{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Exercise 5"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Exercise 5.1: Parameterization of Data\n",
    "### Exercisse 5.1.1 (obligatory)\n",
    "If the underlying probability distribution function (PDF) of a dataset is unknown, empirical fit functions have to be employed.  The most common empirical fit functions are n-th order polynomials with constant coefficients $p_k$ to be determined by the fit:\n",
    "$$ P_n \\left( x \\right) = \\sum_{k = 0}^{n} p_k \\, x^k \\ .$$\n",
    "The fit results can usually be “stabilized” by using orthogonal polynomials\n",
    "$$ L_n \\left( x \\right) = \\sum_{k = 0}^n p_k \\, l_k \\left( x \\right) \\, ,$$\n",
    "where $l_k(x)$ are Legendre polynomials, which can be defined recursively by\n",
    "$$ l_0 (x) = 1; \\quad l_1 (x) = x; \\quad (k + 1)\\, l_{k+1} (x) = (2k + 1)\\, x \\, l_k (x) - k \\, l_{k - 1} (x) \\ .$$\n",
    "The Legendre polynomials fulfill the orthogonality relation\n",
    "$$ \\int\\limits_{-1}^1 \\, \\mathrm{d}x \\, l_m \\left( x \\right) \\, l_n \\left( x \\right) = \\frac{2}{2n -1} \\delta_{mn} \\ ,$$\n",
    "where $\\delta_{mn}$ denotes the Kronecker delta.\n",
    "\n",
    "Fit  the  data  points  given  by  the  following  pairs  of $x$ and $y$ values assuming a constant uncertainty of $\\sigma_y = 0.5$ for $y$ and no uncertainty for $x$:\n",
    "```\n",
    "  x = { -0.9, -0.8, -0.7, -0.6, -0.5, -0.4, -0.3, -0.2, -0.1,\n",
    "         0.0,  0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1.0 }\n",
    "  y = { 5.0935, 2.1777, 0.2089, -2.3949, -2.4457, -3.0430, -2.2731,\n",
    "       -2.0706, -1.6231, -2.5605, -0.7703, -0.3055, 1.6817, 1.8728,\n",
    "        3.6586, 3.2353, 4.2520, 5.2550, 3.8766, 4.2890 }\n",
    "```\n",
    "\n",
    "1. Use $P_2 \\left(x\\right)$, $P_3 \\left(x\\right)$, ..., $P_7 \\left(x\\right)$ as fit functions.\n",
    "\n",
    "2. Use $L_2 \\left(x\\right)$, $L_3 \\left(x\\right)$, ..., $L_7 \\left(x\\right)$ as fit functions.\n",
    "\n",
    "Plot the data and the fitted curves for all fits. Compare the resulting values for $p_k$ and their correlation matrices (to be obtained most conveniently via the `GetCorrelationMatrix()` method of Root class [`TFitResult`](https://root.cern.ch/doc/master/classTFitResult.html) or via the [`scipy.optimize.curve_fit()`](https://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.curve_fit.html) function). In which sense is the fit using orthogonal polynomials “more stable”? Discuss which order you would choose for the fit function.\n",
    "\n",
    "**Hint**: A convenient framework for fitting and visualisation of problems like this one is included in the Root class [`TGraphErrors`](https://root.cern.ch/doc/master/classTGraphErrors.html) and its methods."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import scipy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "nPoints = 20\n",
    "data_x = np.array([-0.9, -0.8, -0.7, -0.6, -0.5, -0.4, -0.3, -0.2, -0.1, 0.0,  0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1.0], dtype=float)\n",
    "data_y = np.array([5.0935, 2.1777, 0.2089, -2.3949, -2.4457, -3.0430, -2.2731, -2.0706, -1.6231, -2.5605, -0.7703, -0.3055, 1.6817, 1.8728, 3.6586, 3.2353, 4.2520, 5.2550, 3.8766, 4.2890], dtype=float)\n",
    "sigma_x = np.array(nPoints*[0.], dtype=float)\n",
    "sigma_y = np.array(nPoints*[0.5], dtype=float)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "# define polynomials\n",
    "def P_2(x, a, b, c):\n",
    "    return a + b * x + c * x**2\n",
    "\n",
    "def P_3(x, a, b, c, d):\n",
    "    return a + b * x + c * x**2 + d * x**3\n",
    "\n",
    "def P_4(x, a, b, c, d, e):\n",
    "    return a + b * x + c * x**2 + d * x**3 + e * x**4\n",
    "\n",
    "def P_5(x, a, b, c, d, e, f):\n",
    "    return a + b * x + c * x**2 + d * x**3 + e * x**4 + f * x**5\n",
    "\n",
    "def P_6(x, a, b, c, d, e, f, g):\n",
    "    return a + b * x + c * x**2 + d * x**3 + e * x**4 + f * x**5 + g * x**6\n",
    "\n",
    "def P_7(x, a, b, c, d, e, f, g, h):\n",
    "    return a + b * x + c * x**2 + d * x**3 + e * x**4 + f * x**5 + g * x**6 + h * x**7\n",
    "\n",
    "# define Legendre polynomials\n",
    "def L_2(x, a, b, c):\n",
    "    return a + b * x + c * 0.5 * (3. * x**2 - 1.)\n",
    "\n",
    "def L_3(x, a, b, c, d):\n",
    "    return a + b * x + c * 0.5 * (3. * x**2 - 1.) + d * 0.5 * (5. * x**3 - 3. * x)\n",
    "\n",
    "def L_4(x, a, b, c, d, e):\n",
    "    return a + b * x + c * 0.5 * (3. * x**2 - 1.) + d * 0.5 * (5. * x**3 - 3. * x) + e * 0.125 * (35. * x**4 - 30. * x**2 + 3.)\n",
    "\n",
    "def L_5(x, a, b, c, d, e, f):\n",
    "    return a + b * x + c * 0.5 * (3. * x**2 - 1.) + d * 0.5 * (5. * x**3 - 3. * x) + e * 0.125 * (35. * x**4 - 30. * x**2 + 3.) + f * 0.125 * (63. * x**5 - 70. * x**3 + 15. * x)\n",
    "\n",
    "def L_6(x, a, b, c, d, e, f, g):\n",
    "    return a + b * x + c * 0.5 * (3. * x**2 - 1.) + d * 0.5 * (5. * x**3 - 3. * x) + e * 0.125 * (35. * x**4 - 30. * x**2 + 3.) + f * 0.125 * (63. * x**5 - 70. * x**3 + 15. * x) + g * 0.0625 * (231. * x**6 - 315. * x**4 + 105. * x**2 - 5.)\n",
    "\n",
    "def L_7(x, a, b, c, d, e, f, g, h):\n",
    "    return a + b * x + c * 0.5 * (3. * x**2 - 1.) + d * 0.5 * (5. * x**3 - 3. * x) + e * 0.125 * (35. * x**4 - 30. * x**2 + 3.) + f * 0.125 * (63. * x**5 - 70. * x**3 + 15. * x) + g * 0.0625 * (231. * x**6 - 315. * x**4 + 105. * x**2 - 5.) + h * 0.0625 * (429. * x**7 - 693. * x**5 + 315. * x**3 -35. * x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[-1.28  2.03  6.22]\n",
      "[-1.57  7.89  7.71 -9.96]\n",
      "[ -1.5    7.97   6.9  -10.15   0.97]\n",
      "[-1.45  7.12  6.28 -6.03  1.93 -3.86]\n",
      "[-1.56  6.87  8.69 -4.49 -5.66 -5.63  5.89]\n",
      "[ -1.49   5.48   6.62   8.79   2.31 -36.8   -1.36  20.71]\n",
      "[[   0.09   -0.04   -0.93    0.49    2.27   -1.35   -1.56    1.02]\n",
      " [  -0.04    2.52    1.18  -17.24   -4.54   33.44    4.12  -19.52]\n",
      " [  -0.93    1.18   16.7   -13.81  -48.58   38.25   36.43  -29.06]\n",
      " [   0.49  -17.24  -13.81  141.53   53.16 -301.04  -48.33  186.26]\n",
      " [   2.27   -4.54  -48.58   53.16  154.21 -147.2  -121.85  111.85]\n",
      " [  -1.35   33.44   38.25 -301.04 -147.2   678.5   133.82 -437.25]\n",
      " [  -1.56    4.12   36.43  -48.33 -121.85  133.82   99.65 -101.69]\n",
      " [   1.02  -19.52  -29.06  186.26  111.85 -437.25 -101.69  290.53]]\n"
     ]
    },
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0.79 2.03 4.14]\n",
      "[ 1.    1.92  5.14 -3.98]\n",
      "[ 1.    1.88  5.16 -4.06  0.22]\n",
      "[ 1.03  1.84  5.29 -4.13  0.44 -0.49]\n",
      "[ 1.04  1.77  5.36 -4.29  0.54 -0.71  0.41]\n",
      "[ 0.98  1.89  5.08 -4.05  0.1  -0.42 -0.09  0.77]\n",
      "[[ 0.02 -0.01  0.02 -0.02  0.03 -0.03  0.03 -0.03]\n",
      " [-0.01  0.08 -0.05  0.06 -0.09  0.07 -0.1   0.06]\n",
      " [ 0.02 -0.05  0.18 -0.11  0.14 -0.15  0.15 -0.14]\n",
      " [-0.02  0.06 -0.11  0.25 -0.18  0.15 -0.21  0.13]\n",
      " [ 0.03 -0.09  0.14 -0.18  0.38 -0.23  0.22 -0.23]\n",
      " [-0.03  0.07 -0.15  0.15 -0.23  0.39 -0.27  0.15]\n",
      " [ 0.03 -0.1   0.15 -0.21  0.22 -0.27  0.48 -0.26]\n",
      " [-0.03  0.06 -0.14  0.13 -0.23  0.15 -0.26  0.4 ]]\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def PP(x, *coeffs):\n",
    "    funcs = [P_2, P_3, P_4, P_5, P_6, P_7]\n",
    "    return funcs[len(coeffs)-3](x, *coeffs)\n",
    "\n",
    "def LL(x, *coeffs):\n",
    "    funcs = [L_2, L_3, L_4, L_5, L_6, L_7]\n",
    "    return funcs[len(coeffs)-3](x, *coeffs)\n",
    "\n",
    "plt.errorbar(data_x, data_y, sigma_y, label=\"data\", fmt=\".\")\n",
    "overhang = 0\n",
    "xlin = np.linspace(np.min(data_x)-overhang, np.max(data_x)+overhang, 200)\n",
    "for i in range(2,8):\n",
    "    coeffs = [1,1,1,1,1,1,1,1]\n",
    "    res = scipy.optimize.curve_fit(PP, data_x, data_y, p0=coeffs[:i+1], sigma=sigma_y)\n",
    "    plt.plot(xlin, PP(xlin, *res[0]), label=f\"P_{i}\")\n",
    "    print(np.round(res[0],2))\n",
    "    np.set_printoptions(suppress=True)\n",
    "    if i == 7: print(np.round(res[1],2))\n",
    "    np.set_printoptions(suppress=False)\n",
    "plt.legend()\n",
    "plt.title(\"Normale Polynome\")\n",
    "plt.show()\n",
    "\n",
    "plt.imshow(res[1], vmin=0, vmax=10)\n",
    "plt.colorbar()\n",
    "plt.show()\n",
    "\n",
    "plt.errorbar(data_x, data_y, sigma_y, label=\"data\", fmt=\".\")\n",
    "for i in range(2,8):\n",
    "    coeffs = [1,1,1,1,1,1,1,1]\n",
    "    res = scipy.optimize.curve_fit(LL, data_x, data_y, p0=coeffs[:i+1], sigma=sigma_y)\n",
    "    plt.plot(xlin, LL(xlin, *res[0]), label=f\"L_{i}\")\n",
    "    print(np.round(res[0],2))\n",
    "    if i == 7: print(np.round(res[1],2))\n",
    "plt.legend()\n",
    "plt.title(\"Legendre Polynome\")\n",
    "plt.show()\n",
    "\n",
    "plt.imshow(res[1], vmin=0, vmax=0.5)\n",
    "plt.colorbar()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It looks like Order 3 Polynomials are sufficient to fit the data given the uncertanties. Anything above order 4 would be overfitting. \n",
    "The 2D-color-Plots show the values of the covariance Matrix. It can be seen that the variance for Lagrange-Polomials is way smaller in general and the covariance between different coefficients is also way smaller. That makes them numerically more stable. Adding a new, higher polinomial does not change the other coefficients."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Exercise 5.1.2:  (obligatory)\n",
    "In an accelerator experiment, the following data are numbers of events measured in 60 energy intervals equally distributed between 0 and 3 GeV:\n",
    "\n",
    "|   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |   | \n",
    "|:-:|:-:|:-:|:-:|:-:|:-:|:-:|:-:|:-:|:-:|:-:|:-:|:-:|:-:|:-:|:-:|:-:|:-:|:-:|:-:|\n",
    "|6  |1  |10 |12 |6  |13 |23 |22 |15 |21 |23 |26 |36 |25 |27 |35 |40 |44 |66 |81 |\n",
    "|75 | 57|48 |45 |46 |41 |35 |36 |53 |32 |40 |37 |38 |31 |36 |44 |42 |37 |32 |32 |\n",
    "|43 |44 |35 |33 |33 |39 |29 |41 |32 |44 |26 |39 |29 |35 |32 |21 |21 |15 |25 |15 |\n",
    "\n",
    "The data show a signal resonance visible on top of a background sample. For the uncertainties of all data points we assume the statistical uncertainty according to a Poisson distribution. The goal of this exercise is to extract information on the signal by parameterizing both signal and background. The information we are interested in are the width of the signal (which is related to the lifetime) and the number of signal events. Let us assume that the background can be parametrized as a polynomial of second order in the energy (i.e., a function with 3 parameters), and the signal as a Lorentz function (also 3 parameters) given by\n",
    "\n",
    "$$ L \\left(x; A_{\\mathrm{norm}}, \\mu, \\Gamma \\right) = \\frac{A_{\\mathrm{norm}}}{\\pi} \\frac{\\Gamma/2}{\\left( x - \\mu \\right)^2 + \\Gamma^2/4}$$\n",
    "\n",
    "There are two possible methods to extract the signal:\n",
    "\n",
    "1. Fit the data with a function with 6 parameters composed by the signal function plus the background function.\n",
    "\n",
    "2. Define two intervals, left and right of the signal peak, to fit the background function. Then, fit the signal function to the data in the signal region after subtracting the background function.\n",
    "\n",
    "   There are (at least) two ways how to exclude certain points for the fit. Either you can define new arrays for the fit which contain only a subset of the original data points, or you can define your own fit function which excludes certain intervals. For a Root example how to do this (not in Python, but in C) see here: [https://root.cern/doc/master/fitExclude_8C.html](https://root.cern/doc/master/fitExclude_8C.html). \n",
    "\n",
    "Plot the fitted functions on top of the data. Determine the width of the Lorentz peak and the number of signal events and their statistical uncertainties, and compare the results of both methods."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "nPoints = 60\n",
    "data_x = np.array(np.arange(0, 3, 0.05), dtype=float) # 3 GeV / 60 bins = 0.05 GeV per bin\n",
    "data_y = np.array([6, 1, 10, 12, 6, 13, 23, 22, 15, 21, 23, 26, 36, 25, 27, 35, 40, 44, 66, 81, 75, 57, 48, 45, 46, 41, 35, 36, 53, 32, 40, 37, 38, 31, 36, 44, 42, 37, 32, 32, 43, 44, 35, 33, 33, 39, 29, 41, 32, 44, 26, 39, 29, 35, 32, 21, 21, 15, 25, 15], dtype=float)\n",
    "sigma_x = np.array(nPoints*[0], dtype=float)\n",
    "sigma_y = np.array(np.sqrt(data_y), dtype=float)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Using ROOT or pure Python, implement your solution following the steps below:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "array([-13.32141374,  45.17729489,   0.27304432,  13.80744981,\n",
       "         0.96228106,   0.17230977])"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "array([-13.81242332,  46.36874167,   0.71021315])"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "array([12.71704027,  0.9623414 ,  0.15864221])"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# For the ROOT approach: Store the values in a TGraphErrors\n",
    "\n",
    "# Part 1: Define the fit function with 6 parameters and fit signal and back simultaneously.\n",
    "def backgound(E,a,b,c):\n",
    "    return a*E**2+b*E+c\n",
    "\n",
    "def Signal(E,Anorm,mu,Gamma):\n",
    "    return Anorm/np.pi*Gamma/2/((E-mu)**2+Gamma**2/4)\n",
    "\n",
    "fullFunc = lambda E,a,b,c,Anorm,mu,Gamma: backgound(E,a,b,c)+Signal(E,Anorm,mu,Gamma)\n",
    "\n",
    "res = scipy.optimize.curve_fit(fullFunc, data_x, data_y, p0=(-10,40,0.1,10,1,0.1), sigma=sigma_y)\n",
    "\n",
    "\n",
    "plt.errorbar(data_x, data_y, sigma_y, label=\"data\", fmt=\".\")\n",
    "xlin = np.linspace(np.min(data_x), np.max(data_x), 200)\n",
    "plt.plot(xlin, fullFunc(xlin, *res[0]))\n",
    "plt.show()\n",
    "display(res[0])\n",
    "\n",
    "# Part 2: Split the data in signal and background region. First fit the background distribution in the background region.\n",
    "#         Afterwards, subtract the background expectation from data in the signal region and fit the signal function.\n",
    "\n",
    "backslice = np.logical_or(np.arange(0,data_x.shape[0]) < 12, np.arange(0,data_x.shape[0]) > 27)\n",
    "plt.errorbar(data_x[np.logical_not(backslice)], data_y[np.logical_not(backslice)], sigma_y[np.logical_not(backslice)], label=\"data\", fmt=\".\")\n",
    "plt.errorbar(data_x[backslice], data_y[backslice], sigma_y[backslice], label=\"data\", fmt=\".r\")\n",
    "\n",
    "backres = scipy.optimize.curve_fit(backgound, data_x[backslice], data_y[backslice], p0=(-10,40,0.1), sigma=sigma_y[backslice])\n",
    "foreres = scipy.optimize.curve_fit(Signal, data_x[np.logical_not(backslice)], data_y[np.logical_not(backslice)]-backgound(data_x[np.logical_not(backslice)], *backres[0]), p0=(10,1,0.1), sigma=sigma_y[np.logical_not(backslice)])\n",
    "\n",
    "xlin = np.linspace(np.min(data_x)-overhang, np.max(data_x)+overhang, 200)\n",
    "plt.plot(xlin, backgound(xlin, *backres[0]))\n",
    "plt.plot(xlin, backgound(xlin, *backres[0]) + Signal(xlin, *foreres[0]))\n",
    "plt.show()\n",
    "display(backres[0], foreres[0])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Exercise 5.2: Minimization via Simulated Annealing (obligatory)\n",
    "\n",
    "Data analysis often requires to find the optimal solution, e.g., the minimum of a function in a multi-dimensional space.\n",
    "\n",
    "As an example we use the following two-dimensional function which has several local minima, but just one global minimum:\n",
    "\n",
    "$$ f(x,y) = (x^2+y−a)^2+ (x+y^2−b)^2+c·(x+y)^2$$\n",
    "\n",
    "with arbitrary parameters $a$ , $b$ and $c$.\n",
    "\n",
    "For $ c= 0$ this function would be the [Rosenbrock function](https://en.wikipedia.org/wiki/Rosenbrock_function) which is often used to validate minimization algorithms.\n",
    "\n",
    "For this exercise sheet, we make the arbitrary choice $a= 11$, $b= 7$, $c= 0.1$. Thus, $f(x,y)$ has four local minima of different depth.\n",
    "\n",
    "In this exercise you will write your own minimization algorithm following the [**Simulated Annealing**](https://en.wikipedia.org/wiki/Simulated_annealing) strategy and test with the above defined function.\n",
    "Use the code fragment given in the jupyter notebook as help.\n",
    "\n",
    "\n",
    "1. Play with the parameters: initial and final temperature, cooling speed, and step size. Choose a starting point close to the global minimum, and check if the algorithm converges into the minimum.\n",
    "\n",
    "2. Choose a starting point close to a local minimum which is not the global minimum, e.g., $(x,y) = (3,−2)$. Find a set of parameters for the algorithm such that it converges to the global minimum, but still keeping the number of iterations as low as possible, and motivate your choice.  \n",
    "\n",
    "   For tuning the parameters, you have two possibilities: Either you perform a scan over a meaningful range for each parameter, or you study how the algorithm reacts on changing certain parameters and then try to tune them by hand. In any case, first think what is the role of each parameter in the algorithm. E.g., both, the difference between initial and final temperature, and the cooling speed directly affect the number of iterations, but the temperature scale in addition affects the probability for jumps.\n",
    "\n",
    "3. Repeat the analysis for different random seeds. If the minimum found depends on the random seed, re-tune the parameters of the algorithm until the result is independent of the random seed."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Python Approach:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "import matplotlib.animation\n",
    "from IPython.display import Image"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "# modified rosenbrock function: f(x,y) = (x^2+y-a)^2 + (x+y^2-b)^2 + c*(x+y)^2\n",
    "def modified_rosenbrock_function(x, par):\n",
    "    xx = x[0]    \n",
    "    yy = x[1]    \n",
    "    a = par[0]       \n",
    "    b = par[1]       \n",
    "    c = par[2]       \n",
    "    \n",
    "    return (xx**2+yy-a)**2 + (xx+yy**2-b)**2 + c*(xx+yy)**2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "def plotFunction(function, listOfPoints):\n",
    "    \"\"\"Draw or return plot objects of scanned values of x and y and the surface of the function.\n",
    "    \n",
    "    Helper function for visualization of the minimization procedure.\n",
    "    \"\"\"\n",
    "    return None"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "# Code fragment for exercise 6.2 of the Computerpraktikum Datenanlyse 2014\n",
    "# Authors: Ralf Ulrich, Frank Schroeder (Karlsruhe Institute of Technology)\n",
    "# Modified: 2020-05-26 Maximilian Burkart (Karlsruhe Institute of Technology)\n",
    "# This code fragment probably is not the best and fastest implementation\n",
    "# for \"simulated annealing\", but it is a simple implementation which does its job.  \n",
    "\n",
    "def simulated_annealing(init_vals=[0,0], rosenbrock_pars=[0, 0, 0],\n",
    "                        init_temp=100, final_temp=1, cool_speed=1, step_size=1,\n",
    "                        seed=None):\n",
    "    \"\"\"Minimize the modified Rosenbrock function using simulated annealing.\n",
    "    \n",
    "    params:\n",
    "        init_vals:       Initial x and y values.\n",
    "        rosenbrock_pars: Parameters of the modified Rosenbrock function.\n",
    "        init_temp:       Initial temperature the cooling starts from.\n",
    "        final_temp:      Final temperature of the cooling.\n",
    "        cool_speed:      Cooling speed in percent of the current temperature.\n",
    "        step_size:       Step size used in the cooling procedure.\n",
    "        \n",
    "    returns:\n",
    "        min_pars: List of floats.\n",
    "                    List of the x and y values at the found minimum.\n",
    "        listOfPoints: List of floats.\n",
    "                    List of the visited points during the minimization process.\n",
    "    \"\"\"\n",
    "    nParameter = 2 # 2 parameters: x and y\n",
    "    if len(init_vals) != nParameter:\n",
    "        raise Exception(\"Number of function parameters does not correspond to given number of initial values.\"\n",
    "                        \"Aborting...\")\n",
    "    \n",
    "    # TODO: Implement setting of seed if a seed is given.\n",
    "    if seed is not None:\n",
    "        np.random.seed(seed)\n",
    " \n",
    "    # Starting point: test the dependence of the algorithm on the initial values\n",
    "    initialXvalue, initialYvalue = init_vals\n",
    "\n",
    "    # Parameters of the  algorithm:\n",
    "    # Find a useful set of parameters which allows to determine the global\n",
    "    # minimum of the given function:\n",
    "    # The temperature scale must be in adequate relation to the scale of the function values,\n",
    "    # the step size must be in adequate relation to the scale of the distance between the \n",
    "    # different local minima\n",
    "    initialTemperature = init_temp\n",
    "    finalTemperature = final_temp\n",
    "    coolingSpeed = cool_speed # in percent of current temperature --> defines number of iterations\n",
    "    stepSize = step_size    \n",
    "    \n",
    "    # Current parameters and cost\n",
    "    currentParameters  = [initialXvalue, initialYvalue] # x and y in our case\n",
    "    currentFunctionValue =  modified_rosenbrock_function(currentParameters, [a,b,c]) # you have to implement the function first!\n",
    "\n",
    "    # keep reference of best parameters\n",
    "    bestParameters = currentParameters\n",
    "    bestFunctionValue = currentFunctionValue\n",
    "\n",
    "    listOfPoints= []\n",
    "    # Heat the system\n",
    "    temperature = initialTemperature\n",
    "\n",
    "    iteration = 0\n",
    "\n",
    "    # Start to slowly cool the system\n",
    "    while (temperature > finalTemperature): \n",
    "\n",
    "        # Change parameters\n",
    "        newParameters = [0]*nParameter\n",
    "\n",
    "        #for ipar in range(nParameter):\n",
    "        #    newParameters[ipar] = gRandom.Gaus(currentParameters[ipar], stepSize)\n",
    "        newParameters = np.array(\n",
    "                [np.random.normal(loc=currentParameters[0], scale=step_size),\n",
    "                 np.random.normal(loc=currentParameters[1], scale=step_size)])\n",
    "\n",
    "        # Get the new value of the function\n",
    "        newFunctionValue = modified_rosenbrock_function(newParameters, [a,b,c])\n",
    "\n",
    "        # Compute Boltzman probability\n",
    "        deltaFunctionValue = newFunctionValue - currentFunctionValue\n",
    "        saProbability = np.exp(-deltaFunctionValue / temperature)\n",
    "\n",
    "        # Acceptance rules :\n",
    "        # if newFunctionValue < currentFunctionValue then saProbability > 1\n",
    "        # else accept the new state with a probability = saProbability\n",
    "        if ( saProbability > np.random.random() ):\n",
    "            currentParameters = newParameters\n",
    "            currentFunctionValue = newFunctionValue\n",
    "            listOfPoints.append(currentParameters)  # log keeping: keep track of path\n",
    "\n",
    "        if (currentFunctionValue < bestFunctionValue):\n",
    "            bestFunctionValue = currentFunctionValue\n",
    "            bestParameters = currentParameters\n",
    "\n",
    "        #print \"T = \", temperature, \"(x,y) = \",currentParameters, \" Current value: \", currentFunctionValue, \" delta = \", deltaFunctionValue # debug output\n",
    "\n",
    "        # Cool the system\n",
    "        temperature *= 1 - coolingSpeed / 100.\n",
    "        \n",
    "        # Count iterations\n",
    "        iteration += 1\n",
    "\n",
    "    # end of cooling loop\n",
    "    \n",
    "    return bestParameters, listOfPoints"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "ename": "NameError",
     "evalue": "name 'np' is not defined",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mNameError\u001b[0m                                 Traceback (most recent call last)",
      "Cell \u001b[0;32mIn[7], line 9\u001b[0m\n\u001b[1;32m      5\u001b[0m initial_values \u001b[38;5;241m=\u001b[39m [\u001b[38;5;241m3\u001b[39m, \u001b[38;5;241m-\u001b[39m\u001b[38;5;241m2\u001b[39m]\n\u001b[1;32m      7\u001b[0m initial_temp, final_temp, cool_speed, step_size \u001b[38;5;241m=\u001b[39m \u001b[38;5;241m5\u001b[39m, \u001b[38;5;241m0.001\u001b[39m, \u001b[38;5;241m0.01\u001b[39m, \u001b[38;5;241m3.15\u001b[39m\n\u001b[0;32m----> 9\u001b[0m bestParameters, listOfPoints \u001b[38;5;241m=\u001b[39m \u001b[43msimulated_annealing\u001b[49m\u001b[43m(\u001b[49m\u001b[43minit_vals\u001b[49m\u001b[38;5;241;43m=\u001b[39;49m\u001b[43minitial_values\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\n\u001b[1;32m     10\u001b[0m \u001b[43m                                                   \u001b[49m\u001b[43mrosenbrock_pars\u001b[49m\u001b[38;5;241;43m=\u001b[39;49m\u001b[43m[\u001b[49m\u001b[43ma\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mb\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mc\u001b[49m\u001b[43m]\u001b[49m\u001b[43m,\u001b[49m\n\u001b[1;32m     11\u001b[0m \u001b[43m                                                   \u001b[49m\u001b[43minit_temp\u001b[49m\u001b[38;5;241;43m=\u001b[39;49m\u001b[43minitial_temp\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\n\u001b[1;32m     12\u001b[0m \u001b[43m                                                   \u001b[49m\u001b[43mfinal_temp\u001b[49m\u001b[38;5;241;43m=\u001b[39;49m\u001b[43mfinal_temp\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\n\u001b[1;32m     13\u001b[0m \u001b[43m                                                   \u001b[49m\u001b[43mcool_speed\u001b[49m\u001b[38;5;241;43m=\u001b[39;49m\u001b[43mcool_speed\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\n\u001b[1;32m     14\u001b[0m \u001b[43m                                                   \u001b[49m\u001b[43mstep_size\u001b[49m\u001b[38;5;241;43m=\u001b[39;49m\u001b[43mstep_size\u001b[49m\n\u001b[1;32m     15\u001b[0m \u001b[43m                                                   \u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m     17\u001b[0m minValue \u001b[38;5;241m=\u001b[39m modified_rosenbrock_function(bestParameters, [a, b, c])\n\u001b[1;32m     19\u001b[0m \u001b[38;5;28mprint\u001b[39m(\u001b[38;5;124mf\u001b[39m\u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mResultat für das Minimum: f(x,y)=\u001b[39m\u001b[38;5;132;01m{\u001b[39;00mminValue\u001b[38;5;132;01m}\u001b[39;00m\u001b[38;5;124m bei x=\u001b[39m\u001b[38;5;132;01m{\u001b[39;00mbestParameters[\u001b[38;5;241m0\u001b[39m]\u001b[38;5;132;01m}\u001b[39;00m\u001b[38;5;124m, y=\u001b[39m\u001b[38;5;132;01m{\u001b[39;00mbestParameters[\u001b[38;5;241m1\u001b[39m]\u001b[38;5;132;01m}\u001b[39;00m\u001b[38;5;124m\"\u001b[39m)\n",
      "Cell \u001b[0;32mIn[5], line 71\u001b[0m, in \u001b[0;36msimulated_annealing\u001b[0;34m(init_vals, rosenbrock_pars, init_temp, final_temp, cool_speed, step_size, seed)\u001b[0m\n\u001b[1;32m     67\u001b[0m newParameters \u001b[38;5;241m=\u001b[39m [\u001b[38;5;241m0\u001b[39m]\u001b[38;5;241m*\u001b[39mnParameter\n\u001b[1;32m     69\u001b[0m \u001b[38;5;66;03m#for ipar in range(nParameter):\u001b[39;00m\n\u001b[1;32m     70\u001b[0m \u001b[38;5;66;03m#    newParameters[ipar] = gRandom.Gaus(currentParameters[ipar], stepSize)\u001b[39;00m\n\u001b[0;32m---> 71\u001b[0m newParameters \u001b[38;5;241m=\u001b[39m \u001b[43mnp\u001b[49m\u001b[38;5;241m.\u001b[39marray(\n\u001b[1;32m     72\u001b[0m         [np\u001b[38;5;241m.\u001b[39mrandom\u001b[38;5;241m.\u001b[39mnormal(loc\u001b[38;5;241m=\u001b[39mcurrentParameters[\u001b[38;5;241m0\u001b[39m], scale\u001b[38;5;241m=\u001b[39mstep_size),\n\u001b[1;32m     73\u001b[0m          np\u001b[38;5;241m.\u001b[39mrandom\u001b[38;5;241m.\u001b[39mnormal(loc\u001b[38;5;241m=\u001b[39mcurrentParameters[\u001b[38;5;241m1\u001b[39m], scale\u001b[38;5;241m=\u001b[39mstep_size)])\n\u001b[1;32m     75\u001b[0m \u001b[38;5;66;03m# Get the new value of the function\u001b[39;00m\n\u001b[1;32m     76\u001b[0m newFunctionValue \u001b[38;5;241m=\u001b[39m modified_rosenbrock_function(newParameters, [a,b,c])\n",
      "\u001b[0;31mNameError\u001b[0m: name 'np' is not defined"
     ]
    }
   ],
   "source": [
    "a = 11\n",
    "b = 7\n",
    "c = 0.1\n",
    "\n",
    "initial_values = [3, -2]\n",
    "\n",
    "initial_temp, final_temp, cool_speed, step_size = 5, 0.001, 0.01, 3.15\n",
    "\n",
    "bestParameters, listOfPoints = simulated_annealing(init_vals=initial_values, \n",
    "                                                   rosenbrock_pars=[a, b, c],\n",
    "                                                   init_temp=initial_temp, \n",
    "                                                   final_temp=final_temp, \n",
    "                                                   cool_speed=cool_speed, \n",
    "                                                   step_size=step_size\n",
    "                                                   )\n",
    "\n",
    "minValue = modified_rosenbrock_function(bestParameters, [a, b, c])\n",
    "\n",
    "print(f\"Resultat für das Minimum: f(x,y)={minValue} bei x={bestParameters[0]}, y={bestParameters[1]}\")\n",
    "\n",
    "# check if minimum is the global one (then the mimimum value should be around 0.01): \n",
    "if minValue < 0.1:\n",
    "    print(\"Ja, das ist das globale Minimum!\")\n",
    "else:\n",
    "    print(\"Oh nein, das ist nicht das globale Minimum, sondern nur ein lokales!\")\n",
    "    \n",
    "grid = np.mgrid[-5:5.1:0.1,-5:5.1:0.1]\n",
    "res = modified_rosenbrock_function(grid, [a, b, c])\n",
    "plt.pcolor(*grid, np.log(res))\n",
    "plt.plot(*zip(*listOfPoints))\n",
    "plt.plot(*bestParameters, \"X\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "from concurrent.futures import ProcessPoolExecutor\n",
    "\n",
    "def score(params):\n",
    "    initial_temp, final_temp, cool_speed, step_size = params\n",
    "    s = 0\n",
    "    N = 30\n",
    "    for i in range(N):\n",
    "        bestParameters, listOfPoints = simulated_annealing(init_vals=initial_values, \n",
    "                                                           rosenbrock_pars=[a, b, c],\n",
    "                                                           init_temp=initial_temp, \n",
    "                                                           final_temp=final_temp, \n",
    "                                                           cool_speed=cool_speed, \n",
    "                                                           step_size=step_size\n",
    "                                                           )\n",
    "        s += (modified_rosenbrock_function(bestParameters, [a, b, c]) < 0.1)\n",
    "    print(-s/N,\":\",params)\n",
    "    return s/N\n",
    "\n",
    "def parallel_score(params_list):\n",
    "    with ProcessPoolExecutor() as executor:\n",
    "        scores = list(executor.map(score, params_list))\n",
    "    return scores\n",
    "\n",
    "def generate_params(params, i, values):\n",
    "    params_list = []\n",
    "    for v in values:\n",
    "        new_params = list(params)\n",
    "        new_params[i] = v\n",
    "        params_list.append(tuple(new_params))\n",
    "    return params_list\n",
    "\n",
    "initial_temp, final_temp, cool_speed, step_size = 5, 0.001, 0.1, 3.15\n",
    "params = [initial_temp, final_temp, cool_speed, step_size]\n",
    "\n",
    "i = 2\n",
    "values = np.linspace(0.01, 0.2, 20)\n",
    "params_list = generate_params(params, i, values)\n",
    "\n",
    "results = parallel_score(params_list)\n",
    "plt.plot(values, results)\n",
    "#scipy.optimize.minimize(score, x0=[10, 0.001, 0.1, 3], method='Nelder-Mead', tol=1e-6)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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