nonlinear-equations

README.md

@@ -7,9 +7,10 @@
 
 | | Matlab | Python | C++ |
 | --- | --- | --- | --- |
-| Bisection method| :octocat: | | |
-| Newton-Raphson method | :octocat: | | |
-| Secant method | :octocat: | | |
+| Bisection method| :octocat: | :octocat: | |
+| Newton-Raphson method | :octocat: | :octocat: | |
+| Secant method | :octocat: | :octocat: | |
+| False Position method | | :octocat: | |
 
 #### Gaussian methods
 

python/nonlinear_equations/bisection_medthod.py

@@ -0,0 +1,40 @@
+# Bisection Method
+
+from __future__ import division, print_function
+from numpy import abs, cos, sin, exp, sqrt, array, append, ceil, log2, arange, linspace
+import matplotlib.pyplot as plt
+
+def bisection(fun, a, b, c, valerr=100, xtol=1e-6, ftol=1e-06, verbose=False):
+# def bisection(fun, a, b, c, valerr=100, nmax=5000, ftol=1e-06, verbose=False):
+    if fun(a) * fun(b) > 0:
+        c = None
+        msg = "The function should have a sign change in the interval."
+    else:
+        nmax = int(ceil(log2((b - a)/xtol)))
+        ax = array([])
+        acont = array([])
+        avalerr = array([])
+        for cont in range(nmax):
+
+            ax = append(ax,c)
+            acont = append(acont,cont)
+            avalerr = append(avalerr,valerr)
+
+            if verbose:
+                print("n: {}, \tx: {}, \terr: {}%".format(cont, c,valerr))
+
+            valp = c
+            c = 0.5*(a + b)
+            valf = c
+            valerr = abs((valf - valp)/valf) * 100
+
+            if abs(fun(c)) < ftol:
+                msg = "Root found with desired accuracy."
+                break
+            elif fun(a) * fun(c) < 0:
+                b = c
+            elif fun(b) * fun(c) < 0:
+                a = c
+            msg = "Maximum number of iterations reached."
+    return ax, avalerr, acont, msg
+

python/nonlinear_equations/false_position_method.py

@@ -0,0 +1,41 @@
+# False Position Method
+
+from __future__ import division, print_function
+from numpy import abs, cos, sin, exp, sqrt, array, append, ceil, log2, arange, linspace
+import matplotlib.pyplot as plt
+
+def regula_falsi(fun, a, b, c, valerr=100, niter=5000, ftol=1e-06, verbose=False):
+    if fun(a) * fun(b) > 0:
+        c = None
+        msg = "The function should have a sign change in the interval."
+    else:
+        ax = array([])
+        acont = array([])
+        avalerr = array([])
+        for cont in range(niter):
+
+            ax = append(ax,c)
+            acont = append(acont,cont)
+            avalerr = append(avalerr,valerr)
+
+            qa = fun(a)
+            qb = fun(b)
+            valp = c
+            c = (a*qb - b*qa)/(qb - qa)
+            qc = fun(c)
+            valf = c
+            valerr = abs((valf - valp)/valf) * 100
+
+            if verbose:
+                print("n: {}, \tx: {}, \terr: {}%".format(cont, c,valerr))
+
+            msg = "Maximum number of iterations reached."
+
+            if abs(qc) < ftol:
+                msg = "Root found with desired accuracy."
+                break
+            elif qa * qc < 0:
+                b = c
+            elif qb * qc < 0:
+                a = c
+    return ax, avalerr, acont, msg

python/nonlinear_equations/newton-raphson_method.py

@@ -0,0 +1,33 @@
+# Newton-Raphson Method
+
+from __future__ import division, print_function
+from numpy import abs, cos, sin, exp, sqrt, array, append, ceil, log2, arange, linspace
+import matplotlib.pyplot as plt
+
+def newton(fun, grad, x, valerr=100, niter=5000, ftol=1e-06, verbose=False):
+    msg = "Maximum number of iterations reached."
+    ax = array([])
+    acont = array([])
+    avalerr = array([])
+    for cont in range(niter):
+        if abs(grad(x)) < ftol:
+            x = None
+            msg = "Derivative near to zero."
+            break
+
+        if verbose:
+            print("n: {}, \tx: {}, \terr: {}%".format(cont, x,valerr))
+
+        ax = append(ax,x)
+        acont = append(acont,cont)
+        avalerr = append(avalerr,valerr)
+
+        valp = x
+        x = x - fun(x)/grad(x)
+        valf = x
+        valerr = abs((valf - valp)/valf) * 100
+
+        if abs(fun(x)) < ftol:
+            msg = "Root found with desired accuracy."
+            break
+    return ax, avalerr, acont, msg

python/nonlinear_equations/secant_method.py

@@ -0,0 +1,29 @@
+# Secant Method
+
+from __future__ import division, print_function
+from numpy import abs, cos, sin, exp, sqrt, array, append, ceil, log2, arange, linspace
+import matplotlib.pyplot as plt
+
+def secant(fun, xp, x, valerr=100, niter=5000, ftol=1e-06, verbose=False):
+    msg = "Maximum number of iterations reached."
+    ax = array([])
+    acont = array([])
+    avalerr = array([])
+    for cont in range(niter):
+
+        if verbose:
+            print("n: {}, \tx: {}, \terr: {}%".format(cont, x,valerr))
+
+        ax = append(ax,x)
+        acont = append(acont,cont)
+        avalerr = append(avalerr,valerr)
+
+        valp = x
+        x = x - ((x - xp)/(fun(x)-fun(xp)))*fun(x)
+        valf = x
+        valerr = abs((valf - valp)/valf) * 100
+
+        if abs(fun(x)) < ftol:
+            msg = "Root found with desired accuracy."
+            break
+    return ax, avalerr, acont, msg