3-Ecosystem.ipynb

{
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   "source": [
    "# Julia ecosystems in scientific computing\n",
    "\n",
    "There are many Julia organizations about seemingly every scientific area. Some examples:\n",
    "\n",
    "- Astrophysics: [JuliaAstro](https://juliaastro.github.io/), [JuliaSpace](https://github.com/JuliaSpace)\n",
    "- Bio/Chemistry: [JuliaBio](https://biojulia.net/), [Molecular simulations](https://github.com/JuliaMolSim)\n",
    "- Complex systems, nonlinear dynamics: [JuliaDynamics](https://juliadynamics.github.io/JuliaDynamics/)\n",
    "- Differential equations and scientific machine learning: [SciML](https://sciml.ai/)\n",
    "- Solid state: [QuantumOptics](https://qojulia.org/), [JuliaPhysics](https://github.com/JuliaPhysics)\n",
    "- Economics: [QuantEcon](https://julia.quantecon.org/), [JuliaQuant](https://github.com/JuliaQuant)\n",
    "- Geosciences/Climate: [JuliaGeo](https://github.com/JuliaGeo), [JuliaEarth](https://github.com/JuliaEarth), [JuliaClimate](https://github.com/JuliaClimate).\n",
    "\n",
    "among many many others, including several mathematics-oriented organizations such as optimization, etc.\n",
    "\n",
    "In this session we will (**very briefly**) overview some powerful Julia packages I found useful for *my own work* and hopefully you will too. Even if the packages relevant for me are not useful in your field, it is still good practice to solve the exercises, to \"learn how to learn Julia packages\". \n",
    "\n",
    "**This session does not attempt to do any _scientific_ teaching. It is likely that some of the things that I'll mention you won't know what they mean. That's okay, because here we are just looking at how some packages work.**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\u001b[32m\u001b[1m  Activating\u001b[22m\u001b[39m project at `c:\\Users\\datse\\OneDrive - University of Exeter\\Teaching\\Zero2Hero-JuliaWorkshop`\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\u001b[32m\u001b[1mStatus\u001b[22m\u001b[39m `C:\\Users\\datse\\OneDrive - University of Exeter\\Teaching\\Zero2Hero-JuliaWorkshop\\Project.toml`\n",
      "  \u001b[90m[6e4b80f9] \u001b[39mBenchmarkTools v1.3.2\n",
      "  \u001b[90m[a134a8b2] \u001b[39mBlackBoxOptim v0.6.2\n",
      "\u001b[32m⌃\u001b[39m \u001b[90m[13f3f980] \u001b[39mCairoMakie v0.10.7\n",
      "  \u001b[90m[a93c6f00] \u001b[39mDataFrames v1.6.1\n",
      "  \u001b[90m[31c24e10] \u001b[39mDistributions v0.25.100\n",
      "  \u001b[90m[634d3b9d] \u001b[39mDrWatson v2.12.7\n",
      "  \u001b[90m[61744808] \u001b[39mDynamicalSystems v3.2.0\n",
      "\u001b[32m⌃\u001b[39m \u001b[90m[1dea7af3] \u001b[39mOrdinaryDiffEq v6.53.4\n",
      "  \u001b[90m[1a8c2f83] \u001b[39mQuery v1.0.0\n",
      "  \u001b[90m[1e83bf80] \u001b[39mStaticArraysCore v1.4.2\n",
      "\u001b[36m\u001b[1mInfo\u001b[22m\u001b[39m Packages marked with \u001b[32m⌃\u001b[39m have new versions available and may be upgradable.\n"
     ]
    }
   ],
   "source": [
    "import Pkg\n",
    "Pkg.activate(@__DIR__)\n",
    "Pkg.status()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "metadata": {},
   "outputs": [],
   "source": [
    "# quick theme change for plotting in zoomed-in notebooks\n",
    "using CairoMakie\n",
    "update_theme!(resolution = (500, 300), fontsize = 16)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# DifferentialEquations.jl\n",
    "\n",
    "[DifferentialEquations.jl](https://docs.sciml.ai/DiffEqDocs/dev/index.html) is by far [the best](https://docs.sciml.ai/SciMLBenchmarksOutput/stable/MultiLanguage/ode_wrapper_packages/) free and open source differential equations solver (not for Julia, for any language): it is orders of magnitude faster and has orders of mangitude more features than anything else out there. It can solve standard ODEs, Delay-DEs, stochastic DEs, has tools for PDEs, event handling, other multiple features, 100s of solvers, and more. Above all, it is the central part of a whole organization focused on scientific machine learning (SciML) and the basis for [ModelingToolkit.jl](https://docs.sciml.ai/ModelingToolkit/dev/), a library for building simulations from symbolic definitions.\n",
    "\n",
    "Here we will focus on Ordinary Differential Equations (ODEs) solving and use the module `OrdinaryDiffEq` only."
   ]
  },
  {
   "attachments": {},
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   "metadata": {},
   "source": [
    "\n",
    "## Defining and solving some ODEs\n",
    "\n",
    "The way DifferentialEquations.jl works is quite straightforward:\n",
    "\n",
    "1. Make your set of ODEs a Julia function `f`\n",
    "2. Put `f`, an initial state and a parameter container into an `ODEProblem`.\n",
    "2. Choose the solvers and the arguments of the solvers you will use (e.g. tolerances, etc.)\n",
    "3. Give `f` as well as the auxiliary arguments to the function `solve`!\n",
    "\n",
    "Let's see it in practice by solving the Thomas cyclical system\n",
    "\n",
    "$$\n",
    "\\begin{aligned}\n",
    "\\dot{x} &= \\sin(y) - bx\\\\\n",
    "\\dot{y} &= \\sin(z) - by\\\\\n",
    "\\dot{z} &= \\sin(x) - bz\n",
    "\\end{aligned}\n",
    "$$\n",
    "\n",
    "First step is to make this a Julia function. There is some strictness when writing this function in Julia (to play well with another software, see below). \n",
    "Specifically, it can only be one of two forms: out-of-place (**oop**) or in-place (**iip**). Here is how to define it (`p` is the parameter container, `t` is time):\n",
    "\n",
    "* **oop** : The `eom` function must be in the form `eom(x, p, t) -> SVector`\n",
    "  which means that given a state `x::SVector` it returns an `SVector`\n",
    "  (from the [StaticArrays.jl](https://github.com/JuliaArrays/StaticArrays.jl) package)\n",
    "  containing the derivatives.\n",
    "* **iip** : The `eom` function must be in the form `eom!(dx, x, p, t)`\n",
    "  which means that given a state `x::AbstractArray` it writes in-place the derivatives in `dx`, which is the same type of `x`. Note that this type of `dx` needs to be mutable.\n",
    "\n",
    "A rule of thumb is to use **oop** for systems with dimension ≤ 10, and use **iip** otherwise, but it is always better to benchmark individual cases."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "thomas_rule (generic function with 1 method)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "using OrdinaryDiffEq, StaticArraysCore\n",
    "\n",
    "function thomas_rule(u, p, t)\n",
    "    x,y,z = u\n",
    "    b = p[1]\n",
    "    xdot = sin(y) - b*x\n",
    "    ydot = sin(z) - b*y\n",
    "    zdot = sin(x) - b*z\n",
    "    return SVector(xdot, ydot, zdot)\n",
    "end"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Then set the initial state and parameter container"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1-element Vector{Float64}:\n",
       " 0.2"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "u₀ = SVector(1.0, 1.0, 2.0)\n",
    "p₀ = [0.2]"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "then put everything into the `ODEProblem` structure:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\u001b[38;2;86;182;194mODEProblem\u001b[0m with uType \u001b[38;2;86;182;194mSVector{3, Float64}\u001b[0m and tType \u001b[38;2;86;182;194mFloat64\u001b[0m. In-place: \u001b[38;2;86;182;194mfalse\u001b[0m\n",
       "timespan: (0.0, 1000.0)\n",
       "u0: 3-element SVector{3, Float64} with indices SOneTo(3):\n",
       " 1.0\n",
       " 1.0\n",
       " 2.0"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# third argument is the timespan to solve in\n",
    "timespan = (0.0, 1000.0)\n",
    "prob = ODEProblem(thomas_rule, u₀, timespan, p₀)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Alright, so now we choose the solver algorithm to use. We will discuss this choice in more detail later, but for now we use the default choice of DifferentialEquations.jl."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "metadata": {},
   "outputs": [],
   "source": [
    "alg = Tsit5();"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now let's solve the Lorenz system using the default settings of DifferentialEquations.jl (without specifying anything else)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "retcode: Success\n",
       "Interpolation: specialized 4th order \"free\" interpolation\n",
       "t: 813-element Vector{Float64}:\n",
       "    0.0\n",
       "    0.1120521120556666\n",
       "    0.44378050362673405\n",
       "    0.9136032386187993\n",
       "    1.4662849360622896\n",
       "    2.1996084447411617\n",
       "    3.2045208465180144\n",
       "    4.085242874574744\n",
       "    5.129213529677106\n",
       "    6.241261975411241\n",
       "    ⋮\n",
       "  989.016132424067\n",
       "  990.5662995899445\n",
       "  992.2501718499245\n",
       "  993.7379049054462\n",
       "  995.4297636802733\n",
       "  996.8774606957784\n",
       "  998.3576943762309\n",
       "  999.7917754461864\n",
       " 1000.0\n",
       "u: 813-element Vector{SVector{3, Float64}}:\n",
       " [1.0, 1.0, 2.0]\n",
       " [1.073328946367455, 1.077382180107541, 2.0510228820916896]\n",
       " [1.3010643606418302, 1.279441630927924, 2.216402304246613]\n",
       " [1.6249069901838225, 1.4855826850617537, 2.4616668952552936]\n",
       " [1.9777425718824548, 1.6017467387163078, 2.7100439922221256]\n",
       " [2.3894984994256565, 1.599089872828173, 2.8904410244887484]\n",
       " [2.8649074514787682, 1.5483523437301538, 2.795240578177487]\n",
       " [3.208555980288333, 1.6972897987475106, 2.4194479820781427]\n",
       " [3.4778227799375907, 2.1819868451227604, 1.753099531195561]\n",
       " [3.3933461412228625, 2.708362984477085, 1.0818668759219525]\n",
       " ⋮\n",
       " [2.460168169657819, 2.8024727962190834, 2.5068456503259045]\n",
       " [2.2852901415734967, 2.689163931499818, 2.785681701963606]\n",
       " [2.52122981822636, 2.2297464182022533, 2.988390666694459]\n",
       " [3.0045071575336513, 1.9933275678600462, 2.6791203178136844]\n",
       " [3.2858784342120217, 2.510241437106069, 1.817283187761961]\n",
       " [2.815492334701153, 3.1283413228966555, 1.4130550225808411]\n",
       " [1.7856597259537317, 3.58847205956326, 1.9596423661484268]\n",
       " [0.7560993635838374, 3.570261227193435, 2.5894890477466204]\n",
       " [0.6443103376380805, 3.529081714957839, 2.614991830749762]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sol = solve(prob; alg) # provide solver algorithm as keyword `alg`"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Okay, so what is the returned result? We didn't specify when to save or anything...\n",
    "\n",
    "The solver we chose, `Tsit5`, is an _adaptive step solver_. The system is evolved with an adaptive step size, so that the step error tolerance stays below a pre-defined level. The system is evolved until we reach the end of the time span. A state is recorded at every step the solver algorithm takes naturally. E.g. the solution at the third step is"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "813-element Vector{Float64}:\n",
       "    0.0\n",
       "    0.1120521120556666\n",
       "    0.44378050362673405\n",
       "    0.9136032386187993\n",
       "    1.4662849360622896\n",
       "    2.1996084447411617\n",
       "    3.2045208465180144\n",
       "    4.085242874574744\n",
       "    5.129213529677106\n",
       "    6.241261975411241\n",
       "    ⋮\n",
       "  989.016132424067\n",
       "  990.5662995899445\n",
       "  992.2501718499245\n",
       "  993.7379049054462\n",
       "  995.4297636802733\n",
       "  996.8774606957784\n",
       "  998.3576943762309\n",
       "  999.7917754461864\n",
       " 1000.0"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sol.t"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The solution is guaranteed to start and stop at the limits of the time span (by default).\n",
    "\n",
    "We can obtain the state at the 3rd time point from the `u` field:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.44378050362673405, [1.3010643606418302, 1.279441630927924, 2.216402304246613])"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "(sol.t[3], sol.u[3])"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Because of the mechanics of the solver, `sol` object allows arbitrary interpolation in time by saving some extra derivative-related numbers. This means that we can use `sol` as a function of time, `sol(t)`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3-element SVector{3, Float64} with indices SOneTo(3):\n",
       " 3.495862759011857\n",
       " 2.4335212815593588\n",
       " 1.4402755303498724"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sol(5.6)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can iterate over some time to create a (multivariate) timeseries"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 87,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "t = timespan[1]:0.1:timespan[end]\n",
    "X, Y, Z = zero(t), zero(t), zero(t)\n",
    "for (i, τ) in enumerate(t)\n",
    "    X[i], Y[i], Z[i] = sol(τ)\n",
    "end\n",
    "lines(X, Y, Z; axis = (type = Axis3, azimuth = 0.75π))"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Notice that it is possible to skip this advanced feature of interpolation (and thus also skip collecting the extra interpolation-related numbers) and only save at some pre-defined time points by passing the extra keyword argument `saveat = points_I_want` to the `solve` call."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "10001-element Vector{Float64}:\n",
       "    0.0\n",
       "    0.1\n",
       "    0.2\n",
       "    0.3\n",
       "    0.4\n",
       "    0.5\n",
       "    0.6\n",
       "    0.7\n",
       "    0.8\n",
       "    0.9\n",
       "    ⋮\n",
       "  999.2\n",
       "  999.3\n",
       "  999.4\n",
       "  999.5\n",
       "  999.6\n",
       "  999.7\n",
       "  999.8\n",
       "  999.9\n",
       " 1000.0"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "t = timespan[1]:0.1:timespan[end]\n",
    "sol = solve(prob; alg, saveat = t)\n",
    "sol.t"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Using callbacks for triggering events during time evolution"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "DifferentialEquations.jl implements a simple interface so that \"events\" (arbitrary things) can be triggered to after your solution as it is progressing in time. This is done with the [`Callback` interface](https://docs.sciml.ai/DiffEqDocs/dev/features/callback_functions/). For example, a `ContinuousCallback` represents an event that \"triggers\" when a continuous univariate function of the (state, time) reaches the value 0. Similarly, a `DiscreteCallback` triggers when a Boolean function of the (state, time) evaluates to `true`.\n",
    "\n",
    "Let's modify the Thomas cyclical system so that a condition triggers each time the third variable becomes zero:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "condition (generic function with 1 method)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# The third argument of this function is mandatory but too advanced for this lecture\n",
    "condition(u, t, integrator) = u[3] "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We then define a function that modifies the integrator object. the integrator object is too complicated to explain within this lecture; but we mainly care about the fields `.u` and `.p` that access current state and parameter values. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "affect! (generic function with 1 method)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "function affect!(integrator)\n",
    "    u = integrator.u\n",
    "    integrator.u = 1.5u\n",
    "end"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The trigger `condition` and how it will `affect!` the integration are wrapped in continuous callback, which is given to the `solve` call."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "metadata": {},
   "outputs": [],
   "source": [
    "cb = ContinuousCallback(condition, affect!);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sol = solve(prob; alg, saveat = t, callback = cb)\n",
    "# plot\n",
    "lines(sol.u; axis = (type = Axis3,))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Choosing a solver\n",
    "\n",
    "So far we have not discussed _how_ the ODE is solved. \n",
    "A solver algorithm is chosen when a solution is requested.\n",
    "So far we have been using `Tsit5`, which is also the overall default that DifferentialEquations.jl uses. But, DifferentialEquations.jl has an impressive list of [100s of solvers one can choose from](https://docs.sciml.ai/DiffEqDocs/dev/solvers/ode_solve/).\n",
    "\n",
    "Choosing the solver is a problem-dependent operation. We'll cover here two typical examples.\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Higher accuracy, higher order\n",
    "\n",
    "The solver `Tsit5` is most performant when medium-high error tolerances are requested. When we require very small errors, choosing a different solver can be more accurate. This can be especially impactful for chaotic dynamical systems. Let's first expliclty ask for a given accuracy when solving the ODE by passing the keywords `abstol, reltol` (for absolute and relative tolerance respectively):\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 93,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sol = solve(prob; alg, saveat = t, abstol = 1e-12, reltol = 1e-12)\n",
    "lines(sol.u; axis = (type = Axis3,))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's now benchmark how much time it takes to solve the problem with the default `Tsit5` solver:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 94,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "  11.610 ms (32 allocations: 719.62 KiB)\n"
     ]
    }
   ],
   "source": [
    "using BenchmarkTools\n",
    "@btime solve(prob; alg, saveat = t, abstol = 1e-12, reltol = 1e-12);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's see how the higher-order solver `Vern9`, which is better suited for high accuracy, performs:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 95,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "  5.304 ms (33 allocations: 720.78 KiB)\n"
     ]
    }
   ],
   "source": [
    "using BenchmarkTools\n",
    "@btime solve(prob; alg = Vern9(), saveat = t, abstol = 1e-12, reltol = 1e-12);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Stiff problems\n",
    "\n",
    "A \"stiff\" ODE problem is one that can be numerically unstable unless the step size (or equivalently, the step error tolerances) are extremely small. There are several situations where a problem may be come \"stiff\":\n",
    "\n",
    "- The derivative values can get very large for some state values.\n",
    "- There is a large _timescale separation_ between the dynamics of the variables\n",
    "- There is a large _timescale separation_ between the dynamics of different state space regions\n",
    "\n",
    "One must be aware whether this is possible for their system and choose a solver that is better suited to tackle stiff problems. If not, a solution may diverge and the ODE integrator will throw an error or a warning.\n",
    "\n",
    "Many of the problems in DifferentialEquations.jl are suitable for dealing with stiff problems. We can create a stiff problem by using the well known Van der Pol  oscillator _with a timescale separation_:\n",
    "\n",
    "$$\n",
    "\\begin{aligned}\n",
    "\\dot{x} & = y \\\\\n",
    "\\dot{y} /  \\mu &= (1-x^2)y - x\n",
    "\\end{aligned}\n",
    "$$\n",
    "\n",
    "with $\\mu$ being the timescale of the $y$ variable in units of the timescale of the $x$ variable. For very large values of $\\mu$ this problem becomes stiff."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 96,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "  826.027 ms (27 allocations: 55.27 KiB)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "  170.600 ms (1744781 allocations: 51.08 MiB)\n"
     ]
    }
   ],
   "source": [
    "function vanderpol_rule(u, μ, t)\n",
    "    x, y = u\n",
    "    dx = y\n",
    "    dy = μ*((1-x^2)*y - x)\n",
    "    return SVector(dx, dy)\n",
    "end\n",
    "\n",
    "μ = 1e6\n",
    "prob = ODEProblem(vanderpol_rule, SVector(1.0, 1.0), (0.0, 10.0), μ)\n",
    "@btime solve(prob; alg = Tsit5(), abstol = 1e-12, reltol = 1e-12, saveat = 0.01, maxiters = typemax(Int))\n",
    "@btime solve(prob; alg = Rodas5P(), abstol = 1e-12, reltol = 1e-12, saveat = 0.01, maxiters = typemax(Int));"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We see that the stiff solver `Rodas5P` is much faster than the default `Tsit5` when there is a large timescale separation. This happened because `Rodas5P` required much less steps to integrated the same total amount of time. In fact, there are cases where regular solvers will _fail_ to integrate the ODE if the problem is very stiff, e.g. in the [ROBER example](https://docs.sciml.ai/SciMLBenchmarksOutput/stable/StiffODE/ROBER/)."
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# DynamicalSystems.jl\n",
    "[DynamicalSystems.jl](https://juliadynamics.github.io/DynamicalSystems.jl/dev/) is an award-winning library for nonlinear dynamics and nonlinear dynamics. \n",
    "\n",
    "*Disclaimer: I am one of the developers of this library.*"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Using a dynamical system"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Part of the functionality offered by DynamicalSystems.jl utilizes OrdinaryDiffEq.jl to evolve continuous time systems and compute quantities relevant for nonlinear dynamics, such as Lyapunov exponents. Same works for discrete time systems but there there is no need for an external package to evolve them."
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Making a `DynamicalSystem` is almost identical to making an `ODEProblem`, but you don't have to specify the time span. In steps:\n",
    "\n",
    "1. Make $f$ a Julia function (using the same syntax as in OrdinaryDiffEq.jl) representing the dynamic rule of the system.\n",
    "2. Choose initial state and parameter container (again same as OrdinaryDiffEq.jl).\n",
    "3. Pass these arguments to the `CoupledODEs` constructor (or `DeterministicIteratedMap`, for discrete systems).\n",
    "\n",
    "Here we already have `thomas_rule, u₀, p₀` defined above for the Thomas system, which is\n",
    "\n",
    "$$\n",
    "\\begin{aligned}\n",
    "\\dot{x} &= \\sin(y) - bx\\\\\n",
    "\\dot{y} &= \\sin(z) - by\\\\\n",
    "\\dot{z} &= \\sin(x) - bz\n",
    "\\end{aligned}\n",
    "$$\n",
    "\n",
    "so to put this in DynamicalSystems.jl is kind of trivial:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 151,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3-dimensional CoupledODEs\n",
       " deterministic: true\n",
       " discrete time: false\n",
       " in-place:      false\n",
       " dynamic rule:  thomas_rule\n",
       " ODE solver:    Tsit5\n",
       " ODE kwargs:    (abstol = 1.0e-6, reltol = 1.0e-6)\n",
       " parameters:    [0.2]\n",
       " time:          0.0\n",
       " state:         [1.0, 1.0, 2.0]\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "using DynamicalSystems\n",
    "thomas = CoupledODEs(thomas_rule, u₀, p₀)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Then we can use this `thomas` object in various functions of the library. For example, to obtain the Lyapunov spectrum you use `lyapunovspectrum`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 98,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3-element Vector{Float64}:\n",
       "  0.002080265970671607\n",
       " -0.005557932793430534\n",
       " -0.5965199974291404"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "lyapunovspectrum(thomas, 10000) # 2nd argument is for how much time to evolve"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Same story happens if you want to get only the maximum Lyapunov exponent. You use the function `lyapunov` (which uses a different algorithm):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 99,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.001914273255323101"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "lyapunov(thomas, 10000.0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Much more advanced behavior is possible. For example, the library has a module dedicated to multistable dynamical systems. We can use it to find all attractors, and their basin state space fraction, for the Thomas system, which becomes multistable at $b = 0.12$. First, we change the system parameter to this $b$ value:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 100,
   "metadata": {},
   "outputs": [],
   "source": [
    "set_parameter!(thomas, 1, 0.1665)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And then we utilize `AttractorsViaRecurrences` to find the attractors"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 101,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Dict{Int64, Float64} with 3 entries:\n",
       "  2 => 0.307\n",
       "  3 => 0.342\n",
       "  1 => 0.351"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# where to search attractors \n",
    "xg = yg = zg = range(-6, 6; length = 200)\n",
    "grid = (xg, yg, zg)\n",
    "mapper = AttractorsViaRecurrences(thomas, grid)\n",
    "sampler, = statespace_sampler(grid)\n",
    "fractions = basins_fractions(mapper, sampler)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 102,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Dict{Int32, StateSpaceSet{3, Float64}} with 3 entries:\n",
       "  2 => 3-dimensional StateSpaceSet{Float64} with 325 points\n",
       "  3 => 3-dimensional StateSpaceSet{Float64} with 325 points\n",
       "  1 => 3-dimensional StateSpaceSet{Float64} with 328 points"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "attractors = extract_attractors(mapper)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 152,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plot found attractors\n",
    "fig = Figure(resolution = (800, 600))\n",
    "ax = Axis3(fig[1,1])\n",
    "for (k, att) in attractors\n",
    "    scatter!(ax, vec(att); markersize = 6)\n",
    "end\n",
    "hidedecorations!(ax)\n",
    "fig"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 104,
   "metadata": {},
   "outputs": [],
   "source": [
    "# reset parameter to previous one\n",
    "set_parameter!(thomas, 1, 0.2)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Nonlinear timeseries analysis\n",
    "\n",
    "Both basic as well as advanced tools for nonlinear timeseries analysis are included in DynamicalSystems.jl. To spare you the boredom I won't talk about them though! I'll only mention entropy, because it is relevant to one of the exercises. Let's say that you have an observed trajectory sampled at discrete times. We can obtain this from an experiment, or from a given dynamical system using the `trajectory` function (which is in fact just a wrapper to `solve`)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 105,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3-dimensional StateSpaceSet{Float64} with 20001 points\n",
       "  1.0       1.0        2.0\n",
       "  1.03238   1.03505    2.02239\n",
       "  1.06532   1.06926    2.04539\n",
       "  1.09873   1.10261    2.06896\n",
       "  1.13255   1.13505    2.09306\n",
       "  1.16671   1.16657    2.11764\n",
       "  1.20114   1.19713    2.14264\n",
       "  1.23577   1.2267     2.16801\n",
       "  1.27054   1.25527    2.1937\n",
       "  1.3054    1.28281    2.21964\n",
       "  ⋮                   \n",
       " -0.36524   0.589317   0.0853953\n",
       " -0.333995  0.587245   0.0675075\n",
       " -0.303164  0.584347   0.0512565\n",
       " -0.272775  0.580711   0.0366206\n",
       " -0.242854  0.576423   0.0235749\n",
       " -0.213422  0.571567   0.012092\n",
       " -0.184496  0.566228   0.00214215\n",
       " -0.156091  0.560483  -0.00630682\n",
       " -0.128217  0.554413  -0.0132889"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Χ, t = trajectory(thomas, 1000.0; Δt = 0.05)\n",
    "Χ"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The above result is a `StateSpaceSet`. It is not a `Matrix`, but a vector-of-vectors (for performance purposes). Typically one is interested in the entropy of this set. There are many ways to obtain an entropy, but the simplest one is to compute the entropy of the _histogram_ of the set.\n",
    "\n",
    "You can get this entropy using the function `entropy`. We provide to this function the information of how to extract probabilities from `X` as the first argument. Here we simply say to make a histogram of `X` using `ε` as the bin size:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 106,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "5.40009259071532"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ε = 0.1\n",
    "H = entropy(ValueHistogram(ε), X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 107,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "8.676224622340218"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ε = 0.01\n",
    "H = entropy(ValueHistogram(ε), X)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This entropy can be used to estimate the _fractal dimension_ of the set. As we can't afford to go into details for the sake of time, here I will just showcase the automated function `generalized_dim` that calculates `entropy` for many different `ε` and uses the result to calculate a fractal dimension:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 108,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.7490663268791462"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Δ = generalized_dim(Χ; show_progress = false)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "You can examine how this computation works using the `@edit` macro."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Optimization with BlackBoxOptim.jl\n",
    "\n",
    "Julia offers an incredible array of optimization packages. There is an ongoing effort to build a _common interface_ across all optimization packages, which can be found in [Optimization.jl](https://docs.sciml.ai/Optimization/stable/). Here, we will show and use only a single optimization package, [BlackBoxOptim.jl](https://github.com/robertfeldt/BlackBoxOptim.jl), that focuses on blackbox optimization problems where the objective function cannot be defined in terms of simple mathematical equations, and is also not differentiable.\n",
    "\n",
    "Our goal is to find the parameter combinations for when the following dynamical system\n",
    "$$\n",
    "\\begin{aligned}\n",
    "\\dot{x} &= -\\mu x +yz \\\\\n",
    "\\dot{y} &= -\\mu y +x(z-\\alpha) \\\\\n",
    "\\dot{z} &= 1 - xz\n",
    "\\end{aligned}\n",
    "$$\n",
    "(called Rikitake's dynamo) has the largest maximum Lyapunov exponent.\n",
    "\n",
    "To do this we must first define an _objective function_: A  function taking in a vector of parameters and returning the objective we want to minimize;\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 206,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "minus_lyapunov (generic function with 1 method)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "using DynamicalSystems\n",
    "\n",
    "function rikitake_rule(u, p, t)\n",
    "    μ, α = p\n",
    "    x, y, z = u\n",
    "    xdot = -μ*x + y*z\n",
    "    ydot = -μ*y + x*(z - α)\n",
    "    zdot = 1 - x*y\n",
    "    return SVector(xdot, ydot, zdot)\n",
    "end\n",
    "\n",
    "function minus_lyapunov(p) # input is parameter values\n",
    "    ds = CoupledODEs(rikitake_rule, SVector(1, 0, 0.6), p)\n",
    "    λ = lyapunov(ds, 1000; Ttr = 10)\n",
    "    # return negative exponent because we minimize objective\n",
    "    return -λ \n",
    "end"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We will now attempt to \"optimize\" this objective `minus_lyapunov`, by providing a search range for the input vector `p` (which is the parameter container)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 222,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Starting optimization with optimizer DiffEvoOpt{FitPopulation{Float64}, RadiusLimitedSelector, BlackBoxOptim.AdaptiveDiffEvoRandBin{3}, RandomBound{ContinuousRectSearchSpace}}\n",
      "0.00 secs, 0 evals, 0 steps\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.50 secs, 187 evals, 118 steps, improv/step: 0.458 (last = 0.4576), fitness=-0.303896466\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.01 secs, 398 evals, 296 steps, improv/step: 0.361 (last = 0.2978), fitness=-0.313028325\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.51 secs, 599 evals, 487 steps, improv/step: 0.329 (last = 0.2775), fitness=-0.326005486"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "2.01 secs, 793 evals, 680 steps, improv/step: 0.299 (last = 0.2228), fitness=-0.334130039\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2.51 secs, 981 evals, 868 steps, improv/step: 0.266 (last = 0.1489), fitness=-0.334130039\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "3.01 secs, 1164 evals, 1051 steps, improv/step: 0.245 (last = 0.1475), fitness=-0.334130039\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "3.52 secs, 1344 evals, 1231 steps, improv/step: 0.223 (last = 0.0889), fitness=-0.334130039"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "4.02 secs, 1522 evals, 1409 steps, improv/step: 0.200 (last = 0.0449), fitness=-0.334130039"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "4.52 secs, 1705 evals, 1592 steps, improv/step: 0.184 (last = 0.0601), fitness=-0.334130039\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "5.02 secs, 1883 evals, 1770 steps, improv/step: 0.170 (last = 0.0449), fitness=-0.336483718\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "5.52 secs, 2061 evals, 1948 steps, improv/step: 0.161 (last = 0.0674), fitness=-0.351834009\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "6.02 secs, 2233 evals, 2120 steps, improv/step: 0.154 (last = 0.0756), fitness=-0.351834009"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "6.53 secs, 2408 evals, 2295 steps, improv/step: 0.145 (last = 0.0400), fitness=-0.351834009\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "7.03 secs, 2583 evals, 2470 steps, improv/step: 0.139 (last = 0.0571), fitness=-0.351834009\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "7.53 secs, 2752 evals, 2639 steps, improv/step: 0.133 (last = 0.0414), fitness=-0.351834009\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "8.03 secs, 2926 evals, 2813 steps, improv/step: 0.126 (last = 0.0287), fitness=-0.351834009"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "8.53 secs, 3099 evals, 2986 steps, improv/step: 0.122 (last = 0.0520), fitness=-0.351834009"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "9.04 secs, 3270 evals, 3157 steps, improv/step: 0.117 (last = 0.0234), fitness=-0.351834009"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "9.54 secs, 3443 evals, 3330 steps, improv/step: 0.113 (last = 0.0405), fitness=-0.351834009\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "10.04 secs, 3615 evals, 3502 steps, improv/step: 0.109 (last = 0.0291), fitness=-0.351834009\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "10.54 secs, 3790 evals, 3677 steps, improv/step: 0.104 (last = 0.0229), fitness=-0.351834009\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "11.04 secs, 3963 evals, 3850 steps, improv/step: 0.101 (last = 0.0289), fitness=-0.351834009\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "11.54 secs, 4138 evals, 4025 steps, improv/step: 0.098 (last = 0.0286), fitness=-0.351834009"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "12.05 secs, 4311 evals, 4198 steps, improv/step: 0.095 (last = 0.0173), fitness=-0.351834009\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "12.55 secs, 4484 evals, 4371 steps, improv/step: 0.092 (last = 0.0173), fitness=-0.351834009\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "13.05 secs, 4656 evals, 4543 steps, improv/step: 0.089 (last = 0.0233), fitness=-0.351834009\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "13.55 secs, 4827 evals, 4714 steps, improv/step: 0.087 (last = 0.0409), fitness=-0.351834009"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "14.05 secs, 4998 evals, 4885 steps, improv/step: 0.086 (last = 0.0468), fitness=-0.351834009"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "14.56 secs, 5168 evals, 5055 steps, improv/step: 0.084 (last = 0.0412), fitness=-0.351834009"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "15.06 secs, 5337 evals, 5224 steps, improv/step: 0.082 (last = 0.0237), fitness=-0.351834009\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "15.56 secs, 5506 evals, 5393 steps, improv/step: 0.082 (last = 0.0592), fitness=-0.351834009\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "16.06 secs, 5676 evals, 5563 steps, improv/step: 0.080 (last = 0.0235), fitness=-0.351834009\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "16.57 secs, 5845 evals, 5733 steps, improv/step: 0.079 (last = 0.0647), fitness=-0.351834009"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "17.07 secs, 6014 evals, 5902 steps, improv/step: 0.078 (last = 0.0296), fitness=-0.371422444\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "17.57 secs, 6183 evals, 6071 steps, improv/step: 0.077 (last = 0.0296), fitness=-0.371422444\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "18.07 secs, 6349 evals, 6237 steps, improv/step: 0.076 (last = 0.0361), fitness=-0.371422444"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "18.57 secs, 6516 evals, 6404 steps, improv/step: 0.074 (last = 0.0299), fitness=-0.371422444\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "19.08 secs, 6681 evals, 6570 steps, improv/step: 0.075 (last = 0.0843), fitness=-0.371422444\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "19.58 secs, 6844 evals, 6734 steps, improv/step: 0.073 (last = 0.0244), fitness=-0.371422444\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "20.08 secs, 7008 evals, 6899 steps, improv/step: 0.072 (last = 0.0364), fitness=-0.371422444\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "20.58 secs, 7174 evals, 7065 steps, improv/step: 0.071 (last = 0.0181), fitness=-0.371422444\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "21.08 secs, 7339 evals, 7234 steps, improv/step: 0.071 (last = 0.0710), fitness=-0.371422444\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "21.59 secs, 7504 evals, 7407 steps, improv/step: 0.071 (last = 0.0578), fitness=-0.371422444\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "22.09 secs, 7665 evals, 7574 steps, improv/step: 0.071 (last = 0.0659), fitness=-0.371422444"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "22.59 secs, 7830 evals, 7746 steps, improv/step: 0.070 (last = 0.0581), fitness=-0.371422444\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "23.09 secs, 7993 evals, 7933 steps, improv/step: 0.070 (last = 0.0481), fitness=-0.371422444\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "23.59 secs, 8157 evals, 8123 steps, improv/step: 0.070 (last = 0.0737), fitness=-0.371422444\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "24.10 secs, 8322 evals, 8322 steps, improv/step: 0.069 (last = 0.0201), fitness=-0.371422444\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "24.60 secs, 8488 evals, 8556 steps, improv/step: 0.068 (last = 0.0513), fitness=-0.371422444\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "25.10 secs, 8639 evals, 8788 steps, improv/step: 0.068 (last = 0.0517), fitness=-0.371422444\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "25.60 secs, 8803 evals, 9077 steps, improv/step: 0.067 (last = 0.0484), fitness=-0.371422444"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "26.11 secs, 8969 evals, 9376 steps, improv/step: 0.067 (last = 0.0435), fitness=-0.371422444\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "26.61 secs, 9141 evals, 9728 steps, improv/step: 0.066 (last = 0.0568), fitness=-0.371422444\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Optimization stopped after 10076 steps and 26.76 seconds\n",
      "Termination reason: Too many steps (101) without any function evaluations (probably search has converged)\n",
      "Steps per second = 376.49\n",
      "Function evals per second = 343.42\n",
      "Improvements/step = Inf\n",
      "Total function evaluations = 9191\n",
      "\n",
      "\n",
      "Best candidate found: [0.960648, 9.76264]\n",
      "\n",
      "Fitness: -0.371422444\n",
      "\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "BlackBoxOptim.OptimizationResults(\"adaptive_de_rand_1_bin_radiuslimited\", \"Too many steps (101) without any function evaluations (probably search has converged)\", 10076, 1.692093897214e9, 26.763000011444092, ParamsDictChain[ParamsDictChain[Dict{Symbol, Any}(:RngSeed => 824175, :MaxTime => 40.0, :SearchRange => [(0.0, 5.0), (-10.0, 10.0)], :MaxFuncEvals => 0, :MaxSteps => 0),Dict{Symbol, Any}()],Dict{Symbol, Any}(:CallbackInterval => -1.0, :TargetFitness => nothing, :TraceMode => :compact, :FitnessScheme => ScalarFitnessScheme{true}(), :MinDeltaFitnessTolerance => 1.0e-50, :NumDimensions => :NotSpecified, :FitnessTolerance => 1.0e-8, :TraceInterval => 0.5, :MaxStepsWithoutProgress => 10000, :MaxSteps => 10000…)], 9191, ScalarFitnessScheme{true}(), BlackBoxOptim.TopListArchiveOutput{Float64, Vector{Float64}}(-0.3714224442806003, [0.9606484936425075, 9.76263583217019]), BlackBoxOptim.PopulationOptimizerOutput{FitPopulation{Float64}}(FitPopulation{Float64}([0.9606484936425075 0.9606484936425075 … 0.9606484936425075 0.9606484936425075; 9.76263583217019 9.76263583217019 … 9.76263583217019 9.76263583217019], NaN, [-0.3714224442806003, -0.3714224442806003, -0.3714224442806003, -0.3714224442806003, -0.3714224442806003, -0.3714224442806003, -0.3714224442806003, -0.3714224442806003, -0.3714224442806003, -0.3714224442806003  …  -0.3714224442806003, -0.3714224442806003, -0.3714224442806003, -0.3714224442806003, -0.3714224442806003, -0.3714224442806003, -0.3714224442806003, -0.3714224442806003, -0.3714224442806003, -0.3714224442806003], 0, BlackBoxOptim.Candidate{Float64}[BlackBoxOptim.Candidate{Float64}([0.9606484936425075, 9.76263583217019], 35, -0.3714224442806003, BlackBoxOptim.AdaptiveDiffEvoRandBin{3}(BlackBoxOptim.AdaptiveDiffEvoParameters(BlackBoxOptim.BimodalCauchy(Cauchy{Float64}(μ=0.65, σ=0.1), Cauchy{Float64}(μ=1.0, σ=0.1), 0.5, false, true), BlackBoxOptim.BimodalCauchy(Cauchy{Float64}(μ=0.1, σ=0.1), Cauchy{Float64}(μ=0.95, σ=0.1), 0.5, false, true), [0.8224020149854215, 1.0, 0.6547615546715201, 0.96291455059517, 0.6318156081382176, 0.9214322230066587, 0.581404586898946, 0.2885065599589641, 0.6090233639902028, 1.0  …  0.7704397439819042, 0.6332524165823242, 1.0, 0.9135818204588795, 0.8728698945830662, 0.7961756611821669, 1.0, 0.9431867821207572, 1.0, 0.7656704769822986], [0.7232067407360354, 1.0, 0.9798083157243406, 1.0, 0.12059400847773086, 0.7346557484330422, 0.9031786713944013, 1.0, 1.0, 0.2020822347500582  …  0.10978748289741967, 0.9276510186507243, 0.036400458934390645, 0.16983320707248084, 0.9362465710639312, 0.812554398974832, 0.0006175308947101721, 1.0, 0.01925044542359111, 0.24867315482464594])), 0), BlackBoxOptim.Candidate{Float64}([0.9606484936425075, 9.76263583217019], 35, -0.3714224442806003, BlackBoxOptim.AdaptiveDiffEvoRandBin{3}(BlackBoxOptim.AdaptiveDiffEvoParameters(BlackBoxOptim.BimodalCauchy(Cauchy{Float64}(μ=0.65, σ=0.1), Cauchy{Float64}(μ=1.0, σ=0.1), 0.5, false, true), BlackBoxOptim.BimodalCauchy(Cauchy{Float64}(μ=0.1, σ=0.1), Cauchy{Float64}(μ=0.95, σ=0.1), 0.5, false, true), [0.8224020149854215, 1.0, 0.6547615546715201, 0.96291455059517, 0.6318156081382176, 0.9214322230066587, 0.581404586898946, 0.2885065599589641, 0.6090233639902028, 1.0  …  0.7704397439819042, 0.6332524165823242, 1.0, 0.9135818204588795, 0.8728698945830662, 0.7961756611821669, 1.0, 0.9431867821207572, 1.0, 0.7656704769822986], [0.7232067407360354, 1.0, 0.9798083157243406, 1.0, 0.12059400847773086, 0.7346557484330422, 0.9031786713944013, 1.0, 1.0, 0.2020822347500582  …  0.10978748289741967, 0.9276510186507243, 0.036400458934390645, 0.16983320707248084, 0.9362465710639312, 0.812554398974832, 0.0006175308947101721, 1.0, 0.01925044542359111, 0.24867315482464594])), 0)], Base.Threads.SpinLock(0))))"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "using BlackBoxOptim\n",
    "\n",
    "μ_range = (0.0, 5.0)\n",
    "α_range = (-10.0, 10.0)\n",
    "\n",
    "bbres = bboptimize(minus_lyapunov; SearchRange = [μ_range, α_range], MaxTime = 30.0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 212,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2-element Vector{Float64}:\n",
       "  0.9676556181264955\n",
       " -9.975925499192703"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pmax = best_candidate(bbres)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 223,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.3714224442806003"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "λmax = -best_fitness(bbres)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 232,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ds = CoupledODEs(rikitake_rule, SVector(1, 0, 0.6), pmax)\n",
    "X, t = trajectory(ds, 1000.0; Ttr = 10, Δt = 0.01)\n",
    "fig, ax = lines(vec(X); axis = (type = Axis3,), figure = (resolution = (800, 600),))\n",
    "hidedecorations!(ax)\n",
    "fig"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Distributions.jl\n",
    "\n",
    "The [`Distributions`](https://juliastats.org/Distributions.jl/stable/) package provides an interface for writing probability-distribution-agnostic code: sampling distributions and getting pdfs, using moments, and more. This means that you can write any code that uses a probability distribution without having to care about the distribution's specifics. The result: your code can be run with _any_ probability distribution!\n",
    "\n",
    "> _Note: the package targets applications scenarios where continuous probabilty density functions with analytically known expressions are used (and optionally fitted to the data). For extracting discrete probability mass functions from input data using a plethora of different discretization methods, see [ComplexityMeasures.jl](https://juliadynamics.github.io/ComplexityMeasures.jl/stable/)._\n",
    "\n",
    "The way it works is quite straightforward: `Distributions` provides a unified API around abstract types representing probability distributions. To keep things simple here we limit ourselves to univariate continuous distributions."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 109,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "WARNING: using Distributions.sampler in module Main conflicts with an existing identifier.\n",
      "WARNING: using Distributions.entropy in module Main conflicts with an existing identifier.\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "Normal{Float64}(μ=0.1, σ=0.25)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# import Pkg; Pkg.add(\"Distributions\")\n",
    "using Distributions\n",
    "d = Normal(0.1, 0.25)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 110,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Distribution{Univariate, Continuous}"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "supertype(typeof(d))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Various distribution-related quantities can be extracted using `Distributions`, by utilizing the analytic form of a specific distribution. For example:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 111,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.5957691216057308"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pdf(d, 0.1) # probability density function at x = 0.1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 112,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.25"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "std(d)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Arguably one of the most important features for `Distributions` is that these objects can be used as samplers in the `rand` function."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 113,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.4578169454967659"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "rand(d) # sample a random variable distributed according to `d`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 114,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "10×10 Matrix{Float64}:\n",
       "  0.0660963   0.525875    0.374555    0.331278   …   0.276103      0.474536\n",
       " -0.296274   -0.0657468  -0.153313   -0.270448      -0.0482234     0.26306\n",
       "  0.0381474  -0.296639    0.376843    0.0960117      0.297911      0.47611\n",
       "  0.116733   -0.447924   -0.116847    0.133897       0.338201      0.223436\n",
       " -0.12044     0.397166    0.462917   -0.0403995      0.0226945     0.0486286\n",
       "  0.335411    0.214113    0.478768    0.102207   …   0.189401     -0.215897\n",
       "  0.117821    0.0607703   0.0625559   0.0123315     -0.000801571  -0.0066611\n",
       "  0.220294    0.212522    0.121289    0.452504      -0.349279     -0.1658\n",
       " -0.0733852  -0.314987    0.306153    0.198295      -0.100006     -0.0339482\n",
       "  0.377515   -0.494683    0.269298    0.421116       0.205603      0.051321"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "rand(d, 10, 10)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And all of this works for any subtype of `Distribution`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 115,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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GVAHiA+GeLNgdTWUwPULomQGIA4R7smB3NJVRkK5IV4gxYQYgDhDuyYJpL7M1msq4OqaKRQgAYg/hniyOdwyyO5rKmJWT2tCFMVWAmEO4J4vjl63TsjUsjqYyZuWkeGiMqQLEHMI9KQSD5FSnld0+GQYzoosxVYBYQ7gnhZZ+x4CT5dFURmG6EmOqAHGAcE8KXBhNZWBMFSA+RJEd1tLS0tzcXFFRkZmZecMdvF7vwMBA6BaFQqHRxPsGQMBgRlNvM7A8msqYlZP62t8u+fwB1gcAAHgs7E+Xx+NZvHhxcXHxkiVLDAbD+vXrb7jb3r17s673s5/9bNzVQoROdFinZrE/mspgxlTPYkwVIJbCbrlv3LjxwIEDhw4duuOOO3bu3LlixYrbb7998eLFI3YzGo25ubm/+93vhrfk5eWNt1iIiM8fONI++PTsXLYLuWruxDRCSF3rQMUE9scAAPgqvHD3+/07d+5ctWpVZWUlIWT58uW7du3asWPHDcN9+vTpDz/8cNQqhUh9fXnQ7qEXFGvZLuSqvDR5Qbrii5b+5+4uYLsWAN4K7+/0tra2rq6u6urq4S3V1dX19fXf3rO5ubm0tPSzzz57/fXXP/nkE5fLNd5KIVIHW/opiswv5Eq4E0IWFGsPtvQHgkG2CwHgrfBa7t3d3YSQ0EFUg8EwMDBA07RIdN1TGY3GEydObN++PTs722g0Tpw4cd++fWVlZaH7bNmyZcuWLaFbcnJyJk+ezJwFbsHhcPh8Pq/XO5ad9zd2lukUtG2AO73cM7Sitx3eL862lukVbNfCOb29vYFAYMQHCnjA5XI5nU6/3x/BsXa7XaUKb0JEeL9Ag4ODhBC1Wj28Ra1WB4NBi8Wi1+uHN7rd7tTU1Mcff/zVV18VCoWtra3V1dUrVqw4dOhQ6LM9+uijc+fODd2ye/duuVyenp4eVlVJSCKReL3esbxQdCB4osv51KxsTr2qD09X/ONfW08PBO6axKGqOMLj8aSnpyPc+cfpdEokksg+iXK5PNxDwvsF0mq1hBCb7ZsWoNVqpSgqLS0tdDeZTNbU1DT8z4KCgn/+539evXq1xWIJ3dNgMBgMhtAD9+7dSwiRSCRhVZWEmJdoLC/UMdOAzUMvKs3g1KtaqJcUpCvqTINrqorZroVzxGKxRCJBuPMPTdM+ny+yT6JQKAz3kPD63JksDu026e7u1uv1o/4iFhQUEELMZnO49cE4cbDDnYFud4CYCi/c8/LyCgoKamtrh7fU1tbOnz9/xG61tbVZWVnHjh0b3tLQ0CCTyQoLC8dTK0Tgi5b+qQaNTsmhZjujqlDb7/BiBTGAGAkv3CmKWrly5VtvvVVXV0fT9LZt2+rr65955hnm0a1bty5dutTj8cybN08kEq1evfrLL7+02Wz79u3793//9zVr1kTwlwWMBx0IfmWycGcSZKhFJTpCyMGWfrYLAeCnsPv11q1bZzKZqqqqhEKhQCDYvHnzokWLmIeOHj363nvv1dTUqFSqffv2LVu2rKqqihAiEAief/75DRs2RLd0GNXRdovNQy8o0rFdyA3kpsoLtZjtDhArYYe7QCDYsmXLK6+80tLSUl5eLpVKhx+qqampqalhfq6oqDh37pzRaLTZbJMnT1YqlVErGcaM6XCfV8jRGSkLinQfnusOBIMCimK7FgC+iXCxEY1GU1FREZrsN3hqgaC0tHTWrFlIdrZ80dI/LYuLHe6MqiJ0uwPECidWkoJYuNrhzsk+GcbCYi1BtztAbCDceYvpcK8q4uJoKmO4253tQgB4COHOWxzvcGcsKNJhtjtALCDceeugkaMz3EMtKNb2O7xnutDtDhBlCHd+srp9X7T0P1iWwXYho7hvkl4ooPadw1JxAFGGcOenjxt7vf7Ao1MNo+/KqgyVtHJi2p4zCHeAKEO489OeM13ZGtmc3LTRd2Xbo1MMJ69YWwecbBcCwCsIdx7y0IH9F/oenWpIiGuDvjctixDy4Vk03gGiCeHOQ/sv9Nk89JIpXO+TYeSnK6ZladAzAxBdCHce2nO2K1Uuns/hGe4jLJlqqDcN9No9bBcCwB8Id77xB4IfN/b8XXmmRJgwb+6SqVn+QPCjcz1sFwLAHwnz+Ycx+lvrQJ/du2RqFtuFhGF6tqZQq0DPDEAUIdz5Zs+ZLrlYeO8k/ei7csmjUwy1zX1DbprtQgB4AuHONx+d67l3kl4pSbD7oiyZmuWhA5+e72W7EACeQLjzyvEOa+uAM1HmyYS6Mz/NoJbuxYRIgChBuPPK3rNdQgH1UHkm24WETUBRf3db5seNPR46wHYtAHyAcOePYJC8e7JzYbGO44uF3cz3pmXbPPQnTZgzAxAFCHf++N/mPqPZsWJOLtuFROieUt3ENPm2w+1sFwLABwh3/th2pF2rlCTWJMhQAopaPidv/4U+E9aZARg3hDtPmB3eD892Pz07VypK4Pf0x3PzBBTZfhSNd4DxSuAggFDbj7R76MDyOXlsFzIuWRrZg2WZNYfbfX4MqwKMC8KdD4JBsv1I+4IibVmmiu1axuvHc/O6bZ5PmjDhHWBcEO588LnR3Gx2rKycyHYhUfBgWcbENPnWr9rYLgQgsSHc+WDr4baEHkoNJaCop+fkfYZhVYDxQbgnPGYo9Uezc2WJPJQaasUdeRRFdhy9zHYhAAmMJ3GQzHYcbff6Az++I7GHUkPlpMgeLMvYfqSdDgTZrgUgUSHcE5ubDvz2b60Li3STMhJ+KDXU6sr8ziH37uMdbBcCkKgQ7olt2+G2K1b3z+8pYbuQKHuwLGN2buqm/2lG4x0gMgj3BOamAy9/bryrIH1hsY7tWqJv/T2lLf2O/z6GxjtAJBDuCWzrV21XrO5ND0xmu5CY+LvbMmfnpr70Pxe9uKAJIHwI90Tl8QdfOWC8uyB9QeLcCDtc/3ZvqWnAiZ53gAgg3BPVzhNdPG62Mx4uz5yTl/rSfjTeAcKGcE9Ibjrw+ldXFhXrqvjbbGf8272lbRYXet4BwoVwT0g1X1/psnlfvK+U7UJi7qGyzDl5qb+sbUbjHSAsCPfE023z/L+DpoWFqfMLed5sZ2x6YHLrgPOVz1vYLgQgkSDcE8+avWfddOA/7i1ku5A4uadU//iM7E21Fy/02tmuBSBhINwTzGcX+t471bl2/sQSrZztWuLntUenKMTC1R80BHFJE8DYINwTicvnf/ZPDaV65Zq7+LOSzFgY1NJfPjj5YEv/7hMYWQUYE4R7Itm4/2LrgPPN709L6HvpRWZV5cQ789Nf+PCc2eFluxaABJB0GZG4znbbXv3i0vI5eYv4uNjAqAQU9dZj04bc9L980sR2LQAJAOGeGFw+/w//cCJNLn75oTK2a2HNFIP6n6oKdxxt//BsN9u1AHAdwj0x/OTPZ8502X7/gxlapYTtWtj00v2TKiemP/nOyfOYOQNwSwj3BLD1cNvbRy//272l90/OYLsWlomFgnefnCkVCR7fddzp9bNdDgB3Idy57nTn0Jq9575Tqv/5d/i2aHtkclPl7z45q7HHtvL902zXAsBdCHdOs7h83935tV4l+eMPZwoFFNvlcEV1ie7n3yn5w4kr2w63sV0LAEch3LnL5fN/9+2vr1jdH/zD7brk7mr/NqaT6rk9Z2sv9rFdCwAXIdw5yusPfP/3x768NPD20hmzc1PZLodzBBT1zg9nTtKrHn3760OmAbbLAeAchDsX+QPBf/jjqb+e7/3d96b+oGIC2+VwVJpcXLu6Mi9N/uC2o8c7rGyXA8AtCHfOCQbJM39qePfklZcfKl9VOZHtcjhNr5LsX1WZphA/sO1wY4+N7XIAOAThzi10ILjqg9PbDre/eG/p2oVFbJeTAHJSZPtXzRVS1L1vHT7TNcR2OQBcgXDnELuHfnTH19sOt6+/p3TDfZPYLidhlOiUtasrKULmvXEI46sADIQ7V3TbPAt+d+jTC71vfm/aS/cj2cNzm0F9dM28Ip3igW1HtmJ+JADCnSPOdA1V/rbuQp/j4xVzVt+JfvZIZGlkB565c1GJbvUHDS9+diGApd8huSHc2bflUNsdr9V56cCXP7kTCwyMh0Ym+njFnKdn5720/+J9W490DbnZrgiANQh3Nlndvh/sPvHMnxruKkg/9sK8igkpbFeU8MRCwfa/n/77H1QcbrNM/80XHzf2sF0RADsQ7qypvdg37ddf/Lmh6zeP3LZ/5dwsjYztivjjqdtzvl4zb0KK7JEdR9fsPWf30GxXBBBvCHcWdA25l+0+cc9bh+Vi4aHn7/5ZVSGFZWOibXKG6qvn5z13d8Hrda3lrxzccwZLwENyQbjHlT8QfL2utezlg3vOdG24b9Lpf6qalYOumFiRiQSvPTql7qd3pSvE39359cM1R1sHnGwXBRAnIrYLSBbBIPmgofPFzy409djvm6R/47tTi3VKtotKCpX5acdemP96XeuLn14oe/nAqsqJ/1pdkqmWsl0XQGwh3OPhk6ae9X+9cPKKdYpBvffp2YunGNiuKLmIBNQL8wv/fkb2S/svvnmobfuR9ufuLli7sDhdIWa7NIBYQbjHkNcfePdk539+2XLqylCJTvmHJ2YurcgWoH+dJdka2ZbvT1u7sGjjZxdfOdDyRr3p6dm5/zi/oEiLP6GAhxDuMdFj82w/2v5GnalryD01S/P20hk/nJUjwt02OKBIq9y1rOJfqot/daBl6+G2zfWmxVMyn59XWFWoxdcu8AnCPZp8/sBfmnp3HL381/O9dCBw/6SMXT+Y8Z1SPdt1wUjlmeq3l874j4fKfldv2vKVac+Z7iKt8kezc380JzcnBXNSgQ8Q7lHgDwS/vNT/QUPXB6e7eu2ebI3s/y4oenpObgmGTLnNoJa+dP+kf/1OyZ8bunYcbX/xswsvfnZhYbH2senZ352apVfh7leQwBDukXN6/Z8bzR839uw5091r9yglwofLM5+8Pef+SRm432kCkYkEy2ZOWDZzgmnA+ftjHX88eWX1Bw0/+fOZqkLto1MND0zOwLwmSEQI9/AEg+Rcj632Yt9fz/d+2dLvpgNqqeih8szvT8t6YHKGQiJku0CIXH664sV7S1+8t/RM1xDzd9jze84SQkp0ygfKMu6blDGvMF0txUcGEgN+U0dHB4Jnu2x1rf1ftPR/cam/z+4lhEzOUD17V/4DkzPmFWqlIlwLxitTszRTszQb75vU0u/49HzfX5p6th1u/+3fWkUCalZO6oJi7bzC9Ll5aVrctRw4DOF+Y5f6nSeuWI9fHjzcZvn68qDD6yeE5KcrHirLXFisW1CkzUuTs10jxFyRVvmTu5Q/uSvfTQe+Mg0cbOk/YDT/5xeXXv7cSFGkVK+aOzFtTm7qzJyUaVka/N0GnIJwJ4QQu4du7LE3dA2d7bKd6Ro6ecVqcfkIIRKhoGJCyv+5Y+Lcial35qcj0JOWTCRYWKxbWKzbeN8kl89/7LL1q7aBr0yWz873/v7ry4QQoYAqy1BNy9ZMzdJMzVLflqnOT1ewXTUktaQLd58/YLK4WswOo9lxvtd+oc9xodd+edDFPKqSim7LVP99RfasnNSZE1KmZKklQnS5wHXkYuG8wvR5henMPzus7hMdgyc6rCeuWA+ZLO+cuMJsV0qEkzJUk/SqyRmqUr2ySKcs1inT5LgmFuKEt+HupgOXB10dg67Lg27TgNNkcZoGXG0WZ7vFRQeu3qMnRSaelKFcWKydnKG6zaCeYtAUpCtwJQuEJSdFlpNieOS2q0tKDLnpc922M91DTT328732w22W9051Dt8WKl0hLkhX5KcrJqbJmf/mpsonpMgyVFjrBqKMP+FuGnD+4n+au23uy4PubpubGfZkUBTJUsvy0xVzJ6Y9MTOnSKso0SuLtEqsHgVRp5GJKvPTKvPThre46cClfofR7DCanS39jtZ+Z2OP7S9NvS6ff3gfmUgwIUWepZFOSJFphP6iTEdWijxDJclOkemVEr1KisubIVwRhntLS0tzc3NFRUVmZkyx95YAAAmmSURBVOb4d4sKXyD46fneCSmygnTFvML0bI0sN1WelyafkCLLS5VjQguwRSYSlGeqyzPVI7Z32zwdg64Oq7vd4uqwurqGPB2DrtOdQ+0Wp9M38gZSWqUkQyXRKiQ6pUSrlOiUknSFOF0hSVeI0+TiNLkkTSFOlYtSZOj2gavCDnePx/P444/v27dPJpO53e6f//znv/jFLyLeLYpKdMorL94T01MARJFBLTWopbfnjtze2dmpStX2uejuIU+fw9s95Om1e8wOb5/D22vzXOp3fn15sN/hddOBbz8nRZFUmThVLk6Vi1NkIo1MrJYK1TJRikycIhMpJSKVVKiWilJkYoVEqBALU+VihUQoEwlSMRjAO2GH+8aNGw8cOHDo0KE77rhj586dK1asuP322xcvXhzZbgDwbQqJsEghvfVylQ6vf8DpHXD6BpzeQRdtcXktTt+g22d10YMun9VND7l9HVbXoMs35KaH3LTXf4Mvg1BysVAmEqTIxRIhpZaK5GKhTCxUSYRioSBFJhJQVJpCLKCoFJmIogjzZZAqE1MUUUtFIgHF7C8WUiqJiBCikYmEAkosoFS47Isl4b3ufr9/586dq1atqqysJIQsX758165dO3bsGJHaY9wNACKmlAiVEnlu6lin5/r8AbvXP+jy2T200+e3uekhD+30+p0+v9VFu2m/w+u3eWgvHbC6aTftd/kCDi9tcXqtbjoQDFqcvkCQWN2+yKpVSUViAUUISZWLKYpQhEqViwghAopKufZHA/MVQghRSIRSoYAwf4hce5T57mF+Zr45mJ+ZrxbmZ6lIoBB/c7VBilw8vMK2kKI0suviLu361fyZr7HI/u+4Kbxwb2tr6+rqqq6uHt5SXV392muvRbYbAMSNWChIkwvGPxczEAxa3XQwSAZdPkKI1e0LBIndQ/v8ATcdcPn8w98BTq/fQwcIIcxVI146wFwM6PL5mT4lh5f2+oNXt/j8FqfX5w/avVfvZm5104FAkBDi9V89MM6Gv5CGSUQC5bcuVVOIhd8e0pOIBErJyHT1+/0v35Onj9cqseGFe3d3NyEkdHTUYDAMDAzQNC0SicLd7dy5c+fOnQt9/r6+vtTUVKcTN7ochdPp9Pl8eKF4yeVyOZ3O0E8K1zCTzAxy5r/Mt0WcuuztXv/wVOYhN+2/9rPT52e+Jwgh/kDQ5qGHD3H6rn7HXPtnILSHykMHXL7rOqyG3LT/2tTVbw751gjHoJsescUfCA6FnNfvv/qFRPsDdq+fEBIIBJwud2QfW5/PJxaH9yKH9ws0ODhICFGrvxn3V6vVwWDQYrHoQ76PxrhbY2PjBx98MOIUSqUSmTUql8vl9XqlUkzl5CHuhzuLBIQML+ijC13aRzai7czFV495Zzka7lqtlhBis9mGt1itVoqi0tLSItjtsccee+yxx0K3bNiwgRCi0+nCqioJyWQyr9ebnp7OdiEQfV6vV6fTIdz5x+l0ymSyyPJNoQh7NYvwBhAMBgO51uvC6O7u1uv1I34Rx7gbAADESHjhnpeXV1BQUFtbO7yltrZ2/vz5ke0GAAAxEl64UxS1cuXKt956q66ujqbpbdu21dfXP/PMM8yjW7duXbp0qcfjufVuAAAQa2H3k6xbt85kMlVVVQmFQoFAsHnz5kWLFjEPHT169L333qupqZFKpbfYDQAAYi3sSfsCgWDLli0Wi+XIkSNWqzW0PV5TUxMMBlUq1a13AwCAWItwhFOj0VRUVERrNwAAiC5eXW4LAAAMbs1NNJlMJpOJme0Ot+D1ev1+v1yO2/7xkM1mUyqVAgEaXnzj8/l8Pl8EM9YJIQcPHszPzw/rEG79As2YMSPc/4HkZDabOzo62K4CYqKxsdHr9Y6+HyQaq9Xa2toa2bH5+fkzZswI6xAqeP0qCpAQ3nzzzYaGhjfffJPtQiD6ioqK9u/fX1RUxHYhEGV79uzZtWvXnj174nM6brXcAQAgKhDuAAA8hHAHAOAhhDsAAA8JMe8wEVEUNWHChNLSUrYLgeijKGru3LmY58o/FEXp9fopU6bE6XSYLQMAwD/olgEA4CGEOwAADyHcAQB4COEOAMBDCPeE1NLS8umnn/b09LBdCEST3+8/derURx99dObMmUAgwHY5EBMNDQ2HDx+Ow4kQ7gnG4/EsXry4uLh4yZIlBoNh/fr1bFcE0dHa2jp79uyKioqnnnpq2rRplZWVJpOJ7aIgyrq6uqqrq9944404nAvhnmA2btx44MCBQ4cOORyO7du3b9q06cMPP2S7KIiCZ599dnBw0Gg0WiyWxsZGs9n85JNPsl0URFMwGHzqqafMZnN8TodwTyR+v3/nzp2rVq2qrKwUCATLly+vqqrasWMH23XBeLlcrv37969du5ZZDLKsrGz9+vV1dXX9/f1slwZR86tf/cpkMsXtIiaEeyJpa2tj/qwb3lJdXV1fX89iSRAVQ0NDP/7xj0PfWYfDQQihaZq9oiCajh07tnHjxnfeeUepVMbnjNy6ExPcWnd3NyEkMzNzeIvBYBgYGKBpWiTCW5nAMjMzt2zZMvzPjo6O3/72t3fffXfoew2Jy263L1u2bP369bNnz47bSdFyTySDg4OEELVaPbxFrVYHg0GLxcJeURBl77777pw5c2ia3r17N9u1QHT89Kc/zcnJWbduXTxPinBPJFqtlhBis9mGt1itVoqi0tLS2CsKoubSpUsLFiz40Y9+tGzZstOnT0+cOJHtiiAK3n///Y8++mjXrl1xvi8uwj2RGAwGcq1zhtHd3a3X69EnwwMnT56sqKiQyWRNTU2//vWvVSoV2xVBdNTX11sslvz8fJFIJBKJjhw58s4774hEon379sX0vFgVMpEEg8GioqIlS5b85je/YbbMmzfPYDC8//777BYG4xQIBCZNmjR16tQ//elPFEWxXQ5E0/nz50MvWXjhhReys7PXrl07c+bMjIyM2J0XLb5EQlHUypUrN23atGTJkrlz57799tv19fW1tbVs1wXjVVdXZzQaH3nkke3bt4duf+KJJ7Cwe6KbPHny5MmTh/+5YcOGrKys+++/P9bnRbgnmHXr1plMpqqqKqFQKBAINm/evGjRIraLgvE6f/48IeTVV18dsf3hhx9GuENk0C2TkIaGhlpaWsrLy6VSKdu1AAAXIdwBAHgIs2UAAHgI4Q4AwEMIdwAAHkK4AwDwEMIdAICHEO4AADyEcAcA4CGEOwAADyHcAQB4COEOAMBDCHcAAB5CuAMA8BDCHQCAhxDuAAA8hHAHAOAhhDsAAA8h3AEAeOj/AxkMZKFQ61q4AAAAAElFTkSuQmCC"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "using CairoMakie\n",
    "cauchy = Cauchy(0.5, 0.25)\n",
    "x = range(-1, 4; length = 101)\n",
    "lines(x, pdf.(cauchy, x))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 116,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.256474742801926"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "rand(cauchy)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 117,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "NaN"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "std(cauchy)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 118,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.5"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "quantile(cauchy, 0.5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "You can also create your own distribution by extending a small amount of methods!"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Or, you can use the `fit` function, to fit a distribution to an e.g. experimental measurement:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 119,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Cauchy{Float64}(μ=-0.02589633201878442, σ=0.6501921573461381)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = randn(5000);\n",
    "cauchyfit = fit(Cauchy, x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 120,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plot the fit\n",
    "hist(x, 50; normalization = :pdf)\n",
    "scatter!(x, pdf.(cauchyfit, x); color = \"red\")\n",
    "current_figure()"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Of course, other fundamental statistical measures, e.g. means, stds, quantiles, work out of the box for any distribution."
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# DrWatson\n",
    "\n",
    "[DrWatson](https://juliadynamics.github.io/DrWatson.jl/dev/) is a scientific project assistant software. It helps people deal with their scientific code base, allowing them to focus more on the science and less on the code management. DrWatson offers a lot of tools and functionality for this purpose, but here I'll only show a couple of them. \n",
    "\n",
    "*Disclaimer: I am one of the developers of DrWatson.*\n",
    "\n",
    "## FileIO\n",
    "\n",
    "Obviously, in order to do science, it is necessary to be able to save files to arbitrary formats and to be able to read them later. `FileIO` (which is used by `DrWatson`) is a Julia package that provides a unified API to save and load files to disk, without caring about their actual file ending type.\n",
    "\n",
    "The interface is as simple as:\n",
    "```julia\n",
    "using FileIO\n",
    "object = load(filename)\n",
    "save(filename, object)\n",
    "```\n",
    "where `filename` is a `String` (arbitrary path) that *includes* the file ending, e.g. `.hdf5`.\n",
    "\n",
    "`FileIO` does not actually install any packages that can save or load files! It provides the interface. If you try to save/load a file with an unsupported ending, `FileIO` will tell you that's impossible."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\"c:\\\\Users\\\\datse\\\\OneDrive - University of Exeter\\\\Teaching\\\\Zero2Hero-JuliaWorkshop\""
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "using DrWatson\n",
    "cd(@__DIR__)\n",
    "pwd() # state current working directory"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Most packages that can save data of arbitrary format expect the final object to save a dictionary"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Dict{String, Int64} with 2 entries:\n",
       "  \"b\" => 4\n",
       "  \"a\" => 5"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "testdata = Dict(\"a\" => 5, \"b\" => 4)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To save the data we need a \"file i/o backend\". I recommend JLD2.jl:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 161,
   "metadata": {},
   "outputs": [],
   "source": [
    "# import Pkg; Pkg.add(\"JLD2\")\n",
    "save(\"test.jld2\", testdata)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 162,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Dict{String, Any} with 2 entries:\n",
       "  \"b\" => 4\n",
       "  \"a\" => 5"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "load(\"test.jld2\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 163,
   "metadata": {},
   "outputs": [],
   "source": [
    "rm(\"test.jld2\") # clean-up"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Savename\n",
    "\n",
    "When saving files, scientists often want to include the parameter values of the simulations in the name of the file. For example, If I had run a simulation with parameters:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 164,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1, 2, 3)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "a, b, c = 1, 2, 3"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "I would like to save my simulation as e.g. `sim_a=1_b=2_c=3.jld2`. This can be achieved with string interpolation like so"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 165,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\"sim_a=1_b=2_c=3.jld2\""
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "filename = \"sim_a=$(a)_b=$(b)_c=$(c).jld2\""
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This works, but besides being tedious, it is not extendable: if I have a different simulation, with different parameter names, I have to modify this command.\n",
    "\n",
    "This is where DrWatson comes in: it provides a tool, called `savename`, that takes as an input **any Julia container** and converts it into a `key=value` chain. It works with dictionaries and arbitrary Julia composite types (it would work with the `Animal` we defined in the previous session). For example:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 174,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Dict{String, Int64} with 3 entries:\n",
       "  \"c\" => 3\n",
       "  \"b\" => 2\n",
       "  \"a\" => 1"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "using DrWatson\n",
    "# the `@strdict` command makes a dictionary from the given variable names\n",
    "# it converts the variable names into strings for the keys of the dictionary\n",
    "# `@strdict` is a \"macro\", something we won't talk about in this workshop\n",
    "pars = @strdict a b c"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 175,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\"a=1_b=2_c=3\""
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "savename(pars)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "You can also call `savename` with prefix and suffix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 176,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\"prefix_a=1_b=2_c=3_model=linear.jld2\""
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "model = \"linear\"\n",
    "pars = @strdict a b c model\n",
    "savename(\"prefix\", pars, \"jld2\")"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "`savename` is highly customizable, and also extendable for your own types, while by default it makes some reasonable assumptions about what should and should not be put into the this name. For example, if you had a vector of numbers as part of your parameters, you probably don't want to include it into the savename (by default)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 179,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Dict{String, Any} with 5 entries:\n",
       "  \"v\"     => [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]\n",
       "  \"c\"     => 3\n",
       "  \"model\" => \"linear\"\n",
       "  \"b\"     => 2\n",
       "  \"a\"     => 1"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pars[\"v\"] = collect(1:10)\n",
    "pars"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 180,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\"a=1_b=2_c=3_model=linear\""
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "savename(pars)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "But you _could_ if you really wanted to:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 181,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\"a=1_b=2_c=3_model=linear_v=[1, 2, 3, 4, 5, 6, 7, 8, 9, 10].jld2\""
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "savename(pars, \"jld2\"; allowedtypes = (Real, String, Vector))"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "`savename` is also convenient for creating titles for figures, by using a different connector:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 182,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\"Simulation, a=1, b=2, c=3, model=linear\""
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "savename(\"Simulation\", pars; connector = \", \")"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Saving tools\n",
    "\n",
    "DrWatson offers some tools that are useful when saving files. The first is\n",
    "`tagsave`, which modifies the dictionary-to-be-saved by adding additional information about the current status of the Git repository of the project (if there exists a Git repository). This allows for reproducibility. For example (notice that `pwd()` is the path of a Git repository)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 183,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "┌ Warning: The Git repository ('c:\\Users\\datse\\OneDrive - University of Exeter\\Teaching\\Zero2Hero-JuliaWorkshop') is dirty! Appending -dirty to the commit ID.\n",
      "└ @ DrWatson C:\\Users\\datse\\.julia\\packages\\DrWatson\\ieY6i\\src\\saving_tools.jl:64\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "Dict{String, Any} with 6 entries:\n",
       "  \"v\"         => [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]\n",
       "  \"c\"         => 3\n",
       "  \"gitcommit\" => \"c91187afcd76068f8e1efc89b5c473a31e57bb48-dirty\"\n",
       "  \"model\"     => \"linear\"\n",
       "  \"b\"         => 2\n",
       "  \"a\"         => 1"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "tagsave(\"test.jld2\", copy(pars); gitpath = pwd())\n",
    "load(\"test.jld2\")"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "You can see that the Git commit ID was included in the saved file! And not only that, but because the git status is currently \"dirty\", this was also added as saved information."
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Another useful tool is `safesave`. We all know how **devastating** it can be to by-mistake overwrite an existing simulation because you saved a new simulation with the same name... `safesave` comes to the rescue because it ensures that no files are overwritten but also all files are saved!\n",
    "\n",
    "It works like this:\n",
    "```julia\n",
    "safesave(\"test.jld2\", ...)\n",
    "```\n",
    "if `\"test.jld2\"` exists, rename it to `test_#1.jld2` (and do this recursively if `test_#1.jld2` also exists, by incrementing the number after the `#`). Then, save the current data as `test.jld2`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 184,
   "metadata": {},
   "outputs": [],
   "source": [
    "safesave(\"test.jld2\", pars)\n",
    "safesave(\"test.jld2\", pars)\n",
    "safesave(\"test.jld2\", pars)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 185,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "19-element Vector{String}:\n",
       " \".git\"\n",
       " \".gitignore\"\n",
       " \"1-JuliaIntro.ipynb\"\n",
       " \"2-MultipleDispatch.ipynb\"\n",
       " \"3-Ecosystem.ipynb\"\n",
       " \"LICENSE.md\"\n",
       " \"Manifest.toml\"\n",
       " \"Project.toml\"\n",
       " \"README.md\"\n",
       " \"add.jpg\"\n",
       " \"makie_ex_fig_1.png\"\n",
       " \"makie_ex_fig_2.png\"\n",
       " \"solutions_1.jl\"\n",
       " \"solutions_2.jl\"\n",
       " \"solutions_3.jl\"\n",
       " \"test.jld2\"\n",
       " \"test_#1.jld2\"\n",
       " \"test_#2.jld2\"\n",
       " \"test_#3.jld2\""
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "readdir(pwd())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 188,
   "metadata": {},
   "outputs": [],
   "source": [
    "# delete all files that end in \"jld2\"\n",
    "[rm(f) for f in readdir(pwd()) if endswith(f, \"jld2\")];"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Collecting results\n",
    "\n",
    "If you run several similar simulations with different parameters, you typically want to collect all of them in a tabular datastrcture to analyze further. You can use `collect_results` to automate the data collection process. \n",
    "\n",
    "Let's say we run first some simulations with varying parameters like so:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 190,
   "metadata": {},
   "outputs": [],
   "source": [
    "model = \"linear\"\n",
    "for a in 1:2\n",
    "    for b in [2, 3]\n",
    "        # perform a fake simulation\n",
    "        r = a + b\n",
    "        # save it:\n",
    "        p = @strdict a b r model\n",
    "        s = @strdict a b model # the result \"r\" doesn't take part in the name\n",
    "        wsave(joinpath(\"data\", savename(s, \"jld2\")), p)\n",
    "    end\n",
    "end"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Then we run a different model, which does not necessarily have the same parameters:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 192,
   "metadata": {},
   "outputs": [],
   "source": [
    "model = \"cubic\"\n",
    "for a in 1:2\n",
    "    for d in [5, 6]\n",
    "        # perform a fake simulation\n",
    "        r = a + d^3\n",
    "        # save it:\n",
    "        p = @strdict a d r model\n",
    "        s = @strdict a d model # the result \"r\" doesn't take part in the name\n",
    "        wsave(joinpath(\"data\", savename(s, \"jld2\")), p)\n",
    "    end\n",
    "end"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now the idea is that we want to collect all of this results in a single tabular structure. We do with `collect_results(folder)`, which collects all results of the `folder` into a `DataFrame`. This is a tabular data structure (and thus we need the Julia package `DataFrames` to use it):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 193,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "┌ Info: Scanning folder data for result files.\n",
      "└ @ DrWatson C:\\Users\\datse\\.julia\\packages\\DrWatson\\ieY6i\\src\\result_collection.jl:115\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "┌ Info: Added 8 entries.\n",
      "└ @ DrWatson C:\\Users\\datse\\.julia\\packages\\DrWatson\\ieY6i\\src\\result_collection.jl:191\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<div><div style = \"float: left;\"><span>8×6 DataFrame</span></div><div style = \"clear: both;\"></div></div><div class = \"data-frame\" style = \"overflow-x: scroll;\"><table class = \"data-frame\" style = \"margin-bottom: 6px;\"><thead><tr class = \"header\"><th class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">Row</th><th style = \"text-align: left;\">model</th><th style = \"text-align: left;\">b</th><th style = \"text-align: left;\">r</th><th style = \"text-align: left;\">a</th><th style = \"text-align: left;\">path</th><th style = \"text-align: left;\">d</th></tr><tr class = \"subheader headerLastRow\"><th class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\"></th><th title = \"Union{Missing, String}\" style = \"text-align: left;\">String?</th><th title = \"Union{Missing, Int64}\" style = \"text-align: left;\">Int64?</th><th title = \"Union{Missing, Int64}\" style = \"text-align: left;\">Int64?</th><th title = \"Union{Missing, Int64}\" style = \"text-align: left;\">Int64?</th><th title = \"Union{Missing, String}\" style = \"text-align: left;\">String?</th><th title = \"Union{Missing, Int64}\" style = \"text-align: left;\">Int64?</th></tr></thead><tbody><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">1</td><td style = \"text-align: left;\">linear</td><td style = \"text-align: right;\">2</td><td style = \"text-align: right;\">3</td><td style = \"text-align: right;\">1</td><td style = \"text-align: left;\">data\\\\a=1_b=2_model=linear.jld2</td><td style = \"font-style: italic; text-align: right;\">missing</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">2</td><td style = \"text-align: left;\">linear</td><td style = \"text-align: right;\">3</td><td style = \"text-align: right;\">4</td><td style = \"text-align: right;\">1</td><td style = \"text-align: left;\">data\\\\a=1_b=3_model=linear.jld2</td><td style = \"font-style: italic; text-align: right;\">missing</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">3</td><td style = \"text-align: left;\">cubic</td><td style = \"font-style: italic; text-align: right;\">missing</td><td style = \"text-align: right;\">126</td><td style = \"text-align: right;\">1</td><td style = \"text-align: left;\">data\\\\a=1_d=5_model=cubic.jld2</td><td style = \"text-align: right;\">5</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">4</td><td style = \"text-align: left;\">cubic</td><td style = \"font-style: italic; text-align: right;\">missing</td><td style = \"text-align: right;\">217</td><td style = \"text-align: right;\">1</td><td style = \"text-align: left;\">data\\\\a=1_d=6_model=cubic.jld2</td><td style = \"text-align: right;\">6</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">5</td><td style = \"text-align: left;\">linear</td><td style = \"text-align: right;\">2</td><td style = \"text-align: right;\">4</td><td style = \"text-align: right;\">2</td><td style = \"text-align: left;\">data\\\\a=2_b=2_model=linear.jld2</td><td style = \"font-style: italic; text-align: right;\">missing</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">6</td><td style = \"text-align: left;\">linear</td><td style = \"text-align: right;\">3</td><td style = \"text-align: right;\">5</td><td style = \"text-align: right;\">2</td><td style = \"text-align: left;\">data\\\\a=2_b=3_model=linear.jld2</td><td style = \"font-style: italic; text-align: right;\">missing</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">7</td><td style = \"text-align: left;\">cubic</td><td style = \"font-style: italic; text-align: right;\">missing</td><td style = \"text-align: right;\">127</td><td style = \"text-align: right;\">2</td><td style = \"text-align: left;\">data\\\\a=2_d=5_model=cubic.jld2</td><td style = \"text-align: right;\">5</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">8</td><td style = \"text-align: left;\">cubic</td><td style = \"font-style: italic; text-align: right;\">missing</td><td style = \"text-align: right;\">218</td><td style = \"text-align: right;\">2</td><td style = \"text-align: left;\">data\\\\a=2_d=6_model=cubic.jld2</td><td style = \"text-align: right;\">6</td></tr></tbody></table></div>"
      ],
      "text/latex": [
       "\\begin{tabular}{r|cccccc}\n",
       "\t& model & b & r & a & path & d\\\\\n",
       "\t\\hline\n",
       "\t& String? & Int64? & Int64? & Int64? & String? & Int64?\\\\\n",
       "\t\\hline\n",
       "\t1 & linear & 2 & 3 & 1 & data\\textbackslash{}\\textbackslash{}a=1\\_b=2\\_model=linear.jld2 & \\emph{missing} \\\\\n",
       "\t2 & linear & 3 & 4 & 1 & data\\textbackslash{}\\textbackslash{}a=1\\_b=3\\_model=linear.jld2 & \\emph{missing} \\\\\n",
       "\t3 & cubic & \\emph{missing} & 126 & 1 & data\\textbackslash{}\\textbackslash{}a=1\\_d=5\\_model=cubic.jld2 & 5 \\\\\n",
       "\t4 & cubic & \\emph{missing} & 217 & 1 & data\\textbackslash{}\\textbackslash{}a=1\\_d=6\\_model=cubic.jld2 & 6 \\\\\n",
       "\t5 & linear & 2 & 4 & 2 & data\\textbackslash{}\\textbackslash{}a=2\\_b=2\\_model=linear.jld2 & \\emph{missing} \\\\\n",
       "\t6 & linear & 3 & 5 & 2 & data\\textbackslash{}\\textbackslash{}a=2\\_b=3\\_model=linear.jld2 & \\emph{missing} \\\\\n",
       "\t7 & cubic & \\emph{missing} & 127 & 2 & data\\textbackslash{}\\textbackslash{}a=2\\_d=5\\_model=cubic.jld2 & 5 \\\\\n",
       "\t8 & cubic & \\emph{missing} & 218 & 2 & data\\textbackslash{}\\textbackslash{}a=2\\_d=6\\_model=cubic.jld2 & 6 \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/plain": [
       "\u001b[1m8×6 DataFrame\u001b[0m\n",
       "\u001b[1m Row \u001b[0m│\u001b[1m model   \u001b[0m\u001b[1m b       \u001b[0m\u001b[1m r      \u001b[0m\u001b[1m a      \u001b[0m\u001b[1m path                            \u001b[0m\u001b[1m d   \u001b[0m ⋯\n",
       "     │\u001b[90m String? \u001b[0m\u001b[90m Int64?  \u001b[0m\u001b[90m Int64? \u001b[0m\u001b[90m Int64? \u001b[0m\u001b[90m String?                         \u001b[0m\u001b[90m Int6\u001b[0m ⋯\n",
       "─────┼──────────────────────────────────────────────────────────────────────────\n",
       "   1 │ linear         2       3       1  data\\\\a=1_b=2_model=linear.jld2 \u001b[90m miss\u001b[0m ⋯\n",
       "   2 │ linear         3       4       1  data\\\\a=1_b=3_model=linear.jld2 \u001b[90m miss\u001b[0m\n",
       "   3 │ cubic   \u001b[90m missing \u001b[0m    126       1  data\\\\a=1_d=5_model=cubic.jld2\n",
       "   4 │ cubic   \u001b[90m missing \u001b[0m    217       1  data\\\\a=1_d=6_model=cubic.jld2\n",
       "   5 │ linear         2       4       2  data\\\\a=2_b=2_model=linear.jld2 \u001b[90m miss\u001b[0m ⋯\n",
       "   6 │ linear         3       5       2  data\\\\a=2_b=3_model=linear.jld2 \u001b[90m miss\u001b[0m\n",
       "   7 │ cubic   \u001b[90m missing \u001b[0m    127       2  data\\\\a=2_d=5_model=cubic.jld2\n",
       "   8 │ cubic   \u001b[90m missing \u001b[0m    218       2  data\\\\a=2_d=6_model=cubic.jld2\n",
       "\u001b[36m                                                                1 column omitted\u001b[0m"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "using DataFrames\n",
    "results = collect_results(\"data\")"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "So `collect_results` collected all files, but also did something extra, something very useful. Simulation parameters that do not exist in one run (see `b` vs `d`) have the value `missing`. `missing` is how Julia represents missing values."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 194,
   "metadata": {},
   "outputs": [],
   "source": [
    "# delete all saved data files (they are loaded in memory)\n",
    "rm(\"data\"; recursive = true)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 5. Tabular data with DataFrames.jl\n",
    "\n",
    "The `result` that we got above is a `DataFrame` from [DataFrames.jl](http://juliadata.github.io/DataFrames.jl/stable/), one of the major Julia packages for tabular data. \n",
    "\n",
    "## Basic stuff\n",
    "One can do basic selection of these data, for example selecting specific columns, removing columns, adding new columns or rows, etc. The `path` column of the `results` is not so useful, so let's remove it:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 195,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div><div style = \"float: left;\"><span>8×5 DataFrame</span></div><div style = \"clear: both;\"></div></div><div class = \"data-frame\" style = \"overflow-x: scroll;\"><table class = \"data-frame\" style = \"margin-bottom: 6px;\"><thead><tr class = \"header\"><th class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">Row</th><th style = \"text-align: left;\">model</th><th style = \"text-align: left;\">b</th><th style = \"text-align: left;\">r</th><th style = \"text-align: left;\">a</th><th style = \"text-align: left;\">d</th></tr><tr class = \"subheader headerLastRow\"><th class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\"></th><th title = \"Union{Missing, String}\" style = \"text-align: left;\">String?</th><th title = \"Union{Missing, Int64}\" style = \"text-align: left;\">Int64?</th><th title = \"Union{Missing, Int64}\" style = \"text-align: left;\">Int64?</th><th title = \"Union{Missing, Int64}\" style = \"text-align: left;\">Int64?</th><th title = \"Union{Missing, Int64}\" style = \"text-align: left;\">Int64?</th></tr></thead><tbody><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">1</td><td style = \"text-align: left;\">linear</td><td style = \"text-align: right;\">2</td><td style = \"text-align: right;\">3</td><td style = \"text-align: right;\">1</td><td style = \"font-style: italic; text-align: right;\">missing</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">2</td><td style = \"text-align: left;\">linear</td><td style = \"text-align: right;\">3</td><td style = \"text-align: right;\">4</td><td style = \"text-align: right;\">1</td><td style = \"font-style: italic; text-align: right;\">missing</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">3</td><td style = \"text-align: left;\">cubic</td><td style = \"font-style: italic; text-align: right;\">missing</td><td style = \"text-align: right;\">126</td><td style = \"text-align: right;\">1</td><td style = \"text-align: right;\">5</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">4</td><td style = \"text-align: left;\">cubic</td><td style = \"font-style: italic; text-align: right;\">missing</td><td style = \"text-align: right;\">217</td><td style = \"text-align: right;\">1</td><td style = \"text-align: right;\">6</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">5</td><td style = \"text-align: left;\">linear</td><td style = \"text-align: right;\">2</td><td style = \"text-align: right;\">4</td><td style = \"text-align: right;\">2</td><td style = \"font-style: italic; text-align: right;\">missing</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">6</td><td style = \"text-align: left;\">linear</td><td style = \"text-align: right;\">3</td><td style = \"text-align: right;\">5</td><td style = \"text-align: right;\">2</td><td style = \"font-style: italic; text-align: right;\">missing</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">7</td><td style = \"text-align: left;\">cubic</td><td style = \"font-style: italic; text-align: right;\">missing</td><td style = \"text-align: right;\">127</td><td style = \"text-align: right;\">2</td><td style = \"text-align: right;\">5</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">8</td><td style = \"text-align: left;\">cubic</td><td style = \"font-style: italic; text-align: right;\">missing</td><td style = \"text-align: right;\">218</td><td style = \"text-align: right;\">2</td><td style = \"text-align: right;\">6</td></tr></tbody></table></div>"
      ],
      "text/latex": [
       "\\begin{tabular}{r|ccccc}\n",
       "\t& model & b & r & a & d\\\\\n",
       "\t\\hline\n",
       "\t& String? & Int64? & Int64? & Int64? & Int64?\\\\\n",
       "\t\\hline\n",
       "\t1 & linear & 2 & 3 & 1 & \\emph{missing} \\\\\n",
       "\t2 & linear & 3 & 4 & 1 & \\emph{missing} \\\\\n",
       "\t3 & cubic & \\emph{missing} & 126 & 1 & 5 \\\\\n",
       "\t4 & cubic & \\emph{missing} & 217 & 1 & 6 \\\\\n",
       "\t5 & linear & 2 & 4 & 2 & \\emph{missing} \\\\\n",
       "\t6 & linear & 3 & 5 & 2 & \\emph{missing} \\\\\n",
       "\t7 & cubic & \\emph{missing} & 127 & 2 & 5 \\\\\n",
       "\t8 & cubic & \\emph{missing} & 218 & 2 & 6 \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/plain": [
       "\u001b[1m8×5 DataFrame\u001b[0m\n",
       "\u001b[1m Row \u001b[0m│\u001b[1m model   \u001b[0m\u001b[1m b       \u001b[0m\u001b[1m r      \u001b[0m\u001b[1m a      \u001b[0m\u001b[1m d       \u001b[0m\n",
       "     │\u001b[90m String? \u001b[0m\u001b[90m Int64?  \u001b[0m\u001b[90m Int64? \u001b[0m\u001b[90m Int64? \u001b[0m\u001b[90m Int64?  \u001b[0m\n",
       "─────┼───────────────────────────────────────────\n",
       "   1 │ linear         2       3       1 \u001b[90m missing \u001b[0m\n",
       "   2 │ linear         3       4       1 \u001b[90m missing \u001b[0m\n",
       "   3 │ cubic   \u001b[90m missing \u001b[0m    126       1        5\n",
       "   4 │ cubic   \u001b[90m missing \u001b[0m    217       1        6\n",
       "   5 │ linear         2       4       2 \u001b[90m missing \u001b[0m\n",
       "   6 │ linear         3       5       2 \u001b[90m missing \u001b[0m\n",
       "   7 │ cubic   \u001b[90m missing \u001b[0m    127       2        5\n",
       "   8 │ cubic   \u001b[90m missing \u001b[0m    218       2        6"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "select!(results, Not(:path))"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To access specific rows or columns you can access a dataframe like a matrix, e.g. `df[:, 1:3]` gives the first three rows while `df[:, [:a, :b]]` gives the rows selected by name.\n",
    "\n",
    "Adding new data to a dataframe is also straight forward. One can add new rows or new columns. New rows are added by either providing a vector (where the vector's length matches the number of columns), or by providing a named tuple that explicitly names which column gets which new value."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 196,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div><div style = \"float: left;\"><span>3×3 DataFrame</span></div><div style = \"clear: both;\"></div></div><div class = \"data-frame\" style = \"overflow-x: scroll;\"><table class = \"data-frame\" style = \"margin-bottom: 6px;\"><thead><tr class = \"header\"><th class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">Row</th><th style = \"text-align: left;\">model</th><th style = \"text-align: left;\">b</th><th style = \"text-align: left;\">r</th></tr><tr class = \"subheader headerLastRow\"><th class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\"></th><th title = \"Union{Missing, String}\" style = \"text-align: left;\">String?</th><th title = \"Union{Missing, Int64}\" style = \"text-align: left;\">Int64?</th><th title = \"Union{Missing, Int64}\" style = \"text-align: left;\">Int64?</th></tr></thead><tbody><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">1</td><td style = \"text-align: left;\">linear</td><td style = \"text-align: right;\">2</td><td style = \"text-align: right;\">3</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">2</td><td style = \"text-align: left;\">linear</td><td style = \"text-align: right;\">3</td><td style = \"text-align: right;\">4</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">3</td><td style = \"text-align: left;\">cubic</td><td style = \"font-style: italic; text-align: right;\">missing</td><td style = \"text-align: right;\">126</td></tr></tbody></table></div>"
      ],
      "text/latex": [
       "\\begin{tabular}{r|ccc}\n",
       "\t& model & b & r\\\\\n",
       "\t\\hline\n",
       "\t& String? & Int64? & Int64?\\\\\n",
       "\t\\hline\n",
       "\t1 & linear & 2 & 3 \\\\\n",
       "\t2 & linear & 3 & 4 \\\\\n",
       "\t3 & cubic & \\emph{missing} & 126 \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/plain": [
       "\u001b[1m3×3 DataFrame\u001b[0m\n",
       "\u001b[1m Row \u001b[0m│\u001b[1m model   \u001b[0m\u001b[1m b       \u001b[0m\u001b[1m r      \u001b[0m\n",
       "     │\u001b[90m String? \u001b[0m\u001b[90m Int64?  \u001b[0m\u001b[90m Int64? \u001b[0m\n",
       "─────┼──────────────────────────\n",
       "   1 │ linear         2       3\n",
       "   2 │ linear         3       4\n",
       "   3 │ cubic   \u001b[90m missing \u001b[0m    126"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "df1 = results[1:3, 1:3]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 198,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div><div style = \"float: left;\"><span>4×3 DataFrame</span></div><div style = \"clear: both;\"></div></div><div class = \"data-frame\" style = \"overflow-x: scroll;\"><table class = \"data-frame\" style = \"margin-bottom: 6px;\"><thead><tr class = \"header\"><th class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">Row</th><th style = \"text-align: left;\">model</th><th style = \"text-align: left;\">b</th><th style = \"text-align: left;\">r</th></tr><tr class = \"subheader headerLastRow\"><th class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\"></th><th title = \"Union{Missing, String}\" style = \"text-align: left;\">String?</th><th title = \"Union{Missing, Int64}\" style = \"text-align: left;\">Int64?</th><th title = \"Union{Missing, Int64}\" style = \"text-align: left;\">Int64?</th></tr></thead><tbody><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">1</td><td style = \"text-align: left;\">linear</td><td style = \"text-align: right;\">2</td><td style = \"text-align: right;\">3</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">2</td><td style = \"text-align: left;\">linear</td><td style = \"text-align: right;\">3</td><td style = \"text-align: right;\">4</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">3</td><td style = \"text-align: left;\">cubic</td><td style = \"font-style: italic; text-align: right;\">missing</td><td style = \"text-align: right;\">126</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">4</td><td style = \"text-align: left;\">test</td><td style = \"text-align: right;\">5</td><td style = \"text-align: right;\">5</td></tr></tbody></table></div>"
      ],
      "text/latex": [
       "\\begin{tabular}{r|ccc}\n",
       "\t& model & b & r\\\\\n",
       "\t\\hline\n",
       "\t& String? & Int64? & Int64?\\\\\n",
       "\t\\hline\n",
       "\t1 & linear & 2 & 3 \\\\\n",
       "\t2 & linear & 3 & 4 \\\\\n",
       "\t3 & cubic & \\emph{missing} & 126 \\\\\n",
       "\t4 & test & 5 & 5 \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/plain": [
       "\u001b[1m4×3 DataFrame\u001b[0m\n",
       "\u001b[1m Row \u001b[0m│\u001b[1m model   \u001b[0m\u001b[1m b       \u001b[0m\u001b[1m r      \u001b[0m\n",
       "     │\u001b[90m String? \u001b[0m\u001b[90m Int64?  \u001b[0m\u001b[90m Int64? \u001b[0m\n",
       "─────┼──────────────────────────\n",
       "   1 │ linear         2       3\n",
       "   2 │ linear         3       4\n",
       "   3 │ cubic   \u001b[90m missing \u001b[0m    126\n",
       "   4 │ test           5       5"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# add new row by order of columns\n",
    "push!(df1, [\"test\", 5, 5])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 200,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div><div style = \"float: left;\"><span>5×3 DataFrame</span></div><div style = \"clear: both;\"></div></div><div class = \"data-frame\" style = \"overflow-x: scroll;\"><table class = \"data-frame\" style = \"margin-bottom: 6px;\"><thead><tr class = \"header\"><th class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">Row</th><th style = \"text-align: left;\">model</th><th style = \"text-align: left;\">b</th><th style = \"text-align: left;\">r</th></tr><tr class = \"subheader headerLastRow\"><th class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\"></th><th title = \"Union{Missing, String}\" style = \"text-align: left;\">String?</th><th title = \"Union{Missing, Int64}\" style = \"text-align: left;\">Int64?</th><th title = \"Union{Missing, Int64}\" style = \"text-align: left;\">Int64?</th></tr></thead><tbody><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">1</td><td style = \"text-align: left;\">linear</td><td style = \"text-align: right;\">2</td><td style = \"text-align: right;\">3</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">2</td><td style = \"text-align: left;\">linear</td><td style = \"text-align: right;\">3</td><td style = \"text-align: right;\">4</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">3</td><td style = \"text-align: left;\">cubic</td><td style = \"font-style: italic; text-align: right;\">missing</td><td style = \"text-align: right;\">126</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">4</td><td style = \"text-align: left;\">test</td><td style = \"text-align: right;\">5</td><td style = \"text-align: right;\">5</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">5</td><td style = \"text-align: left;\">test2</td><td style = \"text-align: right;\">-5</td><td style = \"text-align: right;\">89</td></tr></tbody></table></div>"
      ],
      "text/latex": [
       "\\begin{tabular}{r|ccc}\n",
       "\t& model & b & r\\\\\n",
       "\t\\hline\n",
       "\t& String? & Int64? & Int64?\\\\\n",
       "\t\\hline\n",
       "\t1 & linear & 2 & 3 \\\\\n",
       "\t2 & linear & 3 & 4 \\\\\n",
       "\t3 & cubic & \\emph{missing} & 126 \\\\\n",
       "\t4 & test & 5 & 5 \\\\\n",
       "\t5 & test2 & -5 & 89 \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/plain": [
       "\u001b[1m5×3 DataFrame\u001b[0m\n",
       "\u001b[1m Row \u001b[0m│\u001b[1m model   \u001b[0m\u001b[1m b       \u001b[0m\u001b[1m r      \u001b[0m\n",
       "     │\u001b[90m String? \u001b[0m\u001b[90m Int64?  \u001b[0m\u001b[90m Int64? \u001b[0m\n",
       "─────┼──────────────────────────\n",
       "   1 │ linear         2       3\n",
       "   2 │ linear         3       4\n",
       "   3 │ cubic   \u001b[90m missing \u001b[0m    126\n",
       "   4 │ test           5       5\n",
       "   5 │ test2         -5      89"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# add new row by name of columnns\n",
    "push!(df1, (model = \"test2\", r=89, b = -5))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 202,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div><div style = \"float: left;\"><span>5×4 DataFrame</span></div><div style = \"clear: both;\"></div></div><div class = \"data-frame\" style = \"overflow-x: scroll;\"><table class = \"data-frame\" style = \"margin-bottom: 6px;\"><thead><tr class = \"header\"><th class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">Row</th><th style = \"text-align: left;\">model</th><th style = \"text-align: left;\">b</th><th style = \"text-align: left;\">r</th><th style = \"text-align: left;\">z</th></tr><tr class = \"subheader headerLastRow\"><th class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\"></th><th title = \"Union{Missing, String}\" style = \"text-align: left;\">String?</th><th title = \"Union{Missing, Int64}\" style = \"text-align: left;\">Int64?</th><th title = \"Union{Missing, Int64}\" style = \"text-align: left;\">Int64?</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th></tr></thead><tbody><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">1</td><td style = \"text-align: left;\">linear</td><td style = \"text-align: right;\">2</td><td style = \"text-align: right;\">3</td><td style = \"text-align: right;\">0.108019</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">2</td><td style = \"text-align: left;\">linear</td><td style = \"text-align: right;\">3</td><td style = \"text-align: right;\">4</td><td style = \"text-align: right;\">0.267137</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">3</td><td style = \"text-align: left;\">cubic</td><td style = \"font-style: italic; text-align: right;\">missing</td><td style = \"text-align: right;\">126</td><td style = \"text-align: right;\">0.331057</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">4</td><td style = \"text-align: left;\">test</td><td style = \"text-align: right;\">5</td><td style = \"text-align: right;\">5</td><td style = \"text-align: right;\">0.656981</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">5</td><td style = \"text-align: left;\">test2</td><td style = \"text-align: right;\">-5</td><td style = \"text-align: right;\">89</td><td style = \"text-align: right;\">0.876635</td></tr></tbody></table></div>"
      ],
      "text/latex": [
       "\\begin{tabular}{r|cccc}\n",
       "\t& model & b & r & z\\\\\n",
       "\t\\hline\n",
       "\t& String? & Int64? & Int64? & Float64\\\\\n",
       "\t\\hline\n",
       "\t1 & linear & 2 & 3 & 0.108019 \\\\\n",
       "\t2 & linear & 3 & 4 & 0.267137 \\\\\n",
       "\t3 & cubic & \\emph{missing} & 126 & 0.331057 \\\\\n",
       "\t4 & test & 5 & 5 & 0.656981 \\\\\n",
       "\t5 & test2 & -5 & 89 & 0.876635 \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/plain": [
       "\u001b[1m5×4 DataFrame\u001b[0m\n",
       "\u001b[1m Row \u001b[0m│\u001b[1m model   \u001b[0m\u001b[1m b       \u001b[0m\u001b[1m r      \u001b[0m\u001b[1m z        \u001b[0m\n",
       "     │\u001b[90m String? \u001b[0m\u001b[90m Int64?  \u001b[0m\u001b[90m Int64? \u001b[0m\u001b[90m Float64  \u001b[0m\n",
       "─────┼────────────────────────────────────\n",
       "   1 │ linear         2       3  0.108019\n",
       "   2 │ linear         3       4  0.267137\n",
       "   3 │ cubic   \u001b[90m missing \u001b[0m    126  0.331057\n",
       "   4 │ test           5       5  0.656981\n",
       "   5 │ test2         -5      89  0.876635"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# add new row with given name by field assignment\n",
    "df1.z = rand(size(df1, 1))\n",
    "df1"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Querying and manipulating a `DataFrame`\n",
    "\n",
    "General querying and data manipulation can be done on `DataFrame`s using standard library functions from DataFrames.jl. However, it is [recommended](https://dataframes.juliadata.org/stable/man/querying_frameworks/#Data-manipulation-frameworks) to use a package dedicated to querying and data manupulation that provides simpler/easier syntax for it. Several options exist, each providing a slightly different variant on the syntax, so you can pick whatever you feel most comfortable in. Here we will use a LINQ-like [Query.jl](https://www.queryverse.org/Query.jl/stable/) syntax, which can be used with any tabular Julia data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 203,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div><div style = \"float: left;\"><span>8×5 DataFrame</span></div><div style = \"clear: both;\"></div></div><div class = \"data-frame\" style = \"overflow-x: scroll;\"><table class = \"data-frame\" style = \"margin-bottom: 6px;\"><thead><tr class = \"header\"><th class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">Row</th><th style = \"text-align: left;\">model</th><th style = \"text-align: left;\">b</th><th style = \"text-align: left;\">r</th><th style = \"text-align: left;\">a</th><th style = \"text-align: left;\">d</th></tr><tr class = \"subheader headerLastRow\"><th class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\"></th><th title = \"Union{Missing, String}\" style = \"text-align: left;\">String?</th><th title = \"Union{Missing, Int64}\" style = \"text-align: left;\">Int64?</th><th title = \"Union{Missing, Int64}\" style = \"text-align: left;\">Int64?</th><th title = \"Union{Missing, Int64}\" style = \"text-align: left;\">Int64?</th><th title = \"Union{Missing, Int64}\" style = \"text-align: left;\">Int64?</th></tr></thead><tbody><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">1</td><td style = \"text-align: left;\">linear</td><td style = \"text-align: right;\">2</td><td style = \"text-align: right;\">3</td><td style = \"text-align: right;\">1</td><td style = \"font-style: italic; text-align: right;\">missing</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">2</td><td style = \"text-align: left;\">linear</td><td style = \"text-align: right;\">3</td><td style = \"text-align: right;\">4</td><td style = \"text-align: right;\">1</td><td style = \"font-style: italic; text-align: right;\">missing</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">3</td><td style = \"text-align: left;\">cubic</td><td style = \"font-style: italic; text-align: right;\">missing</td><td style = \"text-align: right;\">126</td><td style = \"text-align: right;\">1</td><td style = \"text-align: right;\">5</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">4</td><td style = \"text-align: left;\">cubic</td><td style = \"font-style: italic; text-align: right;\">missing</td><td style = \"text-align: right;\">217</td><td style = \"text-align: right;\">1</td><td style = \"text-align: right;\">6</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">5</td><td style = \"text-align: left;\">linear</td><td style = \"text-align: right;\">2</td><td style = \"text-align: right;\">4</td><td style = \"text-align: right;\">2</td><td style = \"font-style: italic; text-align: right;\">missing</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">6</td><td style = \"text-align: left;\">linear</td><td style = \"text-align: right;\">3</td><td style = \"text-align: right;\">5</td><td style = \"text-align: right;\">2</td><td style = \"font-style: italic; text-align: right;\">missing</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">7</td><td style = \"text-align: left;\">cubic</td><td style = \"font-style: italic; text-align: right;\">missing</td><td style = \"text-align: right;\">127</td><td style = \"text-align: right;\">2</td><td style = \"text-align: right;\">5</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">8</td><td style = \"text-align: left;\">cubic</td><td style = \"font-style: italic; text-align: right;\">missing</td><td style = \"text-align: right;\">218</td><td style = \"text-align: right;\">2</td><td style = \"text-align: right;\">6</td></tr></tbody></table></div>"
      ],
      "text/latex": [
       "\\begin{tabular}{r|ccccc}\n",
       "\t& model & b & r & a & d\\\\\n",
       "\t\\hline\n",
       "\t& String? & Int64? & Int64? & Int64? & Int64?\\\\\n",
       "\t\\hline\n",
       "\t1 & linear & 2 & 3 & 1 & \\emph{missing} \\\\\n",
       "\t2 & linear & 3 & 4 & 1 & \\emph{missing} \\\\\n",
       "\t3 & cubic & \\emph{missing} & 126 & 1 & 5 \\\\\n",
       "\t4 & cubic & \\emph{missing} & 217 & 1 & 6 \\\\\n",
       "\t5 & linear & 2 & 4 & 2 & \\emph{missing} \\\\\n",
       "\t6 & linear & 3 & 5 & 2 & \\emph{missing} \\\\\n",
       "\t7 & cubic & \\emph{missing} & 127 & 2 & 5 \\\\\n",
       "\t8 & cubic & \\emph{missing} & 218 & 2 & 6 \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/plain": [
       "\u001b[1m8×5 DataFrame\u001b[0m\n",
       "\u001b[1m Row \u001b[0m│\u001b[1m model   \u001b[0m\u001b[1m b       \u001b[0m\u001b[1m r      \u001b[0m\u001b[1m a      \u001b[0m\u001b[1m d       \u001b[0m\n",
       "     │\u001b[90m String? \u001b[0m\u001b[90m Int64?  \u001b[0m\u001b[90m Int64? \u001b[0m\u001b[90m Int64? \u001b[0m\u001b[90m Int64?  \u001b[0m\n",
       "─────┼───────────────────────────────────────────\n",
       "   1 │ linear         2       3       1 \u001b[90m missing \u001b[0m\n",
       "   2 │ linear         3       4       1 \u001b[90m missing \u001b[0m\n",
       "   3 │ cubic   \u001b[90m missing \u001b[0m    126       1        5\n",
       "   4 │ cubic   \u001b[90m missing \u001b[0m    217       1        6\n",
       "   5 │ linear         2       4       2 \u001b[90m missing \u001b[0m\n",
       "   6 │ linear         3       5       2 \u001b[90m missing \u001b[0m\n",
       "   7 │ cubic   \u001b[90m missing \u001b[0m    127       2        5\n",
       "   8 │ cubic   \u001b[90m missing \u001b[0m    218       2        6"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "using Query\n",
    "results"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's perform a basic query that we explain step-by-step:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 204,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div><div style = \"float: left;\"><span>4×3 DataFrame</span></div><div style = \"clear: both;\"></div></div><div class = \"data-frame\" style = \"overflow-x: scroll;\"><table class = \"data-frame\" style = \"margin-bottom: 6px;\"><thead><tr class = \"header\"><th class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">Row</th><th style = \"text-align: left;\">a</th><th style = \"text-align: left;\">r</th><th style = \"text-align: left;\">rsquared</th></tr><tr class = \"subheader headerLastRow\"><th class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\"></th><th title = \"Union{Missing, Int64}\" style = \"text-align: left;\">Int64?</th><th title = \"Union{Missing, Int64}\" style = \"text-align: left;\">Int64?</th><th title = \"Union{Missing, Int64}\" style = \"text-align: left;\">Int64?</th></tr></thead><tbody><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">1</td><td style = \"text-align: right;\">1</td><td style = \"text-align: right;\">3</td><td style = \"text-align: right;\">9</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">2</td><td style = \"text-align: right;\">1</td><td style = \"text-align: right;\">4</td><td style = \"text-align: right;\">16</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">3</td><td style = \"text-align: right;\">2</td><td style = \"text-align: right;\">4</td><td style = \"text-align: right;\">16</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">4</td><td style = \"text-align: right;\">2</td><td style = \"text-align: right;\">5</td><td style = \"text-align: right;\">25</td></tr></tbody></table></div>"
      ],
      "text/latex": [
       "\\begin{tabular}{r|ccc}\n",
       "\t& a & r & rsquared\\\\\n",
       "\t\\hline\n",
       "\t& Int64? & Int64? & Int64?\\\\\n",
       "\t\\hline\n",
       "\t1 & 1 & 3 & 9 \\\\\n",
       "\t2 & 1 & 4 & 16 \\\\\n",
       "\t3 & 2 & 4 & 16 \\\\\n",
       "\t4 & 2 & 5 & 25 \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/plain": [
       "\u001b[1m4×3 DataFrame\u001b[0m\n",
       "\u001b[1m Row \u001b[0m│\u001b[1m a      \u001b[0m\u001b[1m r      \u001b[0m\u001b[1m rsquared \u001b[0m\n",
       "     │\u001b[90m Int64? \u001b[0m\u001b[90m Int64? \u001b[0m\u001b[90m Int64?   \u001b[0m\n",
       "─────┼──────────────────────────\n",
       "   1 │      1       3         9\n",
       "   2 │      1       4        16\n",
       "   3 │      2       4        16\n",
       "   4 │      2       5        25"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# `@from ... begin` initializes a query\n",
    "# here `row` (any name would be fine) is the \n",
    "# iterable of the tabular data. Think of it as a \n",
    "# NamedTuple. You can access its values by name.\n",
    "q = @from row in results begin\n",
    "    # `@where` filters elements where the following\n",
    "    # expression is true. \n",
    "    @where row.model == \"linear\"\n",
    "    # `@select { stuf... }  creates a new named tuple\n",
    "    @select {row.a, row.r, rsquared = row.r^2}\n",
    "    # `@collect` collects the selected results into\n",
    "    # the specified data structure\n",
    "    @collect DataFrame\n",
    "end"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As you can see, you don't have to necessarily collect only existing columns, you can even create new ones (specified by name).\n",
    "\n",
    "Of course, much, much more things are possible to do in such a query. For more, see the documentation of Query.jl."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# A final take-home message\n",
    "\n",
    "One thing that should really, _really_ be added a lot of weight, is **how simple, transparent, and high level are the interfaces of everything** that you have seen so far. Both base Julia, as well as most packages for it, have such a simple interface which means that people can learn the software faster and spend more time actually doing science than trying to figure out how to write the code.\n",
    "\n",
    "This is something that \"old\" programming languages typically fail at: most (young) people that use codebases written in C/FORTRAN without any high level API defined on top (in e.g. Python) always complain that it is \"so hard to use this stuff\".\n",
    "\n",
    "Julia = answer :) "
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Exercises\n",
    "\n",
    "These exercises will require you to search things on the internet (because this is part of the process of \"learning a Julia package\")."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "## Bouncing ball\n",
    "\n",
    "Using the callback functionality of DifferentialEquations.jl, implement the bouncing ball physical system:\n",
    "\n",
    "$$\n",
    "\\begin{aligned}\n",
    "\\dot{x} &= v \\\\\n",
    "\\dot{v} &= -g - \\gamma v \n",
    "\\end{aligned}\n",
    "$$\n",
    "and at $x=0$ there is a table that the ball bounces from. $g$ is the gravity constant and $\\gamma$ the air friction (use e.g. $g=10, \\gamma = 0.99, x = 1, v = 0$). Implement this problem for elastic collisions (elastic collisions preserve velocity measure), and plot the time evolution of $x, v$ versus time.\n",
    "\n",
    "*Hint: whenever the ball reaches the level $x=0$, its velocity should be reversed.*"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "## Distribution quantile\n",
    "\n",
    "To find the $q$-th quantile of a distribution, one can use a Newton method\n",
    "\n",
    "$$\\theta_{n+1} = \\theta_n -\\frac{\\text{cdf}(\\theta)−q}{\\text{pdf}(\\theta)}$$\n",
    "\n",
    "where $\\theta_n$ converges to the value of the $q$-th quantile.\n",
    "\n",
    "Use multiple dispatch to write a generic algorithm for which calculates the qth quantile of any `UnivariateDistribution` in Distributions.jl, and test your result against the `quantile(d::UnivariateDistribution, q::Number)` function from Distributions.jl using the following distributions: `[Gamma(5, 1), Normal(0, 1), Beta(2, 4)]`.\n",
    "\n",
    "*Hint: use `θ₀ = mean(distribution)`*\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "## Plotting subsets of a dataframe\n",
    "\n",
    "`DataFrames` has a default dataset that is used in its test suite. Install the `CSV` package, and load this dataset with the command:\n",
    "```julia\n",
    "using DataFrames, CSV\n",
    "iris = DataFrame(CSV.File(\n",
    "    joinpath(dirname(pathof(DataFrames)), \n",
    "    \"../docs/src/assets/iris.csv\")\n",
    "))\n",
    "```\n",
    "\n",
    "This dataset has various flower species (column `:Species`). For every species create a 1x2 figure with the following plots:\n",
    "\n",
    "* [1,1] = scatter plot of `SepalLength` vs `SepalWidth`. \n",
    "* [1,2] = scatter plot of `PetalLength` vs `PetalWidth`.\n",
    "\n",
    "for each of these sub-scatter plots, calculate and print the Pearson correlaton coefficient.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "## DataFrame of chaos\n",
    "\n",
    "Define the Roessler system as a `DynamicalSystem`:\n",
    "$$\n",
    "\\begin{aligned}\n",
    "\\dot{x} &= -y-z \\\\\n",
    "\\dot{y} &= x+ay \\\\\n",
    "\\dot{z} &= b + z(x-c)\n",
    "\\end{aligned}\n",
    "$$\n",
    "with initial condition `ones(3)`. Loop over all three of the following parameter ranges:\n",
    "```julia\n",
    "as = 0.15:0.025:0.25\n",
    "bs = 0.15:0.025:0.25\n",
    "cs = 4:0.1:6.0\n",
    "```\n",
    "\n",
    "and for each parameter combination calculate (1) the Lyapunov spectrum using `lyapunovspectrum` and (2) the Shannon entropy of the system's trajectory. For the entropy, simulate a `trajectory` of the system with sampling time `Δt=0.1` and use `ε=0.1` for the box size when calling `DynamicalSystems.entropy(ValueHistogram(ε), X))`. For changing parameters you have to use `set_parameter!`. Remember that you can push entries to a `DataFrame` row-by-row using `push!(dataframe, (a = a, b = b, ...))`.\n",
    "\n",
    "Collect this analysis into a dataframe, with columns `a, b, c, λ1, λ3, H` with `λ1, λ3` the first and last elements of `lyapunovspectrum`. Then use the querying framework to query into this dataframe and do the following processes:\n",
    "\n",
    "####  find chaotic parameter sets\n",
    "Select all values `a, b, c` where `λ1 > 0.01` (which indicates chaotic dynamics).\n",
    "\n",
    "####  λ vs H\n",
    "For all chaotic cases, select the `λ1, H` values and then perform a scatter plot of these two.\n",
    "\n",
    "#### heatmap of H\n",
    "For `a` fixed to `0.2`, plot a heatmap of the value of `H` with axis the values of `c` and the values of `b`. Provided that you have a dataframe with columns `:b, :c, :H`, then these commands:\n",
    "```julia\n",
    "unstacked = unstack(df, :b,  :H; renamecols = (x -> \"H for b=$(x)\"))\n",
    "heat = Matrix(unstacked[:, Not(:c)])\n",
    "```\n",
    "will create a matrix with the values of `H` where the row index is the values of `c` and the column index is the values of `b`.\n",
    "\n",
    "*Hint: you can initiallize an empty dataframe with `df = DataFrame()`, and then start pushing into it arbitrary named tuples like `push!(df, (a = 0.5, b = 0.5))`.*\n",
    "\n",
    "*Hint 2: this all sounds like a lot of computation, but if you do the exercise correct running all code should not take more than 10 seconds.*\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "## Reproducible scientific project\n",
    "*this exercise only applies to participants that already know Git*\n",
    "\n",
    "* Use DrWatson's `initialize_project` to start a scientific project somewhere on your computer. \n",
    "* Add the packages `JLD2, Distributions` to this project. \n",
    "* In the `scripts` folder create a new Julia script that uses three parameters `a, b, c ∈ Reals` and creates a random result `r`. Save this result into disk by using `savename` to produce a name from `a, b, c`, and using `tagsave` to do the actual saving.\n",
    "* Save your script, and commit it into Git. Then run the script, load the saved file, and confirm that the saved git commit ID matches that of your Git repo.\n"
   ]
  }
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