,:] = 0. +rhs[e1,:] = 0. +# lower bc at y=0. +stiffness[:,s2,:,:] = 0. +rhs[:,s2] = 0. +# upper bc at y=1. +stiffness[:,e2,:,:] = 0. +rhs[:,e2] = 0. +# ... + +# ... needed for direct solvers +# boundary x = 0 +#stiffness[s1,:,0,:] = 1. +# boundary x = 1 +#stiffness[e1,:,0,:] = 1. +# boundary y = 0 +#stiffness[:,s2,:,0] = 1. +# boundary y = 1 +#stiffness[:,e2,:,0] = 1. +# ... +``` + +From now on, you can use the function **apply_dirichlet** to set the dirichlet boundary conditions for both the matrix and rhs. + +```python +# convert the stencil matrix to scipy sparse +stiffness = stiffness.tosparse() + + +```python +# convert the stencil vector to a nd_array +rhs = rhs.toarray() +``` + +```python +#from scipy.sparse import csc_matrix, linalg as sla + +#lu = sla.splu(csc_matrix(stiffness)) +#x = lu.solve(rhs) +``` + +```python +from scipy.sparse.linalg import cg +x, info = cg( stiffness, rhs, rtol=1e-7, maxiter=100 ) +``` + +```python +from utilities.plot import plot_field_2d +nbasis = [W.nbasis for W in V.spaces] +knots = [W.knots for W in V.spaces] +degrees = [W.degree for W in V.spaces] +u = x.reshape(nbasis) +plot_field_2d(knots, degrees, u) ; plt.colorbar() +``` + +![png](images/poisson-2d/output_20_1.png) diff --git a/_sources/chapter1/install.md b/_sources/chapter1/install.md new file mode 100644 index 0000000..12fa121 --- /dev/null +++ b/_sources/chapter1/install.md @@ -0,0 +1,31 @@ +# Installation + +It is recommanded to use a virtual environement. + + +```shell +# create a virtual environement +python3 -m venv .iga-python + +# activate this environement using +source .iga-python/bin/activate +``` + +Then install dependencies using + +```shell +pip3 install wheel +pip3 install numpy +pip3 install pyccel +pip3 install ipykernel +pip3 install git+https://github.com/pyccel/sympde.git +pip3 install git+https://github.com/pyccel/gelato.git +pip3 install git+https://github.com/pyccel/psydac.git +pip3 install git+https://github.com/girving/igakit.git +``` + +Adding the virtual environement to Jupyter notebook, can be done using + +```shell +python3 -m ipykernel install --user --name=.iga-python +``` diff --git a/_sources/chapter1/poisson.ipynb b/_sources/chapter1/poisson.ipynb new file mode 100644 index 0000000..92fc8fc --- /dev/null +++ b/_sources/chapter1/poisson.ipynb @@ -0,0 +1,330 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "9f28f9af", + "metadata": {}, + "source": [ + "# Your first code using SymPDE & PsyDAC\n", + "\n", + "We first start by writing our first example using SymPDE.\n", + "Let $\\Omega := (0,1)^2$. We consider the Poisson problem with homogeneous Dirichlet boundary conditions. \n", + "\n", + "$$\n", + "\\begin{align}\n", + " - \\nabla^2 u = f \\quad \\text{in $\\Omega$}, \\quad \\quad \n", + " u = 0 \\quad \\text{on $\\partial \\Omega$}. \n", + "\\end{align}\n", + "$$\n", + "\n", + "## Variational Formulation\n", + "\n", + "An $H^1$-conforming variational formulation of the previous problem reads\n", + "\n", + "$$\n", + "\\begin{align}\n", + " \\text{find $u \\in V$ such that} \\quad a(u,v) = l(v) \\quad \\forall v \\in V,\n", + "\\end{align}\n", + "$$\n", + "\n", + "where \n", + "\n", + "- $V \\subset H^1_0(\\Omega)$, \n", + "- $a(u,v) := \\int_{\\Omega} \\nabla u \\cdot \\nabla v ~ d\\Omega$, \n", + "- $l(v) := \\int_{\\Omega} f v ~ d\\Omega$." + ] + }, + { + "cell_type": "markdown", + "id": "5a958607", + "metadata": {}, + "source": [ + "## Formal Model" + ] + }, + { + "cell_type": "code", + "execution_count": 27, + "id": "d742586c", + "metadata": {}, + "outputs": [], + "source": [ + "from sympde.expr import BilinearForm, LinearForm, integral\n", + "from sympde.expr import find, EssentialBC, Norm, SemiNorm\n", + "from sympde.topology import ScalarFunctionSpace, Square, element_of\n", + "from sympde.calculus import grad, dot\n", + "\n", + "from sympy import pi, sin\n", + "\n", + "domain = Square()\n", + "\n", + "V = ScalarFunctionSpace('V', domain)\n", + "\n", + "x,y = domain.coordinates\n", + "\n", + "u,v = [element_of(V, name=i) for i in ['u', 'v']]\n", + "\n", + "# bilinear form\n", + "a = BilinearForm((u,v), integral(domain , dot(grad(v), grad(u))))\n", + "\n", + "# linear form\n", + "f = 2*pi**2*sin(pi*x)*sin(pi*y)\n", + "l = LinearForm(v, integral(domain, f*v))\n", + "\n", + "# Dirichlet boundary conditions\n", + "bc = [EssentialBC(u, 0, domain.boundary)]\n", + "\n", + "# Variational problem\n", + "equation = find(u, forall=v, lhs=a(u, v), rhs=l(v), bc=bc)" + ] + }, + { + "cell_type": "markdown", + "id": "62ac1fd4", + "metadata": {}, + "source": [ + "\n", + "This very simple Python code reflects well the abstract mathematical framework needed for variational formulations.\n", + "The structure of the code is as follows,\n", + "\n", + "1. Create a domain.\n", + "2. Create a space of *scalar* functions over the domain.\n", + "3. Create elements from this function space. These elements will denote the test and trial functions.\n", + "4. Create the Bilinear and Linear forms, $a$ and $l$ respectively.\n", + "5. Create Essential Boundary Conditions.\n", + "6. Create the variational problem.\n", + "\n", + "Most of the time, you will need to follow the same steps, with some minor variants depending on the problem you're considering." + ] + }, + { + "cell_type": "markdown", + "id": "4f983ece", + "metadata": {}, + "source": [ + "## Discretization" + ] + }, + { + "cell_type": "markdown", + "id": "51095918", + "metadata": {}, + "source": [ + "We shall need the **discretize** function from **PsyDAC**." + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "id": "a2a0a2a1", + "metadata": {}, + "outputs": [], + "source": [ + "from psydac.api.discretization import discretize" + ] + }, + { + "cell_type": "code", + "execution_count": 22, + "id": "00e54163", + "metadata": {}, + "outputs": [], + "source": [ + "degree = [3,3]\n", + "ncells = [16,16]" + ] + }, + { + "cell_type": "code", + "execution_count": 23, + "id": "5999c62b", + "metadata": {}, + "outputs": [], + "source": [ + "# Create computational domain from topological domain\n", + "domain_h = discretize(domain, ncells=ncells, comm=None)\n", + "\n", + "# Create discrete spline space\n", + "Vh = discretize(V, domain_h, degree=degree)\n", + "\n", + "# Discretize equation\n", + "equation_h = discretize(equation, domain_h, [Vh, Vh])" + ] + }, + { + "cell_type": "markdown", + "id": "7b29fbcf", + "metadata": {}, + "source": [ + "## Solving the PDE" + ] + }, + { + "cell_type": "code", + "execution_count": 24, + "id": "541192ee", + "metadata": {}, + "outputs": [], + "source": [ + "uh = equation_h.solve()" + ] + }, + { + "cell_type": "markdown", + "id": "5174c4b5", + "metadata": {}, + "source": [ + "## Computing the error norm\n", + "\n", + "When the analytical solution is available, you might be interested in computing the $L^2$ norm or $H^1_0$ semi-norm.\n", + "SymPDE allows you to do so, by creating the **Norm** object.\n", + "In this example, the analytical solution is given by\n", + "\n", + "$$\n", + "u_e = \\sin(\\pi x) \\sin(\\pi y)\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "id": "3a31c46f", + "metadata": {}, + "source": [ + "### Computing the $L^2$ norm" + ] + }, + { + "cell_type": "code", + "execution_count": 26, + "id": "5925c6cd", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "9.49756716724664e-07\n" + ] + } + ], + "source": [ + "ue = sin(pi*x)*sin(pi*y)\n", + "\n", + "u = element_of(V, name='u')\n", + "\n", + "# create the formal Norm object\n", + "l2norm = Norm(u - ue, domain, kind='l2')\n", + "\n", + "# discretize the norm\n", + "l2norm_h = discretize(l2norm, domain_h, Vh)\n", + "\n", + "# assemble the norm\n", + "l2_error = l2norm_h.assemble(u=uh)\n", + "\n", + "# print the result\n", + "print(l2_error)" + ] + }, + { + "cell_type": "markdown", + "id": "a6cbfeae", + "metadata": {}, + "source": [ + "### Computing the $H^1$ semi-norm" + ] + }, + { + "cell_type": "code", + "execution_count": 30, + "id": "e5c1a8b8", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "9.768702410721585e-05\n" + ] + } + ], + "source": [ + "# create the formal Norm object\n", + "h1norm = SemiNorm(u - ue, domain, kind='h1')\n", + "\n", + "# discretize the norm\n", + "h1norm_h = discretize(h1norm, domain_h, Vh)\n", + "\n", + "# assemble the norm\n", + "h1_error = h1norm_h.assemble(u=uh)\n", + "\n", + "# print the result\n", + "print(h1_error)" + ] + }, + { + "cell_type": "markdown", + "id": "3c09131c", + "metadata": {}, + "source": [ + "### Computing the $H^1$ norm" + ] + }, + { + "cell_type": "code", + "execution_count": 29, + "id": "d829e410", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "9.769164089397408e-05\n" + ] + } + ], + "source": [ + "# create the formal Norm object\n", + "h1norm = Norm(u - ue, domain, kind='h1')\n", + "\n", + "# discretize the norm\n", + "h1norm_h = discretize(h1norm, domain_h, Vh)\n", + "\n", + "# assemble the norm\n", + "h1_error = h1norm_h.assemble(u=uh)\n", + "\n", + "# print the result\n", + "print(h1_error)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "9250897b", + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": ".iga-python", + "language": "python", + "name": ".iga-python" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.10.12" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/_sources/chapter1/rules.md b/_sources/chapter1/rules.md new file mode 100644 index 0000000..76b5aed --- /dev/null +++ b/_sources/chapter1/rules.md @@ -0,0 +1,60 @@ +# Algebraic and differential operators evalution rules + +## Evaluation of the $\mathrm{grad}$ operator + +Rule ID | symbolic expression | evaluation +--- | --- | --- +`[OG1]` | $\mathrm{grad}(f+g)$ | $\mathrm{grad}(f) + \mathrm{grad}(g)$ +`[OG2]` | $\mathrm{grad}(\alpha ~ f)$ | $\alpha~\mathrm{grad}(f)$ +`[OG3]` | $\mathrm{grad}(f ~ g)$ | $f~\mathrm{grad}(g) + g~\mathrm{grad}(f)$ +`[OG4]` | $\mathrm{grad}(\frac{f}{g})$ | $-\frac{f}{g^2}\mathrm{grad}(g) + \frac{1}{g}\mathrm{grad}(f)$ +`[OG5]` | $\mathrm{grad}(F+G)$ | $\mathrm{grad}(F) + \mathrm{grad}(G)$ +`[OG6]` | $\mathrm{grad}(\alpha ~ F)$ | $\alpha~\mathrm{grad}(F)$ +`[OG7]` | $\mathrm{grad}(\mathrm{dot}(F, G))$ | $\mathrm{convect}(F, G) + \mathrm{convect}(G, F) + \mathrm{cross}(F, \mathrm{curl}(G)) - \mathrm{cross}(\mathrm{curl}(F), G)$ + +## Evaluation of $\mathrm{curl}$ and $\mathrm{rot}$ operators in 2D + +Rule ID | symbolic expression | evaluation +--- | --- | --- +`[OC1a]` | $\mathrm{curl}(f+g)$ | $\mathrm{curl}(f) + \mathrm{curl}(g)$ +`[OC2a]` | $\mathrm{curl}(\alpha ~ f)$ | $\alpha~\mathrm{curl}(f)$ +`[OC1b]` | $\mathrm{rot}(F+G)$ | $\mathrm{rot}(F) + \mathrm{rot}(G)$ +`[OC2b]` | $\mathrm{rot}(\alpha ~ F)$ | $\alpha~\mathrm{rot}(F)$ + + +## Evaluation of $\mathrm{curl}$ operator in 3D + +Rule ID | symbolic expression | evaluation +--- | --- | --- +`[OC1]` | $\mathrm{curl}(F+G)$ | $\mathrm{curl}(F) + \mathrm{curl}(G)$ +`[OC2]` | $\mathrm{curl}(\alpha ~ F)$ | $\alpha~\mathrm{curl}(F)$ +`[OC3]` | $\mathrm{curl}(f ~ F)$ | $f~\mathrm{curl}(F) + \mathrm{cross}(\mathrm{grad}(f), F)$ +`[OC4]` | $\mathrm{curl}(\mathrm{cross}(F, G))$ | $\mathrm{div}(G)~F - \mathrm{div}(F)~G - \mathrm{convect}(F, G) +\mathrm{convect}(G, F)$ + +## Evaluation of $\mathrm{div}$ operator + +Rule ID | symbolic expression | evaluation +--- | --- | --- +`[OD1]` | $\mathrm{div}(F+G)$ | $\mathrm{div}(F) + \mathrm{div}(G)$ +`[OD2]` | $\mathrm{div}(\alpha ~ F)$ | $\alpha~\mathrm{div}(F)$ +`[OD3]` | $\mathrm{div}(f ~ G)$ | $f~\mathrm{div}(G) + \mathrm{dot}(G, \mathrm{grad}(f))$ +`[OD4]` | $\mathrm{div}(\mathrm{cross}(F, G))$ | $-\mathrm{dot}(F, \mathrm{curl}(G)) + \mathrm{dot}(G, \mathrm{curl}(F))$ + +## Evaluation of $\mathrm{laplace}$ operator + +Rule ID | symbolic expression | evaluation +--- | --- | --- +`[OL1]` | $\mathrm{laplace}(f+g)$ | $\mathrm{laplace}(f) + \mathrm{laplace}(g)$ +`[OL2]` | $\mathrm{laplace}(\alpha ~ f)$ | $\alpha~\mathrm{laplace}(f)$ +`[OL3]` | $\mathrm{laplace}(f~g)$ | $f ~ \mathrm{laplace}(g) + g ~ \mathrm{laplace}(f) + 2 \mathrm{dot}(\mathrm{grad}(f), \mathrm{grad}(g))$ + +## Evaluation of specific combination of operators + +Rule ID | symbolic expression | evaluation +--- | --- | --- +`[OS1]` | $\mathrm{curl}(\mathrm{grad}(f))$ | $0$ +`[OS2]` | $\mathrm{div}(\mathrm{curl}(F))$ | $0$ +`[OS3]` | $\mathrm{div}(\mathrm{cross}(\mathrm{grad}(F), \mathrm{grad}(G)))$ | $0$ +`[OS4]` | $\mathrm{curl}(\mathrm{curl}(F))$ | $\mathrm{grad}(\mathrm{div}(F)) - \mathrm{laplace}(F)$ +`[OS5]` | $\mathrm{curl}(f~\mathrm{grad}(g))$ | $\mathrm{cross}(\mathrm{grad}(f), \mathrm{grad}(g))$ + diff --git a/_sources/chapter1/space.md b/_sources/chapter1/space.md new file mode 100644 index 0000000..544dc79 --- /dev/null +++ b/_sources/chapter1/space.md @@ -0,0 +1,76 @@ +# Function Space concepts + +SymPDE provides two Python classes to describe scalar and vector function spaces, respectively. There is no notion of a discrete representation; for example, we do not need to mention that a space is a Brezzi-Douglas-Marini (BDM) space. In fact, these kind of function spaces can be seen as parametric types having as a basic type **ScalarFunctionSpace** or **VectorFunctionSpace**. SymPDE only needs to know if an element of the space can be indexed or not. A BDM space would then be identified by an annotation added by a third party library to uniquely define a function space at the discrete level. + +## BasicFunctionSpace + +This represents the base class of all our function spaces. It does not reflect a continuous space, but it is more a **type** at the formal/abstract level. + +## ScalarFunctionSpace + +```python +>>> domain = Domain('Omega', dim=2) +>>> V1 = ScalarFunctionSpace('V1', domain) +``` + +## VectorFunctionSpace + +```python +>>> domain = Domain('Omega', dim=2) +>>> W1 = VectorFunctionSpace('W1', domain) +``` + +## Typed Spaces +```python +>>> domain = Domain('Omega', dim=2) +>>> H1 = ScalarFunctionSpace('V0', domain, kind='H1') +>>> Hcurl = VectorFunctionSpace('V1', domain, kind='Hcurl') +>>> Hdiv = VectorFunctionSpace('V2', domain, kind='Hdiv') +>>> L2 = ScalarFunctionSpace('V3', domain, kind='L2') +>>> assert(H1.kind == H1Space) +>>> assert(Hcurl.kind == HcurlSpace) +>>> assert(Hdiv.kind == HdivSpace) +>>> assert(L2.kind == L2Space) +>>> assert(V.kind == UndefinedSpace) +>>> assert(W.kind == UndefinedSpace) +>>> assert(H1.regularity > L2.regularity) +>>> assert(H1.regularity > Hcurl.regularity) +>>> assert(Hcurl.regularity > L2.regularity) +``` + +## ProductSpace + +```python +>>> domain = Domain('Omega', dim=2) +>>> V1 = ScalarFunctionSpace('V1', domain) +>>> V2 = ScalarFunctionSpace('V2', domain) +>>> W1 = VectorFunctionSpace('W1', domain) +>>> X = V1 * V2 * W1 +>>> # or +>>> X = ProductSpace(V1, V2, W1) +``` + +## Derham + +## Functions + +### ScalarFunction +A scalar function is necessary an element of the **ScalarFunctionSpace**. + +### IndexedVectorFunction +### VectorFunction +A vector function is necessary an element of the **VectorFunctionSpace**. It is an extension of the **IndexedVectorFunction**, which means that one can access to its components. + +## Trace + +### trace_0 +### trace_1 + +## Utilities +### element_of and elements_of + +## Projection (Experimental) + +## Projector (Experimental) + + diff --git a/_sources/chapter1/sympde.md b/_sources/chapter1/sympde.md new file mode 100644 index 0000000..d7bdded --- /dev/null +++ b/_sources/chapter1/sympde.md @@ -0,0 +1,128 @@ +# SymPDE concepts and their mathematical meaning + +## Domain + +sympde notation | Mathematical notion +--- | --- +`Domain('Omega', dim=n)` | an abstract domain $\Omega \subset \mathbb{R}^n$ +`Domain('Omega', interiors, boundaries, connectivity)` | an abstract domain $\Omega \subset \mathbb{R}^n$, represented by its interiors, boundaries and connectivity +`Interval('I', coordinate=x)` | an abstract (interior) interval $I \subset \mathbb{R}$, with the coordinate $x$ +`Union(A, B, C)` | union of domains $A \cup B \cup C$ +`ProductDomain(A, B)` | product of two domains $A \times B$ +`Indicator(A)` | Indicator/characteristic function on $A$, *i.e.* $\mathbf{1}\_A$ +`Line('Omega')` | an abstract line segment, $\Omega \subset \mathbb{R}$, having one interval as interior domain +`Square('Omega')` | an abstract square, $\Omega \subset \mathbb{R}^2$, having one interior domain as product of two intervals +`Cube('Omega')` | an abstract cube, $\Omega \subset \mathbb{R}^3$, having one interior domain as product of three intervals +`NormalVector('n')` | Normal vector $\mathbf{n}$ +`TangentVector('t')` | Tangent vector $\mathbf{t}$ +`e = ElementDomain(Omega)` | an element of an abstract domain $e \in \mathcal{T}(\Omega)$ or $e = d\Omega$, where $\mathcal{T}(\Omega)$ is a given tessellation of $\Omega$ +`DomainArea(Omega)` | Area of an abstract domain $\Omega$ +`ElementArea(Omega)` | Area of an abstract element of a domain $\Omega$ +`Area(A)` | Area of an expression of topological domain notions + +## Mapping + +sympde notation | Mathematical notion +--- | --- +`Mapping('F', n)` | a mapping functor $\mathbf{F}\_{\Omega} := \left( \mathbf{F}, \Omega \right): \Omega \rightarrow \mathbb{R}^n$ +`F[i]` | $i^{th}$ physical coordinate from $\{x,y,z\}$ +`F.jacobian` | the jacobian matrix $\mathcal{D}\_\mathbf{F}$ +`F.det_jacobian` | determinant of the jacobian matrix, $J_\mathbf{F}:= \mathrm{det} ~\mathcal{D}\_\mathbf{F}$ +`F.covariant` | the covariant matrix $\left( \mathcal{D}\_\mathbf{F} \right)^{-T}$ +`F.contravariant` | the contravariant matrix $\frac{1}{J_\mathbf{F}} \mathcal{D}\_\mathbf{F}$ +`F.hessian` | the hessian matrix $\mathcal{H}\_\mathbf{F}$ +`Covariant(F, v)` | action of the covariant matrix of $\mathbf{F}$ on $\mathbf{v}$, *i.e.* $\left( \mathcal{D}\_\mathbf{F} \right)^{-T} \mathbf{v}$ +`Contravariant(F, v)` | action of the contravariant matrix of $\mathbf{F}$ on $\mathbf{v}$, *i.e.* $\frac{1}{J_\mathbf{F}} \mathcal{D}\_\mathbf{F} \mathbf{v}$ + +## Function spaces + +sympde notation | Mathematical notion +--- | --- +`ScalarFunctionSpace('V', Omega)` | scalar function space $\mathcal{V}$ +`VectorFunctionSpace('W', Omega)` | vector function space $\mathbf{\mathcal{W}}$ +`ProductSpace(V, W)` or `V*W` | product of spaces, *i.e.* $\mathcal{V} \times \mathcal{W}$ +`element_of_space(V, 'v')` | scalar function $v \in \mathcal{V}$ +`element_of_space(W, 'w')` | vector function $\mathbf{w} \in \mathcal{W}$ +`element_of_space(V*W, ['v', 'w'])` | $\left(v,\mathbf{w}\right) \in \mathcal{V} \times \mathcal{W}$ + +### Function space types + +sympde notation | Mathematical notion +--- | --- +`H1SpaceType` | $H^1$ +`HcurlSpaceType` | ${H}{\mbox{curl}}$ +`HdivSpaceType` | ${H}{\mbox{div}}$ +`L2SpaceType` | $L^2$ + +### Typed function spaces + +sympde notation | Mathematical notion +--- | --- +`ScalarFunctionSpace('V0', Omega, kind='H1')` | scalar function space $\mathcal{V}\_0 \subseteq H^1(\Omega)$ +`VectorFunctionSpace('V1', Omega, kind='Hcurl')` | vector function space $\mathcal{V}\_1 \subseteq H(\mbox{curl}, \Omega)$ +`VectorFunctionSpace('V2', Omega, kind='Hdiv') ` | vector function space $\mathcal{V}\_2 \subseteq H(\mbox{div}, \Omega)$ +`ScalarFunctionSpace('V3', Omega, kind='L2')` | scalar function space $\mathcal{V}\_3 \subseteq L^2(\Omega)$ + +## Projections + +sympde notation | Mathematical notion +--- | --- +`P_V := Projector(V)` | Projector onto the function space $\mathcal{V}$ +`P_V(expr)` | Projection of the expression `expr` onto the function space $\mathcal{V}$ +`Pi_V := Projector(V, 'commuting')` | Commuting projector onto the typed function space $\mathcal{V}$ +`Pi_V(expr)` | Commuting projection of the expression `expr` onto the typed function space $\mathcal{V}$ + +## Atomic variables + +sympde notation | Mathematical notion +--- | --- +`ScalarFunction(V, 'u')` | $u \in \mathcal{V}$ +`VectorFunction(W, 'w')` | $\mathbf{w} \in \mathcal{W}$ +`Constant('mu', real=True)` | constant number $\mu \in \mathbb{R}$ +`int` | integer number +`float` | floating-point number + +## Algebraic operators + +sympde notation | Mathematical notion +--- | --- +`dot(u, v)` | $\mathbf{u} \cdot \mathbf{v}$ +`inner(u, v)` | $\mathbf{u} : \mathbf{v}$ +`cross(u, v)` | $\mathbf{u} \times \mathbf{v}$ +`outer(u, v)` | $\mathbf{u} \otimes \mathbf{v}$ + +## Differential operators + +boldface font is used for vector functions/expressions + +sympde notation | Mathematical notion +--- | --- +`dx(u)`, `dy(u)` or `dz(u)` | $\partial_x u$, $\partial_y u$ or $\partial_z u$ +`grad(u)` | $\nabla u$ or $\nabla \mathbf{u}$ +`div(u)` | $\nabla \cdot \mathbf{u}$ +`curl(u)` | $\nabla \times \mathbf{u}$ +`rot(u) ` | 2D rotational $\nabla \times u$ +`convect(a, u)` | $\left( \mathbf{a} \cdot \nabla \right) \mathbf{u}$ +`trace(u)` | trace $\gamma(u)$ +`Dn(u)` | normal derivative $\partial_{\mathbf{n}} u$ +`D(u)` | Strain tensor $\frac{1}{2}\left(\nabla \mathbf{u} + \nabla \mathbf{u}^T \right) $ +`laplace(u)` | Laplace $\Delta u$ +`hessian(u)` | Hessian $H(u)$ +`bracket(u,v)` | Poisson Bracket $[u,v]$ + +## Additional operators + +sympde notation | Mathematical notion +--- | --- +`jump(u)` | jump of $u$, *i.e.* $[u]$ +`avg(u)` | average of $u$, *i.e.* $\langle u \rangle$ +`conv(K,u)` | convolution of $u$ with a kernel $K$, *i.e.* $K * u$ + +## Integral operators + +sympde notation | Mathematical notion +--- | --- +`DomainIntegral(f)` | integral over a domain, *i.e.* $(f, \Omega) \mapsto \int_{\Omega} f ~d\Omega$ +`BoundaryIntegral(f)` | integral over a boundary, *i.e.* $(f, \Gamma) \mapsto \int_{\Gamma} f ~d\partial\Omega$ +`PathIntegral(F)` | integral over an oriented path, *i.e.* $(\mathbf{F}, C) \mapsto \int_{C} \mathbf{F} \cdot d\mathbf{s}$ +`SurfaceIntegral(F)` | integral over an oriented surface, *i.e.* $(\mathbf{F}, S) \mapsto \int_{S} \mathbf{F} \cdot d\mathbf{S}$ diff --git a/_sources/chapter1/topology.md b/_sources/chapter1/topology.md new file mode 100644 index 0000000..8c82ced --- /dev/null +++ b/_sources/chapter1/topology.md @@ -0,0 +1,225 @@ +# Topology concepts + +## Domain + +Mathematicaly speaking, a domain $\Omega$ is defined as an interior $\a{\Omega}$ and a boundary $\partial \Omega$. +A domain is defined by its **interior** and its **boundaries**. For instance, a domain without a boundary is periodic, since, **sympde** does not consider infinite domains. + +In addition to these two attributes, a **Domain** can also be defined as the image of a *logical domain* using a *mapping*. + +Finally, a **Domain** can have subdomains, in which case, a **connectivity** must be provided as well. + +The simplest **Domain** is the **NCube** object. For instance, **Line**, **Square** and **Cube** are specific cases of **NCube**. + +Let's take a look at the **Line** object. + +```python +>>> from sympde import topology +>>> domain = topology.Line() +>>> print(type(domain)) +sympde.topology.domain.Line +``` + +The parent class of **Line** is **NCube** as we can see in our example + +```python +>>> print(type(topology.Line.__bases__)) +sympde.topology.domain.NCube +``` + +In fact, the objects **Line**, **Square** and **Cube** are subclasses of **NCube** which is a subclasse of **Domain** that is an extension of the **BasicDomain** object. + + +### Properties + +- **name**: returns the domain's name +- **interior**: returns the interior of the domain +- **boundary**: returns the boundary of the domain +- **mapping**: returns the mapping, if associated to the domain +- **logical_domain**: returns the logical domain if a mapping is used +- **connectivity**: returns information about the interfaces of the subdomains +- **dim**: dimension of the space +- **dtype**: a dictionary that contains information about the domain +- **interfaces**: returns the interfaces of the subdomains +- **corners**: returns the corners of the domain + +**TODO** add inherited properties + +### Examples + +#### Example 1 + +```python +>>> from sympde.topology import InteriorDomain, Boundary, Domain + +>>> Omega_1 = InteriorDomain('Omega_1', dim=2) +>>> Omega_2 = InteriorDomain('Omega_2', dim=2) + +>>> Gamma_1 = Boundary('Gamma_1', Omega_1) +>>> Gamma_2 = Boundary('Gamma_2', Omega_2) +>>> Gamma_3 = Boundary('Gamma_3', Omega_2) + +>>> Omega = Domain('Omega', + interiors=[Omega_1, Omega_2], + boundaries=[Gamma_1, Gamma_2, Gamma_3]) + +>>> print( Omega.dim ) +2 +>>> print( len(Omega.interior) ) +2 +>>> print( len(Omega.boundary) ) +3 +``` + +#### Example 2 + +```python +>>> from sympde.topology import InteriorDomain, Boundary, Domain + +>>> Omega_1 = InteriorDomain('Omega_1', dim=2) + +>>> Gamma_1 = Boundary('Gamma_1', Omega_1) +>>> Gamma_2 = Boundary('Gamma_2', Omega_1) + +>>> Omega = Domain('Omega', + interiors=[Omega_1], + boundaries=[Gamma_1, Gamma_2]) + +>>> assert(Omega.boundary == Union(Gamma_1, Gamma_2)) +>>> assert(Omega.boundary.complement(Gamma_1) == Gamma_2) +>>> assert(Omega.boundary - Gamma_1 == Gamma_2) +``` + +## PeriodicDomain + +Similar to the **Domain** object, a **PeriodicDomain** is defined by giving a **Domain** and the associated **periods**. + +### Properties + +- **domain**: returns the domain +- **periods**: returns the flags for each axis +- **boundary**: return the boundary of the domain +- **dim** returns the dimension of the domain +- **coordinates** return the coordinates symbols + +## NCube + +An **NCube** is a **Domain** that models hypercubes in $\mathbb{R}^n$. It is defined by specifying its **name**, **dim**, **min_coords** and **max_coords**. + +The interior of a **NCube** is defined as **NCubeInterior**. +To make things easier, we provide specific classes in the case where $n \in \{ 1, 2, 3 \}$. + +### Line +This corresponds to the case where $n=1$, meaning it is $(x_{min}, x_{max})$. + +#### Properties +- **bounds**: the bounds for the line, i.e. $x_{min}$ and $x_{max}$. + +### Square +This corresponds to the case where $n=2$, meaning it is $(x_{min}, x_{max}) \times (y_{min}, y_{max})$. + +#### Properties +- **bounds1**: the bounds in the first axis, i.e. $x_{min}$ and $x_{max}$. +- **bounds2**: the bounds in the first axis, i.e. $y_{min}$ and $y_{max}$. + +### Cube +This corresponds to the case where $n=3$, meaning it is $(x_{min}, x_{max}) \times (y_{min}, y_{max}) \times (z_{min}, z_{max})$. + +#### Properties +- **bounds1**: the bounds in the first axis, i.e. $x_{min}$ and $x_{max}$. +- **bounds2**: the bounds in the first axis, i.e. $y_{min}$ and $y_{max}$. +- **bounds3**: the bounds in the first axis, i.e. $z_{min}$ and $z_{max}$. + + +## InteriorDomain + +**TODO** + +### Examples +#### Example 1 + +In this example, we create two interior domains and then we build their union. + +```python +>>> from sympde.topology import InteriorDomain, Union + +>>> D1 = InteriorDomain('D1', dim=2) +>>> D2 = InteriorDomain('D2', dim=2) + +>>> # Union is commutative +>>> assert( Union(D2, D1) == Union(D1, D2) ) + +>>> D = Union(D1, D2) +>>> # the union will be of dimension 2, and has a length of 2 +>>> print(D.dim) +2 +>>> print(len(D)) +2 +>>> # we see it clearly when converting it to a dictionary +>>> print(D.todict()) +[{'name': 'D1', 'mapping': 'None'}, {'name': 'D2', 'mapping': 'None'}] +``` + + +## NCubeInterior + +This class defines the interior of a domain which is **NCube**. + +### Properties + +- **min_coords** +- **max_coords** +- **boundary** + + +## Additional geometry objects + +### Vectors + +#### BoundaryVector + +is an extension of the **IndexedBase** object from **sympy**. + +#### NormalVector + +defines the normal vector to boundaries. It is an extension of the **BoundaryVector** object. + +#### MinusNormalVector + +defines the inward normal vector to a boundary. It is an extension of the **NormalVector** object. + +#### MinusNormalVector + +defines the outward normal vector to a boundary. It is an extension of the **NormalVector** object. + +#### TangentVector + +defines the tangent vector to boundaries. It is an extension of the **BoundaryVector** object. + +### ElementDomain + +defines an element of the domain. + +### BasicArea + +A basic class defining the concept of an area. It is an extension of the **AtomicExpr** object from **sympy**, this way we can use it in arithmetic expressions. + +### DomainArea + +defines the area of a **Domain**. + +### ElementArea + +defines the area of an element of a **Domain**. + +### Geometry Operations + +**TODO** + +#### BasicGeometryOperator + +**TODO** + +#### Area + +**TODO** diff --git a/_sources/chapter2/advection-diffusion-stabilized.ipynb b/_sources/chapter2/advection-diffusion-stabilized.ipynb new file mode 100644 index 0000000..f70ea54 --- /dev/null +++ b/_sources/chapter2/advection-diffusion-stabilized.ipynb @@ -0,0 +1,356 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "9f28f9af", + "metadata": {}, + "source": [ + "# Stabilized advection-diffusion equation\n", + "\n", + "In the sequel we consider two different stabilization methods, leading to formulations of the form\n", + "\n", + "$$\n", + "\\begin{align}\n", + " \\text{find $u \\in V$ such that} \\quad \n", + " a(u,v) + a_s(u,v) = l(v) + l_s(v) \\quad \\forall v \\in V,\n", + "\\end{align}\n", + "$$\n", + "\n", + "where $a_s$ and $l_s$ are additional terms depending on the stabilization method.\n", + "\n", + "The streamline upwind Petrov-Galerkin (SUPG) method is given by\n", + "\n", + "$$\n", + "\\begin{align}\n", + " a_s(u,v) = \\int_{\\Omega} \\tau ~ L(u) ~ \\left( \\mathbf{b} \\cdot \\nabla v \\right) ~d\\Omega \n", + " \\quad \\mbox{and} \\quad\n", + " l_s(v) = \\int_{\\Omega} \\tau ~ f ~ \\left( \\mathbf{b} \\cdot \\nabla v \\right) ~d\\Omega \n", + " && \\text{[SUPG]}\n", + "\\end{align}\n", + "$$\n", + "\n", + "while the Galerkin least squares (GLS) method is as follows, \n", + "\n", + "$$\n", + "\\begin{align}\n", + " a_s(u,v) = \\int_{\\Omega} \\tau ~ L(u) ~ L(v) ~d\\Omega \n", + " \\quad \\mbox{and} \\quad\n", + " l_s(v) = \\int_{\\Omega} \\tau ~ f ~ L(v) ~d\\Omega \n", + " && \\text{[GLS]}\n", + "\\end{align}\n", + "$$\n", + "\n", + "where we introduced the differential operator $L(u) := - \\kappa \\nabla^2 u + \\mathbf{b} \\cdot \\nabla u$.\n", + "\n", + "Notice that in these formulations $\\tau$ stands for a piecewise function that is constant on each element of the tessellation associated to the computational domain $\\Omega$." + ] + }, + { + "cell_type": "markdown", + "id": "5a958607", + "metadata": {}, + "source": [ + "## Formal Model" + ] + }, + { + "cell_type": "markdown", + "id": "cccc1cc5", + "metadata": {}, + "source": [ + "### Build a manifactured solution" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "id": "d742586c", + "metadata": {}, + "outputs": [], + "source": [ + "from sympde.expr import BilinearForm, LinearForm, integral\n", + "from sympde.expr import find, EssentialBC, Norm, SemiNorm\n", + "from sympde.topology import ScalarFunctionSpace, Square, element_of\n", + "from sympde.calculus import grad, dot, laplace\n", + "from sympde.core import Constant\n", + "\n", + "from sympy import pi, sin, Tuple\n", + "\n", + "domain = Square()\n", + "\n", + "x,y = domain.coordinates\n", + "\n", + "kappa = Constant('kappa', is_real=True)\n", + "b1 = 1.\n", + "b2 = 0.\n", + "b = Tuple(b1, b2)\n", + "\n", + "L = lambda w: -kappa * laplace(w) + dot(b,grad(w))\n", + "\n", + "ue = sin(pi*x)*sin(pi*y)\n", + "f = L(ue)" + ] + }, + { + "cell_type": "markdown", + "id": "76d3d381", + "metadata": {}, + "source": [ + "You can have the full expression of **f** by calling the **TerminalExpr** as follows" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "id": "87e62069", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "2*kappa*pi**2*sin(pi*x1)*sin(pi*x2) + 1.0*pi*sin(pi*x2)*cos(pi*x1)\n" + ] + } + ], + "source": [ + "from sympde.expr import TerminalExpr\n", + "\n", + "print(TerminalExpr(f, domain))" + ] + }, + { + "cell_type": "markdown", + "id": "fcddd2ca", + "metadata": {}, + "source": [ + "Let's go back now to our formal model." + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "id": "e4bbd1a8", + "metadata": {}, + "outputs": [], + "source": [ + "V = ScalarFunctionSpace('V', domain)\n", + "\n", + "u,v = [element_of(V, name=i) for i in ['u', 'v']]\n", + "\n", + "# bilinear form\n", + "expr = kappa * dot(grad(v), grad(u)) + dot(b, grad(u)) * v\n", + "a = BilinearForm((u,v), integral(domain, expr))\n", + "\n", + "# linear form\n", + "l = LinearForm(v, integral(domain, f*v))\n", + "\n", + "tau = Constant('tau', is_real=True)\n", + "\n", + "# ...\n", + "s_supg = BilinearForm((v,u), integral(domain, tau * L(u) * dot(b, grad(v))))\n", + "\n", + "l_supg = LinearForm(v, integral(domain, tau * f * dot(b, grad(v))))\n", + "# ...\n", + "\n", + "# ...\n", + "s_gls = BilinearForm((v,u), integral(domain, tau * L(u) * L(v)))\n", + "\n", + "l_gls = LinearForm(v, integral(domain, tau * f * L(v)))\n", + "# ...\n", + "\n", + "# Dirichlet boundary conditions\n", + "bc = [EssentialBC(u, 0, domain.boundary)]\n", + "\n", + "# Variational problem\n", + "equation_supg = find(u, forall=v, lhs=a(u, v) + s_supg(u,v), rhs=l(v) + l_supg(v), bc=bc)\n", + "equation_gls = find(u, forall=v, lhs=a(u, v) + s_gls(u,v), rhs=l(v) + l_gls(v), bc=bc)" + ] + }, + { + "cell_type": "markdown", + "id": "4f983ece", + "metadata": {}, + "source": [ + "## Discretization" + ] + }, + { + "cell_type": "markdown", + "id": "51095918", + "metadata": {}, + "source": [ + "We shall need the **discretize** function from **PsyDAC**." + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "id": "a2a0a2a1", + "metadata": {}, + "outputs": [], + "source": [ + "from psydac.api.discretization import discretize" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "id": "00e54163", + "metadata": {}, + "outputs": [], + "source": [ + "degree = [2,2]\n", + "ncells = [8,8]" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "id": "5999c62b", + "metadata": {}, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "/home/ranania/PYCCEL/IGA-Python/.iga-python/lib/python3.10/site-packages/sympy/matrices/repmatrix.py:90: SymPyDeprecationWarning: \n", + "\n", + "non-Expr objects in a Matrix has been deprecated since SymPy 1.9. Use\n", + "list of lists, TableForm or some other data structure instead. See\n", + "https://github.com/sympy/sympy/issues/21497 for more info.\n", + "\n", + " ).warn()\n" + ] + } + ], + "source": [ + "# Create computational domain from topological domain\n", + "domain_h = discretize(domain, ncells=ncells, comm=None)\n", + "\n", + "# Create discrete spline space\n", + "Vh = discretize(V, domain_h, degree=degree)\n", + "\n", + "# Discretize equation SUPG\n", + "equation_supg_h = discretize(equation_supg, domain_h, [Vh, Vh])\n", + "\n", + "# Discretize equation GLS\n", + "equation_gls_h = discretize(equation_gls, domain_h, [Vh, Vh])" + ] + }, + { + "cell_type": "markdown", + "id": "7b29fbcf", + "metadata": {}, + "source": [ + "## Solving the PDE\n", + "\n", + "Since the problem is not symmetric, we shall use **gmres** for the linear solver." + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "id": "67b32148", + "metadata": {}, + "outputs": [], + "source": [ + "equation_supg_h.set_solver('gmres', info=False, tol=1e-8)\n", + "equation_gls_h.set_solver('gmres', info=False, tol=1e-8)" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "id": "541192ee", + "metadata": {}, + "outputs": [], + "source": [ + "uh_supg = equation_supg_h.solve(kappa=1.e-1, tau=1.e-3)\n", + "uh_gls = equation_gls_h.solve(kappa=1.e-1, tau=1.e-3)" + ] + }, + { + "cell_type": "markdown", + "id": "5174c4b5", + "metadata": {}, + "source": [ + "## Computing the error norm" + ] + }, + { + "cell_type": "markdown", + "id": "3a31c46f", + "metadata": {}, + "source": [ + "### Computing the $L^2$ norm" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "id": "5925c6cd", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + ">>> SUPG = 0.002139370600719921\n", + ">>> GLS = 0.00021873265193415864\n" + ] + } + ], + "source": [ + "u = element_of(V, name='u')\n", + "\n", + "# create the formal Norm object\n", + "l2norm = Norm(u - ue, domain, kind='l2')\n", + "\n", + "# discretize the norm\n", + "l2norm_h = discretize(l2norm, domain_h, Vh)\n", + "\n", + "# assemble the norm\n", + "l2_error = l2norm_h.assemble(u=uh_supg)\n", + "\n", + "# print the result\n", + "print('>>> SUPG = ', l2_error)\n", + "\n", + "# assemble the norm\n", + "l2_error = l2norm_h.assemble(u=uh_gls)\n", + "\n", + "# print the result\n", + "print('>>> GLS = ', l2_error)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "0a972a4f", + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": ".iga-python", + "language": "python", + "name": ".iga-python" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.10.12" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/_sources/chapter2/advection-diffusion.ipynb b/_sources/chapter2/advection-diffusion.ipynb new file mode 100644 index 0000000..ebe73e1 --- /dev/null +++ b/_sources/chapter2/advection-diffusion.ipynb @@ -0,0 +1,377 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "9f28f9af", + "metadata": {}, + "source": [ + "# Advection-diffusion equation\n", + "\n", + "We consider the advection-diffusion problem consisting of finding a scalar-valued function $u$ such that\n", + "\n", + "$$\n", + "\\begin{align}\n", + " \\begin{cases}\n", + " - \\kappa \\nabla^2 u + \\mathbf{b} \\cdot \\nabla u = f &\\text{in $\\Omega$}, \\\\\n", + " u = 0 &\\text{on $\\partial \\Omega$}.\n", + " \\end{cases}\n", + "\\end{align}\n", + "$$\n", + "\n", + "## The Variational Formulation\n", + "\n", + "The variational formulation reads\n", + "\n", + "$$\n", + "\\begin{align}\n", + " \\text{find $u \\in V$ such that} \\quad a(u,v) = l(v) \\quad \\forall v \\in V,\n", + "\\end{align}\n", + "$$\n", + "\n", + "where \n", + "\n", + "- $V \\subset H_0^1(\\Omega)$, \n", + "- $a(u,v) := \\int_{\\Omega} \\left( \\kappa \\nabla u \\cdot \\nabla v + \\left( \\mathbf{b} \\cdot \\nabla u \\right) v \\right) d\\Omega$,\n", + "- $l(v) := \\int_{\\Omega} f v~d\\Omega$." + ] + }, + { + "cell_type": "markdown", + "id": "5a958607", + "metadata": {}, + "source": [ + "## Formal Model" + ] + }, + { + "cell_type": "markdown", + "id": "cccc1cc5", + "metadata": {}, + "source": [ + "### Build a manifactured solution" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "id": "d742586c", + "metadata": {}, + "outputs": [], + "source": [ + "from sympde.expr import BilinearForm, LinearForm, integral\n", + "from sympde.expr import find, EssentialBC, Norm, SemiNorm\n", + "from sympde.topology import ScalarFunctionSpace, Square, element_of\n", + "from sympde.calculus import grad, dot, laplace\n", + "from sympde.core import Constant\n", + "\n", + "from sympy import pi, sin, Tuple\n", + "\n", + "domain = Square()\n", + "\n", + "x,y = domain.coordinates\n", + "\n", + "kappa = Constant('kappa', is_real=True)\n", + "b1 = 1.\n", + "b2 = 0.\n", + "b = Tuple(b1, b2)\n", + "\n", + "L = lambda w: -kappa * laplace(w) + dot(b,grad(w))\n", + "\n", + "ue = sin(pi*x)*sin(pi*y)\n", + "f = L(ue)" + ] + }, + { + "cell_type": "markdown", + "id": "76d3d381", + "metadata": {}, + "source": [ + "You can have the full expression of **f** by calling the **TerminalExpr** as follows" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "id": "87e62069", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "2*kappa*pi**2*sin(pi*x1)*sin(pi*x2) + 1.0*pi*sin(pi*x2)*cos(pi*x1)\n" + ] + } + ], + "source": [ + "from sympde.expr import TerminalExpr\n", + "\n", + "print(TerminalExpr(f, domain))" + ] + }, + { + "cell_type": "markdown", + "id": "fcddd2ca", + "metadata": {}, + "source": [ + "Let's go back now to our formal model." + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "id": "e4bbd1a8", + "metadata": {}, + "outputs": [], + "source": [ + "V = ScalarFunctionSpace('V', domain)\n", + "\n", + "u,v = [element_of(V, name=i) for i in ['u', 'v']]\n", + "\n", + "# bilinear form\n", + "expr = kappa * dot(grad(v), grad(u)) + dot(b, grad(u)) * v\n", + "a = BilinearForm((u,v), integral(domain, expr))\n", + "\n", + "# linear form\n", + "l = LinearForm(v, integral(domain, f*v))\n", + "\n", + "# Dirichlet boundary conditions\n", + "bc = [EssentialBC(u, 0, domain.boundary)]\n", + "\n", + "# Variational problem\n", + "equation = find(u, forall=v, lhs=a(u, v), rhs=l(v), bc=bc)" + ] + }, + { + "cell_type": "markdown", + "id": "4f983ece", + "metadata": {}, + "source": [ + "## Discretization" + ] + }, + { + "cell_type": "markdown", + "id": "51095918", + "metadata": {}, + "source": [ + "We shall need the **discretize** function from **PsyDAC**." + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "id": "a2a0a2a1", + "metadata": {}, + "outputs": [], + "source": [ + "from psydac.api.discretization import discretize" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "id": "00e54163", + "metadata": {}, + "outputs": [], + "source": [ + "degree = [2,2]\n", + "ncells = [8,8]" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "id": "5999c62b", + "metadata": {}, + "outputs": [], + "source": [ + "# Create computational domain from topological domain\n", + "domain_h = discretize(domain, ncells=ncells, comm=None)\n", + "\n", + "# Create discrete spline space\n", + "Vh = discretize(V, domain_h, degree=degree)\n", + "\n", + "# Discretize equation\n", + "equation_h = discretize(equation, domain_h, [Vh, Vh])" + ] + }, + { + "cell_type": "markdown", + "id": "7b29fbcf", + "metadata": {}, + "source": [ + "## Solving the PDE\n", + "\n", + "Since the problem is not symmetric, we shall use **gmres** for the linear solver." + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "id": "67b32148", + "metadata": {}, + "outputs": [], + "source": [ + "equation_h.set_solver('gmres', info=False, tol=1e-8)" + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "id": "541192ee", + "metadata": {}, + "outputs": [], + "source": [ + "uh = equation_h.solve(kappa=1.e-1)" + ] + }, + { + "cell_type": "markdown", + "id": "5174c4b5", + "metadata": {}, + "source": [ + "## Computing the error norm" + ] + }, + { + "cell_type": "markdown", + "id": "3a31c46f", + "metadata": {}, + "source": [ + "### Computing the $L^2$ norm" + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "id": "5925c6cd", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "0.00022156219679932395\n" + ] + } + ], + "source": [ + "u = element_of(V, name='u')\n", + "\n", + "# create the formal Norm object\n", + "l2norm = Norm(u - ue, domain, kind='l2')\n", + "\n", + "# discretize the norm\n", + "l2norm_h = discretize(l2norm, domain_h, Vh)\n", + "\n", + "# assemble the norm\n", + "l2_error = l2norm_h.assemble(u=uh)\n", + "\n", + "# print the result\n", + "print(l2_error)" + ] + }, + { + "cell_type": "markdown", + "id": "a6cbfeae", + "metadata": {}, + "source": [ + "### Computing the $H^1$ semi-norm" + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "id": "e5c1a8b8", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "0.013033907531543579\n" + ] + } + ], + "source": [ + "# create the formal Norm object\n", + "h1norm = SemiNorm(u - ue, domain, kind='h1')\n", + "\n", + "# discretize the norm\n", + "h1norm_h = discretize(h1norm, domain_h, Vh)\n", + "\n", + "# assemble the norm\n", + "h1_error = h1norm_h.assemble(u=uh)\n", + "\n", + "# print the result\n", + "print(h1_error)" + ] + }, + { + "cell_type": "markdown", + "id": "3c09131c", + "metadata": {}, + "source": [ + "### Computing the $H^1$ norm" + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "id": "d829e410", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "0.013035790553238334\n" + ] + } + ], + "source": [ + "# create the formal Norm object\n", + "h1norm = Norm(u - ue, domain, kind='h1')\n", + "\n", + "# discretize the norm\n", + "h1norm_h = discretize(h1norm, domain_h, Vh)\n", + "\n", + "# assemble the norm\n", + "h1_error = h1norm_h.assemble(u=uh)\n", + "\n", + "# print the result\n", + "print(h1_error)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "0a972a4f", + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": ".iga-python", + "language": "python", + "name": ".iga-python" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.10.12" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/_sources/chapter2/biharmonic.ipynb b/_sources/chapter2/biharmonic.ipynb new file mode 100644 index 0000000..ea848e1 --- /dev/null +++ b/_sources/chapter2/biharmonic.ipynb @@ -0,0 +1,374 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "9f28f9af", + "metadata": {}, + "source": [ + "# The Biharmonic problem\n", + "\n", + "We consider the (inhomogeneous) biharmonic equation with homogeneous essential boundary conditions,\n", + "\n", + "$$\n", + "\\begin{align}\n", + " \\nabla^2 \\nabla^2 u = f \\quad \\text{in $\\Omega$} , \\quad \\quad \n", + " u = 0 \\quad \\text{on $\\partial \\Omega$}, \\quad \\quad\n", + " \\nabla u \\cdot \\mathbf{n} = 0 \\quad \\text{on $\\partial \\Omega$}.\n", + "\\end{align}\n", + "$$\n", + "\n", + "## The Variational Formulation\n", + "\n", + "An $H^2$-conforming variational formulation reads \n", + "\n", + "$$\n", + "\\begin{align}\n", + " \\text{find $u \\in V$ such that} \\quad a(u,v) = l(v) \\quad \\forall v \\in V,\n", + "\\end{align}\n", + "$$\n", + "\n", + "where \n", + "\n", + "- $V \\subset H^2(\\Omega)$, \n", + "- $a(u,v) := \\int_{\\Omega} \\nabla^2 u ~ \\nabla^2 v ~ d\\Omega$,\n", + "- $l(v) := \\int_{\\Omega} f v ~ d\\Omega$." + ] + }, + { + "cell_type": "markdown", + "id": "5a958607", + "metadata": {}, + "source": [ + "## Formal Model" + ] + }, + { + "cell_type": "markdown", + "id": "f223516b", + "metadata": {}, + "source": [ + "In this example, the analytical solution is given by\n", + "\n", + "$$\n", + "u_e = \\sin(\\pi x)^2 \\sin(\\pi y)^2\n", + "$$" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "id": "811c0b9b", + "metadata": {}, + "outputs": [], + "source": [ + "from sympde.expr import BilinearForm, LinearForm, integral\n", + "from sympde.expr import find, EssentialBC, Norm, SemiNorm\n", + "from sympde.topology import ScalarFunctionSpace, Square, element_of\n", + "from sympde.calculus import laplace, dot\n", + "\n", + "from sympy import pi, sin" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "id": "d742586c", + "metadata": {}, + "outputs": [], + "source": [ + "domain = Square()\n", + "\n", + "V = ScalarFunctionSpace('V', domain)\n", + "\n", + "x,y = domain.coordinates\n", + "\n", + "u,v = [element_of(V, name=i) for i in ['u', 'v']]\n", + "\n", + "# the analytical solution and its rhs\n", + "ue = sin(pi * x)**2 * sin(pi * y)**2\n", + "f = laplace(laplace(ue))\n", + "\n", + "# bilinear form\n", + "a = BilinearForm((u,v), integral(domain , laplace(u)*laplace(v)))\n", + "\n", + "# linear form\n", + "l = LinearForm(v, integral(domain, f*v))\n", + "\n", + "# Dirichlet boundary conditions\n", + "bc = [EssentialBC(u, 0, domain.boundary)]\n", + "\n", + "# Variational problem\n", + "equation = find(u, forall=v, lhs=a(u, v), rhs=l(v), bc=bc)" + ] + }, + { + "cell_type": "markdown", + "id": "4f983ece", + "metadata": {}, + "source": [ + "## Discretization" + ] + }, + { + "cell_type": "markdown", + "id": "51095918", + "metadata": {}, + "source": [ + "We shall need the **discretize** function from **PsyDAC**." + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "id": "a2a0a2a1", + "metadata": {}, + "outputs": [], + "source": [ + "from psydac.api.discretization import discretize" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "id": "00e54163", + "metadata": {}, + "outputs": [], + "source": [ + "degree = [2,2]\n", + "ncells = [8,8]" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "id": "5999c62b", + "metadata": {}, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "/home/ranania/PYCCEL/IGA-Python/.iga-python/lib/python3.10/site-packages/sympy/matrices/repmatrix.py:90: SymPyDeprecationWarning: \n", + "\n", + "non-Expr objects in a Matrix has been deprecated since SymPy 1.9. Use\n", + "list of lists, TableForm or some other data structure instead. See\n", + "https://github.com/sympy/sympy/issues/21497 for more info.\n", + "\n", + " ).warn()\n" + ] + } + ], + "source": [ + "# Create computational domain from topological domain\n", + "domain_h = discretize(domain, ncells=ncells, comm=None)\n", + "\n", + "# Create discrete spline space\n", + "Vh = discretize(V, domain_h, degree=degree)\n", + "\n", + "# Discretize equation\n", + "equation_h = discretize(equation, domain_h, [Vh, Vh])" + ] + }, + { + "cell_type": "markdown", + "id": "7b29fbcf", + "metadata": {}, + "source": [ + "## Solving the PDE" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "id": "541192ee", + "metadata": {}, + "outputs": [], + "source": [ + "uh = equation_h.solve()" + ] + }, + { + "cell_type": "markdown", + "id": "5174c4b5", + "metadata": {}, + "source": [ + "## Computing the error norm" + ] + }, + { + "cell_type": "markdown", + "id": "3a31c46f", + "metadata": {}, + "source": [ + "### Computing the $L^2$ norm" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "id": "5925c6cd", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "0.5367871671842632\n" + ] + } + ], + "source": [ + "u = element_of(V, name='u')\n", + "\n", + "# create the formal Norm object\n", + "l2norm = Norm(u - ue, domain, kind='l2')\n", + "\n", + "# discretize the norm\n", + "l2norm_h = discretize(l2norm, domain_h, Vh)\n", + "\n", + "# assemble the norm\n", + "l2_error = l2norm_h.assemble(u=uh)\n", + "\n", + "# print the result\n", + "print(l2_error)" + ] + }, + { + "cell_type": "markdown", + "id": "a6cbfeae", + "metadata": {}, + "source": [ + "### Computing the $H^1$ semi-norm" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "id": "e5c1a8b8", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "2.4343747827631277\n" + ] + } + ], + "source": [ + "# create the formal Norm object\n", + "h1norm = SemiNorm(u - ue, domain, kind='h1')\n", + "\n", + "# discretize the norm\n", + "h1norm_h = discretize(h1norm, domain_h, Vh)\n", + "\n", + "# assemble the norm\n", + "h1_error = h1norm_h.assemble(u=uh)\n", + "\n", + "# print the result\n", + "print(h1_error)" + ] + }, + { + "cell_type": "markdown", + "id": "3c09131c", + "metadata": {}, + "source": [ + "### Computing the $H^1$ norm" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "id": "d829e410", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "2.492853996086961\n" + ] + } + ], + "source": [ + "# create the formal Norm object\n", + "h1norm = Norm(u - ue, domain, kind='h1')\n", + "\n", + "# discretize the norm\n", + "h1norm_h = discretize(h1norm, domain_h, Vh)\n", + "\n", + "# assemble the norm\n", + "h1_error = h1norm_h.assemble(u=uh)\n", + "\n", + "# print the result\n", + "print(h1_error)" + ] + }, + { + "cell_type": "markdown", + "id": "fe684489", + "metadata": {}, + "source": [ + "### Computing the H^2 semi-norm" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "id": "8a4adf8d", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "9.115861322114647\n" + ] + } + ], + "source": [ + "# create the formal Norm object\n", + "h2norm = SemiNorm(u - ue, domain, kind='h2')\n", + "\n", + "# discretize the norm\n", + "h2norm_h = discretize(h2norm, domain_h, Vh)\n", + "\n", + "# assemble the norm\n", + "h2_error = h2norm_h.assemble(u=uh)\n", + "\n", + "# print the result\n", + "print(h2_error)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "531105ea", + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": ".iga-python", + "language": "python", + "name": ".iga-python" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.10.12" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/_sources/chapter2/elliptic-curl.ipynb b/_sources/chapter2/elliptic-curl.ipynb new file mode 100644 index 0000000..2e4c928 --- /dev/null +++ b/_sources/chapter2/elliptic-curl.ipynb @@ -0,0 +1,341 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "9f28f9af", + "metadata": {}, + "source": [ + "# Elliptic-curl Problem\n", + "\n", + "Let $\\Omega \\subset \\mathbb{R}^d$ be an open Liptschitz bounded set, and we look for the solution of the following problem\n", + "\n", + "$$\n", + "\\begin{align}\n", + " \\left\\{ \n", + " \\begin{array}{rl}\n", + " \\nabla \\times \\nabla \\times \\mathbf{u} + \\mu \\mathbf{u} &= \\mathbf{f}, \\quad \\Omega \n", + " \\\\\n", + " \\mathbf{u} \\times \\mathbf{n} &= 0, \\quad \\partial\\Omega\n", + " \\end{array} \\right.\n", + "\\end{align}\n", + "$$\n", + "\n", + "where $\\mathbf{f} \\in \\mathbf{L}^2(\\Omega)$, $\\mu \\in L^\\infty(\\Omega)$ and there exists $\\mu_0 > 0$ such that $\\mu \\geq \\mu_0$ almost everywhere.\n", + "\n", + "## The Variational Formulation\n", + "\n", + "We take the Hilbert space $V := \\mathbf{H}\\_0(\\mbox{curl}, \\Omega)$, in which case the variational formulation writes \n", + "\n", + "Find $\\mathbf{u} \\in V$ such that\n", + "\n", + "$$\n", + "\\begin{align}\n", + " a(\\mathbf{u},\\mathbf{v}) = l(\\mathbf{v}) \\quad \\forall \\mathbf{v} \\in V \n", + "\\end{align}\n", + "$$\n", + "\n", + "where \n", + "\n", + "$$\n", + "\\begin{align}\n", + "\\left\\{ \n", + "\\begin{array}{rll}\n", + "a(\\mathbf{u}, \\mathbf{v}) &:= \\int_{\\Omega} \\nabla \\times \\mathbf{u} \\cdot \\nabla \\times \\mathbf{v} + \\int_{\\Omega} \\mu \\mathbf{u} \\cdot \\mathbf{v}, & \\forall \\mathbf{u}, \\mathbf{v} \\in V \\\\\n", + "l(\\mathbf{v}) &:= \\int_{\\Omega} \\mathbf{v} \\cdot \\mathbf{f}, & \\forall \\mathbf{v} \\in V \n", + "\\end{array} \\right.\n", + "\\end{align}\n", + "$$\n", + "\n", + "We recall that in $\\mathbf{H}_0(\\mbox{curl}, \\Omega)$, the bilinear form $a$ is equivalent to the inner product and is therefor continuous and coercive. Hence, our abstract theory applies and there exists a unique solution to the problem." + ] + }, + { + "cell_type": "markdown", + "id": "8d905be9", + "metadata": {}, + "source": [ + "```{warning}\n", + "This NB needs to be fixed\n", + "```" + ] + }, + { + "cell_type": "markdown", + "id": "5a958607", + "metadata": {}, + "source": [ + "## Formal Model" + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "id": "d742586c", + "metadata": {}, + "outputs": [], + "source": [ + "from sympde.expr import BilinearForm, LinearForm, integral\n", + "from sympde.expr import find, EssentialBC\n", + "from sympde.topology import VectorFunctionSpace, Cube, element_of\n", + "from sympde.calculus import curl, dot, grad, div\n", + "from sympde.core import Constant\n", + "\n", + "from sympy import pi, sin, cos, Tuple\n", + "\n", + "mu = Constant('mu', is_real=True)\n", + "\n", + "domain = Cube()\n", + "\n", + "V = VectorFunctionSpace('V', domain, kind='Hcurl')\n", + "\n", + "x,y,z = domain.coordinates\n", + "\n", + "u,v = [element_of(V, name=i) for i in ['u', 'v']]\n", + "\n", + "# bilinear form\n", + "a = BilinearForm((u,v), integral(domain, dot(curl(v), curl(u)) + mu * dot(u,v)))\n", + "\n", + "# linear form\n", + "f1 = sin(pi*x)*sin(pi*y)*sin(pi*z)\n", + "f2 = sin(pi*x)*sin(pi*y)*sin(pi*z)\n", + "f3 = sin(pi*x)*sin(pi*y)*sin(pi*z)\n", + "f = Tuple(f1, f2, f3)\n", + "\n", + "l = LinearForm(v, integral(domain, dot(f,v)))\n", + "\n", + "# Dirichlet boundary conditions\n", + "bc = [EssentialBC(u, 0, domain.boundary)]\n", + "\n", + "# Variational problem\n", + "equation = find(u, forall=v, lhs=a(u, v), rhs=l(v), bc=bc)" + ] + }, + { + "cell_type": "markdown", + "id": "4f983ece", + "metadata": {}, + "source": [ + "## Discretization" + ] + }, + { + "cell_type": "markdown", + "id": "51095918", + "metadata": {}, + "source": [ + "We shall need the **discretize** function from **PsyDAC**." + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "id": "a2a0a2a1", + "metadata": {}, + "outputs": [], + "source": [ + "from psydac.api.discretization import discretize" + ] + }, + { + "cell_type": "code", + "execution_count": 22, + "id": "00e54163", + "metadata": {}, + "outputs": [], + "source": [ + "degree = [2,2,2]\n", + "ncells = [8,8,8]" + ] + }, + { + "cell_type": "code", + "execution_count": 23, + "id": "5999c62b", + "metadata": {}, + "outputs": [], + "source": [ + "# Create computational domain from topological domain\n", + "domain_h = discretize(domain, ncells=ncells, comm=None)\n", + "\n", + "# Create discrete spline space\n", + "Vh = discretize(V, domain_h, degree=degree)\n", + "\n", + "# Discretize equation\n", + "equation_h = discretize(equation, domain_h, [Vh, Vh])" + ] + }, + { + "cell_type": "markdown", + "id": "7b29fbcf", + "metadata": {}, + "source": [ + "## Solving the PDE" + ] + }, + { + "cell_type": "code", + "execution_count": 24, + "id": "541192ee", + "metadata": {}, + "outputs": [], + "source": [ + "#uh = equation_h.solve()" + ] + }, + { + "cell_type": "markdown", + "id": "5174c4b5", + "metadata": {}, + "source": [ + "## Computing the error norm\n", + "\n", + "When the analytical solution is available, you might be interested in computing the $L^2$ norm or $H^1_0$ semi-norm.\n", + "SymPDE allows you to do so, by creating the **Norm** object.\n", + "In this example, the analytical solution is given by\n", + "\n", + "$$\n", + "u_e = \\sin(\\pi x) \\sin(\\pi y)\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "id": "3a31c46f", + "metadata": {}, + "source": [ + "### Computing the $L^2$ norm" + ] + }, + { + "cell_type": "code", + "execution_count": 26, + "id": "5925c6cd", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "9.49756716724664e-07\n" + ] + } + ], + "source": [ + "#u = element_of(V, name='u')\n", + "\n", + "# create the formal Norm object\n", + "#l2norm = Norm(u - ue, domain, kind='l2')\n", + "\n", + "# discretize the norm\n", + "#l2norm_h = discretize(l2norm, domain_h, Vh)\n", + "\n", + "# assemble the norm\n", + "#l2_error = l2norm_h.assemble(u=uh)\n", + "\n", + "# print the result\n", + "#print(l2_error)" + ] + }, + { + "cell_type": "markdown", + "id": "a6cbfeae", + "metadata": {}, + "source": [ + "### Computing the $H^1$ semi-norm" + ] + }, + { + "cell_type": "code", + "execution_count": 30, + "id": "e5c1a8b8", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "9.768702410721585e-05\n" + ] + } + ], + "source": [ + "# create the formal Norm object\n", + "#h1norm = SemiNorm(u - ue, domain, kind='h1')\n", + "\n", + "# discretize the norm\n", + "#h1norm_h = discretize(h1norm, domain_h, Vh)\n", + "\n", + "# assemble the norm\n", + "#h1_error = h1norm_h.assemble(u=uh)\n", + "\n", + "# print the result\n", + "#print(h1_error)" + ] + }, + { + "cell_type": "markdown", + "id": "3c09131c", + "metadata": {}, + "source": [ + "### Computing the $H^1$ norm" + ] + }, + { + "cell_type": "code", + "execution_count": 29, + "id": "d829e410", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "9.769164089397408e-05\n" + ] + } + ], + "source": [ + "# create the formal Norm object\n", + "#h1norm = Norm(u - ue, domain, kind='h1')\n", + "\n", + "# discretize the norm\n", + "#h1norm_h = discretize(h1norm, domain_h, Vh)\n", + "\n", + "# assemble the norm\n", + "#h1_error = h1norm_h.assemble(u=uh)\n", + "\n", + "# print the result\n", + "#print(h1_error)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "9250897b", + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": ".iga-python", + "language": "python", + "name": ".iga-python" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.10.12" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/_sources/chapter2/elliptic-div.ipynb b/_sources/chapter2/elliptic-div.ipynb new file mode 100644 index 0000000..f4b6601 --- /dev/null +++ b/_sources/chapter2/elliptic-div.ipynb @@ -0,0 +1,350 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "9f28f9af", + "metadata": {}, + "source": [ + "# Elliptic-div Problem\n", + "\n", + "Let $\\Omega \\subset \\mathbb{R}^d$ be an open Liptschitz bounded set, and we look for the solution of the following problem\n", + "\n", + "$$\n", + "\\begin{align}\n", + " \\left\\{ \n", + " \\begin{array}{rl}\n", + " - \\nabla \\nabla \\cdot \\mathbf{u} + \\mu \\mathbf{u} &= \\mathbf{f}, \\quad \\Omega \n", + " \\\\\n", + " \\mathbf{u} \\times \\mathbf{n} &= 0, \\quad \\partial\\Omega\n", + " \\end{array} \\right.\n", + "\\end{align}\n", + "$$\n", + "\n", + "where $\\mathbf{f} \\in \\mathbf{L}^2(\\Omega)$, $\\mu \\in L^\\infty(\\Omega)$ and there exists $\\mu_0 > 0$ such that $\\mu \\geq \\mu_0$ almost everywhere.\n", + "\n", + "## The Variational Formulation\n", + "\n", + "We take the Hilbert space $V := \\mathbf{H}\\_0(\\mbox{div}, \\Omega)$, in which case the variational formulation writes \n", + "\n", + "\n", + "Find $\\mathbf{u} \\in V$ such that\n", + "\n", + "$$\n", + "\\begin{align}\n", + " a(\\mathbf{u},\\mathbf{v}) = l(\\mathbf{v}) \\quad \\forall \\mathbf{v} \\in V \n", + "\\end{align}\n", + "$$\n", + "\n", + "where \n", + "\n", + "$$\n", + "\\begin{align}\n", + "\\left\\{ \n", + "\\begin{array}{rll}\n", + "a(\\mathbf{u}, \\mathbf{v}) &:= \\int_{\\Omega} \\nabla \\cdot \\mathbf{u} ~ \\nabla \\cdot \\mathbf{v} + \\int_{\\Omega} \\mu \\mathbf{u} \\cdot \\mathbf{v}, & \\forall \\mathbf{u}, \\mathbf{v} \\in V \\\\\n", + "l(\\mathbf{v}) &:= \\int_{\\Omega} \\mathbf{v} \\cdot \\mathbf{f}, & \\forall \\mathbf{v} \\in V \n", + "\\end{array} \\right.\n", + "\\end{align}\n", + "$$\n", + "\n", + "We recall that in $\\mathbf{H}\\_0(\\mbox{div}, \\Omega)$, the bilinear form $a$ is equivalent to the inner product and is therefor continuous and coercive. Hence, our abstract theory applies and there exists a unique solution." + ] + }, + { + "cell_type": "markdown", + "id": "2092b000", + "metadata": {}, + "source": [ + "```{warning}\n", + "This NB needs to be fixed\n", + "```" + ] + }, + { + "cell_type": "markdown", + "id": "5a958607", + "metadata": {}, + "source": [ + "## Formal Model" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "id": "d742586c", + "metadata": {}, + "outputs": [], + "source": [ + "from sympde.expr import BilinearForm, LinearForm, integral\n", + "from sympde.expr import find, EssentialBC\n", + "from sympde.topology import VectorFunctionSpace, Cube, element_of\n", + "from sympde.calculus import div, dot\n", + "from sympde.core import Constant\n", + "\n", + "from sympy import pi, sin, Tuple\n", + "\n", + "mu = Constant('mu', is_real=True)\n", + "\n", + "domain = Cube()\n", + "\n", + "V = VectorFunctionSpace('V', domain, kind='Hdiv')\n", + "\n", + "x,y,z = domain.coordinates\n", + "\n", + "u,v = [element_of(V, name=i) for i in ['u', 'v']]\n", + "\n", + "# bilinear form\n", + "a = BilinearForm((u,v), integral(domain, div(v)*div(u) + mu * dot(u,v)))\n", + "\n", + "# linear form\n", + "f1 = sin(pi*x)*sin(pi*y)*sin(pi*z)\n", + "f2 = sin(pi*x)*sin(pi*y)*sin(pi*z)\n", + "f3 = sin(pi*x)*sin(pi*y)*sin(pi*z)\n", + "f = Tuple(f1, f2, f3)\n", + "\n", + "l = LinearForm(v, integral(domain, dot(f,v)))\n", + "\n", + "# Dirichlet boundary conditions\n", + "bc = [EssentialBC(u, 0, domain.boundary)]\n", + "\n", + "# Variational problem\n", + "equation = find(u, forall=v, lhs=a(u, v), rhs=l(v), bc=bc)\n" + ] + }, + { + "cell_type": "markdown", + "id": "4f983ece", + "metadata": {}, + "source": [ + "## Discretization" + ] + }, + { + "cell_type": "markdown", + "id": "51095918", + "metadata": {}, + "source": [ + "We shall need the **discretize** function from **PsyDAC**." + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "id": "a2a0a2a1", + "metadata": {}, + "outputs": [], + "source": [ + "from psydac.api.discretization import discretize" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "id": "00e54163", + "metadata": {}, + "outputs": [], + "source": [ + "degree = [2,2,2]\n", + "ncells = [8,8,8]" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "id": "5999c62b", + "metadata": {}, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "/home/ranania/PYCCEL/IGA-Python/.iga-python/lib/python3.10/site-packages/sympy/matrices/repmatrix.py:90: SymPyDeprecationWarning: \n", + "\n", + "non-Expr objects in a Matrix has been deprecated since SymPy 1.9. Use\n", + "list of lists, TableForm or some other data structure instead. See\n", + "https://github.com/sympy/sympy/issues/21497 for more info.\n", + "\n", + " ).warn()\n" + ] + } + ], + "source": [ + "# Create computational domain from topological domain\n", + "domain_h = discretize(domain, ncells=ncells, comm=None)\n", + "\n", + "# Create discrete spline space\n", + "Vh = discretize(V, domain_h, degree=degree)\n", + "\n", + "# Discretize equation\n", + "equation_h = discretize(equation, domain_h, [Vh, Vh])" + ] + }, + { + "cell_type": "markdown", + "id": "7b29fbcf", + "metadata": {}, + "source": [ + "## Solving the PDE" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "id": "541192ee", + "metadata": {}, + "outputs": [], + "source": [ + "#uh = equation_h.solve()" + ] + }, + { + "cell_type": "markdown", + "id": "5174c4b5", + "metadata": {}, + "source": [ + "## Computing the error norm" + ] + }, + { + "cell_type": "markdown", + "id": "3a31c46f", + "metadata": {}, + "source": [ + "### Computing the $L^2$ norm" + ] + }, + { + "cell_type": "code", + "execution_count": 26, + "id": "5925c6cd", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "9.49756716724664e-07\n" + ] + } + ], + "source": [ + "#ue = sin(pi*x)*sin(pi*y)\n", + "\n", + "#u = element_of(V, name='u')\n", + "\n", + "# create the formal Norm object\n", + "#l2norm = Norm(u - ue, domain, kind='l2')\n", + "\n", + "# discretize the norm\n", + "#l2norm_h = discretize(l2norm, domain_h, Vh)\n", + "\n", + "# assemble the norm\n", + "#l2_error = l2norm_h.assemble(u=uh)\n", + "\n", + "# print the result\n", + "#print(l2_error)" + ] + }, + { + "cell_type": "markdown", + "id": "a6cbfeae", + "metadata": {}, + "source": [ + "### Computing the $H^1$ semi-norm" + ] + }, + { + "cell_type": "code", + "execution_count": 30, + "id": "e5c1a8b8", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "9.768702410721585e-05\n" + ] + } + ], + "source": [ + "# create the formal Norm object\n", + "#h1norm = SemiNorm(u - ue, domain, kind='h1')\n", + "\n", + "# discretize the norm\n", + "#h1norm_h = discretize(h1norm, domain_h, Vh)\n", + "\n", + "# assemble the norm\n", + "#h1_error = h1norm_h.assemble(u=uh)\n", + "\n", + "# print the result\n", + "#print(h1_error)" + ] + }, + { + "cell_type": "markdown", + "id": "3c09131c", + "metadata": {}, + "source": [ + "### Computing the $H^1$ norm" + ] + }, + { + "cell_type": "code", + "execution_count": 29, + "id": "d829e410", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "9.769164089397408e-05\n" + ] + } + ], + "source": [ + "# create the formal Norm object\n", + "#h1norm = Norm(u - ue, domain, kind='h1')\n", + "\n", + "# discretize the norm\n", + "#h1norm_h = discretize(h1norm, domain_h, Vh)\n", + "\n", + "# assemble the norm\n", + "#h1_error = h1norm_h.assemble(u=uh)\n", + "\n", + "# print the result\n", + "#print(h1_error)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "9250897b", + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": ".iga-python", + "language": "python", + "name": ".iga-python" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.10.12" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/_sources/chapter2/linear-elasticity.ipynb b/_sources/chapter2/linear-elasticity.ipynb new file mode 100644 index 0000000..82b9f1a --- /dev/null +++ b/_sources/chapter2/linear-elasticity.ipynb @@ -0,0 +1,267 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "9f28f9af", + "metadata": {}, + "source": [ + "# Linear Elasticity Problem\n", + "\n", + "Analysis of deformable structures is essential in engineering, with the equations of linear elasticity being fundamental in this field. In this section, we present the variational formulation of linear elasticity equations using the principle of virtual work.\n", + "\n", + "## The PDE problem\n", + "The governing equations for small elastic deformations of a body $ \\Omega $ can be expressed as:\n", + "\n", + "$$\n", + "\\begin{align}\n", + " -\\nabla \\cdot \\sigma(u) &= f & \\text{in } \\Omega \\\\\n", + " \\sigma(u) &= \\kappa \\text{tr}(\\epsilon(u))I + 2 \\mu \\epsilon(u)\n", + "\\end{align}\n", + "$$\n", + "\n", + "where $ \\sigma $ is the stress tensor, $ f $ represents the body force per unit volume, $ \\kappa $ and $ \\mu $ are Lamé's elasticity parameters for the material, $ I $ denotes the identity tensor, and $ \\epsilon $ is the symmetric strain tensor. The displacement vector field is denoted by $ u $.\n", + "\n", + "By substituting $ \\epsilon(u) $ into $ \\sigma $, we obtain:\n", + "\n", + "$$\n", + "\\sigma(u) = \\kappa (\\nabla \\cdot u)I + \\mu(\\nabla u + (\\nabla u)^T)\n", + "$$\n", + "\n", + "## The Variational Formulation\n", + "The variational formulation of the linear elasticity equations involves forming the inner product of the PDE with a vector test function $ v \\in \\hat{V} $ and integrating over the domain $ \\Omega $. This yields:\n", + "\n", + "$$\n", + "\\int_{\\Omega} \\sigma : \\nabla v \\, \\mathrm{d} x = \\int_{\\Omega} f \\cdot v \\, \\mathrm{d} x\n", + "$$\n", + "\n", + "Integrating the term $ \\nabla \\cdot \\sigma \\cdot v $ by parts, considering boundary conditions, we obtain:\n", + "\n", + "$$\n", + "\\int_{\\Omega} \\sigma : \\nabla v \\, \\mathrm{d} x = \\int_{\\Omega} f \\cdot v \\, \\mathrm{d} x + \\int_{\\partial \\Omega_T} T \\cdot v \\, \\mathrm{d} s\n", + "$$\n", + "\n", + "where $ T $ represents the traction vector on the part $ \\partial \\Omega_T $ of the boundary where it's prescribed.\n", + "\n", + "This leads to the variational formulation: Find $ u \\in V $ such that\n", + "\n", + "$$\n", + "a(u, v) = L(v) \\quad \\forall v \\in \\hat{V}\n", + "$$\n", + "\n", + "where\n", + "\n", + "$$\n", + "\\begin{align}\n", + " a(u, v) &= \\int_{\\Omega} \\sigma(u) : \\nabla v \\, \\mathrm{d} x \\\\\n", + " L(v) &= \\int_{\\Omega} f \\cdot v \\, \\mathrm{d} x + \\int_{\\partial \\Omega_T} T \\cdot v \\, \\mathrm{d} s\n", + "\\end{align}\n", + "$$\n", + "\n", + "This formulation can be alternatively expressed as:\n", + "\n", + "$$\n", + "a(u, v) = \\int_{\\Omega} \\sigma(u) : \\epsilon(v) \\, \\mathrm{d} x\n", + "$$\n", + "\n", + "where $ \\epsilon(v) = \\frac{1}{2} (\\nabla v + (\\nabla v)^T) $ is the symmetric strain tensor.\n", + "\n", + "This variational formulation is essential for solving linear elasticity problems numerically using methods like the finite element method (FEM)." + ] + }, + { + "cell_type": "markdown", + "id": "5a958607", + "metadata": {}, + "source": [ + "## Formal Model" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "id": "d742586c", + "metadata": {}, + "outputs": [], + "source": [ + "from sympde.expr import BilinearForm, LinearForm, integral\n", + "from sympde.expr import find, EssentialBC, Norm, SemiNorm\n", + "from sympde.topology import VectorFunctionSpace, Cube, element_of\n", + "from sympde.calculus import grad, dot, inner, outer, cross, div\n", + "from sympde.core import Constant\n", + "from sympde.core import Matrix, Vector, Transpose\n", + "\n", + "domain = Cube()\n", + "\n", + "I = Matrix([[1, 0, 0], [0, 1, 0], [0, 0, 1]], name='I')\n", + "\n", + "kappa = Constant('kappa', is_real=True)\n", + "mu = Constant('mu', is_real=True)\n", + "rho = Constant('rho', is_real=True)\n", + "\n", + "epsilon = lambda w: 0.5*(grad(w) + Transpose(grad(w)))\n", + "sigma = lambda w: kappa * div(w) * I + 2 * mu * epsilon(w)\n", + "\n", + "V = VectorFunctionSpace('V', domain)\n", + "\n", + "x,y,z = domain.coordinates\n", + "\n", + "u,v = [element_of(V, name=i) for i in ['u', 'v']]" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "id": "b16cc745", + "metadata": { + "scrolled": true + }, + "outputs": [], + "source": [ + "# bilinear form\n", + "a = BilinearForm((u,v), integral(domain , inner(sigma(u), epsilon(v))))" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "id": "0a0f152c", + "metadata": {}, + "outputs": [], + "source": [ + "L = 1\n", + "W = 1 #0.2\n", + "delta = W / L\n", + "\n", + "#mu = 1\n", + "#rho = 1\n", + "#kappa = 1.25\n", + "g = 0.4 * delta**2\n", + "\n", + "# linear form\n", + "f = Vector([0, 0, -rho*g], name='f')\n", + "l = LinearForm(v, integral(domain, dot(f,v)))\n", + "\n", + "# Dirichlet boundary conditions\n", + "bc = [EssentialBC(u, 0, domain.boundary)]\n", + "\n", + "# Variational problem\n", + "equation = find(u, forall=v, lhs=a(u, v), rhs=l(v), bc=bc)" + ] + }, + { + "cell_type": "markdown", + "id": "4f983ece", + "metadata": {}, + "source": [ + "## Discretization" + ] + }, + { + "cell_type": "markdown", + "id": "51095918", + "metadata": {}, + "source": [ + "We shall need the **discretize** function from **PsyDAC**." + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "id": "a2a0a2a1", + "metadata": {}, + "outputs": [], + "source": [ + "from psydac.api.discretization import discretize" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "id": "00e54163", + "metadata": {}, + "outputs": [], + "source": [ + "degree = [2,2,2]\n", + "ncells = [8,8,8]" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "id": "5999c62b", + "metadata": {}, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "/home/ranania/PYCCEL/IGA-Python/.iga-python/lib/python3.10/site-packages/sympy/matrices/repmatrix.py:90: SymPyDeprecationWarning: \n", + "\n", + "non-Expr objects in a Matrix has been deprecated since SymPy 1.9. Use\n", + "list of lists, TableForm or some other data structure instead. See\n", + "https://github.com/sympy/sympy/issues/21497 for more info.\n", + "\n", + " ).warn()\n" + ] + } + ], + "source": [ + "# Create computational domain from topological domain\n", + "domain_h = discretize(domain, ncells=ncells, comm=None)\n", + "\n", + "# Create discrete spline space\n", + "Vh = discretize(V, domain_h, degree=degree)\n", + "\n", + "# Discretize equation\n", + "equation_h = discretize(equation, domain_h, [Vh, Vh])" + ] + }, + { + "cell_type": "markdown", + "id": "7b29fbcf", + "metadata": {}, + "source": [ + "## Solving the PDE" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "id": "541192ee", + "metadata": {}, + "outputs": [], + "source": [ + "uh = equation_h.solve(mu=1, rho=1, kappa=1.25)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "9250897b", + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": ".iga-python", + "language": "python", + "name": ".iga-python" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.10.12" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/_sources/chapter2/poisson-mixed-v1.ipynb b/_sources/chapter2/poisson-mixed-v1.ipynb new file mode 100644 index 0000000..5d8106a --- /dev/null +++ b/_sources/chapter2/poisson-mixed-v1.ipynb @@ -0,0 +1,283 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "cce2131b", + "metadata": {}, + "source": [ + "# First mixed formulation of the Poisson problem\n", + "\n", + "Instead of having one unknown, we now have two, along with the above two equations.\n", + "In order to get a mixed variational formulation, we first take the dot product of the first one by $ \\mathbf{v}$ and integrate by parts\n", + "\n", + "$$\n", + "\\begin{align}\n", + "\\int_{\\Omega} \\mathbf{u}\\cdot \\mathbf{v}~\\mathrm{d} \\mathbf{x} -\\int_{\\Omega} p ~ \\nabla\\cdot \\mathbf{v}~\\mathrm{d} \\mathbf{x} + \\int_{\\partial\\Omega} p ~ \\mathbf{v}\\cdot \\mathbf{n}~\\mathrm{d} \\sigma = \\int_{\\Omega} \\mathbf{u}\\cdot \\mathbf{v}~\\mathrm{d} \\mathbf{x} -\\int_{\\Omega} p ~ \\nabla\\cdot \\mathbf{v}~\\mathrm{d} \\mathbf{x}=0,\n", + "\\end{align}\n", + "$$\n", + "\n", + "using $p=0$ as a natural boundary condition. Then multiplying the second equation by $q$ and integrating yields\n", + "\n", + "$$\n", + "\\begin{align}\n", + "\\int_{\\Omega} \\nabla\\cdot\\mathbf{u} ~ q ~\\mathrm{d} \\mathbf{x} = \\int_{\\Omega} f q ~\\mathrm{d} \\mathbf{x}.\n", + "\\end{align}\n", + "$$\n", + "\n", + "No integration by parts is necessary here. And we thus get the following mixed variational formulation:\n", + "\n", + "Find $(\\mathbf{u},p) \\in H(\\mathrm{div},\\Omega)\\times L^2(\\Omega)$ such that\n", + "\n", + "$$\n", + "\\begin{align}\n", + "\\left\\{ \n", + "\\begin{array}{llll}\n", + " \\int_{\\Omega} \\mathbf{u}\\cdot \\mathbf{v}~\\mathrm{d} \\mathbf{x} &- \\int_{\\Omega} p ~ \\nabla\\cdot \\mathbf{v}~\\mathrm{d} \\mathbf{x} &=0, & \\forall \\mathbf{v}\\in H(\\mathrm{div},\\Omega) \\\\\n", + " \\int_{\\Omega} \\nabla\\cdot\\mathbf{u} ~ q ~\\mathrm{d} \\mathbf{x} & &= \\int_{\\Omega} f q ~\\mathrm{d} \\mathbf{x}, & \\forall q\\in L^2(\\Omega)\n", + "\\end{array} \\right.\n", + "\\end{align}\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "id": "fc928232", + "metadata": {}, + "source": [ + "## Formal Model" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "id": "bcb6daca", + "metadata": {}, + "outputs": [], + "source": [ + "from sympde.expr import BilinearForm, LinearForm, integral\n", + "from sympde.expr import find, EssentialBC, Norm, SemiNorm\n", + "from sympde.topology import (ScalarFunctionSpace, VectorFunctionSpace, Square,\n", + " element_of)\n", + "from sympde.calculus import grad, dot, div, inner\n", + "from sympde.core import Constant\n", + "\n", + "from psydac.api.discretization import discretize\n", + "\n", + "from sympy import pi, sin, cos, Tuple\n", + "\n", + "from psydac.api.discretization import discretize\n", + "\n", + "domain = Square()\n", + "\n", + "V1 = VectorFunctionSpace('V1', domain, kind='Hdiv')\n", + "V2 = ScalarFunctionSpace('V2', domain, kind='L2')\n", + "X = V1*V2\n", + "\n", + "x,y = domain.coordinates\n", + "\n", + "# rhs\n", + "f = 2*pi**2*sin(pi*x)*sin(pi*y)\n", + "# exact solution\n", + "pe = sin(pi*x)*sin(pi*y)\n", + "#ue = -grad(pe) # not working when computing the norm\n", + "ue = Tuple(-pi*cos(pi*x)*sin(pi*y), -pi*sin(pi*x)*cos(pi*y))\n", + "\n", + "u,v = [element_of(V1, name=i) for i in ['u', 'v']]\n", + "p,q = [element_of(V2, name=i) for i in ['p', 'q']]\n", + "\n", + "# bilinear form\n", + "a = BilinearForm(((u,p),(v,q)), integral(domain, dot(u,v) - p*div(v) + div(u)*q) )\n", + "\n", + "# linear form\n", + "l = LinearForm((v,q), integral(domain, f*q))\n", + "\n", + "# Variational problem\n", + "equation = find([u,p], forall=[v,q], lhs=a((u,p),(v,q)), rhs=l(v,q))" + ] + }, + { + "cell_type": "markdown", + "id": "3cc341c5", + "metadata": {}, + "source": [ + "## Discretization" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "id": "e5234456", + "metadata": {}, + "outputs": [], + "source": [ + "degree = [2,2]\n", + "ncells = [8,8]" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "id": "1d8e59bb", + "metadata": {}, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "/home/ranania/PYCCEL/IGA-Python/.iga-python/lib/python3.10/site-packages/sympy/matrices/repmatrix.py:90: SymPyDeprecationWarning: \n", + "\n", + "non-Expr objects in a Matrix has been deprecated since SymPy 1.9. Use\n", + "list of lists, TableForm or some other data structure instead. See\n", + "https://github.com/sympy/sympy/issues/21497 for more info.\n", + "\n", + " ).warn()\n" + ] + } + ], + "source": [ + "# Create computational domain from topological domain\n", + "domain_h = discretize(domain, ncells=ncells, comm=None)\n", + "\n", + "# Create discrete spline space\n", + "V1h = discretize(V1, domain_h, degree=degree)\n", + "V2h = discretize(V2, domain_h, degree=degree)\n", + "Xh = discretize(X, domain_h, degree=degree)\n", + "\n", + "# Discretize equation\n", + "equation_h = discretize(equation, domain_h, [Xh, Xh])" + ] + }, + { + "cell_type": "markdown", + "id": "4c473ba3", + "metadata": {}, + "source": [ + "## Solving the PDE" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "id": "02abfb7d", + "metadata": {}, + "outputs": [], + "source": [ + "equation_h.set_solver('gmres', info=False, tol=1e-8)" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "id": "e2d935e8", + "metadata": {}, + "outputs": [], + "source": [ + "#uh, ph = equation_h.solve()\n", + "\n", + "from psydac.fem.basic import FemField\n", + "\n", + "phi_h = equation_h.solve()\n", + "\n", + "uh = FemField(V1h)\n", + "uh.coeffs[0][:] = phi_h.coeffs[0][:]\n", + "uh.coeffs[1][:] = phi_h.coeffs[1][:]\n", + "\n", + "ph = FemField(V2h)\n", + "ph.coeffs[:] = phi_h.coeffs[2][:]" + ] + }, + { + "cell_type": "markdown", + "id": "9c790f00", + "metadata": {}, + "source": [ + "## Computing the error norm" + ] + }, + { + "cell_type": "markdown", + "id": "432b8d59", + "metadata": {}, + "source": [ + "### Computing the $L^2$ norm" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "id": "b6c85077", + "metadata": {}, + "outputs": [], + "source": [ + "# L2 error norm of the velocity field\n", + "error_u = [ue[0]-u[0], ue[1]-u[1]]\n", + "l2norm_u = Norm(error_u, domain, kind='l2')\n", + "l2norm_uh = discretize(l2norm_u, domain_h, V1h)\n", + "\n", + "# L2 error norm of the pressure, after removing the average value from the field\n", + "l2norm_p = Norm(pe - p, domain, kind='l2')\n", + "l2norm_ph = discretize(l2norm_p, domain_h, V2h)" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "id": "52fdeaec", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + ">>> norm-l2 uh = 0.012985071480053038\n", + ">>> norm-l2 ph = 0.004127522959699811\n" + ] + } + ], + "source": [ + "l2norm = l2norm_uh.assemble(u=uh)\n", + "print('>>> norm-l2 uh = ', l2norm)\n", + "\n", + "l2norm = l2norm_ph.assemble(p=ph)\n", + "print('>>> norm-l2 ph = ', l2norm)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "a82ae495", + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "494e2cca", + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": ".iga-python", + "language": "python", + "name": ".iga-python" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.10.12" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/_sources/chapter2/poisson-mixed-v2.ipynb b/_sources/chapter2/poisson-mixed-v2.ipynb new file mode 100644 index 0000000..103f2ab --- /dev/null +++ b/_sources/chapter2/poisson-mixed-v2.ipynb @@ -0,0 +1,284 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "cce2131b", + "metadata": {}, + "source": [ + "# Second mixed formulation of the Poisson problem\n", + "\n", + "Here, we get an alternative formulation by not integrating by parts, the mixed term in the first formulation but in the second. The first formulation simply becomes\n", + "\n", + "$$\n", + "\\begin{align}\n", + "\\int_{\\Omega} \\mathbf{u}\\cdot \\mathbf{v}~\\mathrm{d} \\mathbf{x} +\\int_{\\Omega} \\nabla p \\cdot \\mathbf{v}~\\mathrm{d} \\mathbf{x}=0,\n", + "\\end{align}\n", + "$$\n", + "\n", + "and the second, removing immediately the boundary term due to the essential boundary condition $q=0$\n", + "\n", + "$$\n", + "\\begin{align}\n", + "\\int_{\\Omega}\\nabla \\cdot\\mathbf{u} ~ q ~\\mathrm{d} \\mathbf{x} = -\\int_{\\Omega} \\mathbf{u} \\cdot \\nabla q ~\\mathrm{d} \\mathbf{x} = \\int_{\\Omega} f q ~\\mathrm{d} \\mathbf{x},\n", + "\\end{align}\n", + "$$\n", + "\n", + "which leads to the variational formulation\n", + "\n", + "Find $(\\mathbf{u},p) \\in L^2(\\Omega)^3 \\times H^1_0(\\Omega)$ such that\n", + "\n", + "$$\n", + "\\begin{align}\n", + "\\left\\{ \n", + "\\begin{array}{llll}\n", + " \\int_{\\Omega} \\mathbf{u}\\cdot \\mathbf{v}~\\mathrm{d} \\mathbf{x} &+ \\int_{\\Omega} \\nabla p \\cdot \\mathbf{v}~\\mathrm{d} \\mathbf{x} &=0, & \\forall \\mathbf{v}\\in L^2(\\Omega)^3 \\\\\n", + " \\int_{\\Omega} \\mathbf{u} \\cdot \\nabla q ~\\mathrm{d} \\mathbf{x} & & = -\\int_{\\Omega} f q ~\\mathrm{d} \\mathbf{x}, & \\forall q\\in H^1_0(\\Omega)\n", + "\\end{array} \\right.\n", + "\\end{align}\n", + "$$\n", + "\n", + "\n", + "Note that this formulation actually contains the classical variational formulation for the Poisson equation. Indeed for $q\\in H^1_0(\\Omega)$, $\\nabla q \\in L^2(\\Omega)^3$ can be used as a test function in the first equation. And plugging this into the second we get\n", + "\n", + "$$\n", + "\\int_{\\Omega} \\nabla p \\cdot \\nabla q ~\\mathrm{d} \\mathbf{x} = \\int_{\\Omega} f q ~\\mathrm{d} \\mathbf{x}, \\quad \\forall q\\in H^1_0(\\Omega).\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "id": "fc928232", + "metadata": {}, + "source": [ + "## Formal Model" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "id": "bcb6daca", + "metadata": {}, + "outputs": [], + "source": [ + "from sympde.expr import BilinearForm, LinearForm, integral\n", + "from sympde.expr import find, EssentialBC, Norm, SemiNorm\n", + "from sympde.topology import (ScalarFunctionSpace, VectorFunctionSpace, Square,\n", + " element_of)\n", + "from sympde.calculus import grad, dot, div, inner\n", + "from sympde.core import Constant\n", + "\n", + "from psydac.api.discretization import discretize\n", + "\n", + "from sympy import pi, sin, cos, Tuple\n", + "\n", + "from psydac.api.discretization import discretize\n", + "\n", + "domain = Square()\n", + "\n", + "V1 = VectorFunctionSpace('V1', domain, kind='L2')\n", + "V2 = ScalarFunctionSpace('V2', domain, kind='H1')\n", + "X = V1*V2\n", + "\n", + "x,y = domain.coordinates\n", + "\n", + "# rhs\n", + "f = 2*pi**2*sin(pi*x)*sin(pi*y)\n", + "# exact solution\n", + "pe = sin(pi*x)*sin(pi*y)\n", + "#ue = -grad(pe) # not working when computing the norm\n", + "ue = Tuple(-pi*cos(pi*x)*sin(pi*y), -pi*sin(pi*x)*cos(pi*y))\n", + "\n", + "u,v = [element_of(V1, name=i) for i in ['u', 'v']]\n", + "p,q = [element_of(V2, name=i) for i in ['p', 'q']]\n", + "\n", + "# bilinear form\n", + "a = BilinearForm(((u,p),(v,q)), integral(domain, dot(u,v) + dot(grad(p),v) + dot(u,grad(q))) )\n", + "\n", + "# linear form\n", + "l = LinearForm((v,q), integral(domain, -f*q))\n", + "\n", + "# Dirichlet boundary conditions\n", + "bc = [EssentialBC(p, 0, domain.boundary)]\n", + "\n", + "# Variational problem\n", + "equation = find([u,p], forall=[v,q], lhs=a((u,p),(v,q)), rhs=l(v,q), bc=bc)" + ] + }, + { + "cell_type": "markdown", + "id": "3cc341c5", + "metadata": {}, + "source": [ + "## Discretization" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "id": "e5234456", + "metadata": {}, + "outputs": [], + "source": [ + "degree = [2,2]\n", + "ncells = [8,8]" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "id": "1d8e59bb", + "metadata": {}, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "/home/ranania/PYCCEL/IGA-Python/.iga-python/lib/python3.10/site-packages/sympy/matrices/repmatrix.py:90: SymPyDeprecationWarning: \n", + "\n", + "non-Expr objects in a Matrix has been deprecated since SymPy 1.9. Use\n", + "list of lists, TableForm or some other data structure instead. See\n", + "https://github.com/sympy/sympy/issues/21497 for more info.\n", + "\n", + " ).warn()\n" + ] + } + ], + "source": [ + "# Create computational domain from topological domain\n", + "domain_h = discretize(domain, ncells=ncells, comm=None)\n", + "\n", + "# Create discrete spline space\n", + "V1h = discretize(V1, domain_h, degree=degree)\n", + "V2h = discretize(V2, domain_h, degree=degree)\n", + "Xh = discretize(X, domain_h, degree=degree)\n", + "\n", + "# Discretize equation\n", + "equation_h = discretize(equation, domain_h, [Xh, Xh])" + ] + }, + { + "cell_type": "markdown", + "id": "4c473ba3", + "metadata": {}, + "source": [ + "## Solving the PDE" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "id": "02abfb7d", + "metadata": {}, + "outputs": [], + "source": [ + "equation_h.set_solver('gmres', info=False, tol=1e-8)" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "id": "e2d935e8", + "metadata": {}, + "outputs": [], + "source": [ + "#uh, ph = equation_h.solve()\n", + "\n", + "from psydac.fem.basic import FemField\n", + "\n", + "phi_h = equation_h.solve()\n", + "\n", + "uh = FemField(V1h)\n", + "uh.coeffs[0][:] = phi_h.coeffs[0][:]\n", + "uh.coeffs[1][:] = phi_h.coeffs[1][:]\n", + "\n", + "ph = FemField(V2h)\n", + "ph.coeffs[:] = phi_h.coeffs[2][:]" + ] + }, + { + "cell_type": "markdown", + "id": "b7f03590", + "metadata": {}, + "source": [ + "## Computing the error norm" + ] + }, + { + "cell_type": "markdown", + "id": "62ad7d46", + "metadata": {}, + "source": [ + "### Computing the $L^2$ norm" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "id": "31967fb4", + "metadata": {}, + "outputs": [], + "source": [ + "# L2 error norm of the velocity field\n", + "error_u = [ue[0]-u[0], ue[1]-u[1]]\n", + "l2norm_u = Norm(error_u, domain, kind='l2')\n", + "l2norm_uh = discretize(l2norm_u, domain_h, V1h)\n", + "\n", + "# L2 error norm of the pressure, after removing the average value from the field\n", + "l2norm_p = Norm(pe - p, domain, kind='l2')\n", + "l2norm_ph = discretize(l2norm_p, domain_h, V2h)" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "id": "9c3f7e15", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + ">>> norm-l2 uh = 64.20821457571618\n", + ">>> norm-l2 ph = 3254706679445337.5\n" + ] + } + ], + "source": [ + "l2norm = l2norm_uh.assemble(u=uh)\n", + "print('>>> norm-l2 uh = ', l2norm)\n", + "\n", + "l2norm = l2norm_ph.assemble(p=ph)\n", + "print('>>> norm-l2 ph = ', l2norm)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "d7adf378", + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": ".iga-python", + "language": "python", + "name": ".iga-python" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.10.12" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/_sources/chapter2/poisson-mixed.ipynb b/_sources/chapter2/poisson-mixed.ipynb new file mode 100644 index 0000000..5243e3b --- /dev/null +++ b/_sources/chapter2/poisson-mixed.ipynb @@ -0,0 +1,57 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "1a4e2078", + "metadata": {}, + "source": [ + "# Mixed FEM for the Poisson problem\n", + "\n", + "Let $\\Omega \\subset \\mathbb{R}^3$ and consider the Poisson problem\n", + "\n", + "$$\n", + "\\begin{align}\n", + " \\left\\{ \n", + " \\begin{array}{clr}\n", + " -\\Delta p & =f & ,~\\Omega \\\\\n", + " p & =0 & ,~\\partial \\Omega\n", + " \\end{array} \\right.\n", + "\\end{align}\n", + "$$\n", + "\n", + "Using that $\\Delta p = \\nabla\\cdot\\nabla p$, we set $ \\mathbf{u}=\\nabla p$, then the Poisson equation can be written equivalently\n", + "\n", + "$$ \\mathbf{u}=-\\nabla p, ~~~ \\nabla\\cdot \\mathbf{u}= f.$$" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "46339ba9", + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": ".iga-python", + "language": "python", + "name": ".iga-python" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.10.12" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/_sources/chapter2/poisson-nitsche.ipynb b/_sources/chapter2/poisson-nitsche.ipynb new file mode 100644 index 0000000..e6c862e --- /dev/null +++ b/_sources/chapter2/poisson-nitsche.ipynb @@ -0,0 +1,210 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "119eb328", + "metadata": {}, + "source": [ + "# The Poisson equation with weak imposition of Dirichlet conditions" + ] + }, + { + "cell_type": "markdown", + "id": "3a5e01a2", + "metadata": {}, + "source": [ + "In this example, we consider the following Poisson problem\n", + "\n", + "$$\n", + "\\begin{align}\n", + " - \\nabla^2 u = f \\quad \\text{in~$\\Omega$}, \\quad \\quad \n", + " u = g \\quad \\text{on~$\\partial \\Omega$}.\n", + "\\end{align}\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "id": "505861ef", + "metadata": {}, + "source": [ + "## The variational formulation\n", + "\n", + "$$\n", + "\\begin{align}\n", + " \\text{find $u \\in V$ such that} \\quad a(u,v) = l(v) \\quad \\forall v \\in V,\n", + "\\end{align}\n", + "$$\n", + "\n", + "where \n", + "\n", + "- $V \\subset H^1(\\Omega)$, \n", + "- $a(u,v) := \\int_{\\Omega} \\nabla u \\cdot \\nabla v ~ d\\Omega + \\int_{\\partial \\Omega} \\left( \\kappa u v - u \\partial_n v - v \\partial_n u \\right)~d\\partial\\Omega $,\n", + "- $l(v) := \\int_{\\Omega} f v ~ d\\Omega + \\int_{\\partial\\Omega} \\left( \\kappa g v - g \\partial_n v \\right) ~ d\\Gamma$.\n" + ] + }, + { + "cell_type": "markdown", + "id": "d4f55f53", + "metadata": {}, + "source": [ + "## Formal Model" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "id": "ecd1330a", + "metadata": {}, + "outputs": [], + "source": [ + "from sympde.expr import BilinearForm, LinearForm, integral\n", + "from sympde.expr import find, EssentialBC\n", + "from sympde.topology import ScalarFunctionSpace, Square, element_of\n", + "from sympde.calculus import grad, dot, Dn\n", + "from sympde.core import Constant\n", + "\n", + "from psydac.api.discretization import discretize\n", + "\n", + "from sympy import pi, sin\n", + "\n", + "kappa = Constant('kappa', is_real=True)\n", + "\n", + "domain = Square()\n", + "\n", + "V = ScalarFunctionSpace('V', domain)\n", + "\n", + "x,y = domain.coordinates\n", + "\n", + "u,v = [element_of(V, name=i) for i in ['u', 'v']]\n", + "\n", + "# bilinear form\n", + "a = BilinearForm((u,v), integral(domain, dot(grad(v), grad(u)) + kappa*u*v - u*Dn(v) - v*Dn(u)))\n", + "\n", + "# linear form\n", + "g = sin(pi*x)*sin(pi*y)\n", + "f = 2*pi**2*sin(pi*x)*sin(pi*y)\n", + "\n", + "l = LinearForm(v, integral(domain, f*v + kappa*g*v - g*Dn(v)))\n", + "\n", + "# Variational problem\n", + "equation = find(u, forall=v, lhs=a(u, v), rhs=l(v))" + ] + }, + { + "cell_type": "markdown", + "id": "11ed2bc5", + "metadata": {}, + "source": [ + "## Discretization" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "id": "3d86674b", + "metadata": {}, + "outputs": [], + "source": [ + "degree = [2,2]\n", + "ncells = [8,8]" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "id": "94c83267", + "metadata": {}, + "outputs": [], + "source": [ + "# Create computational domain from topological domain\n", + "domain_h = discretize(domain, ncells=ncells, comm=None)\n", + "\n", + "# Create discrete spline space\n", + "Vh = discretize(V, domain_h, degree=degree)\n", + "\n", + "# Discretize equation\n", + "#equation_h = discretize(equation, domain_h, [Vh, Vh])" + ] + }, + { + "cell_type": "markdown", + "id": "85318e35", + "metadata": {}, + "source": [ + "### Solving the PDE" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "id": "8f1b2d68", + "metadata": {}, + "outputs": [], + "source": [ + "#uh = equation_h.solve()" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "e96f321c", + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "c7ae0b9e", + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "9ad386a6", + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "068bdb95", + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "aa88a918", + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": ".iga-python", + "language": "python", + "name": ".iga-python" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.10.12" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/_sources/chapter2/poisson.ipynb b/_sources/chapter2/poisson.ipynb new file mode 100644 index 0000000..b4d9f01 --- /dev/null +++ b/_sources/chapter2/poisson.ipynb @@ -0,0 +1,336 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "9f28f9af", + "metadata": {}, + "source": [ + "# The Poisson equation\n", + "\n", + "As a first example, we consider the Poisson equation\n", + "\n", + "$$\n", + "\\begin{align}\n", + " - \\nabla^2 u = f \\quad \\text{in $\\Omega$}, \\quad \\quad \n", + " u = 0 \\quad \\text{on $\\Gamma_D$}, \\quad \\quad \n", + " \\partial_n u = g \\quad \\text{on $\\Gamma_N$}.\n", + "\\end{align}\n", + "$$\n", + "\n", + "## Variational Formulation\n", + "\n", + "An $H^1$-conforming variational formulation of reads\n", + "\n", + "$$\n", + "\\begin{align}\n", + " \\text{find $u \\in V$ such that} \\quad a(u,v) = l(v) \\quad \\forall v \\in V,\n", + "\\end{align}\n", + "$$\n", + "\n", + "where \n", + "\n", + "- $V \\subset H^1(\\Omega)$, \n", + "- $a(u,v) := \\int_{\\Omega} \\nabla u \\cdot \\nabla v ~ d\\Omega$,\n", + "- $l(v) := \\int_{\\Omega} f v ~ d\\Omega + \\int_{\\Gamma_N} g v ~ d\\Gamma$.\n", + "\n", + "## Examples\n", + "\n", + "- [Poisson on a square domain with Homogeneous Boundary Conditions](https://github.com/pyccel/sympde/blob/devel-documentation/docs/examples/2d_poisson_dir0.py)\n", + "- [Poisson on a square domain with Homogeneous and Neumann Boundary Conditions](https://github.com/pyccel/sympde/blob/devel-documentation/docs/examples/2d_poisson_dir0_neu.py)\n", + "- [Poisson on a square domain with Homogeneous, Inhomogeneous and Neumann Boundary Conditions](https://github.com/pyccel/sympde/blob/devel-documentation/docs/examples/2d_poisson_dir_neu.py)" + ] + }, + { + "cell_type": "markdown", + "id": "5a958607", + "metadata": {}, + "source": [ + "## Formal Model" + ] + }, + { + "cell_type": "code", + "execution_count": 27, + "id": "d742586c", + "metadata": {}, + "outputs": [], + "source": [ + "from sympde.expr import BilinearForm, LinearForm, integral\n", + "from sympde.expr import find, EssentialBC, Norm, SemiNorm\n", + "from sympde.topology import ScalarFunctionSpace, Square, element_of\n", + "from sympde.calculus import grad, dot\n", + "\n", + "from sympy import pi, sin\n", + "\n", + "domain = Square()\n", + "\n", + "V = ScalarFunctionSpace('V', domain)\n", + "\n", + "x,y = domain.coordinates\n", + "\n", + "u,v = [element_of(V, name=i) for i in ['u', 'v']]\n", + "\n", + "# bilinear form\n", + "a = BilinearForm((u,v), integral(domain , dot(grad(v), grad(u))))\n", + "\n", + "# linear form\n", + "f = 2*pi**2*sin(pi*x)*sin(pi*y)\n", + "l = LinearForm(v, integral(domain, f*v))\n", + "\n", + "# Dirichlet boundary conditions\n", + "bc = [EssentialBC(u, 0, domain.boundary)]\n", + "\n", + "# Variational problem\n", + "equation = find(u, forall=v, lhs=a(u, v), rhs=l(v), bc=bc)" + ] + }, + { + "cell_type": "markdown", + "id": "62ac1fd4", + "metadata": {}, + "source": [ + "\n", + "This very simple Python code reflects well the abstract mathematical framework needed for variational formulations.\n", + "The structure of the code is as follows,\n", + "\n", + "1. Create a domain.\n", + "2. Create a space of *scalar* functions over the domain.\n", + "3. Create elements from this function space. These elements will denote the test and trial functions.\n", + "4. Create the Bilinear and Linear forms, $a$ and $l$ respectively.\n", + "5. Create Essential Boundary Conditions.\n", + "6. Create the variational problem.\n", + "\n", + "Most of the time, you will need to follow the same steps, with some minor variants depending on the problem you're considering." + ] + }, + { + "cell_type": "markdown", + "id": "4f983ece", + "metadata": {}, + "source": [ + "## Discretization" + ] + }, + { + "cell_type": "markdown", + "id": "51095918", + "metadata": {}, + "source": [ + "We shall need the **discretize** function from **PsyDAC**." + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "id": "a2a0a2a1", + "metadata": {}, + "outputs": [], + "source": [ + "from psydac.api.discretization import discretize" + ] + }, + { + "cell_type": "code", + "execution_count": 22, + "id": "00e54163", + "metadata": {}, + "outputs": [], + "source": [ + "degree = [2,2]\n", + "ncells = [8,8]" + ] + }, + { + "cell_type": "code", + "execution_count": 23, + "id": "5999c62b", + "metadata": {}, + "outputs": [], + "source": [ + "# Create computational domain from topological domain\n", + "domain_h = discretize(domain, ncells=ncells, comm=None)\n", + "\n", + "# Create discrete spline space\n", + "Vh = discretize(V, domain_h, degree=degree)\n", + "\n", + "# Discretize equation\n", + "equation_h = discretize(equation, domain_h, [Vh, Vh])" + ] + }, + { + "cell_type": "markdown", + "id": "7b29fbcf", + "metadata": {}, + "source": [ + "## Solving the PDE" + ] + }, + { + "cell_type": "code", + "execution_count": 24, + "id": "541192ee", + "metadata": {}, + "outputs": [], + "source": [ + "uh = equation_h.solve()" + ] + }, + { + "cell_type": "markdown", + "id": "5174c4b5", + "metadata": {}, + "source": [ + "## Computing the error norm\n", + "\n", + "When the analytical solution is available, you might be interested in computing the $L^2$ norm or $H^1_0$ semi-norm.\n", + "SymPDE allows you to do so, by creating the **Norm** object.\n", + "In this example, the analytical solution is given by\n", + "\n", + "$$\n", + "u_e = \\sin(\\pi x) \\sin(\\pi y)\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "id": "3a31c46f", + "metadata": {}, + "source": [ + "### Computing the $L^2$ norm" + ] + }, + { + "cell_type": "code", + "execution_count": 26, + "id": "5925c6cd", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "9.49756716724664e-07\n" + ] + } + ], + "source": [ + "ue = sin(pi*x)*sin(pi*y)\n", + "\n", + "u = element_of(V, name='u')\n", + "\n", + "# create the formal Norm object\n", + "l2norm = Norm(u - ue, domain, kind='l2')\n", + "\n", + "# discretize the norm\n", + "l2norm_h = discretize(l2norm, domain_h, Vh)\n", + "\n", + "# assemble the norm\n", + "l2_error = l2norm_h.assemble(u=uh)\n", + "\n", + "# print the result\n", + "print(l2_error)" + ] + }, + { + "cell_type": "markdown", + "id": "a6cbfeae", + "metadata": {}, + "source": [ + "### Computing the $H^1$ semi-norm" + ] + }, + { + "cell_type": "code", + "execution_count": 30, + "id": "e5c1a8b8", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "9.768702410721585e-05\n" + ] + } + ], + "source": [ + "# create the formal Norm object\n", + "h1norm = SemiNorm(u - ue, domain, kind='h1')\n", + "\n", + "# discretize the norm\n", + "h1norm_h = discretize(h1norm, domain_h, Vh)\n", + "\n", + "# assemble the norm\n", + "h1_error = h1norm_h.assemble(u=uh)\n", + "\n", + "# print the result\n", + "print(h1_error)" + ] + }, + { + "cell_type": "markdown", + "id": "3c09131c", + "metadata": {}, + "source": [ + "### Computing the $H^1$ norm" + ] + }, + { + "cell_type": "code", + "execution_count": 29, + "id": "d829e410", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "9.769164089397408e-05\n" + ] + } + ], + "source": [ + "# create the formal Norm object\n", + "h1norm = Norm(u - ue, domain, kind='h1')\n", + "\n", + "# discretize the norm\n", + "h1norm_h = discretize(h1norm, domain_h, Vh)\n", + "\n", + "# assemble the norm\n", + "h1_error = h1norm_h.assemble(u=uh)\n", + "\n", + "# print the result\n", + "print(h1_error)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "9250897b", + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": ".iga-python", + "language": "python", + "name": ".iga-python" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.10.12" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/_sources/chapter2/stokes-v1.ipynb b/_sources/chapter2/stokes-v1.ipynb new file mode 100644 index 0000000..785159e --- /dev/null +++ b/_sources/chapter2/stokes-v1.ipynb @@ -0,0 +1,268 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "bee50521", + "metadata": {}, + "source": [ + "# First mixed formulation of the Stokes problem\n", + "\n", + "For the variational formulation, we take the dot product of the first equation with $v$ and integrate over the whole domain\n", + "\n", + "$$\n", + "\\int_{\\Omega} (-\\Delta \\mathbf{u} + \\nabla p)\\cdot \\mathbf{v} ~\\mathrm{d} \\mathbf{x} = \\int_{\\Omega}\\nabla \\mathbf{u}:\\nabla \\mathbf{v} ~\\mathrm{d} \\mathbf{x} + \\int_{\\Omega} \\nabla p \\cdot \\mathbf{v} ~\\mathrm{d} \\mathbf{x} = \\int_{\\Omega} \\mathbf{f}\\cdot \\mathbf{v} ~\\mathrm{d} \\mathbf{x}\n", + "$$\n", + "\n", + "The integration by parts is performed component by component. We impose the essential boundary condition $\\mathbf{v}=0$ on $\\partial\\Omega$, and we denote by\n", + "\n", + "$$\n", + "\\int_{\\Omega}\\nabla \\mathbf{u}:\\nabla \\mathbf{v} ~\\mathrm{d} \\mathbf{x} =\\sum_{i=1}^3 \\int_{\\Omega}\\nabla u_i\\cdot\\nabla v_i ~\\mathrm{d} \\mathbf{x} =\\sum_{i,j=1}^3 \\int_{\\Omega}\\partial_j u_i\\partial_j v_i ~\\mathrm{d} \\mathbf{x} .\n", + "$$\n", + "\n", + "We now need to deal with the constraint $\\nabla\\cdot \\mathbf{u}=0$. The theoretical framework for saddle point problems requires that the corresponding bilinear form is the same as the second one appearing in the first part of the variational formulation. To this aim we multiply $\\nabla\\cdot \\mathbf{u}=0$ by a scalar test function (which will be associated to $p$) and integrate on the full domain, with an integration by parts in order to get the same bilinear form as in the first equation\n", + "\n", + "$$\n", + "\\int_{\\Omega} \\nabla\\cdot \\mathbf{u} ~ q ~\\mathrm{d} \\mathbf{x}= - \\int_{\\Omega} \\mathbf{u}\\cdot \\nabla q~\\mathrm{d} \\mathbf{x}=0,\n", + "$$\n", + "\n", + "using that $q=0$ on the boundary as an essential boundary condition.\n", + "We finally obtain the mixed variational formulation: \n", + "\n", + "Find $( \\mathbf{u},p)\\in H^1_0(\\Omega)^3\\times H^1_0(\\Omega)$ such that\n", + "\n", + "$$\n", + "\\begin{align}\n", + "\\left\\{\n", + " \\begin{array}{llll}\n", + " \\int_{\\Omega}\\nabla \\mathbf{u}:\\nabla \\mathbf{v} ~\\mathrm{d} \\mathbf{x} &+ \\int_{\\Omega} \\nabla p \\cdot \\mathbf{v} ~\\mathrm{d} \\mathbf{x}\n", + " &= \\int_{\\Omega} \\mathbf{f}\\cdot \\mathbf{v} ~\\mathrm{d} \\mathbf{x}, & \\forall \\mathbf{v}\\in H_0^1(\\Omega)^3 \\\\\n", + " \\int_{\\Omega} \\mathbf{u}\\cdot \\nabla q~\\mathrm{d} \\mathbf{x} & &=0, & \\forall p\\in H^1_0(\\Omega)\n", + " \\end{array}\n", + " \\right.\n", + "\\end{align}\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "id": "5a958607", + "metadata": {}, + "source": [ + "## Formal Model" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "id": "d742586c", + "metadata": {}, + "outputs": [], + "source": [ + "from sympde.expr import BilinearForm, LinearForm, integral\n", + "from sympde.expr import find, EssentialBC, Norm, SemiNorm\n", + "from sympde.topology import (ScalarFunctionSpace, VectorFunctionSpace, Square,\n", + " elements_of)\n", + "from sympde.calculus import grad, dot, div, inner\n", + "from sympde.core import Constant\n", + "\n", + "from psydac.api.discretization import discretize\n", + "\n", + "from sympy import pi, sin, cos, Tuple\n", + "\n", + "domain = Square()\n", + "x, y = domain.coordinates\n", + "\n", + "V1 = VectorFunctionSpace('V1', domain, kind='H1')\n", + "V2 = ScalarFunctionSpace('V2', domain, kind='H1')\n", + "X = V1*V2\n", + "\n", + "# rhs\n", + "fx = -x**2*(x - 1)**2*(24*y - 12) - 4*y*(x**2 + 4*x*(x - 1) + (x - 1)**2)*(2*y**2 - 3*y + 1) - 2*pi*cos(2*pi*x)\n", + "fy = 4*x*(2*x**2 - 3*x + 1)*(y**2 + 4*y*(y - 1) + (y - 1)**2) + y**2*(24*x - 12)*(y - 1)**2 + 2*pi*cos(2*pi*y)\n", + "f = Tuple(fx, fy)\n", + "\n", + "# exact solution\n", + "ue1 = x**2*(-x + 1)**2*(4*y**3 - 6*y**2 + 2*y)\n", + "ue2 =-y**2*(-y + 1)**2*(4*x**3 - 6*x**2 + 2*x)\n", + "ue = Tuple(ue1, ue2)\n", + "pe = -sin(2*pi*x) + sin(2*pi*y)\n", + "\n", + "u, v = elements_of(V1, names='u, v')\n", + "p, q = elements_of(V2, names='p, q')\n", + "\n", + "# bilinear form\n", + "a = BilinearForm(((u, p), (v, q)), integral(domain, inner(grad(u), grad(v)) + dot(grad(p), v) + dot(u, grad(q)) ) )\n", + "\n", + "# linear form\n", + "l = LinearForm((v, q), integral(domain, dot(f, v)))\n", + "\n", + "# Dirichlet boundary conditions\n", + "bc = EssentialBC(u, 0, domain.boundary)\n", + "\n", + "equation = find((u, p), forall=(v, q), lhs=a((u, p), (v, q)), rhs=l(v, q), bc=bc)" + ] + }, + { + "cell_type": "markdown", + "id": "4f983ece", + "metadata": {}, + "source": [ + "## Discretization" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "id": "00e54163", + "metadata": {}, + "outputs": [], + "source": [ + "degree = [2,2]\n", + "ncells = [8,8]" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "id": "5999c62b", + "metadata": {}, + "outputs": [], + "source": [ + "# Create computational domain from topological domain\n", + "domain_h = discretize(domain, ncells=ncells, comm=None)\n", + "\n", + "# Create discrete spline space\n", + "V1h = discretize(V1, domain_h, degree=degree)\n", + "V2h = discretize(V2, domain_h, degree=degree)\n", + "Xh = discretize(X, domain_h, degree=degree)\n", + "\n", + "# Discretize equation\n", + "equation_h = discretize(equation, domain_h, [Xh, Xh])" + ] + }, + { + "cell_type": "markdown", + "id": "7b29fbcf", + "metadata": {}, + "source": [ + "## Solving the PDE" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "id": "6230e0ac", + "metadata": {}, + "outputs": [], + "source": [ + "equation_h.set_solver('gmres', info=False, tol=1e-8)" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "id": "541192ee", + "metadata": {}, + "outputs": [], + "source": [ + "#uh, ph = equation_h.solve()\n", + "\n", + "from psydac.fem.basic import FemField\n", + "\n", + "phi_h = equation_h.solve()\n", + "\n", + "uh = FemField(V1h)\n", + "uh.coeffs[0][:] = phi_h.coeffs[0][:]\n", + "uh.coeffs[1][:] = phi_h.coeffs[1][:]\n", + "\n", + "ph = FemField(V2h)\n", + "ph.coeffs[:] = phi_h.coeffs[2][:]" + ] + }, + { + "cell_type": "markdown", + "id": "5174c4b5", + "metadata": {}, + "source": [ + "## Computing the error norm" + ] + }, + { + "cell_type": "markdown", + "id": "3a31c46f", + "metadata": {}, + "source": [ + "### Computing the $L^2$ norm" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "id": "5925c6cd", + "metadata": {}, + "outputs": [], + "source": [ + "# L2 error norm of the velocity field\n", + "error_u = [ue[0]-u[0], ue[1]-u[1]]\n", + "l2norm_u = Norm(error_u, domain, kind='l2')\n", + "l2norm_uh = discretize(l2norm_u, domain_h, V1h)\n", + "\n", + "# L2 error norm of the pressure, after removing the average value from the field\n", + "l2norm_p = Norm(pe - p, domain, kind='l2')\n", + "l2norm_ph = discretize(l2norm_p, domain_h, V2h)" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "id": "d829e410", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + ">>> norm-l2 uh = 5.852908166372369e-05\n", + ">>> norm-l2 ph = 0.01411215698700372\n" + ] + } + ], + "source": [ + "l2norm = l2norm_uh.assemble(u=uh)\n", + "print('>>> norm-l2 uh = ', l2norm)\n", + "\n", + "l2norm = l2norm_ph.assemble(p=ph)\n", + "print('>>> norm-l2 ph = ', l2norm)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "9250897b", + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": ".iga-python", + "language": "python", + "name": ".iga-python" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.10.12" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/_sources/chapter2/stokes-v2.ipynb b/_sources/chapter2/stokes-v2.ipynb new file mode 100644 index 0000000..7bd746e --- /dev/null +++ b/_sources/chapter2/stokes-v2.ipynb @@ -0,0 +1,255 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "48ac8740", + "metadata": {}, + "source": [ + "# Second mixed formulation of the Stokes problem\n", + "\n", + "Another possibility to obtained a well posed variational formulation, is to integrate by parts the\n", + "$\\int_{\\Omega} \\nabla p \\cdot \\mathbf{v} ~\\mathrm{d} \\mathbf{x}$ term in the first formulation:\n", + "\n", + "$$ \n", + "\\int_{\\Omega} \\nabla p \\cdot \\mathbf{v} ~\\mathrm{d} \\mathbf{x} = - \\int_{\\Omega} p \\nabla \\cdot \\mathbf{v} ~\\mathrm{d} \\mathbf{x} + \\int_{\\partial\\Omega} p \\mathbf{v} \\cdot \\mathbf{n}~\\mathrm{d} \\sigma= -\\int_{\\Omega} p ~ \\nabla \\cdot \\mathbf{v} ~\\mathrm{d} \\mathbf{x} ,\n", + "$$\n", + "\n", + " using here $p=0$ as a natural boundary condition. Note that in the other variational formulation the same boundary condition was essential. In this case, for the second variational formulation, we just multiply $\\nabla\\cdot \\mathbf{u}=0$ by $q$ and integrate. No integration by parts is needed in this case.\n", + "\n", + "$$\n", + "\\int_{\\Omega} \\nabla \\cdot \\mathbf{u} ~ q ~\\mathrm{d} \\mathbf{x} =0.\n", + "$$\n", + "\n", + "This then leads to the following variational formulation:\n", + "\n", + "Find $( \\mathbf{u},p)\\in H^1(\\Omega)^3\\times L^2(\\Omega)$ such that \n", + "\n", + "$$\n", + "\\begin{align}\n", + "\\left\\{\n", + " \\begin{array}{llll}\n", + " \\int_{\\Omega}\\nabla \\mathbf{u}:\\nabla \\mathbf{v} ~\\mathrm{d} \\mathbf{x} &- \\int_{\\Omega} p ~ \\nabla\\cdot \\mathbf{v} ~\\mathrm{d} \\mathbf{x}\n", + " &= \\int_{\\Omega} \\mathbf{f}\\cdot \\mathbf{v} ~\\mathrm{d} \\mathbf{x}, &\\forall \\mathbf{v}\\in H^1(\\Omega)^3\n", + " \\\\\n", + " \\int_{\\Omega} \\nabla\\cdot\\mathbf{u} ~ q~\\mathrm{d} \\mathbf{x} & &=0, &\\forall q\\in L^2(\\Omega)\n", + " \\end{array}\n", + " \\right.\n", + "\\end{align}\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "id": "5a958607", + "metadata": {}, + "source": [ + "## Formal Model" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "id": "d742586c", + "metadata": {}, + "outputs": [], + "source": [ + "from sympde.expr import BilinearForm, LinearForm, integral\n", + "from sympde.expr import find, EssentialBC, Norm, SemiNorm\n", + "from sympde.topology import (ScalarFunctionSpace, VectorFunctionSpace, Square,\n", + " elements_of)\n", + "from sympde.calculus import grad, dot, div, inner\n", + "from sympde.core import Constant\n", + "\n", + "from psydac.api.discretization import discretize\n", + "\n", + "from sympy import pi, sin, cos, Tuple\n", + "\n", + "domain = Square()\n", + "x, y = domain.coordinates\n", + "\n", + "V1 = VectorFunctionSpace('V1', domain, kind='H1')\n", + "V2 = ScalarFunctionSpace('V2', domain, kind='L2')\n", + "X = V1*V2\n", + "\n", + "# rhs\n", + "fx = -x**2*(x - 1)**2*(24*y - 12) - 4*y*(x**2 + 4*x*(x - 1) + (x - 1)**2)*(2*y**2 - 3*y + 1) - 2*pi*cos(2*pi*x)\n", + "fy = 4*x*(2*x**2 - 3*x + 1)*(y**2 + 4*y*(y - 1) + (y - 1)**2) + y**2*(24*x - 12)*(y - 1)**2 + 2*pi*cos(2*pi*y)\n", + "f = Tuple(fx, fy)\n", + "\n", + "# exact solution\n", + "ue1 = x**2*(-x + 1)**2*(4*y**3 - 6*y**2 + 2*y)\n", + "ue2 =-y**2*(-y + 1)**2*(4*x**3 - 6*x**2 + 2*x)\n", + "ue = Tuple(ue1, ue2)\n", + "pe = -sin(2*pi*x) + sin(2*pi*y)\n", + "\n", + "u, v = elements_of(V1, names='u, v')\n", + "p, q = elements_of(V2, names='p, q')\n", + "\n", + "# bilinear form\n", + "a = BilinearForm(((u, p), (v, q)), integral(domain, inner(grad(u), grad(v)) - div(u)*q - p*div(v)) )\n", + "\n", + "# linear form\n", + "l = LinearForm((v, q), integral(domain, dot(f, v)))\n", + "\n", + "# Dirichlet boundary conditions\n", + "bc = EssentialBC(u, 0, domain.boundary)\n", + "\n", + "equation = find((u, p), forall=(v, q), lhs=a((u, p), (v, q)), rhs=l(v, q), bc=bc)" + ] + }, + { + "cell_type": "markdown", + "id": "4f983ece", + "metadata": {}, + "source": [ + "## Discretization" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "id": "00e54163", + "metadata": {}, + "outputs": [], + "source": [ + "degree = [2,2]\n", + "ncells = [8,8]" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "id": "5999c62b", + "metadata": {}, + "outputs": [], + "source": [ + "# Create computational domain from topological domain\n", + "domain_h = discretize(domain, ncells=ncells, comm=None)\n", + "\n", + "# Create discrete spline space\n", + "V1h = discretize(V1, domain_h, degree=degree)\n", + "V2h = discretize(V2, domain_h, degree=degree)\n", + "Xh = discretize(X, domain_h, degree=degree)\n", + "\n", + "# Discretize equation\n", + "equation_h = discretize(equation, domain_h, [Xh, Xh])" + ] + }, + { + "cell_type": "markdown", + "id": "7b29fbcf", + "metadata": {}, + "source": [ + "## Solving the PDE" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "id": "541192ee", + "metadata": {}, + "outputs": [], + "source": [ + "equation_h.set_solver('gmres', info=False, tol=1e-8)" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "id": "504a182d", + "metadata": {}, + "outputs": [], + "source": [ + "#uh, ph = equation_h.solve()\n", + "\n", + "from psydac.fem.basic import FemField\n", + "\n", + "phi_h = equation_h.solve()\n", + "\n", + "uh = FemField(V1h)\n", + "uh.coeffs[0][:] = phi_h.coeffs[0][:]\n", + "uh.coeffs[1][:] = phi_h.coeffs[1][:]\n", + "\n", + "ph = FemField(V2h)\n", + "ph.coeffs[:] = phi_h.coeffs[2][:]" + ] + }, + { + "cell_type": "markdown", + "id": "5174c4b5", + "metadata": {}, + "source": [ + "## Computing the error norm" + ] + }, + { + "cell_type": "markdown", + "id": "3a31c46f", + "metadata": {}, + "source": [ + "### Computing the $L^2$ norm" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "id": "5925c6cd", + "metadata": {}, + "outputs": [], + "source": [ + "# L2 error norm of the velocity field\n", + "error_u = [ue[0]-u[0], ue[1]-u[1]]\n", + "l2norm_u = Norm(error_u, domain, kind='l2')\n", + "l2norm_uh = discretize(l2norm_u, domain_h, V1h)\n", + "\n", + "# L2 error norm of the pressure, after removing the average value from the field\n", + "l2norm_p = Norm(pe - p, domain, kind='l2')\n", + "l2norm_ph = discretize(l2norm_p, domain_h, V2h)" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "id": "e5c1a8b8", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + ">>> norm-l2 uh = 1.860724404008467e-05\n", + ">>> norm-l2 ph = 0.024428172461472355\n" + ] + } + ], + "source": [ + "l2norm = l2norm_uh.assemble(u=uh)\n", + "print('>>> norm-l2 uh = ', l2norm)\n", + "\n", + "l2norm = l2norm_ph.assemble(p=ph)\n", + "print('>>> norm-l2 ph = ', l2norm)" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": ".iga-python", + "language": "python", + "name": ".iga-python" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.10.12" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/_sources/chapter2/stokes.ipynb b/_sources/chapter2/stokes.ipynb new file mode 100644 index 0000000..04d45a5 --- /dev/null +++ b/_sources/chapter2/stokes.ipynb @@ -0,0 +1,47 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "9f28f9af", + "metadata": {}, + "source": [ + "# Mixed FEM for the Stokes problem \n", + "\n", + "We consider now the Stokes problem for the steady-state modelling of an incompressible fluid\n", + "\n", + "$$\n", + "\\begin{align}\n", + " \\left\\{\n", + " \\begin{array}{rl}\n", + " - \\nabla^2 \\mathbf{u} + \\nabla p = \\mathbf{f} & \\mbox{in} ~ \\Omega, \\\\\n", + " \\nabla \\cdot \\mathbf{u} = 0 & \\mbox{in} ~ \\Omega, \\\\\n", + " \\mathbf{u} = 0 & \\mbox{on} ~ \\partial \\Omega,\n", + " \\end{array}\n", + " \\right.\n", + "\\end{align}\n", + "$$" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": ".iga-python", + "language": "python", + "name": ".iga-python" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.10.12" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/_sources/chapter2/vector-poisson.ipynb b/_sources/chapter2/vector-poisson.ipynb new file mode 100644 index 0000000..e7ed0a2 --- /dev/null +++ b/_sources/chapter2/vector-poisson.ipynb @@ -0,0 +1,320 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "9f28f9af", + "metadata": {}, + "source": [ + "# Vector Poisson equation \n", + "\n", + "In this example we consider the vector Poisson equation with homogeneous Dirichlet boundary conditions:\n", + "\n", + "$$\n", + "\\begin{align}\n", + " - \\nabla^2 \\mathbf{u} = \\mathbf{f} \\quad \\mbox{in} ~ \\Omega, \\quad \\quad \n", + " \\mathbf{u} = 0 \\quad \\mbox{on} ~ \\partial \\Omega.\n", + "\\end{align}\n", + "$$\n", + "\n", + "## The Variational Formulation\n", + "\n", + "The corresponding variational formulation, using $\\mathbf{H}^1$ formulation, *i.e.* all components are in $H^1$, reads \n", + "\n", + "$$\n", + "\\begin{align}\n", + " \\text{find $\\mathbf{u} \\in V$ such that} \\quad \n", + " a(\\mathbf{u},\\mathbf{v}) = l(\\mathbf{v}) \\quad \\forall \\mathbf{v} \\in V,\n", + "\\end{align}\n", + "$$\n", + "\n", + "where \n", + "\n", + "- $V \\subset \\mathbf{H}_0^1(\\Omega)$, \n", + "- $a(\\mathbf{u},\\mathbf{v}) := \\int_{\\Omega} \\nabla \\mathbf{u} : \\nabla \\mathbf{v} ~ d\\Omega$,\n", + "- $l(\\mathbf{v}) := \\int_{\\Omega} \\mathbf{f} \\cdot \\mathbf{v} ~ d\\Omega$." + ] + }, + { + "cell_type": "markdown", + "id": "5a958607", + "metadata": {}, + "source": [ + "## Formal Model" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "id": "d742586c", + "metadata": {}, + "outputs": [], + "source": [ + "from sympde.expr import BilinearForm, LinearForm, integral\n", + "from sympde.expr import find, EssentialBC, Norm, SemiNorm\n", + "from sympde.topology import VectorFunctionSpace, Cube, element_of\n", + "from sympde.calculus import grad, inner, dot\n", + "\n", + "from sympy import pi, sin, Tuple, Matrix\n", + "\n", + "domain = Cube()\n", + "\n", + "V = VectorFunctionSpace('V', domain)\n", + "\n", + "x,y,z = domain.coordinates\n", + "\n", + "u,v = [element_of(V, name=i) for i in ['u', 'v']]\n", + "\n", + "# bilinear form\n", + "a = BilinearForm((u,v), integral(domain , inner(grad(v), grad(u))))\n", + "\n", + "# linear form\n", + "f1 = 3*pi**2*sin(pi*x)*sin(pi*y)*sin(pi*z)\n", + "f2 = 3*pi**2*sin(pi*x)*sin(pi*y)*sin(pi*z)\n", + "f3 = 3*pi**2*sin(pi*x)*sin(pi*y)*sin(pi*z)\n", + "f = Tuple(f1, f2, f3)\n", + "\n", + "l = LinearForm(v, integral(domain, dot(f,v)))\n", + "\n", + "# Dirichlet boundary conditions\n", + "bc = [EssentialBC(u, 0, domain.boundary)]\n", + "\n", + "# Variational problem\n", + "equation = find(u, forall=v, lhs=a(u, v), rhs=l(v), bc=bc)" + ] + }, + { + "cell_type": "markdown", + "id": "4f983ece", + "metadata": {}, + "source": [ + "## Discretization" + ] + }, + { + "cell_type": "markdown", + "id": "51095918", + "metadata": {}, + "source": [ + "We shall need the **discretize** function from **PsyDAC**." + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "id": "a2a0a2a1", + "metadata": {}, + "outputs": [], + "source": [ + "from psydac.api.discretization import discretize" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "id": "00e54163", + "metadata": {}, + "outputs": [], + "source": [ + "degree = [2,2,2]\n", + "ncells = [8,8,8]" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "id": "5999c62b", + "metadata": {}, + "outputs": [], + "source": [ + "# Create computational domain from topological domain\n", + "domain_h = discretize(domain, ncells=ncells, comm=None)\n", + "\n", + "# Create discrete spline space\n", + "Vh = discretize(V, domain_h, degree=degree)\n", + "\n", + "# Discretize equation\n", + "equation_h = discretize(equation, domain_h, [Vh, Vh])" + ] + }, + { + "cell_type": "markdown", + "id": "7b29fbcf", + "metadata": {}, + "source": [ + "## Solving the PDE" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "id": "541192ee", + "metadata": {}, + "outputs": [], + "source": [ + "uh = equation_h.solve()" + ] + }, + { + "cell_type": "markdown", + "id": "5174c4b5", + "metadata": {}, + "source": [ + "## Computing the error norm\n", + "\n", + "When the analytical solution is available, you might be interested in computing the $L^2$ norm or $H^1_0$ semi-norm.\n", + "SymPDE allows you to do so, by creating the **Norm** object.\n", + "In this example, the analytical solution is given by\n", + "\n", + "$$\n", + "u_e = \\sin(\\pi x) \\sin(\\pi y) \\sin(\\pi z)\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "id": "3a31c46f", + "metadata": {}, + "source": [ + "### Computing the $L^2$ norm" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "id": "5925c6cd", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "0.0003267962376349343\n" + ] + } + ], + "source": [ + "ue1 = sin(pi*x)*sin(pi*y)*sin(pi*z)\n", + "ue2 = sin(pi*x)*sin(pi*y)*sin(pi*z)\n", + "ue3 = sin(pi*x)*sin(pi*y)*sin(pi*z)\n", + "ue = Tuple(ue1, ue2, ue3)\n", + "\n", + "u = element_of(V, name='u')\n", + "\n", + "error = Matrix([u[0]-ue[0], u[1]-ue[1], u[2]-ue[2]])\n", + "\n", + "# create the formal Norm object\n", + "l2norm = Norm(error, domain, kind='l2')\n", + "\n", + "# discretize the norm\n", + "l2norm_h = discretize(l2norm, domain_h, Vh)\n", + "\n", + "# assemble the norm\n", + "l2_error = l2norm_h.assemble(u=uh)\n", + "\n", + "# print the result\n", + "print(l2_error)" + ] + }, + { + "cell_type": "markdown", + "id": "a6cbfeae", + "metadata": {}, + "source": [ + "### Computing the $H^1$ semi-norm" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "id": "e5c1a8b8", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "0.01956220393797005\n" + ] + } + ], + "source": [ + "# create the formal Norm object\n", + "h1norm = SemiNorm(error, domain, kind='h1')\n", + "\n", + "# discretize the norm\n", + "h1norm_h = discretize(h1norm, domain_h, Vh)\n", + "\n", + "# assemble the norm\n", + "h1_error = h1norm_h.assemble(u=uh)\n", + "\n", + "# print the result\n", + "print(h1_error)" + ] + }, + { + "cell_type": "markdown", + "id": "3c09131c", + "metadata": {}, + "source": [ + "### Computing the $H^1$ norm" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "id": "d829e410", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "0.01956493339348906\n" + ] + } + ], + "source": [ + "# create the formal Norm object\n", + "h1norm = Norm(error, domain, kind='h1')\n", + "\n", + "# discretize the norm\n", + "h1norm_h = discretize(h1norm, domain_h, Vh)\n", + "\n", + "# assemble the norm\n", + "h1_error = h1norm_h.assemble(u=uh)\n", + "\n", + "# print the result\n", + "print(h1_error)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "9250897b", + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": ".iga-python", + "language": "python", + "name": ".iga-python" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.10.12" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/_sources/chapter3/burgers.md b/_sources/chapter3/burgers.md new file mode 100644 index 0000000..d5070f7 --- /dev/null +++ b/_sources/chapter3/burgers.md @@ -0,0 +1,154 @@ +# 1D Burgers equation + +We consider the 1d Burgers equation + +$$ +\partial_t u + u \partial_x u = \nu \frac{\partial ^2u}{\partial x^2} +$$ + +$u_0(x) := u(x,t)$ denotes the initial condition. +We choose homogeneous neumann boundary conditions in this example, i.e. +$$\partial_n u = 0, \partial \Omega$$ with $\Omega = (0,1)$ + +## Time scheme +We shall use a $\theta$-scheme in this case and consider the following problem + +$$ +\begin{align} +\frac{u^{n+1}-u^n}{\Delta t} + +\theta~ u^{n+1} \partial_x u^{n+1} + (1-\theta)~ u^n \partial_x u^n = \theta~\nu \frac{\partial ^2u^{n+1}}{\partial x^2} + (1-\theta)~\nu \frac{\partial ^2u^{n}}{\partial x^2} +\end{align} +$$ + +hence + +$$ +\begin{align} +u^{n+1} + \Delta t ~ \theta~ u^{n+1} \partial_x u^{n+1} - \Delta t ~ \theta~\nu \frac{\partial ^2u^{n+1}}{\partial x^2} = +u^{n} - \Delta t ~ (1-\theta)~ u^{n} \partial_x u^{n} + \Delta t ~ (1-\theta)~\nu \frac{\partial ^2u^{n}}{\partial x^2} +\end{align} +$$ + +from now on, we shall denote by $f^n$ the right hand side of the previous equation + +$$f^n := u^{n} - \Delta t ~ (1-\theta)~ u^{n} \partial_x u^{n} + \Delta t ~ (1-\theta)~\nu \frac{\partial ^2u^{n}}{\partial x^2}$$ + +## Weak formulation + +Let $v \in \mathcal{V}$ be a function test, we have by integrating by parts the highest order term: + +$$ +\begin{align} +\langle v, u^{n+1} \rangle + \Delta t ~ \theta~ \langle v, u^{n+1} \partial_x u^{n+1} \rangle + \Delta t ~ \theta~\nu \langle \frac{\partial v}{\partial x}, \frac{\partial u^{n+1}}{\partial x} \rangle = \langle v, f^n \rangle +\end{align} +$$ + +The previous weak formulation is still nonlinear with respect to $u^{n+1}$. We shall then follow the same strategy as for the previous chapter on nonlinear Poisson problem. + +The strategy is to define the left hand side as a **LinearForm** with respect to $v$, then linearize it around $u^{n+1}$. We therefor can use either Picard or Newton method to treat the nonlinearity. + +We consider the following linear form + +$$ +\begin{align} +G(v;u,w) := \langle v, u \rangle + \Delta t ~ \theta~ \langle v, w \partial_x u \rangle + \Delta t ~ \theta~\nu \langle \frac{\partial v}{\partial x}, \frac{\partial u}{\partial x} \rangle , \quad \forall u,v,w \in \mathcal{V} +\end{align} +$$ + +Our problem is then + +$$ +\begin{align} +\mbox{Find } u^{n+1} \in \mathcal{V}, \mbox{such that}\\ +G(v;u^{n+1},u^{n+1}) = l(v), \quad \forall v \in \mathcal{V} +\end{align} +$$ + +where + +$$ +l(v) := \int_{\Omega} f^n v ~d\Omega, \quad \forall v \in \mathcal{V} +$$ + +## SymPDE code + +```python +domain = Line() + +V = ScalarFunctionSpace('V', domain) +u = element_of(V, name='u') +v = element_of(V, name='v') +w = element_of(V, name='w') +un = element_of(V, name='un') # time iteration +uk = element_of(V, name='uk') # nonlinear solver iteration + +x = domain.coordinates + +nu = Constant('nu') +theta = Constant('theta') +dt = Constant('dt') +``` + +### Defining the Linear form $G$ + +```python +# Linear form g: V --> R +expr = v * u + dt*theta*v*w*dx(u) + dt*theta*nu*dx(v)*dx(u) +g = LinearForm(v, integral(domain, expr)) +``` + +### Defining the Linear form $l$ + +```python +# Linear form l: V --> R +expr = v * un - dt*theta*v*un*dx(un) - dt*theta*nu*dx(v)*dx(un) +l = LinearForm(v, integral(domain, expr)) +``` + + +### Picard Method + +$$ +\begin{align} +\mbox{Find } u_{n+1} \in \mathcal{V}\_h, \mbox{such that}\\ +G(v;u_{n+1},u_n) = l(v), \quad \forall v \in \mathcal{V}\_h +\end{align} +$$ + +#### Picard iteration + +```python +# Variational problem +picard = find(u, forall=v, lhs=g(v, u=u,w=uk), rhs=l(v)) +``` + +### Newton Method + +Let's define + +$$ +F(v;u) := G(v;u,u) -l(v), \quad \forall v \in \mathcal{V} +$$ + +Newton method writes + +$$ +\begin{align} +\mbox{Find } u_{n+1} \in \mathcal{V}\_h, \mbox{such that}\\ +F^{\prime}(\delta u,v; u_n) = - F(v;u_n), \quad \forall v \in \mathcal{V} \\ +u_{n+1} := u_{n} + \delta u, \quad \delta u \in \mathcal{V} +\end{align} +$$ + +#### Newton iteration + +```python +F = LinearForm(v, g(v,w=u)-l(v)) +du = element_of(V, name='du') + +Fprime = linearize(F, u, trials=du) + +# Variational problem +newton = find(du, forall=v, lhs=Fprime(du, v,u=uk), rhs=-F(v,u=uk)) +``` + diff --git a/_sources/chapter3/navier-stokes-steady-streamfunction-velocity.md b/_sources/chapter3/navier-stokes-steady-streamfunction-velocity.md new file mode 100644 index 0000000..2569a83 --- /dev/null +++ b/_sources/chapter3/navier-stokes-steady-streamfunction-velocity.md @@ -0,0 +1,36 @@ +# The streamfunction-velocity formulation of the steady-state Navier-Stokes equations for incompressible fluids + +When $\Omega$ is a simply connected 2D domain, there exists a unique function $\psi$ such that $\mathbf{u} = \boldsymbol{\nabla} \times \psi:= \left( \partial_y \psi, - \partial_x \psi \right)$; +substituting this expression for $\mathbf{u}$ into \eqref{eq:steady-navier-stokes} leads to the so-called ``streamfunction-velocity formulation'' of the steady-state Navier-Stokes equations for an incompressible fluid. +For more details we refer the reader to \cite{TAGLIABUE2014277}. +The variational formulation is then given by: + +$$ +\begin{align} + \text{find $\psi \in V$ such that} \quad + a(\psi,\phi) + b(\psi,\phi;\psi) = l(\phi) + \quad \forall \phi \in V, +\end{align} +$$ + +where $V \subset H^2(\Omega)$ and + +$$ +\begin{align*} + a(\psi, \phi) := \int_{\Omega} D\left( \boldsymbol{\nabla} \times \psi \right) : D\left(\boldsymbol{\nabla} \times \phi \right) ~d\Omega, + \quad + b(\psi, \phi; \xi) := \int_{\Omega} \left( \left(\boldsymbol{\nabla} \times \xi \cdot \nabla \right) \boldsymbol{\nabla} \times \psi \right) \cdot \boldsymbol{\nabla} \times \phi ~d\Omega, + \quad + l(\phi) := \int_{\Omega} \mathbf{f} \cdot \boldsymbol{\nabla} \times \phi ~d\Omega. +\end{align*} +$$ + +%As in the previous example, one can use a Picard method, by considering $\xi$ as a \texttt{Field} in Eq. \ref{eq:steady-streamfunction-velocity-vf-a}, which will lead to the Python code described in \ref{code:steady-streamfunction-velocity-picard}. %, or consider $a$ as a \texttt{LinearForm} where $\xi = \psi$ are \texttt{Field} objects, and use the \texttt{NewtonIteration} constructor to get a \texttt{BilinearForm}, as described in the Python code \ref{code:steady-streamfunction-velocity-newton}. + + +## Linearization of the streamfunction-velocity linear form + +In the sequel, we use SymPDE to linearize the streamfunction-velocity formulation, starting from a \texttt{LinearForm}. +As presented in the previous example, we shall write our weak formulation as a linear form where the velocity $\mathbf{u}$ (\textit{i.e.} \texttt{u}) is considered as a \textit{field}, which is implemented in Python code \ref{code:steady-navier-stokes-nl}. +Using the function \texttt{linearize} allows us to construct the bilinear form associated to the linearization of the given linear form, around the field \texttt{psi}, see Python code \ref{code:steady-streamfunction-velocity-lin}. +To get an \texttt{Equation}, the user can add the left-hand-side for the Navier-Stokes equation to the linear form, the appropriate essential boundary conditions, then use the \texttt{NewtonIteration} as presented in the previous example. diff --git a/_sources/chapter3/navier-stokes-steady.md b/_sources/chapter3/navier-stokes-steady.md new file mode 100644 index 0000000..60e6a93 --- /dev/null +++ b/_sources/chapter3/navier-stokes-steady.md @@ -0,0 +1,41 @@ +# the steady-state Navier-Stokes equations for incompressible fluids + +The steady-state Navier Stokes problem for an incompressible fluid, with homogeneous Dirichlet boundary conditions (``no slip'' condition), is defined as + +$$ +\begin{equation} +\left\{ +\begin{aligned} + \left( \mathbf{u} \cdot \nabla \right) \mathbf{u} + \nabla p - 2 \nabla \cdot \left( \frac{1}{R_e} D\left( \mathbf{u} \right) \right) &= \mathbf{f} && \text{in $\Omega$}, + \\ + \nabla \cdot \mathbf{u} &= 0 && \text{in $\Omega$}, + \\ + \mathbf{u} &= 0 && \text{on $\partial\Omega$}, +\end{aligned} +\right. +\end{equation} +$$ + +where $R_e$ is the Reynolds number and $D\left( \mathbf{u} \right) := \frac{1}{2}\left( \nabla \mathbf{u} + \nabla \mathbf{u}^T \right)$ is the strain rate tensor. +The weak formulation reads + +$$ +\begin{align} + \text{find $\mathbf{u} \in W$ such that} \quad + a(\mathbf{u},\mathbf{v}) + b(\mathbf{u},\mathbf{v};\mathbf{u}) = l(\mathbf{v}) \quad + \forall \mathbf{v} \in W +\end{align} +$$ + +where $W \subset \{ \mathbf{v} \in \mathbf{H}_0^1(\Omega): \nabla \cdot \mathbf{v} = 0 \}$ and + +$$ +\begin{align*} + a(\mathbf{u}, \mathbf{v}) := \frac{2}{R_e} \int_{\Omega} D\left( \mathbf{u} \right) : D\left(\mathbf{v} \right) ~d\Omega, + \quad + b(\mathbf{u}, \mathbf{v}; \mathbf{w}) := \int_{\Omega} \left( \left( \mathbf{w} \cdot \nabla \right) \mathbf{u} \right) \cdot \mathbf{v} ~d\Omega, + \quad + l(\mathbf{v}) := \int_{\Omega} \mathbf{f} \cdot \mathbf{v} ~d\Omega. +\end{align*} +$$ + diff --git a/_sources/chapter3/poisson.md b/_sources/chapter3/poisson.md new file mode 100644 index 0000000..5f4671c --- /dev/null +++ b/_sources/chapter3/poisson.md @@ -0,0 +1,145 @@ +# Nonlinear Poisson in 2D + +In this section, we consider the non-linear Poisson problem: + +$$ +\begin{align} +-\nabla \cdot \left( (1+u^2) \nabla u \right) &= f, \Omega +\\ +u &= 0, \partial \Omega +\end{align} +$$ + +where $\Omega$ denotes the unit square. + +For testing, we shall take a function $u$ that fulfills the boundary condition, the compute $f$ as + +$$ +f(x,y) = -\nabla^2 u - F(u) +$$ + +The weak formulation is + +$$ +\int_{\Omega} (1+u^2) \nabla u \cdot \nabla v ~ d\Omega = \int_{\Omega} f v ~d\Omega, \quad \forall v \in \mathcal{V} +$$ + +For the sack of generality, we shall consider the linear form + +$$ +G(v;u,w) := \int_{\Omega} (1+w^2) \nabla u \cdot \nabla v ~ d\Omega, \quad \forall u,v,w \in \mathcal{V} +$$ + +Our problem is then + +$$ +\begin{align} +\mbox{Find } u \in \mathcal{V}, \mbox{such that}\\ +G(v;u,u) = l(v), \quad \forall v \in \mathcal{V} +\end{align} +$$ + +where + +$$ +l(v) := \int_{\Omega} f v ~d\Omega, \quad \forall v \in \mathcal{V} +$$ + +As usual, we'll follow the classical steps, + +1. Create a domain +2. Create the Function space +3. Define the different linear/bilinear forms +4. Define the Picard/Newton iteration + +## 1. The topological domain +```python +domain = Square() +B_dirichlet_0 = domain.boundary +``` +## 2. Function space +```python +V = ScalarFunctionSpace('V', domain) +``` +## 3.1. Define the Linear form $G$ +```python +u = element_of(V, name='u') +v = element_of(V, name='v') +w = element_of(V, name='w') + +# Linear form g: V --> R +g = LinearForm(v, integral(domain, (1+w**2)*dot(grad(u), grad(v)))) +``` +## 3.2. Define the linear form $L$ +```python +solution = sin(pi*x)*sin(pi*y) +f = 2*pi**2*(sin(pi*x)**2*sin(pi*y)**2 + 1)*sin(pi*x)*sin(pi*y) - 2*pi**2*sin(pi*x)**3*sin(pi*y)*cos(pi*y)**2 - 2*pi**2*sin(pi*x)*sin(pi*y)**3*cos(pi*x)**2 + +# Linear form l: V --> R +l = LinearForm(v, integral(domain, f * v)) +``` +## 4.1. Picard iteration + +$$ +\begin{align} +\mbox{Find } u_{n+1} \in \mathcal{V}\_h, \mbox{such that}\\ +G(v;u_{n+1},u_n) = l(v), \quad \forall v \in \mathcal{V}\_h +\end{align} +$$ + +The Picard iteration for our problem can be created this way + +```python +un = element_of(V, name='un') + +# Bilinear form a: V x V --> R +a = BilinearForm((u, v), g(v, u=u,w=un)) + +# Dirichlet boundary conditions +bc = [EssentialBC(u, 0, B_dirichlet_0)] + +# Variational problem +equation = find(u, forall=v, lhs=a(u, v), rhs=l(v), bc=bc) + +# Error norms +error = u - solution +l2norm = Norm(error, domain, kind='l2') +``` +## 4.2. Newton iteration +Let's define + +$$ +F(v;u) := G(v;u,u) -l(v), \quad \forall v \in \mathcal{V} +$$ + +Newton method writes + +$$ +\begin{align} +\mbox{Find } u_{n+1} \in \mathcal{V}\_h, \mbox{such that} \\ +F^{\prime}(\delta u,v; u_n) = - F(v;u_n), \quad \forall v \in \mathcal{V}, \\ +u_{n+1} := u_{n} + \delta u, \quad \delta u \in \mathcal{V} +\end{align} +$$ + +### Computing $F^{\prime}$ the derivative of $F$ + +**SymPDE** allows you to linearize a linear form and get a bilinear form, using the function **linearize** + +```python +F = LinearForm(v, g(v,w=u)-l(v)) +du = element_of(V, name='du') + +Fprime = linearize(F, u, trials=du) +``` + +The Newton iteration is then defined as follows, + +```python +# Dirichlet boundary conditions +bc = [EssentialBC(du, 0, B_dirichlet_0)] + +# Variational problem +equation = find(du, forall=v, lhs=Fprime(du, v,u=un), rhs=-F(v,u=un), bc=bc) +``` + diff --git a/_sources/chapter4/poisson-nitsche.md b/_sources/chapter4/poisson-nitsche.md new file mode 100644 index 0000000..a9920de --- /dev/null +++ b/_sources/chapter4/poisson-nitsche.md @@ -0,0 +1,45 @@ +# The Poisson problem using Nitsche method + +In this section, we consider a domain $\Omega$ which a union of multiple subdomain, *i.e.* + +$$ +\Omega := \bigcup_{i=1}^n \Omega_i, \quad \Omega_i \bigcap \Omega_j = \emptyset, ~ i \neq j +$$ + +We shall denote by $\mathcal{I}$ the set of all internal interfaces of $\Omega$. + +We shall also need the following operators + +- The jump of the function $u$, defined as $[\![ u ]\!] := u|\_{\Omega_{i_1}} - u|\_{\Omega_{i_2}}$ for two adjacent subdomains $\Omega_{i_1}$ and $\Omega_{i_2}$ +- The average of the function $u$, defined as $\{u\} := \frac{1}{2} \left( u|\_{\Omega_{i_1}} + u|\_{\Omega_{i_2}} \right)$ for two adjacent subdomains $\Omega_{i_1}$ and $\Omega_{i_2}$ + +We consider the Poisson equation + +$$ +\begin{align} + - \nabla^2 u = f \quad \text{in~$\Omega$}, \quad \quad + u = 0 \quad \text{on~$\partial \Omega$}, \quad \quad + [\![ u ]\!] = 0 \quad \text{on~$\mathcal{I}$}, \quad \quad + [\![\partial_n u ]\!] = 0 \quad \text{on~$\mathcal{I}$}. +\end{align} +$$ + +The variational formulation reads + +$$ +\begin{align} + \text{find $u \in V$ such that} \quad a(u,v) = l(v) \quad \forall v \in V, +\end{align} +$$ + +where + +- $V \subset H^1(\Omega)$, +- $a(u,v) := \int_{\Omega} \nabla u \cdot \nabla v ~ d\Omega + \int_{\mathcal{I}} \left( \kappa [\![ u ]\!] ~ [\![ v ]\!] - [\![ u ]\!] ~ \partial_n v - \partial_n u ~ [\![ v ]\!] \right) ~ d\mathcal{I} $, +- $l(v) := \int_{\Omega} f v ~ d\Omega ~ d\Gamma$. + +## Examples + +- [Poisson on a square with two subdomains and Homogeneous Boundary Conditions](https://github.com/pyccel/sympde/blob/devel-documentation/docs/examples/2d_poisson_subdomains_nitsche_dir0.py) + + diff --git a/_sources/chapter4/subdomains.md b/_sources/chapter4/subdomains.md new file mode 100644 index 0000000..a6dcdc5 --- /dev/null +++ b/_sources/chapter4/subdomains.md @@ -0,0 +1 @@ +# Subdomains diff --git a/_sources/intro.md b/_sources/intro.md new file mode 100644 index 0000000..02df7d4 --- /dev/null +++ b/_sources/intro.md @@ -0,0 +1,6 @@ +# IGA-Python + +Welcome to IGA-Python, a tutorial for Isogeometric Analysis using Python. + +```{tableofcontents} +``` diff --git a/_sphinx_design_static/design-style.1e8bd061cd6da7fc9cf755528e8ffc24.min.css b/_sphinx_design_static/design-style.1e8bd061cd6da7fc9cf755528e8ffc24.min.css new file mode 100644 index 0000000..eb19f69 --- /dev/null +++ b/_sphinx_design_static/design-style.1e8bd061cd6da7fc9cf755528e8ffc24.min.css @@ -0,0 +1 @@ +.sd-bg-primary{background-color:var(--sd-color-primary) !important}.sd-bg-text-primary{color:var(--sd-color-primary-text) !important}button.sd-bg-primary:focus,button.sd-bg-primary:hover{background-color:var(--sd-color-primary-highlight) !important}a.sd-bg-primary:focus,a.sd-bg-primary:hover{background-color:var(--sd-color-primary-highlight) 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{ + display: inline; +} + +div.related li.right { + float: right; + margin-right: 5px; +} + +/* -- sidebar --------------------------------------------------------------- */ + +div.sphinxsidebarwrapper { + padding: 10px 5px 0 10px; +} + +div.sphinxsidebar { + float: left; + width: 270px; + margin-left: -100%; + font-size: 90%; + word-wrap: break-word; + overflow-wrap : break-word; +} + +div.sphinxsidebar ul { + list-style: none; +} + +div.sphinxsidebar ul ul, +div.sphinxsidebar ul.want-points { + margin-left: 20px; + list-style: square; +} + +div.sphinxsidebar ul ul { + margin-top: 0; + margin-bottom: 0; +} + +div.sphinxsidebar form { + margin-top: 10px; +} + +div.sphinxsidebar input { + border: 1px solid #98dbcc; + font-family: sans-serif; + font-size: 1em; +} + +div.sphinxsidebar #searchbox form.search { + overflow: hidden; +} + +div.sphinxsidebar #searchbox input[type="text"] { + float: left; + width: 80%; + padding: 0.25em; + box-sizing: border-box; +} + +div.sphinxsidebar #searchbox input[type="submit"] { + float: left; + width: 20%; + border-left: none; + padding: 0.25em; + box-sizing: border-box; +} + + +img { + border: 0; + max-width: 100%; +} + +/* -- search page ----------------------------------------------------------- */ + +ul.search { + margin: 10px 0 0 20px; + padding: 0; +} + +ul.search li { + padding: 5px 0 5px 20px; + background-image: url(file.png); + background-repeat: no-repeat; + background-position: 0 7px; +} + +ul.search li a { + font-weight: bold; +} + +ul.search li p.context { + color: #888; + margin: 2px 0 0 30px; + text-align: left; +} + +ul.keywordmatches li.goodmatch a { + font-weight: bold; +} + +/* -- index page ------------------------------------------------------------ */ + +table.contentstable { + width: 90%; + margin-left: auto; + margin-right: auto; +} + +table.contentstable p.biglink { + line-height: 150%; +} + +a.biglink { + font-size: 1.3em; +} + +span.linkdescr { + font-style: italic; + padding-top: 5px; + font-size: 90%; +} + +/* -- general index --------------------------------------------------------- */ + +table.indextable { + width: 100%; +} + +table.indextable td { + text-align: left; + vertical-align: top; +} + +table.indextable ul { + margin-top: 0; + margin-bottom: 0; + list-style-type: none; +} + +table.indextable > tbody > tr > td > ul { + padding-left: 0em; +} + +table.indextable tr.pcap { + height: 10px; +} + +table.indextable tr.cap { + margin-top: 10px; + background-color: #f2f2f2; +} + +img.toggler { + margin-right: 3px; + margin-top: 3px; + cursor: pointer; +} + +div.modindex-jumpbox { + border-top: 1px solid #ddd; + border-bottom: 1px solid #ddd; + margin: 1em 0 1em 0; + padding: 0.4em; +} + +div.genindex-jumpbox { + border-top: 1px solid #ddd; + border-bottom: 1px solid #ddd; + margin: 1em 0 1em 0; + padding: 0.4em; +} + +/* -- domain module index --------------------------------------------------- */ + +table.modindextable td { + padding: 2px; + border-collapse: collapse; +} + +/* -- general body styles --------------------------------------------------- */ + +div.body { + min-width: 360px; + max-width: 800px; +} + +div.body p, div.body dd, div.body li, div.body blockquote { + -moz-hyphens: auto; + -ms-hyphens: auto; + -webkit-hyphens: auto; + hyphens: auto; +} + +a.headerlink { + visibility: hidden; +} + +a:visited { + color: #551A8B; +} + +h1:hover > a.headerlink, +h2:hover > a.headerlink, +h3:hover > a.headerlink, +h4:hover > a.headerlink, +h5:hover > a.headerlink, +h6:hover > a.headerlink, +dt:hover > a.headerlink, +caption:hover > a.headerlink, +p.caption:hover > a.headerlink, +div.code-block-caption:hover > a.headerlink { + visibility: visible; +} + +div.body p.caption { + text-align: inherit; +} + +div.body td { + text-align: left; +} + +.first { + margin-top: 0 !important; +} + +p.rubric { + margin-top: 30px; + font-weight: bold; +} + +img.align-left, figure.align-left, .figure.align-left, object.align-left { + clear: left; + float: left; + margin-right: 1em; +} + +img.align-right, figure.align-right, .figure.align-right, object.align-right { + clear: right; + float: right; + margin-left: 1em; +} + +img.align-center, figure.align-center, .figure.align-center, object.align-center { + display: block; + margin-left: auto; + margin-right: auto; +} + +img.align-default, figure.align-default, .figure.align-default { + display: block; + margin-left: auto; + margin-right: auto; +} + +.align-left { + text-align: left; +} + +.align-center { + text-align: center; +} + +.align-default { + text-align: center; +} + +.align-right { + text-align: right; +} + +/* -- sidebars -------------------------------------------------------------- */ + +div.sidebar, +aside.sidebar { + margin: 0 0 0.5em 1em; + border: 1px solid #ddb; + padding: 7px; + background-color: #ffe; + width: 40%; + float: right; + clear: right; + overflow-x: auto; +} + +p.sidebar-title { + font-weight: bold; +} + +nav.contents, +aside.topic, +div.admonition, div.topic, blockquote { + clear: left; +} + +/* -- topics ---------------------------------------------------------------- */ + +nav.contents, +aside.topic, +div.topic { + border: 1px solid #ccc; + padding: 7px; + margin: 10px 0 10px 0; +} + +p.topic-title { + font-size: 1.1em; + font-weight: bold; + margin-top: 10px; +} + +/* -- admonitions ----------------------------------------------------------- */ + +div.admonition { + margin-top: 10px; + margin-bottom: 10px; + padding: 7px; +} + +div.admonition dt { + font-weight: bold; +} + +p.admonition-title { + margin: 0px 10px 5px 0px; + font-weight: bold; +} + +div.body p.centered { + text-align: center; + margin-top: 25px; +} + +/* -- content of sidebars/topics/admonitions -------------------------------- */ + +div.sidebar > :last-child, +aside.sidebar > :last-child, +nav.contents > :last-child, +aside.topic > :last-child, +div.topic > :last-child, +div.admonition > :last-child { + margin-bottom: 0; +} + +div.sidebar::after, +aside.sidebar::after, +nav.contents::after, +aside.topic::after, +div.topic::after, +div.admonition::after, +blockquote::after { + display: block; + content: ''; + clear: both; +} + +/* -- tables ---------------------------------------------------------------- */ + +table.docutils { + margin-top: 10px; + margin-bottom: 10px; + border: 0; + border-collapse: collapse; +} + +table.align-center { + margin-left: auto; + margin-right: auto; +} + +table.align-default { + margin-left: auto; + margin-right: auto; +} + +table caption span.caption-number { + font-style: italic; +} + +table caption span.caption-text { +} + +table.docutils td, table.docutils th { + padding: 1px 8px 1px 5px; + border-top: 0; + border-left: 0; + border-right: 0; + border-bottom: 1px solid #aaa; +} + +th { + text-align: left; + padding-right: 5px; +} + +table.citation { + border-left: solid 1px gray; + margin-left: 1px; +} + +table.citation td { + border-bottom: none; +} + +th > :first-child, +td > :first-child { + margin-top: 0px; +} + +th > :last-child, +td > :last-child { + margin-bottom: 0px; +} + +/* -- figures --------------------------------------------------------------- */ + +div.figure, figure { + margin: 0.5em; + padding: 0.5em; +} + +div.figure p.caption, figcaption { + padding: 0.3em; +} + +div.figure p.caption span.caption-number, +figcaption span.caption-number { + font-style: italic; +} + +div.figure p.caption span.caption-text, +figcaption span.caption-text { +} + +/* -- field list styles ----------------------------------------------------- */ + +table.field-list td, table.field-list th { + border: 0 !important; +} + +.field-list ul { + margin: 0; + padding-left: 1em; +} + +.field-list p { + margin: 0; +} + +.field-name { + -moz-hyphens: manual; + -ms-hyphens: manual; + -webkit-hyphens: manual; + hyphens: manual; +} + +/* -- hlist styles ---------------------------------------------------------- */ + +table.hlist { + margin: 1em 0; +} + +table.hlist td { + vertical-align: top; +} + +/* -- object description styles --------------------------------------------- */ + +.sig { + font-family: 'Consolas', 'Menlo', 'DejaVu Sans Mono', 'Bitstream Vera Sans Mono', monospace; +} + +.sig-name, code.descname { + background-color: transparent; + font-weight: bold; +} + +.sig-name { + font-size: 1.1em; +} + +code.descname { + font-size: 1.2em; +} + +.sig-prename, code.descclassname { + background-color: transparent; +} + +.optional { + font-size: 1.3em; +} + +.sig-paren { + font-size: larger; +} + +.sig-param.n { + font-style: italic; +} + +/* C++ specific styling */ + +.sig-inline.c-texpr, +.sig-inline.cpp-texpr { + font-family: unset; +} + +.sig.c .k, .sig.c .kt, +.sig.cpp .k, .sig.cpp .kt { + color: #0033B3; +} + +.sig.c .m, +.sig.cpp .m { + color: #1750EB; +} + +.sig.c .s, .sig.c .sc, +.sig.cpp .s, .sig.cpp .sc { + color: #067D17; +} + + +/* -- other body styles ----------------------------------------------------- */ + +ol.arabic { + list-style: decimal; +} + +ol.loweralpha { + list-style: lower-alpha; +} + +ol.upperalpha { + list-style: upper-alpha; +} + +ol.lowerroman { + list-style: lower-roman; +} + +ol.upperroman { + list-style: upper-roman; +} + +:not(li) > ol > li:first-child > :first-child, +:not(li) > ul > li:first-child > :first-child { + margin-top: 0px; +} + +:not(li) > ol > li:last-child > :last-child, +:not(li) > ul > li:last-child > :last-child { + margin-bottom: 0px; +} + +ol.simple ol p, +ol.simple ul p, +ul.simple ol p, +ul.simple ul p { + margin-top: 0; +} + +ol.simple > li:not(:first-child) > p, +ul.simple > li:not(:first-child) > p { + margin-top: 0; +} + +ol.simple p, +ul.simple p { + margin-bottom: 0; +} + +aside.footnote > span, +div.citation > span { + float: left; +} +aside.footnote > span:last-of-type, +div.citation > span:last-of-type { + padding-right: 0.5em; +} +aside.footnote > p { + margin-left: 2em; +} +div.citation > p { + margin-left: 4em; +} +aside.footnote > p:last-of-type, +div.citation > p:last-of-type { + margin-bottom: 0em; +} +aside.footnote > p:last-of-type:after, +div.citation > p:last-of-type:after { + content: ""; + clear: both; +} + +dl.field-list { + display: grid; + grid-template-columns: fit-content(30%) auto; +} + +dl.field-list > dt { + font-weight: bold; + word-break: break-word; + padding-left: 0.5em; + padding-right: 5px; +} + +dl.field-list > dd { + padding-left: 0.5em; + margin-top: 0em; + margin-left: 0em; + margin-bottom: 0em; +} + +dl { + margin-bottom: 15px; +} + +dd > :first-child { + margin-top: 0px; +} + +dd ul, dd table { + margin-bottom: 10px; +} + +dd { + margin-top: 3px; + margin-bottom: 10px; + margin-left: 30px; +} + +.sig dd { + margin-top: 0px; + margin-bottom: 0px; +} + +.sig dl { + margin-top: 0px; + margin-bottom: 0px; +} + +dl > dd:last-child, +dl > dd:last-child > :last-child { + margin-bottom: 0; +} + +dt:target, span.highlighted { + background-color: #fbe54e; +} + +rect.highlighted { + fill: #fbe54e; +} + +dl.glossary dt { + font-weight: bold; + font-size: 1.1em; +} + +.versionmodified { + font-style: italic; +} + +.system-message { + background-color: #fda; + padding: 5px; + border: 3px solid red; +} + +.footnote:target { + background-color: #ffa; +} + +.line-block { + display: block; + margin-top: 1em; + margin-bottom: 1em; +} + +.line-block .line-block { + margin-top: 0; + margin-bottom: 0; + margin-left: 1.5em; +} + +.guilabel, .menuselection { + font-family: sans-serif; +} + +.accelerator { + text-decoration: underline; +} + +.classifier { + font-style: oblique; +} + +.classifier:before { + font-style: normal; + margin: 0 0.5em; + content: ":"; + display: inline-block; +} + +abbr, acronym { + border-bottom: dotted 1px; + cursor: help; +} + +.translated { + background-color: rgba(207, 255, 207, 0.2) +} + +.untranslated { + background-color: rgba(255, 207, 207, 0.2) +} + +/* -- code displays --------------------------------------------------------- */ + +pre { + overflow: auto; + overflow-y: hidden; /* fixes display issues on Chrome browsers */ +} + +pre, div[class*="highlight-"] { + clear: both; +} + +span.pre { + -moz-hyphens: none; + -ms-hyphens: none; + -webkit-hyphens: none; + hyphens: none; + white-space: nowrap; +} + +div[class*="highlight-"] { + margin: 1em 0; +} + +td.linenos pre { + border: 0; + background-color: transparent; + color: #aaa; +} + +table.highlighttable { + display: block; +} + +table.highlighttable tbody { + display: block; +} + +table.highlighttable tr { + display: flex; +} + +table.highlighttable td { + margin: 0; + padding: 0; +} + +table.highlighttable td.linenos { + padding-right: 0.5em; +} + +table.highlighttable td.code { + flex: 1; + overflow: hidden; +} + +.highlight .hll { + display: block; +} + +div.highlight pre, +table.highlighttable pre { + margin: 0; +} + +div.code-block-caption + div { + margin-top: 0; +} + +div.code-block-caption { + margin-top: 1em; + padding: 2px 5px; + font-size: small; +} + +div.code-block-caption code { + background-color: transparent; +} + +table.highlighttable td.linenos, +span.linenos, +div.highlight span.gp { /* gp: Generic.Prompt */ + user-select: none; + -webkit-user-select: text; /* Safari fallback only */ + -webkit-user-select: none; /* Chrome/Safari */ + -moz-user-select: none; /* Firefox */ + -ms-user-select: none; /* IE10+ */ +} + +div.code-block-caption span.caption-number { + padding: 0.1em 0.3em; + font-style: italic; +} + +div.code-block-caption span.caption-text { +} + +div.literal-block-wrapper { + margin: 1em 0; +} + +code.xref, a code { + background-color: transparent; + font-weight: bold; +} + +h1 code, h2 code, h3 code, h4 code, h5 code, h6 code { + background-color: transparent; +} + +.viewcode-link { + float: right; +} + +.viewcode-back { + float: right; + font-family: sans-serif; +} + +div.viewcode-block:target { + margin: -1px -10px; + padding: 0 10px; +} + +/* -- math display ---------------------------------------------------------- */ + +img.math { + vertical-align: middle; +} + +div.body div.math p { + text-align: center; +} + +span.eqno { + float: right; +} + +span.eqno a.headerlink { + position: absolute; + z-index: 1; +} + +div.math:hover a.headerlink { + visibility: visible; +} + +/* -- printout stylesheet --------------------------------------------------- */ + +@media print { + div.document, + div.documentwrapper, + div.bodywrapper { + margin: 0 !important; + width: 100%; + } + + div.sphinxsidebar, + div.related, + div.footer, + #top-link { + display: none; + } +} \ No newline at end of file diff --git a/_static/check-solid.svg b/_static/check-solid.svg new file mode 100644 index 0000000..92fad4b --- /dev/null +++ b/_static/check-solid.svg @@ -0,0 +1,4 @@ + + + + diff --git a/_static/clipboard.min.js b/_static/clipboard.min.js new file mode 100644 index 0000000..54b3c46 --- /dev/null +++ b/_static/clipboard.min.js @@ -0,0 +1,7 @@ +/*! + * clipboard.js v2.0.8 + * https://clipboardjs.com/ + * + * Licensed MIT © Zeno Rocha + */ +!function(t,e){"object"==typeof exports&&"object"==typeof module?module.exports=e():"function"==typeof define&&define.amd?define([],e):"object"==typeof exports?exports.ClipboardJS=e():t.ClipboardJS=e()}(this,function(){return n={686:function(t,e,n){"use strict";n.d(e,{default:function(){return o}});var e=n(279),i=n.n(e),e=n(370),u=n.n(e),e=n(817),c=n.n(e);function a(t){try{return document.execCommand(t)}catch(t){return}}var f=function(t){t=c()(t);return a("cut"),t};var l=function(t){var e,n,o,r=1 + + + + diff --git a/_static/copybutton.css b/_static/copybutton.css new file mode 100644 index 0000000..f1916ec --- /dev/null +++ b/_static/copybutton.css @@ -0,0 +1,94 @@ +/* Copy buttons */ +button.copybtn { + position: absolute; + display: flex; + top: .3em; + right: .3em; + width: 1.7em; + height: 1.7em; + opacity: 0; + transition: opacity 0.3s, border .3s, background-color .3s; + user-select: none; + padding: 0; + border: none; + outline: none; + border-radius: 0.4em; + /* The colors that GitHub uses */ + border: #1b1f2426 1px solid; + background-color: #f6f8fa; + color: #57606a; +} + +button.copybtn.success { + border-color: #22863a; + color: #22863a; +} + +button.copybtn svg { + stroke: currentColor; + width: 1.5em; + height: 1.5em; + padding: 0.1em; +} + +div.highlight { + position: relative; +} + +/* Show the copybutton */ +.highlight:hover button.copybtn, button.copybtn.success { + opacity: 1; +} + +.highlight button.copybtn:hover { + background-color: rgb(235, 235, 235); +} + +.highlight button.copybtn:active { + background-color: rgb(187, 187, 187); +} + +/** + * A minimal CSS-only tooltip copied from: + * https://codepen.io/mildrenben/pen/rVBrpK + * + * To use, write HTML like the following: + * + *

Short

+ */ + .o-tooltip--left { + position: relative; + } + + .o-tooltip--left:after { + opacity: 0; + visibility: hidden; + position: absolute; + content: attr(data-tooltip); + padding: .2em; + font-size: .8em; + left: -.2em; + background: grey; + color: white; + white-space: nowrap; + z-index: 2; + border-radius: 2px; + transform: translateX(-102%) translateY(0); + transition: opacity 0.2s cubic-bezier(0.64, 0.09, 0.08, 1), transform 0.2s cubic-bezier(0.64, 0.09, 0.08, 1); +} + +.o-tooltip--left:hover:after { + display: block; + opacity: 1; + visibility: visible; + transform: translateX(-100%) translateY(0); + transition: opacity 0.2s cubic-bezier(0.64, 0.09, 0.08, 1), transform 0.2s cubic-bezier(0.64, 0.09, 0.08, 1); + transition-delay: .5s; +} + +/* By default the copy button shouldn't show up when printing a page */ +@media print { + button.copybtn { + display: none; + } +} diff --git a/_static/copybutton.js b/_static/copybutton.js new file mode 100644 index 0000000..2ea7ff3 --- /dev/null +++ b/_static/copybutton.js @@ -0,0 +1,248 @@ +// Localization support +const messages = { + 'en': { + 'copy': 'Copy', + 'copy_to_clipboard': 'Copy to clipboard', + 'copy_success': 'Copied!', + 'copy_failure': 'Failed to copy', + }, + 'es' : { + 'copy': 'Copiar', + 'copy_to_clipboard': 'Copiar al portapapeles', + 'copy_success': '¡Copiado!', + 'copy_failure': 'Error al copiar', + }, + 'de' : { + 'copy': 'Kopieren', + 'copy_to_clipboard': 'In die Zwischenablage kopieren', + 'copy_success': 'Kopiert!', + 'copy_failure': 'Fehler beim Kopieren', + }, + 'fr' : { + 'copy': 'Copier', + 'copy_to_clipboard': 'Copier dans le presse-papier', + 'copy_success': 'Copié !', + 'copy_failure': 'Échec de la copie', + }, + 'ru': { + 'copy': 'Скопировать', + 'copy_to_clipboard': 'Скопировать в буфер', + 'copy_success': 'Скопировано!', + 'copy_failure': 'Не удалось скопировать', + }, + 'zh-CN': { + 'copy': '复制', + 'copy_to_clipboard': '复制到剪贴板', + 'copy_success': '复制成功!', + 'copy_failure': '复制失败', + }, + 'it' : { + 'copy': 'Copiare', + 'copy_to_clipboard': 'Copiato negli appunti', + 'copy_success': 'Copiato!', + 'copy_failure': 'Errore durante la copia', + } +} + +let locale = 'en' +if( document.documentElement.lang !== undefined + && messages[document.documentElement.lang] !== undefined ) { + locale = document.documentElement.lang +} + +let doc_url_root = DOCUMENTATION_OPTIONS.URL_ROOT; +if (doc_url_root == '#') { + doc_url_root = ''; +} + +/** + * SVG files for our copy buttons + */ +let iconCheck = ` + ${messages[locale]['copy_success']} + + +` + +// If the user specified their own SVG use that, otherwise use the default +let iconCopy = ``; +if (!iconCopy) { + iconCopy = ` + ${messages[locale]['copy_to_clipboard']} + + + +` +} + +/** + * Set up copy/paste for code blocks + */ + +const runWhenDOMLoaded = cb => { + if (document.readyState != 'loading') { + cb() + } else if (document.addEventListener) { + document.addEventListener('DOMContentLoaded', cb) + } else { + document.attachEvent('onreadystatechange', function() { + if (document.readyState == 'complete') cb() + }) + } +} + +const codeCellId = index => `codecell${index}` + +// Clears selected text since ClipboardJS will select the text when copying +const clearSelection = () => { + if (window.getSelection) { + window.getSelection().removeAllRanges() + } else if (document.selection) { + document.selection.empty() + } +} + +// Changes tooltip text for a moment, then changes it back +// We want the timeout of our `success` class to be a bit shorter than the +// tooltip and icon change, so that we can hide the icon before changing back. +var timeoutIcon = 2000; +var timeoutSuccessClass = 1500; + +const temporarilyChangeTooltip = (el, oldText, newText) => { + el.setAttribute('data-tooltip', newText) + el.classList.add('success') + // Remove success a little bit sooner than we change the tooltip + // So that we can use CSS to hide the copybutton first + setTimeout(() => el.classList.remove('success'), timeoutSuccessClass) + setTimeout(() => el.setAttribute('data-tooltip', oldText), timeoutIcon) +} + +// Changes the copy button icon for two seconds, then changes it back +const temporarilyChangeIcon = (el) => { + el.innerHTML = iconCheck; + setTimeout(() => {el.innerHTML = iconCopy}, timeoutIcon) +} + +const addCopyButtonToCodeCells = () => { + // If ClipboardJS hasn't loaded, wait a bit and try again. This + // happens because we load ClipboardJS asynchronously. + if (window.ClipboardJS === undefined) { + setTimeout(addCopyButtonToCodeCells, 250) + return + } + + // Add copybuttons to all of our code cells + const COPYBUTTON_SELECTOR = 'div.highlight pre'; + const codeCells = document.querySelectorAll(COPYBUTTON_SELECTOR) + codeCells.forEach((codeCell, index) => { + const id = codeCellId(index) + codeCell.setAttribute('id', id) + + const clipboardButton = id => + `` + codeCell.insertAdjacentHTML('afterend', clipboardButton(id)) + }) + +function escapeRegExp(string) { + return string.replace(/[.*+?^${}()|[\]\\]/g, '\\$&'); // $& means the whole matched string +} + +/** + * Removes excluded text from a Node. + * + * @param {Node} target Node to filter. + * @param {string} exclude CSS selector of nodes to exclude. + * @returns {DOMString} Text from `target` with text removed. + */ +function filterText(target, exclude) { + const clone = target.cloneNode(true); // clone as to not modify the live DOM + if (exclude) { + // remove excluded nodes + clone.querySelectorAll(exclude).forEach(node => node.remove()); + } + return clone.innerText; +} + +// Callback when a copy button is clicked. Will be passed the node that was clicked +// should then grab the text and replace pieces of text that shouldn't be used in output +function formatCopyText(textContent, copybuttonPromptText, isRegexp = false, onlyCopyPromptLines = true, removePrompts = true, copyEmptyLines = true, lineContinuationChar = "", hereDocDelim = "") { + var regexp; + var match; + + // Do we check for line continuation characters and "HERE-documents"? + var useLineCont = !!lineContinuationChar + var useHereDoc = !!hereDocDelim + + // create regexp to capture prompt and remaining line + if (isRegexp) { + regexp = new RegExp('^(' + copybuttonPromptText + ')(.*)') + } else { + regexp = new RegExp('^(' + escapeRegExp(copybuttonPromptText) + ')(.*)') + } + + const outputLines = []; + var promptFound = false; + var gotLineCont = false; + var gotHereDoc = false; + const lineGotPrompt = []; + for (const line of textContent.split('\n')) { + match = line.match(regexp) + if (match || gotLineCont || gotHereDoc) { + promptFound = regexp.test(line) + lineGotPrompt.push(promptFound) + if (removePrompts && promptFound) { + outputLines.push(match[2]) + } else { + outputLines.push(line) + } + gotLineCont = line.endsWith(lineContinuationChar) & useLineCont + if (line.includes(hereDocDelim) & useHereDoc) + gotHereDoc = !gotHereDoc + } else if (!onlyCopyPromptLines) { + outputLines.push(line) + } else if (copyEmptyLines && line.trim() === '') { + outputLines.push(line) + } + } + + // If no lines with the prompt were found then just use original lines + if (lineGotPrompt.some(v => v === true)) { + textContent = outputLines.join('\n'); + } + + // Remove a trailing newline to avoid auto-running when pasting + if (textContent.endsWith("\n")) { + textContent = textContent.slice(0, -1) + } + return textContent +} + + +var copyTargetText = (trigger) => { + var target = document.querySelector(trigger.attributes['data-clipboard-target'].value); + + // get filtered text + let exclude = '.linenos'; + + let text = filterText(target, exclude); + return formatCopyText(text, '', false, true, true, true, '', '') +} + + // Initialize with a callback so we can modify the text before copy + const clipboard = new ClipboardJS('.copybtn', {text: copyTargetText}) + + // Update UI with error/success messages + clipboard.on('success', event => { + clearSelection() + temporarilyChangeTooltip(event.trigger, messages[locale]['copy'], messages[locale]['copy_success']) + temporarilyChangeIcon(event.trigger) + }) + + clipboard.on('error', event => { + temporarilyChangeTooltip(event.trigger, messages[locale]['copy'], messages[locale]['copy_failure']) + }) +} + +runWhenDOMLoaded(addCopyButtonToCodeCells) \ No newline at end of file diff --git a/_static/copybutton_funcs.js b/_static/copybutton_funcs.js new file mode 100644 index 0000000..dbe1aaa --- /dev/null +++ b/_static/copybutton_funcs.js @@ -0,0 +1,73 @@ +function escapeRegExp(string) { + return string.replace(/[.*+?^${}()|[\]\\]/g, '\\$&'); // $& means the whole matched string +} + +/** + * Removes excluded text from a Node. + * + * @param {Node} target Node to filter. + * @param {string} exclude CSS selector of nodes to exclude. + * @returns {DOMString} Text from `target` with text removed. + */ +export function filterText(target, exclude) { + const clone = target.cloneNode(true); // clone as to not modify the live DOM + if (exclude) { + // remove excluded nodes + clone.querySelectorAll(exclude).forEach(node => node.remove()); + } + return clone.innerText; +} + +// Callback when a copy button is clicked. Will be passed the node that was clicked +// should then grab the text and replace pieces of text that shouldn't be used in output +export function formatCopyText(textContent, copybuttonPromptText, isRegexp = false, onlyCopyPromptLines = true, removePrompts = true, copyEmptyLines = true, lineContinuationChar = "", hereDocDelim = "") { + var regexp; + var match; + + // Do we check for line continuation characters and "HERE-documents"? + var useLineCont = !!lineContinuationChar + var useHereDoc = !!hereDocDelim + + // create regexp to capture prompt and remaining line + if (isRegexp) { + regexp = new RegExp('^(' + copybuttonPromptText + ')(.*)') + } else { + regexp = new RegExp('^(' + escapeRegExp(copybuttonPromptText) + ')(.*)') + } + + const outputLines = []; + var promptFound = false; + var gotLineCont = false; + var gotHereDoc = false; + const lineGotPrompt = []; + for (const line of textContent.split('\n')) { + match = line.match(regexp) + if (match || gotLineCont || gotHereDoc) { + promptFound = regexp.test(line) + lineGotPrompt.push(promptFound) + if (removePrompts && promptFound) { + outputLines.push(match[2]) + } else { + outputLines.push(line) + } + gotLineCont = line.endsWith(lineContinuationChar) & useLineCont + if (line.includes(hereDocDelim) & useHereDoc) + gotHereDoc = !gotHereDoc + } else if (!onlyCopyPromptLines) { + outputLines.push(line) + } else if (copyEmptyLines && line.trim() === '') { + outputLines.push(line) + } + } + + // If no lines with the prompt were found then just use original lines + if (lineGotPrompt.some(v => v === true)) { + textContent = outputLines.join('\n'); + } + + // Remove a trailing newline to avoid auto-running when pasting + if (textContent.endsWith("\n")) { + textContent = textContent.slice(0, -1) + } + return textContent +} diff --git a/_static/design-style.1e8bd061cd6da7fc9cf755528e8ffc24.min.css b/_static/design-style.1e8bd061cd6da7fc9cf755528e8ffc24.min.css new file mode 100644 index 0000000..eb19f69 --- /dev/null +++ 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rgba(178, 206, 245, 0.62);--sd-color-tabs-underline-inactive: transparent;--sd-color-tabs-overline: rgb(222, 222, 222);--sd-color-tabs-underline: rgb(222, 222, 222);--sd-fontsize-tabs-label: 1rem} diff --git a/_static/design-tabs.js b/_static/design-tabs.js new file mode 100644 index 0000000..36b38cf --- /dev/null +++ b/_static/design-tabs.js @@ -0,0 +1,27 @@ +var sd_labels_by_text = {}; + +function ready() { + const li = document.getElementsByClassName("sd-tab-label"); + for (const label of li) { + syncId = label.getAttribute("data-sync-id"); + if (syncId) { + label.onclick = onLabelClick; + if (!sd_labels_by_text[syncId]) { + sd_labels_by_text[syncId] = []; + } + sd_labels_by_text[syncId].push(label); + } + } +} + +function onLabelClick() { + // Activate other inputs with the same sync id. + syncId = this.getAttribute("data-sync-id"); + for (label of sd_labels_by_text[syncId]) { + if (label === this) continue; + label.previousElementSibling.checked = true; + } + window.localStorage.setItem("sphinx-design-last-tab", syncId); +} + +document.addEventListener("DOMContentLoaded", ready, false); diff --git a/_static/doctools.js b/_static/doctools.js new file mode 100644 index 0000000..d06a71d --- /dev/null +++ b/_static/doctools.js @@ -0,0 +1,156 @@ +/* + * doctools.js + * ~~~~~~~~~~~ + * + * Base JavaScript utilities for all Sphinx HTML documentation. + * + * :copyright: Copyright 2007-2023 by the Sphinx team, see AUTHORS. + * :license: BSD, see LICENSE for details. + * + */ +"use strict"; + +const BLACKLISTED_KEY_CONTROL_ELEMENTS = new Set([ + "TEXTAREA", + "INPUT", + "SELECT", + "BUTTON", +]); + +const _ready = (callback) => { + if (document.readyState !== "loading") { + callback(); + } else { + document.addEventListener("DOMContentLoaded", callback); + } +}; + +/** + * Small JavaScript module for the documentation. + */ +const Documentation = { + init: () => { + Documentation.initDomainIndexTable(); + Documentation.initOnKeyListeners(); + }, + + /** + * i18n support + */ + TRANSLATIONS: {}, + PLURAL_EXPR: (n) => (n === 1 ? 0 : 1), + LOCALE: "unknown", + + // gettext and ngettext don't access this so that the functions + // can safely bound to a different name (_ = Documentation.gettext) + gettext: (string) => { + const translated = Documentation.TRANSLATIONS[string]; + switch (typeof translated) { + case "undefined": + return string; // no translation + case "string": + return translated; // translation exists + default: + return translated[0]; // (singular, plural) translation tuple exists + } + }, + + ngettext: (singular, plural, n) => { + const translated = Documentation.TRANSLATIONS[singular]; + if (typeof translated !== "undefined") + return translated[Documentation.PLURAL_EXPR(n)]; + return n === 1 ? singular : plural; + }, + + addTranslations: (catalog) => { + Object.assign(Documentation.TRANSLATIONS, catalog.messages); + Documentation.PLURAL_EXPR = new Function( + "n", + `return (${catalog.plural_expr})` + ); + Documentation.LOCALE = catalog.locale; + }, + + /** + * helper function to focus on search bar + */ + focusSearchBar: () => { + document.querySelectorAll("input[name=q]")[0]?.focus(); + }, + + /** + * Initialise the domain index toggle buttons + */ + initDomainIndexTable: () => { + const toggler = (el) => { + const idNumber = el.id.substr(7); + const toggledRows = document.querySelectorAll(`tr.cg-${idNumber}`); + if (el.src.substr(-9) === "minus.png") { + el.src = `${el.src.substr(0, el.src.length - 9)}plus.png`; + toggledRows.forEach((el) => (el.style.display = "none")); + } else { + el.src = `${el.src.substr(0, el.src.length - 8)}minus.png`; + toggledRows.forEach((el) => (el.style.display = "")); + } + }; + + const togglerElements = document.querySelectorAll("img.toggler"); + togglerElements.forEach((el) => + el.addEventListener("click", (event) => toggler(event.currentTarget)) + ); + togglerElements.forEach((el) => (el.style.display = "")); + if (DOCUMENTATION_OPTIONS.COLLAPSE_INDEX) togglerElements.forEach(toggler); + }, + + initOnKeyListeners: () => { + // only install a listener if it is really needed + if ( + !DOCUMENTATION_OPTIONS.NAVIGATION_WITH_KEYS && + !DOCUMENTATION_OPTIONS.ENABLE_SEARCH_SHORTCUTS + ) + return; + + document.addEventListener("keydown", (event) => { + // bail for input elements + if (BLACKLISTED_KEY_CONTROL_ELEMENTS.has(document.activeElement.tagName)) return; + // bail with special keys + if (event.altKey || event.ctrlKey || event.metaKey) return; + + if (!event.shiftKey) { + switch (event.key) { + case "ArrowLeft": + if (!DOCUMENTATION_OPTIONS.NAVIGATION_WITH_KEYS) break; + + const prevLink = document.querySelector('link[rel="prev"]'); + if (prevLink && prevLink.href) { + window.location.href = prevLink.href; + event.preventDefault(); + } + break; + case "ArrowRight": + if (!DOCUMENTATION_OPTIONS.NAVIGATION_WITH_KEYS) break; + + const nextLink = document.querySelector('link[rel="next"]'); + if (nextLink && nextLink.href) { + window.location.href = nextLink.href; + event.preventDefault(); + } + break; + } + } + + // some keyboard layouts may need Shift to get / + switch (event.key) { + case "/": + if (!DOCUMENTATION_OPTIONS.ENABLE_SEARCH_SHORTCUTS) break; + Documentation.focusSearchBar(); + event.preventDefault(); + } + }); + }, +}; + +// quick alias for translations +const _ = Documentation.gettext; + +_ready(Documentation.init); diff --git a/_static/documentation_options.js b/_static/documentation_options.js new file mode 100644 index 0000000..dab586c --- /dev/null +++ b/_static/documentation_options.js @@ -0,0 +1,13 @@ +const DOCUMENTATION_OPTIONS = { + VERSION: '', + LANGUAGE: 'en', + COLLAPSE_INDEX: false, + BUILDER: 'html', + FILE_SUFFIX: '.html', + LINK_SUFFIX: '.html', + HAS_SOURCE: true, + SOURCELINK_SUFFIX: '', + NAVIGATION_WITH_KEYS: false, + SHOW_SEARCH_SUMMARY: true, + ENABLE_SEARCH_SHORTCUTS: true, +}; \ No newline at end of file diff --git a/_static/file.png b/_static/file.png new file mode 100644 index 0000000..a858a41 Binary files /dev/null and b/_static/file.png differ diff --git a/_static/images/logo_binder.svg b/_static/images/logo_binder.svg new file mode 100644 index 0000000..45fecf7 --- /dev/null +++ b/_static/images/logo_binder.svg @@ -0,0 +1,19 @@ + + + + +logo + + + + + + + + diff --git a/_static/images/logo_colab.png b/_static/images/logo_colab.png new file mode 100644 index 0000000..b7560ec Binary files /dev/null and b/_static/images/logo_colab.png differ diff --git a/_static/images/logo_deepnote.svg b/_static/images/logo_deepnote.svg new file mode 100644 index 0000000..fa77ebf --- /dev/null +++ b/_static/images/logo_deepnote.svg @@ -0,0 +1 @@ + diff --git a/_static/images/logo_jupyterhub.svg b/_static/images/logo_jupyterhub.svg new file mode 100644 index 0000000..60cfe9f --- /dev/null +++ b/_static/images/logo_jupyterhub.svg @@ -0,0 +1 @@ +logo_jupyterhubHub diff --git a/_static/language_data.js b/_static/language_data.js new file mode 100644 index 0000000..250f566 --- /dev/null +++ b/_static/language_data.js @@ -0,0 +1,199 @@ +/* + * language_data.js + * ~~~~~~~~~~~~~~~~ + * + * This script contains the language-specific data used by searchtools.js, + * namely the list of stopwords, stemmer, scorer and splitter. + * + * :copyright: Copyright 2007-2023 by the Sphinx team, see AUTHORS. + * :license: BSD, see LICENSE for details. + * + */ + +var stopwords = ["a", "and", "are", "as", "at", "be", "but", "by", "for", "if", "in", "into", "is", "it", "near", "no", "not", "of", "on", "or", "such", "that", "the", "their", "then", "there", "these", "they", "this", "to", "was", "will", "with"]; + + +/* Non-minified version is copied as a separate JS file, is available */ + +/** + * Porter Stemmer + */ +var Stemmer = function() { + + var step2list = { + ational: 'ate', + tional: 'tion', + enci: 'ence', + anci: 'ance', + izer: 'ize', + bli: 'ble', + alli: 'al', + entli: 'ent', + eli: 'e', + ousli: 'ous', + ization: 'ize', + ation: 'ate', + ator: 'ate', + alism: 'al', + iveness: 'ive', + fulness: 'ful', + ousness: 'ous', + aliti: 'al', + iviti: 'ive', + biliti: 'ble', + logi: 'log' + }; + + var step3list = { + icate: 'ic', + ative: '', + alize: 'al', + iciti: 'ic', + ical: 'ic', + ful: '', + ness: '' + }; + + var c = "[^aeiou]"; // consonant + var v = "[aeiouy]"; // vowel + var C = c + "[^aeiouy]*"; // consonant sequence + var V = v + "[aeiou]*"; // vowel sequence + + var mgr0 = "^(" + C + ")?" + V + C; // [C]VC... is m>0 + var meq1 = "^(" + C + ")?" + V + C + "(" + V + ")?$"; // [C]VC[V] is m=1 + var mgr1 = "^(" + C + ")?" + V + C + V + C; // [C]VCVC... is m>1 + var s_v = "^(" + C + ")?" + v; // vowel in stem + + this.stemWord = function (w) { + var stem; + var suffix; + var firstch; + var origword = w; + + if (w.length < 3) + return w; + + var re; + var re2; + var re3; + var re4; + + firstch = w.substr(0,1); + if (firstch == "y") + w = firstch.toUpperCase() + w.substr(1); + + // Step 1a + re = /^(.+?)(ss|i)es$/; + re2 = /^(.+?)([^s])s$/; + + if (re.test(w)) + w = w.replace(re,"$1$2"); + else if (re2.test(w)) + w = w.replace(re2,"$1$2"); + + // Step 1b + re = /^(.+?)eed$/; + re2 = /^(.+?)(ed|ing)$/; + if (re.test(w)) { + var fp = re.exec(w); + re = new RegExp(mgr0); + if (re.test(fp[1])) { + re = /.$/; + w = w.replace(re,""); + } + } + else if (re2.test(w)) { + var fp = re2.exec(w); + stem = fp[1]; + re2 = new RegExp(s_v); + if (re2.test(stem)) { + w = stem; + re2 = /(at|bl|iz)$/; + re3 = new RegExp("([^aeiouylsz])\\1$"); + re4 = new RegExp("^" + C + v + "[^aeiouwxy]$"); + if (re2.test(w)) + w = w + "e"; + else if (re3.test(w)) { + re = /.$/; + w = w.replace(re,""); + } + else if (re4.test(w)) + w = w + "e"; + } + } + + // Step 1c + re = /^(.+?)y$/; + if (re.test(w)) { + var fp = re.exec(w); + stem = fp[1]; + re = new RegExp(s_v); + if (re.test(stem)) + w = stem + "i"; + } + + // Step 2 + re = /^(.+?)(ational|tional|enci|anci|izer|bli|alli|entli|eli|ousli|ization|ation|ator|alism|iveness|fulness|ousness|aliti|iviti|biliti|logi)$/; + if (re.test(w)) { + var fp = re.exec(w); + stem = fp[1]; + suffix = fp[2]; + re = new RegExp(mgr0); + if (re.test(stem)) + w = stem + step2list[suffix]; + } + + // Step 3 + re = /^(.+?)(icate|ative|alize|iciti|ical|ful|ness)$/; + if (re.test(w)) { + var fp = re.exec(w); + stem = fp[1]; + suffix = fp[2]; + re = new RegExp(mgr0); + if (re.test(stem)) + w = stem + step3list[suffix]; + } + + // Step 4 + re = /^(.+?)(al|ance|ence|er|ic|able|ible|ant|ement|ment|ent|ou|ism|ate|iti|ous|ive|ize)$/; + re2 = /^(.+?)(s|t)(ion)$/; + if (re.test(w)) { + var fp = re.exec(w); + stem = fp[1]; + re = new RegExp(mgr1); + if (re.test(stem)) + w = stem; + } + else if (re2.test(w)) { + var fp = re2.exec(w); + stem = fp[1] + fp[2]; + re2 = new RegExp(mgr1); + if (re2.test(stem)) + w = stem; + } + + // Step 5 + re = /^(.+?)e$/; + if (re.test(w)) { + var fp = re.exec(w); + stem = fp[1]; + re = new RegExp(mgr1); + re2 = new RegExp(meq1); + re3 = new RegExp("^" + C + v + "[^aeiouwxy]$"); + if (re.test(stem) || (re2.test(stem) && !(re3.test(stem)))) + w = stem; + } + re = /ll$/; + re2 = new RegExp(mgr1); + if (re.test(w) && re2.test(w)) { + re = /.$/; + w = w.replace(re,""); + } + + // and turn initial Y back to y + if (firstch == "y") + w = firstch.toLowerCase() + w.substr(1); + return w; + } +} + diff --git a/_static/locales/ar/LC_MESSAGES/booktheme.mo b/_static/locales/ar/LC_MESSAGES/booktheme.mo new file mode 100644 index 0000000..15541a6 Binary files /dev/null and b/_static/locales/ar/LC_MESSAGES/booktheme.mo differ diff --git a/_static/locales/ar/LC_MESSAGES/booktheme.po b/_static/locales/ar/LC_MESSAGES/booktheme.po new file mode 100644 index 0000000..edae2ec --- /dev/null +++ b/_static/locales/ar/LC_MESSAGES/booktheme.po @@ -0,0 +1,75 @@ + +msgid "" +msgstr "" +"Project-Id-Version: Sphinx-Book-Theme\n" +"MIME-Version: 1.0\n" +"Content-Type: text/plain; charset=UTF-8\n" +"Content-Transfer-Encoding: 8bit\n" +"Language: ar\n" +"Plural-Forms: nplurals=2; plural=(n != 1);\n" + +msgid "Theme by the" +msgstr "موضوع بواسطة" + +msgid "Open an issue" +msgstr "افتح قضية" + +msgid "Contents" +msgstr "محتويات" + +msgid "Download notebook file" +msgstr "تنزيل ملف دفتر الملاحظات" + +msgid "Sphinx Book Theme" +msgstr "موضوع كتاب أبو الهول" + +msgid "Fullscreen mode" +msgstr "وضع ملء الشاشة" + +msgid "Edit this page" +msgstr "قم بتحرير هذه الصفحة" + +msgid "By" +msgstr "بواسطة" + +msgid "Copyright" +msgstr "حقوق النشر" + +msgid "Source repository" +msgstr "مستودع المصدر" + +msgid "previous page" +msgstr "الصفحة السابقة" + +msgid "next page" +msgstr "الصفحة التالية" + +msgid "Toggle navigation" +msgstr "تبديل التنقل" + +msgid "repository" +msgstr "مخزن" + +msgid "suggest edit" +msgstr "أقترح تحرير" + +msgid "open issue" +msgstr "قضية مفتوحة" + +msgid "Launch" +msgstr "إطلاق" + +msgid "Print to PDF" +msgstr "طباعة إلى PDF" + +msgid "By the" +msgstr "بواسطة" + +msgid "Last updated on" +msgstr "آخر تحديث في" + +msgid "Download source file" +msgstr "تنزيل ملف المصدر" + +msgid "Download this page" +msgstr "قم بتنزيل هذه الصفحة" diff --git a/_static/locales/bg/LC_MESSAGES/booktheme.mo b/_static/locales/bg/LC_MESSAGES/booktheme.mo new file mode 100644 index 0000000..da95120 Binary files /dev/null and b/_static/locales/bg/LC_MESSAGES/booktheme.mo differ diff --git a/_static/locales/bg/LC_MESSAGES/booktheme.po b/_static/locales/bg/LC_MESSAGES/booktheme.po new file mode 100644 index 0000000..1f363b9 --- /dev/null +++ b/_static/locales/bg/LC_MESSAGES/booktheme.po @@ -0,0 +1,75 @@ + +msgid "" +msgstr "" +"Project-Id-Version: Sphinx-Book-Theme\n" +"MIME-Version: 1.0\n" +"Content-Type: text/plain; charset=UTF-8\n" +"Content-Transfer-Encoding: 8bit\n" +"Language: bg\n" +"Plural-Forms: nplurals=2; plural=(n != 1);\n" + +msgid "Theme by the" +msgstr "Тема от" + +msgid "Open an issue" +msgstr "Отворете проблем" + +msgid "Contents" +msgstr "Съдържание" + +msgid "Download notebook file" +msgstr "Изтеглете файла на бележника" + +msgid "Sphinx Book Theme" +msgstr "Тема на книгата Sphinx" + +msgid "Fullscreen mode" +msgstr "Режим на цял екран" + +msgid "Edit this page" +msgstr "Редактирайте тази страница" + +msgid "By" +msgstr "От" + +msgid "Copyright" +msgstr "Авторско право" + +msgid "Source repository" +msgstr "Хранилище на източника" + +msgid "previous page" +msgstr "предишна страница" + +msgid "next page" +msgstr "Следваща страница" + +msgid "Toggle navigation" +msgstr "Превключване на навигацията" + +msgid "repository" +msgstr "хранилище" + +msgid "suggest edit" +msgstr "предложи редактиране" + +msgid "open issue" +msgstr "отворен брой" + +msgid "Launch" +msgstr "Стартиране" + +msgid "Print to PDF" +msgstr "Печат в PDF" + +msgid "By the" +msgstr "По" + +msgid "Last updated on" +msgstr "Последна актуализация на" + +msgid "Download source file" +msgstr "Изтеглете изходния файл" + +msgid "Download this page" +msgstr "Изтеглете тази страница" diff --git a/_static/locales/bn/LC_MESSAGES/booktheme.mo b/_static/locales/bn/LC_MESSAGES/booktheme.mo new file mode 100644 index 0000000..6b96639 Binary files /dev/null and b/_static/locales/bn/LC_MESSAGES/booktheme.mo differ diff --git a/_static/locales/bn/LC_MESSAGES/booktheme.po b/_static/locales/bn/LC_MESSAGES/booktheme.po new file mode 100644 index 0000000..fa54372 --- /dev/null +++ b/_static/locales/bn/LC_MESSAGES/booktheme.po @@ -0,0 +1,63 @@ + +msgid "" +msgstr "" +"Project-Id-Version: Sphinx-Book-Theme\n" +"MIME-Version: 1.0\n" +"Content-Type: text/plain; charset=UTF-8\n" +"Content-Transfer-Encoding: 8bit\n" +"Language: bn\n" +"Plural-Forms: nplurals=2; plural=(n != 1);\n" + +msgid "Theme by the" +msgstr "থিম দ্বারা" + +msgid "Open an issue" +msgstr "একটি সমস্যা খুলুন" + +msgid "Download notebook file" +msgstr "নোটবুক ফাইল ডাউনলোড করুন" + +msgid "Sphinx Book Theme" +msgstr "স্পিনিক্স বুক থিম" + +msgid "Edit this page" +msgstr "এই পৃষ্ঠাটি সম্পাদনা করুন" + +msgid "By" +msgstr "দ্বারা" + +msgid "Copyright" +msgstr "কপিরাইট" + +msgid "Source repository" +msgstr "উত্স সংগ্রহস্থল" + +msgid "previous page" +msgstr "আগের পৃষ্ঠা" + +msgid "next page" +msgstr "পরবর্তী পৃষ্ঠা" + +msgid "Toggle navigation" +msgstr "নেভিগেশন টগল করুন" + +msgid "open issue" +msgstr "খোলা সমস্যা" + +msgid "Launch" +msgstr "শুরু করা" + +msgid "Print to PDF" +msgstr "পিডিএফ প্রিন্ট করুন" + +msgid "By the" +msgstr "দ্বারা" + +msgid "Last updated on" +msgstr "সর্বশেষ আপডেট" + +msgid "Download source file" +msgstr "উত্স ফাইল ডাউনলোড করুন" + +msgid "Download this page" +msgstr "এই পৃষ্ঠাটি ডাউনলোড করুন" diff --git a/_static/locales/ca/LC_MESSAGES/booktheme.mo b/_static/locales/ca/LC_MESSAGES/booktheme.mo new file mode 100644 index 0000000..a4dd30e Binary files /dev/null and b/_static/locales/ca/LC_MESSAGES/booktheme.mo differ diff --git a/_static/locales/ca/LC_MESSAGES/booktheme.po b/_static/locales/ca/LC_MESSAGES/booktheme.po new file mode 100644 index 0000000..22f1569 --- /dev/null +++ b/_static/locales/ca/LC_MESSAGES/booktheme.po @@ -0,0 +1,66 @@ + +msgid "" +msgstr "" +"Project-Id-Version: Sphinx-Book-Theme\n" +"MIME-Version: 1.0\n" +"Content-Type: text/plain; charset=UTF-8\n" +"Content-Transfer-Encoding: 8bit\n" +"Language: ca\n" +"Plural-Forms: nplurals=2; plural=(n != 1);\n" + +msgid "Theme by the" +msgstr "Tema del" + +msgid "Open an issue" +msgstr "Obriu un número" + +msgid "Download notebook file" +msgstr "Descarregar fitxer de quadern" + +msgid "Sphinx Book Theme" +msgstr "Tema del llibre Esfinx" + +msgid "Edit this page" +msgstr "Editeu aquesta pàgina" + +msgid "By" +msgstr "Per" + +msgid "Copyright" +msgstr "Copyright" + +msgid "Source repository" +msgstr "Dipòsit de fonts" + +msgid "previous page" +msgstr "Pàgina anterior" + +msgid "next page" +msgstr "pàgina següent" + +msgid "Toggle navigation" +msgstr "Commuta la navegació" + +msgid "suggest edit" +msgstr "suggerir edició" + +msgid "open issue" +msgstr "número obert" + +msgid "Launch" +msgstr "Llançament" + +msgid "Print to PDF" +msgstr "Imprimeix a PDF" + +msgid "By the" +msgstr "Per la" + +msgid "Last updated on" +msgstr "Darrera actualització el" + +msgid "Download source file" +msgstr "Baixeu el fitxer font" + +msgid "Download this page" +msgstr "Descarregueu aquesta pàgina" diff --git a/_static/locales/cs/LC_MESSAGES/booktheme.mo b/_static/locales/cs/LC_MESSAGES/booktheme.mo new file mode 100644 index 0000000..c39e01a Binary files /dev/null and b/_static/locales/cs/LC_MESSAGES/booktheme.mo differ diff --git a/_static/locales/cs/LC_MESSAGES/booktheme.po b/_static/locales/cs/LC_MESSAGES/booktheme.po new file mode 100644 index 0000000..afecd9e --- /dev/null +++ b/_static/locales/cs/LC_MESSAGES/booktheme.po @@ -0,0 +1,75 @@ + +msgid "" +msgstr "" +"Project-Id-Version: Sphinx-Book-Theme\n" +"MIME-Version: 1.0\n" +"Content-Type: text/plain; charset=UTF-8\n" +"Content-Transfer-Encoding: 8bit\n" +"Language: cs\n" +"Plural-Forms: nplurals=2; plural=(n != 1);\n" + +msgid "Theme by the" +msgstr "Téma od" + +msgid "Open an issue" +msgstr "Otevřete problém" + +msgid "Contents" +msgstr "Obsah" + +msgid "Download notebook file" +msgstr "Stáhnout soubor poznámkového bloku" + +msgid "Sphinx Book Theme" +msgstr "Téma knihy Sfinga" + +msgid "Fullscreen mode" +msgstr "Režim celé obrazovky" + +msgid "Edit this page" +msgstr "Upravit tuto stránku" + +msgid "By" +msgstr "Podle" + +msgid "Copyright" +msgstr "autorská práva" + +msgid "Source repository" +msgstr "Zdrojové úložiště" + +msgid "previous page" +msgstr "předchozí stránka" + +msgid "next page" +msgstr "další strana" + +msgid "Toggle navigation" +msgstr "Přepnout navigaci" + +msgid "repository" +msgstr "úložiště" + +msgid "suggest edit" +msgstr "navrhnout úpravy" + +msgid "open issue" +msgstr "otevřené číslo" + +msgid "Launch" +msgstr "Zahájení" + +msgid "Print to PDF" +msgstr "Tisk do PDF" + +msgid "By the" +msgstr "Podle" + +msgid "Last updated on" +msgstr "Naposledy aktualizováno" + +msgid "Download source file" +msgstr "Stáhněte si zdrojový soubor" + +msgid "Download this page" +msgstr "Stáhněte si tuto stránku" diff --git a/_static/locales/da/LC_MESSAGES/booktheme.mo b/_static/locales/da/LC_MESSAGES/booktheme.mo new file mode 100644 index 0000000..f43157d Binary files /dev/null and b/_static/locales/da/LC_MESSAGES/booktheme.mo differ diff --git a/_static/locales/da/LC_MESSAGES/booktheme.po b/_static/locales/da/LC_MESSAGES/booktheme.po new file mode 100644 index 0000000..649c78a --- /dev/null +++ b/_static/locales/da/LC_MESSAGES/booktheme.po @@ -0,0 +1,75 @@ + +msgid "" +msgstr "" +"Project-Id-Version: Sphinx-Book-Theme\n" +"MIME-Version: 1.0\n" +"Content-Type: text/plain; charset=UTF-8\n" +"Content-Transfer-Encoding: 8bit\n" +"Language: da\n" +"Plural-Forms: nplurals=2; plural=(n != 1);\n" + +msgid "Theme by the" +msgstr "Tema af" + +msgid "Open an issue" +msgstr "Åbn et problem" + +msgid "Contents" +msgstr "Indhold" + +msgid "Download notebook file" +msgstr "Download notesbog-fil" + +msgid "Sphinx Book Theme" +msgstr "Sphinx bogtema" + +msgid "Fullscreen mode" +msgstr "Fuldskærmstilstand" + +msgid "Edit this page" +msgstr "Rediger denne side" + +msgid "By" +msgstr "Ved" + +msgid "Copyright" +msgstr "ophavsret" + +msgid "Source repository" +msgstr "Kildelager" + +msgid "previous page" +msgstr "forrige side" + +msgid "next page" +msgstr "Næste side" + +msgid "Toggle navigation" +msgstr "Skift navigation" + +msgid "repository" +msgstr "lager" + +msgid "suggest edit" +msgstr "foreslå redigering" + +msgid "open issue" +msgstr "åbent nummer" + +msgid "Launch" +msgstr "Start" + +msgid "Print to PDF" +msgstr "Udskriv til PDF" + +msgid "By the" +msgstr "Ved" + +msgid "Last updated on" +msgstr "Sidst opdateret den" + +msgid "Download source file" +msgstr "Download kildefil" + +msgid "Download this page" +msgstr "Download denne side" diff --git a/_static/locales/de/LC_MESSAGES/booktheme.mo b/_static/locales/de/LC_MESSAGES/booktheme.mo new file mode 100644 index 0000000..648b565 Binary files /dev/null and b/_static/locales/de/LC_MESSAGES/booktheme.mo differ diff --git a/_static/locales/de/LC_MESSAGES/booktheme.po b/_static/locales/de/LC_MESSAGES/booktheme.po new file mode 100644 index 0000000..f51d2ec --- /dev/null +++ b/_static/locales/de/LC_MESSAGES/booktheme.po @@ -0,0 +1,75 @@ + +msgid "" +msgstr "" +"Project-Id-Version: Sphinx-Book-Theme\n" +"MIME-Version: 1.0\n" +"Content-Type: text/plain; charset=UTF-8\n" +"Content-Transfer-Encoding: 8bit\n" +"Language: de\n" +"Plural-Forms: nplurals=2; plural=(n != 1);\n" + +msgid "Theme by the" +msgstr "Thema von der" + +msgid "Open an issue" +msgstr "Öffnen Sie ein Problem" + +msgid "Contents" +msgstr "Inhalt" + +msgid "Download notebook file" +msgstr "Notebook-Datei herunterladen" + +msgid "Sphinx Book Theme" +msgstr "Sphinx-Buch-Thema" + +msgid "Fullscreen mode" +msgstr "Vollbildmodus" + +msgid "Edit this page" +msgstr "Bearbeite diese Seite" + +msgid "By" +msgstr "Durch" + +msgid "Copyright" +msgstr "Urheberrechte ©" + +msgid "Source repository" +msgstr "Quell-Repository" + +msgid "previous page" +msgstr "vorherige Seite" + +msgid "next page" +msgstr "Nächste Seite" + +msgid "Toggle navigation" +msgstr "Navigation umschalten" + +msgid "repository" +msgstr "Repository" + +msgid "suggest edit" +msgstr "vorschlagen zu bearbeiten" + +msgid "open issue" +msgstr "offenes Thema" + +msgid "Launch" +msgstr "Starten" + +msgid "Print to PDF" +msgstr "In PDF drucken" + +msgid "By the" +msgstr "Bis zum" + +msgid "Last updated on" +msgstr "Zuletzt aktualisiert am" + +msgid "Download source file" +msgstr "Quelldatei herunterladen" + +msgid "Download this page" +msgstr "Laden Sie diese Seite herunter" diff --git a/_static/locales/el/LC_MESSAGES/booktheme.mo b/_static/locales/el/LC_MESSAGES/booktheme.mo new file mode 100644 index 0000000..fca6e93 Binary files /dev/null and b/_static/locales/el/LC_MESSAGES/booktheme.mo differ diff --git a/_static/locales/el/LC_MESSAGES/booktheme.po b/_static/locales/el/LC_MESSAGES/booktheme.po new file mode 100644 index 0000000..8bec790 --- /dev/null +++ b/_static/locales/el/LC_MESSAGES/booktheme.po @@ -0,0 +1,75 @@ + +msgid "" +msgstr "" +"Project-Id-Version: Sphinx-Book-Theme\n" +"MIME-Version: 1.0\n" +"Content-Type: text/plain; charset=UTF-8\n" +"Content-Transfer-Encoding: 8bit\n" +"Language: el\n" +"Plural-Forms: nplurals=2; plural=(n != 1);\n" + +msgid "Theme by the" +msgstr "Θέμα από το" + +msgid "Open an issue" +msgstr "Ανοίξτε ένα ζήτημα" + +msgid "Contents" +msgstr "Περιεχόμενα" + +msgid "Download notebook file" +msgstr "Λήψη αρχείου σημειωματάριου" + +msgid "Sphinx Book Theme" +msgstr "Θέμα βιβλίου Sphinx" + +msgid "Fullscreen mode" +msgstr "ΛΕΙΤΟΥΡΓΙΑ ΠΛΗΡΟΥΣ ΟΘΟΝΗΣ" + +msgid "Edit this page" +msgstr "Επεξεργαστείτε αυτήν τη σελίδα" + +msgid "By" +msgstr "Με" + +msgid "Copyright" +msgstr "Πνευματική ιδιοκτησία" + +msgid "Source repository" +msgstr "Αποθήκη πηγής" + +msgid "previous page" +msgstr "προηγούμενη σελίδα" + +msgid "next page" +msgstr "επόμενη σελίδα" + +msgid "Toggle navigation" +msgstr "Εναλλαγή πλοήγησης" + +msgid "repository" +msgstr "αποθήκη" + +msgid "suggest edit" +msgstr "προτείνω επεξεργασία" + +msgid "open issue" +msgstr "ανοιχτό ζήτημα" + +msgid "Launch" +msgstr "Εκτόξευση" + +msgid "Print to PDF" +msgstr "Εκτύπωση σε PDF" + +msgid "By the" +msgstr "Από το" + +msgid "Last updated on" +msgstr "Τελευταία ενημέρωση στις" + +msgid "Download source file" +msgstr "Λήψη αρχείου προέλευσης" + +msgid "Download this page" +msgstr "Λήψη αυτής της σελίδας" diff --git a/_static/locales/eo/LC_MESSAGES/booktheme.mo b/_static/locales/eo/LC_MESSAGES/booktheme.mo new file mode 100644 index 0000000..d1072bb Binary files /dev/null and b/_static/locales/eo/LC_MESSAGES/booktheme.mo differ diff --git a/_static/locales/eo/LC_MESSAGES/booktheme.po b/_static/locales/eo/LC_MESSAGES/booktheme.po new file mode 100644 index 0000000..d72a048 --- /dev/null +++ b/_static/locales/eo/LC_MESSAGES/booktheme.po @@ -0,0 +1,75 @@ + +msgid "" +msgstr "" +"Project-Id-Version: Sphinx-Book-Theme\n" +"MIME-Version: 1.0\n" +"Content-Type: text/plain; charset=UTF-8\n" +"Content-Transfer-Encoding: 8bit\n" +"Language: eo\n" +"Plural-Forms: nplurals=2; plural=(n != 1);\n" + +msgid "Theme by the" +msgstr "Temo de la" + +msgid "Open an issue" +msgstr "Malfermu numeron" + +msgid "Contents" +msgstr "Enhavo" + +msgid "Download notebook file" +msgstr "Elŝutu kajeran dosieron" + +msgid "Sphinx Book Theme" +msgstr "Sfinksa Libro-Temo" + +msgid "Fullscreen mode" +msgstr "Plenekrana reĝimo" + +msgid "Edit this page" +msgstr "Redaktu ĉi tiun paĝon" + +msgid "By" +msgstr "De" + +msgid "Copyright" +msgstr "Kopirajto" + +msgid "Source repository" +msgstr "Fonto-deponejo" + +msgid "previous page" +msgstr "antaŭa paĝo" + +msgid "next page" +msgstr "sekva paĝo" + +msgid "Toggle navigation" +msgstr "Ŝalti navigadon" + +msgid "repository" +msgstr "deponejo" + +msgid "suggest edit" +msgstr "sugesti redaktadon" + +msgid "open issue" +msgstr "malferma numero" + +msgid "Launch" +msgstr "Lanĉo" + +msgid "Print to PDF" +msgstr "Presi al PDF" + +msgid "By the" +msgstr "Per la" + +msgid "Last updated on" +msgstr "Laste ĝisdatigita la" + +msgid "Download source file" +msgstr "Elŝutu fontodosieron" + +msgid "Download this page" +msgstr "Elŝutu ĉi tiun paĝon" diff --git a/_static/locales/es/LC_MESSAGES/booktheme.mo b/_static/locales/es/LC_MESSAGES/booktheme.mo new file mode 100644 index 0000000..ba2ee4d Binary files /dev/null and b/_static/locales/es/LC_MESSAGES/booktheme.mo differ diff --git a/_static/locales/es/LC_MESSAGES/booktheme.po b/_static/locales/es/LC_MESSAGES/booktheme.po new file mode 100644 index 0000000..611834b --- /dev/null +++ b/_static/locales/es/LC_MESSAGES/booktheme.po @@ -0,0 +1,75 @@ + +msgid "" +msgstr "" +"Project-Id-Version: Sphinx-Book-Theme\n" +"MIME-Version: 1.0\n" +"Content-Type: text/plain; charset=UTF-8\n" +"Content-Transfer-Encoding: 8bit\n" +"Language: es\n" +"Plural-Forms: nplurals=2; plural=(n != 1);\n" + +msgid "Theme by the" +msgstr "Tema por el" + +msgid "Open an issue" +msgstr "Abrir un problema" + +msgid "Contents" +msgstr "Contenido" + +msgid "Download notebook file" +msgstr "Descargar archivo de cuaderno" + +msgid "Sphinx Book Theme" +msgstr "Tema del libro de la esfinge" + +msgid "Fullscreen mode" +msgstr "Modo de pantalla completa" + +msgid "Edit this page" +msgstr "Edita esta página" + +msgid "By" +msgstr "Por" + +msgid "Copyright" +msgstr "Derechos de autor" + +msgid "Source repository" +msgstr "Repositorio de origen" + +msgid "previous page" +msgstr "pagina anterior" + +msgid "next page" +msgstr "siguiente página" + +msgid "Toggle navigation" +msgstr "Navegación de palanca" + +msgid "repository" +msgstr "repositorio" + +msgid "suggest edit" +msgstr "sugerir editar" + +msgid "open issue" +msgstr "Tema abierto" + +msgid "Launch" +msgstr "Lanzamiento" + +msgid "Print to PDF" +msgstr "Imprimir en PDF" + +msgid "By the" +msgstr "Por el" + +msgid "Last updated on" +msgstr "Ultima actualización en" + +msgid "Download source file" +msgstr "Descargar archivo fuente" + +msgid "Download this page" +msgstr "Descarga esta pagina" diff --git a/_static/locales/et/LC_MESSAGES/booktheme.mo b/_static/locales/et/LC_MESSAGES/booktheme.mo new file mode 100644 index 0000000..983b823 Binary files /dev/null and b/_static/locales/et/LC_MESSAGES/booktheme.mo differ diff --git a/_static/locales/et/LC_MESSAGES/booktheme.po b/_static/locales/et/LC_MESSAGES/booktheme.po new file mode 100644 index 0000000..345088f --- /dev/null +++ b/_static/locales/et/LC_MESSAGES/booktheme.po @@ -0,0 +1,75 @@ + +msgid "" +msgstr "" +"Project-Id-Version: Sphinx-Book-Theme\n" +"MIME-Version: 1.0\n" +"Content-Type: text/plain; charset=UTF-8\n" +"Content-Transfer-Encoding: 8bit\n" +"Language: et\n" +"Plural-Forms: nplurals=2; plural=(n != 1);\n" + +msgid "Theme by the" +msgstr "Teema" + +msgid "Open an issue" +msgstr "Avage probleem" + +msgid "Contents" +msgstr "Sisu" + +msgid "Download notebook file" +msgstr "Laadige sülearvuti fail alla" + +msgid "Sphinx Book Theme" +msgstr "Sfinksiraamatu teema" + +msgid "Fullscreen mode" +msgstr "Täisekraanirežiim" + +msgid "Edit this page" +msgstr "Muutke seda lehte" + +msgid "By" +msgstr "Kõrval" + +msgid "Copyright" +msgstr "Autoriõigus" + +msgid "Source repository" +msgstr "Allikahoidla" + +msgid "previous page" +msgstr "eelmine leht" + +msgid "next page" +msgstr "järgmine leht" + +msgid "Toggle navigation" +msgstr "Lülita navigeerimine sisse" + +msgid "repository" +msgstr "hoidla" + +msgid "suggest edit" +msgstr "soovita muuta" + +msgid "open issue" +msgstr "avatud küsimus" + +msgid "Launch" +msgstr "Käivitage" + +msgid "Print to PDF" +msgstr "Prindi PDF-i" + +msgid "By the" +msgstr "Autor" + +msgid "Last updated on" +msgstr "Viimati uuendatud" + +msgid "Download source file" +msgstr "Laadige alla lähtefail" + +msgid "Download this page" +msgstr "Laadige see leht alla" diff --git a/_static/locales/fi/LC_MESSAGES/booktheme.mo b/_static/locales/fi/LC_MESSAGES/booktheme.mo new file mode 100644 index 0000000..d8ac054 Binary files /dev/null and b/_static/locales/fi/LC_MESSAGES/booktheme.mo differ diff --git a/_static/locales/fi/LC_MESSAGES/booktheme.po b/_static/locales/fi/LC_MESSAGES/booktheme.po new file mode 100644 index 0000000..d97a08d --- /dev/null +++ b/_static/locales/fi/LC_MESSAGES/booktheme.po @@ -0,0 +1,75 @@ + +msgid "" +msgstr "" +"Project-Id-Version: Sphinx-Book-Theme\n" +"MIME-Version: 1.0\n" +"Content-Type: text/plain; charset=UTF-8\n" +"Content-Transfer-Encoding: 8bit\n" +"Language: fi\n" +"Plural-Forms: nplurals=2; plural=(n != 1);\n" + +msgid "Theme by the" +msgstr "Teeman tekijä" + +msgid "Open an issue" +msgstr "Avaa ongelma" + +msgid "Contents" +msgstr "Sisällys" + +msgid "Download notebook file" +msgstr "Lataa muistikirjatiedosto" + +msgid "Sphinx Book Theme" +msgstr "Sphinx-kirjan teema" + +msgid "Fullscreen mode" +msgstr "Koko näytön tila" + +msgid "Edit this page" +msgstr "Muokkaa tätä sivua" + +msgid "By" +msgstr "Tekijä" + +msgid "Copyright" +msgstr "Tekijänoikeus" + +msgid "Source repository" +msgstr "Lähteen arkisto" + +msgid "previous page" +msgstr "Edellinen sivu" + +msgid "next page" +msgstr "seuraava sivu" + +msgid "Toggle navigation" +msgstr "Vaihda navigointia" + +msgid "repository" +msgstr "arkisto" + +msgid "suggest edit" +msgstr "ehdottaa muokkausta" + +msgid "open issue" +msgstr "avoin ongelma" + +msgid "Launch" +msgstr "Tuoda markkinoille" + +msgid "Print to PDF" +msgstr "Tulosta PDF-tiedostoon" + +msgid "By the" +msgstr "Mukaan" + +msgid "Last updated on" +msgstr "Viimeksi päivitetty" + +msgid "Download source file" +msgstr "Lataa lähdetiedosto" + +msgid "Download this page" +msgstr "Lataa tämä sivu" diff --git a/_static/locales/fr/LC_MESSAGES/booktheme.mo b/_static/locales/fr/LC_MESSAGES/booktheme.mo new file mode 100644 index 0000000..f663d39 Binary files /dev/null and b/_static/locales/fr/LC_MESSAGES/booktheme.mo differ diff --git a/_static/locales/fr/LC_MESSAGES/booktheme.po b/_static/locales/fr/LC_MESSAGES/booktheme.po new file mode 100644 index 0000000..88f3517 --- /dev/null +++ b/_static/locales/fr/LC_MESSAGES/booktheme.po @@ -0,0 +1,75 @@ + +msgid "" +msgstr "" +"Project-Id-Version: Sphinx-Book-Theme\n" +"MIME-Version: 1.0\n" +"Content-Type: text/plain; charset=UTF-8\n" +"Content-Transfer-Encoding: 8bit\n" +"Language: fr\n" +"Plural-Forms: nplurals=2; plural=(n != 1);\n" + +msgid "Theme by the" +msgstr "Thème par le" + +msgid "Open an issue" +msgstr "Ouvrez un problème" + +msgid "Contents" +msgstr "Contenu" + +msgid "Download notebook file" +msgstr "Télécharger le fichier notebook" + +msgid "Sphinx Book Theme" +msgstr "Thème du livre Sphinx" + +msgid "Fullscreen mode" +msgstr "Mode plein écran" + +msgid "Edit this page" +msgstr "Modifier cette page" + +msgid "By" +msgstr "Par" + +msgid "Copyright" +msgstr "droits d'auteur" + +msgid "Source repository" +msgstr "Dépôt source" + +msgid "previous page" +msgstr "page précédente" + +msgid "next page" +msgstr "page suivante" + +msgid "Toggle navigation" +msgstr "Basculer la navigation" + +msgid "repository" +msgstr "dépôt" + +msgid "suggest edit" +msgstr "suggestion de modification" + +msgid "open issue" +msgstr "signaler un problème" + +msgid "Launch" +msgstr "lancement" + +msgid "Print to PDF" +msgstr "Imprimer au format PDF" + +msgid "By the" +msgstr "Par le" + +msgid "Last updated on" +msgstr "Dernière mise à jour le" + +msgid "Download source file" +msgstr "Télécharger le fichier source" + +msgid "Download this page" +msgstr "Téléchargez cette page" diff --git a/_static/locales/hr/LC_MESSAGES/booktheme.mo b/_static/locales/hr/LC_MESSAGES/booktheme.mo new file mode 100644 index 0000000..eca4a1a Binary files /dev/null and b/_static/locales/hr/LC_MESSAGES/booktheme.mo differ diff --git a/_static/locales/hr/LC_MESSAGES/booktheme.po b/_static/locales/hr/LC_MESSAGES/booktheme.po new file mode 100644 index 0000000..fb9440a --- /dev/null +++ b/_static/locales/hr/LC_MESSAGES/booktheme.po @@ -0,0 +1,75 @@ + +msgid "" +msgstr "" +"Project-Id-Version: Sphinx-Book-Theme\n" +"MIME-Version: 1.0\n" +"Content-Type: text/plain; charset=UTF-8\n" +"Content-Transfer-Encoding: 8bit\n" +"Language: hr\n" +"Plural-Forms: nplurals=2; plural=(n != 1);\n" + +msgid "Theme by the" +msgstr "Tema autora" + +msgid "Open an issue" +msgstr "Otvorite izdanje" + +msgid "Contents" +msgstr "Sadržaj" + +msgid "Download notebook file" +msgstr "Preuzmi datoteku bilježnice" + +msgid "Sphinx Book Theme" +msgstr "Tema knjige Sphinx" + +msgid "Fullscreen mode" +msgstr "Način preko cijelog zaslona" + +msgid "Edit this page" +msgstr "Uredite ovu stranicu" + +msgid "By" +msgstr "Po" + +msgid "Copyright" +msgstr "Autorska prava" + +msgid "Source repository" +msgstr "Izvorno spremište" + +msgid "previous page" +msgstr "Prethodna stranica" + +msgid "next page" +msgstr "sljedeća stranica" + +msgid "Toggle navigation" +msgstr "Uključi / isključi navigaciju" + +msgid "repository" +msgstr "spremište" + +msgid "suggest edit" +msgstr "predloži uređivanje" + +msgid "open issue" +msgstr "otvoreno izdanje" + +msgid "Launch" +msgstr "Pokrenite" + +msgid "Print to PDF" +msgstr "Ispis u PDF" + +msgid "By the" +msgstr "Od strane" + +msgid "Last updated on" +msgstr "Posljednje ažuriranje:" + +msgid "Download source file" +msgstr "Preuzmi izvornu datoteku" + +msgid "Download this page" +msgstr "Preuzmite ovu stranicu" diff --git a/_static/locales/id/LC_MESSAGES/booktheme.mo b/_static/locales/id/LC_MESSAGES/booktheme.mo new file mode 100644 index 0000000..d07a06a Binary files /dev/null and b/_static/locales/id/LC_MESSAGES/booktheme.mo differ diff --git a/_static/locales/id/LC_MESSAGES/booktheme.po b/_static/locales/id/LC_MESSAGES/booktheme.po new file mode 100644 index 0000000..9ffb56f --- /dev/null +++ b/_static/locales/id/LC_MESSAGES/booktheme.po @@ -0,0 +1,75 @@ + +msgid "" +msgstr "" +"Project-Id-Version: Sphinx-Book-Theme\n" +"MIME-Version: 1.0\n" +"Content-Type: text/plain; charset=UTF-8\n" +"Content-Transfer-Encoding: 8bit\n" +"Language: id\n" +"Plural-Forms: nplurals=2; plural=(n != 1);\n" + +msgid "Theme by the" +msgstr "Tema oleh" + +msgid "Open an issue" +msgstr "Buka masalah" + +msgid "Contents" +msgstr "Isi" + +msgid "Download notebook file" +msgstr "Unduh file notebook" + +msgid "Sphinx Book Theme" +msgstr "Tema Buku Sphinx" + +msgid "Fullscreen mode" +msgstr "Mode layar penuh" + +msgid "Edit this page" +msgstr "Edit halaman ini" + +msgid "By" +msgstr "Oleh" + +msgid "Copyright" +msgstr "hak cipta" + +msgid "Source repository" +msgstr "Repositori sumber" + +msgid "previous page" +msgstr "halaman sebelumnya" + +msgid "next page" +msgstr "halaman selanjutnya" + +msgid "Toggle navigation" +msgstr "Alihkan navigasi" + +msgid "repository" +msgstr "gudang" + +msgid "suggest edit" +msgstr "menyarankan edit" + +msgid "open issue" +msgstr "masalah terbuka" + +msgid "Launch" +msgstr "Meluncurkan" + +msgid "Print to PDF" +msgstr "Cetak ke PDF" + +msgid "By the" +msgstr "Oleh" + +msgid "Last updated on" +msgstr "Terakhir diperbarui saat" + +msgid "Download source file" +msgstr "Unduh file sumber" + +msgid "Download this page" +msgstr "Unduh halaman ini" diff --git a/_static/locales/it/LC_MESSAGES/booktheme.mo b/_static/locales/it/LC_MESSAGES/booktheme.mo new file mode 100644 index 0000000..53ba476 Binary files /dev/null and b/_static/locales/it/LC_MESSAGES/booktheme.mo differ diff --git a/_static/locales/it/LC_MESSAGES/booktheme.po b/_static/locales/it/LC_MESSAGES/booktheme.po new file mode 100644 index 0000000..04308dd --- /dev/null +++ b/_static/locales/it/LC_MESSAGES/booktheme.po @@ -0,0 +1,75 @@ + +msgid "" +msgstr "" +"Project-Id-Version: Sphinx-Book-Theme\n" +"MIME-Version: 1.0\n" +"Content-Type: text/plain; charset=UTF-8\n" +"Content-Transfer-Encoding: 8bit\n" +"Language: it\n" +"Plural-Forms: nplurals=2; plural=(n != 1);\n" + +msgid "Theme by the" +msgstr "Tema di" + +msgid "Open an issue" +msgstr "Apri un problema" + +msgid "Contents" +msgstr "Contenuti" + +msgid "Download notebook file" +msgstr "Scarica il file del taccuino" + +msgid "Sphinx Book Theme" +msgstr "Tema del libro della Sfinge" + +msgid "Fullscreen mode" +msgstr "Modalità schermo intero" + +msgid "Edit this page" +msgstr "Modifica questa pagina" + +msgid "By" +msgstr "Di" + +msgid "Copyright" +msgstr "Diritto d'autore" + +msgid "Source repository" +msgstr "Repository di origine" + +msgid "previous page" +msgstr "pagina precedente" + +msgid "next page" +msgstr "pagina successiva" + +msgid "Toggle navigation" +msgstr "Attiva / disattiva la navigazione" + +msgid "repository" +msgstr "repository" + +msgid "suggest edit" +msgstr "suggerisci modifica" + +msgid "open issue" +msgstr "questione aperta" + +msgid "Launch" +msgstr "Lanciare" + +msgid "Print to PDF" +msgstr "Stampa in PDF" + +msgid "By the" +msgstr "Dal" + +msgid "Last updated on" +msgstr "Ultimo aggiornamento il" + +msgid "Download source file" +msgstr "Scarica il file sorgente" + +msgid "Download this page" +msgstr "Scarica questa pagina" diff --git a/_static/locales/iw/LC_MESSAGES/booktheme.mo b/_static/locales/iw/LC_MESSAGES/booktheme.mo new file mode 100644 index 0000000..a45c657 Binary files /dev/null and b/_static/locales/iw/LC_MESSAGES/booktheme.mo differ diff --git a/_static/locales/iw/LC_MESSAGES/booktheme.po b/_static/locales/iw/LC_MESSAGES/booktheme.po new file mode 100644 index 0000000..4ea190d --- /dev/null +++ b/_static/locales/iw/LC_MESSAGES/booktheme.po @@ -0,0 +1,75 @@ + +msgid "" +msgstr "" +"Project-Id-Version: Sphinx-Book-Theme\n" +"MIME-Version: 1.0\n" +"Content-Type: text/plain; charset=UTF-8\n" +"Content-Transfer-Encoding: 8bit\n" +"Language: iw\n" +"Plural-Forms: nplurals=2; plural=(n != 1);\n" + +msgid "Theme by the" +msgstr "נושא מאת" + +msgid "Open an issue" +msgstr "פתח גיליון" + +msgid "Contents" +msgstr "תוכן" + +msgid "Download notebook file" +msgstr "הורד קובץ מחברת" + +msgid "Sphinx Book Theme" +msgstr "נושא ספר ספינקס" + +msgid "Fullscreen mode" +msgstr "מצב מסך מלא" + +msgid "Edit this page" +msgstr "ערוך דף זה" + +msgid "By" +msgstr "על ידי" + +msgid "Copyright" +msgstr "זכויות יוצרים" + +msgid "Source repository" +msgstr "מאגר המקורות" + +msgid "previous page" +msgstr "עמוד קודם" + +msgid "next page" +msgstr "עמוד הבא" + +msgid "Toggle navigation" +msgstr "החלף ניווט" + +msgid "repository" +msgstr "מאגר" + +msgid "suggest edit" +msgstr "מציע לערוך" + +msgid "open issue" +msgstr "בעיה פתוחה" + +msgid "Launch" +msgstr "לְהַשִׁיק" + +msgid "Print to PDF" +msgstr "הדפס לקובץ PDF" + +msgid "By the" +msgstr "דרך" + +msgid "Last updated on" +msgstr "עודכן לאחרונה ב" + +msgid "Download source file" +msgstr "הורד את קובץ המקור" + +msgid "Download this page" +msgstr "הורד דף זה" diff --git a/_static/locales/ja/LC_MESSAGES/booktheme.mo b/_static/locales/ja/LC_MESSAGES/booktheme.mo new file mode 100644 index 0000000..1cefd29 Binary files /dev/null and b/_static/locales/ja/LC_MESSAGES/booktheme.mo differ diff --git a/_static/locales/ja/LC_MESSAGES/booktheme.po b/_static/locales/ja/LC_MESSAGES/booktheme.po new file mode 100644 index 0000000..77d5a09 --- /dev/null +++ b/_static/locales/ja/LC_MESSAGES/booktheme.po @@ -0,0 +1,75 @@ + +msgid "" +msgstr "" +"Project-Id-Version: Sphinx-Book-Theme\n" +"MIME-Version: 1.0\n" +"Content-Type: text/plain; charset=UTF-8\n" +"Content-Transfer-Encoding: 8bit\n" +"Language: ja\n" +"Plural-Forms: nplurals=2; plural=(n != 1);\n" + +msgid "Theme by the" +msgstr "のテーマ" + +msgid "Open an issue" +msgstr "問題を報告" + +msgid "Contents" +msgstr "目次" + +msgid "Download notebook file" +msgstr "ノートブックファイルをダウンロード" + +msgid "Sphinx Book Theme" +msgstr "スフィンクスの本のテーマ" + +msgid "Fullscreen mode" +msgstr "全画面モード" + +msgid "Edit this page" +msgstr "このページを編集" + +msgid "By" +msgstr "著者" + +msgid "Copyright" +msgstr "Copyright" + +msgid "Source repository" +msgstr "ソースリポジトリ" + +msgid "previous page" +msgstr "前のページ" + +msgid "next page" +msgstr "次のページ" + +msgid "Toggle navigation" +msgstr "ナビゲーションを切り替え" + +msgid "repository" +msgstr "リポジトリ" + +msgid "suggest edit" +msgstr "編集を提案する" + +msgid "open issue" +msgstr "未解決の問題" + +msgid "Launch" +msgstr "起動" + +msgid "Print to PDF" +msgstr "PDFに印刷" + +msgid "By the" +msgstr "によって" + +msgid "Last updated on" +msgstr "最終更新日" + +msgid "Download source file" +msgstr "ソースファイルをダウンロード" + +msgid "Download this page" +msgstr "このページをダウンロード" diff --git a/_static/locales/ko/LC_MESSAGES/booktheme.mo b/_static/locales/ko/LC_MESSAGES/booktheme.mo new file mode 100644 index 0000000..06c7ec9 Binary files /dev/null and b/_static/locales/ko/LC_MESSAGES/booktheme.mo differ diff --git a/_static/locales/ko/LC_MESSAGES/booktheme.po b/_static/locales/ko/LC_MESSAGES/booktheme.po new file mode 100644 index 0000000..6ee3d78 --- /dev/null +++ b/_static/locales/ko/LC_MESSAGES/booktheme.po @@ -0,0 +1,75 @@ + +msgid "" +msgstr "" +"Project-Id-Version: Sphinx-Book-Theme\n" +"MIME-Version: 1.0\n" +"Content-Type: text/plain; charset=UTF-8\n" +"Content-Transfer-Encoding: 8bit\n" +"Language: ko\n" +"Plural-Forms: nplurals=2; plural=(n != 1);\n" + +msgid "Theme by the" +msgstr "테마별" + +msgid "Open an issue" +msgstr "이슈 열기" + +msgid "Contents" +msgstr "내용" + +msgid "Download notebook file" +msgstr "노트북 파일 다운로드" + +msgid "Sphinx Book Theme" +msgstr "스핑크스 도서 테마" + +msgid "Fullscreen mode" +msgstr "전체 화면으로보기" + +msgid "Edit this page" +msgstr "이 페이지 편집" + +msgid "By" +msgstr "으로" + +msgid "Copyright" +msgstr "저작권" + +msgid "Source repository" +msgstr "소스 저장소" + +msgid "previous page" +msgstr "이전 페이지" + +msgid "next page" +msgstr "다음 페이지" + +msgid "Toggle navigation" +msgstr "탐색 전환" + +msgid "repository" +msgstr "저장소" + +msgid "suggest edit" +msgstr "편집 제안" + +msgid "open issue" +msgstr "열린 문제" + +msgid "Launch" +msgstr "시작하다" + +msgid "Print to PDF" +msgstr "PDF로 인쇄" + +msgid "By the" +msgstr "에 의해" + +msgid "Last updated on" +msgstr "마지막 업데이트" + +msgid "Download source file" +msgstr "소스 파일 다운로드" + +msgid "Download this page" +msgstr "이 페이지 다운로드" diff --git a/_static/locales/lt/LC_MESSAGES/booktheme.mo b/_static/locales/lt/LC_MESSAGES/booktheme.mo new file mode 100644 index 0000000..4468ba0 Binary files /dev/null and b/_static/locales/lt/LC_MESSAGES/booktheme.mo differ diff --git a/_static/locales/lt/LC_MESSAGES/booktheme.po b/_static/locales/lt/LC_MESSAGES/booktheme.po new file mode 100644 index 0000000..01be267 --- /dev/null +++ b/_static/locales/lt/LC_MESSAGES/booktheme.po @@ -0,0 +1,75 @@ + +msgid "" +msgstr "" +"Project-Id-Version: Sphinx-Book-Theme\n" +"MIME-Version: 1.0\n" +"Content-Type: text/plain; charset=UTF-8\n" +"Content-Transfer-Encoding: 8bit\n" +"Language: lt\n" +"Plural-Forms: nplurals=2; plural=(n != 1);\n" + +msgid "Theme by the" +msgstr "Tema" + +msgid "Open an issue" +msgstr "Atidarykite problemą" + +msgid "Contents" +msgstr "Turinys" + +msgid "Download notebook file" +msgstr "Atsisiųsti nešiojamojo kompiuterio failą" + +msgid "Sphinx Book Theme" +msgstr "Sfinkso knygos tema" + +msgid "Fullscreen mode" +msgstr "Pilno ekrano režimas" + +msgid "Edit this page" +msgstr "Redaguoti šį puslapį" + +msgid "By" +msgstr "Iki" + +msgid "Copyright" +msgstr "Autorių teisės" + +msgid "Source repository" +msgstr "Šaltinio saugykla" + +msgid "previous page" +msgstr "Ankstesnis puslapis" + +msgid "next page" +msgstr "Kitas puslapis" + +msgid "Toggle navigation" +msgstr "Perjungti naršymą" + +msgid "repository" +msgstr "saugykla" + +msgid "suggest edit" +msgstr "pasiūlyti redaguoti" + +msgid "open issue" +msgstr "atviras klausimas" + +msgid "Launch" +msgstr "Paleiskite" + +msgid "Print to PDF" +msgstr "Spausdinti į PDF" + +msgid "By the" +msgstr "Prie" + +msgid "Last updated on" +msgstr "Paskutinį kartą atnaujinta" + +msgid "Download source file" +msgstr "Atsisiųsti šaltinio failą" + +msgid "Download this page" +msgstr "Atsisiųskite šį puslapį" diff --git a/_static/locales/lv/LC_MESSAGES/booktheme.mo b/_static/locales/lv/LC_MESSAGES/booktheme.mo new file mode 100644 index 0000000..74aa4d8 Binary files /dev/null and b/_static/locales/lv/LC_MESSAGES/booktheme.mo differ diff --git a/_static/locales/lv/LC_MESSAGES/booktheme.po b/_static/locales/lv/LC_MESSAGES/booktheme.po new file mode 100644 index 0000000..993a1e4 --- /dev/null +++ b/_static/locales/lv/LC_MESSAGES/booktheme.po @@ -0,0 +1,75 @@ + +msgid "" +msgstr "" +"Project-Id-Version: Sphinx-Book-Theme\n" +"MIME-Version: 1.0\n" +"Content-Type: text/plain; charset=UTF-8\n" +"Content-Transfer-Encoding: 8bit\n" +"Language: lv\n" +"Plural-Forms: nplurals=2; plural=(n != 1);\n" + +msgid "Theme by the" +msgstr "Autora tēma" + +msgid "Open an issue" +msgstr "Atveriet problēmu" + +msgid "Contents" +msgstr "Saturs" + +msgid "Download notebook file" +msgstr "Lejupielādēt piezīmju grāmatiņu" + +msgid "Sphinx Book Theme" +msgstr "Sfinksa grāmatas tēma" + +msgid "Fullscreen mode" +msgstr "Pilnekrāna režīms" + +msgid "Edit this page" +msgstr "Rediģēt šo lapu" + +msgid "By" +msgstr "Autors" + +msgid "Copyright" +msgstr "Autortiesības" + +msgid "Source repository" +msgstr "Avota krātuve" + +msgid "previous page" +msgstr "iepriekšējā lapa" + +msgid "next page" +msgstr "nākamā lapaspuse" + +msgid "Toggle navigation" +msgstr "Pārslēgt navigāciju" + +msgid "repository" +msgstr "krātuve" + +msgid "suggest edit" +msgstr "ieteikt rediģēt" + +msgid "open issue" +msgstr "atklāts jautājums" + +msgid "Launch" +msgstr "Uzsākt" + +msgid "Print to PDF" +msgstr "Drukāt PDF formātā" + +msgid "By the" +msgstr "Ar" + +msgid "Last updated on" +msgstr "Pēdējoreiz atjaunināts" + +msgid "Download source file" +msgstr "Lejupielādēt avota failu" + +msgid "Download this page" +msgstr "Lejupielādējiet šo lapu" diff --git a/_static/locales/ml/LC_MESSAGES/booktheme.mo b/_static/locales/ml/LC_MESSAGES/booktheme.mo new file mode 100644 index 0000000..2736e8f Binary files /dev/null and b/_static/locales/ml/LC_MESSAGES/booktheme.mo differ diff --git a/_static/locales/ml/LC_MESSAGES/booktheme.po b/_static/locales/ml/LC_MESSAGES/booktheme.po new file mode 100644 index 0000000..81daf7c --- /dev/null +++ b/_static/locales/ml/LC_MESSAGES/booktheme.po @@ -0,0 +1,66 @@ + +msgid "" +msgstr "" +"Project-Id-Version: Sphinx-Book-Theme\n" +"MIME-Version: 1.0\n" +"Content-Type: text/plain; charset=UTF-8\n" +"Content-Transfer-Encoding: 8bit\n" +"Language: ml\n" +"Plural-Forms: nplurals=2; plural=(n != 1);\n" + +msgid "Theme by the" +msgstr "പ്രമേയം" + +msgid "Open an issue" +msgstr "ഒരു പ്രശ്നം തുറക്കുക" + +msgid "Download notebook file" +msgstr "നോട്ട്ബുക്ക് ഫയൽ ഡൺലോഡ് ചെയ്യുക" + +msgid "Sphinx Book Theme" +msgstr "സ്ഫിങ്ക്സ് പുസ്തക തീം" + +msgid "Edit this page" +msgstr "ഈ പേജ് എഡിറ്റുചെയ്യുക" + +msgid "By" +msgstr "എഴുതിയത്" + +msgid "Copyright" +msgstr "പകർപ്പവകാശം" + +msgid "Source repository" +msgstr "ഉറവിട ശേഖരം" + +msgid "previous page" +msgstr "മുൻപത്തെ താൾ" + +msgid "next page" +msgstr "അടുത്ത പേജ്" + +msgid "Toggle navigation" +msgstr "നാവിഗേഷൻ ടോഗിൾ ചെയ്യുക" + +msgid "suggest edit" +msgstr "എഡിറ്റുചെയ്യാൻ നിർദ്ദേശിക്കുക" + +msgid "open issue" +msgstr "തുറന്ന പ്രശ്നം" + +msgid "Launch" +msgstr "സമാരംഭിക്കുക" + +msgid "Print to PDF" +msgstr "PDF- ലേക്ക് പ്രിന്റുചെയ്യുക" + +msgid "By the" +msgstr "എഴുതിയത്" + +msgid "Last updated on" +msgstr "അവസാനം അപ്‌ഡേറ്റുചെയ്‌തത്" + +msgid "Download source file" +msgstr "ഉറവിട ഫയൽ ഡൗൺലോഡുചെയ്യുക" + +msgid "Download this page" +msgstr "ഈ പേജ് ഡൗൺലോഡുചെയ്യുക" diff --git a/_static/locales/mr/LC_MESSAGES/booktheme.mo b/_static/locales/mr/LC_MESSAGES/booktheme.mo new file mode 100644 index 0000000..fe53010 Binary files /dev/null and b/_static/locales/mr/LC_MESSAGES/booktheme.mo differ diff --git a/_static/locales/mr/LC_MESSAGES/booktheme.po b/_static/locales/mr/LC_MESSAGES/booktheme.po new file mode 100644 index 0000000..fd857bf --- /dev/null +++ b/_static/locales/mr/LC_MESSAGES/booktheme.po @@ -0,0 +1,66 @@ + +msgid "" +msgstr "" +"Project-Id-Version: Sphinx-Book-Theme\n" +"MIME-Version: 1.0\n" +"Content-Type: text/plain; charset=UTF-8\n" +"Content-Transfer-Encoding: 8bit\n" +"Language: mr\n" +"Plural-Forms: nplurals=2; plural=(n != 1);\n" + +msgid "Theme by the" +msgstr "द्वारा थीम" + +msgid "Open an issue" +msgstr "एक मुद्दा उघडा" + +msgid "Download notebook file" +msgstr "नोटबुक फाईल डाउनलोड करा" + +msgid "Sphinx Book Theme" +msgstr "स्फिंक्स बुक थीम" + +msgid "Edit this page" +msgstr "हे पृष्ठ संपादित करा" + +msgid "By" +msgstr "द्वारा" + +msgid "Copyright" +msgstr "कॉपीराइट" + +msgid "Source repository" +msgstr "स्त्रोत भांडार" + +msgid "previous page" +msgstr "मागील पान" + +msgid "next page" +msgstr "पुढील पृष्ठ" + +msgid "Toggle navigation" +msgstr "नेव्हिगेशन टॉगल करा" + +msgid "suggest edit" +msgstr "संपादन सुचवा" + +msgid "open issue" +msgstr "खुला मुद्दा" + +msgid "Launch" +msgstr "लाँच करा" + +msgid "Print to PDF" +msgstr "पीडीएफवर मुद्रित करा" + +msgid "By the" +msgstr "द्वारा" + +msgid "Last updated on" +msgstr "अखेरचे अद्यतनित" + +msgid "Download source file" +msgstr "स्त्रोत फाइल डाउनलोड करा" + +msgid "Download this page" +msgstr "हे पृष्ठ डाउनलोड करा" diff --git a/_static/locales/ms/LC_MESSAGES/booktheme.mo b/_static/locales/ms/LC_MESSAGES/booktheme.mo new file mode 100644 index 0000000..f02603f Binary files /dev/null and b/_static/locales/ms/LC_MESSAGES/booktheme.mo differ diff --git a/_static/locales/ms/LC_MESSAGES/booktheme.po b/_static/locales/ms/LC_MESSAGES/booktheme.po new file mode 100644 index 0000000..b616d70 --- /dev/null +++ b/_static/locales/ms/LC_MESSAGES/booktheme.po @@ -0,0 +1,66 @@ + +msgid "" +msgstr "" +"Project-Id-Version: Sphinx-Book-Theme\n" +"MIME-Version: 1.0\n" +"Content-Type: text/plain; charset=UTF-8\n" +"Content-Transfer-Encoding: 8bit\n" +"Language: ms\n" +"Plural-Forms: nplurals=2; plural=(n != 1);\n" + +msgid "Theme by the" +msgstr "Tema oleh" + +msgid "Open an issue" +msgstr "Buka masalah" + +msgid "Download notebook file" +msgstr "Muat turun fail buku nota" + +msgid "Sphinx Book Theme" +msgstr "Tema Buku Sphinx" + +msgid "Edit this page" +msgstr "Edit halaman ini" + +msgid "By" +msgstr "Oleh" + +msgid "Copyright" +msgstr "hak cipta" + +msgid "Source repository" +msgstr "Repositori sumber" + +msgid "previous page" +msgstr "halaman sebelumnya" + +msgid "next page" +msgstr "muka surat seterusnya" + +msgid "Toggle navigation" +msgstr "Togol navigasi" + +msgid "suggest edit" +msgstr "cadangkan edit" + +msgid "open issue" +msgstr "isu terbuka" + +msgid "Launch" +msgstr "Lancarkan" + +msgid "Print to PDF" +msgstr "Cetak ke PDF" + +msgid "By the" +msgstr "Oleh" + +msgid "Last updated on" +msgstr "Terakhir dikemas kini pada" + +msgid "Download source file" +msgstr "Muat turun fail sumber" + +msgid "Download this page" +msgstr "Muat turun halaman ini" diff --git a/_static/locales/nl/LC_MESSAGES/booktheme.mo b/_static/locales/nl/LC_MESSAGES/booktheme.mo new file mode 100644 index 0000000..e59e7ec Binary files /dev/null and b/_static/locales/nl/LC_MESSAGES/booktheme.mo differ diff --git a/_static/locales/nl/LC_MESSAGES/booktheme.po b/_static/locales/nl/LC_MESSAGES/booktheme.po new file mode 100644 index 0000000..f16f4bc --- /dev/null +++ b/_static/locales/nl/LC_MESSAGES/booktheme.po @@ -0,0 +1,75 @@ + +msgid "" +msgstr "" +"Project-Id-Version: Sphinx-Book-Theme\n" +"MIME-Version: 1.0\n" +"Content-Type: text/plain; charset=UTF-8\n" +"Content-Transfer-Encoding: 8bit\n" +"Language: nl\n" +"Plural-Forms: nplurals=2; plural=(n != 1);\n" + +msgid "Theme by the" +msgstr "Thema door de" + +msgid "Open an issue" +msgstr "Open een probleem" + +msgid "Contents" +msgstr "Inhoud" + +msgid "Download notebook file" +msgstr "Download notebookbestand" + +msgid "Sphinx Book Theme" +msgstr "Sphinx-boekthema" + +msgid "Fullscreen mode" +msgstr "Volledig scherm" + +msgid "Edit this page" +msgstr "bewerk deze pagina" + +msgid "By" +msgstr "Door" + +msgid "Copyright" +msgstr "auteursrechten" + +msgid "Source repository" +msgstr "Bronopslagplaats" + +msgid "previous page" +msgstr "vorige pagina" + +msgid "next page" +msgstr "volgende bladzijde" + +msgid "Toggle navigation" +msgstr "Schakel navigatie" + +msgid "repository" +msgstr "repository" + +msgid "suggest edit" +msgstr "suggereren bewerken" + +msgid "open issue" +msgstr "open probleem" + +msgid "Launch" +msgstr "Lancering" + +msgid "Print to PDF" +msgstr "Afdrukken naar pdf" + +msgid "By the" +msgstr "Door de" + +msgid "Last updated on" +msgstr "Laatst geupdate op" + +msgid "Download source file" +msgstr "Download het bronbestand" + +msgid "Download this page" +msgstr "Download deze pagina" diff --git a/_static/locales/no/LC_MESSAGES/booktheme.mo b/_static/locales/no/LC_MESSAGES/booktheme.mo new file mode 100644 index 0000000..6cd15c8 Binary files /dev/null and b/_static/locales/no/LC_MESSAGES/booktheme.mo differ diff --git a/_static/locales/no/LC_MESSAGES/booktheme.po b/_static/locales/no/LC_MESSAGES/booktheme.po new file mode 100644 index 0000000..b1d304e --- /dev/null +++ b/_static/locales/no/LC_MESSAGES/booktheme.po @@ -0,0 +1,75 @@ + +msgid "" +msgstr "" +"Project-Id-Version: Sphinx-Book-Theme\n" +"MIME-Version: 1.0\n" +"Content-Type: text/plain; charset=UTF-8\n" +"Content-Transfer-Encoding: 8bit\n" +"Language: no\n" +"Plural-Forms: nplurals=2; plural=(n != 1);\n" + +msgid "Theme by the" +msgstr "Tema av" + +msgid "Open an issue" +msgstr "Åpne et problem" + +msgid "Contents" +msgstr "Innhold" + +msgid "Download notebook file" +msgstr "Last ned notatbokfilen" + +msgid "Sphinx Book Theme" +msgstr "Sphinx boktema" + +msgid "Fullscreen mode" +msgstr "Fullskjerm-modus" + +msgid "Edit this page" +msgstr "Rediger denne siden" + +msgid "By" +msgstr "Av" + +msgid "Copyright" +msgstr "opphavsrett" + +msgid "Source repository" +msgstr "Kildedepot" + +msgid "previous page" +msgstr "forrige side" + +msgid "next page" +msgstr "neste side" + +msgid "Toggle navigation" +msgstr "Bytt navigasjon" + +msgid "repository" +msgstr "oppbevaringssted" + +msgid "suggest edit" +msgstr "foreslå redigering" + +msgid "open issue" +msgstr "åpent nummer" + +msgid "Launch" +msgstr "Start" + +msgid "Print to PDF" +msgstr "Skriv ut til PDF" + +msgid "By the" +msgstr "Ved" + +msgid "Last updated on" +msgstr "Sist oppdatert den" + +msgid "Download source file" +msgstr "Last ned kildefilen" + +msgid "Download this page" +msgstr "Last ned denne siden" diff --git a/_static/locales/pl/LC_MESSAGES/booktheme.mo b/_static/locales/pl/LC_MESSAGES/booktheme.mo new file mode 100644 index 0000000..9ebb584 Binary files /dev/null and b/_static/locales/pl/LC_MESSAGES/booktheme.mo differ diff --git a/_static/locales/pl/LC_MESSAGES/booktheme.po b/_static/locales/pl/LC_MESSAGES/booktheme.po new file mode 100644 index 0000000..80d2c89 --- /dev/null +++ b/_static/locales/pl/LC_MESSAGES/booktheme.po @@ -0,0 +1,75 @@ + +msgid "" +msgstr "" +"Project-Id-Version: Sphinx-Book-Theme\n" +"MIME-Version: 1.0\n" +"Content-Type: text/plain; charset=UTF-8\n" +"Content-Transfer-Encoding: 8bit\n" +"Language: pl\n" +"Plural-Forms: nplurals=2; plural=(n != 1);\n" + +msgid "Theme by the" +msgstr "Motyw autorstwa" + +msgid "Open an issue" +msgstr "Otwórz problem" + +msgid "Contents" +msgstr "Zawartość" + +msgid "Download notebook file" +msgstr "Pobierz plik notatnika" + +msgid "Sphinx Book Theme" +msgstr "Motyw książki Sphinx" + +msgid "Fullscreen mode" +msgstr "Pełny ekran" + +msgid "Edit this page" +msgstr "Edytuj tę strone" + +msgid "By" +msgstr "Przez" + +msgid "Copyright" +msgstr "prawa autorskie" + +msgid "Source repository" +msgstr "Repozytorium źródłowe" + +msgid "previous page" +msgstr "Poprzednia strona" + +msgid "next page" +msgstr "Następna strona" + +msgid "Toggle navigation" +msgstr "Przełącz nawigację" + +msgid "repository" +msgstr "magazyn" + +msgid "suggest edit" +msgstr "zaproponuj edycję" + +msgid "open issue" +msgstr "otwarty problem" + +msgid "Launch" +msgstr "Uruchomić" + +msgid "Print to PDF" +msgstr "Drukuj do PDF" + +msgid "By the" +msgstr "Przez" + +msgid "Last updated on" +msgstr "Ostatnia aktualizacja" + +msgid "Download source file" +msgstr "Pobierz plik źródłowy" + +msgid "Download this page" +msgstr "Pobierz tę stronę" diff --git a/_static/locales/pt/LC_MESSAGES/booktheme.mo b/_static/locales/pt/LC_MESSAGES/booktheme.mo new file mode 100644 index 0000000..d0ddb87 Binary files /dev/null and b/_static/locales/pt/LC_MESSAGES/booktheme.mo differ diff --git a/_static/locales/pt/LC_MESSAGES/booktheme.po b/_static/locales/pt/LC_MESSAGES/booktheme.po new file mode 100644 index 0000000..45ac847 --- /dev/null +++ b/_static/locales/pt/LC_MESSAGES/booktheme.po @@ -0,0 +1,75 @@ + +msgid "" +msgstr "" +"Project-Id-Version: Sphinx-Book-Theme\n" +"MIME-Version: 1.0\n" +"Content-Type: text/plain; charset=UTF-8\n" +"Content-Transfer-Encoding: 8bit\n" +"Language: pt\n" +"Plural-Forms: nplurals=2; plural=(n != 1);\n" + +msgid "Theme by the" +msgstr "Tema por" + +msgid "Open an issue" +msgstr "Abra um problema" + +msgid "Contents" +msgstr "Conteúdo" + +msgid "Download notebook file" +msgstr "Baixar arquivo de notebook" + +msgid "Sphinx Book Theme" +msgstr "Tema do livro Sphinx" + +msgid "Fullscreen mode" +msgstr "Modo tela cheia" + +msgid "Edit this page" +msgstr "Edite essa página" + +msgid "By" +msgstr "De" + +msgid "Copyright" +msgstr "direito autoral" + +msgid "Source repository" +msgstr "Repositório fonte" + +msgid "previous page" +msgstr "página anterior" + +msgid "next page" +msgstr "próxima página" + +msgid "Toggle navigation" +msgstr "Alternar de navegação" + +msgid "repository" +msgstr "repositório" + +msgid "suggest edit" +msgstr "sugerir edição" + +msgid "open issue" +msgstr "questão aberta" + +msgid "Launch" +msgstr "Lançamento" + +msgid "Print to PDF" +msgstr "Imprimir em PDF" + +msgid "By the" +msgstr "Pelo" + +msgid "Last updated on" +msgstr "Última atualização em" + +msgid "Download source file" +msgstr "Baixar arquivo fonte" + +msgid "Download this page" +msgstr "Baixe esta página" diff --git a/_static/locales/ro/LC_MESSAGES/booktheme.mo b/_static/locales/ro/LC_MESSAGES/booktheme.mo new file mode 100644 index 0000000..3c36ab1 Binary files /dev/null and b/_static/locales/ro/LC_MESSAGES/booktheme.mo differ diff --git a/_static/locales/ro/LC_MESSAGES/booktheme.po b/_static/locales/ro/LC_MESSAGES/booktheme.po new file mode 100644 index 0000000..532b3b8 --- /dev/null +++ b/_static/locales/ro/LC_MESSAGES/booktheme.po @@ -0,0 +1,75 @@ + +msgid "" +msgstr "" +"Project-Id-Version: Sphinx-Book-Theme\n" +"MIME-Version: 1.0\n" +"Content-Type: text/plain; charset=UTF-8\n" +"Content-Transfer-Encoding: 8bit\n" +"Language: ro\n" +"Plural-Forms: nplurals=2; plural=(n != 1);\n" + +msgid "Theme by the" +msgstr "Tema de" + +msgid "Open an issue" +msgstr "Deschideți o problemă" + +msgid "Contents" +msgstr "Cuprins" + +msgid "Download notebook file" +msgstr "Descărcați fișierul notebook" + +msgid "Sphinx Book Theme" +msgstr "Tema Sphinx Book" + +msgid "Fullscreen mode" +msgstr "Modul ecran întreg" + +msgid "Edit this page" +msgstr "Editați această pagină" + +msgid "By" +msgstr "De" + +msgid "Copyright" +msgstr "Drepturi de autor" + +msgid "Source repository" +msgstr "Depozit sursă" + +msgid "previous page" +msgstr "pagina anterioară" + +msgid "next page" +msgstr "pagina următoare" + +msgid "Toggle navigation" +msgstr "Comutare navigare" + +msgid "repository" +msgstr "repertoriu" + +msgid "suggest edit" +msgstr "sugerează editare" + +msgid "open issue" +msgstr "problema deschisă" + +msgid "Launch" +msgstr "Lansa" + +msgid "Print to PDF" +msgstr "Imprimați în PDF" + +msgid "By the" +msgstr "Langa" + +msgid "Last updated on" +msgstr "Ultima actualizare la" + +msgid "Download source file" +msgstr "Descărcați fișierul sursă" + +msgid "Download this page" +msgstr "Descarcă această pagină" diff --git a/_static/locales/ru/LC_MESSAGES/booktheme.mo b/_static/locales/ru/LC_MESSAGES/booktheme.mo new file mode 100644 index 0000000..6b8ca41 Binary files /dev/null and b/_static/locales/ru/LC_MESSAGES/booktheme.mo differ diff --git a/_static/locales/ru/LC_MESSAGES/booktheme.po b/_static/locales/ru/LC_MESSAGES/booktheme.po new file mode 100644 index 0000000..b718b48 --- /dev/null +++ b/_static/locales/ru/LC_MESSAGES/booktheme.po @@ -0,0 +1,75 @@ + +msgid "" +msgstr "" +"Project-Id-Version: Sphinx-Book-Theme\n" +"MIME-Version: 1.0\n" +"Content-Type: text/plain; charset=UTF-8\n" +"Content-Transfer-Encoding: 8bit\n" +"Language: ru\n" +"Plural-Forms: nplurals=2; plural=(n != 1);\n" + +msgid "Theme by the" +msgstr "Тема от" + +msgid "Open an issue" +msgstr "Открыть вопрос" + +msgid "Contents" +msgstr "Содержание" + +msgid "Download notebook file" +msgstr "Скачать файл записной книжки" + +msgid "Sphinx Book Theme" +msgstr "Тема книги Сфинкс" + +msgid "Fullscreen mode" +msgstr "Полноэкранный режим" + +msgid "Edit this page" +msgstr "Редактировать эту страницу" + +msgid "By" +msgstr "По" + +msgid "Copyright" +msgstr "авторское право" + +msgid "Source repository" +msgstr "Исходный репозиторий" + +msgid "previous page" +msgstr "Предыдущая страница" + +msgid "next page" +msgstr "Следующая страница" + +msgid "Toggle navigation" +msgstr "Переключить навигацию" + +msgid "repository" +msgstr "хранилище" + +msgid "suggest edit" +msgstr "предложить редактировать" + +msgid "open issue" +msgstr "открытый вопрос" + +msgid "Launch" +msgstr "Запуск" + +msgid "Print to PDF" +msgstr "Распечатать в PDF" + +msgid "By the" +msgstr "Посредством" + +msgid "Last updated on" +msgstr "Последнее обновление" + +msgid "Download source file" +msgstr "Скачать исходный файл" + +msgid "Download this page" +msgstr "Загрузите эту страницу" diff --git a/_static/locales/sk/LC_MESSAGES/booktheme.mo b/_static/locales/sk/LC_MESSAGES/booktheme.mo new file mode 100644 index 0000000..59bd0dd Binary files /dev/null and b/_static/locales/sk/LC_MESSAGES/booktheme.mo differ diff --git a/_static/locales/sk/LC_MESSAGES/booktheme.po b/_static/locales/sk/LC_MESSAGES/booktheme.po new file mode 100644 index 0000000..f6c423b --- /dev/null +++ b/_static/locales/sk/LC_MESSAGES/booktheme.po @@ -0,0 +1,75 @@ + +msgid "" +msgstr "" +"Project-Id-Version: Sphinx-Book-Theme\n" +"MIME-Version: 1.0\n" +"Content-Type: text/plain; charset=UTF-8\n" +"Content-Transfer-Encoding: 8bit\n" +"Language: sk\n" +"Plural-Forms: nplurals=2; plural=(n != 1);\n" + +msgid "Theme by the" +msgstr "Téma od" + +msgid "Open an issue" +msgstr "Otvorte problém" + +msgid "Contents" +msgstr "Obsah" + +msgid "Download notebook file" +msgstr "Stiahnite si zošit" + +msgid "Sphinx Book Theme" +msgstr "Téma knihy Sfinga" + +msgid "Fullscreen mode" +msgstr "Režim celej obrazovky" + +msgid "Edit this page" +msgstr "Upraviť túto stránku" + +msgid "By" +msgstr "Autor:" + +msgid "Copyright" +msgstr "Autorské práva" + +msgid "Source repository" +msgstr "Zdrojové úložisko" + +msgid "previous page" +msgstr "predchádzajúca strana" + +msgid "next page" +msgstr "ďalšia strana" + +msgid "Toggle navigation" +msgstr "Prepnúť navigáciu" + +msgid "repository" +msgstr "Úložisko" + +msgid "suggest edit" +msgstr "navrhnúť úpravu" + +msgid "open issue" +msgstr "otvorené vydanie" + +msgid "Launch" +msgstr "Spustiť" + +msgid "Print to PDF" +msgstr "Tlač do PDF" + +msgid "By the" +msgstr "Podľa" + +msgid "Last updated on" +msgstr "Posledná aktualizácia dňa" + +msgid "Download source file" +msgstr "Stiahnite si zdrojový súbor" + +msgid "Download this page" +msgstr "Stiahnite si túto stránku" diff --git a/_static/locales/sl/LC_MESSAGES/booktheme.mo b/_static/locales/sl/LC_MESSAGES/booktheme.mo new file mode 100644 index 0000000..87bf26d Binary files /dev/null and b/_static/locales/sl/LC_MESSAGES/booktheme.mo differ diff --git a/_static/locales/sl/LC_MESSAGES/booktheme.po b/_static/locales/sl/LC_MESSAGES/booktheme.po new file mode 100644 index 0000000..9822dc5 --- /dev/null +++ b/_static/locales/sl/LC_MESSAGES/booktheme.po @@ -0,0 +1,75 @@ + +msgid "" +msgstr "" +"Project-Id-Version: Sphinx-Book-Theme\n" +"MIME-Version: 1.0\n" +"Content-Type: text/plain; charset=UTF-8\n" +"Content-Transfer-Encoding: 8bit\n" +"Language: sl\n" +"Plural-Forms: nplurals=2; plural=(n != 1);\n" + +msgid "Theme by the" +msgstr "Tema avtorja" + +msgid "Open an issue" +msgstr "Odprite številko" + +msgid "Contents" +msgstr "Vsebina" + +msgid "Download notebook file" +msgstr "Prenesite datoteko zvezka" + +msgid "Sphinx Book Theme" +msgstr "Tema knjige Sphinx" + +msgid "Fullscreen mode" +msgstr "Celozaslonski način" + +msgid "Edit this page" +msgstr "Uredite to stran" + +msgid "By" +msgstr "Avtor" + +msgid "Copyright" +msgstr "avtorske pravice" + +msgid "Source repository" +msgstr "Izvorno skladišče" + +msgid "previous page" +msgstr "Prejšnja stran" + +msgid "next page" +msgstr "Naslednja stran" + +msgid "Toggle navigation" +msgstr "Preklopi navigacijo" + +msgid "repository" +msgstr "odlagališče" + +msgid "suggest edit" +msgstr "predlagajte urejanje" + +msgid "open issue" +msgstr "odprto vprašanje" + +msgid "Launch" +msgstr "Kosilo" + +msgid "Print to PDF" +msgstr "Natisni v PDF" + +msgid "By the" +msgstr "Avtor" + +msgid "Last updated on" +msgstr "Nazadnje posodobljeno dne" + +msgid "Download source file" +msgstr "Prenesite izvorno datoteko" + +msgid "Download this page" +msgstr "Prenesite to stran" diff --git a/_static/locales/sr/LC_MESSAGES/booktheme.mo b/_static/locales/sr/LC_MESSAGES/booktheme.mo new file mode 100644 index 0000000..ec740f4 Binary files /dev/null and b/_static/locales/sr/LC_MESSAGES/booktheme.mo differ diff --git a/_static/locales/sr/LC_MESSAGES/booktheme.po b/_static/locales/sr/LC_MESSAGES/booktheme.po new file mode 100644 index 0000000..e809230 --- /dev/null +++ b/_static/locales/sr/LC_MESSAGES/booktheme.po @@ -0,0 +1,75 @@ + +msgid "" +msgstr "" +"Project-Id-Version: Sphinx-Book-Theme\n" +"MIME-Version: 1.0\n" +"Content-Type: text/plain; charset=UTF-8\n" +"Content-Transfer-Encoding: 8bit\n" +"Language: sr\n" +"Plural-Forms: nplurals=2; plural=(n != 1);\n" + +msgid "Theme by the" +msgstr "Тхеме би" + +msgid "Open an issue" +msgstr "Отворите издање" + +msgid "Contents" +msgstr "Садржај" + +msgid "Download notebook file" +msgstr "Преузмите датотеку бележнице" + +msgid "Sphinx Book Theme" +msgstr "Тема књиге Спхинк" + +msgid "Fullscreen mode" +msgstr "Режим целог екрана" + +msgid "Edit this page" +msgstr "Уредите ову страницу" + +msgid "By" +msgstr "Од стране" + +msgid "Copyright" +msgstr "Ауторско право" + +msgid "Source repository" +msgstr "Изворно спремиште" + +msgid "previous page" +msgstr "Претходна страница" + +msgid "next page" +msgstr "Следећа страна" + +msgid "Toggle navigation" +msgstr "Укључи / искључи навигацију" + +msgid "repository" +msgstr "спремиште" + +msgid "suggest edit" +msgstr "предложи уређивање" + +msgid "open issue" +msgstr "отворено издање" + +msgid "Launch" +msgstr "Лансирање" + +msgid "Print to PDF" +msgstr "Испис у ПДФ" + +msgid "By the" +msgstr "Од" + +msgid "Last updated on" +msgstr "Последње ажурирање" + +msgid "Download source file" +msgstr "Преузми изворну датотеку" + +msgid "Download this page" +msgstr "Преузмите ову страницу" diff --git a/_static/locales/sv/LC_MESSAGES/booktheme.mo b/_static/locales/sv/LC_MESSAGES/booktheme.mo new file mode 100644 index 0000000..b07dc76 Binary files /dev/null and b/_static/locales/sv/LC_MESSAGES/booktheme.mo differ diff --git a/_static/locales/sv/LC_MESSAGES/booktheme.po b/_static/locales/sv/LC_MESSAGES/booktheme.po new file mode 100644 index 0000000..2421b00 --- /dev/null +++ b/_static/locales/sv/LC_MESSAGES/booktheme.po @@ -0,0 +1,75 @@ + +msgid "" +msgstr "" +"Project-Id-Version: Sphinx-Book-Theme\n" +"MIME-Version: 1.0\n" +"Content-Type: text/plain; charset=UTF-8\n" +"Content-Transfer-Encoding: 8bit\n" +"Language: sv\n" +"Plural-Forms: nplurals=2; plural=(n != 1);\n" + +msgid "Theme by the" +msgstr "Tema av" + +msgid "Open an issue" +msgstr "Öppna en problemrapport" + +msgid "Contents" +msgstr "Innehåll" + +msgid "Download notebook file" +msgstr "Ladda ner notebook-fil" + +msgid "Sphinx Book Theme" +msgstr "Sphinx Boktema" + +msgid "Fullscreen mode" +msgstr "Fullskärmsläge" + +msgid "Edit this page" +msgstr "Redigera den här sidan" + +msgid "By" +msgstr "Av" + +msgid "Copyright" +msgstr "Upphovsrätt" + +msgid "Source repository" +msgstr "Källkodsrepositorium" + +msgid "previous page" +msgstr "föregående sida" + +msgid "next page" +msgstr "nästa sida" + +msgid "Toggle navigation" +msgstr "Växla navigering" + +msgid "repository" +msgstr "repositorium" + +msgid "suggest edit" +msgstr "föreslå ändring" + +msgid "open issue" +msgstr "öppna problemrapport" + +msgid "Launch" +msgstr "Öppna" + +msgid "Print to PDF" +msgstr "Skriv ut till PDF" + +msgid "By the" +msgstr "Av den" + +msgid "Last updated on" +msgstr "Senast uppdaterad den" + +msgid "Download source file" +msgstr "Ladda ner källfil" + +msgid "Download this page" +msgstr "Ladda ner den här sidan" diff --git a/_static/locales/ta/LC_MESSAGES/booktheme.mo b/_static/locales/ta/LC_MESSAGES/booktheme.mo new file mode 100644 index 0000000..29f52e1 Binary files /dev/null and b/_static/locales/ta/LC_MESSAGES/booktheme.mo differ diff --git a/_static/locales/ta/LC_MESSAGES/booktheme.po b/_static/locales/ta/LC_MESSAGES/booktheme.po new file mode 100644 index 0000000..500042f --- /dev/null +++ b/_static/locales/ta/LC_MESSAGES/booktheme.po @@ -0,0 +1,66 @@ + +msgid "" +msgstr "" +"Project-Id-Version: Sphinx-Book-Theme\n" +"MIME-Version: 1.0\n" +"Content-Type: text/plain; charset=UTF-8\n" +"Content-Transfer-Encoding: 8bit\n" +"Language: ta\n" +"Plural-Forms: nplurals=2; plural=(n != 1);\n" + +msgid "Theme by the" +msgstr "வழங்கிய தீம்" + +msgid "Open an issue" +msgstr "சிக்கலைத் திறக்கவும்" + +msgid "Download notebook file" +msgstr "நோட்புக் கோப்பைப் பதிவிறக்கவும்" + +msgid "Sphinx Book Theme" +msgstr "ஸ்பிங்க்ஸ் புத்தக தீம்" + +msgid "Edit this page" +msgstr "இந்தப் பக்கத்தைத் திருத்தவும்" + +msgid "By" +msgstr "வழங்கியவர்" + +msgid "Copyright" +msgstr "பதிப்புரிமை" + +msgid "Source repository" +msgstr "மூல களஞ்சியம்" + +msgid "previous page" +msgstr "முந்தைய பக்கம்" + +msgid "next page" +msgstr "அடுத்த பக்கம்" + +msgid "Toggle navigation" +msgstr "வழிசெலுத்தலை நிலைமாற்று" + +msgid "suggest edit" +msgstr "திருத்த பரிந்துரைக்கவும்" + +msgid "open issue" +msgstr "திறந்த பிரச்சினை" + +msgid "Launch" +msgstr "தொடங்க" + +msgid "Print to PDF" +msgstr "PDF இல் அச்சிடுக" + +msgid "By the" +msgstr "மூலம்" + +msgid "Last updated on" +msgstr "கடைசியாக புதுப்பிக்கப்பட்டது" + +msgid "Download source file" +msgstr "மூல கோப்பைப் பதிவிறக்குக" + +msgid "Download this page" +msgstr "இந்தப் பக்கத்தைப் பதிவிறக்கவும்" diff --git a/_static/locales/te/LC_MESSAGES/booktheme.mo b/_static/locales/te/LC_MESSAGES/booktheme.mo new file mode 100644 index 0000000..0a5f4b4 Binary files /dev/null and b/_static/locales/te/LC_MESSAGES/booktheme.mo differ diff --git a/_static/locales/te/LC_MESSAGES/booktheme.po b/_static/locales/te/LC_MESSAGES/booktheme.po new file mode 100644 index 0000000..b1afebb --- /dev/null +++ b/_static/locales/te/LC_MESSAGES/booktheme.po @@ -0,0 +1,66 @@ + +msgid "" +msgstr "" +"Project-Id-Version: Sphinx-Book-Theme\n" +"MIME-Version: 1.0\n" +"Content-Type: text/plain; charset=UTF-8\n" +"Content-Transfer-Encoding: 8bit\n" +"Language: te\n" +"Plural-Forms: nplurals=2; plural=(n != 1);\n" + +msgid "Theme by the" +msgstr "ద్వారా థీమ్" + +msgid "Open an issue" +msgstr "సమస్యను తెరవండి" + +msgid "Download notebook file" +msgstr "నోట్బుక్ ఫైల్ను డౌన్లోడ్ చేయండి" + +msgid "Sphinx Book Theme" +msgstr "సింహిక పుస్తక థీమ్" + +msgid "Edit this page" +msgstr "ఈ పేజీని సవరించండి" + +msgid "By" +msgstr "ద్వారా" + +msgid "Copyright" +msgstr "కాపీరైట్" + +msgid "Source repository" +msgstr "మూల రిపోజిటరీ" + +msgid "previous page" +msgstr "ముందు పేజి" + +msgid "next page" +msgstr "తరువాతి పేజీ" + +msgid "Toggle navigation" +msgstr "నావిగేషన్‌ను టోగుల్ చేయండి" + +msgid "suggest edit" +msgstr "సవరించమని సూచించండి" + +msgid "open issue" +msgstr "ఓపెన్ ఇష్యూ" + +msgid "Launch" +msgstr "ప్రారంభించండి" + +msgid "Print to PDF" +msgstr "PDF కి ముద్రించండి" + +msgid "By the" +msgstr "ద్వారా" + +msgid "Last updated on" +msgstr "చివరిగా నవీకరించబడింది" + +msgid "Download source file" +msgstr "మూల ఫైల్‌ను డౌన్‌లోడ్ చేయండి" + +msgid "Download this page" +msgstr "ఈ పేజీని డౌన్‌లోడ్ చేయండి" diff --git a/_static/locales/tg/LC_MESSAGES/booktheme.mo b/_static/locales/tg/LC_MESSAGES/booktheme.mo new file mode 100644 index 0000000..b21c6c6 Binary files /dev/null and b/_static/locales/tg/LC_MESSAGES/booktheme.mo differ diff --git a/_static/locales/tg/LC_MESSAGES/booktheme.po b/_static/locales/tg/LC_MESSAGES/booktheme.po new file mode 100644 index 0000000..29b8237 --- /dev/null +++ b/_static/locales/tg/LC_MESSAGES/booktheme.po @@ -0,0 +1,75 @@ + +msgid "" +msgstr "" +"Project-Id-Version: Sphinx-Book-Theme\n" +"MIME-Version: 1.0\n" +"Content-Type: text/plain; charset=UTF-8\n" +"Content-Transfer-Encoding: 8bit\n" +"Language: tg\n" +"Plural-Forms: nplurals=2; plural=(n != 1);\n" + +msgid "Theme by the" +msgstr "Мавзӯъи аз" + +msgid "Open an issue" +msgstr "Масъаларо кушоед" + +msgid "Contents" +msgstr "Мундариҷа" + +msgid "Download notebook file" +msgstr "Файли дафтарро зеркашӣ кунед" + +msgid "Sphinx Book Theme" +msgstr "Сфинкс Мавзӯи китоб" + +msgid "Fullscreen mode" +msgstr "Ҳолати экрани пурра" + +msgid "Edit this page" +msgstr "Ин саҳифаро таҳрир кунед" + +msgid "By" +msgstr "Бо" + +msgid "Copyright" +msgstr "Ҳуқуқи муаллиф" + +msgid "Source repository" +msgstr "Анбори манбаъ" + +msgid "previous page" +msgstr "саҳифаи қаблӣ" + +msgid "next page" +msgstr "саҳифаи оянда" + +msgid "Toggle navigation" +msgstr "Гузаришро иваз кунед" + +msgid "repository" +msgstr "анбор" + +msgid "suggest edit" +msgstr "пешниҳод вироиш" + +msgid "open issue" +msgstr "барориши кушод" + +msgid "Launch" +msgstr "Оғоз" + +msgid "Print to PDF" +msgstr "Чоп ба PDF" + +msgid "By the" +msgstr "Бо" + +msgid "Last updated on" +msgstr "Last навсозӣ дар" + +msgid "Download source file" +msgstr "Файли манбаъро зеркашӣ кунед" + +msgid "Download this page" +msgstr "Ин саҳифаро зеркашӣ кунед" diff --git a/_static/locales/th/LC_MESSAGES/booktheme.mo b/_static/locales/th/LC_MESSAGES/booktheme.mo new file mode 100644 index 0000000..abede98 Binary files /dev/null and b/_static/locales/th/LC_MESSAGES/booktheme.mo differ diff --git a/_static/locales/th/LC_MESSAGES/booktheme.po b/_static/locales/th/LC_MESSAGES/booktheme.po new file mode 100644 index 0000000..ac65ee0 --- /dev/null +++ b/_static/locales/th/LC_MESSAGES/booktheme.po @@ -0,0 +1,75 @@ + +msgid "" +msgstr "" +"Project-Id-Version: Sphinx-Book-Theme\n" +"MIME-Version: 1.0\n" +"Content-Type: text/plain; charset=UTF-8\n" +"Content-Transfer-Encoding: 8bit\n" +"Language: th\n" +"Plural-Forms: nplurals=2; plural=(n != 1);\n" + +msgid "Theme by the" +msgstr "ธีมโดย" + +msgid "Open an issue" +msgstr "เปิดปัญหา" + +msgid "Contents" +msgstr "สารบัญ" + +msgid "Download notebook file" +msgstr "ดาวน์โหลดไฟล์สมุดบันทึก" + +msgid "Sphinx Book Theme" +msgstr "ธีมหนังสือสฟิงซ์" + +msgid "Fullscreen mode" +msgstr "โหมดเต็มหน้าจอ" + +msgid "Edit this page" +msgstr "แก้ไขหน้านี้" + +msgid "By" +msgstr "โดย" + +msgid "Copyright" +msgstr "ลิขสิทธิ์" + +msgid "Source repository" +msgstr "ที่เก็บซอร์ส" + +msgid "previous page" +msgstr "หน้าที่แล้ว" + +msgid "next page" +msgstr "หน้าต่อไป" + +msgid "Toggle navigation" +msgstr "ไม่ต้องสลับช่องทาง" + +msgid "repository" +msgstr "ที่เก็บ" + +msgid "suggest edit" +msgstr "แนะนำแก้ไข" + +msgid "open issue" +msgstr "เปิดปัญหา" + +msgid "Launch" +msgstr "เปิด" + +msgid "Print to PDF" +msgstr "พิมพ์เป็น PDF" + +msgid "By the" +msgstr "โดย" + +msgid "Last updated on" +msgstr "ปรับปรุงล่าสุดเมื่อ" + +msgid "Download source file" +msgstr "ดาวน์โหลดไฟล์ต้นฉบับ" + +msgid "Download this page" +msgstr "ดาวน์โหลดหน้านี้" diff --git a/_static/locales/tl/LC_MESSAGES/booktheme.mo b/_static/locales/tl/LC_MESSAGES/booktheme.mo new file mode 100644 index 0000000..8df1b73 Binary files /dev/null and b/_static/locales/tl/LC_MESSAGES/booktheme.mo differ diff --git a/_static/locales/tl/LC_MESSAGES/booktheme.po b/_static/locales/tl/LC_MESSAGES/booktheme.po new file mode 100644 index 0000000..662d66c --- /dev/null +++ b/_static/locales/tl/LC_MESSAGES/booktheme.po @@ -0,0 +1,66 @@ + +msgid "" +msgstr "" +"Project-Id-Version: Sphinx-Book-Theme\n" +"MIME-Version: 1.0\n" +"Content-Type: text/plain; charset=UTF-8\n" +"Content-Transfer-Encoding: 8bit\n" +"Language: tl\n" +"Plural-Forms: nplurals=2; plural=(n != 1);\n" + +msgid "Theme by the" +msgstr "Tema ng" + +msgid "Open an issue" +msgstr "Magbukas ng isyu" + +msgid "Download notebook file" +msgstr "Mag-download ng file ng notebook" + +msgid "Sphinx Book Theme" +msgstr "Tema ng Sphinx Book" + +msgid "Edit this page" +msgstr "I-edit ang pahinang ito" + +msgid "By" +msgstr "Ni" + +msgid "Copyright" +msgstr "Copyright" + +msgid "Source repository" +msgstr "Pinagmulan ng imbakan" + +msgid "previous page" +msgstr "Nakaraang pahina" + +msgid "next page" +msgstr "Susunod na pahina" + +msgid "Toggle navigation" +msgstr "I-toggle ang pag-navigate" + +msgid "suggest edit" +msgstr "iminumungkahi i-edit" + +msgid "open issue" +msgstr "bukas na isyu" + +msgid "Launch" +msgstr "Ilunsad" + +msgid "Print to PDF" +msgstr "I-print sa PDF" + +msgid "By the" +msgstr "Sa pamamagitan ng" + +msgid "Last updated on" +msgstr "Huling na-update noong" + +msgid "Download source file" +msgstr "Mag-download ng file ng pinagmulan" + +msgid "Download this page" +msgstr "I-download ang pahinang ito" diff --git a/_static/locales/tr/LC_MESSAGES/booktheme.mo b/_static/locales/tr/LC_MESSAGES/booktheme.mo new file mode 100644 index 0000000..029ae18 Binary files /dev/null and b/_static/locales/tr/LC_MESSAGES/booktheme.mo differ diff --git a/_static/locales/tr/LC_MESSAGES/booktheme.po b/_static/locales/tr/LC_MESSAGES/booktheme.po new file mode 100644 index 0000000..d1ae723 --- /dev/null +++ b/_static/locales/tr/LC_MESSAGES/booktheme.po @@ -0,0 +1,75 @@ + +msgid "" +msgstr "" +"Project-Id-Version: Sphinx-Book-Theme\n" +"MIME-Version: 1.0\n" +"Content-Type: text/plain; charset=UTF-8\n" +"Content-Transfer-Encoding: 8bit\n" +"Language: tr\n" +"Plural-Forms: nplurals=2; plural=(n != 1);\n" + +msgid "Theme by the" +msgstr "Tarafından tema" + +msgid "Open an issue" +msgstr "Bir sorunu açın" + +msgid "Contents" +msgstr "İçindekiler" + +msgid "Download notebook file" +msgstr "Defter dosyasını indirin" + +msgid "Sphinx Book Theme" +msgstr "Sfenks Kitap Teması" + +msgid "Fullscreen mode" +msgstr "Tam ekran modu" + +msgid "Edit this page" +msgstr "Bu sayfayı düzenle" + +msgid "By" +msgstr "Tarafından" + +msgid "Copyright" +msgstr "Telif hakkı" + +msgid "Source repository" +msgstr "Kaynak kod deposu" + +msgid "previous page" +msgstr "önceki sayfa" + +msgid "next page" +msgstr "sonraki Sayfa" + +msgid "Toggle navigation" +msgstr "Gezinmeyi değiştir" + +msgid "repository" +msgstr "depo" + +msgid "suggest edit" +msgstr "düzenleme öner" + +msgid "open issue" +msgstr "Açık konu" + +msgid "Launch" +msgstr "Başlatmak" + +msgid "Print to PDF" +msgstr "PDF olarak yazdır" + +msgid "By the" +msgstr "Tarafından" + +msgid "Last updated on" +msgstr "Son güncelleme tarihi" + +msgid "Download source file" +msgstr "Kaynak dosyayı indirin" + +msgid "Download this page" +msgstr "Bu sayfayı indirin" diff --git a/_static/locales/uk/LC_MESSAGES/booktheme.mo b/_static/locales/uk/LC_MESSAGES/booktheme.mo new file mode 100644 index 0000000..16ab789 Binary files /dev/null and b/_static/locales/uk/LC_MESSAGES/booktheme.mo differ diff --git a/_static/locales/uk/LC_MESSAGES/booktheme.po b/_static/locales/uk/LC_MESSAGES/booktheme.po new file mode 100644 index 0000000..be49ab8 --- /dev/null +++ b/_static/locales/uk/LC_MESSAGES/booktheme.po @@ -0,0 +1,75 @@ + +msgid "" +msgstr "" +"Project-Id-Version: Sphinx-Book-Theme\n" +"MIME-Version: 1.0\n" +"Content-Type: text/plain; charset=UTF-8\n" +"Content-Transfer-Encoding: 8bit\n" +"Language: uk\n" +"Plural-Forms: nplurals=2; plural=(n != 1);\n" + +msgid "Theme by the" +msgstr "Тема від" + +msgid "Open an issue" +msgstr "Відкрийте випуск" + +msgid "Contents" +msgstr "Зміст" + +msgid "Download notebook file" +msgstr "Завантажте файл блокнота" + +msgid "Sphinx Book Theme" +msgstr "Тема книги \"Сфінкс\"" + +msgid "Fullscreen mode" +msgstr "Повноекранний режим" + +msgid "Edit this page" +msgstr "Редагувати цю сторінку" + +msgid "By" +msgstr "Автор" + +msgid "Copyright" +msgstr "Авторське право" + +msgid "Source repository" +msgstr "Джерело сховища" + +msgid "previous page" +msgstr "Попередня сторінка" + +msgid "next page" +msgstr "Наступна сторінка" + +msgid "Toggle navigation" +msgstr "Переключити навігацію" + +msgid "repository" +msgstr "сховище" + +msgid "suggest edit" +msgstr "запропонувати редагувати" + +msgid "open issue" +msgstr "відкритий випуск" + +msgid "Launch" +msgstr "Запуск" + +msgid "Print to PDF" +msgstr "Друк у форматі PDF" + +msgid "By the" +msgstr "По" + +msgid "Last updated on" +msgstr "Останнє оновлення:" + +msgid "Download source file" +msgstr "Завантажити вихідний файл" + +msgid "Download this page" +msgstr "Завантажте цю сторінку" diff --git a/_static/locales/ur/LC_MESSAGES/booktheme.mo b/_static/locales/ur/LC_MESSAGES/booktheme.mo new file mode 100644 index 0000000..de8c84b Binary files /dev/null and b/_static/locales/ur/LC_MESSAGES/booktheme.mo differ diff --git a/_static/locales/ur/LC_MESSAGES/booktheme.po b/_static/locales/ur/LC_MESSAGES/booktheme.po new file mode 100644 index 0000000..94bcab3 --- /dev/null +++ b/_static/locales/ur/LC_MESSAGES/booktheme.po @@ -0,0 +1,66 @@ + +msgid "" +msgstr "" +"Project-Id-Version: Sphinx-Book-Theme\n" +"MIME-Version: 1.0\n" +"Content-Type: text/plain; charset=UTF-8\n" +"Content-Transfer-Encoding: 8bit\n" +"Language: ur\n" +"Plural-Forms: nplurals=2; plural=(n != 1);\n" + +msgid "Theme by the" +msgstr "کے ذریعہ تھیم" + +msgid "Open an issue" +msgstr "ایک مسئلہ کھولیں" + +msgid "Download notebook file" +msgstr "نوٹ بک فائل ڈاؤن لوڈ کریں" + +msgid "Sphinx Book Theme" +msgstr "سپنکس بک تھیم" + +msgid "Edit this page" +msgstr "اس صفحے میں ترمیم کریں" + +msgid "By" +msgstr "بذریعہ" + +msgid "Copyright" +msgstr "کاپی رائٹ" + +msgid "Source repository" +msgstr "ماخذ ذخیرہ" + +msgid "previous page" +msgstr "سابقہ ​​صفحہ" + +msgid "next page" +msgstr "اگلا صفحہ" + +msgid "Toggle navigation" +msgstr "نیویگیشن ٹوگل کریں" + +msgid "suggest edit" +msgstr "ترمیم کی تجویز کریں" + +msgid "open issue" +msgstr "کھلا مسئلہ" + +msgid "Launch" +msgstr "لانچ کریں" + +msgid "Print to PDF" +msgstr "پی ڈی ایف پرنٹ کریں" + +msgid "By the" +msgstr "کی طرف" + +msgid "Last updated on" +msgstr "آخری بار تازہ کاری ہوئی" + +msgid "Download source file" +msgstr "سورس فائل ڈاؤن لوڈ کریں" + +msgid "Download this page" +msgstr "اس صفحے کو ڈاؤن لوڈ کریں" diff --git a/_static/locales/vi/LC_MESSAGES/booktheme.mo b/_static/locales/vi/LC_MESSAGES/booktheme.mo new file mode 100644 index 0000000..2bb3255 Binary files /dev/null and b/_static/locales/vi/LC_MESSAGES/booktheme.mo differ diff --git a/_static/locales/vi/LC_MESSAGES/booktheme.po b/_static/locales/vi/LC_MESSAGES/booktheme.po new file mode 100644 index 0000000..116236d --- /dev/null +++ b/_static/locales/vi/LC_MESSAGES/booktheme.po @@ -0,0 +1,75 @@ + +msgid "" +msgstr "" +"Project-Id-Version: Sphinx-Book-Theme\n" +"MIME-Version: 1.0\n" +"Content-Type: text/plain; charset=UTF-8\n" +"Content-Transfer-Encoding: 8bit\n" +"Language: vi\n" +"Plural-Forms: nplurals=2; plural=(n != 1);\n" + +msgid "Theme by the" +msgstr "Chủ đề của" + +msgid "Open an issue" +msgstr "Mở một vấn đề" + +msgid "Contents" +msgstr "Nội dung" + +msgid "Download notebook file" +msgstr "Tải xuống tệp sổ tay" + +msgid "Sphinx Book Theme" +msgstr "Chủ đề sách nhân sư" + +msgid "Fullscreen mode" +msgstr "Chế độ toàn màn hình" + +msgid "Edit this page" +msgstr "chỉnh sửa trang này" + +msgid "By" +msgstr "Bởi" + +msgid "Copyright" +msgstr "Bản quyền" + +msgid "Source repository" +msgstr "Kho nguồn" + +msgid "previous page" +msgstr "trang trước" + +msgid "next page" +msgstr "Trang tiếp theo" + +msgid "Toggle navigation" +msgstr "Chuyển đổi điều hướng thành" + +msgid "repository" +msgstr "kho" + +msgid "suggest edit" +msgstr "đề nghị chỉnh sửa" + +msgid "open issue" +msgstr "vấn đề mở" + +msgid "Launch" +msgstr "Phóng" + +msgid "Print to PDF" +msgstr "In sang PDF" + +msgid "By the" +msgstr "Bằng" + +msgid "Last updated on" +msgstr "Cập nhật lần cuối vào" + +msgid "Download source file" +msgstr "Tải xuống tệp nguồn" + +msgid "Download this page" +msgstr "Tải xuống trang này" diff --git a/_static/locales/zh_CN/LC_MESSAGES/booktheme.mo b/_static/locales/zh_CN/LC_MESSAGES/booktheme.mo new file mode 100644 index 0000000..0e3235d Binary files /dev/null and b/_static/locales/zh_CN/LC_MESSAGES/booktheme.mo differ diff --git a/_static/locales/zh_CN/LC_MESSAGES/booktheme.po b/_static/locales/zh_CN/LC_MESSAGES/booktheme.po new file mode 100644 index 0000000..4f4ab57 --- /dev/null +++ b/_static/locales/zh_CN/LC_MESSAGES/booktheme.po @@ -0,0 +1,75 @@ + +msgid "" +msgstr "" +"Project-Id-Version: Sphinx-Book-Theme\n" +"MIME-Version: 1.0\n" +"Content-Type: text/plain; charset=UTF-8\n" +"Content-Transfer-Encoding: 8bit\n" +"Language: zh_CN\n" +"Plural-Forms: nplurals=2; plural=(n != 1);\n" + +msgid "Theme by the" +msgstr "主题作者：" + +msgid "Open an issue" +msgstr "创建议题" + +msgid "Contents" +msgstr "目录" + +msgid "Download notebook file" +msgstr "下载笔记本文件" + +msgid "Sphinx Book Theme" +msgstr "Sphinx Book 主题" + +msgid "Fullscreen mode" +msgstr "全屏模式" + +msgid "Edit this page" +msgstr "编辑此页面" + +msgid "By" +msgstr "作者：" + +msgid "Copyright" +msgstr "版权" + +msgid "Source repository" +msgstr "源码库" + +msgid "previous page" +msgstr "上一页" + +msgid "next page" +msgstr "下一页" + +msgid "Toggle navigation" +msgstr "显示或隐藏导航栏" + +msgid "repository" +msgstr "仓库" + +msgid "suggest edit" +msgstr "提出修改建议" + +msgid "open issue" +msgstr "创建议题" + +msgid "Launch" +msgstr "启动" + +msgid "Print to PDF" +msgstr "列印成 PDF" + +msgid "By the" +msgstr "作者：" + +msgid "Last updated on" +msgstr "上次更新时间：" + +msgid "Download source file" +msgstr "下载源文件" + +msgid "Download this page" +msgstr "下载此页面" diff --git a/_static/locales/zh_TW/LC_MESSAGES/booktheme.mo b/_static/locales/zh_TW/LC_MESSAGES/booktheme.mo new file mode 100644 index 0000000..9116fa9 Binary files /dev/null and b/_static/locales/zh_TW/LC_MESSAGES/booktheme.mo differ diff --git a/_static/locales/zh_TW/LC_MESSAGES/booktheme.po b/_static/locales/zh_TW/LC_MESSAGES/booktheme.po new file mode 100644 index 0000000..42b43b8 --- /dev/null +++ b/_static/locales/zh_TW/LC_MESSAGES/booktheme.po @@ -0,0 +1,75 @@ + +msgid "" +msgstr "" +"Project-Id-Version: Sphinx-Book-Theme\n" +"MIME-Version: 1.0\n" +"Content-Type: text/plain; charset=UTF-8\n" +"Content-Transfer-Encoding: 8bit\n" +"Language: zh_TW\n" +"Plural-Forms: nplurals=2; plural=(n != 1);\n" + +msgid "Theme by the" +msgstr "佈景主題作者：" + +msgid "Open an issue" +msgstr "開啟議題" + +msgid "Contents" +msgstr "目錄" + +msgid "Download notebook file" +msgstr "下載 Notebook 檔案" + +msgid "Sphinx Book Theme" +msgstr "Sphinx Book 佈景主題" + +msgid "Fullscreen mode" +msgstr "全螢幕模式" + +msgid "Edit this page" +msgstr "編輯此頁面" + +msgid "By" +msgstr "作者：" + +msgid "Copyright" +msgstr "Copyright" + +msgid "Source repository" +msgstr "來源儲存庫" + +msgid "previous page" +msgstr "上一頁" + +msgid "next page" +msgstr "下一頁" + +msgid "Toggle navigation" +msgstr "顯示或隱藏導覽列" + +msgid "repository" +msgstr "儲存庫" + +msgid "suggest edit" +msgstr "提出修改建議" + +msgid "open issue" +msgstr "公開的問題" + +msgid "Launch" +msgstr "啟動" + +msgid "Print to PDF" +msgstr "列印成 PDF" + +msgid "By the" +msgstr "作者：" + +msgid "Last updated on" +msgstr "最後更新時間：" + +msgid "Download source file" +msgstr "下載原始檔" + +msgid "Download this page" +msgstr "下載此頁面" diff --git a/_static/logo.png b/_static/logo.png new file mode 100644 index 0000000..fc529c5 Binary files /dev/null and b/_static/logo.png differ diff --git a/_static/minus.png b/_static/minus.png new file mode 100644 index 0000000..d96755f Binary files /dev/null and b/_static/minus.png differ diff --git a/_static/mystnb.4510f1fc1dee50b3e5859aac5469c37c29e427902b24a333a5f9fcb2f0b3ac41.css b/_static/mystnb.4510f1fc1dee50b3e5859aac5469c37c29e427902b24a333a5f9fcb2f0b3ac41.css new file mode 100644 index 0000000..3356631 --- /dev/null +++ b/_static/mystnb.4510f1fc1dee50b3e5859aac5469c37c29e427902b24a333a5f9fcb2f0b3ac41.css @@ -0,0 +1,2342 @@ +/* Variables */ +:root { + --mystnb-source-bg-color: #f7f7f7; + --mystnb-stdout-bg-color: #fcfcfc; + --mystnb-stderr-bg-color: #fdd; + --mystnb-traceback-bg-color: #fcfcfc; + --mystnb-source-border-color: #ccc; + --mystnb-source-margin-color: green; + --mystnb-stdout-border-color: #f7f7f7; + --mystnb-stderr-border-color: #f7f7f7; + 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0em !important; + border: none !important; +} + +/* All cell outputs */ +.cell_output { + padding-left: 1em; + padding-right: 0em; + margin-top: 1em; +} + +/* Text outputs from cells */ +.cell_output .output.text_plain, +.cell_output .output.traceback, +.cell_output .output.stream, +.cell_output .output.stderr { + margin-top: 1em; + margin-bottom: 0em; + box-shadow: none; +} + +.cell_output .output.text_plain, +.cell_output .output.stream { + background: var(--mystnb-stdout-bg-color); + border: 1px solid var(--mystnb-stdout-border-color); +} + +.cell_output .output.stderr { + background: var(--mystnb-stderr-bg-color); + border: 1px solid var(--mystnb-stderr-border-color); +} + +.cell_output .output.traceback { + background: var(--mystnb-traceback-bg-color); + border: 1px solid var(--mystnb-traceback-border-color); +} + +/* Collapsible cell content */ +div.cell details.above-input div.cell_input { + border-top-left-radius: 0; + border-top-right-radius: 0; + border-top: var(--mystnb-source-border-width) var(--mystnb-source-border-color) dashed; +} + +div.cell div.cell_input.above-output-prompt { + border-bottom-left-radius: 0; + border-bottom-right-radius: 0; +} + +div.cell details.above-input>summary { + border-bottom-left-radius: 0; + border-bottom-right-radius: 0; + border-bottom: var(--mystnb-source-border-width) var(--mystnb-source-border-color) dashed; + padding-left: 1em; + margin-bottom: 0; +} + +div.cell details.above-output>summary { + background-color: var(--mystnb-source-bg-color); + padding-left: 1em; + padding-right: 0em; + border: var(--mystnb-source-border-width) var(--mystnb-source-border-color) solid; + border-radius: var(--mystnb-source-border-radius); + border-left-color: var(--mystnb-source-margin-color); + border-left-width: medium; +} + +div.cell details.below-input>summary { + background-color: var(--mystnb-source-bg-color); + padding-left: 1em; + padding-right: 0em; + border: var(--mystnb-source-border-width) 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+div.highlight .-Color[class*=-BGC48] { + background-color: #00FF87 +} + +div.highlight .-Color[class*=-C49] { + color: #00FFAF +} + +div.highlight .-Color[class*=-BGC49] { + background-color: #00FFAF +} + +div.highlight .-Color[class*=-C50] { + color: #00FFD7 +} + +div.highlight .-Color[class*=-BGC50] { + background-color: #00FFD7 +} + +div.highlight .-Color[class*=-C51] { + color: #00FFFF +} + +div.highlight .-Color[class*=-BGC51] { + background-color: #00FFFF +} + +div.highlight .-Color[class*=-C52] { + color: #5F0000 +} + +div.highlight .-Color[class*=-BGC52] { + background-color: #5F0000 +} + +div.highlight .-Color[class*=-C53] { + color: #5F005F +} + +div.highlight .-Color[class*=-BGC53] { + background-color: #5F005F +} + +div.highlight .-Color[class*=-C54] { + color: #5F0087 +} + +div.highlight .-Color[class*=-BGC54] { + background-color: #5F0087 +} + +div.highlight .-Color[class*=-C55] { + color: #5F00AF +} + +div.highlight .-Color[class*=-BGC55] { + background-color: #5F00AF +} + +div.highlight .-Color[class*=-C56] { + color: #5F00D7 +} + +div.highlight .-Color[class*=-BGC56] { + background-color: #5F00D7 +} + +div.highlight .-Color[class*=-C57] { + color: #5F00FF +} + +div.highlight .-Color[class*=-BGC57] { + background-color: #5F00FF +} + +div.highlight .-Color[class*=-C58] { + color: #5F5F00 +} + +div.highlight .-Color[class*=-BGC58] { + background-color: #5F5F00 +} + +div.highlight .-Color[class*=-C59] { + color: #5F5F5F +} + +div.highlight .-Color[class*=-BGC59] { + background-color: #5F5F5F +} + +div.highlight .-Color[class*=-C60] { + color: #5F5F87 +} + +div.highlight .-Color[class*=-BGC60] { + background-color: #5F5F87 +} + +div.highlight .-Color[class*=-C61] { + color: #5F5FAF +} + +div.highlight .-Color[class*=-BGC61] { + background-color: #5F5FAF +} + +div.highlight .-Color[class*=-C62] { + color: #5F5FD7 +} + +div.highlight .-Color[class*=-BGC62] { + background-color: #5F5FD7 +} + +div.highlight .-Color[class*=-C63] { + color: #5F5FFF +} + +div.highlight .-Color[class*=-BGC63] { + background-color: #5F5FFF +} + +div.highlight .-Color[class*=-C64] { + color: #5F8700 +} + +div.highlight .-Color[class*=-BGC64] { + background-color: #5F8700 +} + +div.highlight .-Color[class*=-C65] { + color: #5F875F +} + +div.highlight .-Color[class*=-BGC65] { + background-color: #5F875F +} + +div.highlight .-Color[class*=-C66] { + color: #5F8787 +} + +div.highlight .-Color[class*=-BGC66] { + background-color: #5F8787 +} + +div.highlight .-Color[class*=-C67] { + color: #5F87AF +} + +div.highlight .-Color[class*=-BGC67] { + background-color: #5F87AF +} + +div.highlight .-Color[class*=-C68] { + color: #5F87D7 +} + +div.highlight .-Color[class*=-BGC68] { + background-color: #5F87D7 +} + +div.highlight .-Color[class*=-C69] { + color: #5F87FF +} + +div.highlight .-Color[class*=-BGC69] { + background-color: #5F87FF +} + +div.highlight .-Color[class*=-C70] { + color: #5FAF00 +} + +div.highlight .-Color[class*=-BGC70] { + background-color: #5FAF00 +} + +div.highlight .-Color[class*=-C71] { + color: #5FAF5F +} + +div.highlight .-Color[class*=-BGC71] { + background-color: #5FAF5F +} + +div.highlight .-Color[class*=-C72] { + color: #5FAF87 +} + +div.highlight .-Color[class*=-BGC72] { + background-color: #5FAF87 +} + +div.highlight .-Color[class*=-C73] { + color: #5FAFAF +} + +div.highlight .-Color[class*=-BGC73] { + background-color: #5FAFAF +} + +div.highlight .-Color[class*=-C74] { + color: #5FAFD7 +} + +div.highlight .-Color[class*=-BGC74] { + background-color: #5FAFD7 +} + +div.highlight .-Color[class*=-C75] { + color: #5FAFFF +} + +div.highlight .-Color[class*=-BGC75] { + background-color: #5FAFFF +} + +div.highlight .-Color[class*=-C76] { + color: #5FD700 +} + +div.highlight .-Color[class*=-BGC76] { + background-color: #5FD700 +} + +div.highlight .-Color[class*=-C77] { + color: #5FD75F +} + +div.highlight .-Color[class*=-BGC77] { + background-color: #5FD75F +} + +div.highlight .-Color[class*=-C78] { + color: #5FD787 +} + +div.highlight .-Color[class*=-BGC78] { + background-color: #5FD787 +} + +div.highlight .-Color[class*=-C79] { + color: #5FD7AF +} + +div.highlight .-Color[class*=-BGC79] { + background-color: #5FD7AF +} + +div.highlight .-Color[class*=-C80] { + color: #5FD7D7 +} + +div.highlight .-Color[class*=-BGC80] { + background-color: #5FD7D7 +} + +div.highlight .-Color[class*=-C81] { + color: #5FD7FF +} + +div.highlight .-Color[class*=-BGC81] { + background-color: #5FD7FF +} + +div.highlight .-Color[class*=-C82] { + color: #5FFF00 +} + +div.highlight .-Color[class*=-BGC82] { + background-color: #5FFF00 +} + +div.highlight .-Color[class*=-C83] { + color: #5FFF5F +} + +div.highlight .-Color[class*=-BGC83] { + background-color: #5FFF5F +} + +div.highlight .-Color[class*=-C84] { + color: #5FFF87 +} + +div.highlight .-Color[class*=-BGC84] { + background-color: #5FFF87 +} + +div.highlight .-Color[class*=-C85] { + color: #5FFFAF +} + +div.highlight .-Color[class*=-BGC85] { + background-color: #5FFFAF +} + +div.highlight .-Color[class*=-C86] { + color: #5FFFD7 +} + +div.highlight .-Color[class*=-BGC86] { + background-color: #5FFFD7 +} + +div.highlight .-Color[class*=-C87] { + color: #5FFFFF +} + +div.highlight .-Color[class*=-BGC87] { + background-color: #5FFFFF +} + +div.highlight .-Color[class*=-C88] { + color: #870000 +} + +div.highlight .-Color[class*=-BGC88] { + background-color: #870000 +} + +div.highlight .-Color[class*=-C89] { + color: #87005F +} + +div.highlight .-Color[class*=-BGC89] { + background-color: #87005F +} + +div.highlight .-Color[class*=-C90] { + color: #870087 +} + +div.highlight .-Color[class*=-BGC90] { + background-color: #870087 +} + +div.highlight .-Color[class*=-C91] { + color: #8700AF +} + +div.highlight .-Color[class*=-BGC91] { + background-color: #8700AF +} + +div.highlight .-Color[class*=-C92] { + color: #8700D7 +} + +div.highlight .-Color[class*=-BGC92] { + background-color: #8700D7 +} + +div.highlight .-Color[class*=-C93] { + color: #8700FF +} + +div.highlight .-Color[class*=-BGC93] { + background-color: #8700FF +} + +div.highlight .-Color[class*=-C94] { + color: #875F00 +} + +div.highlight .-Color[class*=-BGC94] { + background-color: #875F00 +} + +div.highlight .-Color[class*=-C95] { + color: #875F5F +} + +div.highlight .-Color[class*=-BGC95] { + background-color: #875F5F +} + +div.highlight .-Color[class*=-C96] { + color: #875F87 +} + +div.highlight .-Color[class*=-BGC96] { + background-color: #875F87 +} + +div.highlight .-Color[class*=-C97] { + color: #875FAF +} + +div.highlight .-Color[class*=-BGC97] { + background-color: #875FAF +} + +div.highlight .-Color[class*=-C98] { + color: #875FD7 +} + +div.highlight .-Color[class*=-BGC98] { + background-color: #875FD7 +} + +div.highlight .-Color[class*=-C99] { + color: #875FFF +} + +div.highlight .-Color[class*=-BGC99] { + background-color: #875FFF +} + +div.highlight .-Color[class*=-C100] { + color: #878700 +} + +div.highlight .-Color[class*=-BGC100] { + background-color: #878700 +} + +div.highlight .-Color[class*=-C101] { + color: #87875F +} + +div.highlight .-Color[class*=-BGC101] { + background-color: #87875F +} + +div.highlight .-Color[class*=-C102] { + color: #878787 +} + +div.highlight .-Color[class*=-BGC102] { + background-color: #878787 +} + +div.highlight .-Color[class*=-C103] { + color: #8787AF +} + +div.highlight .-Color[class*=-BGC103] { + background-color: #8787AF +} + +div.highlight .-Color[class*=-C104] { + color: #8787D7 +} + +div.highlight .-Color[class*=-BGC104] { + background-color: #8787D7 +} + +div.highlight .-Color[class*=-C105] { + color: #8787FF +} + +div.highlight .-Color[class*=-BGC105] { + background-color: #8787FF +} + +div.highlight .-Color[class*=-C106] { + color: #87AF00 +} + +div.highlight .-Color[class*=-BGC106] { + background-color: #87AF00 +} + +div.highlight .-Color[class*=-C107] { + color: #87AF5F +} + +div.highlight .-Color[class*=-BGC107] { + background-color: #87AF5F +} + +div.highlight .-Color[class*=-C108] { + color: #87AF87 +} + +div.highlight .-Color[class*=-BGC108] { + background-color: #87AF87 +} + +div.highlight .-Color[class*=-C109] { + color: #87AFAF +} + +div.highlight .-Color[class*=-BGC109] { + background-color: #87AFAF +} + +div.highlight .-Color[class*=-C110] { + color: #87AFD7 +} + +div.highlight .-Color[class*=-BGC110] { + background-color: #87AFD7 +} + +div.highlight .-Color[class*=-C111] { + color: #87AFFF +} + +div.highlight .-Color[class*=-BGC111] { + background-color: #87AFFF +} + +div.highlight .-Color[class*=-C112] { + color: #87D700 +} + +div.highlight .-Color[class*=-BGC112] { + background-color: #87D700 +} + +div.highlight .-Color[class*=-C113] { + color: #87D75F +} + +div.highlight .-Color[class*=-BGC113] { + background-color: #87D75F +} + +div.highlight .-Color[class*=-C114] { + color: #87D787 +} + +div.highlight .-Color[class*=-BGC114] { + background-color: #87D787 +} + +div.highlight .-Color[class*=-C115] { + color: #87D7AF +} + +div.highlight .-Color[class*=-BGC115] { + background-color: #87D7AF +} + +div.highlight .-Color[class*=-C116] { + color: #87D7D7 +} + +div.highlight .-Color[class*=-BGC116] { + background-color: #87D7D7 +} + +div.highlight .-Color[class*=-C117] { + color: #87D7FF +} + +div.highlight .-Color[class*=-BGC117] { + background-color: #87D7FF +} + +div.highlight .-Color[class*=-C118] { + color: #87FF00 +} + +div.highlight .-Color[class*=-BGC118] { + background-color: #87FF00 +} + +div.highlight .-Color[class*=-C119] { + color: #87FF5F +} + +div.highlight .-Color[class*=-BGC119] { + background-color: #87FF5F +} + +div.highlight .-Color[class*=-C120] { + color: #87FF87 +} + +div.highlight .-Color[class*=-BGC120] { + background-color: #87FF87 +} + +div.highlight .-Color[class*=-C121] { + color: #87FFAF +} + +div.highlight .-Color[class*=-BGC121] { + background-color: #87FFAF +} + +div.highlight .-Color[class*=-C122] { + color: #87FFD7 +} + +div.highlight .-Color[class*=-BGC122] { + background-color: #87FFD7 +} + +div.highlight .-Color[class*=-C123] { + color: #87FFFF +} + +div.highlight .-Color[class*=-BGC123] { + background-color: #87FFFF +} + +div.highlight .-Color[class*=-C124] { + color: #AF0000 +} + +div.highlight .-Color[class*=-BGC124] { + background-color: #AF0000 +} + +div.highlight .-Color[class*=-C125] { + color: #AF005F +} + +div.highlight .-Color[class*=-BGC125] { + background-color: #AF005F +} + +div.highlight .-Color[class*=-C126] { + color: #AF0087 +} + +div.highlight .-Color[class*=-BGC126] { + background-color: #AF0087 +} + +div.highlight .-Color[class*=-C127] { + color: #AF00AF +} + +div.highlight .-Color[class*=-BGC127] { + background-color: #AF00AF +} + +div.highlight .-Color[class*=-C128] { + color: #AF00D7 +} + +div.highlight .-Color[class*=-BGC128] { + background-color: #AF00D7 +} + +div.highlight .-Color[class*=-C129] { + color: #AF00FF +} + +div.highlight .-Color[class*=-BGC129] { + background-color: #AF00FF +} + +div.highlight .-Color[class*=-C130] { + color: #AF5F00 +} + +div.highlight .-Color[class*=-BGC130] { + background-color: #AF5F00 +} + +div.highlight .-Color[class*=-C131] { + color: #AF5F5F +} + +div.highlight .-Color[class*=-BGC131] { + background-color: #AF5F5F +} + +div.highlight .-Color[class*=-C132] { + color: #AF5F87 +} + +div.highlight .-Color[class*=-BGC132] { + background-color: #AF5F87 +} + +div.highlight .-Color[class*=-C133] { + color: #AF5FAF +} + +div.highlight .-Color[class*=-BGC133] { + background-color: #AF5FAF +} + +div.highlight .-Color[class*=-C134] { + color: #AF5FD7 +} + +div.highlight .-Color[class*=-BGC134] { + background-color: #AF5FD7 +} + +div.highlight .-Color[class*=-C135] { + color: #AF5FFF +} + +div.highlight .-Color[class*=-BGC135] { + background-color: #AF5FFF +} + +div.highlight .-Color[class*=-C136] { + color: #AF8700 +} + +div.highlight .-Color[class*=-BGC136] { + background-color: #AF8700 +} + +div.highlight .-Color[class*=-C137] { + color: #AF875F +} + +div.highlight .-Color[class*=-BGC137] { + background-color: #AF875F +} + +div.highlight .-Color[class*=-C138] { + color: #AF8787 +} + +div.highlight .-Color[class*=-BGC138] { + background-color: #AF8787 +} + +div.highlight .-Color[class*=-C139] { + color: #AF87AF +} + +div.highlight .-Color[class*=-BGC139] { + background-color: #AF87AF +} + +div.highlight .-Color[class*=-C140] { + color: #AF87D7 +} + +div.highlight .-Color[class*=-BGC140] { + background-color: #AF87D7 +} + +div.highlight .-Color[class*=-C141] { + color: #AF87FF +} + +div.highlight .-Color[class*=-BGC141] { + background-color: #AF87FF +} + +div.highlight .-Color[class*=-C142] { + color: #AFAF00 +} + +div.highlight .-Color[class*=-BGC142] { + background-color: #AFAF00 +} + +div.highlight .-Color[class*=-C143] { + color: #AFAF5F +} + +div.highlight .-Color[class*=-BGC143] { + background-color: #AFAF5F +} + +div.highlight .-Color[class*=-C144] { + color: #AFAF87 +} + +div.highlight .-Color[class*=-BGC144] { + background-color: #AFAF87 +} + +div.highlight .-Color[class*=-C145] { + color: #AFAFAF +} + +div.highlight .-Color[class*=-BGC145] { + background-color: #AFAFAF +} + +div.highlight .-Color[class*=-C146] { + color: #AFAFD7 +} + +div.highlight .-Color[class*=-BGC146] { + background-color: #AFAFD7 +} + +div.highlight .-Color[class*=-C147] { + color: #AFAFFF +} + +div.highlight .-Color[class*=-BGC147] { + background-color: #AFAFFF +} + +div.highlight .-Color[class*=-C148] { + color: #AFD700 +} + +div.highlight .-Color[class*=-BGC148] { + background-color: #AFD700 +} + +div.highlight .-Color[class*=-C149] { + color: #AFD75F +} + +div.highlight .-Color[class*=-BGC149] { + background-color: #AFD75F +} + +div.highlight .-Color[class*=-C150] { + color: #AFD787 +} + +div.highlight .-Color[class*=-BGC150] { + background-color: #AFD787 +} + +div.highlight .-Color[class*=-C151] { + color: #AFD7AF +} + +div.highlight .-Color[class*=-BGC151] { + background-color: #AFD7AF +} + +div.highlight .-Color[class*=-C152] { + color: #AFD7D7 +} + +div.highlight .-Color[class*=-BGC152] { + background-color: #AFD7D7 +} + +div.highlight .-Color[class*=-C153] { + color: #AFD7FF +} + +div.highlight .-Color[class*=-BGC153] { + background-color: #AFD7FF +} + +div.highlight .-Color[class*=-C154] { + color: #AFFF00 +} + +div.highlight .-Color[class*=-BGC154] { + background-color: #AFFF00 +} + +div.highlight .-Color[class*=-C155] { + color: #AFFF5F +} + +div.highlight .-Color[class*=-BGC155] { + background-color: #AFFF5F +} + +div.highlight .-Color[class*=-C156] { + color: #AFFF87 +} + +div.highlight .-Color[class*=-BGC156] { + background-color: #AFFF87 +} + +div.highlight .-Color[class*=-C157] { + color: #AFFFAF +} + +div.highlight .-Color[class*=-BGC157] { + background-color: #AFFFAF +} + +div.highlight .-Color[class*=-C158] { + color: #AFFFD7 +} + +div.highlight .-Color[class*=-BGC158] { + background-color: #AFFFD7 +} + +div.highlight .-Color[class*=-C159] { + color: #AFFFFF +} + +div.highlight .-Color[class*=-BGC159] { + background-color: #AFFFFF +} + +div.highlight .-Color[class*=-C160] { + color: #D70000 +} + +div.highlight .-Color[class*=-BGC160] { + background-color: #D70000 +} + +div.highlight .-Color[class*=-C161] { + color: #D7005F +} + +div.highlight .-Color[class*=-BGC161] { + background-color: #D7005F +} + +div.highlight .-Color[class*=-C162] { + color: #D70087 +} + +div.highlight .-Color[class*=-BGC162] { + background-color: #D70087 +} + +div.highlight .-Color[class*=-C163] { + color: #D700AF +} + +div.highlight .-Color[class*=-BGC163] { + background-color: #D700AF +} + +div.highlight .-Color[class*=-C164] { + color: #D700D7 +} + +div.highlight .-Color[class*=-BGC164] { + background-color: #D700D7 +} + +div.highlight .-Color[class*=-C165] { + color: #D700FF +} + +div.highlight .-Color[class*=-BGC165] { + background-color: #D700FF +} + +div.highlight .-Color[class*=-C166] { + color: #D75F00 +} + +div.highlight .-Color[class*=-BGC166] { + background-color: #D75F00 +} + +div.highlight .-Color[class*=-C167] { + color: #D75F5F +} + +div.highlight .-Color[class*=-BGC167] { + background-color: #D75F5F +} + +div.highlight .-Color[class*=-C168] { + color: #D75F87 +} + +div.highlight .-Color[class*=-BGC168] { + background-color: #D75F87 +} + +div.highlight .-Color[class*=-C169] { + color: #D75FAF +} + +div.highlight .-Color[class*=-BGC169] { + background-color: #D75FAF +} + +div.highlight .-Color[class*=-C170] { + color: #D75FD7 +} + +div.highlight .-Color[class*=-BGC170] { + background-color: #D75FD7 +} + +div.highlight .-Color[class*=-C171] { + color: #D75FFF +} + +div.highlight .-Color[class*=-BGC171] { + background-color: #D75FFF +} + +div.highlight .-Color[class*=-C172] { + color: #D78700 +} + +div.highlight .-Color[class*=-BGC172] { + background-color: #D78700 +} + +div.highlight .-Color[class*=-C173] { + color: #D7875F +} + +div.highlight .-Color[class*=-BGC173] { + background-color: #D7875F +} + +div.highlight .-Color[class*=-C174] { + color: #D78787 +} + +div.highlight .-Color[class*=-BGC174] { + background-color: #D78787 +} + +div.highlight .-Color[class*=-C175] { + color: #D787AF +} + +div.highlight .-Color[class*=-BGC175] { + background-color: #D787AF +} + +div.highlight .-Color[class*=-C176] { + color: #D787D7 +} + +div.highlight .-Color[class*=-BGC176] { + background-color: #D787D7 +} + +div.highlight .-Color[class*=-C177] { + color: #D787FF +} + +div.highlight .-Color[class*=-BGC177] { + background-color: #D787FF +} + +div.highlight .-Color[class*=-C178] { + color: #D7AF00 +} + +div.highlight .-Color[class*=-BGC178] { + background-color: #D7AF00 +} + +div.highlight .-Color[class*=-C179] { + color: #D7AF5F +} + +div.highlight .-Color[class*=-BGC179] { + background-color: #D7AF5F +} + +div.highlight .-Color[class*=-C180] { + color: #D7AF87 +} + +div.highlight .-Color[class*=-BGC180] { + background-color: #D7AF87 +} + +div.highlight .-Color[class*=-C181] { + color: #D7AFAF +} + +div.highlight .-Color[class*=-BGC181] { + background-color: #D7AFAF +} + +div.highlight .-Color[class*=-C182] { + color: #D7AFD7 +} + +div.highlight .-Color[class*=-BGC182] { + background-color: #D7AFD7 +} + +div.highlight .-Color[class*=-C183] { + color: #D7AFFF +} + +div.highlight .-Color[class*=-BGC183] { + background-color: #D7AFFF +} + +div.highlight .-Color[class*=-C184] { + color: #D7D700 +} + +div.highlight .-Color[class*=-BGC184] { + background-color: #D7D700 +} + +div.highlight .-Color[class*=-C185] { + color: #D7D75F +} + +div.highlight .-Color[class*=-BGC185] { + background-color: #D7D75F +} + +div.highlight .-Color[class*=-C186] { + color: #D7D787 +} + +div.highlight .-Color[class*=-BGC186] { + background-color: #D7D787 +} + +div.highlight .-Color[class*=-C187] { + color: #D7D7AF +} + +div.highlight .-Color[class*=-BGC187] { + background-color: #D7D7AF +} + +div.highlight .-Color[class*=-C188] { + color: #D7D7D7 +} + +div.highlight .-Color[class*=-BGC188] { + background-color: #D7D7D7 +} + +div.highlight 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.-Color[class*=-C255] { + color: #EEEEEE +} + +div.highlight .-Color[class*=-BGC255] { + background-color: #EEEEEE +} diff --git a/_static/play-solid.svg b/_static/play-solid.svg new file mode 100644 index 0000000..bcd81f7 --- /dev/null +++ b/_static/play-solid.svg @@ -0,0 +1 @@ + \ No newline at end of file diff --git a/_static/plus.png b/_static/plus.png new file mode 100644 index 0000000..7107cec Binary files /dev/null and b/_static/plus.png differ diff --git a/_static/proof.css b/_static/proof.css new file mode 100644 index 0000000..51e0c9f --- /dev/null +++ b/_static/proof.css @@ -0,0 +1,196 @@ +/********************************************* +* Variables * +*********************************************/ +:root { + --note-title-color: rgba(68,138,255,.1); + --note-border-color: #007bff; + --warning-title-color: rgba(220,53,69,.1); + --warning-border-color: #dc3545; + --hint-title-color: rgba(255,193,7,.2); + --hint-border-color: #ffc107; + --caution-title-color: rgba(253,126,20,.1); + --caution-border-color: #fd7e14; + --grey-title-color: rgba(204,204,204,.2); + --grey-border-color: #ccc; +} + +/********************************************* +* Main body * +*********************************************/ + +/* Remove content box */ +div.proof p.admonition-title::before { + content: none; +} + +/********************************************* +* Proof * +*********************************************/ +div#proof{ + padding: .4rem .6rem .4rem 2rem !important; + border-color: var(--grey-border-color); + background-color: none; +} + +/********************************************* +* Theorem * +*********************************************/ +div.theorem { + border-color: var(--note-border-color); + background-color: var(--note-title-color); +} + +div.theorem p.admonition-title { + background-color: var(--note-title-color); +} + +/********************************************* +* Axiom * +*********************************************/ +div.axiom { + border-color: var(--hint-border-color); + background-color: var(--hint-title-color); +} + +div.axiom p.admonition-title { + background-color: var(--hint-title-color); +} + +/********************************************* +* Criterion * +*********************************************/ +div.criterion { + border-color: var(--caution-border-color); + background-color: var(--caution-title-color); +} + +div.criterion p.admonition-title { + background-color: var(--caution-title-color); +} + +/********************************************* +* Lemma * +*********************************************/ +div.lemma { + border-color: var(--hint-border-color); + background-color: var(--hint-title-color); +} + +div.lemma p.admonition-title { + background-color: var(--hint-title-color); +} + +/********************************************* +* Definition * +*********************************************/ +div.definition { + border-color: var(--note-border-color); + background-color: var(--note-title-color); +} + +div.definition p.admonition-title { + background-color: var(--note-title-color); +} + +/********************************************* +* Remark * +*********************************************/ +div.remark { + border-color: var(--warning-border-color); + background-color: var(--warning-title-color); +} + +div.remark p.admonition-title { + background-color: var(--warning-title-color); +} + +/********************************************* +* Conjecture * +*********************************************/ +div.conjecture { + border-color: var(--hint-border-color); + background-color: var(--hint-title-color); +} + +div.conjecture p.admonition-title { + background-color: var(--hint-title-color); +} + +/********************************************* +* Corollary * +*********************************************/ +div.corollary { + border-color: var(--caution-border-color); + background-color: var(--caution-title-color); +} + +div.corollary p.admonition-title { + background-color: var(--caution-title-color); +} + +/********************************************* +* Algorithm * +*********************************************/ +div.algorithm { + border: none; + background-color: none; +} + +div.algorithm p.admonition-title { + background-color: transparent; + border-top: .15rem solid var(--grey-border-color); + border-bottom: .15rem solid var(--grey-border-color); +} + +div.algorithm div.section { + font-family: SFMono-Regular,Menlo,Monaco,Consolas,Liberation Mono,Courier New,monospace; + font-size: .85rem; +} + +/********************************************* +* Example * +*********************************************/ +div.example { + border-color: var(--hint-border-color); + background-color: none; +} + +div.example p.admonition-title { + background-color: transparent; +} + +/********************************************* +* Property * +*********************************************/ +div.property { + border-color: var(--caution-border-color); + background-color: var(--caution-title-color); +} + +div.property p.admonition-title { + background-color: var(--caution-title-color); +} + +/********************************************* +* Observation * +*********************************************/ +div.observation { + border-color: var(--hint-border-color); + background-color: var(--hint-title-color); +} + +div.observation p.admonition-title { + background-color: var(--hint-title-color); +} + +/********************************************* +* Proposition * +*********************************************/ +div.proposition { + border-color: var(--note-border-color); + background-color: var(--note-title-color); +} + +div.proposition p.admonition-title { + background-color: var(--note-title-color); +} diff --git a/_static/pygments.css b/_static/pygments.css new file mode 100644 index 0000000..997797f --- /dev/null +++ b/_static/pygments.css @@ -0,0 +1,152 @@ +html[data-theme="light"] .highlight pre { line-height: 125%; } +html[data-theme="light"] 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e},we={find:(t,e=document.documentElement)=>[].concat(...Element.prototype.querySelectorAll.call(e,t)),findOne:(t,e=document.documentElement)=>Element.prototype.querySelector.call(e,t),children:(t,e)=>[].concat(...t.children).filter((t=>t.matches(e))),parents(t,e){const i=[];let n=t.parentNode.closest(e);for(;n;)i.push(n),n=n.parentNode.closest(e);return i},prev(t,e){let i=t.previousElementSibling;for(;i;){if(i.matches(e))return[i];i=i.previousElementSibling}return[]},next(t,e){let i=t.nextElementSibling;for(;i;){if(i.matches(e))return[i];i=i.nextElementSibling}return[]},focusableChildren(t){const e=["a","button","input","textarea","select","details","[tabindex]",'[contenteditable="true"]'].map((t=>`${t}:not([tabindex^="-"])`)).join(",");return this.find(e,t).filter((t=>!Wt(t)&&Bt(t)))},getSelectorFromElement(t){const e=ye(t);return e&&we.findOne(e)?e:null},getElementFromSelector(t){const e=ye(t);return e?we.findOne(e):null},getMultipleElementsFromSelector(t){const e=ye(t);return e?we.find(e):[]}},Ee=(t,e="hide")=>{const i=`click.dismiss${t.EVENT_KEY}`,n=t.NAME;fe.on(document,i,`[data-bs-dismiss="${n}"]`,(function(i){if(["A","AREA"].includes(this.tagName)&&i.preventDefault(),Wt(this))return;const s=we.getElementFromSelector(this)||this.closest(`.${n}`);t.getOrCreateInstance(s)[e]()}))},Ae=".bs.alert",Te=`close${Ae}`,Ce=`closed${Ae}`;class Oe extends ve{static get NAME(){return"alert"}close(){if(fe.trigger(this._element,Te).defaultPrevented)return;this._element.classList.remove("show");const t=this._element.classList.contains("fade");this._queueCallback((()=>this._destroyElement()),this._element,t)}_destroyElement(){this._element.remove(),fe.trigger(this._element,Ce),this.dispose()}static jQueryInterface(t){return this.each((function(){const e=Oe.getOrCreateInstance(this);if("string"==typeof t){if(void 0===e[t]||t.startsWith("_")||"constructor"===t)throw new TypeError(`No method named "${t}"`);e[t](this)}}))}}Ee(Oe,"close"),Qt(Oe);const xe='[data-bs-toggle="button"]';class ke extends ve{static get NAME(){return"button"}toggle(){this._element.setAttribute("aria-pressed",this._element.classList.toggle("active"))}static jQueryInterface(t){return this.each((function(){const e=ke.getOrCreateInstance(this);"toggle"===t&&e[t]()}))}}fe.on(document,"click.bs.button.data-api",xe,(t=>{t.preventDefault();const e=t.target.closest(xe);ke.getOrCreateInstance(e).toggle()})),Qt(ke);const Le=".bs.swipe",Se=`touchstart${Le}`,De=`touchmove${Le}`,$e=`touchend${Le}`,Ie=`pointerdown${Le}`,Ne=`pointerup${Le}`,Pe={endCallback:null,leftCallback:null,rightCallback:null},Me={endCallback:"(function|null)",leftCallback:"(function|null)",rightCallback:"(function|null)"};class je extends be{constructor(t,e){super(),this._element=t,t&&je.isSupported()&&(this._config=this._getConfig(e),this._deltaX=0,this._supportPointerEvents=Boolean(window.PointerEvent),this._initEvents())}static get Default(){return Pe}static get DefaultType(){return Me}static get NAME(){return"swipe"}dispose(){fe.off(this._element,Le)}_start(t){this._supportPointerEvents?this._eventIsPointerPenTouch(t)&&(this._deltaX=t.clientX):this._deltaX=t.touches[0].clientX}_end(t){this._eventIsPointerPenTouch(t)&&(this._deltaX=t.clientX-this._deltaX),this._handleSwipe(),Xt(this._config.endCallback)}_move(t){this._deltaX=t.touches&&t.touches.length>1?0:t.touches[0].clientX-this._deltaX}_handleSwipe(){const t=Math.abs(this._deltaX);if(t<=40)return;const e=t/this._deltaX;this._deltaX=0,e&&Xt(e>0?this._config.rightCallback:this._config.leftCallback)}_initEvents(){this._supportPointerEvents?(fe.on(this._element,Ie,(t=>this._start(t))),fe.on(this._element,Ne,(t=>this._end(t))),this._element.classList.add("pointer-event")):(fe.on(this._element,Se,(t=>this._start(t))),fe.on(this._element,De,(t=>this._move(t))),fe.on(this._element,$e,(t=>this._end(t))))}_eventIsPointerPenTouch(t){return this._supportPointerEvents&&("pen"===t.pointerType||"touch"===t.pointerType)}static isSupported(){return"ontouchstart"in document.documentElement||navigator.maxTouchPoints>0}}const Fe=".bs.carousel",He=".data-api",Be="next",We="prev",ze="left",Re="right",qe=`slide${Fe}`,Ve=`slid${Fe}`,Ye=`keydown${Fe}`,Ke=`mouseenter${Fe}`,Qe=`mouseleave${Fe}`,Xe=`dragstart${Fe}`,Ue=`load${Fe}${He}`,Ge=`click${Fe}${He}`,Je="carousel",Ze="active",ti=".active",ei=".carousel-item",ii=ti+ei,ni={ArrowLeft:Re,ArrowRight:ze},si={interval:5e3,keyboard:!0,pause:"hover",ride:!1,touch:!0,wrap:!0},oi={interval:"(number|boolean)",keyboard:"boolean",pause:"(string|boolean)",ride:"(boolean|string)",touch:"boolean",wrap:"boolean"};class ri extends ve{constructor(t,e){super(t,e),this._interval=null,this._activeElement=null,this._isSliding=!1,this.touchTimeout=null,this._swipeHelper=null,this._indicatorsElement=we.findOne(".carousel-indicators",this._element),this._addEventListeners(),this._config.ride===Je&&this.cycle()}static get Default(){return si}static get DefaultType(){return oi}static get NAME(){return"carousel"}next(){this._slide(Be)}nextWhenVisible(){!document.hidden&&Bt(this._element)&&this.next()}prev(){this._slide(We)}pause(){this._isSliding&&jt(this._element),this._clearInterval()}cycle(){this._clearInterval(),this._updateInterval(),this._interval=setInterval((()=>this.nextWhenVisible()),this._config.interval)}_maybeEnableCycle(){this._config.ride&&(this._isSliding?fe.one(this._element,Ve,(()=>this.cycle())):this.cycle())}to(t){const e=this._getItems();if(t>e.length-1||t<0)return;if(this._isSliding)return void fe.one(this._element,Ve,(()=>this.to(t)));const i=this._getItemIndex(this._getActive());if(i===t)return;const n=t>i?Be:We;this._slide(n,e[t])}dispose(){this._swipeHelper&&this._swipeHelper.dispose(),super.dispose()}_configAfterMerge(t){return t.defaultInterval=t.interval,t}_addEventListeners(){this._config.keyboard&&fe.on(this._element,Ye,(t=>this._keydown(t))),"hover"===this._config.pause&&(fe.on(this._element,Ke,(()=>this.pause())),fe.on(this._element,Qe,(()=>this._maybeEnableCycle()))),this._config.touch&&je.isSupported()&&this._addTouchEventListeners()}_addTouchEventListeners(){for(const t of we.find(".carousel-item img",this._element))fe.on(t,Xe,(t=>t.preventDefault()));const t={leftCallback:()=>this._slide(this._directionToOrder(ze)),rightCallback:()=>this._slide(this._directionToOrder(Re)),endCallback:()=>{"hover"===this._config.pause&&(this.pause(),this.touchTimeout&&clearTimeout(this.touchTimeout),this.touchTimeout=setTimeout((()=>this._maybeEnableCycle()),500+this._config.interval))}};this._swipeHelper=new je(this._element,t)}_keydown(t){if(/input|textarea/i.test(t.target.tagName))return;const e=ni[t.key];e&&(t.preventDefault(),this._slide(this._directionToOrder(e)))}_getItemIndex(t){return this._getItems().indexOf(t)}_setActiveIndicatorElement(t){if(!this._indicatorsElement)return;const e=we.findOne(ti,this._indicatorsElement);e.classList.remove(Ze),e.removeAttribute("aria-current");const i=we.findOne(`[data-bs-slide-to="${t}"]`,this._indicatorsElement);i&&(i.classList.add(Ze),i.setAttribute("aria-current","true"))}_updateInterval(){const t=this._activeElement||this._getActive();if(!t)return;const e=Number.parseInt(t.getAttribute("data-bs-interval"),10);this._config.interval=e||this._config.defaultInterval}_slide(t,e=null){if(this._isSliding)return;const i=this._getActive(),n=t===Be,s=e||Gt(this._getItems(),i,n,this._config.wrap);if(s===i)return;const o=this._getItemIndex(s),r=e=>fe.trigger(this._element,e,{relatedTarget:s,direction:this._orderToDirection(t),from:this._getItemIndex(i),to:o});if(r(qe).defaultPrevented)return;if(!i||!s)return;const a=Boolean(this._interval);this.pause(),this._isSliding=!0,this._setActiveIndicatorElement(o),this._activeElement=s;const l=n?"carousel-item-start":"carousel-item-end",c=n?"carousel-item-next":"carousel-item-prev";s.classList.add(c),qt(s),i.classList.add(l),s.classList.add(l),this._queueCallback((()=>{s.classList.remove(l,c),s.classList.add(Ze),i.classList.remove(Ze,c,l),this._isSliding=!1,r(Ve)}),i,this._isAnimated()),a&&this.cycle()}_isAnimated(){return this._element.classList.contains("slide")}_getActive(){return we.findOne(ii,this._element)}_getItems(){return we.find(ei,this._element)}_clearInterval(){this._interval&&(clearInterval(this._interval),this._interval=null)}_directionToOrder(t){return Kt()?t===ze?We:Be:t===ze?Be:We}_orderToDirection(t){return Kt()?t===We?ze:Re:t===We?Re:ze}static jQueryInterface(t){return this.each((function(){const e=ri.getOrCreateInstance(this,t);if("number"!=typeof t){if("string"==typeof t){if(void 0===e[t]||t.startsWith("_")||"constructor"===t)throw new TypeError(`No method named "${t}"`);e[t]()}}else e.to(t)}))}}fe.on(document,Ge,"[data-bs-slide], [data-bs-slide-to]",(function(t){const e=we.getElementFromSelector(this);if(!e||!e.classList.contains(Je))return;t.preventDefault();const i=ri.getOrCreateInstance(e),n=this.getAttribute("data-bs-slide-to");return n?(i.to(n),void i._maybeEnableCycle()):"next"===_e.getDataAttribute(this,"slide")?(i.next(),void i._maybeEnableCycle()):(i.prev(),void i._maybeEnableCycle())})),fe.on(window,Ue,(()=>{const t=we.find('[data-bs-ride="carousel"]');for(const e of t)ri.getOrCreateInstance(e)})),Qt(ri);const ai=".bs.collapse",li=`show${ai}`,ci=`shown${ai}`,hi=`hide${ai}`,di=`hidden${ai}`,ui=`click${ai}.data-api`,fi="show",pi="collapse",mi="collapsing",gi=`:scope .${pi} .${pi}`,_i='[data-bs-toggle="collapse"]',bi={parent:null,toggle:!0},vi={parent:"(null|element)",toggle:"boolean"};class yi extends ve{constructor(t,e){super(t,e),this._isTransitioning=!1,this._triggerArray=[];const i=we.find(_i);for(const t of i){const e=we.getSelectorFromElement(t),i=we.find(e).filter((t=>t===this._element));null!==e&&i.length&&this._triggerArray.push(t)}this._initializeChildren(),this._config.parent||this._addAriaAndCollapsedClass(this._triggerArray,this._isShown()),this._config.toggle&&this.toggle()}static get Default(){return bi}static get DefaultType(){return vi}static get NAME(){return"collapse"}toggle(){this._isShown()?this.hide():this.show()}show(){if(this._isTransitioning||this._isShown())return;let t=[];if(this._config.parent&&(t=this._getFirstLevelChildren(".collapse.show, .collapse.collapsing").filter((t=>t!==this._element)).map((t=>yi.getOrCreateInstance(t,{toggle:!1})))),t.length&&t[0]._isTransitioning)return;if(fe.trigger(this._element,li).defaultPrevented)return;for(const e of t)e.hide();const e=this._getDimension();this._element.classList.remove(pi),this._element.classList.add(mi),this._element.style[e]=0,this._addAriaAndCollapsedClass(this._triggerArray,!0),this._isTransitioning=!0;const i=`scroll${e[0].toUpperCase()+e.slice(1)}`;this._queueCallback((()=>{this._isTransitioning=!1,this._element.classList.remove(mi),this._element.classList.add(pi,fi),this._element.style[e]="",fe.trigger(this._element,ci)}),this._element,!0),this._element.style[e]=`${this._element[i]}px`}hide(){if(this._isTransitioning||!this._isShown())return;if(fe.trigger(this._element,hi).defaultPrevented)return;const t=this._getDimension();this._element.style[t]=`${this._element.getBoundingClientRect()[t]}px`,qt(this._element),this._element.classList.add(mi),this._element.classList.remove(pi,fi);for(const t of this._triggerArray){const e=we.getElementFromSelector(t);e&&!this._isShown(e)&&this._addAriaAndCollapsedClass([t],!1)}this._isTransitioning=!0,this._element.style[t]="",this._queueCallback((()=>{this._isTransitioning=!1,this._element.classList.remove(mi),this._element.classList.add(pi),fe.trigger(this._element,di)}),this._element,!0)}_isShown(t=this._element){return t.classList.contains(fi)}_configAfterMerge(t){return t.toggle=Boolean(t.toggle),t.parent=Ht(t.parent),t}_getDimension(){return this._element.classList.contains("collapse-horizontal")?"width":"height"}_initializeChildren(){if(!this._config.parent)return;const t=this._getFirstLevelChildren(_i);for(const e of t){const t=we.getElementFromSelector(e);t&&this._addAriaAndCollapsedClass([e],this._isShown(t))}}_getFirstLevelChildren(t){const e=we.find(gi,this._config.parent);return we.find(t,this._config.parent).filter((t=>!e.includes(t)))}_addAriaAndCollapsedClass(t,e){if(t.length)for(const i of t)i.classList.toggle("collapsed",!e),i.setAttribute("aria-expanded",e)}static jQueryInterface(t){const e={};return"string"==typeof t&&/show|hide/.test(t)&&(e.toggle=!1),this.each((function(){const i=yi.getOrCreateInstance(this,e);if("string"==typeof t){if(void 0===i[t])throw new TypeError(`No method named "${t}"`);i[t]()}}))}}fe.on(document,ui,_i,(function(t){("A"===t.target.tagName||t.delegateTarget&&"A"===t.delegateTarget.tagName)&&t.preventDefault();for(const t of we.getMultipleElementsFromSelector(this))yi.getOrCreateInstance(t,{toggle:!1}).toggle()})),Qt(yi);const wi="dropdown",Ei=".bs.dropdown",Ai=".data-api",Ti="ArrowUp",Ci="ArrowDown",Oi=`hide${Ei}`,xi=`hidden${Ei}`,ki=`show${Ei}`,Li=`shown${Ei}`,Si=`click${Ei}${Ai}`,Di=`keydown${Ei}${Ai}`,$i=`keyup${Ei}${Ai}`,Ii="show",Ni='[data-bs-toggle="dropdown"]:not(.disabled):not(:disabled)',Pi=`${Ni}.${Ii}`,Mi=".dropdown-menu",ji=Kt()?"top-end":"top-start",Fi=Kt()?"top-start":"top-end",Hi=Kt()?"bottom-end":"bottom-start",Bi=Kt()?"bottom-start":"bottom-end",Wi=Kt()?"left-start":"right-start",zi=Kt()?"right-start":"left-start",Ri={autoClose:!0,boundary:"clippingParents",display:"dynamic",offset:[0,2],popperConfig:null,reference:"toggle"},qi={autoClose:"(boolean|string)",boundary:"(string|element)",display:"string",offset:"(array|string|function)",popperConfig:"(null|object|function)",reference:"(string|element|object)"};class Vi extends ve{constructor(t,e){super(t,e),this._popper=null,this._parent=this._element.parentNode,this._menu=we.next(this._element,Mi)[0]||we.prev(this._element,Mi)[0]||we.findOne(Mi,this._parent),this._inNavbar=this._detectNavbar()}static get Default(){return Ri}static get DefaultType(){return qi}static get NAME(){return wi}toggle(){return this._isShown()?this.hide():this.show()}show(){if(Wt(this._element)||this._isShown())return;const t={relatedTarget:this._element};if(!fe.trigger(this._element,ki,t).defaultPrevented){if(this._createPopper(),"ontouchstart"in document.documentElement&&!this._parent.closest(".navbar-nav"))for(const t of[].concat(...document.body.children))fe.on(t,"mouseover",Rt);this._element.focus(),this._element.setAttribute("aria-expanded",!0),this._menu.classList.add(Ii),this._element.classList.add(Ii),fe.trigger(this._element,Li,t)}}hide(){if(Wt(this._element)||!this._isShown())return;const t={relatedTarget:this._element};this._completeHide(t)}dispose(){this._popper&&this._popper.destroy(),super.dispose()}update(){this._inNavbar=this._detectNavbar(),this._popper&&this._popper.update()}_completeHide(t){if(!fe.trigger(this._element,Oi,t).defaultPrevented){if("ontouchstart"in document.documentElement)for(const t of[].concat(...document.body.children))fe.off(t,"mouseover",Rt);this._popper&&this._popper.destroy(),this._menu.classList.remove(Ii),this._element.classList.remove(Ii),this._element.setAttribute("aria-expanded","false"),_e.removeDataAttribute(this._menu,"popper"),fe.trigger(this._element,xi,t)}}_getConfig(t){if("object"==typeof(t=super._getConfig(t)).reference&&!Ft(t.reference)&&"function"!=typeof t.reference.getBoundingClientRect)throw new TypeError(`${wi.toUpperCase()}: Option "reference" provided type "object" without a required "getBoundingClientRect" method.`);return t}_createPopper(){if(void 0===e)throw new TypeError("Bootstrap's dropdowns require Popper (https://popper.js.org)");let t=this._element;"parent"===this._config.reference?t=this._parent:Ft(this._config.reference)?t=Ht(this._config.reference):"object"==typeof this._config.reference&&(t=this._config.reference);const i=this._getPopperConfig();this._popper=Dt(t,this._menu,i)}_isShown(){return this._menu.classList.contains(Ii)}_getPlacement(){const t=this._parent;if(t.classList.contains("dropend"))return Wi;if(t.classList.contains("dropstart"))return zi;if(t.classList.contains("dropup-center"))return"top";if(t.classList.contains("dropdown-center"))return"bottom";const e="end"===getComputedStyle(this._menu).getPropertyValue("--bs-position").trim();return t.classList.contains("dropup")?e?Fi:ji:e?Bi:Hi}_detectNavbar(){return null!==this._element.closest(".navbar")}_getOffset(){const{offset:t}=this._config;return"string"==typeof t?t.split(",").map((t=>Number.parseInt(t,10))):"function"==typeof t?e=>t(e,this._element):t}_getPopperConfig(){const t={placement:this._getPlacement(),modifiers:[{name:"preventOverflow",options:{boundary:this._config.boundary}},{name:"offset",options:{offset:this._getOffset()}}]};return(this._inNavbar||"static"===this._config.display)&&(_e.setDataAttribute(this._menu,"popper","static"),t.modifiers=[{name:"applyStyles",enabled:!1}]),{...t,...Xt(this._config.popperConfig,[t])}}_selectMenuItem({key:t,target:e}){const i=we.find(".dropdown-menu .dropdown-item:not(.disabled):not(:disabled)",this._menu).filter((t=>Bt(t)));i.length&&Gt(i,e,t===Ci,!i.includes(e)).focus()}static jQueryInterface(t){return this.each((function(){const e=Vi.getOrCreateInstance(this,t);if("string"==typeof t){if(void 0===e[t])throw new TypeError(`No method named "${t}"`);e[t]()}}))}static clearMenus(t){if(2===t.button||"keyup"===t.type&&"Tab"!==t.key)return;const e=we.find(Pi);for(const i of e){const e=Vi.getInstance(i);if(!e||!1===e._config.autoClose)continue;const n=t.composedPath(),s=n.includes(e._menu);if(n.includes(e._element)||"inside"===e._config.autoClose&&!s||"outside"===e._config.autoClose&&s)continue;if(e._menu.contains(t.target)&&("keyup"===t.type&&"Tab"===t.key||/input|select|option|textarea|form/i.test(t.target.tagName)))continue;const o={relatedTarget:e._element};"click"===t.type&&(o.clickEvent=t),e._completeHide(o)}}static dataApiKeydownHandler(t){const e=/input|textarea/i.test(t.target.tagName),i="Escape"===t.key,n=[Ti,Ci].includes(t.key);if(!n&&!i)return;if(e&&!i)return;t.preventDefault();const s=this.matches(Ni)?this:we.prev(this,Ni)[0]||we.next(this,Ni)[0]||we.findOne(Ni,t.delegateTarget.parentNode),o=Vi.getOrCreateInstance(s);if(n)return t.stopPropagation(),o.show(),void o._selectMenuItem(t);o._isShown()&&(t.stopPropagation(),o.hide(),s.focus())}}fe.on(document,Di,Ni,Vi.dataApiKeydownHandler),fe.on(document,Di,Mi,Vi.dataApiKeydownHandler),fe.on(document,Si,Vi.clearMenus),fe.on(document,$i,Vi.clearMenus),fe.on(document,Si,Ni,(function(t){t.preventDefault(),Vi.getOrCreateInstance(this).toggle()})),Qt(Vi);const Yi="backdrop",Ki="show",Qi=`mousedown.bs.${Yi}`,Xi={className:"modal-backdrop",clickCallback:null,isAnimated:!1,isVisible:!0,rootElement:"body"},Ui={className:"string",clickCallback:"(function|null)",isAnimated:"boolean",isVisible:"boolean",rootElement:"(element|string)"};class Gi extends be{constructor(t){super(),this._config=this._getConfig(t),this._isAppended=!1,this._element=null}static get Default(){return Xi}static get DefaultType(){return Ui}static get NAME(){return Yi}show(t){if(!this._config.isVisible)return void Xt(t);this._append();const e=this._getElement();this._config.isAnimated&&qt(e),e.classList.add(Ki),this._emulateAnimation((()=>{Xt(t)}))}hide(t){this._config.isVisible?(this._getElement().classList.remove(Ki),this._emulateAnimation((()=>{this.dispose(),Xt(t)}))):Xt(t)}dispose(){this._isAppended&&(fe.off(this._element,Qi),this._element.remove(),this._isAppended=!1)}_getElement(){if(!this._element){const t=document.createElement("div");t.className=this._config.className,this._config.isAnimated&&t.classList.add("fade"),this._element=t}return this._element}_configAfterMerge(t){return t.rootElement=Ht(t.rootElement),t}_append(){if(this._isAppended)return;const t=this._getElement();this._config.rootElement.append(t),fe.on(t,Qi,(()=>{Xt(this._config.clickCallback)})),this._isAppended=!0}_emulateAnimation(t){Ut(t,this._getElement(),this._config.isAnimated)}}const Ji=".bs.focustrap",Zi=`focusin${Ji}`,tn=`keydown.tab${Ji}`,en="backward",nn={autofocus:!0,trapElement:null},sn={autofocus:"boolean",trapElement:"element"};class on extends be{constructor(t){super(),this._config=this._getConfig(t),this._isActive=!1,this._lastTabNavDirection=null}static get Default(){return nn}static get DefaultType(){return sn}static get NAME(){return"focustrap"}activate(){this._isActive||(this._config.autofocus&&this._config.trapElement.focus(),fe.off(document,Ji),fe.on(document,Zi,(t=>this._handleFocusin(t))),fe.on(document,tn,(t=>this._handleKeydown(t))),this._isActive=!0)}deactivate(){this._isActive&&(this._isActive=!1,fe.off(document,Ji))}_handleFocusin(t){const{trapElement:e}=this._config;if(t.target===document||t.target===e||e.contains(t.target))return;const i=we.focusableChildren(e);0===i.length?e.focus():this._lastTabNavDirection===en?i[i.length-1].focus():i[0].focus()}_handleKeydown(t){"Tab"===t.key&&(this._lastTabNavDirection=t.shiftKey?en:"forward")}}const rn=".fixed-top, .fixed-bottom, .is-fixed, .sticky-top",an=".sticky-top",ln="padding-right",cn="margin-right";class hn{constructor(){this._element=document.body}getWidth(){const t=document.documentElement.clientWidth;return Math.abs(window.innerWidth-t)}hide(){const t=this.getWidth();this._disableOverFlow(),this._setElementAttributes(this._element,ln,(e=>e+t)),this._setElementAttributes(rn,ln,(e=>e+t)),this._setElementAttributes(an,cn,(e=>e-t))}reset(){this._resetElementAttributes(this._element,"overflow"),this._resetElementAttributes(this._element,ln),this._resetElementAttributes(rn,ln),this._resetElementAttributes(an,cn)}isOverflowing(){return this.getWidth()>0}_disableOverFlow(){this._saveInitialAttribute(this._element,"overflow"),this._element.style.overflow="hidden"}_setElementAttributes(t,e,i){const n=this.getWidth();this._applyManipulationCallback(t,(t=>{if(t!==this._element&&window.innerWidth>t.clientWidth+n)return;this._saveInitialAttribute(t,e);const s=window.getComputedStyle(t).getPropertyValue(e);t.style.setProperty(e,`${i(Number.parseFloat(s))}px`)}))}_saveInitialAttribute(t,e){const i=t.style.getPropertyValue(e);i&&_e.setDataAttribute(t,e,i)}_resetElementAttributes(t,e){this._applyManipulationCallback(t,(t=>{const i=_e.getDataAttribute(t,e);null!==i?(_e.removeDataAttribute(t,e),t.style.setProperty(e,i)):t.style.removeProperty(e)}))}_applyManipulationCallback(t,e){if(Ft(t))e(t);else for(const i of we.find(t,this._element))e(i)}}const dn=".bs.modal",un=`hide${dn}`,fn=`hidePrevented${dn}`,pn=`hidden${dn}`,mn=`show${dn}`,gn=`shown${dn}`,_n=`resize${dn}`,bn=`click.dismiss${dn}`,vn=`mousedown.dismiss${dn}`,yn=`keydown.dismiss${dn}`,wn=`click${dn}.data-api`,En="modal-open",An="show",Tn="modal-static",Cn={backdrop:!0,focus:!0,keyboard:!0},On={backdrop:"(boolean|string)",focus:"boolean",keyboard:"boolean"};class xn extends ve{constructor(t,e){super(t,e),this._dialog=we.findOne(".modal-dialog",this._element),this._backdrop=this._initializeBackDrop(),this._focustrap=this._initializeFocusTrap(),this._isShown=!1,this._isTransitioning=!1,this._scrollBar=new hn,this._addEventListeners()}static get Default(){return Cn}static get DefaultType(){return On}static get NAME(){return"modal"}toggle(t){return this._isShown?this.hide():this.show(t)}show(t){this._isShown||this._isTransitioning||fe.trigger(this._element,mn,{relatedTarget:t}).defaultPrevented||(this._isShown=!0,this._isTransitioning=!0,this._scrollBar.hide(),document.body.classList.add(En),this._adjustDialog(),this._backdrop.show((()=>this._showElement(t))))}hide(){this._isShown&&!this._isTransitioning&&(fe.trigger(this._element,un).defaultPrevented||(this._isShown=!1,this._isTransitioning=!0,this._focustrap.deactivate(),this._element.classList.remove(An),this._queueCallback((()=>this._hideModal()),this._element,this._isAnimated())))}dispose(){fe.off(window,dn),fe.off(this._dialog,dn),this._backdrop.dispose(),this._focustrap.deactivate(),super.dispose()}handleUpdate(){this._adjustDialog()}_initializeBackDrop(){return new Gi({isVisible:Boolean(this._config.backdrop),isAnimated:this._isAnimated()})}_initializeFocusTrap(){return new on({trapElement:this._element})}_showElement(t){document.body.contains(this._element)||document.body.append(this._element),this._element.style.display="block",this._element.removeAttribute("aria-hidden"),this._element.setAttribute("aria-modal",!0),this._element.setAttribute("role","dialog"),this._element.scrollTop=0;const e=we.findOne(".modal-body",this._dialog);e&&(e.scrollTop=0),qt(this._element),this._element.classList.add(An),this._queueCallback((()=>{this._config.focus&&this._focustrap.activate(),this._isTransitioning=!1,fe.trigger(this._element,gn,{relatedTarget:t})}),this._dialog,this._isAnimated())}_addEventListeners(){fe.on(this._element,yn,(t=>{"Escape"===t.key&&(this._config.keyboard?this.hide():this._triggerBackdropTransition())})),fe.on(window,_n,(()=>{this._isShown&&!this._isTransitioning&&this._adjustDialog()})),fe.on(this._element,vn,(t=>{fe.one(this._element,bn,(e=>{this._element===t.target&&this._element===e.target&&("static"!==this._config.backdrop?this._config.backdrop&&this.hide():this._triggerBackdropTransition())}))}))}_hideModal(){this._element.style.display="none",this._element.setAttribute("aria-hidden",!0),this._element.removeAttribute("aria-modal"),this._element.removeAttribute("role"),this._isTransitioning=!1,this._backdrop.hide((()=>{document.body.classList.remove(En),this._resetAdjustments(),this._scrollBar.reset(),fe.trigger(this._element,pn)}))}_isAnimated(){return this._element.classList.contains("fade")}_triggerBackdropTransition(){if(fe.trigger(this._element,fn).defaultPrevented)return;const t=this._element.scrollHeight>document.documentElement.clientHeight,e=this._element.style.overflowY;"hidden"===e||this._element.classList.contains(Tn)||(t||(this._element.style.overflowY="hidden"),this._element.classList.add(Tn),this._queueCallback((()=>{this._element.classList.remove(Tn),this._queueCallback((()=>{this._element.style.overflowY=e}),this._dialog)}),this._dialog),this._element.focus())}_adjustDialog(){const t=this._element.scrollHeight>document.documentElement.clientHeight,e=this._scrollBar.getWidth(),i=e>0;if(i&&!t){const t=Kt()?"paddingLeft":"paddingRight";this._element.style[t]=`${e}px`}if(!i&&t){const t=Kt()?"paddingRight":"paddingLeft";this._element.style[t]=`${e}px`}}_resetAdjustments(){this._element.style.paddingLeft="",this._element.style.paddingRight=""}static jQueryInterface(t,e){return this.each((function(){const i=xn.getOrCreateInstance(this,t);if("string"==typeof t){if(void 0===i[t])throw new TypeError(`No method named "${t}"`);i[t](e)}}))}}fe.on(document,wn,'[data-bs-toggle="modal"]',(function(t){const e=we.getElementFromSelector(this);["A","AREA"].includes(this.tagName)&&t.preventDefault(),fe.one(e,mn,(t=>{t.defaultPrevented||fe.one(e,pn,(()=>{Bt(this)&&this.focus()}))}));const i=we.findOne(".modal.show");i&&xn.getInstance(i).hide(),xn.getOrCreateInstance(e).toggle(this)})),Ee(xn),Qt(xn);const kn=".bs.offcanvas",Ln=".data-api",Sn=`load${kn}${Ln}`,Dn="show",$n="showing",In="hiding",Nn=".offcanvas.show",Pn=`show${kn}`,Mn=`shown${kn}`,jn=`hide${kn}`,Fn=`hidePrevented${kn}`,Hn=`hidden${kn}`,Bn=`resize${kn}`,Wn=`click${kn}${Ln}`,zn=`keydown.dismiss${kn}`,Rn={backdrop:!0,keyboard:!0,scroll:!1},qn={backdrop:"(boolean|string)",keyboard:"boolean",scroll:"boolean"};class Vn extends ve{constructor(t,e){super(t,e),this._isShown=!1,this._backdrop=this._initializeBackDrop(),this._focustrap=this._initializeFocusTrap(),this._addEventListeners()}static get Default(){return Rn}static get DefaultType(){return qn}static get NAME(){return"offcanvas"}toggle(t){return this._isShown?this.hide():this.show(t)}show(t){this._isShown||fe.trigger(this._element,Pn,{relatedTarget:t}).defaultPrevented||(this._isShown=!0,this._backdrop.show(),this._config.scroll||(new hn).hide(),this._element.setAttribute("aria-modal",!0),this._element.setAttribute("role","dialog"),this._element.classList.add($n),this._queueCallback((()=>{this._config.scroll&&!this._config.backdrop||this._focustrap.activate(),this._element.classList.add(Dn),this._element.classList.remove($n),fe.trigger(this._element,Mn,{relatedTarget:t})}),this._element,!0))}hide(){this._isShown&&(fe.trigger(this._element,jn).defaultPrevented||(this._focustrap.deactivate(),this._element.blur(),this._isShown=!1,this._element.classList.add(In),this._backdrop.hide(),this._queueCallback((()=>{this._element.classList.remove(Dn,In),this._element.removeAttribute("aria-modal"),this._element.removeAttribute("role"),this._config.scroll||(new hn).reset(),fe.trigger(this._element,Hn)}),this._element,!0)))}dispose(){this._backdrop.dispose(),this._focustrap.deactivate(),super.dispose()}_initializeBackDrop(){const t=Boolean(this._config.backdrop);return new Gi({className:"offcanvas-backdrop",isVisible:t,isAnimated:!0,rootElement:this._element.parentNode,clickCallback:t?()=>{"static"!==this._config.backdrop?this.hide():fe.trigger(this._element,Fn)}:null})}_initializeFocusTrap(){return new on({trapElement:this._element})}_addEventListeners(){fe.on(this._element,zn,(t=>{"Escape"===t.key&&(this._config.keyboard?this.hide():fe.trigger(this._element,Fn))}))}static jQueryInterface(t){return this.each((function(){const e=Vn.getOrCreateInstance(this,t);if("string"==typeof t){if(void 0===e[t]||t.startsWith("_")||"constructor"===t)throw new TypeError(`No method named "${t}"`);e[t](this)}}))}}fe.on(document,Wn,'[data-bs-toggle="offcanvas"]',(function(t){const e=we.getElementFromSelector(this);if(["A","AREA"].includes(this.tagName)&&t.preventDefault(),Wt(this))return;fe.one(e,Hn,(()=>{Bt(this)&&this.focus()}));const i=we.findOne(Nn);i&&i!==e&&Vn.getInstance(i).hide(),Vn.getOrCreateInstance(e).toggle(this)})),fe.on(window,Sn,(()=>{for(const t of we.find(Nn))Vn.getOrCreateInstance(t).show()})),fe.on(window,Bn,(()=>{for(const t of we.find("[aria-modal][class*=show][class*=offcanvas-]"))"fixed"!==getComputedStyle(t).position&&Vn.getOrCreateInstance(t).hide()})),Ee(Vn),Qt(Vn);const Yn={"*":["class","dir","id","lang","role",/^aria-[\w-]*$/i],a:["target","href","title","rel"],area:[],b:[],br:[],col:[],code:[],div:[],em:[],hr:[],h1:[],h2:[],h3:[],h4:[],h5:[],h6:[],i:[],img:["src","srcset","alt","title","width","height"],li:[],ol:[],p:[],pre:[],s:[],small:[],span:[],sub:[],sup:[],strong:[],u:[],ul:[]},Kn=new Set(["background","cite","href","itemtype","longdesc","poster","src","xlink:href"]),Qn=/^(?!javascript:)(?:[a-z0-9+.-]+:|[^&:/?#]*(?:[/?#]|$))/i,Xn=(t,e)=>{const i=t.nodeName.toLowerCase();return e.includes(i)?!Kn.has(i)||Boolean(Qn.test(t.nodeValue)):e.filter((t=>t instanceof RegExp)).some((t=>t.test(i)))},Un={allowList:Yn,content:{},extraClass:"",html:!1,sanitize:!0,sanitizeFn:null,template:"
"},Gn={allowList:"object",content:"object",extraClass:"(string|function)",html:"boolean",sanitize:"boolean",sanitizeFn:"(null|function)",template:"string"},Jn={entry:"(string|element|function|null)",selector:"(string|element)"};class Zn extends be{constructor(t){super(),this._config=this._getConfig(t)}static get Default(){return Un}static get DefaultType(){return Gn}static get NAME(){return"TemplateFactory"}getContent(){return Object.values(this._config.content).map((t=>this._resolvePossibleFunction(t))).filter(Boolean)}hasContent(){return this.getContent().length>0}changeContent(t){return this._checkContent(t),this._config.content={...this._config.content,...t},this}toHtml(){const t=document.createElement("div");t.innerHTML=this._maybeSanitize(this._config.template);for(const[e,i]of Object.entries(this._config.content))this._setContent(t,i,e);const e=t.children[0],i=this._resolvePossibleFunction(this._config.extraClass);return i&&e.classList.add(...i.split(" ")),e}_typeCheckConfig(t){super._typeCheckConfig(t),this._checkContent(t.content)}_checkContent(t){for(const[e,i]of Object.entries(t))super._typeCheckConfig({selector:e,entry:i},Jn)}_setContent(t,e,i){const n=we.findOne(i,t);n&&((e=this._resolvePossibleFunction(e))?Ft(e)?this._putElementInTemplate(Ht(e),n):this._config.html?n.innerHTML=this._maybeSanitize(e):n.textContent=e:n.remove())}_maybeSanitize(t){return this._config.sanitize?function(t,e,i){if(!t.length)return t;if(i&&"function"==typeof i)return i(t);const n=(new window.DOMParser).parseFromString(t,"text/html"),s=[].concat(...n.body.querySelectorAll("*"));for(const t of s){const i=t.nodeName.toLowerCase();if(!Object.keys(e).includes(i)){t.remove();continue}const n=[].concat(...t.attributes),s=[].concat(e["*"]||[],e[i]||[]);for(const e of n)Xn(e,s)||t.removeAttribute(e.nodeName)}return n.body.innerHTML}(t,this._config.allowList,this._config.sanitizeFn):t}_resolvePossibleFunction(t){return Xt(t,[this])}_putElementInTemplate(t,e){if(this._config.html)return e.innerHTML="",void e.append(t);e.textContent=t.textContent}}const ts=new Set(["sanitize","allowList","sanitizeFn"]),es="fade",is="show",ns=".modal",ss="hide.bs.modal",os="hover",rs="focus",as={AUTO:"auto",TOP:"top",RIGHT:Kt()?"left":"right",BOTTOM:"bottom",LEFT:Kt()?"right":"left"},ls={allowList:Yn,animation:!0,boundary:"clippingParents",container:!1,customClass:"",delay:0,fallbackPlacements:["top","right","bottom","left"],html:!1,offset:[0,6],placement:"top",popperConfig:null,sanitize:!0,sanitizeFn:null,selector:!1,template:'',title:"",trigger:"hover focus"},cs={allowList:"object",animation:"boolean",boundary:"(string|element)",container:"(string|element|boolean)",customClass:"(string|function)",delay:"(number|object)",fallbackPlacements:"array",html:"boolean",offset:"(array|string|function)",placement:"(string|function)",popperConfig:"(null|object|function)",sanitize:"boolean",sanitizeFn:"(null|function)",selector:"(string|boolean)",template:"string",title:"(string|element|function)",trigger:"string"};class hs extends ve{constructor(t,i){if(void 0===e)throw new TypeError("Bootstrap's tooltips require Popper (https://popper.js.org)");super(t,i),this._isEnabled=!0,this._timeout=0,this._isHovered=null,this._activeTrigger={},this._popper=null,this._templateFactory=null,this._newContent=null,this.tip=null,this._setListeners(),this._config.selector||this._fixTitle()}static get Default(){return ls}static get DefaultType(){return cs}static get NAME(){return"tooltip"}enable(){this._isEnabled=!0}disable(){this._isEnabled=!1}toggleEnabled(){this._isEnabled=!this._isEnabled}toggle(){this._isEnabled&&(this._activeTrigger.click=!this._activeTrigger.click,this._isShown()?this._leave():this._enter())}dispose(){clearTimeout(this._timeout),fe.off(this._element.closest(ns),ss,this._hideModalHandler),this._element.getAttribute("data-bs-original-title")&&this._element.setAttribute("title",this._element.getAttribute("data-bs-original-title")),this._disposePopper(),super.dispose()}show(){if("none"===this._element.style.display)throw new Error("Please use show on visible elements");if(!this._isWithContent()||!this._isEnabled)return;const t=fe.trigger(this._element,this.constructor.eventName("show")),e=(zt(this._element)||this._element.ownerDocument.documentElement).contains(this._element);if(t.defaultPrevented||!e)return;this._disposePopper();const i=this._getTipElement();this._element.setAttribute("aria-describedby",i.getAttribute("id"));const{container:n}=this._config;if(this._element.ownerDocument.documentElement.contains(this.tip)||(n.append(i),fe.trigger(this._element,this.constructor.eventName("inserted"))),this._popper=this._createPopper(i),i.classList.add(is),"ontouchstart"in document.documentElement)for(const t of[].concat(...document.body.children))fe.on(t,"mouseover",Rt);this._queueCallback((()=>{fe.trigger(this._element,this.constructor.eventName("shown")),!1===this._isHovered&&this._leave(),this._isHovered=!1}),this.tip,this._isAnimated())}hide(){if(this._isShown()&&!fe.trigger(this._element,this.constructor.eventName("hide")).defaultPrevented){if(this._getTipElement().classList.remove(is),"ontouchstart"in document.documentElement)for(const t of[].concat(...document.body.children))fe.off(t,"mouseover",Rt);this._activeTrigger.click=!1,this._activeTrigger[rs]=!1,this._activeTrigger[os]=!1,this._isHovered=null,this._queueCallback((()=>{this._isWithActiveTrigger()||(this._isHovered||this._disposePopper(),this._element.removeAttribute("aria-describedby"),fe.trigger(this._element,this.constructor.eventName("hidden")))}),this.tip,this._isAnimated())}}update(){this._popper&&this._popper.update()}_isWithContent(){return Boolean(this._getTitle())}_getTipElement(){return this.tip||(this.tip=this._createTipElement(this._newContent||this._getContentForTemplate())),this.tip}_createTipElement(t){const e=this._getTemplateFactory(t).toHtml();if(!e)return null;e.classList.remove(es,is),e.classList.add(`bs-${this.constructor.NAME}-auto`);const i=(t=>{do{t+=Math.floor(1e6*Math.random())}while(document.getElementById(t));return t})(this.constructor.NAME).toString();return e.setAttribute("id",i),this._isAnimated()&&e.classList.add(es),e}setContent(t){this._newContent=t,this._isShown()&&(this._disposePopper(),this.show())}_getTemplateFactory(t){return this._templateFactory?this._templateFactory.changeContent(t):this._templateFactory=new Zn({...this._config,content:t,extraClass:this._resolvePossibleFunction(this._config.customClass)}),this._templateFactory}_getContentForTemplate(){return{".tooltip-inner":this._getTitle()}}_getTitle(){return this._resolvePossibleFunction(this._config.title)||this._element.getAttribute("data-bs-original-title")}_initializeOnDelegatedTarget(t){return this.constructor.getOrCreateInstance(t.delegateTarget,this._getDelegateConfig())}_isAnimated(){return this._config.animation||this.tip&&this.tip.classList.contains(es)}_isShown(){return this.tip&&this.tip.classList.contains(is)}_createPopper(t){const e=Xt(this._config.placement,[this,t,this._element]),i=as[e.toUpperCase()];return Dt(this._element,t,this._getPopperConfig(i))}_getOffset(){const{offset:t}=this._config;return"string"==typeof t?t.split(",").map((t=>Number.parseInt(t,10))):"function"==typeof t?e=>t(e,this._element):t}_resolvePossibleFunction(t){return Xt(t,[this._element])}_getPopperConfig(t){const e={placement:t,modifiers:[{name:"flip",options:{fallbackPlacements:this._config.fallbackPlacements}},{name:"offset",options:{offset:this._getOffset()}},{name:"preventOverflow",options:{boundary:this._config.boundary}},{name:"arrow",options:{element:`.${this.constructor.NAME}-arrow`}},{name:"preSetPlacement",enabled:!0,phase:"beforeMain",fn:t=>{this._getTipElement().setAttribute("data-popper-placement",t.state.placement)}}]};return{...e,...Xt(this._config.popperConfig,[e])}}_setListeners(){const t=this._config.trigger.split(" ");for(const e of t)if("click"===e)fe.on(this._element,this.constructor.eventName("click"),this._config.selector,(t=>{this._initializeOnDelegatedTarget(t).toggle()}));else if("manual"!==e){const t=e===os?this.constructor.eventName("mouseenter"):this.constructor.eventName("focusin"),i=e===os?this.constructor.eventName("mouseleave"):this.constructor.eventName("focusout");fe.on(this._element,t,this._config.selector,(t=>{const e=this._initializeOnDelegatedTarget(t);e._activeTrigger["focusin"===t.type?rs:os]=!0,e._enter()})),fe.on(this._element,i,this._config.selector,(t=>{const e=this._initializeOnDelegatedTarget(t);e._activeTrigger["focusout"===t.type?rs:os]=e._element.contains(t.relatedTarget),e._leave()}))}this._hideModalHandler=()=>{this._element&&this.hide()},fe.on(this._element.closest(ns),ss,this._hideModalHandler)}_fixTitle(){const t=this._element.getAttribute("title");t&&(this._element.getAttribute("aria-label")||this._element.textContent.trim()||this._element.setAttribute("aria-label",t),this._element.setAttribute("data-bs-original-title",t),this._element.removeAttribute("title"))}_enter(){this._isShown()||this._isHovered?this._isHovered=!0:(this._isHovered=!0,this._setTimeout((()=>{this._isHovered&&this.show()}),this._config.delay.show))}_leave(){this._isWithActiveTrigger()||(this._isHovered=!1,this._setTimeout((()=>{this._isHovered||this.hide()}),this._config.delay.hide))}_setTimeout(t,e){clearTimeout(this._timeout),this._timeout=setTimeout(t,e)}_isWithActiveTrigger(){return Object.values(this._activeTrigger).includes(!0)}_getConfig(t){const e=_e.getDataAttributes(this._element);for(const t of Object.keys(e))ts.has(t)&&delete e[t];return t={...e,..."object"==typeof t&&t?t:{}},t=this._mergeConfigObj(t),t=this._configAfterMerge(t),this._typeCheckConfig(t),t}_configAfterMerge(t){return t.container=!1===t.container?document.body:Ht(t.container),"number"==typeof t.delay&&(t.delay={show:t.delay,hide:t.delay}),"number"==typeof t.title&&(t.title=t.title.toString()),"number"==typeof t.content&&(t.content=t.content.toString()),t}_getDelegateConfig(){const t={};for(const[e,i]of Object.entries(this._config))this.constructor.Default[e]!==i&&(t[e]=i);return t.selector=!1,t.trigger="manual",t}_disposePopper(){this._popper&&(this._popper.destroy(),this._popper=null),this.tip&&(this.tip.remove(),this.tip=null)}static jQueryInterface(t){return this.each((function(){const e=hs.getOrCreateInstance(this,t);if("string"==typeof t){if(void 0===e[t])throw new TypeError(`No method named "${t}"`);e[t]()}}))}}Qt(hs);const ds={...hs.Default,content:"",offset:[0,8],placement:"right",template:'',trigger:"click"},us={...hs.DefaultType,content:"(null|string|element|function)"};class fs extends hs{static get Default(){return ds}static get DefaultType(){return us}static get 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0000000..10f979d --- /dev/null +++ b/_static/scripts/bootstrap.js.LICENSE.txt @@ -0,0 +1,5 @@ +/*! + * Bootstrap v5.3.2 (https://getbootstrap.com/) + * Copyright 2011-2023 The Bootstrap Authors (https://github.com/twbs/bootstrap/graphs/contributors) + * Licensed under MIT (https://github.com/twbs/bootstrap/blob/main/LICENSE) + */ diff --git a/_static/scripts/bootstrap.js.map b/_static/scripts/bootstrap.js.map new file mode 100644 index 0000000..64e212b --- /dev/null +++ b/_static/scripts/bootstrap.js.map @@ -0,0 +1 @@ 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(element.nodeName || '').toLowerCase() : null;\n}","export default function getWindow(node) {\n if (node == null) {\n return window;\n }\n\n if (node.toString() !== '[object Window]') {\n var ownerDocument = node.ownerDocument;\n return ownerDocument ? ownerDocument.defaultView || window : window;\n }\n\n return node;\n}","import getWindow from \"./getWindow.js\";\n\nfunction isElement(node) {\n var OwnElement = getWindow(node).Element;\n return node instanceof OwnElement || node instanceof Element;\n}\n\nfunction isHTMLElement(node) {\n var OwnElement = getWindow(node).HTMLElement;\n return node instanceof OwnElement || node instanceof HTMLElement;\n}\n\nfunction isShadowRoot(node) {\n // IE 11 has no ShadowRoot\n if (typeof ShadowRoot === 'undefined') {\n return false;\n }\n\n var OwnElement = getWindow(node).ShadowRoot;\n return node instanceof OwnElement || node instanceof ShadowRoot;\n}\n\nexport { isElement, isHTMLElement, isShadowRoot };","import getNodeName from \"../dom-utils/getNodeName.js\";\nimport { isHTMLElement } from \"../dom-utils/instanceOf.js\"; // This modifier takes the styles prepared by the `computeStyles` modifier\n// and applies them to the HTMLElements such as popper and arrow\n\nfunction applyStyles(_ref) {\n var state = _ref.state;\n Object.keys(state.elements).forEach(function (name) {\n var style = state.styles[name] || {};\n var attributes = state.attributes[name] || {};\n var element = state.elements[name]; // arrow is optional + virtual elements\n\n if (!isHTMLElement(element) || !getNodeName(element)) {\n return;\n } // Flow doesn't support to extend this property, but it's the most\n // effective way to apply styles to an HTMLElement\n // $FlowFixMe[cannot-write]\n\n\n Object.assign(element.style, style);\n Object.keys(attributes).forEach(function (name) {\n var value = attributes[name];\n\n if (value === false) {\n element.removeAttribute(name);\n } else {\n element.setAttribute(name, value === true ? '' : value);\n }\n });\n });\n}\n\nfunction effect(_ref2) {\n var state = _ref2.state;\n var initialStyles = {\n popper: {\n position: state.options.strategy,\n left: '0',\n top: '0',\n margin: '0'\n },\n arrow: {\n position: 'absolute'\n },\n reference: {}\n };\n Object.assign(state.elements.popper.style, initialStyles.popper);\n state.styles = initialStyles;\n\n if (state.elements.arrow) {\n Object.assign(state.elements.arrow.style, initialStyles.arrow);\n }\n\n return function () {\n Object.keys(state.elements).forEach(function (name) {\n var element = state.elements[name];\n var attributes = state.attributes[name] || {};\n var styleProperties = Object.keys(state.styles.hasOwnProperty(name) ? state.styles[name] : initialStyles[name]); // Set all values to an empty string to unset them\n\n var style = styleProperties.reduce(function (style, property) {\n style[property] = '';\n return style;\n }, {}); // arrow is optional + virtual elements\n\n if (!isHTMLElement(element) || !getNodeName(element)) {\n return;\n }\n\n Object.assign(element.style, style);\n Object.keys(attributes).forEach(function (attribute) {\n element.removeAttribute(attribute);\n });\n });\n };\n} // eslint-disable-next-line import/no-unused-modules\n\n\nexport default {\n name: 'applyStyles',\n enabled: true,\n phase: 'write',\n fn: applyStyles,\n effect: effect,\n requires: ['computeStyles']\n};","import { auto } from \"../enums.js\";\nexport default function getBasePlacement(placement) {\n return placement.split('-')[0];\n}","export var max = Math.max;\nexport var min = Math.min;\nexport var round = Math.round;","export default function getUAString() {\n var uaData = navigator.userAgentData;\n\n if (uaData != null && uaData.brands && Array.isArray(uaData.brands)) {\n return uaData.brands.map(function (item) {\n return item.brand + \"/\" + item.version;\n }).join(' ');\n }\n\n return navigator.userAgent;\n}","import getUAString from \"../utils/userAgent.js\";\nexport default function isLayoutViewport() {\n return !/^((?!chrome|android).)*safari/i.test(getUAString());\n}","import { isElement, isHTMLElement } from \"./instanceOf.js\";\nimport { round } from \"../utils/math.js\";\nimport getWindow from \"./getWindow.js\";\nimport isLayoutViewport from \"./isLayoutViewport.js\";\nexport default function getBoundingClientRect(element, includeScale, isFixedStrategy) {\n if (includeScale === void 0) {\n includeScale = false;\n }\n\n if (isFixedStrategy === void 0) {\n isFixedStrategy = false;\n }\n\n var clientRect = element.getBoundingClientRect();\n var scaleX = 1;\n var scaleY = 1;\n\n if (includeScale && isHTMLElement(element)) {\n scaleX = element.offsetWidth > 0 ? round(clientRect.width) / element.offsetWidth || 1 : 1;\n scaleY = element.offsetHeight > 0 ? round(clientRect.height) / element.offsetHeight || 1 : 1;\n }\n\n var _ref = isElement(element) ? getWindow(element) : window,\n visualViewport = _ref.visualViewport;\n\n var addVisualOffsets = !isLayoutViewport() && isFixedStrategy;\n var x = (clientRect.left + (addVisualOffsets && visualViewport ? visualViewport.offsetLeft : 0)) / scaleX;\n var y = (clientRect.top + (addVisualOffsets && visualViewport ? visualViewport.offsetTop : 0)) / scaleY;\n var width = clientRect.width / scaleX;\n var height = clientRect.height / scaleY;\n return {\n width: width,\n height: height,\n top: y,\n right: x + width,\n bottom: y + height,\n left: x,\n x: x,\n y: y\n };\n}","import getBoundingClientRect from \"./getBoundingClientRect.js\"; // Returns the layout rect of an element relative to its offsetParent. Layout\n// means it doesn't take into account transforms.\n\nexport default function getLayoutRect(element) {\n var clientRect = getBoundingClientRect(element); // Use the clientRect sizes if it's not been transformed.\n // Fixes https://github.com/popperjs/popper-core/issues/1223\n\n var width = element.offsetWidth;\n var height = element.offsetHeight;\n\n if (Math.abs(clientRect.width - width) <= 1) {\n width = clientRect.width;\n }\n\n if (Math.abs(clientRect.height - height) <= 1) {\n height = clientRect.height;\n }\n\n return {\n x: element.offsetLeft,\n y: element.offsetTop,\n width: width,\n height: height\n };\n}","import { isShadowRoot } from \"./instanceOf.js\";\nexport default function contains(parent, child) {\n var rootNode = child.getRootNode && child.getRootNode(); // First, attempt with faster native method\n\n if (parent.contains(child)) {\n return true;\n } // then fallback to custom implementation with Shadow DOM support\n else if (rootNode && isShadowRoot(rootNode)) {\n var next = child;\n\n do {\n if (next && parent.isSameNode(next)) {\n return true;\n } // $FlowFixMe[prop-missing]: need a better way to handle this...\n\n\n next = next.parentNode || next.host;\n } while (next);\n } // Give up, the result is false\n\n\n return false;\n}","import getWindow from \"./getWindow.js\";\nexport default function getComputedStyle(element) {\n return getWindow(element).getComputedStyle(element);\n}","import getNodeName from \"./getNodeName.js\";\nexport default function isTableElement(element) {\n return ['table', 'td', 'th'].indexOf(getNodeName(element)) >= 0;\n}","import { isElement } from \"./instanceOf.js\";\nexport default function getDocumentElement(element) {\n // $FlowFixMe[incompatible-return]: assume body is always available\n return ((isElement(element) ? element.ownerDocument : // $FlowFixMe[prop-missing]\n element.document) || window.document).documentElement;\n}","import getNodeName from \"./getNodeName.js\";\nimport getDocumentElement from \"./getDocumentElement.js\";\nimport { isShadowRoot } from \"./instanceOf.js\";\nexport default function getParentNode(element) {\n if (getNodeName(element) === 'html') {\n return element;\n }\n\n return (// this is a quicker (but less type safe) way to save quite some bytes from the bundle\n // $FlowFixMe[incompatible-return]\n // $FlowFixMe[prop-missing]\n element.assignedSlot || // step into the shadow DOM of the parent of a slotted node\n element.parentNode || ( // DOM Element detected\n isShadowRoot(element) ? element.host : null) || // ShadowRoot detected\n // $FlowFixMe[incompatible-call]: HTMLElement is a Node\n getDocumentElement(element) // fallback\n\n );\n}","import getWindow from \"./getWindow.js\";\nimport getNodeName from \"./getNodeName.js\";\nimport getComputedStyle from \"./getComputedStyle.js\";\nimport { isHTMLElement, isShadowRoot } from \"./instanceOf.js\";\nimport isTableElement from \"./isTableElement.js\";\nimport getParentNode from \"./getParentNode.js\";\nimport getUAString from \"../utils/userAgent.js\";\n\nfunction getTrueOffsetParent(element) {\n if (!isHTMLElement(element) || // https://github.com/popperjs/popper-core/issues/837\n getComputedStyle(element).position === 'fixed') {\n return null;\n }\n\n return element.offsetParent;\n} // `.offsetParent` reports `null` for fixed elements, while absolute elements\n// return the containing block\n\n\nfunction getContainingBlock(element) {\n var isFirefox = /firefox/i.test(getUAString());\n var isIE = /Trident/i.test(getUAString());\n\n if (isIE && isHTMLElement(element)) {\n // In IE 9, 10 and 11 fixed elements containing block is always established by the viewport\n var elementCss = getComputedStyle(element);\n\n if (elementCss.position === 'fixed') {\n return null;\n }\n }\n\n var currentNode = getParentNode(element);\n\n if (isShadowRoot(currentNode)) {\n currentNode = currentNode.host;\n }\n\n while (isHTMLElement(currentNode) && ['html', 'body'].indexOf(getNodeName(currentNode)) < 0) {\n var css = getComputedStyle(currentNode); // This is non-exhaustive but covers the most common CSS properties that\n // create a containing block.\n // https://developer.mozilla.org/en-US/docs/Web/CSS/Containing_block#identifying_the_containing_block\n\n if (css.transform !== 'none' || css.perspective !== 'none' || css.contain === 'paint' || ['transform', 'perspective'].indexOf(css.willChange) !== -1 || isFirefox && css.willChange === 'filter' || isFirefox && css.filter && css.filter !== 'none') {\n return currentNode;\n } else {\n currentNode = currentNode.parentNode;\n }\n }\n\n return null;\n} // Gets the closest ancestor positioned element. Handles some edge cases,\n// such as table ancestors and cross browser bugs.\n\n\nexport default function getOffsetParent(element) {\n var window = getWindow(element);\n var offsetParent = getTrueOffsetParent(element);\n\n while (offsetParent && isTableElement(offsetParent) && getComputedStyle(offsetParent).position === 'static') {\n offsetParent = getTrueOffsetParent(offsetParent);\n }\n\n if (offsetParent && (getNodeName(offsetParent) === 'html' || getNodeName(offsetParent) === 'body' && getComputedStyle(offsetParent).position === 'static')) {\n return window;\n }\n\n return offsetParent || getContainingBlock(element) || window;\n}","export default function getMainAxisFromPlacement(placement) {\n return ['top', 'bottom'].indexOf(placement) >= 0 ? 'x' : 'y';\n}","import { max as mathMax, min as mathMin } from \"./math.js\";\nexport function within(min, value, max) {\n return mathMax(min, mathMin(value, max));\n}\nexport function withinMaxClamp(min, value, max) {\n var v = within(min, value, max);\n return v > max ? max : v;\n}","import getFreshSideObject from \"./getFreshSideObject.js\";\nexport default function mergePaddingObject(paddingObject) {\n return Object.assign({}, getFreshSideObject(), paddingObject);\n}","export default function getFreshSideObject() {\n return {\n top: 0,\n right: 0,\n bottom: 0,\n left: 0\n };\n}","export default function expandToHashMap(value, keys) {\n return keys.reduce(function (hashMap, key) {\n hashMap[key] = value;\n return hashMap;\n }, {});\n}","import getBasePlacement from \"../utils/getBasePlacement.js\";\nimport getLayoutRect from \"../dom-utils/getLayoutRect.js\";\nimport contains from \"../dom-utils/contains.js\";\nimport getOffsetParent from \"../dom-utils/getOffsetParent.js\";\nimport getMainAxisFromPlacement from \"../utils/getMainAxisFromPlacement.js\";\nimport { within } from \"../utils/within.js\";\nimport mergePaddingObject from \"../utils/mergePaddingObject.js\";\nimport expandToHashMap from \"../utils/expandToHashMap.js\";\nimport { left, right, basePlacements, top, bottom } from \"../enums.js\"; // eslint-disable-next-line import/no-unused-modules\n\nvar toPaddingObject = function toPaddingObject(padding, state) {\n padding = typeof padding === 'function' ? padding(Object.assign({}, state.rects, {\n placement: state.placement\n })) : padding;\n return mergePaddingObject(typeof padding !== 'number' ? padding : expandToHashMap(padding, basePlacements));\n};\n\nfunction arrow(_ref) {\n var _state$modifiersData$;\n\n var state = _ref.state,\n name = _ref.name,\n options = _ref.options;\n var arrowElement = state.elements.arrow;\n var popperOffsets = state.modifiersData.popperOffsets;\n var basePlacement = getBasePlacement(state.placement);\n var axis = getMainAxisFromPlacement(basePlacement);\n var isVertical = [left, right].indexOf(basePlacement) >= 0;\n var len = isVertical ? 'height' : 'width';\n\n if (!arrowElement || !popperOffsets) {\n return;\n }\n\n var paddingObject = toPaddingObject(options.padding, state);\n var arrowRect = getLayoutRect(arrowElement);\n var minProp = axis === 'y' ? top : left;\n var maxProp = axis === 'y' ? bottom : right;\n var endDiff = state.rects.reference[len] + state.rects.reference[axis] - popperOffsets[axis] - state.rects.popper[len];\n var startDiff = popperOffsets[axis] - state.rects.reference[axis];\n var arrowOffsetParent = getOffsetParent(arrowElement);\n var clientSize = arrowOffsetParent ? axis === 'y' ? arrowOffsetParent.clientHeight || 0 : arrowOffsetParent.clientWidth || 0 : 0;\n var centerToReference = endDiff / 2 - startDiff / 2; // Make sure the arrow doesn't overflow the popper if the center point is\n // outside of the popper bounds\n\n var min = paddingObject[minProp];\n var max = clientSize - arrowRect[len] - paddingObject[maxProp];\n var center = clientSize / 2 - arrowRect[len] / 2 + centerToReference;\n var offset = within(min, center, max); // Prevents breaking syntax highlighting...\n\n var axisProp = axis;\n state.modifiersData[name] = (_state$modifiersData$ = {}, _state$modifiersData$[axisProp] = offset, _state$modifiersData$.centerOffset = offset - center, _state$modifiersData$);\n}\n\nfunction effect(_ref2) {\n var state = _ref2.state,\n options = _ref2.options;\n var _options$element = options.element,\n arrowElement = _options$element === void 0 ? '[data-popper-arrow]' : _options$element;\n\n if (arrowElement == null) {\n return;\n } // CSS selector\n\n\n if (typeof arrowElement === 'string') {\n arrowElement = state.elements.popper.querySelector(arrowElement);\n\n if (!arrowElement) {\n return;\n }\n }\n\n if (!contains(state.elements.popper, arrowElement)) {\n return;\n }\n\n state.elements.arrow = arrowElement;\n} // eslint-disable-next-line import/no-unused-modules\n\n\nexport default {\n name: 'arrow',\n enabled: true,\n phase: 'main',\n fn: arrow,\n effect: effect,\n requires: ['popperOffsets'],\n requiresIfExists: ['preventOverflow']\n};","export default function getVariation(placement) {\n return placement.split('-')[1];\n}","import { top, left, right, bottom, end } from \"../enums.js\";\nimport getOffsetParent from \"../dom-utils/getOffsetParent.js\";\nimport getWindow from \"../dom-utils/getWindow.js\";\nimport getDocumentElement from \"../dom-utils/getDocumentElement.js\";\nimport getComputedStyle from \"../dom-utils/getComputedStyle.js\";\nimport getBasePlacement from \"../utils/getBasePlacement.js\";\nimport getVariation from \"../utils/getVariation.js\";\nimport { round } from \"../utils/math.js\"; // eslint-disable-next-line import/no-unused-modules\n\nvar unsetSides = {\n top: 'auto',\n right: 'auto',\n bottom: 'auto',\n left: 'auto'\n}; // Round the offsets to the nearest suitable subpixel based on the DPR.\n// Zooming can change the DPR, but it seems to report a value that will\n// cleanly divide the values into the appropriate subpixels.\n\nfunction roundOffsetsByDPR(_ref, win) {\n var x = _ref.x,\n y = _ref.y;\n var dpr = win.devicePixelRatio || 1;\n return {\n x: round(x * dpr) / dpr || 0,\n y: round(y * dpr) / dpr || 0\n };\n}\n\nexport function mapToStyles(_ref2) {\n var _Object$assign2;\n\n var popper = _ref2.popper,\n popperRect = _ref2.popperRect,\n placement = _ref2.placement,\n variation = _ref2.variation,\n offsets = _ref2.offsets,\n position = _ref2.position,\n gpuAcceleration = _ref2.gpuAcceleration,\n adaptive = _ref2.adaptive,\n roundOffsets = _ref2.roundOffsets,\n isFixed = _ref2.isFixed;\n var _offsets$x = offsets.x,\n x = _offsets$x === void 0 ? 0 : _offsets$x,\n _offsets$y = offsets.y,\n y = _offsets$y === void 0 ? 0 : _offsets$y;\n\n var _ref3 = typeof roundOffsets === 'function' ? roundOffsets({\n x: x,\n y: y\n }) : {\n x: x,\n y: y\n };\n\n x = _ref3.x;\n y = _ref3.y;\n var hasX = offsets.hasOwnProperty('x');\n var hasY = offsets.hasOwnProperty('y');\n var sideX = left;\n var sideY = top;\n var win = window;\n\n if (adaptive) {\n var offsetParent = getOffsetParent(popper);\n var heightProp = 'clientHeight';\n var widthProp = 'clientWidth';\n\n if (offsetParent === getWindow(popper)) {\n offsetParent = getDocumentElement(popper);\n\n if (getComputedStyle(offsetParent).position !== 'static' && position === 'absolute') {\n heightProp = 'scrollHeight';\n widthProp = 'scrollWidth';\n }\n } // $FlowFixMe[incompatible-cast]: force type refinement, we compare offsetParent with window above, but Flow doesn't detect it\n\n\n offsetParent = offsetParent;\n\n if (placement === top || (placement === left || placement === right) && variation === end) {\n sideY = bottom;\n var offsetY = isFixed && offsetParent === win && win.visualViewport ? win.visualViewport.height : // $FlowFixMe[prop-missing]\n offsetParent[heightProp];\n y -= offsetY - popperRect.height;\n y *= gpuAcceleration ? 1 : -1;\n }\n\n if (placement === left || (placement === top || placement === bottom) && variation === end) {\n sideX = right;\n var offsetX = isFixed && offsetParent === win && win.visualViewport ? win.visualViewport.width : // $FlowFixMe[prop-missing]\n offsetParent[widthProp];\n x -= offsetX - popperRect.width;\n x *= gpuAcceleration ? 1 : -1;\n }\n }\n\n var commonStyles = Object.assign({\n position: position\n }, adaptive && unsetSides);\n\n var _ref4 = roundOffsets === true ? roundOffsetsByDPR({\n x: x,\n y: y\n }, getWindow(popper)) : {\n x: x,\n y: y\n };\n\n x = _ref4.x;\n y = _ref4.y;\n\n if (gpuAcceleration) {\n var _Object$assign;\n\n return Object.assign({}, commonStyles, (_Object$assign = {}, _Object$assign[sideY] = hasY ? '0' : '', _Object$assign[sideX] = hasX ? '0' : '', _Object$assign.transform = (win.devicePixelRatio || 1) <= 1 ? \"translate(\" + x + \"px, \" + y + \"px)\" : \"translate3d(\" + x + \"px, \" + y + \"px, 0)\", _Object$assign));\n }\n\n return Object.assign({}, commonStyles, (_Object$assign2 = {}, _Object$assign2[sideY] = hasY ? y + \"px\" : '', _Object$assign2[sideX] = hasX ? x + \"px\" : '', _Object$assign2.transform = '', _Object$assign2));\n}\n\nfunction computeStyles(_ref5) {\n var state = _ref5.state,\n options = _ref5.options;\n var _options$gpuAccelerat = options.gpuAcceleration,\n gpuAcceleration = _options$gpuAccelerat === void 0 ? true : _options$gpuAccelerat,\n _options$adaptive = options.adaptive,\n adaptive = _options$adaptive === void 0 ? true : _options$adaptive,\n _options$roundOffsets = options.roundOffsets,\n roundOffsets = _options$roundOffsets === void 0 ? true : _options$roundOffsets;\n var commonStyles = {\n placement: getBasePlacement(state.placement),\n variation: getVariation(state.placement),\n popper: state.elements.popper,\n popperRect: state.rects.popper,\n gpuAcceleration: gpuAcceleration,\n isFixed: state.options.strategy === 'fixed'\n };\n\n if (state.modifiersData.popperOffsets != null) {\n state.styles.popper = Object.assign({}, state.styles.popper, mapToStyles(Object.assign({}, commonStyles, {\n offsets: state.modifiersData.popperOffsets,\n position: state.options.strategy,\n adaptive: adaptive,\n roundOffsets: roundOffsets\n })));\n }\n\n if (state.modifiersData.arrow != null) {\n state.styles.arrow = Object.assign({}, state.styles.arrow, mapToStyles(Object.assign({}, commonStyles, {\n offsets: state.modifiersData.arrow,\n position: 'absolute',\n adaptive: false,\n roundOffsets: roundOffsets\n })));\n }\n\n state.attributes.popper = Object.assign({}, state.attributes.popper, {\n 'data-popper-placement': state.placement\n });\n} // eslint-disable-next-line import/no-unused-modules\n\n\nexport default {\n name: 'computeStyles',\n enabled: true,\n phase: 'beforeWrite',\n fn: computeStyles,\n data: {}\n};","import getWindow from \"../dom-utils/getWindow.js\"; // eslint-disable-next-line import/no-unused-modules\n\nvar passive = {\n passive: true\n};\n\nfunction effect(_ref) {\n var state = _ref.state,\n instance = _ref.instance,\n options = _ref.options;\n var _options$scroll = options.scroll,\n scroll = _options$scroll === void 0 ? true : _options$scroll,\n _options$resize = options.resize,\n resize = _options$resize === void 0 ? true : _options$resize;\n var window = getWindow(state.elements.popper);\n var scrollParents = [].concat(state.scrollParents.reference, state.scrollParents.popper);\n\n if (scroll) {\n scrollParents.forEach(function (scrollParent) {\n scrollParent.addEventListener('scroll', instance.update, passive);\n });\n }\n\n if (resize) {\n window.addEventListener('resize', instance.update, passive);\n }\n\n return function () {\n if (scroll) {\n scrollParents.forEach(function (scrollParent) {\n scrollParent.removeEventListener('scroll', instance.update, passive);\n });\n }\n\n if (resize) {\n window.removeEventListener('resize', instance.update, passive);\n }\n };\n} // eslint-disable-next-line import/no-unused-modules\n\n\nexport default {\n name: 'eventListeners',\n enabled: true,\n phase: 'write',\n fn: function fn() {},\n effect: effect,\n data: {}\n};","var hash = {\n left: 'right',\n right: 'left',\n bottom: 'top',\n top: 'bottom'\n};\nexport default function getOppositePlacement(placement) {\n return placement.replace(/left|right|bottom|top/g, function (matched) {\n return hash[matched];\n });\n}","var hash = {\n start: 'end',\n end: 'start'\n};\nexport default function getOppositeVariationPlacement(placement) {\n return placement.replace(/start|end/g, function (matched) {\n return hash[matched];\n });\n}","import getWindow from \"./getWindow.js\";\nexport default function getWindowScroll(node) {\n var win = getWindow(node);\n var scrollLeft = win.pageXOffset;\n var scrollTop = win.pageYOffset;\n return {\n scrollLeft: scrollLeft,\n scrollTop: scrollTop\n };\n}","import getBoundingClientRect from \"./getBoundingClientRect.js\";\nimport getDocumentElement from \"./getDocumentElement.js\";\nimport getWindowScroll from \"./getWindowScroll.js\";\nexport default function getWindowScrollBarX(element) {\n // If has a CSS width greater than the viewport, then this will be\n // incorrect for RTL.\n // Popper 1 is broken in this case and never had a bug report so let's assume\n // it's not an issue. I don't think anyone ever specifies width on \n // anyway.\n // Browsers where the left scrollbar doesn't cause an issue report `0` for\n // this (e.g. Edge 2019, IE11, Safari)\n return getBoundingClientRect(getDocumentElement(element)).left + getWindowScroll(element).scrollLeft;\n}","import getComputedStyle from \"./getComputedStyle.js\";\nexport default function isScrollParent(element) {\n // Firefox wants us to check `-x` and `-y` variations as well\n var _getComputedStyle = getComputedStyle(element),\n overflow = _getComputedStyle.overflow,\n overflowX = _getComputedStyle.overflowX,\n overflowY = _getComputedStyle.overflowY;\n\n return /auto|scroll|overlay|hidden/.test(overflow + overflowY + overflowX);\n}","import getParentNode from \"./getParentNode.js\";\nimport isScrollParent from \"./isScrollParent.js\";\nimport getNodeName from \"./getNodeName.js\";\nimport { isHTMLElement } from \"./instanceOf.js\";\nexport default function getScrollParent(node) {\n if (['html', 'body', '#document'].indexOf(getNodeName(node)) >= 0) {\n // $FlowFixMe[incompatible-return]: assume body is always available\n return node.ownerDocument.body;\n }\n\n if (isHTMLElement(node) && isScrollParent(node)) {\n return node;\n }\n\n return getScrollParent(getParentNode(node));\n}","import getScrollParent from \"./getScrollParent.js\";\nimport getParentNode from \"./getParentNode.js\";\nimport getWindow from \"./getWindow.js\";\nimport isScrollParent from \"./isScrollParent.js\";\n/*\ngiven a DOM element, return the list of all scroll parents, up the list of ancesors\nuntil we get to the top window object. This list is what we attach scroll listeners\nto, because if any of these parent elements scroll, we'll need to re-calculate the\nreference element's position.\n*/\n\nexport default function listScrollParents(element, list) {\n var _element$ownerDocumen;\n\n if (list === void 0) {\n list = [];\n }\n\n var scrollParent = getScrollParent(element);\n var isBody = scrollParent === ((_element$ownerDocumen = element.ownerDocument) == null ? void 0 : _element$ownerDocumen.body);\n var win = getWindow(scrollParent);\n var target = isBody ? [win].concat(win.visualViewport || [], isScrollParent(scrollParent) ? scrollParent : []) : scrollParent;\n var updatedList = list.concat(target);\n return isBody ? updatedList : // $FlowFixMe[incompatible-call]: isBody tells us target will be an HTMLElement here\n updatedList.concat(listScrollParents(getParentNode(target)));\n}","export default function rectToClientRect(rect) {\n return Object.assign({}, rect, {\n left: rect.x,\n top: rect.y,\n right: rect.x + rect.width,\n bottom: rect.y + rect.height\n });\n}","import { viewport } from \"../enums.js\";\nimport getViewportRect from \"./getViewportRect.js\";\nimport getDocumentRect from \"./getDocumentRect.js\";\nimport listScrollParents from \"./listScrollParents.js\";\nimport getOffsetParent from \"./getOffsetParent.js\";\nimport getDocumentElement from \"./getDocumentElement.js\";\nimport getComputedStyle from \"./getComputedStyle.js\";\nimport { isElement, isHTMLElement } from \"./instanceOf.js\";\nimport getBoundingClientRect from \"./getBoundingClientRect.js\";\nimport getParentNode from \"./getParentNode.js\";\nimport contains from \"./contains.js\";\nimport getNodeName from \"./getNodeName.js\";\nimport rectToClientRect from \"../utils/rectToClientRect.js\";\nimport { max, min } from \"../utils/math.js\";\n\nfunction getInnerBoundingClientRect(element, strategy) {\n var rect = getBoundingClientRect(element, false, strategy === 'fixed');\n rect.top = rect.top + element.clientTop;\n rect.left = rect.left + element.clientLeft;\n rect.bottom = rect.top + element.clientHeight;\n rect.right = rect.left + element.clientWidth;\n rect.width = element.clientWidth;\n rect.height = element.clientHeight;\n rect.x = rect.left;\n rect.y = rect.top;\n return rect;\n}\n\nfunction getClientRectFromMixedType(element, clippingParent, strategy) {\n return clippingParent === viewport ? rectToClientRect(getViewportRect(element, strategy)) : isElement(clippingParent) ? getInnerBoundingClientRect(clippingParent, strategy) : rectToClientRect(getDocumentRect(getDocumentElement(element)));\n} // A \"clipping parent\" is an overflowable container with the characteristic of\n// clipping (or hiding) overflowing elements with a position different from\n// `initial`\n\n\nfunction getClippingParents(element) {\n var clippingParents = listScrollParents(getParentNode(element));\n var canEscapeClipping = ['absolute', 'fixed'].indexOf(getComputedStyle(element).position) >= 0;\n var clipperElement = canEscapeClipping && isHTMLElement(element) ? getOffsetParent(element) : element;\n\n if (!isElement(clipperElement)) {\n return [];\n } // $FlowFixMe[incompatible-return]: https://github.com/facebook/flow/issues/1414\n\n\n return clippingParents.filter(function (clippingParent) {\n return isElement(clippingParent) && contains(clippingParent, clipperElement) && getNodeName(clippingParent) !== 'body';\n });\n} // Gets the maximum area that the element is visible in due to any number of\n// clipping parents\n\n\nexport default function getClippingRect(element, boundary, rootBoundary, strategy) {\n var mainClippingParents = boundary === 'clippingParents' ? getClippingParents(element) : [].concat(boundary);\n var clippingParents = [].concat(mainClippingParents, [rootBoundary]);\n var firstClippingParent = clippingParents[0];\n var clippingRect = clippingParents.reduce(function (accRect, clippingParent) {\n var rect = getClientRectFromMixedType(element, clippingParent, strategy);\n accRect.top = max(rect.top, accRect.top);\n accRect.right = min(rect.right, accRect.right);\n accRect.bottom = min(rect.bottom, accRect.bottom);\n accRect.left = max(rect.left, accRect.left);\n return accRect;\n }, getClientRectFromMixedType(element, firstClippingParent, strategy));\n clippingRect.width = clippingRect.right - clippingRect.left;\n clippingRect.height = clippingRect.bottom - clippingRect.top;\n clippingRect.x = clippingRect.left;\n clippingRect.y = clippingRect.top;\n return clippingRect;\n}","import getWindow from \"./getWindow.js\";\nimport getDocumentElement from \"./getDocumentElement.js\";\nimport getWindowScrollBarX from \"./getWindowScrollBarX.js\";\nimport isLayoutViewport from \"./isLayoutViewport.js\";\nexport default function getViewportRect(element, strategy) {\n var win = getWindow(element);\n var html = getDocumentElement(element);\n var visualViewport = win.visualViewport;\n var width = html.clientWidth;\n var height = html.clientHeight;\n var x = 0;\n var y = 0;\n\n if (visualViewport) {\n width = visualViewport.width;\n height = visualViewport.height;\n var layoutViewport = isLayoutViewport();\n\n if (layoutViewport || !layoutViewport && strategy === 'fixed') {\n x = visualViewport.offsetLeft;\n y = visualViewport.offsetTop;\n }\n }\n\n return {\n width: width,\n height: height,\n x: x + getWindowScrollBarX(element),\n y: y\n };\n}","import getDocumentElement from \"./getDocumentElement.js\";\nimport getComputedStyle from \"./getComputedStyle.js\";\nimport getWindowScrollBarX from \"./getWindowScrollBarX.js\";\nimport getWindowScroll from \"./getWindowScroll.js\";\nimport { max } from \"../utils/math.js\"; // Gets the entire size of the scrollable document area, even extending outside\n// of the `` and `` rect bounds if horizontally scrollable\n\nexport default function getDocumentRect(element) {\n var _element$ownerDocumen;\n\n var html = getDocumentElement(element);\n var winScroll = getWindowScroll(element);\n var body = (_element$ownerDocumen = element.ownerDocument) == null ? void 0 : _element$ownerDocumen.body;\n var width = max(html.scrollWidth, html.clientWidth, body ? body.scrollWidth : 0, body ? body.clientWidth : 0);\n var height = max(html.scrollHeight, html.clientHeight, body ? body.scrollHeight : 0, body ? body.clientHeight : 0);\n var x = -winScroll.scrollLeft + getWindowScrollBarX(element);\n var y = -winScroll.scrollTop;\n\n if (getComputedStyle(body || html).direction === 'rtl') {\n x += max(html.clientWidth, body ? body.clientWidth : 0) - width;\n }\n\n return {\n width: width,\n height: height,\n x: x,\n y: y\n };\n}","import getBasePlacement from \"./getBasePlacement.js\";\nimport getVariation from \"./getVariation.js\";\nimport getMainAxisFromPlacement from \"./getMainAxisFromPlacement.js\";\nimport { top, right, bottom, left, start, end } from \"../enums.js\";\nexport default function computeOffsets(_ref) {\n var reference = _ref.reference,\n element = _ref.element,\n placement = _ref.placement;\n var basePlacement = placement ? getBasePlacement(placement) : null;\n var variation = placement ? getVariation(placement) : null;\n var commonX = reference.x + reference.width / 2 - element.width / 2;\n var commonY = reference.y + reference.height / 2 - element.height / 2;\n var offsets;\n\n switch (basePlacement) {\n case top:\n offsets = {\n x: commonX,\n y: reference.y - element.height\n };\n break;\n\n case bottom:\n offsets = {\n x: commonX,\n y: reference.y + reference.height\n };\n break;\n\n case right:\n offsets = {\n x: reference.x + reference.width,\n y: commonY\n };\n break;\n\n case left:\n offsets = {\n x: reference.x - element.width,\n y: commonY\n };\n break;\n\n default:\n offsets = {\n x: reference.x,\n y: reference.y\n };\n }\n\n var mainAxis = basePlacement ? getMainAxisFromPlacement(basePlacement) : null;\n\n if (mainAxis != null) {\n var len = mainAxis === 'y' ? 'height' : 'width';\n\n switch (variation) {\n case start:\n offsets[mainAxis] = offsets[mainAxis] - (reference[len] / 2 - element[len] / 2);\n break;\n\n case end:\n offsets[mainAxis] = offsets[mainAxis] + (reference[len] / 2 - element[len] / 2);\n break;\n\n default:\n }\n }\n\n return offsets;\n}","import getClippingRect from \"../dom-utils/getClippingRect.js\";\nimport getDocumentElement from \"../dom-utils/getDocumentElement.js\";\nimport getBoundingClientRect from \"../dom-utils/getBoundingClientRect.js\";\nimport computeOffsets from \"./computeOffsets.js\";\nimport rectToClientRect from \"./rectToClientRect.js\";\nimport { clippingParents, reference, popper, bottom, top, right, basePlacements, viewport } from \"../enums.js\";\nimport { isElement } from \"../dom-utils/instanceOf.js\";\nimport mergePaddingObject from \"./mergePaddingObject.js\";\nimport expandToHashMap from \"./expandToHashMap.js\"; // eslint-disable-next-line import/no-unused-modules\n\nexport default function detectOverflow(state, options) {\n if (options === void 0) {\n options = {};\n }\n\n var _options = options,\n _options$placement = _options.placement,\n placement = _options$placement === void 0 ? state.placement : _options$placement,\n _options$strategy = _options.strategy,\n strategy = _options$strategy === void 0 ? state.strategy : _options$strategy,\n _options$boundary = _options.boundary,\n boundary = _options$boundary === void 0 ? clippingParents : _options$boundary,\n _options$rootBoundary = _options.rootBoundary,\n rootBoundary = _options$rootBoundary === void 0 ? viewport : _options$rootBoundary,\n _options$elementConte = _options.elementContext,\n elementContext = _options$elementConte === void 0 ? popper : _options$elementConte,\n _options$altBoundary = _options.altBoundary,\n altBoundary = _options$altBoundary === void 0 ? false : _options$altBoundary,\n _options$padding = _options.padding,\n padding = _options$padding === void 0 ? 0 : _options$padding;\n var paddingObject = mergePaddingObject(typeof padding !== 'number' ? padding : expandToHashMap(padding, basePlacements));\n var altContext = elementContext === popper ? reference : popper;\n var popperRect = state.rects.popper;\n var element = state.elements[altBoundary ? altContext : elementContext];\n var clippingClientRect = getClippingRect(isElement(element) ? element : element.contextElement || getDocumentElement(state.elements.popper), boundary, rootBoundary, strategy);\n var referenceClientRect = getBoundingClientRect(state.elements.reference);\n var popperOffsets = computeOffsets({\n reference: referenceClientRect,\n element: popperRect,\n strategy: 'absolute',\n placement: placement\n });\n var popperClientRect = rectToClientRect(Object.assign({}, popperRect, popperOffsets));\n var elementClientRect = elementContext === popper ? popperClientRect : referenceClientRect; // positive = overflowing the clipping rect\n // 0 or negative = within the clipping rect\n\n var overflowOffsets = {\n top: clippingClientRect.top - elementClientRect.top + paddingObject.top,\n bottom: elementClientRect.bottom - clippingClientRect.bottom + paddingObject.bottom,\n left: clippingClientRect.left - elementClientRect.left + paddingObject.left,\n right: elementClientRect.right - clippingClientRect.right + paddingObject.right\n };\n var offsetData = state.modifiersData.offset; // Offsets can be applied only to the popper element\n\n if (elementContext === popper && offsetData) {\n var offset = offsetData[placement];\n Object.keys(overflowOffsets).forEach(function (key) {\n var multiply = [right, bottom].indexOf(key) >= 0 ? 1 : -1;\n var axis = [top, bottom].indexOf(key) >= 0 ? 'y' : 'x';\n overflowOffsets[key] += offset[axis] * multiply;\n });\n }\n\n return overflowOffsets;\n}","import getOppositePlacement from \"../utils/getOppositePlacement.js\";\nimport getBasePlacement from \"../utils/getBasePlacement.js\";\nimport getOppositeVariationPlacement from \"../utils/getOppositeVariationPlacement.js\";\nimport detectOverflow from \"../utils/detectOverflow.js\";\nimport computeAutoPlacement from \"../utils/computeAutoPlacement.js\";\nimport { bottom, top, start, right, left, auto } from \"../enums.js\";\nimport getVariation from \"../utils/getVariation.js\"; // eslint-disable-next-line import/no-unused-modules\n\nfunction getExpandedFallbackPlacements(placement) {\n if (getBasePlacement(placement) === auto) {\n return [];\n }\n\n var oppositePlacement = getOppositePlacement(placement);\n return [getOppositeVariationPlacement(placement), oppositePlacement, getOppositeVariationPlacement(oppositePlacement)];\n}\n\nfunction flip(_ref) {\n var state = _ref.state,\n options = _ref.options,\n name = _ref.name;\n\n if (state.modifiersData[name]._skip) {\n return;\n }\n\n var _options$mainAxis = options.mainAxis,\n checkMainAxis = _options$mainAxis === void 0 ? true : _options$mainAxis,\n _options$altAxis = options.altAxis,\n checkAltAxis = _options$altAxis === void 0 ? true : _options$altAxis,\n specifiedFallbackPlacements = options.fallbackPlacements,\n padding = options.padding,\n boundary = options.boundary,\n rootBoundary = options.rootBoundary,\n altBoundary = options.altBoundary,\n _options$flipVariatio = options.flipVariations,\n flipVariations = _options$flipVariatio === void 0 ? true : _options$flipVariatio,\n allowedAutoPlacements = options.allowedAutoPlacements;\n var preferredPlacement = state.options.placement;\n var basePlacement = getBasePlacement(preferredPlacement);\n var isBasePlacement = basePlacement === preferredPlacement;\n var fallbackPlacements = specifiedFallbackPlacements || (isBasePlacement || !flipVariations ? [getOppositePlacement(preferredPlacement)] : getExpandedFallbackPlacements(preferredPlacement));\n var placements = [preferredPlacement].concat(fallbackPlacements).reduce(function (acc, placement) {\n return acc.concat(getBasePlacement(placement) === auto ? computeAutoPlacement(state, {\n placement: placement,\n boundary: boundary,\n rootBoundary: rootBoundary,\n padding: padding,\n flipVariations: flipVariations,\n allowedAutoPlacements: allowedAutoPlacements\n }) : placement);\n }, []);\n var referenceRect = state.rects.reference;\n var popperRect = state.rects.popper;\n var checksMap = new Map();\n var makeFallbackChecks = true;\n var firstFittingPlacement = placements[0];\n\n for (var i = 0; i < placements.length; i++) {\n var placement = placements[i];\n\n var _basePlacement = getBasePlacement(placement);\n\n var isStartVariation = getVariation(placement) === start;\n var isVertical = [top, bottom].indexOf(_basePlacement) >= 0;\n var len = isVertical ? 'width' : 'height';\n var overflow = detectOverflow(state, {\n placement: placement,\n boundary: boundary,\n rootBoundary: rootBoundary,\n altBoundary: altBoundary,\n padding: padding\n });\n var mainVariationSide = isVertical ? isStartVariation ? right : left : isStartVariation ? bottom : top;\n\n if (referenceRect[len] > popperRect[len]) {\n mainVariationSide = getOppositePlacement(mainVariationSide);\n }\n\n var altVariationSide = getOppositePlacement(mainVariationSide);\n var checks = [];\n\n if (checkMainAxis) {\n checks.push(overflow[_basePlacement] <= 0);\n }\n\n if (checkAltAxis) {\n checks.push(overflow[mainVariationSide] <= 0, overflow[altVariationSide] <= 0);\n }\n\n if (checks.every(function (check) {\n return check;\n })) {\n firstFittingPlacement = placement;\n makeFallbackChecks = false;\n break;\n }\n\n checksMap.set(placement, checks);\n }\n\n if (makeFallbackChecks) {\n // `2` may be desired in some cases – research later\n var numberOfChecks = flipVariations ? 3 : 1;\n\n var _loop = function _loop(_i) {\n var fittingPlacement = placements.find(function (placement) {\n var checks = checksMap.get(placement);\n\n if (checks) {\n return checks.slice(0, _i).every(function (check) {\n return check;\n });\n }\n });\n\n if (fittingPlacement) {\n firstFittingPlacement = fittingPlacement;\n return \"break\";\n }\n };\n\n for (var _i = numberOfChecks; _i > 0; _i--) {\n var _ret = _loop(_i);\n\n if (_ret === \"break\") break;\n }\n }\n\n if (state.placement !== firstFittingPlacement) {\n state.modifiersData[name]._skip = true;\n state.placement = firstFittingPlacement;\n state.reset = true;\n }\n} // eslint-disable-next-line import/no-unused-modules\n\n\nexport default {\n name: 'flip',\n enabled: true,\n phase: 'main',\n fn: flip,\n requiresIfExists: ['offset'],\n data: {\n _skip: false\n }\n};","import getVariation from \"./getVariation.js\";\nimport { variationPlacements, basePlacements, placements as allPlacements } from \"../enums.js\";\nimport detectOverflow from \"./detectOverflow.js\";\nimport getBasePlacement from \"./getBasePlacement.js\";\nexport default function computeAutoPlacement(state, options) {\n if (options === void 0) {\n options = {};\n }\n\n var _options = options,\n placement = _options.placement,\n boundary = _options.boundary,\n rootBoundary = _options.rootBoundary,\n padding = _options.padding,\n flipVariations = _options.flipVariations,\n _options$allowedAutoP = _options.allowedAutoPlacements,\n allowedAutoPlacements = _options$allowedAutoP === void 0 ? allPlacements : _options$allowedAutoP;\n var variation = getVariation(placement);\n var placements = variation ? flipVariations ? variationPlacements : variationPlacements.filter(function (placement) {\n return getVariation(placement) === variation;\n }) : basePlacements;\n var allowedPlacements = placements.filter(function (placement) {\n return allowedAutoPlacements.indexOf(placement) >= 0;\n });\n\n if (allowedPlacements.length === 0) {\n allowedPlacements = placements;\n } // $FlowFixMe[incompatible-type]: Flow seems to have problems with two array unions...\n\n\n var overflows = allowedPlacements.reduce(function (acc, placement) {\n acc[placement] = detectOverflow(state, {\n placement: placement,\n boundary: boundary,\n rootBoundary: rootBoundary,\n padding: padding\n })[getBasePlacement(placement)];\n return acc;\n }, {});\n return Object.keys(overflows).sort(function (a, b) {\n return overflows[a] - overflows[b];\n });\n}","import { top, bottom, left, right } from \"../enums.js\";\nimport detectOverflow from \"../utils/detectOverflow.js\";\n\nfunction getSideOffsets(overflow, rect, preventedOffsets) {\n if (preventedOffsets === void 0) {\n preventedOffsets = {\n x: 0,\n y: 0\n };\n }\n\n return {\n top: overflow.top - rect.height - preventedOffsets.y,\n right: overflow.right - rect.width + preventedOffsets.x,\n bottom: overflow.bottom - rect.height + preventedOffsets.y,\n left: overflow.left - rect.width - preventedOffsets.x\n };\n}\n\nfunction isAnySideFullyClipped(overflow) {\n return [top, right, bottom, left].some(function (side) {\n return overflow[side] >= 0;\n });\n}\n\nfunction hide(_ref) {\n var state = _ref.state,\n name = _ref.name;\n var referenceRect = state.rects.reference;\n var popperRect = state.rects.popper;\n var preventedOffsets = state.modifiersData.preventOverflow;\n var referenceOverflow = detectOverflow(state, {\n elementContext: 'reference'\n });\n var popperAltOverflow = detectOverflow(state, {\n altBoundary: true\n });\n var referenceClippingOffsets = getSideOffsets(referenceOverflow, referenceRect);\n var popperEscapeOffsets = getSideOffsets(popperAltOverflow, popperRect, preventedOffsets);\n var isReferenceHidden = isAnySideFullyClipped(referenceClippingOffsets);\n var hasPopperEscaped = isAnySideFullyClipped(popperEscapeOffsets);\n state.modifiersData[name] = {\n referenceClippingOffsets: referenceClippingOffsets,\n popperEscapeOffsets: popperEscapeOffsets,\n isReferenceHidden: isReferenceHidden,\n hasPopperEscaped: hasPopperEscaped\n };\n state.attributes.popper = Object.assign({}, state.attributes.popper, {\n 'data-popper-reference-hidden': isReferenceHidden,\n 'data-popper-escaped': hasPopperEscaped\n });\n} // eslint-disable-next-line import/no-unused-modules\n\n\nexport default {\n name: 'hide',\n enabled: true,\n phase: 'main',\n requiresIfExists: ['preventOverflow'],\n fn: hide\n};","import getBasePlacement from \"../utils/getBasePlacement.js\";\nimport { top, left, right, placements } from \"../enums.js\"; // eslint-disable-next-line import/no-unused-modules\n\nexport function distanceAndSkiddingToXY(placement, rects, offset) {\n var basePlacement = getBasePlacement(placement);\n var invertDistance = [left, top].indexOf(basePlacement) >= 0 ? -1 : 1;\n\n var _ref = typeof offset === 'function' ? offset(Object.assign({}, rects, {\n placement: placement\n })) : offset,\n skidding = _ref[0],\n distance = _ref[1];\n\n skidding = skidding || 0;\n distance = (distance || 0) * invertDistance;\n return [left, right].indexOf(basePlacement) >= 0 ? {\n x: distance,\n y: skidding\n } : {\n x: skidding,\n y: distance\n };\n}\n\nfunction offset(_ref2) {\n var state = _ref2.state,\n options = _ref2.options,\n name = _ref2.name;\n var _options$offset = options.offset,\n offset = _options$offset === void 0 ? [0, 0] : _options$offset;\n var data = placements.reduce(function (acc, placement) {\n acc[placement] = distanceAndSkiddingToXY(placement, state.rects, offset);\n return acc;\n }, {});\n var _data$state$placement = data[state.placement],\n x = _data$state$placement.x,\n y = _data$state$placement.y;\n\n if (state.modifiersData.popperOffsets != null) {\n state.modifiersData.popperOffsets.x += x;\n state.modifiersData.popperOffsets.y += y;\n }\n\n state.modifiersData[name] = data;\n} // eslint-disable-next-line import/no-unused-modules\n\n\nexport default {\n name: 'offset',\n enabled: true,\n phase: 'main',\n requires: ['popperOffsets'],\n fn: offset\n};","import computeOffsets from \"../utils/computeOffsets.js\";\n\nfunction popperOffsets(_ref) {\n var state = _ref.state,\n name = _ref.name;\n // Offsets are the actual position the popper needs to have to be\n // properly positioned near its reference element\n // This is the most basic placement, and will be adjusted by\n // the modifiers in the next step\n state.modifiersData[name] = computeOffsets({\n reference: state.rects.reference,\n element: state.rects.popper,\n strategy: 'absolute',\n placement: state.placement\n });\n} // eslint-disable-next-line import/no-unused-modules\n\n\nexport default {\n name: 'popperOffsets',\n enabled: true,\n phase: 'read',\n fn: popperOffsets,\n data: {}\n};","import { top, left, right, bottom, start } from \"../enums.js\";\nimport getBasePlacement from \"../utils/getBasePlacement.js\";\nimport getMainAxisFromPlacement from \"../utils/getMainAxisFromPlacement.js\";\nimport getAltAxis from \"../utils/getAltAxis.js\";\nimport { within, withinMaxClamp } from \"../utils/within.js\";\nimport getLayoutRect from \"../dom-utils/getLayoutRect.js\";\nimport getOffsetParent from \"../dom-utils/getOffsetParent.js\";\nimport detectOverflow from \"../utils/detectOverflow.js\";\nimport getVariation from \"../utils/getVariation.js\";\nimport getFreshSideObject from \"../utils/getFreshSideObject.js\";\nimport { min as mathMin, max as mathMax } from \"../utils/math.js\";\n\nfunction preventOverflow(_ref) {\n var state = _ref.state,\n options = _ref.options,\n name = _ref.name;\n var _options$mainAxis = options.mainAxis,\n checkMainAxis = _options$mainAxis === void 0 ? true : _options$mainAxis,\n _options$altAxis = options.altAxis,\n checkAltAxis = _options$altAxis === void 0 ? false : _options$altAxis,\n boundary = options.boundary,\n rootBoundary = options.rootBoundary,\n altBoundary = options.altBoundary,\n padding = options.padding,\n _options$tether = options.tether,\n tether = _options$tether === void 0 ? true : _options$tether,\n _options$tetherOffset = options.tetherOffset,\n tetherOffset = _options$tetherOffset === void 0 ? 0 : _options$tetherOffset;\n var overflow = detectOverflow(state, {\n boundary: boundary,\n rootBoundary: rootBoundary,\n padding: padding,\n altBoundary: altBoundary\n });\n var basePlacement = getBasePlacement(state.placement);\n var variation = getVariation(state.placement);\n var isBasePlacement = !variation;\n var mainAxis = getMainAxisFromPlacement(basePlacement);\n var altAxis = getAltAxis(mainAxis);\n var popperOffsets = state.modifiersData.popperOffsets;\n var referenceRect = state.rects.reference;\n var popperRect = state.rects.popper;\n var tetherOffsetValue = typeof tetherOffset === 'function' ? tetherOffset(Object.assign({}, state.rects, {\n placement: state.placement\n })) : tetherOffset;\n var normalizedTetherOffsetValue = typeof tetherOffsetValue === 'number' ? {\n mainAxis: tetherOffsetValue,\n altAxis: tetherOffsetValue\n } : Object.assign({\n mainAxis: 0,\n altAxis: 0\n }, tetherOffsetValue);\n var offsetModifierState = state.modifiersData.offset ? state.modifiersData.offset[state.placement] : null;\n var data = {\n x: 0,\n y: 0\n };\n\n if (!popperOffsets) {\n return;\n }\n\n if (checkMainAxis) {\n var _offsetModifierState$;\n\n var mainSide = mainAxis === 'y' ? top : left;\n var altSide = mainAxis === 'y' ? bottom : right;\n var len = mainAxis === 'y' ? 'height' : 'width';\n var offset = popperOffsets[mainAxis];\n var min = offset + overflow[mainSide];\n var max = offset - overflow[altSide];\n var additive = tether ? -popperRect[len] / 2 : 0;\n var minLen = variation === start ? referenceRect[len] : popperRect[len];\n var maxLen = variation === start ? -popperRect[len] : -referenceRect[len]; // We need to include the arrow in the calculation so the arrow doesn't go\n // outside the reference bounds\n\n var arrowElement = state.elements.arrow;\n var arrowRect = tether && arrowElement ? getLayoutRect(arrowElement) : {\n width: 0,\n height: 0\n };\n var arrowPaddingObject = state.modifiersData['arrow#persistent'] ? state.modifiersData['arrow#persistent'].padding : getFreshSideObject();\n var arrowPaddingMin = arrowPaddingObject[mainSide];\n var arrowPaddingMax = arrowPaddingObject[altSide]; // If the reference length is smaller than the arrow length, we don't want\n // to include its full size in the calculation. If the reference is small\n // and near the edge of a boundary, the popper can overflow even if the\n // reference is not overflowing as well (e.g. virtual elements with no\n // width or height)\n\n var arrowLen = within(0, referenceRect[len], arrowRect[len]);\n var minOffset = isBasePlacement ? referenceRect[len] / 2 - additive - arrowLen - arrowPaddingMin - normalizedTetherOffsetValue.mainAxis : minLen - arrowLen - arrowPaddingMin - normalizedTetherOffsetValue.mainAxis;\n var maxOffset = isBasePlacement ? -referenceRect[len] / 2 + additive + arrowLen + arrowPaddingMax + normalizedTetherOffsetValue.mainAxis : maxLen + arrowLen + arrowPaddingMax + normalizedTetherOffsetValue.mainAxis;\n var arrowOffsetParent = state.elements.arrow && getOffsetParent(state.elements.arrow);\n var clientOffset = arrowOffsetParent ? mainAxis === 'y' ? arrowOffsetParent.clientTop || 0 : arrowOffsetParent.clientLeft || 0 : 0;\n var offsetModifierValue = (_offsetModifierState$ = offsetModifierState == null ? void 0 : offsetModifierState[mainAxis]) != null ? _offsetModifierState$ : 0;\n var tetherMin = offset + minOffset - offsetModifierValue - clientOffset;\n var tetherMax = offset + maxOffset - offsetModifierValue;\n var preventedOffset = within(tether ? mathMin(min, tetherMin) : min, offset, tether ? mathMax(max, tetherMax) : max);\n popperOffsets[mainAxis] = preventedOffset;\n data[mainAxis] = preventedOffset - offset;\n }\n\n if (checkAltAxis) {\n var _offsetModifierState$2;\n\n var _mainSide = mainAxis === 'x' ? top : left;\n\n var _altSide = mainAxis === 'x' ? bottom : right;\n\n var _offset = popperOffsets[altAxis];\n\n var _len = altAxis === 'y' ? 'height' : 'width';\n\n var _min = _offset + overflow[_mainSide];\n\n var _max = _offset - overflow[_altSide];\n\n var isOriginSide = [top, left].indexOf(basePlacement) !== -1;\n\n var _offsetModifierValue = (_offsetModifierState$2 = offsetModifierState == null ? void 0 : offsetModifierState[altAxis]) != null ? _offsetModifierState$2 : 0;\n\n var _tetherMin = isOriginSide ? _min : _offset - referenceRect[_len] - popperRect[_len] - _offsetModifierValue + normalizedTetherOffsetValue.altAxis;\n\n var _tetherMax = isOriginSide ? _offset + referenceRect[_len] + popperRect[_len] - _offsetModifierValue - normalizedTetherOffsetValue.altAxis : _max;\n\n var _preventedOffset = tether && isOriginSide ? withinMaxClamp(_tetherMin, _offset, _tetherMax) : within(tether ? _tetherMin : _min, _offset, tether ? _tetherMax : _max);\n\n popperOffsets[altAxis] = _preventedOffset;\n data[altAxis] = _preventedOffset - _offset;\n }\n\n state.modifiersData[name] = data;\n} // eslint-disable-next-line import/no-unused-modules\n\n\nexport default {\n name: 'preventOverflow',\n enabled: true,\n phase: 'main',\n fn: preventOverflow,\n requiresIfExists: ['offset']\n};","export default function getAltAxis(axis) {\n return axis === 'x' ? 'y' : 'x';\n}","import getBoundingClientRect from \"./getBoundingClientRect.js\";\nimport getNodeScroll from \"./getNodeScroll.js\";\nimport getNodeName from \"./getNodeName.js\";\nimport { isHTMLElement } from \"./instanceOf.js\";\nimport getWindowScrollBarX from \"./getWindowScrollBarX.js\";\nimport getDocumentElement from \"./getDocumentElement.js\";\nimport isScrollParent from \"./isScrollParent.js\";\nimport { round } from \"../utils/math.js\";\n\nfunction isElementScaled(element) {\n var rect = element.getBoundingClientRect();\n var scaleX = round(rect.width) / element.offsetWidth || 1;\n var scaleY = round(rect.height) / element.offsetHeight || 1;\n return scaleX !== 1 || scaleY !== 1;\n} // Returns the composite rect of an element relative to its offsetParent.\n// Composite means it takes into account transforms as well as layout.\n\n\nexport default function getCompositeRect(elementOrVirtualElement, offsetParent, isFixed) {\n if (isFixed === void 0) {\n isFixed = false;\n }\n\n var isOffsetParentAnElement = isHTMLElement(offsetParent);\n var offsetParentIsScaled = isHTMLElement(offsetParent) && isElementScaled(offsetParent);\n var documentElement = getDocumentElement(offsetParent);\n var rect = getBoundingClientRect(elementOrVirtualElement, offsetParentIsScaled, isFixed);\n var scroll = {\n scrollLeft: 0,\n scrollTop: 0\n };\n var offsets = {\n x: 0,\n y: 0\n };\n\n if (isOffsetParentAnElement || !isOffsetParentAnElement && !isFixed) {\n if (getNodeName(offsetParent) !== 'body' || // https://github.com/popperjs/popper-core/issues/1078\n isScrollParent(documentElement)) {\n scroll = getNodeScroll(offsetParent);\n }\n\n if (isHTMLElement(offsetParent)) {\n offsets = getBoundingClientRect(offsetParent, true);\n offsets.x += offsetParent.clientLeft;\n offsets.y += offsetParent.clientTop;\n } else if (documentElement) {\n offsets.x = getWindowScrollBarX(documentElement);\n }\n }\n\n return {\n x: rect.left + scroll.scrollLeft - offsets.x,\n y: rect.top + scroll.scrollTop - offsets.y,\n width: rect.width,\n height: rect.height\n };\n}","import getWindowScroll from \"./getWindowScroll.js\";\nimport getWindow from \"./getWindow.js\";\nimport { isHTMLElement } from \"./instanceOf.js\";\nimport getHTMLElementScroll from \"./getHTMLElementScroll.js\";\nexport default function getNodeScroll(node) {\n if (node === getWindow(node) || !isHTMLElement(node)) {\n return getWindowScroll(node);\n } else {\n return getHTMLElementScroll(node);\n }\n}","export default function getHTMLElementScroll(element) {\n return {\n scrollLeft: element.scrollLeft,\n scrollTop: element.scrollTop\n };\n}","import { modifierPhases } from \"../enums.js\"; // source: https://stackoverflow.com/questions/49875255\n\nfunction order(modifiers) {\n var map = new Map();\n var visited = new Set();\n var result = [];\n modifiers.forEach(function (modifier) {\n map.set(modifier.name, modifier);\n }); // On visiting object, check for its dependencies and visit them recursively\n\n function sort(modifier) {\n visited.add(modifier.name);\n var requires = [].concat(modifier.requires || [], modifier.requiresIfExists || []);\n requires.forEach(function (dep) {\n if (!visited.has(dep)) {\n var depModifier = map.get(dep);\n\n if (depModifier) {\n sort(depModifier);\n }\n }\n });\n result.push(modifier);\n }\n\n modifiers.forEach(function (modifier) {\n if (!visited.has(modifier.name)) {\n // check for visited object\n sort(modifier);\n }\n });\n return result;\n}\n\nexport default function orderModifiers(modifiers) {\n // order based on dependencies\n var orderedModifiers = order(modifiers); // order based on phase\n\n return modifierPhases.reduce(function (acc, phase) {\n return acc.concat(orderedModifiers.filter(function (modifier) {\n return modifier.phase === phase;\n }));\n }, []);\n}","import getCompositeRect from \"./dom-utils/getCompositeRect.js\";\nimport getLayoutRect from \"./dom-utils/getLayoutRect.js\";\nimport listScrollParents from \"./dom-utils/listScrollParents.js\";\nimport getOffsetParent from \"./dom-utils/getOffsetParent.js\";\nimport orderModifiers from \"./utils/orderModifiers.js\";\nimport debounce from \"./utils/debounce.js\";\nimport mergeByName from \"./utils/mergeByName.js\";\nimport detectOverflow from \"./utils/detectOverflow.js\";\nimport { isElement } from \"./dom-utils/instanceOf.js\";\nvar DEFAULT_OPTIONS = {\n placement: 'bottom',\n modifiers: [],\n strategy: 'absolute'\n};\n\nfunction areValidElements() {\n for (var _len = arguments.length, args = new Array(_len), _key = 0; _key < _len; _key++) {\n args[_key] = arguments[_key];\n }\n\n return !args.some(function (element) {\n return !(element && typeof element.getBoundingClientRect === 'function');\n });\n}\n\nexport function popperGenerator(generatorOptions) {\n if (generatorOptions === void 0) {\n generatorOptions = {};\n }\n\n var _generatorOptions = generatorOptions,\n _generatorOptions$def = _generatorOptions.defaultModifiers,\n defaultModifiers = _generatorOptions$def === void 0 ? [] : _generatorOptions$def,\n _generatorOptions$def2 = _generatorOptions.defaultOptions,\n defaultOptions = _generatorOptions$def2 === void 0 ? DEFAULT_OPTIONS : _generatorOptions$def2;\n return function createPopper(reference, popper, options) {\n if (options === void 0) {\n options = defaultOptions;\n }\n\n var state = {\n placement: 'bottom',\n orderedModifiers: [],\n options: Object.assign({}, DEFAULT_OPTIONS, defaultOptions),\n modifiersData: {},\n elements: {\n reference: reference,\n popper: popper\n },\n attributes: {},\n styles: {}\n };\n var effectCleanupFns = [];\n var isDestroyed = false;\n var instance = {\n state: state,\n setOptions: function setOptions(setOptionsAction) {\n var options = typeof setOptionsAction === 'function' ? setOptionsAction(state.options) : setOptionsAction;\n cleanupModifierEffects();\n state.options = Object.assign({}, defaultOptions, state.options, options);\n state.scrollParents = {\n reference: isElement(reference) ? listScrollParents(reference) : reference.contextElement ? listScrollParents(reference.contextElement) : [],\n popper: listScrollParents(popper)\n }; // Orders the modifiers based on their dependencies and `phase`\n // properties\n\n var orderedModifiers = orderModifiers(mergeByName([].concat(defaultModifiers, state.options.modifiers))); // Strip out disabled modifiers\n\n state.orderedModifiers = orderedModifiers.filter(function (m) {\n return m.enabled;\n });\n runModifierEffects();\n return instance.update();\n },\n // Sync update – it will always be executed, even if not necessary. This\n // is useful for low frequency updates where sync behavior simplifies the\n // logic.\n // For high frequency updates (e.g. `resize` and `scroll` events), always\n // prefer the async Popper#update method\n forceUpdate: function forceUpdate() {\n if (isDestroyed) {\n return;\n }\n\n var _state$elements = state.elements,\n reference = _state$elements.reference,\n popper = _state$elements.popper; // Don't proceed if `reference` or `popper` are not valid elements\n // anymore\n\n if (!areValidElements(reference, popper)) {\n return;\n } // Store the reference and popper rects to be read by modifiers\n\n\n state.rects = {\n reference: getCompositeRect(reference, getOffsetParent(popper), state.options.strategy === 'fixed'),\n popper: getLayoutRect(popper)\n }; // Modifiers have the ability to reset the current update cycle. The\n // most common use case for this is the `flip` modifier changing the\n // placement, which then needs to re-run all the modifiers, because the\n // logic was previously ran for the previous placement and is therefore\n // stale/incorrect\n\n state.reset = false;\n state.placement = state.options.placement; // On each update cycle, the `modifiersData` property for each modifier\n // is filled with the initial data specified by the modifier. This means\n // it doesn't persist and is fresh on each update.\n // To ensure persistent data, use `${name}#persistent`\n\n state.orderedModifiers.forEach(function (modifier) {\n return state.modifiersData[modifier.name] = Object.assign({}, modifier.data);\n });\n\n for (var index = 0; index < state.orderedModifiers.length; index++) {\n if (state.reset === true) {\n state.reset = false;\n index = -1;\n continue;\n }\n\n var _state$orderedModifie = state.orderedModifiers[index],\n fn = _state$orderedModifie.fn,\n _state$orderedModifie2 = _state$orderedModifie.options,\n _options = _state$orderedModifie2 === void 0 ? {} : _state$orderedModifie2,\n name = _state$orderedModifie.name;\n\n if (typeof fn === 'function') {\n state = fn({\n state: state,\n options: _options,\n name: name,\n instance: instance\n }) || state;\n }\n }\n },\n // Async and optimistically optimized update – it will not be executed if\n // not necessary (debounced to run at most once-per-tick)\n update: debounce(function () {\n return new Promise(function (resolve) {\n instance.forceUpdate();\n resolve(state);\n });\n }),\n destroy: function destroy() {\n cleanupModifierEffects();\n isDestroyed = true;\n }\n };\n\n if (!areValidElements(reference, popper)) {\n return instance;\n }\n\n instance.setOptions(options).then(function (state) {\n if (!isDestroyed && options.onFirstUpdate) {\n options.onFirstUpdate(state);\n }\n }); // Modifiers have the ability to execute arbitrary code before the first\n // update cycle runs. They will be executed in the same order as the update\n // cycle. This is useful when a modifier adds some persistent data that\n // other modifiers need to use, but the modifier is run after the dependent\n // one.\n\n function runModifierEffects() {\n state.orderedModifiers.forEach(function (_ref) {\n var name = _ref.name,\n _ref$options = _ref.options,\n options = _ref$options === void 0 ? {} : _ref$options,\n effect = _ref.effect;\n\n if (typeof effect === 'function') {\n var cleanupFn = effect({\n state: state,\n name: name,\n instance: instance,\n options: options\n });\n\n var noopFn = function noopFn() {};\n\n effectCleanupFns.push(cleanupFn || noopFn);\n }\n });\n }\n\n function cleanupModifierEffects() {\n effectCleanupFns.forEach(function (fn) {\n return fn();\n });\n effectCleanupFns = [];\n }\n\n return instance;\n };\n}\nexport var createPopper = /*#__PURE__*/popperGenerator(); // eslint-disable-next-line import/no-unused-modules\n\nexport { detectOverflow };","export default function debounce(fn) {\n var pending;\n return function () {\n if (!pending) {\n pending = new Promise(function (resolve) {\n Promise.resolve().then(function () {\n pending = undefined;\n resolve(fn());\n });\n });\n }\n\n return pending;\n };\n}","export default function mergeByName(modifiers) {\n var merged = modifiers.reduce(function (merged, current) {\n var existing = merged[current.name];\n merged[current.name] = existing ? Object.assign({}, existing, current, {\n options: Object.assign({}, existing.options, current.options),\n data: Object.assign({}, existing.data, current.data)\n }) : current;\n return merged;\n }, {}); // IE11 does not support Object.values\n\n return Object.keys(merged).map(function (key) {\n return merged[key];\n });\n}","import { popperGenerator, detectOverflow } from \"./createPopper.js\";\nimport eventListeners from \"./modifiers/eventListeners.js\";\nimport popperOffsets from \"./modifiers/popperOffsets.js\";\nimport computeStyles from \"./modifiers/computeStyles.js\";\nimport applyStyles from \"./modifiers/applyStyles.js\";\nimport offset from \"./modifiers/offset.js\";\nimport flip from \"./modifiers/flip.js\";\nimport preventOverflow from \"./modifiers/preventOverflow.js\";\nimport arrow from \"./modifiers/arrow.js\";\nimport hide from \"./modifiers/hide.js\";\nvar defaultModifiers = [eventListeners, popperOffsets, computeStyles, applyStyles, offset, flip, preventOverflow, arrow, hide];\nvar createPopper = /*#__PURE__*/popperGenerator({\n defaultModifiers: defaultModifiers\n}); // eslint-disable-next-line import/no-unused-modules\n\nexport { createPopper, popperGenerator, defaultModifiers, detectOverflow }; // eslint-disable-next-line import/no-unused-modules\n\nexport { createPopper as createPopperLite } from \"./popper-lite.js\"; // eslint-disable-next-line import/no-unused-modules\n\nexport * from \"./modifiers/index.js\";","import { popperGenerator, detectOverflow } from \"./createPopper.js\";\nimport eventListeners from \"./modifiers/eventListeners.js\";\nimport popperOffsets from \"./modifiers/popperOffsets.js\";\nimport computeStyles from \"./modifiers/computeStyles.js\";\nimport applyStyles from \"./modifiers/applyStyles.js\";\nvar defaultModifiers = [eventListeners, popperOffsets, computeStyles, applyStyles];\nvar createPopper = /*#__PURE__*/popperGenerator({\n defaultModifiers: defaultModifiers\n}); // eslint-disable-next-line import/no-unused-modules\n\nexport { createPopper, popperGenerator, defaultModifiers, detectOverflow };","/*!\n * Bootstrap v5.3.2 (https://getbootstrap.com/)\n * Copyright 2011-2023 The Bootstrap Authors (https://github.com/twbs/bootstrap/graphs/contributors)\n * Licensed under MIT (https://github.com/twbs/bootstrap/blob/main/LICENSE)\n */\nimport * as Popper from '@popperjs/core';\n\n/**\n * --------------------------------------------------------------------------\n * Bootstrap dom/data.js\n * Licensed under MIT (https://github.com/twbs/bootstrap/blob/main/LICENSE)\n * --------------------------------------------------------------------------\n */\n\n/**\n * Constants\n */\n\nconst elementMap = new Map();\nconst Data = {\n set(element, key, instance) {\n if (!elementMap.has(element)) {\n elementMap.set(element, new Map());\n }\n const instanceMap = elementMap.get(element);\n\n // make it clear we only want one instance per element\n // can be removed later when multiple key/instances are fine to be used\n if (!instanceMap.has(key) && instanceMap.size !== 0) {\n // eslint-disable-next-line no-console\n console.error(`Bootstrap doesn't allow more than one instance per element. Bound instance: ${Array.from(instanceMap.keys())[0]}.`);\n return;\n }\n instanceMap.set(key, instance);\n },\n get(element, key) {\n if (elementMap.has(element)) {\n return elementMap.get(element).get(key) || null;\n }\n return null;\n },\n remove(element, key) {\n if (!elementMap.has(element)) {\n return;\n }\n const instanceMap = elementMap.get(element);\n instanceMap.delete(key);\n\n // free up element references if there are no instances left for an element\n if (instanceMap.size === 0) {\n elementMap.delete(element);\n }\n }\n};\n\n/**\n * --------------------------------------------------------------------------\n * Bootstrap util/index.js\n * Licensed under MIT (https://github.com/twbs/bootstrap/blob/main/LICENSE)\n * --------------------------------------------------------------------------\n */\n\nconst MAX_UID = 1000000;\nconst MILLISECONDS_MULTIPLIER = 1000;\nconst TRANSITION_END = 'transitionend';\n\n/**\n * Properly escape IDs selectors to handle weird IDs\n * @param {string} selector\n * @returns {string}\n */\nconst parseSelector = selector => {\n if (selector && window.CSS && window.CSS.escape) {\n // document.querySelector needs escaping to handle IDs (html5+) containing for instance /\n selector = selector.replace(/#([^\\s\"#']+)/g, (match, id) => `#${CSS.escape(id)}`);\n }\n return selector;\n};\n\n// Shout-out Angus Croll (https://goo.gl/pxwQGp)\nconst toType = object => {\n if (object === null || object === undefined) {\n return `${object}`;\n }\n return Object.prototype.toString.call(object).match(/\\s([a-z]+)/i)[1].toLowerCase();\n};\n\n/**\n * Public Util API\n */\n\nconst getUID = prefix => {\n do {\n prefix += Math.floor(Math.random() * MAX_UID);\n } while (document.getElementById(prefix));\n return prefix;\n};\nconst getTransitionDurationFromElement = element => {\n if (!element) {\n return 0;\n }\n\n // Get transition-duration of the element\n let {\n transitionDuration,\n transitionDelay\n } = window.getComputedStyle(element);\n const floatTransitionDuration = Number.parseFloat(transitionDuration);\n const floatTransitionDelay = Number.parseFloat(transitionDelay);\n\n // Return 0 if element or transition duration is not found\n if (!floatTransitionDuration && !floatTransitionDelay) {\n return 0;\n }\n\n // If multiple durations are defined, take the first\n transitionDuration = transitionDuration.split(',')[0];\n transitionDelay = transitionDelay.split(',')[0];\n return (Number.parseFloat(transitionDuration) + Number.parseFloat(transitionDelay)) * MILLISECONDS_MULTIPLIER;\n};\nconst triggerTransitionEnd = element => {\n element.dispatchEvent(new Event(TRANSITION_END));\n};\nconst isElement = object => {\n if (!object || typeof object !== 'object') {\n return false;\n }\n if (typeof object.jquery !== 'undefined') {\n object = object[0];\n }\n return typeof object.nodeType !== 'undefined';\n};\nconst getElement = object => {\n // it's a jQuery object or a node element\n if (isElement(object)) {\n return object.jquery ? object[0] : object;\n }\n if (typeof object === 'string' && object.length > 0) {\n return document.querySelector(parseSelector(object));\n }\n return null;\n};\nconst isVisible = element => {\n if (!isElement(element) || element.getClientRects().length === 0) {\n return false;\n }\n const elementIsVisible = getComputedStyle(element).getPropertyValue('visibility') === 'visible';\n // Handle `details` element as its content may falsie appear visible when it is closed\n const closedDetails = element.closest('details:not([open])');\n if (!closedDetails) {\n return elementIsVisible;\n }\n if (closedDetails !== element) {\n const summary = element.closest('summary');\n if (summary && summary.parentNode !== closedDetails) {\n return false;\n }\n if (summary === null) {\n return false;\n }\n }\n return elementIsVisible;\n};\nconst isDisabled = element => {\n if (!element || element.nodeType !== Node.ELEMENT_NODE) {\n return true;\n }\n if (element.classList.contains('disabled')) {\n return true;\n }\n if (typeof element.disabled !== 'undefined') {\n return element.disabled;\n }\n return element.hasAttribute('disabled') && element.getAttribute('disabled') !== 'false';\n};\nconst findShadowRoot = element => {\n if (!document.documentElement.attachShadow) {\n return null;\n }\n\n // Can find the shadow root otherwise it'll return the document\n if (typeof element.getRootNode === 'function') {\n const root = element.getRootNode();\n return root instanceof ShadowRoot ? root : null;\n }\n if (element instanceof ShadowRoot) {\n return element;\n }\n\n // when we don't find a shadow root\n if (!element.parentNode) {\n return null;\n }\n return findShadowRoot(element.parentNode);\n};\nconst noop = () => {};\n\n/**\n * Trick to restart an element's animation\n *\n * @param {HTMLElement} element\n * @return void\n *\n * @see https://www.charistheo.io/blog/2021/02/restart-a-css-animation-with-javascript/#restarting-a-css-animation\n */\nconst reflow = element => {\n element.offsetHeight; // eslint-disable-line no-unused-expressions\n};\n\nconst getjQuery = () => {\n if (window.jQuery && !document.body.hasAttribute('data-bs-no-jquery')) {\n return window.jQuery;\n }\n return null;\n};\nconst DOMContentLoadedCallbacks = [];\nconst onDOMContentLoaded = callback => {\n if (document.readyState === 'loading') {\n // add listener on the first call when the document is in loading state\n if (!DOMContentLoadedCallbacks.length) {\n document.addEventListener('DOMContentLoaded', () => {\n for (const callback of DOMContentLoadedCallbacks) {\n callback();\n }\n });\n }\n DOMContentLoadedCallbacks.push(callback);\n } else {\n callback();\n }\n};\nconst isRTL = () => document.documentElement.dir === 'rtl';\nconst defineJQueryPlugin = plugin => {\n onDOMContentLoaded(() => {\n const $ = getjQuery();\n /* istanbul ignore if */\n if ($) {\n const name = plugin.NAME;\n const JQUERY_NO_CONFLICT = $.fn[name];\n $.fn[name] = plugin.jQueryInterface;\n $.fn[name].Constructor = plugin;\n $.fn[name].noConflict = () => {\n $.fn[name] = JQUERY_NO_CONFLICT;\n return plugin.jQueryInterface;\n };\n }\n });\n};\nconst execute = (possibleCallback, args = [], defaultValue = possibleCallback) => {\n return typeof possibleCallback === 'function' ? possibleCallback(...args) : defaultValue;\n};\nconst executeAfterTransition = (callback, transitionElement, waitForTransition = true) => {\n if (!waitForTransition) {\n execute(callback);\n return;\n }\n const durationPadding = 5;\n const emulatedDuration = getTransitionDurationFromElement(transitionElement) + durationPadding;\n let called = false;\n const handler = ({\n target\n }) => {\n if (target !== transitionElement) {\n return;\n }\n called = true;\n transitionElement.removeEventListener(TRANSITION_END, handler);\n execute(callback);\n };\n transitionElement.addEventListener(TRANSITION_END, handler);\n setTimeout(() => {\n if (!called) {\n triggerTransitionEnd(transitionElement);\n }\n }, emulatedDuration);\n};\n\n/**\n * Return the previous/next element of a list.\n *\n * @param {array} list The list of elements\n * @param activeElement The active element\n * @param shouldGetNext Choose to get next or previous element\n * @param isCycleAllowed\n * @return {Element|elem} The proper element\n */\nconst getNextActiveElement = (list, activeElement, shouldGetNext, isCycleAllowed) => {\n const listLength = list.length;\n let index = list.indexOf(activeElement);\n\n // if the element does not exist in the list return an element\n // depending on the direction and if cycle is allowed\n if (index === -1) {\n return !shouldGetNext && isCycleAllowed ? list[listLength - 1] : list[0];\n }\n index += shouldGetNext ? 1 : -1;\n if (isCycleAllowed) {\n index = (index + listLength) % listLength;\n }\n return list[Math.max(0, Math.min(index, listLength - 1))];\n};\n\n/**\n * --------------------------------------------------------------------------\n * Bootstrap dom/event-handler.js\n * Licensed under MIT (https://github.com/twbs/bootstrap/blob/main/LICENSE)\n * --------------------------------------------------------------------------\n */\n\n\n/**\n * Constants\n */\n\nconst namespaceRegex = /[^.]*(?=\\..*)\\.|.*/;\nconst stripNameRegex = /\\..*/;\nconst stripUidRegex = /::\\d+$/;\nconst eventRegistry = {}; // Events storage\nlet uidEvent = 1;\nconst customEvents = {\n mouseenter: 'mouseover',\n mouseleave: 'mouseout'\n};\nconst nativeEvents = new Set(['click', 'dblclick', 'mouseup', 'mousedown', 'contextmenu', 'mousewheel', 'DOMMouseScroll', 'mouseover', 'mouseout', 'mousemove', 'selectstart', 'selectend', 'keydown', 'keypress', 'keyup', 'orientationchange', 'touchstart', 'touchmove', 'touchend', 'touchcancel', 'pointerdown', 'pointermove', 'pointerup', 'pointerleave', 'pointercancel', 'gesturestart', 'gesturechange', 'gestureend', 'focus', 'blur', 'change', 'reset', 'select', 'submit', 'focusin', 'focusout', 'load', 'unload', 'beforeunload', 'resize', 'move', 'DOMContentLoaded', 'readystatechange', 'error', 'abort', 'scroll']);\n\n/**\n * Private methods\n */\n\nfunction makeEventUid(element, uid) {\n return uid && `${uid}::${uidEvent++}` || element.uidEvent || uidEvent++;\n}\nfunction getElementEvents(element) {\n const uid = makeEventUid(element);\n element.uidEvent = uid;\n eventRegistry[uid] = eventRegistry[uid] || {};\n return eventRegistry[uid];\n}\nfunction bootstrapHandler(element, fn) {\n return function handler(event) {\n hydrateObj(event, {\n delegateTarget: element\n });\n if (handler.oneOff) {\n EventHandler.off(element, event.type, fn);\n }\n return fn.apply(element, [event]);\n };\n}\nfunction bootstrapDelegationHandler(element, selector, fn) {\n return function handler(event) {\n const domElements = element.querySelectorAll(selector);\n for (let {\n target\n } = event; target && target !== this; target = target.parentNode) {\n for (const domElement of domElements) {\n if (domElement !== target) {\n continue;\n }\n hydrateObj(event, {\n delegateTarget: target\n });\n if (handler.oneOff) {\n EventHandler.off(element, event.type, selector, fn);\n }\n return fn.apply(target, [event]);\n }\n }\n };\n}\nfunction findHandler(events, callable, delegationSelector = null) {\n return Object.values(events).find(event => event.callable === callable && event.delegationSelector === delegationSelector);\n}\nfunction normalizeParameters(originalTypeEvent, handler, delegationFunction) {\n const isDelegated = typeof handler === 'string';\n // TODO: tooltip passes `false` instead of selector, so we need to check\n const callable = isDelegated ? delegationFunction : handler || delegationFunction;\n let typeEvent = getTypeEvent(originalTypeEvent);\n if (!nativeEvents.has(typeEvent)) {\n typeEvent = originalTypeEvent;\n }\n return [isDelegated, callable, typeEvent];\n}\nfunction addHandler(element, originalTypeEvent, handler, delegationFunction, oneOff) {\n if (typeof originalTypeEvent !== 'string' || !element) {\n return;\n }\n let [isDelegated, callable, typeEvent] = normalizeParameters(originalTypeEvent, handler, delegationFunction);\n\n // in case of mouseenter or mouseleave wrap the handler within a function that checks for its DOM position\n // this prevents the handler from being dispatched the same way as mouseover or mouseout does\n if (originalTypeEvent in customEvents) {\n const wrapFunction = fn => {\n return function (event) {\n if (!event.relatedTarget || event.relatedTarget !== event.delegateTarget && !event.delegateTarget.contains(event.relatedTarget)) {\n return fn.call(this, event);\n }\n };\n };\n callable = wrapFunction(callable);\n }\n const events = getElementEvents(element);\n const handlers = events[typeEvent] || (events[typeEvent] = {});\n const previousFunction = findHandler(handlers, callable, isDelegated ? handler : null);\n if (previousFunction) {\n previousFunction.oneOff = previousFunction.oneOff && oneOff;\n return;\n }\n const uid = makeEventUid(callable, originalTypeEvent.replace(namespaceRegex, ''));\n const fn = isDelegated ? bootstrapDelegationHandler(element, handler, callable) : bootstrapHandler(element, callable);\n fn.delegationSelector = isDelegated ? handler : null;\n fn.callable = callable;\n fn.oneOff = oneOff;\n fn.uidEvent = uid;\n handlers[uid] = fn;\n element.addEventListener(typeEvent, fn, isDelegated);\n}\nfunction removeHandler(element, events, typeEvent, handler, delegationSelector) {\n const fn = findHandler(events[typeEvent], handler, delegationSelector);\n if (!fn) {\n return;\n }\n element.removeEventListener(typeEvent, fn, Boolean(delegationSelector));\n delete events[typeEvent][fn.uidEvent];\n}\nfunction removeNamespacedHandlers(element, events, typeEvent, namespace) {\n const storeElementEvent = events[typeEvent] || {};\n for (const [handlerKey, event] of Object.entries(storeElementEvent)) {\n if (handlerKey.includes(namespace)) {\n removeHandler(element, events, typeEvent, event.callable, event.delegationSelector);\n }\n }\n}\nfunction getTypeEvent(event) {\n // allow to get the native events from namespaced events ('click.bs.button' --> 'click')\n event = event.replace(stripNameRegex, '');\n return customEvents[event] || event;\n}\nconst EventHandler = {\n on(element, event, handler, delegationFunction) {\n addHandler(element, event, handler, delegationFunction, false);\n },\n one(element, event, handler, delegationFunction) {\n addHandler(element, event, handler, delegationFunction, true);\n },\n off(element, originalTypeEvent, handler, delegationFunction) {\n if (typeof originalTypeEvent !== 'string' || !element) {\n return;\n }\n const [isDelegated, callable, typeEvent] = normalizeParameters(originalTypeEvent, handler, delegationFunction);\n const inNamespace = typeEvent !== originalTypeEvent;\n const events = getElementEvents(element);\n const storeElementEvent = events[typeEvent] || {};\n const isNamespace = originalTypeEvent.startsWith('.');\n if (typeof callable !== 'undefined') {\n // Simplest case: handler is passed, remove that listener ONLY.\n if (!Object.keys(storeElementEvent).length) {\n return;\n }\n removeHandler(element, events, typeEvent, callable, isDelegated ? handler : null);\n return;\n }\n if (isNamespace) {\n for (const elementEvent of Object.keys(events)) {\n removeNamespacedHandlers(element, events, elementEvent, originalTypeEvent.slice(1));\n }\n }\n for (const [keyHandlers, event] of Object.entries(storeElementEvent)) {\n const handlerKey = keyHandlers.replace(stripUidRegex, '');\n if (!inNamespace || originalTypeEvent.includes(handlerKey)) {\n removeHandler(element, events, typeEvent, event.callable, event.delegationSelector);\n }\n }\n },\n trigger(element, event, args) {\n if (typeof event !== 'string' || !element) {\n return null;\n }\n const $ = getjQuery();\n const typeEvent = getTypeEvent(event);\n const inNamespace = event !== typeEvent;\n let jQueryEvent = null;\n let bubbles = true;\n let nativeDispatch = true;\n let defaultPrevented = false;\n if (inNamespace && $) {\n jQueryEvent = $.Event(event, args);\n $(element).trigger(jQueryEvent);\n bubbles = !jQueryEvent.isPropagationStopped();\n nativeDispatch = !jQueryEvent.isImmediatePropagationStopped();\n defaultPrevented = jQueryEvent.isDefaultPrevented();\n }\n const evt = hydrateObj(new Event(event, {\n bubbles,\n cancelable: true\n }), args);\n if (defaultPrevented) {\n evt.preventDefault();\n }\n if (nativeDispatch) {\n element.dispatchEvent(evt);\n }\n if (evt.defaultPrevented && jQueryEvent) {\n jQueryEvent.preventDefault();\n }\n return evt;\n }\n};\nfunction hydrateObj(obj, meta = {}) {\n for (const [key, value] of Object.entries(meta)) {\n try {\n obj[key] = value;\n } catch (_unused) {\n Object.defineProperty(obj, key, {\n configurable: true,\n get() {\n return value;\n }\n });\n }\n }\n return obj;\n}\n\n/**\n * --------------------------------------------------------------------------\n * Bootstrap dom/manipulator.js\n * Licensed under MIT (https://github.com/twbs/bootstrap/blob/main/LICENSE)\n * --------------------------------------------------------------------------\n */\n\nfunction normalizeData(value) {\n if (value === 'true') {\n return true;\n }\n if (value === 'false') {\n return false;\n }\n if (value === Number(value).toString()) {\n return Number(value);\n }\n if (value === '' || value === 'null') {\n return null;\n }\n if (typeof value !== 'string') {\n return value;\n }\n try {\n return JSON.parse(decodeURIComponent(value));\n } catch (_unused) {\n return value;\n }\n}\nfunction normalizeDataKey(key) {\n return key.replace(/[A-Z]/g, chr => `-${chr.toLowerCase()}`);\n}\nconst Manipulator = {\n setDataAttribute(element, key, value) {\n element.setAttribute(`data-bs-${normalizeDataKey(key)}`, value);\n },\n removeDataAttribute(element, key) {\n element.removeAttribute(`data-bs-${normalizeDataKey(key)}`);\n },\n getDataAttributes(element) {\n if (!element) {\n return {};\n }\n const attributes = {};\n const bsKeys = Object.keys(element.dataset).filter(key => key.startsWith('bs') && !key.startsWith('bsConfig'));\n for (const key of bsKeys) {\n let pureKey = key.replace(/^bs/, '');\n pureKey = pureKey.charAt(0).toLowerCase() + pureKey.slice(1, pureKey.length);\n attributes[pureKey] = normalizeData(element.dataset[key]);\n }\n return attributes;\n },\n getDataAttribute(element, key) {\n return normalizeData(element.getAttribute(`data-bs-${normalizeDataKey(key)}`));\n }\n};\n\n/**\n * --------------------------------------------------------------------------\n * Bootstrap util/config.js\n * Licensed under MIT (https://github.com/twbs/bootstrap/blob/main/LICENSE)\n * --------------------------------------------------------------------------\n */\n\n\n/**\n * Class definition\n */\n\nclass Config {\n // Getters\n static get Default() {\n return {};\n }\n static get DefaultType() {\n return {};\n }\n static get NAME() {\n throw new Error('You have to implement the static method \"NAME\", for each component!');\n }\n _getConfig(config) {\n config = this._mergeConfigObj(config);\n config = this._configAfterMerge(config);\n this._typeCheckConfig(config);\n return config;\n }\n _configAfterMerge(config) {\n return config;\n }\n _mergeConfigObj(config, element) {\n const jsonConfig = isElement(element) ? Manipulator.getDataAttribute(element, 'config') : {}; // try to parse\n\n return {\n ...this.constructor.Default,\n ...(typeof jsonConfig === 'object' ? jsonConfig : {}),\n ...(isElement(element) ? Manipulator.getDataAttributes(element) : {}),\n ...(typeof config === 'object' ? config : {})\n };\n }\n _typeCheckConfig(config, configTypes = this.constructor.DefaultType) {\n for (const [property, expectedTypes] of Object.entries(configTypes)) {\n const value = config[property];\n const valueType = isElement(value) ? 'element' : toType(value);\n if (!new RegExp(expectedTypes).test(valueType)) {\n throw new TypeError(`${this.constructor.NAME.toUpperCase()}: Option \"${property}\" provided type \"${valueType}\" but expected type \"${expectedTypes}\".`);\n }\n }\n }\n}\n\n/**\n * --------------------------------------------------------------------------\n * Bootstrap base-component.js\n * Licensed under MIT (https://github.com/twbs/bootstrap/blob/main/LICENSE)\n * --------------------------------------------------------------------------\n */\n\n\n/**\n * Constants\n */\n\nconst VERSION = '5.3.2';\n\n/**\n * Class definition\n */\n\nclass BaseComponent extends Config {\n constructor(element, config) {\n super();\n element = getElement(element);\n if (!element) {\n return;\n }\n this._element = element;\n this._config = this._getConfig(config);\n Data.set(this._element, this.constructor.DATA_KEY, this);\n }\n\n // Public\n dispose() {\n Data.remove(this._element, this.constructor.DATA_KEY);\n EventHandler.off(this._element, this.constructor.EVENT_KEY);\n for (const propertyName of Object.getOwnPropertyNames(this)) {\n this[propertyName] = null;\n }\n }\n _queueCallback(callback, element, isAnimated = true) {\n executeAfterTransition(callback, element, isAnimated);\n }\n _getConfig(config) {\n config = this._mergeConfigObj(config, this._element);\n config = this._configAfterMerge(config);\n this._typeCheckConfig(config);\n return config;\n }\n\n // Static\n static getInstance(element) {\n return Data.get(getElement(element), this.DATA_KEY);\n }\n static getOrCreateInstance(element, config = {}) {\n return this.getInstance(element) || new this(element, typeof config === 'object' ? config : null);\n }\n static get VERSION() {\n return VERSION;\n }\n static get DATA_KEY() {\n return `bs.${this.NAME}`;\n }\n static get EVENT_KEY() {\n return `.${this.DATA_KEY}`;\n }\n static eventName(name) {\n return `${name}${this.EVENT_KEY}`;\n }\n}\n\n/**\n * --------------------------------------------------------------------------\n * Bootstrap dom/selector-engine.js\n * Licensed under MIT (https://github.com/twbs/bootstrap/blob/main/LICENSE)\n * --------------------------------------------------------------------------\n */\n\nconst getSelector = element => {\n let selector = element.getAttribute('data-bs-target');\n if (!selector || selector === '#') {\n let hrefAttribute = element.getAttribute('href');\n\n // The only valid content that could double as a selector are IDs or classes,\n // so everything starting with `#` or `.`. If a \"real\" URL is used as the selector,\n // `document.querySelector` will rightfully complain it is invalid.\n // See https://github.com/twbs/bootstrap/issues/32273\n if (!hrefAttribute || !hrefAttribute.includes('#') && !hrefAttribute.startsWith('.')) {\n return null;\n }\n\n // Just in case some CMS puts out a full URL with the anchor appended\n if (hrefAttribute.includes('#') && !hrefAttribute.startsWith('#')) {\n hrefAttribute = `#${hrefAttribute.split('#')[1]}`;\n }\n selector = hrefAttribute && hrefAttribute !== '#' ? parseSelector(hrefAttribute.trim()) : null;\n }\n return selector;\n};\nconst SelectorEngine = {\n find(selector, element = document.documentElement) {\n return [].concat(...Element.prototype.querySelectorAll.call(element, selector));\n },\n findOne(selector, element = document.documentElement) {\n return Element.prototype.querySelector.call(element, selector);\n },\n children(element, selector) {\n return [].concat(...element.children).filter(child => child.matches(selector));\n },\n parents(element, selector) {\n const parents = [];\n let ancestor = element.parentNode.closest(selector);\n while (ancestor) {\n parents.push(ancestor);\n ancestor = ancestor.parentNode.closest(selector);\n }\n return parents;\n },\n prev(element, selector) {\n let previous = element.previousElementSibling;\n while (previous) {\n if (previous.matches(selector)) {\n return [previous];\n }\n previous = previous.previousElementSibling;\n }\n return [];\n },\n // TODO: this is now unused; remove later along with prev()\n next(element, selector) {\n let next = element.nextElementSibling;\n while (next) {\n if (next.matches(selector)) {\n return [next];\n }\n next = next.nextElementSibling;\n }\n return [];\n },\n focusableChildren(element) {\n const focusables = ['a', 'button', 'input', 'textarea', 'select', 'details', '[tabindex]', '[contenteditable=\"true\"]'].map(selector => `${selector}:not([tabindex^=\"-\"])`).join(',');\n return this.find(focusables, element).filter(el => !isDisabled(el) && isVisible(el));\n },\n getSelectorFromElement(element) {\n const selector = getSelector(element);\n if (selector) {\n return SelectorEngine.findOne(selector) ? selector : null;\n }\n return null;\n },\n getElementFromSelector(element) {\n const selector = getSelector(element);\n return selector ? SelectorEngine.findOne(selector) : null;\n },\n getMultipleElementsFromSelector(element) {\n const selector = getSelector(element);\n return selector ? SelectorEngine.find(selector) : [];\n }\n};\n\n/**\n * --------------------------------------------------------------------------\n * Bootstrap util/component-functions.js\n * Licensed under MIT (https://github.com/twbs/bootstrap/blob/main/LICENSE)\n * --------------------------------------------------------------------------\n */\n\nconst enableDismissTrigger = (component, method = 'hide') => {\n const clickEvent = `click.dismiss${component.EVENT_KEY}`;\n const name = component.NAME;\n EventHandler.on(document, clickEvent, `[data-bs-dismiss=\"${name}\"]`, function (event) {\n if (['A', 'AREA'].includes(this.tagName)) {\n event.preventDefault();\n }\n if (isDisabled(this)) {\n return;\n }\n const target = SelectorEngine.getElementFromSelector(this) || this.closest(`.${name}`);\n const instance = component.getOrCreateInstance(target);\n\n // Method argument is left, for Alert and only, as it doesn't implement the 'hide' method\n instance[method]();\n });\n};\n\n/**\n * --------------------------------------------------------------------------\n * Bootstrap alert.js\n * Licensed under MIT (https://github.com/twbs/bootstrap/blob/main/LICENSE)\n * --------------------------------------------------------------------------\n */\n\n\n/**\n * Constants\n */\n\nconst NAME$f = 'alert';\nconst DATA_KEY$a = 'bs.alert';\nconst EVENT_KEY$b = `.${DATA_KEY$a}`;\nconst EVENT_CLOSE = `close${EVENT_KEY$b}`;\nconst EVENT_CLOSED = `closed${EVENT_KEY$b}`;\nconst CLASS_NAME_FADE$5 = 'fade';\nconst CLASS_NAME_SHOW$8 = 'show';\n\n/**\n * Class definition\n */\n\nclass Alert extends BaseComponent {\n // Getters\n static get NAME() {\n return NAME$f;\n }\n\n // Public\n close() {\n const closeEvent = EventHandler.trigger(this._element, EVENT_CLOSE);\n if (closeEvent.defaultPrevented) {\n return;\n }\n this._element.classList.remove(CLASS_NAME_SHOW$8);\n const isAnimated = this._element.classList.contains(CLASS_NAME_FADE$5);\n this._queueCallback(() => this._destroyElement(), this._element, isAnimated);\n }\n\n // Private\n _destroyElement() {\n this._element.remove();\n EventHandler.trigger(this._element, EVENT_CLOSED);\n this.dispose();\n }\n\n // Static\n static jQueryInterface(config) {\n return this.each(function () {\n const data = Alert.getOrCreateInstance(this);\n if (typeof config !== 'string') {\n return;\n }\n if (data[config] === undefined || config.startsWith('_') || config === 'constructor') {\n throw new TypeError(`No method named \"${config}\"`);\n }\n data[config](this);\n });\n }\n}\n\n/**\n * Data API implementation\n */\n\nenableDismissTrigger(Alert, 'close');\n\n/**\n * jQuery\n */\n\ndefineJQueryPlugin(Alert);\n\n/**\n * --------------------------------------------------------------------------\n * Bootstrap button.js\n * Licensed under MIT (https://github.com/twbs/bootstrap/blob/main/LICENSE)\n * --------------------------------------------------------------------------\n */\n\n\n/**\n * Constants\n */\n\nconst NAME$e = 'button';\nconst DATA_KEY$9 = 'bs.button';\nconst EVENT_KEY$a = `.${DATA_KEY$9}`;\nconst DATA_API_KEY$6 = '.data-api';\nconst CLASS_NAME_ACTIVE$3 = 'active';\nconst SELECTOR_DATA_TOGGLE$5 = '[data-bs-toggle=\"button\"]';\nconst EVENT_CLICK_DATA_API$6 = `click${EVENT_KEY$a}${DATA_API_KEY$6}`;\n\n/**\n * Class definition\n */\n\nclass Button extends BaseComponent {\n // Getters\n static get NAME() {\n return NAME$e;\n }\n\n // Public\n toggle() {\n // Toggle class and sync the `aria-pressed` attribute with the return value of the `.toggle()` method\n this._element.setAttribute('aria-pressed', this._element.classList.toggle(CLASS_NAME_ACTIVE$3));\n }\n\n // Static\n static jQueryInterface(config) {\n return this.each(function () {\n const data = Button.getOrCreateInstance(this);\n if (config === 'toggle') {\n data[config]();\n }\n });\n }\n}\n\n/**\n * Data API implementation\n */\n\nEventHandler.on(document, EVENT_CLICK_DATA_API$6, SELECTOR_DATA_TOGGLE$5, event => {\n event.preventDefault();\n const button = event.target.closest(SELECTOR_DATA_TOGGLE$5);\n const data = Button.getOrCreateInstance(button);\n data.toggle();\n});\n\n/**\n * jQuery\n */\n\ndefineJQueryPlugin(Button);\n\n/**\n * --------------------------------------------------------------------------\n * Bootstrap util/swipe.js\n * Licensed under MIT (https://github.com/twbs/bootstrap/blob/main/LICENSE)\n * --------------------------------------------------------------------------\n */\n\n\n/**\n * Constants\n */\n\nconst NAME$d = 'swipe';\nconst EVENT_KEY$9 = '.bs.swipe';\nconst EVENT_TOUCHSTART = `touchstart${EVENT_KEY$9}`;\nconst EVENT_TOUCHMOVE = `touchmove${EVENT_KEY$9}`;\nconst EVENT_TOUCHEND = `touchend${EVENT_KEY$9}`;\nconst EVENT_POINTERDOWN = `pointerdown${EVENT_KEY$9}`;\nconst EVENT_POINTERUP = `pointerup${EVENT_KEY$9}`;\nconst POINTER_TYPE_TOUCH = 'touch';\nconst POINTER_TYPE_PEN = 'pen';\nconst CLASS_NAME_POINTER_EVENT = 'pointer-event';\nconst SWIPE_THRESHOLD = 40;\nconst Default$c = {\n endCallback: null,\n leftCallback: null,\n rightCallback: null\n};\nconst DefaultType$c = {\n endCallback: '(function|null)',\n leftCallback: '(function|null)',\n rightCallback: '(function|null)'\n};\n\n/**\n * Class definition\n */\n\nclass Swipe extends Config {\n constructor(element, config) {\n super();\n this._element = element;\n if (!element || !Swipe.isSupported()) {\n return;\n }\n this._config = this._getConfig(config);\n this._deltaX = 0;\n this._supportPointerEvents = Boolean(window.PointerEvent);\n this._initEvents();\n }\n\n // Getters\n static get Default() {\n return Default$c;\n }\n static get DefaultType() {\n return DefaultType$c;\n }\n static get NAME() {\n return NAME$d;\n }\n\n // Public\n dispose() {\n EventHandler.off(this._element, EVENT_KEY$9);\n }\n\n // Private\n _start(event) {\n if (!this._supportPointerEvents) {\n this._deltaX = event.touches[0].clientX;\n return;\n }\n if (this._eventIsPointerPenTouch(event)) {\n this._deltaX = event.clientX;\n }\n }\n _end(event) {\n if (this._eventIsPointerPenTouch(event)) {\n this._deltaX = event.clientX - this._deltaX;\n }\n this._handleSwipe();\n execute(this._config.endCallback);\n }\n _move(event) {\n this._deltaX = event.touches && event.touches.length > 1 ? 0 : event.touches[0].clientX - this._deltaX;\n }\n _handleSwipe() {\n const absDeltaX = Math.abs(this._deltaX);\n if (absDeltaX <= SWIPE_THRESHOLD) {\n return;\n }\n const direction = absDeltaX / this._deltaX;\n this._deltaX = 0;\n if (!direction) {\n return;\n }\n execute(direction > 0 ? this._config.rightCallback : this._config.leftCallback);\n }\n _initEvents() {\n if (this._supportPointerEvents) {\n EventHandler.on(this._element, EVENT_POINTERDOWN, event => this._start(event));\n EventHandler.on(this._element, EVENT_POINTERUP, event => this._end(event));\n this._element.classList.add(CLASS_NAME_POINTER_EVENT);\n } else {\n EventHandler.on(this._element, EVENT_TOUCHSTART, event => this._start(event));\n EventHandler.on(this._element, EVENT_TOUCHMOVE, event => this._move(event));\n EventHandler.on(this._element, EVENT_TOUCHEND, event => this._end(event));\n }\n }\n _eventIsPointerPenTouch(event) {\n return this._supportPointerEvents && (event.pointerType === POINTER_TYPE_PEN || event.pointerType === POINTER_TYPE_TOUCH);\n }\n\n // Static\n static isSupported() {\n return 'ontouchstart' in document.documentElement || navigator.maxTouchPoints > 0;\n }\n}\n\n/**\n * --------------------------------------------------------------------------\n * Bootstrap carousel.js\n * Licensed under MIT (https://github.com/twbs/bootstrap/blob/main/LICENSE)\n * --------------------------------------------------------------------------\n */\n\n\n/**\n * Constants\n */\n\nconst NAME$c = 'carousel';\nconst DATA_KEY$8 = 'bs.carousel';\nconst EVENT_KEY$8 = `.${DATA_KEY$8}`;\nconst DATA_API_KEY$5 = '.data-api';\nconst ARROW_LEFT_KEY$1 = 'ArrowLeft';\nconst ARROW_RIGHT_KEY$1 = 'ArrowRight';\nconst TOUCHEVENT_COMPAT_WAIT = 500; // Time for mouse compat events to fire after touch\n\nconst ORDER_NEXT = 'next';\nconst ORDER_PREV = 'prev';\nconst DIRECTION_LEFT = 'left';\nconst DIRECTION_RIGHT = 'right';\nconst EVENT_SLIDE = `slide${EVENT_KEY$8}`;\nconst EVENT_SLID = `slid${EVENT_KEY$8}`;\nconst EVENT_KEYDOWN$1 = `keydown${EVENT_KEY$8}`;\nconst EVENT_MOUSEENTER$1 = `mouseenter${EVENT_KEY$8}`;\nconst EVENT_MOUSELEAVE$1 = `mouseleave${EVENT_KEY$8}`;\nconst EVENT_DRAG_START = `dragstart${EVENT_KEY$8}`;\nconst EVENT_LOAD_DATA_API$3 = `load${EVENT_KEY$8}${DATA_API_KEY$5}`;\nconst EVENT_CLICK_DATA_API$5 = `click${EVENT_KEY$8}${DATA_API_KEY$5}`;\nconst CLASS_NAME_CAROUSEL = 'carousel';\nconst CLASS_NAME_ACTIVE$2 = 'active';\nconst CLASS_NAME_SLIDE = 'slide';\nconst CLASS_NAME_END = 'carousel-item-end';\nconst CLASS_NAME_START = 'carousel-item-start';\nconst CLASS_NAME_NEXT = 'carousel-item-next';\nconst CLASS_NAME_PREV = 'carousel-item-prev';\nconst SELECTOR_ACTIVE = '.active';\nconst SELECTOR_ITEM = '.carousel-item';\nconst SELECTOR_ACTIVE_ITEM = SELECTOR_ACTIVE + SELECTOR_ITEM;\nconst SELECTOR_ITEM_IMG = '.carousel-item img';\nconst SELECTOR_INDICATORS = '.carousel-indicators';\nconst SELECTOR_DATA_SLIDE = '[data-bs-slide], [data-bs-slide-to]';\nconst SELECTOR_DATA_RIDE = '[data-bs-ride=\"carousel\"]';\nconst KEY_TO_DIRECTION = {\n [ARROW_LEFT_KEY$1]: DIRECTION_RIGHT,\n [ARROW_RIGHT_KEY$1]: DIRECTION_LEFT\n};\nconst Default$b = {\n interval: 5000,\n keyboard: true,\n pause: 'hover',\n ride: false,\n touch: true,\n wrap: true\n};\nconst DefaultType$b = {\n interval: '(number|boolean)',\n // TODO:v6 remove boolean support\n keyboard: 'boolean',\n pause: '(string|boolean)',\n ride: '(boolean|string)',\n touch: 'boolean',\n wrap: 'boolean'\n};\n\n/**\n * Class definition\n */\n\nclass Carousel extends BaseComponent {\n constructor(element, config) {\n super(element, config);\n this._interval = null;\n this._activeElement = null;\n this._isSliding = false;\n this.touchTimeout = null;\n this._swipeHelper = null;\n this._indicatorsElement = SelectorEngine.findOne(SELECTOR_INDICATORS, this._element);\n this._addEventListeners();\n if (this._config.ride === CLASS_NAME_CAROUSEL) {\n this.cycle();\n }\n }\n\n // Getters\n static get Default() {\n return Default$b;\n }\n static get DefaultType() {\n return DefaultType$b;\n }\n static get NAME() {\n return NAME$c;\n }\n\n // Public\n next() {\n this._slide(ORDER_NEXT);\n }\n nextWhenVisible() {\n // FIXME TODO use `document.visibilityState`\n // Don't call next when the page isn't visible\n // or the carousel or its parent isn't visible\n if (!document.hidden && isVisible(this._element)) {\n this.next();\n }\n }\n prev() {\n this._slide(ORDER_PREV);\n }\n pause() {\n if (this._isSliding) {\n triggerTransitionEnd(this._element);\n }\n this._clearInterval();\n }\n cycle() {\n this._clearInterval();\n this._updateInterval();\n this._interval = setInterval(() => this.nextWhenVisible(), this._config.interval);\n }\n _maybeEnableCycle() {\n if (!this._config.ride) {\n return;\n }\n if (this._isSliding) {\n EventHandler.one(this._element, EVENT_SLID, () => this.cycle());\n return;\n }\n this.cycle();\n }\n to(index) {\n const items = this._getItems();\n if (index > items.length - 1 || index < 0) {\n return;\n }\n if (this._isSliding) {\n EventHandler.one(this._element, EVENT_SLID, () => this.to(index));\n return;\n }\n const activeIndex = this._getItemIndex(this._getActive());\n if (activeIndex === index) {\n return;\n }\n const order = index > activeIndex ? ORDER_NEXT : ORDER_PREV;\n this._slide(order, items[index]);\n }\n dispose() {\n if (this._swipeHelper) {\n this._swipeHelper.dispose();\n }\n super.dispose();\n }\n\n // Private\n _configAfterMerge(config) {\n config.defaultInterval = config.interval;\n return config;\n }\n _addEventListeners() {\n if (this._config.keyboard) {\n EventHandler.on(this._element, EVENT_KEYDOWN$1, event => this._keydown(event));\n }\n if (this._config.pause === 'hover') {\n EventHandler.on(this._element, EVENT_MOUSEENTER$1, () => this.pause());\n EventHandler.on(this._element, EVENT_MOUSELEAVE$1, () => this._maybeEnableCycle());\n }\n if (this._config.touch && Swipe.isSupported()) {\n this._addTouchEventListeners();\n }\n }\n _addTouchEventListeners() {\n for (const img of SelectorEngine.find(SELECTOR_ITEM_IMG, this._element)) {\n EventHandler.on(img, EVENT_DRAG_START, event => event.preventDefault());\n }\n const endCallBack = () => {\n if (this._config.pause !== 'hover') {\n return;\n }\n\n // If it's a touch-enabled device, mouseenter/leave are fired as\n // part of the mouse compatibility events on first tap - the carousel\n // would stop cycling until user tapped out of it;\n // here, we listen for touchend, explicitly pause the carousel\n // (as if it's the second time we tap on it, mouseenter compat event\n // is NOT fired) and after a timeout (to allow for mouse compatibility\n // events to fire) we explicitly restart cycling\n\n this.pause();\n if (this.touchTimeout) {\n clearTimeout(this.touchTimeout);\n }\n this.touchTimeout = setTimeout(() => this._maybeEnableCycle(), TOUCHEVENT_COMPAT_WAIT + this._config.interval);\n };\n const swipeConfig = {\n leftCallback: () => this._slide(this._directionToOrder(DIRECTION_LEFT)),\n rightCallback: () => this._slide(this._directionToOrder(DIRECTION_RIGHT)),\n endCallback: endCallBack\n };\n this._swipeHelper = new Swipe(this._element, swipeConfig);\n }\n _keydown(event) {\n if (/input|textarea/i.test(event.target.tagName)) {\n return;\n }\n const direction = KEY_TO_DIRECTION[event.key];\n if (direction) {\n event.preventDefault();\n this._slide(this._directionToOrder(direction));\n }\n }\n _getItemIndex(element) {\n return this._getItems().indexOf(element);\n }\n _setActiveIndicatorElement(index) {\n if (!this._indicatorsElement) {\n return;\n }\n const activeIndicator = SelectorEngine.findOne(SELECTOR_ACTIVE, this._indicatorsElement);\n activeIndicator.classList.remove(CLASS_NAME_ACTIVE$2);\n activeIndicator.removeAttribute('aria-current');\n const newActiveIndicator = SelectorEngine.findOne(`[data-bs-slide-to=\"${index}\"]`, this._indicatorsElement);\n if (newActiveIndicator) {\n newActiveIndicator.classList.add(CLASS_NAME_ACTIVE$2);\n newActiveIndicator.setAttribute('aria-current', 'true');\n }\n }\n _updateInterval() {\n const element = this._activeElement || this._getActive();\n if (!element) {\n return;\n }\n const elementInterval = Number.parseInt(element.getAttribute('data-bs-interval'), 10);\n this._config.interval = elementInterval || this._config.defaultInterval;\n }\n _slide(order, element = null) {\n if (this._isSliding) {\n return;\n }\n const activeElement = this._getActive();\n const isNext = order === ORDER_NEXT;\n const nextElement = element || getNextActiveElement(this._getItems(), activeElement, isNext, this._config.wrap);\n if (nextElement === activeElement) {\n return;\n }\n const nextElementIndex = this._getItemIndex(nextElement);\n const triggerEvent = eventName => {\n return EventHandler.trigger(this._element, eventName, {\n relatedTarget: nextElement,\n direction: this._orderToDirection(order),\n from: this._getItemIndex(activeElement),\n to: nextElementIndex\n });\n };\n const slideEvent = triggerEvent(EVENT_SLIDE);\n if (slideEvent.defaultPrevented) {\n return;\n }\n if (!activeElement || !nextElement) {\n // Some weirdness is happening, so we bail\n // TODO: change tests that use empty divs to avoid this check\n return;\n }\n const isCycling = Boolean(this._interval);\n this.pause();\n this._isSliding = true;\n this._setActiveIndicatorElement(nextElementIndex);\n this._activeElement = nextElement;\n const directionalClassName = isNext ? CLASS_NAME_START : CLASS_NAME_END;\n const orderClassName = isNext ? CLASS_NAME_NEXT : CLASS_NAME_PREV;\n nextElement.classList.add(orderClassName);\n reflow(nextElement);\n activeElement.classList.add(directionalClassName);\n nextElement.classList.add(directionalClassName);\n const completeCallBack = () => {\n nextElement.classList.remove(directionalClassName, orderClassName);\n nextElement.classList.add(CLASS_NAME_ACTIVE$2);\n activeElement.classList.remove(CLASS_NAME_ACTIVE$2, orderClassName, directionalClassName);\n this._isSliding = false;\n triggerEvent(EVENT_SLID);\n };\n this._queueCallback(completeCallBack, activeElement, this._isAnimated());\n if (isCycling) {\n this.cycle();\n }\n }\n _isAnimated() {\n return this._element.classList.contains(CLASS_NAME_SLIDE);\n }\n _getActive() {\n return SelectorEngine.findOne(SELECTOR_ACTIVE_ITEM, this._element);\n }\n _getItems() {\n return SelectorEngine.find(SELECTOR_ITEM, this._element);\n }\n _clearInterval() {\n if (this._interval) {\n clearInterval(this._interval);\n this._interval = null;\n }\n }\n _directionToOrder(direction) {\n if (isRTL()) {\n return direction === DIRECTION_LEFT ? ORDER_PREV : ORDER_NEXT;\n }\n return direction === DIRECTION_LEFT ? ORDER_NEXT : ORDER_PREV;\n }\n _orderToDirection(order) {\n if (isRTL()) {\n return order === ORDER_PREV ? DIRECTION_LEFT : DIRECTION_RIGHT;\n }\n return order === ORDER_PREV ? DIRECTION_RIGHT : DIRECTION_LEFT;\n }\n\n // Static\n static jQueryInterface(config) {\n return this.each(function () {\n const data = Carousel.getOrCreateInstance(this, config);\n if (typeof config === 'number') {\n data.to(config);\n return;\n }\n if (typeof config === 'string') {\n if (data[config] === undefined || config.startsWith('_') || config === 'constructor') {\n throw new TypeError(`No method named \"${config}\"`);\n }\n data[config]();\n }\n });\n }\n}\n\n/**\n * Data API implementation\n */\n\nEventHandler.on(document, EVENT_CLICK_DATA_API$5, SELECTOR_DATA_SLIDE, function (event) {\n const target = SelectorEngine.getElementFromSelector(this);\n if (!target || !target.classList.contains(CLASS_NAME_CAROUSEL)) {\n return;\n }\n event.preventDefault();\n const carousel = Carousel.getOrCreateInstance(target);\n const slideIndex = this.getAttribute('data-bs-slide-to');\n if (slideIndex) {\n carousel.to(slideIndex);\n carousel._maybeEnableCycle();\n return;\n }\n if (Manipulator.getDataAttribute(this, 'slide') === 'next') {\n carousel.next();\n carousel._maybeEnableCycle();\n return;\n }\n carousel.prev();\n carousel._maybeEnableCycle();\n});\nEventHandler.on(window, EVENT_LOAD_DATA_API$3, () => {\n const carousels = SelectorEngine.find(SELECTOR_DATA_RIDE);\n for (const carousel of carousels) {\n Carousel.getOrCreateInstance(carousel);\n }\n});\n\n/**\n * jQuery\n */\n\ndefineJQueryPlugin(Carousel);\n\n/**\n * --------------------------------------------------------------------------\n * Bootstrap collapse.js\n * Licensed under MIT (https://github.com/twbs/bootstrap/blob/main/LICENSE)\n * --------------------------------------------------------------------------\n */\n\n\n/**\n * Constants\n */\n\nconst NAME$b = 'collapse';\nconst DATA_KEY$7 = 'bs.collapse';\nconst EVENT_KEY$7 = `.${DATA_KEY$7}`;\nconst DATA_API_KEY$4 = '.data-api';\nconst EVENT_SHOW$6 = `show${EVENT_KEY$7}`;\nconst EVENT_SHOWN$6 = `shown${EVENT_KEY$7}`;\nconst EVENT_HIDE$6 = `hide${EVENT_KEY$7}`;\nconst EVENT_HIDDEN$6 = `hidden${EVENT_KEY$7}`;\nconst EVENT_CLICK_DATA_API$4 = `click${EVENT_KEY$7}${DATA_API_KEY$4}`;\nconst CLASS_NAME_SHOW$7 = 'show';\nconst CLASS_NAME_COLLAPSE = 'collapse';\nconst CLASS_NAME_COLLAPSING = 'collapsing';\nconst CLASS_NAME_COLLAPSED = 'collapsed';\nconst CLASS_NAME_DEEPER_CHILDREN = `:scope .${CLASS_NAME_COLLAPSE} .${CLASS_NAME_COLLAPSE}`;\nconst CLASS_NAME_HORIZONTAL = 'collapse-horizontal';\nconst WIDTH = 'width';\nconst HEIGHT = 'height';\nconst SELECTOR_ACTIVES = '.collapse.show, .collapse.collapsing';\nconst SELECTOR_DATA_TOGGLE$4 = '[data-bs-toggle=\"collapse\"]';\nconst Default$a = {\n parent: null,\n toggle: true\n};\nconst DefaultType$a = {\n parent: '(null|element)',\n toggle: 'boolean'\n};\n\n/**\n * Class definition\n */\n\nclass Collapse extends BaseComponent {\n constructor(element, config) {\n super(element, config);\n this._isTransitioning = false;\n this._triggerArray = [];\n const toggleList = SelectorEngine.find(SELECTOR_DATA_TOGGLE$4);\n for (const elem of toggleList) {\n const selector = SelectorEngine.getSelectorFromElement(elem);\n const filterElement = SelectorEngine.find(selector).filter(foundElement => foundElement === this._element);\n if (selector !== null && filterElement.length) {\n this._triggerArray.push(elem);\n }\n }\n this._initializeChildren();\n if (!this._config.parent) {\n this._addAriaAndCollapsedClass(this._triggerArray, this._isShown());\n }\n if (this._config.toggle) {\n this.toggle();\n }\n }\n\n // Getters\n static get Default() {\n return Default$a;\n }\n static get DefaultType() {\n return DefaultType$a;\n }\n static get NAME() {\n return NAME$b;\n }\n\n // Public\n toggle() {\n if (this._isShown()) {\n this.hide();\n } else {\n this.show();\n }\n }\n show() {\n if (this._isTransitioning || this._isShown()) {\n return;\n }\n let activeChildren = [];\n\n // find active children\n if (this._config.parent) {\n activeChildren = this._getFirstLevelChildren(SELECTOR_ACTIVES).filter(element => element !== this._element).map(element => Collapse.getOrCreateInstance(element, {\n toggle: false\n }));\n }\n if (activeChildren.length && activeChildren[0]._isTransitioning) {\n return;\n }\n const startEvent = EventHandler.trigger(this._element, EVENT_SHOW$6);\n if (startEvent.defaultPrevented) {\n return;\n }\n for (const activeInstance of activeChildren) {\n activeInstance.hide();\n }\n const dimension = this._getDimension();\n this._element.classList.remove(CLASS_NAME_COLLAPSE);\n this._element.classList.add(CLASS_NAME_COLLAPSING);\n this._element.style[dimension] = 0;\n this._addAriaAndCollapsedClass(this._triggerArray, true);\n this._isTransitioning = true;\n const complete = () => {\n this._isTransitioning = false;\n this._element.classList.remove(CLASS_NAME_COLLAPSING);\n this._element.classList.add(CLASS_NAME_COLLAPSE, CLASS_NAME_SHOW$7);\n this._element.style[dimension] = '';\n EventHandler.trigger(this._element, EVENT_SHOWN$6);\n };\n const capitalizedDimension = dimension[0].toUpperCase() + dimension.slice(1);\n const scrollSize = `scroll${capitalizedDimension}`;\n this._queueCallback(complete, this._element, true);\n this._element.style[dimension] = `${this._element[scrollSize]}px`;\n }\n hide() {\n if (this._isTransitioning || !this._isShown()) {\n return;\n }\n const startEvent = EventHandler.trigger(this._element, EVENT_HIDE$6);\n if (startEvent.defaultPrevented) {\n return;\n }\n const dimension = this._getDimension();\n this._element.style[dimension] = `${this._element.getBoundingClientRect()[dimension]}px`;\n reflow(this._element);\n this._element.classList.add(CLASS_NAME_COLLAPSING);\n this._element.classList.remove(CLASS_NAME_COLLAPSE, CLASS_NAME_SHOW$7);\n for (const trigger of this._triggerArray) {\n const element = SelectorEngine.getElementFromSelector(trigger);\n if (element && !this._isShown(element)) {\n this._addAriaAndCollapsedClass([trigger], false);\n }\n }\n this._isTransitioning = true;\n const complete = () => {\n this._isTransitioning = false;\n this._element.classList.remove(CLASS_NAME_COLLAPSING);\n this._element.classList.add(CLASS_NAME_COLLAPSE);\n EventHandler.trigger(this._element, EVENT_HIDDEN$6);\n };\n this._element.style[dimension] = '';\n this._queueCallback(complete, this._element, true);\n }\n _isShown(element = this._element) {\n return element.classList.contains(CLASS_NAME_SHOW$7);\n }\n\n // Private\n _configAfterMerge(config) {\n config.toggle = Boolean(config.toggle); // Coerce string values\n config.parent = getElement(config.parent);\n return config;\n }\n _getDimension() {\n return this._element.classList.contains(CLASS_NAME_HORIZONTAL) ? WIDTH : HEIGHT;\n }\n _initializeChildren() {\n if (!this._config.parent) {\n return;\n }\n const children = this._getFirstLevelChildren(SELECTOR_DATA_TOGGLE$4);\n for (const element of children) {\n const selected = SelectorEngine.getElementFromSelector(element);\n if (selected) {\n this._addAriaAndCollapsedClass([element], this._isShown(selected));\n }\n }\n }\n _getFirstLevelChildren(selector) {\n const children = SelectorEngine.find(CLASS_NAME_DEEPER_CHILDREN, this._config.parent);\n // remove children if greater depth\n return SelectorEngine.find(selector, this._config.parent).filter(element => !children.includes(element));\n }\n _addAriaAndCollapsedClass(triggerArray, isOpen) {\n if (!triggerArray.length) {\n return;\n }\n for (const element of triggerArray) {\n element.classList.toggle(CLASS_NAME_COLLAPSED, !isOpen);\n element.setAttribute('aria-expanded', isOpen);\n }\n }\n\n // Static\n static jQueryInterface(config) {\n const _config = {};\n if (typeof config === 'string' && /show|hide/.test(config)) {\n _config.toggle = false;\n }\n return this.each(function () {\n const data = Collapse.getOrCreateInstance(this, _config);\n if (typeof config === 'string') {\n if (typeof data[config] === 'undefined') {\n throw new TypeError(`No method named \"${config}\"`);\n }\n data[config]();\n }\n });\n }\n}\n\n/**\n * Data API implementation\n */\n\nEventHandler.on(document, EVENT_CLICK_DATA_API$4, SELECTOR_DATA_TOGGLE$4, function (event) {\n // preventDefault only for elements (which change the URL) not inside the collapsible element\n if (event.target.tagName === 'A' || event.delegateTarget && event.delegateTarget.tagName === 'A') {\n event.preventDefault();\n }\n for (const element of SelectorEngine.getMultipleElementsFromSelector(this)) {\n Collapse.getOrCreateInstance(element, {\n toggle: false\n }).toggle();\n }\n});\n\n/**\n * jQuery\n */\n\ndefineJQueryPlugin(Collapse);\n\n/**\n * --------------------------------------------------------------------------\n * Bootstrap dropdown.js\n * Licensed under MIT (https://github.com/twbs/bootstrap/blob/main/LICENSE)\n * --------------------------------------------------------------------------\n */\n\n\n/**\n * Constants\n */\n\nconst NAME$a = 'dropdown';\nconst DATA_KEY$6 = 'bs.dropdown';\nconst EVENT_KEY$6 = `.${DATA_KEY$6}`;\nconst DATA_API_KEY$3 = '.data-api';\nconst ESCAPE_KEY$2 = 'Escape';\nconst TAB_KEY$1 = 'Tab';\nconst ARROW_UP_KEY$1 = 'ArrowUp';\nconst ARROW_DOWN_KEY$1 = 'ArrowDown';\nconst RIGHT_MOUSE_BUTTON = 2; // MouseEvent.button value for the secondary button, usually the right button\n\nconst EVENT_HIDE$5 = `hide${EVENT_KEY$6}`;\nconst EVENT_HIDDEN$5 = `hidden${EVENT_KEY$6}`;\nconst EVENT_SHOW$5 = `show${EVENT_KEY$6}`;\nconst EVENT_SHOWN$5 = `shown${EVENT_KEY$6}`;\nconst EVENT_CLICK_DATA_API$3 = `click${EVENT_KEY$6}${DATA_API_KEY$3}`;\nconst EVENT_KEYDOWN_DATA_API = `keydown${EVENT_KEY$6}${DATA_API_KEY$3}`;\nconst EVENT_KEYUP_DATA_API = `keyup${EVENT_KEY$6}${DATA_API_KEY$3}`;\nconst CLASS_NAME_SHOW$6 = 'show';\nconst CLASS_NAME_DROPUP = 'dropup';\nconst CLASS_NAME_DROPEND = 'dropend';\nconst CLASS_NAME_DROPSTART = 'dropstart';\nconst CLASS_NAME_DROPUP_CENTER = 'dropup-center';\nconst CLASS_NAME_DROPDOWN_CENTER = 'dropdown-center';\nconst SELECTOR_DATA_TOGGLE$3 = '[data-bs-toggle=\"dropdown\"]:not(.disabled):not(:disabled)';\nconst SELECTOR_DATA_TOGGLE_SHOWN = `${SELECTOR_DATA_TOGGLE$3}.${CLASS_NAME_SHOW$6}`;\nconst SELECTOR_MENU = '.dropdown-menu';\nconst SELECTOR_NAVBAR = '.navbar';\nconst SELECTOR_NAVBAR_NAV = '.navbar-nav';\nconst SELECTOR_VISIBLE_ITEMS = '.dropdown-menu .dropdown-item:not(.disabled):not(:disabled)';\nconst PLACEMENT_TOP = isRTL() ? 'top-end' : 'top-start';\nconst PLACEMENT_TOPEND = isRTL() ? 'top-start' : 'top-end';\nconst PLACEMENT_BOTTOM = isRTL() ? 'bottom-end' : 'bottom-start';\nconst PLACEMENT_BOTTOMEND = isRTL() ? 'bottom-start' : 'bottom-end';\nconst PLACEMENT_RIGHT = isRTL() ? 'left-start' : 'right-start';\nconst PLACEMENT_LEFT = isRTL() ? 'right-start' : 'left-start';\nconst PLACEMENT_TOPCENTER = 'top';\nconst PLACEMENT_BOTTOMCENTER = 'bottom';\nconst Default$9 = {\n autoClose: true,\n boundary: 'clippingParents',\n display: 'dynamic',\n offset: [0, 2],\n popperConfig: null,\n reference: 'toggle'\n};\nconst DefaultType$9 = {\n autoClose: '(boolean|string)',\n boundary: '(string|element)',\n display: 'string',\n offset: '(array|string|function)',\n popperConfig: '(null|object|function)',\n reference: '(string|element|object)'\n};\n\n/**\n * Class definition\n */\n\nclass Dropdown extends BaseComponent {\n constructor(element, config) {\n super(element, config);\n this._popper = null;\n this._parent = this._element.parentNode; // dropdown wrapper\n // TODO: v6 revert #37011 & change markup https://getbootstrap.com/docs/5.3/forms/input-group/\n this._menu = SelectorEngine.next(this._element, SELECTOR_MENU)[0] || SelectorEngine.prev(this._element, SELECTOR_MENU)[0] || SelectorEngine.findOne(SELECTOR_MENU, this._parent);\n this._inNavbar = this._detectNavbar();\n }\n\n // Getters\n static get Default() {\n return Default$9;\n }\n static get DefaultType() {\n return DefaultType$9;\n }\n static get NAME() {\n return NAME$a;\n }\n\n // Public\n toggle() {\n return this._isShown() ? this.hide() : this.show();\n }\n show() {\n if (isDisabled(this._element) || this._isShown()) {\n return;\n }\n const relatedTarget = {\n relatedTarget: this._element\n };\n const showEvent = EventHandler.trigger(this._element, EVENT_SHOW$5, relatedTarget);\n if (showEvent.defaultPrevented) {\n return;\n }\n this._createPopper();\n\n // If this is a touch-enabled device we add extra\n // empty mouseover listeners to the body's immediate children;\n // only needed because of broken event delegation on iOS\n // https://www.quirksmode.org/blog/archives/2014/02/mouse_event_bub.html\n if ('ontouchstart' in document.documentElement && !this._parent.closest(SELECTOR_NAVBAR_NAV)) {\n for (const element of [].concat(...document.body.children)) {\n EventHandler.on(element, 'mouseover', noop);\n }\n }\n this._element.focus();\n this._element.setAttribute('aria-expanded', true);\n this._menu.classList.add(CLASS_NAME_SHOW$6);\n this._element.classList.add(CLASS_NAME_SHOW$6);\n EventHandler.trigger(this._element, EVENT_SHOWN$5, relatedTarget);\n }\n hide() {\n if (isDisabled(this._element) || !this._isShown()) {\n return;\n }\n const relatedTarget = {\n relatedTarget: this._element\n };\n this._completeHide(relatedTarget);\n }\n dispose() {\n if (this._popper) {\n this._popper.destroy();\n }\n super.dispose();\n }\n update() {\n this._inNavbar = this._detectNavbar();\n if (this._popper) {\n this._popper.update();\n }\n }\n\n // Private\n _completeHide(relatedTarget) {\n const hideEvent = EventHandler.trigger(this._element, EVENT_HIDE$5, relatedTarget);\n if (hideEvent.defaultPrevented) {\n return;\n }\n\n // If this is a touch-enabled device we remove the extra\n // empty mouseover listeners we added for iOS support\n if ('ontouchstart' in document.documentElement) {\n for (const element of [].concat(...document.body.children)) {\n EventHandler.off(element, 'mouseover', noop);\n }\n }\n if (this._popper) {\n this._popper.destroy();\n }\n this._menu.classList.remove(CLASS_NAME_SHOW$6);\n this._element.classList.remove(CLASS_NAME_SHOW$6);\n this._element.setAttribute('aria-expanded', 'false');\n Manipulator.removeDataAttribute(this._menu, 'popper');\n EventHandler.trigger(this._element, EVENT_HIDDEN$5, relatedTarget);\n }\n _getConfig(config) {\n config = super._getConfig(config);\n if (typeof config.reference === 'object' && !isElement(config.reference) && typeof config.reference.getBoundingClientRect !== 'function') {\n // Popper virtual elements require a getBoundingClientRect method\n throw new TypeError(`${NAME$a.toUpperCase()}: Option \"reference\" provided type \"object\" without a required \"getBoundingClientRect\" method.`);\n }\n return config;\n }\n _createPopper() {\n if (typeof Popper === 'undefined') {\n throw new TypeError('Bootstrap\\'s dropdowns require Popper (https://popper.js.org)');\n }\n let referenceElement = this._element;\n if (this._config.reference === 'parent') {\n referenceElement = this._parent;\n } else if (isElement(this._config.reference)) {\n referenceElement = getElement(this._config.reference);\n } else if (typeof this._config.reference === 'object') {\n referenceElement = this._config.reference;\n }\n const popperConfig = this._getPopperConfig();\n this._popper = Popper.createPopper(referenceElement, this._menu, popperConfig);\n }\n _isShown() {\n return this._menu.classList.contains(CLASS_NAME_SHOW$6);\n }\n _getPlacement() {\n const parentDropdown = this._parent;\n if (parentDropdown.classList.contains(CLASS_NAME_DROPEND)) {\n return PLACEMENT_RIGHT;\n }\n if (parentDropdown.classList.contains(CLASS_NAME_DROPSTART)) {\n return PLACEMENT_LEFT;\n }\n if (parentDropdown.classList.contains(CLASS_NAME_DROPUP_CENTER)) {\n return PLACEMENT_TOPCENTER;\n }\n if (parentDropdown.classList.contains(CLASS_NAME_DROPDOWN_CENTER)) {\n return PLACEMENT_BOTTOMCENTER;\n }\n\n // We need to trim the value because custom properties can also include spaces\n const isEnd = getComputedStyle(this._menu).getPropertyValue('--bs-position').trim() === 'end';\n if (parentDropdown.classList.contains(CLASS_NAME_DROPUP)) {\n return isEnd ? PLACEMENT_TOPEND : PLACEMENT_TOP;\n }\n return isEnd ? PLACEMENT_BOTTOMEND : PLACEMENT_BOTTOM;\n }\n _detectNavbar() {\n return this._element.closest(SELECTOR_NAVBAR) !== null;\n }\n _getOffset() {\n const {\n offset\n } = this._config;\n if (typeof offset === 'string') {\n return offset.split(',').map(value => Number.parseInt(value, 10));\n }\n if (typeof offset === 'function') {\n return popperData => offset(popperData, this._element);\n }\n return offset;\n }\n _getPopperConfig() {\n const defaultBsPopperConfig = {\n placement: this._getPlacement(),\n modifiers: [{\n name: 'preventOverflow',\n options: {\n boundary: this._config.boundary\n }\n }, {\n name: 'offset',\n options: {\n offset: this._getOffset()\n }\n }]\n };\n\n // Disable Popper if we have a static display or Dropdown is in Navbar\n if (this._inNavbar || this._config.display === 'static') {\n Manipulator.setDataAttribute(this._menu, 'popper', 'static'); // TODO: v6 remove\n defaultBsPopperConfig.modifiers = [{\n name: 'applyStyles',\n enabled: false\n }];\n }\n return {\n ...defaultBsPopperConfig,\n ...execute(this._config.popperConfig, [defaultBsPopperConfig])\n };\n }\n _selectMenuItem({\n key,\n target\n }) {\n const items = SelectorEngine.find(SELECTOR_VISIBLE_ITEMS, this._menu).filter(element => isVisible(element));\n if (!items.length) {\n return;\n }\n\n // if target isn't included in items (e.g. when expanding the dropdown)\n // allow cycling to get the last item in case key equals ARROW_UP_KEY\n getNextActiveElement(items, target, key === ARROW_DOWN_KEY$1, !items.includes(target)).focus();\n }\n\n // Static\n static jQueryInterface(config) {\n return this.each(function () {\n const data = Dropdown.getOrCreateInstance(this, config);\n if (typeof config !== 'string') {\n return;\n }\n if (typeof data[config] === 'undefined') {\n throw new TypeError(`No method named \"${config}\"`);\n }\n data[config]();\n });\n }\n static clearMenus(event) {\n if (event.button === RIGHT_MOUSE_BUTTON || event.type === 'keyup' && event.key !== TAB_KEY$1) {\n return;\n }\n const openToggles = SelectorEngine.find(SELECTOR_DATA_TOGGLE_SHOWN);\n for (const toggle of openToggles) {\n const context = Dropdown.getInstance(toggle);\n if (!context || context._config.autoClose === false) {\n continue;\n }\n const composedPath = event.composedPath();\n const isMenuTarget = composedPath.includes(context._menu);\n if (composedPath.includes(context._element) || context._config.autoClose === 'inside' && !isMenuTarget || context._config.autoClose === 'outside' && isMenuTarget) {\n continue;\n }\n\n // Tab navigation through the dropdown menu or events from contained inputs shouldn't close the menu\n if (context._menu.contains(event.target) && (event.type === 'keyup' && event.key === TAB_KEY$1 || /input|select|option|textarea|form/i.test(event.target.tagName))) {\n continue;\n }\n const relatedTarget = {\n relatedTarget: context._element\n };\n if (event.type === 'click') {\n relatedTarget.clickEvent = event;\n }\n context._completeHide(relatedTarget);\n }\n }\n static dataApiKeydownHandler(event) {\n // If not an UP | DOWN | ESCAPE key => not a dropdown command\n // If input/textarea && if key is other than ESCAPE => not a dropdown command\n\n const isInput = /input|textarea/i.test(event.target.tagName);\n const isEscapeEvent = event.key === ESCAPE_KEY$2;\n const isUpOrDownEvent = [ARROW_UP_KEY$1, ARROW_DOWN_KEY$1].includes(event.key);\n if (!isUpOrDownEvent && !isEscapeEvent) {\n return;\n }\n if (isInput && !isEscapeEvent) {\n return;\n }\n event.preventDefault();\n\n // TODO: v6 revert #37011 & change markup https://getbootstrap.com/docs/5.3/forms/input-group/\n const getToggleButton = this.matches(SELECTOR_DATA_TOGGLE$3) ? this : SelectorEngine.prev(this, SELECTOR_DATA_TOGGLE$3)[0] || SelectorEngine.next(this, SELECTOR_DATA_TOGGLE$3)[0] || SelectorEngine.findOne(SELECTOR_DATA_TOGGLE$3, event.delegateTarget.parentNode);\n const instance = Dropdown.getOrCreateInstance(getToggleButton);\n if (isUpOrDownEvent) {\n event.stopPropagation();\n instance.show();\n instance._selectMenuItem(event);\n return;\n }\n if (instance._isShown()) {\n // else is escape and we check if it is shown\n event.stopPropagation();\n instance.hide();\n getToggleButton.focus();\n }\n }\n}\n\n/**\n * Data API implementation\n */\n\nEventHandler.on(document, EVENT_KEYDOWN_DATA_API, SELECTOR_DATA_TOGGLE$3, Dropdown.dataApiKeydownHandler);\nEventHandler.on(document, EVENT_KEYDOWN_DATA_API, SELECTOR_MENU, Dropdown.dataApiKeydownHandler);\nEventHandler.on(document, EVENT_CLICK_DATA_API$3, Dropdown.clearMenus);\nEventHandler.on(document, EVENT_KEYUP_DATA_API, Dropdown.clearMenus);\nEventHandler.on(document, EVENT_CLICK_DATA_API$3, SELECTOR_DATA_TOGGLE$3, function (event) {\n event.preventDefault();\n Dropdown.getOrCreateInstance(this).toggle();\n});\n\n/**\n * jQuery\n */\n\ndefineJQueryPlugin(Dropdown);\n\n/**\n * --------------------------------------------------------------------------\n * Bootstrap util/backdrop.js\n * Licensed under MIT (https://github.com/twbs/bootstrap/blob/main/LICENSE)\n * --------------------------------------------------------------------------\n */\n\n\n/**\n * Constants\n */\n\nconst NAME$9 = 'backdrop';\nconst CLASS_NAME_FADE$4 = 'fade';\nconst CLASS_NAME_SHOW$5 = 'show';\nconst EVENT_MOUSEDOWN = `mousedown.bs.${NAME$9}`;\nconst Default$8 = {\n className: 'modal-backdrop',\n clickCallback: null,\n isAnimated: false,\n isVisible: true,\n // if false, we use the backdrop helper without adding any element to the dom\n rootElement: 'body' // give the choice to place backdrop under different elements\n};\n\nconst DefaultType$8 = {\n className: 'string',\n clickCallback: '(function|null)',\n isAnimated: 'boolean',\n isVisible: 'boolean',\n rootElement: '(element|string)'\n};\n\n/**\n * Class definition\n */\n\nclass Backdrop extends Config {\n constructor(config) {\n super();\n this._config = this._getConfig(config);\n this._isAppended = false;\n this._element = null;\n }\n\n // Getters\n static get Default() {\n return Default$8;\n }\n static get DefaultType() {\n return DefaultType$8;\n }\n static get NAME() {\n return NAME$9;\n }\n\n // Public\n show(callback) {\n if (!this._config.isVisible) {\n execute(callback);\n return;\n }\n this._append();\n const element = this._getElement();\n if (this._config.isAnimated) {\n reflow(element);\n }\n element.classList.add(CLASS_NAME_SHOW$5);\n this._emulateAnimation(() => {\n execute(callback);\n });\n }\n hide(callback) {\n if (!this._config.isVisible) {\n execute(callback);\n return;\n }\n this._getElement().classList.remove(CLASS_NAME_SHOW$5);\n this._emulateAnimation(() => {\n this.dispose();\n execute(callback);\n });\n }\n dispose() {\n if (!this._isAppended) {\n return;\n }\n EventHandler.off(this._element, EVENT_MOUSEDOWN);\n this._element.remove();\n this._isAppended = false;\n }\n\n // Private\n _getElement() {\n if (!this._element) {\n const backdrop = document.createElement('div');\n backdrop.className = this._config.className;\n if (this._config.isAnimated) {\n backdrop.classList.add(CLASS_NAME_FADE$4);\n }\n this._element = backdrop;\n }\n return this._element;\n }\n _configAfterMerge(config) {\n // use getElement() with the default \"body\" to get a fresh Element on each instantiation\n config.rootElement = getElement(config.rootElement);\n return config;\n }\n _append() {\n if (this._isAppended) {\n return;\n }\n const element = this._getElement();\n this._config.rootElement.append(element);\n EventHandler.on(element, EVENT_MOUSEDOWN, () => {\n execute(this._config.clickCallback);\n });\n this._isAppended = true;\n }\n _emulateAnimation(callback) {\n executeAfterTransition(callback, this._getElement(), this._config.isAnimated);\n }\n}\n\n/**\n * --------------------------------------------------------------------------\n * Bootstrap util/focustrap.js\n * Licensed under MIT (https://github.com/twbs/bootstrap/blob/main/LICENSE)\n * --------------------------------------------------------------------------\n */\n\n\n/**\n * Constants\n */\n\nconst NAME$8 = 'focustrap';\nconst DATA_KEY$5 = 'bs.focustrap';\nconst EVENT_KEY$5 = `.${DATA_KEY$5}`;\nconst EVENT_FOCUSIN$2 = `focusin${EVENT_KEY$5}`;\nconst EVENT_KEYDOWN_TAB = `keydown.tab${EVENT_KEY$5}`;\nconst TAB_KEY = 'Tab';\nconst TAB_NAV_FORWARD = 'forward';\nconst TAB_NAV_BACKWARD = 'backward';\nconst Default$7 = {\n autofocus: true,\n trapElement: null // The element to trap focus inside of\n};\n\nconst DefaultType$7 = {\n autofocus: 'boolean',\n trapElement: 'element'\n};\n\n/**\n * Class definition\n */\n\nclass FocusTrap extends Config {\n constructor(config) {\n super();\n this._config = this._getConfig(config);\n this._isActive = false;\n this._lastTabNavDirection = null;\n }\n\n // Getters\n static get Default() {\n return Default$7;\n }\n static get DefaultType() {\n return DefaultType$7;\n }\n static get NAME() {\n return NAME$8;\n }\n\n // Public\n activate() {\n if (this._isActive) {\n return;\n }\n if (this._config.autofocus) {\n this._config.trapElement.focus();\n }\n EventHandler.off(document, EVENT_KEY$5); // guard against infinite focus loop\n EventHandler.on(document, EVENT_FOCUSIN$2, event => this._handleFocusin(event));\n EventHandler.on(document, EVENT_KEYDOWN_TAB, event => this._handleKeydown(event));\n this._isActive = true;\n }\n deactivate() {\n if (!this._isActive) {\n return;\n }\n this._isActive = false;\n EventHandler.off(document, EVENT_KEY$5);\n }\n\n // Private\n _handleFocusin(event) {\n const {\n trapElement\n } = this._config;\n if (event.target === document || event.target === trapElement || trapElement.contains(event.target)) {\n return;\n }\n const elements = SelectorEngine.focusableChildren(trapElement);\n if (elements.length === 0) {\n trapElement.focus();\n } else if (this._lastTabNavDirection === TAB_NAV_BACKWARD) {\n elements[elements.length - 1].focus();\n } else {\n elements[0].focus();\n }\n }\n _handleKeydown(event) {\n if (event.key !== TAB_KEY) {\n return;\n }\n this._lastTabNavDirection = event.shiftKey ? TAB_NAV_BACKWARD : TAB_NAV_FORWARD;\n }\n}\n\n/**\n * --------------------------------------------------------------------------\n * Bootstrap util/scrollBar.js\n * Licensed under MIT (https://github.com/twbs/bootstrap/blob/main/LICENSE)\n * --------------------------------------------------------------------------\n */\n\n\n/**\n * Constants\n */\n\nconst SELECTOR_FIXED_CONTENT = '.fixed-top, .fixed-bottom, .is-fixed, .sticky-top';\nconst SELECTOR_STICKY_CONTENT = '.sticky-top';\nconst PROPERTY_PADDING = 'padding-right';\nconst PROPERTY_MARGIN = 'margin-right';\n\n/**\n * Class definition\n */\n\nclass ScrollBarHelper {\n constructor() {\n this._element = document.body;\n }\n\n // Public\n getWidth() {\n // https://developer.mozilla.org/en-US/docs/Web/API/Window/innerWidth#usage_notes\n const documentWidth = document.documentElement.clientWidth;\n return Math.abs(window.innerWidth - documentWidth);\n }\n hide() {\n const width = this.getWidth();\n this._disableOverFlow();\n // give padding to element to balance the hidden scrollbar width\n this._setElementAttributes(this._element, PROPERTY_PADDING, calculatedValue => calculatedValue + width);\n // trick: We adjust positive paddingRight and negative marginRight to sticky-top elements to keep showing fullwidth\n this._setElementAttributes(SELECTOR_FIXED_CONTENT, PROPERTY_PADDING, calculatedValue => calculatedValue + width);\n this._setElementAttributes(SELECTOR_STICKY_CONTENT, PROPERTY_MARGIN, calculatedValue => calculatedValue - width);\n }\n reset() {\n this._resetElementAttributes(this._element, 'overflow');\n this._resetElementAttributes(this._element, PROPERTY_PADDING);\n this._resetElementAttributes(SELECTOR_FIXED_CONTENT, PROPERTY_PADDING);\n this._resetElementAttributes(SELECTOR_STICKY_CONTENT, PROPERTY_MARGIN);\n }\n isOverflowing() {\n return this.getWidth() > 0;\n }\n\n // Private\n _disableOverFlow() {\n this._saveInitialAttribute(this._element, 'overflow');\n this._element.style.overflow = 'hidden';\n }\n _setElementAttributes(selector, styleProperty, callback) {\n const scrollbarWidth = this.getWidth();\n const manipulationCallBack = element => {\n if (element !== this._element && window.innerWidth > element.clientWidth + scrollbarWidth) {\n return;\n }\n this._saveInitialAttribute(element, styleProperty);\n const calculatedValue = window.getComputedStyle(element).getPropertyValue(styleProperty);\n element.style.setProperty(styleProperty, `${callback(Number.parseFloat(calculatedValue))}px`);\n };\n this._applyManipulationCallback(selector, manipulationCallBack);\n }\n _saveInitialAttribute(element, styleProperty) {\n const actualValue = element.style.getPropertyValue(styleProperty);\n if (actualValue) {\n Manipulator.setDataAttribute(element, styleProperty, actualValue);\n }\n }\n _resetElementAttributes(selector, styleProperty) {\n const manipulationCallBack = element => {\n const value = Manipulator.getDataAttribute(element, styleProperty);\n // We only want to remove the property if the value is `null`; the value can also be zero\n if (value === null) {\n element.style.removeProperty(styleProperty);\n return;\n }\n Manipulator.removeDataAttribute(element, styleProperty);\n element.style.setProperty(styleProperty, value);\n };\n this._applyManipulationCallback(selector, manipulationCallBack);\n }\n _applyManipulationCallback(selector, callBack) {\n if (isElement(selector)) {\n callBack(selector);\n return;\n }\n for (const sel of SelectorEngine.find(selector, this._element)) {\n callBack(sel);\n }\n }\n}\n\n/**\n * --------------------------------------------------------------------------\n * Bootstrap modal.js\n * Licensed under MIT (https://github.com/twbs/bootstrap/blob/main/LICENSE)\n * --------------------------------------------------------------------------\n */\n\n\n/**\n * Constants\n */\n\nconst NAME$7 = 'modal';\nconst DATA_KEY$4 = 'bs.modal';\nconst EVENT_KEY$4 = `.${DATA_KEY$4}`;\nconst DATA_API_KEY$2 = '.data-api';\nconst ESCAPE_KEY$1 = 'Escape';\nconst EVENT_HIDE$4 = `hide${EVENT_KEY$4}`;\nconst EVENT_HIDE_PREVENTED$1 = `hidePrevented${EVENT_KEY$4}`;\nconst EVENT_HIDDEN$4 = `hidden${EVENT_KEY$4}`;\nconst EVENT_SHOW$4 = `show${EVENT_KEY$4}`;\nconst EVENT_SHOWN$4 = `shown${EVENT_KEY$4}`;\nconst EVENT_RESIZE$1 = `resize${EVENT_KEY$4}`;\nconst EVENT_CLICK_DISMISS = `click.dismiss${EVENT_KEY$4}`;\nconst EVENT_MOUSEDOWN_DISMISS = `mousedown.dismiss${EVENT_KEY$4}`;\nconst EVENT_KEYDOWN_DISMISS$1 = `keydown.dismiss${EVENT_KEY$4}`;\nconst EVENT_CLICK_DATA_API$2 = `click${EVENT_KEY$4}${DATA_API_KEY$2}`;\nconst CLASS_NAME_OPEN = 'modal-open';\nconst CLASS_NAME_FADE$3 = 'fade';\nconst CLASS_NAME_SHOW$4 = 'show';\nconst CLASS_NAME_STATIC = 'modal-static';\nconst OPEN_SELECTOR$1 = '.modal.show';\nconst SELECTOR_DIALOG = '.modal-dialog';\nconst SELECTOR_MODAL_BODY = '.modal-body';\nconst SELECTOR_DATA_TOGGLE$2 = '[data-bs-toggle=\"modal\"]';\nconst Default$6 = {\n backdrop: true,\n focus: true,\n keyboard: true\n};\nconst DefaultType$6 = {\n backdrop: '(boolean|string)',\n focus: 'boolean',\n keyboard: 'boolean'\n};\n\n/**\n * Class definition\n */\n\nclass Modal extends BaseComponent {\n constructor(element, config) {\n super(element, config);\n this._dialog = SelectorEngine.findOne(SELECTOR_DIALOG, this._element);\n this._backdrop = this._initializeBackDrop();\n this._focustrap = this._initializeFocusTrap();\n this._isShown = false;\n this._isTransitioning = false;\n this._scrollBar = new ScrollBarHelper();\n this._addEventListeners();\n }\n\n // Getters\n static get Default() {\n return Default$6;\n }\n static get DefaultType() {\n return DefaultType$6;\n }\n static get NAME() {\n return NAME$7;\n }\n\n // Public\n toggle(relatedTarget) {\n return this._isShown ? this.hide() : this.show(relatedTarget);\n }\n show(relatedTarget) {\n if (this._isShown || this._isTransitioning) {\n return;\n }\n const showEvent = EventHandler.trigger(this._element, EVENT_SHOW$4, {\n relatedTarget\n });\n if (showEvent.defaultPrevented) {\n return;\n }\n this._isShown = true;\n this._isTransitioning = true;\n this._scrollBar.hide();\n document.body.classList.add(CLASS_NAME_OPEN);\n this._adjustDialog();\n this._backdrop.show(() => this._showElement(relatedTarget));\n }\n hide() {\n if (!this._isShown || this._isTransitioning) {\n return;\n }\n const hideEvent = EventHandler.trigger(this._element, EVENT_HIDE$4);\n if (hideEvent.defaultPrevented) {\n return;\n }\n this._isShown = false;\n this._isTransitioning = true;\n this._focustrap.deactivate();\n this._element.classList.remove(CLASS_NAME_SHOW$4);\n this._queueCallback(() => this._hideModal(), this._element, this._isAnimated());\n }\n dispose() {\n EventHandler.off(window, EVENT_KEY$4);\n EventHandler.off(this._dialog, EVENT_KEY$4);\n this._backdrop.dispose();\n this._focustrap.deactivate();\n super.dispose();\n }\n handleUpdate() {\n this._adjustDialog();\n }\n\n // Private\n _initializeBackDrop() {\n return new Backdrop({\n isVisible: Boolean(this._config.backdrop),\n // 'static' option will be translated to true, and booleans will keep their value,\n isAnimated: this._isAnimated()\n });\n }\n _initializeFocusTrap() {\n return new FocusTrap({\n trapElement: this._element\n });\n }\n _showElement(relatedTarget) {\n // try to append dynamic modal\n if (!document.body.contains(this._element)) {\n document.body.append(this._element);\n }\n this._element.style.display = 'block';\n this._element.removeAttribute('aria-hidden');\n this._element.setAttribute('aria-modal', true);\n this._element.setAttribute('role', 'dialog');\n this._element.scrollTop = 0;\n const modalBody = SelectorEngine.findOne(SELECTOR_MODAL_BODY, this._dialog);\n if (modalBody) {\n modalBody.scrollTop = 0;\n }\n reflow(this._element);\n this._element.classList.add(CLASS_NAME_SHOW$4);\n const transitionComplete = () => {\n if (this._config.focus) {\n this._focustrap.activate();\n }\n this._isTransitioning = false;\n EventHandler.trigger(this._element, EVENT_SHOWN$4, {\n relatedTarget\n });\n };\n this._queueCallback(transitionComplete, this._dialog, this._isAnimated());\n }\n _addEventListeners() {\n EventHandler.on(this._element, EVENT_KEYDOWN_DISMISS$1, event => {\n if (event.key !== ESCAPE_KEY$1) {\n return;\n }\n if (this._config.keyboard) {\n this.hide();\n return;\n }\n this._triggerBackdropTransition();\n });\n EventHandler.on(window, EVENT_RESIZE$1, () => {\n if (this._isShown && !this._isTransitioning) {\n this._adjustDialog();\n }\n });\n EventHandler.on(this._element, EVENT_MOUSEDOWN_DISMISS, event => {\n // a bad trick to segregate clicks that may start inside dialog but end outside, and avoid listen to scrollbar clicks\n EventHandler.one(this._element, EVENT_CLICK_DISMISS, event2 => {\n if (this._element !== event.target || this._element !== event2.target) {\n return;\n }\n if (this._config.backdrop === 'static') {\n this._triggerBackdropTransition();\n return;\n }\n if (this._config.backdrop) {\n this.hide();\n }\n });\n });\n }\n _hideModal() {\n this._element.style.display = 'none';\n this._element.setAttribute('aria-hidden', true);\n this._element.removeAttribute('aria-modal');\n this._element.removeAttribute('role');\n this._isTransitioning = false;\n this._backdrop.hide(() => {\n document.body.classList.remove(CLASS_NAME_OPEN);\n this._resetAdjustments();\n this._scrollBar.reset();\n EventHandler.trigger(this._element, EVENT_HIDDEN$4);\n });\n }\n _isAnimated() {\n return this._element.classList.contains(CLASS_NAME_FADE$3);\n }\n _triggerBackdropTransition() {\n const hideEvent = EventHandler.trigger(this._element, EVENT_HIDE_PREVENTED$1);\n if (hideEvent.defaultPrevented) {\n return;\n }\n const isModalOverflowing = this._element.scrollHeight > document.documentElement.clientHeight;\n const initialOverflowY = this._element.style.overflowY;\n // return if the following background transition hasn't yet completed\n if (initialOverflowY === 'hidden' || this._element.classList.contains(CLASS_NAME_STATIC)) {\n return;\n }\n if (!isModalOverflowing) {\n this._element.style.overflowY = 'hidden';\n }\n this._element.classList.add(CLASS_NAME_STATIC);\n this._queueCallback(() => {\n this._element.classList.remove(CLASS_NAME_STATIC);\n this._queueCallback(() => {\n this._element.style.overflowY = initialOverflowY;\n }, this._dialog);\n }, this._dialog);\n this._element.focus();\n }\n\n /**\n * The following methods are used to handle overflowing modals\n */\n\n _adjustDialog() {\n const isModalOverflowing = this._element.scrollHeight > document.documentElement.clientHeight;\n const scrollbarWidth = this._scrollBar.getWidth();\n const isBodyOverflowing = scrollbarWidth > 0;\n if (isBodyOverflowing && !isModalOverflowing) {\n const property = isRTL() ? 'paddingLeft' : 'paddingRight';\n this._element.style[property] = `${scrollbarWidth}px`;\n }\n if (!isBodyOverflowing && isModalOverflowing) {\n const property = isRTL() ? 'paddingRight' : 'paddingLeft';\n this._element.style[property] = `${scrollbarWidth}px`;\n }\n }\n _resetAdjustments() {\n this._element.style.paddingLeft = '';\n this._element.style.paddingRight = '';\n }\n\n // Static\n static jQueryInterface(config, relatedTarget) {\n return this.each(function () {\n const data = Modal.getOrCreateInstance(this, config);\n if (typeof config !== 'string') {\n return;\n }\n if (typeof data[config] === 'undefined') {\n throw new TypeError(`No method named \"${config}\"`);\n }\n data[config](relatedTarget);\n });\n }\n}\n\n/**\n * Data API implementation\n */\n\nEventHandler.on(document, EVENT_CLICK_DATA_API$2, SELECTOR_DATA_TOGGLE$2, function (event) {\n const target = SelectorEngine.getElementFromSelector(this);\n if (['A', 'AREA'].includes(this.tagName)) {\n event.preventDefault();\n }\n EventHandler.one(target, EVENT_SHOW$4, showEvent => {\n if (showEvent.defaultPrevented) {\n // only register focus restorer if modal will actually get shown\n return;\n }\n EventHandler.one(target, EVENT_HIDDEN$4, () => {\n if (isVisible(this)) {\n this.focus();\n }\n });\n });\n\n // avoid conflict when clicking modal toggler while another one is open\n const alreadyOpen = SelectorEngine.findOne(OPEN_SELECTOR$1);\n if (alreadyOpen) {\n Modal.getInstance(alreadyOpen).hide();\n }\n const data = Modal.getOrCreateInstance(target);\n data.toggle(this);\n});\nenableDismissTrigger(Modal);\n\n/**\n * jQuery\n */\n\ndefineJQueryPlugin(Modal);\n\n/**\n * --------------------------------------------------------------------------\n * Bootstrap offcanvas.js\n * Licensed under MIT (https://github.com/twbs/bootstrap/blob/main/LICENSE)\n * --------------------------------------------------------------------------\n */\n\n\n/**\n * Constants\n */\n\nconst NAME$6 = 'offcanvas';\nconst DATA_KEY$3 = 'bs.offcanvas';\nconst EVENT_KEY$3 = `.${DATA_KEY$3}`;\nconst DATA_API_KEY$1 = '.data-api';\nconst EVENT_LOAD_DATA_API$2 = `load${EVENT_KEY$3}${DATA_API_KEY$1}`;\nconst ESCAPE_KEY = 'Escape';\nconst CLASS_NAME_SHOW$3 = 'show';\nconst CLASS_NAME_SHOWING$1 = 'showing';\nconst CLASS_NAME_HIDING = 'hiding';\nconst CLASS_NAME_BACKDROP = 'offcanvas-backdrop';\nconst OPEN_SELECTOR = '.offcanvas.show';\nconst EVENT_SHOW$3 = `show${EVENT_KEY$3}`;\nconst EVENT_SHOWN$3 = `shown${EVENT_KEY$3}`;\nconst EVENT_HIDE$3 = `hide${EVENT_KEY$3}`;\nconst EVENT_HIDE_PREVENTED = `hidePrevented${EVENT_KEY$3}`;\nconst EVENT_HIDDEN$3 = `hidden${EVENT_KEY$3}`;\nconst EVENT_RESIZE = `resize${EVENT_KEY$3}`;\nconst EVENT_CLICK_DATA_API$1 = `click${EVENT_KEY$3}${DATA_API_KEY$1}`;\nconst EVENT_KEYDOWN_DISMISS = `keydown.dismiss${EVENT_KEY$3}`;\nconst SELECTOR_DATA_TOGGLE$1 = '[data-bs-toggle=\"offcanvas\"]';\nconst Default$5 = {\n backdrop: true,\n keyboard: true,\n scroll: false\n};\nconst DefaultType$5 = {\n backdrop: '(boolean|string)',\n keyboard: 'boolean',\n scroll: 'boolean'\n};\n\n/**\n * Class definition\n */\n\nclass Offcanvas extends BaseComponent {\n constructor(element, config) {\n super(element, config);\n this._isShown = false;\n this._backdrop = this._initializeBackDrop();\n this._focustrap = this._initializeFocusTrap();\n this._addEventListeners();\n }\n\n // Getters\n static get Default() {\n return Default$5;\n }\n static get DefaultType() {\n return DefaultType$5;\n }\n static get NAME() {\n return NAME$6;\n }\n\n // Public\n toggle(relatedTarget) {\n return this._isShown ? this.hide() : this.show(relatedTarget);\n }\n show(relatedTarget) {\n if (this._isShown) {\n return;\n }\n const showEvent = EventHandler.trigger(this._element, EVENT_SHOW$3, {\n relatedTarget\n });\n if (showEvent.defaultPrevented) {\n return;\n }\n this._isShown = true;\n this._backdrop.show();\n if (!this._config.scroll) {\n new ScrollBarHelper().hide();\n }\n this._element.setAttribute('aria-modal', true);\n this._element.setAttribute('role', 'dialog');\n this._element.classList.add(CLASS_NAME_SHOWING$1);\n const completeCallBack = () => {\n if (!this._config.scroll || this._config.backdrop) {\n this._focustrap.activate();\n }\n this._element.classList.add(CLASS_NAME_SHOW$3);\n this._element.classList.remove(CLASS_NAME_SHOWING$1);\n EventHandler.trigger(this._element, EVENT_SHOWN$3, {\n relatedTarget\n });\n };\n this._queueCallback(completeCallBack, this._element, true);\n }\n hide() {\n if (!this._isShown) {\n return;\n }\n const hideEvent = EventHandler.trigger(this._element, EVENT_HIDE$3);\n if (hideEvent.defaultPrevented) {\n return;\n }\n this._focustrap.deactivate();\n this._element.blur();\n this._isShown = false;\n this._element.classList.add(CLASS_NAME_HIDING);\n this._backdrop.hide();\n const completeCallback = () => {\n this._element.classList.remove(CLASS_NAME_SHOW$3, CLASS_NAME_HIDING);\n this._element.removeAttribute('aria-modal');\n this._element.removeAttribute('role');\n if (!this._config.scroll) {\n new ScrollBarHelper().reset();\n }\n EventHandler.trigger(this._element, EVENT_HIDDEN$3);\n };\n this._queueCallback(completeCallback, this._element, true);\n }\n dispose() {\n this._backdrop.dispose();\n this._focustrap.deactivate();\n super.dispose();\n }\n\n // Private\n _initializeBackDrop() {\n const clickCallback = () => {\n if (this._config.backdrop === 'static') {\n EventHandler.trigger(this._element, EVENT_HIDE_PREVENTED);\n return;\n }\n this.hide();\n };\n\n // 'static' option will be translated to true, and booleans will keep their value\n const isVisible = Boolean(this._config.backdrop);\n return new Backdrop({\n className: CLASS_NAME_BACKDROP,\n isVisible,\n isAnimated: true,\n rootElement: this._element.parentNode,\n clickCallback: isVisible ? clickCallback : null\n });\n }\n _initializeFocusTrap() {\n return new FocusTrap({\n trapElement: this._element\n });\n }\n _addEventListeners() {\n EventHandler.on(this._element, EVENT_KEYDOWN_DISMISS, event => {\n if (event.key !== ESCAPE_KEY) {\n return;\n }\n if (this._config.keyboard) {\n this.hide();\n return;\n }\n EventHandler.trigger(this._element, EVENT_HIDE_PREVENTED);\n });\n }\n\n // Static\n static jQueryInterface(config) {\n return this.each(function () {\n const data = Offcanvas.getOrCreateInstance(this, config);\n if (typeof config !== 'string') {\n return;\n }\n if (data[config] === undefined || config.startsWith('_') || config === 'constructor') {\n throw new TypeError(`No method named \"${config}\"`);\n }\n data[config](this);\n });\n }\n}\n\n/**\n * Data API implementation\n */\n\nEventHandler.on(document, EVENT_CLICK_DATA_API$1, SELECTOR_DATA_TOGGLE$1, function (event) {\n const target = SelectorEngine.getElementFromSelector(this);\n if (['A', 'AREA'].includes(this.tagName)) {\n event.preventDefault();\n }\n if (isDisabled(this)) {\n return;\n }\n EventHandler.one(target, EVENT_HIDDEN$3, () => {\n // focus on trigger when it is closed\n if (isVisible(this)) {\n this.focus();\n }\n });\n\n // avoid conflict when clicking a toggler of an offcanvas, while another is open\n const alreadyOpen = SelectorEngine.findOne(OPEN_SELECTOR);\n if (alreadyOpen && alreadyOpen !== target) {\n Offcanvas.getInstance(alreadyOpen).hide();\n }\n const data = Offcanvas.getOrCreateInstance(target);\n data.toggle(this);\n});\nEventHandler.on(window, EVENT_LOAD_DATA_API$2, () => {\n for (const selector of SelectorEngine.find(OPEN_SELECTOR)) {\n Offcanvas.getOrCreateInstance(selector).show();\n }\n});\nEventHandler.on(window, EVENT_RESIZE, () => {\n for (const element of SelectorEngine.find('[aria-modal][class*=show][class*=offcanvas-]')) {\n if (getComputedStyle(element).position !== 'fixed') {\n Offcanvas.getOrCreateInstance(element).hide();\n }\n }\n});\nenableDismissTrigger(Offcanvas);\n\n/**\n * jQuery\n */\n\ndefineJQueryPlugin(Offcanvas);\n\n/**\n * --------------------------------------------------------------------------\n * Bootstrap util/sanitizer.js\n * Licensed under MIT (https://github.com/twbs/bootstrap/blob/main/LICENSE)\n * --------------------------------------------------------------------------\n */\n\n// js-docs-start allow-list\nconst ARIA_ATTRIBUTE_PATTERN = /^aria-[\\w-]*$/i;\nconst DefaultAllowlist = {\n // Global attributes allowed on any supplied element below.\n '*': ['class', 'dir', 'id', 'lang', 'role', ARIA_ATTRIBUTE_PATTERN],\n a: ['target', 'href', 'title', 'rel'],\n area: [],\n b: [],\n br: [],\n col: [],\n code: [],\n div: [],\n em: [],\n hr: [],\n h1: [],\n h2: [],\n h3: [],\n h4: [],\n h5: [],\n h6: [],\n i: [],\n img: ['src', 'srcset', 'alt', 'title', 'width', 'height'],\n li: [],\n ol: [],\n p: [],\n pre: [],\n s: [],\n small: [],\n span: [],\n sub: [],\n sup: [],\n strong: [],\n u: [],\n ul: []\n};\n// js-docs-end allow-list\n\nconst uriAttributes = new Set(['background', 'cite', 'href', 'itemtype', 'longdesc', 'poster', 'src', 'xlink:href']);\n\n/**\n * A pattern that recognizes URLs that are safe wrt. XSS in URL navigation\n * contexts.\n *\n * Shout-out to Angular https://github.com/angular/angular/blob/15.2.8/packages/core/src/sanitization/url_sanitizer.ts#L38\n */\n// eslint-disable-next-line unicorn/better-regex\nconst SAFE_URL_PATTERN = /^(?!javascript:)(?:[a-z0-9+.-]+:|[^&:/?#]*(?:[/?#]|$))/i;\nconst allowedAttribute = (attribute, allowedAttributeList) => {\n const attributeName = attribute.nodeName.toLowerCase();\n if (allowedAttributeList.includes(attributeName)) {\n if (uriAttributes.has(attributeName)) {\n return Boolean(SAFE_URL_PATTERN.test(attribute.nodeValue));\n }\n return true;\n }\n\n // Check if a regular expression validates the attribute.\n return allowedAttributeList.filter(attributeRegex => attributeRegex instanceof RegExp).some(regex => regex.test(attributeName));\n};\nfunction sanitizeHtml(unsafeHtml, allowList, sanitizeFunction) {\n if (!unsafeHtml.length) {\n return unsafeHtml;\n }\n if (sanitizeFunction && typeof sanitizeFunction === 'function') {\n return sanitizeFunction(unsafeHtml);\n }\n const domParser = new window.DOMParser();\n const createdDocument = domParser.parseFromString(unsafeHtml, 'text/html');\n const elements = [].concat(...createdDocument.body.querySelectorAll('*'));\n for (const element of elements) {\n const elementName = element.nodeName.toLowerCase();\n if (!Object.keys(allowList).includes(elementName)) {\n element.remove();\n continue;\n }\n const attributeList = [].concat(...element.attributes);\n const allowedAttributes = [].concat(allowList['*'] || [], allowList[elementName] || []);\n for (const attribute of attributeList) {\n if (!allowedAttribute(attribute, allowedAttributes)) {\n element.removeAttribute(attribute.nodeName);\n }\n }\n }\n return createdDocument.body.innerHTML;\n}\n\n/**\n * --------------------------------------------------------------------------\n * Bootstrap util/template-factory.js\n * Licensed under MIT (https://github.com/twbs/bootstrap/blob/main/LICENSE)\n * --------------------------------------------------------------------------\n */\n\n\n/**\n * Constants\n */\n\nconst NAME$5 = 'TemplateFactory';\nconst Default$4 = {\n allowList: DefaultAllowlist,\n content: {},\n // { selector : text , selector2 : text2 , }\n extraClass: '',\n html: false,\n sanitize: true,\n sanitizeFn: null,\n template: '
'\n};\nconst DefaultType$4 = {\n allowList: 'object',\n content: 'object',\n extraClass: '(string|function)',\n html: 'boolean',\n sanitize: 'boolean',\n sanitizeFn: '(null|function)',\n template: 'string'\n};\nconst DefaultContentType = {\n entry: '(string|element|function|null)',\n selector: '(string|element)'\n};\n\n/**\n * Class definition\n */\n\nclass TemplateFactory extends Config {\n constructor(config) {\n super();\n this._config = this._getConfig(config);\n }\n\n // Getters\n static get Default() {\n return Default$4;\n }\n static get DefaultType() {\n return DefaultType$4;\n }\n static get NAME() {\n return NAME$5;\n }\n\n // Public\n getContent() {\n return Object.values(this._config.content).map(config => this._resolvePossibleFunction(config)).filter(Boolean);\n }\n hasContent() {\n return this.getContent().length > 0;\n }\n changeContent(content) {\n this._checkContent(content);\n this._config.content = {\n ...this._config.content,\n ...content\n };\n return this;\n }\n toHtml() {\n const templateWrapper = document.createElement('div');\n templateWrapper.innerHTML = this._maybeSanitize(this._config.template);\n for (const [selector, text] of Object.entries(this._config.content)) {\n this._setContent(templateWrapper, text, selector);\n }\n const template = templateWrapper.children[0];\n const extraClass = this._resolvePossibleFunction(this._config.extraClass);\n if (extraClass) {\n template.classList.add(...extraClass.split(' '));\n }\n return template;\n }\n\n // Private\n _typeCheckConfig(config) {\n super._typeCheckConfig(config);\n this._checkContent(config.content);\n }\n _checkContent(arg) {\n for (const [selector, content] of Object.entries(arg)) {\n super._typeCheckConfig({\n selector,\n entry: content\n }, DefaultContentType);\n }\n }\n _setContent(template, content, selector) {\n const templateElement = SelectorEngine.findOne(selector, template);\n if (!templateElement) {\n return;\n }\n content = this._resolvePossibleFunction(content);\n if (!content) {\n templateElement.remove();\n return;\n }\n if (isElement(content)) {\n this._putElementInTemplate(getElement(content), templateElement);\n return;\n }\n if (this._config.html) {\n templateElement.innerHTML = this._maybeSanitize(content);\n return;\n }\n templateElement.textContent = content;\n }\n _maybeSanitize(arg) {\n return this._config.sanitize ? sanitizeHtml(arg, this._config.allowList, this._config.sanitizeFn) : arg;\n }\n _resolvePossibleFunction(arg) {\n return execute(arg, [this]);\n }\n _putElementInTemplate(element, templateElement) {\n if (this._config.html) {\n templateElement.innerHTML = '';\n templateElement.append(element);\n return;\n }\n templateElement.textContent = element.textContent;\n }\n}\n\n/**\n * --------------------------------------------------------------------------\n * Bootstrap tooltip.js\n * Licensed under MIT (https://github.com/twbs/bootstrap/blob/main/LICENSE)\n * --------------------------------------------------------------------------\n */\n\n\n/**\n * Constants\n */\n\nconst NAME$4 = 'tooltip';\nconst DISALLOWED_ATTRIBUTES = new Set(['sanitize', 'allowList', 'sanitizeFn']);\nconst CLASS_NAME_FADE$2 = 'fade';\nconst CLASS_NAME_MODAL = 'modal';\nconst CLASS_NAME_SHOW$2 = 'show';\nconst SELECTOR_TOOLTIP_INNER = '.tooltip-inner';\nconst SELECTOR_MODAL = `.${CLASS_NAME_MODAL}`;\nconst EVENT_MODAL_HIDE = 'hide.bs.modal';\nconst TRIGGER_HOVER = 'hover';\nconst TRIGGER_FOCUS = 'focus';\nconst TRIGGER_CLICK = 'click';\nconst TRIGGER_MANUAL = 'manual';\nconst EVENT_HIDE$2 = 'hide';\nconst EVENT_HIDDEN$2 = 'hidden';\nconst EVENT_SHOW$2 = 'show';\nconst EVENT_SHOWN$2 = 'shown';\nconst EVENT_INSERTED = 'inserted';\nconst EVENT_CLICK$1 = 'click';\nconst EVENT_FOCUSIN$1 = 'focusin';\nconst EVENT_FOCUSOUT$1 = 'focusout';\nconst EVENT_MOUSEENTER = 'mouseenter';\nconst EVENT_MOUSELEAVE = 'mouseleave';\nconst AttachmentMap = {\n AUTO: 'auto',\n TOP: 'top',\n RIGHT: isRTL() ? 'left' : 'right',\n BOTTOM: 'bottom',\n LEFT: isRTL() ? 'right' : 'left'\n};\nconst Default$3 = {\n allowList: DefaultAllowlist,\n animation: true,\n boundary: 'clippingParents',\n container: false,\n customClass: '',\n delay: 0,\n fallbackPlacements: ['top', 'right', 'bottom', 'left'],\n html: false,\n offset: [0, 6],\n placement: 'top',\n popperConfig: null,\n sanitize: true,\n sanitizeFn: null,\n selector: false,\n template: '
' + '
' + '
' + '
',\n title: '',\n trigger: 'hover focus'\n};\nconst DefaultType$3 = {\n allowList: 'object',\n animation: 'boolean',\n boundary: '(string|element)',\n container: '(string|element|boolean)',\n customClass: '(string|function)',\n delay: '(number|object)',\n fallbackPlacements: 'array',\n html: 'boolean',\n offset: '(array|string|function)',\n placement: '(string|function)',\n popperConfig: '(null|object|function)',\n sanitize: 'boolean',\n sanitizeFn: '(null|function)',\n selector: '(string|boolean)',\n template: 'string',\n title: '(string|element|function)',\n trigger: 'string'\n};\n\n/**\n * Class definition\n */\n\nclass Tooltip extends BaseComponent {\n constructor(element, config) {\n if (typeof Popper === 'undefined') {\n throw new TypeError('Bootstrap\\'s tooltips require Popper (https://popper.js.org)');\n }\n super(element, config);\n\n // Private\n this._isEnabled = true;\n this._timeout = 0;\n this._isHovered = null;\n this._activeTrigger = {};\n this._popper = null;\n this._templateFactory = null;\n this._newContent = null;\n\n // Protected\n this.tip = null;\n this._setListeners();\n if (!this._config.selector) {\n this._fixTitle();\n }\n }\n\n // Getters\n static get Default() {\n return Default$3;\n }\n static get DefaultType() {\n return DefaultType$3;\n }\n static get NAME() {\n return NAME$4;\n }\n\n // Public\n enable() {\n this._isEnabled = true;\n }\n disable() {\n this._isEnabled = false;\n }\n toggleEnabled() {\n this._isEnabled = !this._isEnabled;\n }\n toggle() {\n if (!this._isEnabled) {\n return;\n }\n this._activeTrigger.click = !this._activeTrigger.click;\n if (this._isShown()) {\n this._leave();\n return;\n }\n this._enter();\n }\n dispose() {\n clearTimeout(this._timeout);\n EventHandler.off(this._element.closest(SELECTOR_MODAL), EVENT_MODAL_HIDE, this._hideModalHandler);\n if (this._element.getAttribute('data-bs-original-title')) {\n this._element.setAttribute('title', this._element.getAttribute('data-bs-original-title'));\n }\n this._disposePopper();\n super.dispose();\n }\n show() {\n if (this._element.style.display === 'none') {\n throw new Error('Please use show on visible elements');\n }\n if (!(this._isWithContent() && this._isEnabled)) {\n return;\n }\n const showEvent = EventHandler.trigger(this._element, this.constructor.eventName(EVENT_SHOW$2));\n const shadowRoot = findShadowRoot(this._element);\n const isInTheDom = (shadowRoot || this._element.ownerDocument.documentElement).contains(this._element);\n if (showEvent.defaultPrevented || !isInTheDom) {\n return;\n }\n\n // TODO: v6 remove this or make it optional\n this._disposePopper();\n const tip = this._getTipElement();\n this._element.setAttribute('aria-describedby', tip.getAttribute('id'));\n const {\n container\n } = this._config;\n if (!this._element.ownerDocument.documentElement.contains(this.tip)) {\n container.append(tip);\n EventHandler.trigger(this._element, this.constructor.eventName(EVENT_INSERTED));\n }\n this._popper = this._createPopper(tip);\n tip.classList.add(CLASS_NAME_SHOW$2);\n\n // If this is a touch-enabled device we add extra\n // empty mouseover listeners to the body's immediate children;\n // only needed because of broken event delegation on iOS\n // https://www.quirksmode.org/blog/archives/2014/02/mouse_event_bub.html\n if ('ontouchstart' in document.documentElement) {\n for (const element of [].concat(...document.body.children)) {\n EventHandler.on(element, 'mouseover', noop);\n }\n }\n const complete = () => {\n EventHandler.trigger(this._element, this.constructor.eventName(EVENT_SHOWN$2));\n if (this._isHovered === false) {\n this._leave();\n }\n this._isHovered = false;\n };\n this._queueCallback(complete, this.tip, this._isAnimated());\n }\n hide() {\n if (!this._isShown()) {\n return;\n }\n const hideEvent = EventHandler.trigger(this._element, this.constructor.eventName(EVENT_HIDE$2));\n if (hideEvent.defaultPrevented) {\n return;\n }\n const tip = this._getTipElement();\n tip.classList.remove(CLASS_NAME_SHOW$2);\n\n // If this is a touch-enabled device we remove the extra\n // empty mouseover listeners we added for iOS support\n if ('ontouchstart' in document.documentElement) {\n for (const element of [].concat(...document.body.children)) {\n EventHandler.off(element, 'mouseover', noop);\n }\n }\n this._activeTrigger[TRIGGER_CLICK] = false;\n this._activeTrigger[TRIGGER_FOCUS] = false;\n this._activeTrigger[TRIGGER_HOVER] = false;\n this._isHovered = null; // it is a trick to support manual triggering\n\n const complete = () => {\n if (this._isWithActiveTrigger()) {\n return;\n }\n if (!this._isHovered) {\n this._disposePopper();\n }\n this._element.removeAttribute('aria-describedby');\n EventHandler.trigger(this._element, this.constructor.eventName(EVENT_HIDDEN$2));\n };\n this._queueCallback(complete, this.tip, this._isAnimated());\n }\n update() {\n if (this._popper) {\n this._popper.update();\n }\n }\n\n // Protected\n _isWithContent() {\n return Boolean(this._getTitle());\n }\n _getTipElement() {\n if (!this.tip) {\n this.tip = this._createTipElement(this._newContent || this._getContentForTemplate());\n }\n return this.tip;\n }\n _createTipElement(content) {\n const tip = this._getTemplateFactory(content).toHtml();\n\n // TODO: remove this check in v6\n if (!tip) {\n return null;\n }\n tip.classList.remove(CLASS_NAME_FADE$2, CLASS_NAME_SHOW$2);\n // TODO: v6 the following can be achieved with CSS only\n tip.classList.add(`bs-${this.constructor.NAME}-auto`);\n const tipId = getUID(this.constructor.NAME).toString();\n tip.setAttribute('id', tipId);\n if (this._isAnimated()) {\n tip.classList.add(CLASS_NAME_FADE$2);\n }\n return tip;\n }\n setContent(content) {\n this._newContent = content;\n if (this._isShown()) {\n this._disposePopper();\n this.show();\n }\n }\n _getTemplateFactory(content) {\n if (this._templateFactory) {\n this._templateFactory.changeContent(content);\n } else {\n this._templateFactory = new TemplateFactory({\n ...this._config,\n // the `content` var has to be after `this._config`\n // to override config.content in case of popover\n content,\n extraClass: this._resolvePossibleFunction(this._config.customClass)\n });\n }\n return this._templateFactory;\n }\n _getContentForTemplate() {\n return {\n [SELECTOR_TOOLTIP_INNER]: this._getTitle()\n };\n }\n _getTitle() {\n return this._resolvePossibleFunction(this._config.title) || this._element.getAttribute('data-bs-original-title');\n }\n\n // Private\n _initializeOnDelegatedTarget(event) {\n return this.constructor.getOrCreateInstance(event.delegateTarget, this._getDelegateConfig());\n }\n _isAnimated() {\n return this._config.animation || this.tip && this.tip.classList.contains(CLASS_NAME_FADE$2);\n }\n _isShown() {\n return this.tip && this.tip.classList.contains(CLASS_NAME_SHOW$2);\n }\n _createPopper(tip) {\n const placement = execute(this._config.placement, [this, tip, this._element]);\n const attachment = AttachmentMap[placement.toUpperCase()];\n return Popper.createPopper(this._element, tip, this._getPopperConfig(attachment));\n }\n _getOffset() {\n const {\n offset\n } = this._config;\n if (typeof offset === 'string') {\n return offset.split(',').map(value => Number.parseInt(value, 10));\n }\n if (typeof offset === 'function') {\n return popperData => offset(popperData, this._element);\n }\n return offset;\n }\n _resolvePossibleFunction(arg) {\n return execute(arg, [this._element]);\n }\n _getPopperConfig(attachment) {\n const defaultBsPopperConfig = {\n placement: attachment,\n modifiers: [{\n name: 'flip',\n options: {\n fallbackPlacements: this._config.fallbackPlacements\n }\n }, {\n name: 'offset',\n options: {\n offset: this._getOffset()\n }\n }, {\n name: 'preventOverflow',\n options: {\n boundary: this._config.boundary\n }\n }, {\n name: 'arrow',\n options: {\n element: `.${this.constructor.NAME}-arrow`\n }\n }, {\n name: 'preSetPlacement',\n enabled: true,\n phase: 'beforeMain',\n fn: data => {\n // Pre-set Popper's placement attribute in order to read the arrow sizes properly.\n // Otherwise, Popper mixes up the width and height dimensions since the initial arrow style is for top placement\n this._getTipElement().setAttribute('data-popper-placement', data.state.placement);\n }\n }]\n };\n return {\n ...defaultBsPopperConfig,\n ...execute(this._config.popperConfig, [defaultBsPopperConfig])\n };\n }\n _setListeners() {\n const triggers = this._config.trigger.split(' ');\n for (const trigger of triggers) {\n if (trigger === 'click') {\n EventHandler.on(this._element, this.constructor.eventName(EVENT_CLICK$1), this._config.selector, event => {\n const context = this._initializeOnDelegatedTarget(event);\n context.toggle();\n });\n } else if (trigger !== TRIGGER_MANUAL) {\n const eventIn = trigger === TRIGGER_HOVER ? this.constructor.eventName(EVENT_MOUSEENTER) : this.constructor.eventName(EVENT_FOCUSIN$1);\n const eventOut = trigger === TRIGGER_HOVER ? this.constructor.eventName(EVENT_MOUSELEAVE) : this.constructor.eventName(EVENT_FOCUSOUT$1);\n EventHandler.on(this._element, eventIn, this._config.selector, event => {\n const context = this._initializeOnDelegatedTarget(event);\n context._activeTrigger[event.type === 'focusin' ? TRIGGER_FOCUS : TRIGGER_HOVER] = true;\n context._enter();\n });\n EventHandler.on(this._element, eventOut, this._config.selector, event => {\n const context = this._initializeOnDelegatedTarget(event);\n context._activeTrigger[event.type === 'focusout' ? TRIGGER_FOCUS : TRIGGER_HOVER] = context._element.contains(event.relatedTarget);\n context._leave();\n });\n }\n }\n this._hideModalHandler = () => {\n if (this._element) {\n this.hide();\n }\n };\n EventHandler.on(this._element.closest(SELECTOR_MODAL), EVENT_MODAL_HIDE, this._hideModalHandler);\n }\n _fixTitle() {\n const title = this._element.getAttribute('title');\n if (!title) {\n return;\n }\n if (!this._element.getAttribute('aria-label') && !this._element.textContent.trim()) {\n this._element.setAttribute('aria-label', title);\n }\n this._element.setAttribute('data-bs-original-title', title); // DO NOT USE IT. Is only for backwards compatibility\n this._element.removeAttribute('title');\n }\n _enter() {\n if (this._isShown() || this._isHovered) {\n this._isHovered = true;\n return;\n }\n this._isHovered = true;\n this._setTimeout(() => {\n if (this._isHovered) {\n this.show();\n }\n }, this._config.delay.show);\n }\n _leave() {\n if (this._isWithActiveTrigger()) {\n return;\n }\n this._isHovered = false;\n this._setTimeout(() => {\n if (!this._isHovered) {\n this.hide();\n }\n }, this._config.delay.hide);\n }\n _setTimeout(handler, timeout) {\n clearTimeout(this._timeout);\n this._timeout = setTimeout(handler, timeout);\n }\n _isWithActiveTrigger() {\n return Object.values(this._activeTrigger).includes(true);\n }\n _getConfig(config) {\n const dataAttributes = Manipulator.getDataAttributes(this._element);\n for (const dataAttribute of Object.keys(dataAttributes)) {\n if (DISALLOWED_ATTRIBUTES.has(dataAttribute)) {\n delete dataAttributes[dataAttribute];\n }\n }\n config = {\n ...dataAttributes,\n ...(typeof config === 'object' && config ? config : {})\n };\n config = this._mergeConfigObj(config);\n config = this._configAfterMerge(config);\n this._typeCheckConfig(config);\n return config;\n }\n _configAfterMerge(config) {\n config.container = config.container === false ? document.body : getElement(config.container);\n if (typeof config.delay === 'number') {\n config.delay = {\n show: config.delay,\n hide: config.delay\n };\n }\n if (typeof config.title === 'number') {\n config.title = config.title.toString();\n }\n if (typeof config.content === 'number') {\n config.content = config.content.toString();\n }\n return config;\n }\n _getDelegateConfig() {\n const config = {};\n for (const [key, value] of Object.entries(this._config)) {\n if (this.constructor.Default[key] !== value) {\n config[key] = value;\n }\n }\n config.selector = false;\n config.trigger = 'manual';\n\n // In the future can be replaced with:\n // const keysWithDifferentValues = Object.entries(this._config).filter(entry => this.constructor.Default[entry[0]] !== this._config[entry[0]])\n // `Object.fromEntries(keysWithDifferentValues)`\n return config;\n }\n _disposePopper() {\n if (this._popper) {\n this._popper.destroy();\n this._popper = null;\n }\n if (this.tip) {\n this.tip.remove();\n this.tip = null;\n }\n }\n\n // Static\n static jQueryInterface(config) {\n return this.each(function () {\n const data = Tooltip.getOrCreateInstance(this, config);\n if (typeof config !== 'string') {\n return;\n }\n if (typeof data[config] === 'undefined') {\n throw new TypeError(`No method named \"${config}\"`);\n }\n data[config]();\n });\n }\n}\n\n/**\n * jQuery\n */\n\ndefineJQueryPlugin(Tooltip);\n\n/**\n * --------------------------------------------------------------------------\n * Bootstrap popover.js\n * Licensed under MIT (https://github.com/twbs/bootstrap/blob/main/LICENSE)\n * --------------------------------------------------------------------------\n */\n\n\n/**\n * Constants\n */\n\nconst NAME$3 = 'popover';\nconst SELECTOR_TITLE = '.popover-header';\nconst SELECTOR_CONTENT = '.popover-body';\nconst Default$2 = {\n ...Tooltip.Default,\n content: '',\n offset: [0, 8],\n placement: 'right',\n template: '
' + '
' + '

' + '
' + '
',\n trigger: 'click'\n};\nconst DefaultType$2 = {\n ...Tooltip.DefaultType,\n content: '(null|string|element|function)'\n};\n\n/**\n * Class definition\n */\n\nclass Popover extends Tooltip {\n // Getters\n static get Default() {\n return Default$2;\n }\n static get DefaultType() {\n return DefaultType$2;\n }\n static get NAME() {\n return NAME$3;\n }\n\n // Overrides\n _isWithContent() {\n return this._getTitle() || this._getContent();\n }\n\n // Private\n _getContentForTemplate() {\n return {\n [SELECTOR_TITLE]: this._getTitle(),\n [SELECTOR_CONTENT]: this._getContent()\n };\n }\n _getContent() {\n return this._resolvePossibleFunction(this._config.content);\n }\n\n // Static\n static jQueryInterface(config) {\n return this.each(function () {\n const data = Popover.getOrCreateInstance(this, config);\n if (typeof config !== 'string') {\n return;\n }\n if (typeof data[config] === 'undefined') {\n throw new TypeError(`No method named \"${config}\"`);\n }\n data[config]();\n });\n }\n}\n\n/**\n * jQuery\n */\n\ndefineJQueryPlugin(Popover);\n\n/**\n * --------------------------------------------------------------------------\n * Bootstrap scrollspy.js\n * Licensed under MIT (https://github.com/twbs/bootstrap/blob/main/LICENSE)\n * --------------------------------------------------------------------------\n */\n\n\n/**\n * Constants\n */\n\nconst NAME$2 = 'scrollspy';\nconst DATA_KEY$2 = 'bs.scrollspy';\nconst EVENT_KEY$2 = `.${DATA_KEY$2}`;\nconst DATA_API_KEY = '.data-api';\nconst EVENT_ACTIVATE = `activate${EVENT_KEY$2}`;\nconst EVENT_CLICK = `click${EVENT_KEY$2}`;\nconst EVENT_LOAD_DATA_API$1 = `load${EVENT_KEY$2}${DATA_API_KEY}`;\nconst CLASS_NAME_DROPDOWN_ITEM = 'dropdown-item';\nconst CLASS_NAME_ACTIVE$1 = 'active';\nconst SELECTOR_DATA_SPY = '[data-bs-spy=\"scroll\"]';\nconst SELECTOR_TARGET_LINKS = '[href]';\nconst SELECTOR_NAV_LIST_GROUP = '.nav, .list-group';\nconst SELECTOR_NAV_LINKS = '.nav-link';\nconst SELECTOR_NAV_ITEMS = '.nav-item';\nconst SELECTOR_LIST_ITEMS = '.list-group-item';\nconst SELECTOR_LINK_ITEMS = `${SELECTOR_NAV_LINKS}, ${SELECTOR_NAV_ITEMS} > ${SELECTOR_NAV_LINKS}, ${SELECTOR_LIST_ITEMS}`;\nconst SELECTOR_DROPDOWN = '.dropdown';\nconst SELECTOR_DROPDOWN_TOGGLE$1 = '.dropdown-toggle';\nconst Default$1 = {\n offset: null,\n // TODO: v6 @deprecated, keep it for backwards compatibility reasons\n rootMargin: '0px 0px -25%',\n smoothScroll: false,\n target: null,\n threshold: [0.1, 0.5, 1]\n};\nconst DefaultType$1 = {\n offset: '(number|null)',\n // TODO v6 @deprecated, keep it for backwards compatibility reasons\n rootMargin: 'string',\n smoothScroll: 'boolean',\n target: 'element',\n threshold: 'array'\n};\n\n/**\n * Class definition\n */\n\nclass ScrollSpy extends BaseComponent {\n constructor(element, config) {\n super(element, config);\n\n // this._element is the observablesContainer and config.target the menu links wrapper\n this._targetLinks = new Map();\n this._observableSections = new Map();\n this._rootElement = getComputedStyle(this._element).overflowY === 'visible' ? null : this._element;\n this._activeTarget = null;\n this._observer = null;\n this._previousScrollData = {\n visibleEntryTop: 0,\n parentScrollTop: 0\n };\n this.refresh(); // initialize\n }\n\n // Getters\n static get Default() {\n return Default$1;\n }\n static get DefaultType() {\n return DefaultType$1;\n }\n static get NAME() {\n return NAME$2;\n }\n\n // Public\n refresh() {\n this._initializeTargetsAndObservables();\n this._maybeEnableSmoothScroll();\n if (this._observer) {\n this._observer.disconnect();\n } else {\n this._observer = this._getNewObserver();\n }\n for (const section of this._observableSections.values()) {\n this._observer.observe(section);\n }\n }\n dispose() {\n this._observer.disconnect();\n super.dispose();\n }\n\n // Private\n _configAfterMerge(config) {\n // TODO: on v6 target should be given explicitly & remove the {target: 'ss-target'} case\n config.target = getElement(config.target) || document.body;\n\n // TODO: v6 Only for backwards compatibility reasons. Use rootMargin only\n config.rootMargin = config.offset ? `${config.offset}px 0px -30%` : config.rootMargin;\n if (typeof config.threshold === 'string') {\n config.threshold = config.threshold.split(',').map(value => Number.parseFloat(value));\n }\n return config;\n }\n _maybeEnableSmoothScroll() {\n if (!this._config.smoothScroll) {\n return;\n }\n\n // unregister any previous listeners\n EventHandler.off(this._config.target, EVENT_CLICK);\n EventHandler.on(this._config.target, EVENT_CLICK, SELECTOR_TARGET_LINKS, event => {\n const observableSection = this._observableSections.get(event.target.hash);\n if (observableSection) {\n event.preventDefault();\n const root = this._rootElement || window;\n const height = observableSection.offsetTop - this._element.offsetTop;\n if (root.scrollTo) {\n root.scrollTo({\n top: height,\n behavior: 'smooth'\n });\n return;\n }\n\n // Chrome 60 doesn't support `scrollTo`\n root.scrollTop = height;\n }\n });\n }\n _getNewObserver() {\n const options = {\n root: this._rootElement,\n threshold: this._config.threshold,\n rootMargin: this._config.rootMargin\n };\n return new IntersectionObserver(entries => this._observerCallback(entries), options);\n }\n\n // The logic of selection\n _observerCallback(entries) {\n const targetElement = entry => this._targetLinks.get(`#${entry.target.id}`);\n const activate = entry => {\n this._previousScrollData.visibleEntryTop = entry.target.offsetTop;\n this._process(targetElement(entry));\n };\n const parentScrollTop = (this._rootElement || document.documentElement).scrollTop;\n const userScrollsDown = parentScrollTop >= this._previousScrollData.parentScrollTop;\n this._previousScrollData.parentScrollTop = parentScrollTop;\n for (const entry of entries) {\n if (!entry.isIntersecting) {\n this._activeTarget = null;\n this._clearActiveClass(targetElement(entry));\n continue;\n }\n const entryIsLowerThanPrevious = entry.target.offsetTop >= this._previousScrollData.visibleEntryTop;\n // if we are scrolling down, pick the bigger offsetTop\n if (userScrollsDown && entryIsLowerThanPrevious) {\n activate(entry);\n // if parent isn't scrolled, let's keep the first visible item, breaking the iteration\n if (!parentScrollTop) {\n return;\n }\n continue;\n }\n\n // if we are scrolling up, pick the smallest offsetTop\n if (!userScrollsDown && !entryIsLowerThanPrevious) {\n activate(entry);\n }\n }\n }\n _initializeTargetsAndObservables() {\n this._targetLinks = new Map();\n this._observableSections = new Map();\n const targetLinks = SelectorEngine.find(SELECTOR_TARGET_LINKS, this._config.target);\n for (const anchor of targetLinks) {\n // ensure that the anchor has an id and is not disabled\n if (!anchor.hash || isDisabled(anchor)) {\n continue;\n }\n const observableSection = SelectorEngine.findOne(decodeURI(anchor.hash), this._element);\n\n // ensure that the observableSection exists & is visible\n if (isVisible(observableSection)) {\n this._targetLinks.set(decodeURI(anchor.hash), anchor);\n this._observableSections.set(anchor.hash, observableSection);\n }\n }\n }\n _process(target) {\n if (this._activeTarget === target) {\n return;\n }\n this._clearActiveClass(this._config.target);\n this._activeTarget = target;\n target.classList.add(CLASS_NAME_ACTIVE$1);\n this._activateParents(target);\n EventHandler.trigger(this._element, EVENT_ACTIVATE, {\n relatedTarget: target\n });\n }\n _activateParents(target) {\n // Activate dropdown parents\n if (target.classList.contains(CLASS_NAME_DROPDOWN_ITEM)) {\n SelectorEngine.findOne(SELECTOR_DROPDOWN_TOGGLE$1, target.closest(SELECTOR_DROPDOWN)).classList.add(CLASS_NAME_ACTIVE$1);\n return;\n }\n for (const listGroup of SelectorEngine.parents(target, SELECTOR_NAV_LIST_GROUP)) {\n // Set triggered links parents as active\n // With both