{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "48974d97",
   "metadata": {},
   "source": [
    "# Eigenvalue problem: Coupled oscillators \n",
    "- by Börge Göbel"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "ce43e36c",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from scipy import integrate\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "id": "421f538a",
   "metadata": {},
   "source": [
    "![Coupled_oscillators](figure_08_coupled_oscillators.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ef352f47",
   "metadata": {},
   "source": [
    "\\begin{align}\n",
    "m\\ddot{r}_1 &= -k(r_1-r_l-a) -k(r_1-r_2-a)\\\\\n",
    "m\\ddot{r}_2 &= -k(r_2-r_1-a) -k(r_2-r_3-a)\\\\\n",
    "m\\ddot{r}_3 &= -k(r_3-r_2-a) -k(r_3-r_r-a)\n",
    "\\end{align}\n",
    "\n",
    "The constants can be dropped, since we can transform \\\\( (r_1 - a) \\rightarrow r_1, (r_2 - 2a) \\rightarrow r_2, (r_3 - 3a) \\rightarrow r_3, \\\\) and use \\\\(r_l=0, r_r=4a\\\\)\n",
    "\n",
    "\\begin{align}\n",
    "m\\ddot{r}_1 &= -k(r_1) -k(r_1-r_2)\\\\\n",
    "m\\ddot{r}_2 &= -k(r_2-r_1) -k(r_2-r_3)\\\\\n",
    "m\\ddot{r}_3 &= -k(r_3-r_2) -k(r_3)\n",
    "\\end{align}\n",
    "\n",
    "This is identical to\n",
    "\n",
    "\\begin{align}\n",
    "\\begin{pmatrix}\\ddot{r}_1\\\\\\ddot{r}_2\\\\\\ddot{r}_3\\end{pmatrix}=-\\frac{k}{m}\n",
    "\\begin{pmatrix}2&-1&0\\\\-1&2&-1\\\\0&-1&2\\end{pmatrix}\n",
    "\\begin{pmatrix}r_1\\\\ r_2\\\\ r_3\\end{pmatrix}\n",
    "\\end{align}\n",
    "\n",
    "We can, of course, solve this system of equations numerically. "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "86a7ad2c",
   "metadata": {},
   "source": [
    "## 1. Solving the coupled differential equations numerically "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "3b46f20b",
   "metadata": {},
   "outputs": [],
   "source": [
    "k = 1\n",
    "m = 1\n",
    "\n",
    "def f_3osc(t,y):\n",
    "    r = y[0:3]\n",
    "    v = y[3:6]\n",
    "    eq1 = (2*r[0] -r[1]) * -k/m\n",
    "    eq2 = (-r[0] +2*r[1] -r[2]) * -k/m\n",
    "    eq3 = (-r[1] +2*r[2]) * -k/m\n",
    "    return [v[0], v[1], v[2], eq1, eq2, eq3]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "0ba4be0e",
   "metadata": {},
   "outputs": [],
   "source": [
    "tStart = 0\n",
    "tEnd = 100\n",
    "\n",
    "a = 1\n",
    "\n",
    "yStart = 0.3 * (2*np.random.rand(6)-1) * a\n",
    "\n",
    "solution_3osc = integrate.solve_ivp(f_3osc, [tStart, tEnd], yStart, method='RK45', t_eval = np.linspace(tStart, tEnd, 1001))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "f947e852",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x16df505ac40>]"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.xlabel('Time t')\n",
    "plt.ylabel('Coordinates')\n",
    "\n",
    "plt.plot(solution_3osc.t, solution_3osc.y[0] + 1*a)\n",
    "plt.plot(solution_3osc.t, solution_3osc.y[1] + 2*a)\n",
    "plt.plot(solution_3osc.t, solution_3osc.y[2] + 3*a)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6a70a97b",
   "metadata": {},
   "source": [
    "## 2. The eigenvalue problem"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "462014cf",
   "metadata": {},
   "source": [
    "### 2.1 Why is it an eigenvalue problem?"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6392a25b",
   "metadata": {},
   "source": [
    "The equation for 3 oscillators was \n",
    "\n",
    "\\begin{align}\n",
    "\\begin{pmatrix}\\ddot{r}_1\\\\\\ddot{r}_2\\\\\\ddot{r}_3\\end{pmatrix}=-\\frac{k}{m}\n",
    "\\begin{pmatrix}2&-1&0\\\\-1&2&-1\\\\0&-1&2\\end{pmatrix}\n",
    "\\begin{pmatrix}r_1\\\\ r_2\\\\ r_3\\end{pmatrix}\n",
    "\\end{align}\n",
    "\n",
    "Solving the system numerically is nice. However, it would be much easier if the matrix would be just a diagonal matrix or even a scalar:\n",
    "\n",
    "\\begin{align}\n",
    "\\begin{pmatrix}\\ddot{q}_1\\\\\\ddot{q}_2\\\\\\ddot{q}_3\\end{pmatrix}=-\\frac{k}{m}\n",
    "\\lambda\n",
    "\\begin{pmatrix}q_1\\\\ q_2\\\\ q_3\\end{pmatrix}\n",
    "\\end{align}\n",
    "\n",
    "In this case the solution would be harmonic oscillators with a frequency \\\\( \\omega = \\sqrt{\\frac{k}{m}\\lambda}\\\\). \n",
    "\n",
    "We must find a unitary matrix \\\\(\\underline{u}\\\\) with \\\\(\\underline{u}^{-1}\\underline{u} = \\underline{u}\\,\\underline{u}^{-1} = 1\\\\) and \\\\( \\underline{u}^{-1}\\underline{A}\\,\\underline{u} = \\lambda\\\\) so that\n",
    "\n",
    "\\begin{align} \n",
    "\\ddot{\\vec{r}}&=-\\frac{k}{m}\\underline{A}\\vec{r}\\\\\n",
    "\\ddot{\\vec{r}}&=-\\frac{k}{m}\\left(\\underline{u}\\,\\underline{u}^{-1}\\right)\\,\\underline{A}\\,\\left(\\underline{u}\\,\\underline{u}^{-1}\\right)\\vec{r}\\\\\n",
    "\\left(\\underline{u}^{-1}\\ddot{\\vec{r}}\\right)&=-\\frac{k}{m}\\left(\\underline{u}^{-1}\\,\\underline{A}\\,\\underline{u}\\right)\\,\\left(\\underline{u}^{-1}\\vec{r}\\right)\\\\\n",
    "\\ddot{\\vec{q}}&=-\\frac{k}{m}\\lambda \\vec{q}\n",
    "\\end{align}"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1a38f224",
   "metadata": {},
   "source": [
    "This means we must find:\n",
    "\n",
    "\\begin{align}\n",
    "\\underline{u}^{-1}\\,\\underline{A}\\,\\underline{u} &= \\lambda\\\\\n",
    "\\underline{A}\\,\\underline{u} &= \\lambda\\underline{u}\n",
    "\\end{align}\n",
    "\n",
    "or\n",
    "\n",
    "\\begin{align}\n",
    "\\underline{u}^{-1}\\,\\underline{A}\\,\\underline{u}\\vec{r} &= \\lambda\\vec{r}\\\\\n",
    "\\underline{A}\\,\\underline{u}\\vec{r} &= \\lambda\\underline{u}\\vec{r}\\\\\n",
    "\\end{align}\n",
    "\n",
    "In other words, we must find the eigenvalues and eigenvectors of \\\\( \\underline{A} \\\\)."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3751672b",
   "metadata": {},
   "source": [
    "### a) Calculate the eigenvalues using a numpy routine"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "428ab94f",
   "metadata": {},
   "source": [
    "We want to determine the eigenvalues of the matrix\n",
    "\n",
    "\\begin{align}\n",
    "\\underline{A} = \\begin{pmatrix}2&-1&0\\\\-1&2&-1\\\\0&-1&2\\end{pmatrix}\n",
    "\\end{align}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "218c128a",
   "metadata": {},
   "outputs": [],
   "source": [
    "A = np.array([[2,-1,0],[-1,2,-1],[0,-1,2]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "14a08683",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([3.41421356, 2.        , 0.58578644])"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.linalg.eigvals(A)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5959358c",
   "metadata": {},
   "source": [
    "### b) Exercise: Program a routine ourselves"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5e3f01ba",
   "metadata": {},
   "source": [
    "We have to solve the following equation\n",
    "\n",
    "\\begin{align}\n",
    "0 = \\det(\\underline{A}-\\lambda\\underline{1})\n",
    "\\end{align}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "5d4856c1",
   "metadata": {},
   "outputs": [],
   "source": [
    "def det3(A):\n",
    "    term1 = A[0,0] * (A[1,1]*A[2,2]-A[1,2]*A[2,1])\n",
    "    term2 = A[1,0] * (A[0,1]*A[2,2]-A[0,2]*A[2,1])\n",
    "    term3 = A[2,0] * (A[0,1]*A[1,2]-A[1,2]*A[1,1])\n",
    "    return term1 -term2 +term3"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2d0916fd",
   "metadata": {},
   "source": [
    "\\begin{align}\n",
    "0 &= \\det\\begin{pmatrix}2-\\lambda&-1&0\\\\-1&2-\\lambda&-1\\\\0&-1&2-\\lambda\\end{pmatrix}\\\\\n",
    "0 &= (2-\\lambda)\\det\\begin{pmatrix}2-\\lambda&-1\\\\-1&2-\\lambda\\end{pmatrix}-(-1)\\det\\begin{pmatrix}-1&-1\\\\0&2-\\lambda\\end{pmatrix}\\\\\n",
    "0 &= (2-\\lambda)^3-(2-\\lambda)-(2-\\lambda)\\\\\n",
    "0 &= -\\lambda^3 +6\\lambda^2 - 12\\lambda + 8 -4 +2\\lambda\n",
    "\\end{align}\n",
    "\n",
    "We have to find the roots of a cubic function (characteristic polynomial)\n",
    "\n",
    "\\begin{align}\n",
    "0 &= -\\lambda^3 +6\\lambda^2 - 10\\lambda + 4\n",
    "\\end{align}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "d799f5d4",
   "metadata": {},
   "outputs": [],
   "source": [
    "def characteristicPolynomial(x):\n",
    "    return det3(A-x*np.identity(3))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "07f72c3f",
   "metadata": {},
   "outputs": [],
   "source": [
    "def findRoot(f, n, xmin, xmax, startStep):\n",
    "    # f: Function\n",
    "    # n: Number of roots\n",
    "    # [xmin, xmax]: Range in which the roots are expected\n",
    "    # startStep: Starting value for the step\n",
    "    x = xmin\n",
    "    d = startStep\n",
    "    signA = np.sign(f(x))\n",
    "    signB = np.sign(f(x))\n",
    "    root = []\n",
    "    while len(root) < n:\n",
    "        while d > 0.0000001:\n",
    "            # compare sign of neighboring points\n",
    "            while signA-signB == 0:\n",
    "                signA = signB\n",
    "                x = x+d\n",
    "                signB = np.sign(f(x))\n",
    "            # decrease d whenever the sign changes until desired accuracy is reached\n",
    "            x = x-d\n",
    "            signA = np.sign(f(x-d))\n",
    "            signB = np.sign(f(x))\n",
    "            d = d*0.1\n",
    "        # store x in root\n",
    "        root.append(x)\n",
    "        # reset d\n",
    "        d = startStep\n",
    "        # go to next x and reset signs\n",
    "        x = x+d\n",
    "        signA = np.sign(f(x))\n",
    "        signB = np.sign(f(x))\n",
    "    return root"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "5d390f3c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[0.5857863999999998, 1.9999999000000004, 3.41421349999997]"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "findRoot(characteristicPolynomial, 3, 0, 4, 0.01)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1bc60590",
   "metadata": {},
   "source": [
    "### c) Analyzing the eigensystem"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a59c622a",
   "metadata": {},
   "source": [
    "The analytical solutions are:\n",
    "\\\\( \\quad \\lambda_1 = 2+\\sqrt{2}, \\lambda_2 = 2, \\quad \\lambda_3 = 2-\\sqrt{2}\\\\)\n",
    "\n",
    "This leads us to the eigenfrequencies: \\\\( \\omega = \\sqrt{\\frac{k}{m}\\lambda}\\\\)\n",
    "\n",
    "\\begin{align} \n",
    "\\omega_1 = \\sqrt{\\frac{k}{m}}\\sqrt{2+\\sqrt{2}}, \\quad \\omega_2 = \\sqrt{\\frac{k}{m}}\\sqrt{2}, \\quad \\omega_3 = \\sqrt{\\frac{k}{m}}\\sqrt{2-\\sqrt{2}}\n",
    "\\end{align}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "fc2f1947",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([3.41421356, 2.        , 0.58578644]),\n",
       " array([[-5.00000000e-01, -7.07106781e-01,  5.00000000e-01],\n",
       "        [ 7.07106781e-01,  4.19803081e-16,  7.07106781e-01],\n",
       "        [-5.00000000e-01,  7.07106781e-01,  5.00000000e-01]]))"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.linalg.eig(A)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6fefcf01",
   "metadata": {},
   "source": [
    "The eigenvectors are \n",
    "\\begin{align}\n",
    "\\begin{pmatrix}-\\frac{1}{2}\\\\-\\frac{1}{\\sqrt{2}}\\\\\\frac{1}{2}\\end{pmatrix}\\quad\\quad\n",
    "\\begin{pmatrix}\\frac{1}{\\sqrt{2}}\\\\0\\\\\\frac{1}{\\sqrt{2}}\\end{pmatrix}\\quad\\quad\n",
    "\\begin{pmatrix}-\\frac{1}{2}\\\\\\frac{1}{\\sqrt{2}}\\\\\\frac{1}{2}\\end{pmatrix}\n",
    "\\end{align}"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2971acc0",
   "metadata": {},
   "source": [
    "## 3. Fourier transform"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "734a9800",
   "metadata": {},
   "source": [
    "\\\\(\n",
    "\\tilde{y}(\\omega) = \\frac{1}{\\sqrt{2\\pi}} \\int_{-\\infty}^{\\infty} y(t) e^{i\\omega t}\\mathrm{d}t\n",
    "\\\\)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "3bd63c85",
   "metadata": {},
   "outputs": [],
   "source": [
    "def integralTrapezoidal(data):\n",
    "    a = 0\n",
    "    for i in range( len(data[0]) -1 ):\n",
    "        a = a + ( data[1,i+1] + data[1,i] ) / 2 * (data[0,i+1] - data[0,i])\n",
    "    return a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "8383ad40",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x16df51850d0>]"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.xlabel('Time t')\n",
    "plt.ylabel('Coordinates')\n",
    "\n",
    "plt.plot(solution_3osc.t, solution_3osc.y[0] + 1*a)\n",
    "plt.plot(solution_3osc.t, solution_3osc.y[1] + 2*a)\n",
    "plt.plot(solution_3osc.t, solution_3osc.y[2] + 3*a)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "eb1d54ab",
   "metadata": {},
   "outputs": [],
   "source": [
    "ft = np.array(\n",
    "    [[[om,\n",
    "    integralTrapezoidal( np.array([solution_3osc.t, 1/np.sqrt(2*np.pi) * solution_3osc.y[i] * np.exp(1j*om*solution_3osc.t)]) )] for om in np.linspace(0,3,301)]\n",
    "    for i in range(3)]\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "cacf8859",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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CYYSHWiyIR0XkpyJyiRT3CjIiSbZMR7moPRhdCyLAkoqYUBrhphaBOA63Wur7gO0i8s8iclx9m2U0Kk7JgEHgu5ii9WB0AmpSmQVhhI2qAqEu93qlM/4KuBp4TET+KCKvq3sLjYYhn1fySkAWU/SydzIBNakSMQtSG+GiUj8IAERkNvBfcC2IfcDHgTuAU4GfAsvr2D6jgSgdRc0nGZfIPRidXJ6W1Mh/n1TCgtRGuKgqELgVWf8deIeqdhUtX+tXYzWiQekoaj6JWCyCWUxB/UGsJ7URLmqJQfwPVf1fxeIgIu8CUNX/W7eWGQ1HQSCs1EaZooUxMlaLyQgRtQjEZwOW/d14N8RofIZdTEGlNqL1YMzm8qQS1h/ECDdlXUwicjHuGA2LSgr1deCOJ21EjGEXk/WDcALKfVtPaiNsVLIgduMW6RsC1hV97gD+otoPi8jNIrJfRDYVLZslIveKyLPe98wy+14kIltFZLuIBFkwxiSQDRhm052P3oMxqNy39aQ2wkZZgVDVDV7BvhWq+sOizy9U9eUafvsHwEUlyz4L3KeqK4H7CHBfiUgc+BZwMbAKuEpEVtV2OkY98QOwgR3EIuZacfJ5UiWxmJT1gzBCRlmBEJGfeJNPiMhTRZ+NIvJUtR9W1QeAQyWLLwX8KrE/BN4RsOtZwHZV3aGqGeA2bz9jkvH7OgSNpBY1F1M5CyJq18EIN5XSXP1hRt86jsebp6p7AFR1j4jMDdhmEfBS0XwX8NpyPygi1wDXACxdunQcm2qU4ruRgiyIqL05Bw05mvQGDFLVEWNVG8ZUpZKLaY83eQB4SVVfAJqAU3DjE/Ui6D+r7GuZqt6oqqtVdXVnZ2cdm2X4bqRRFkRES20EZXMBkYvHGOGlljTXB4BmEVmEGzf4IG584WjYJyILALzv/QHbdAFLiuYXU19BMmokW+gHMbqDWM57c44K2YBSG75gRM2aMsJLLQIhqnoEuBz4hqpehhs8PhruwK3lhPf9q4BtHgdWishyEUkBV3r7GZOMH4Mo/2CMhkCoavDY3J5lZXEIIyzUJBBeUb73Ar/1ltVSw+lW3DIdx4tIl4h8GPgi8BYReRZ4izePiCwUkTUAquoA1wJ3A1uAn6jq5rGdllEPfDfSqFIb3oMyKplMhWyu0mquCfc62LjURliopRbTdbg9p29X1c0icixwf7WdvOqvQVwQsO1u3E55/vwaYE0NbTMmkOF+EKM7yrnro/Hm7FsIviD4+IIRFaE0wk9VgfDSVR8omt8BfKKejTIaE6dsFpPvWonGgzFTSPctE6R2oiGURvipxVV0HPApYFnx9qr6pvo1y2hEKmUxueuj8WAsF4vxr0PU6lIZ4aUWF9NPgRuAm4BcfZtjNDJl+0HE/PTOaDwYC7GYkuuQikfrOhjhpxaBcFT1O3VvidHwFCyIMm/OUcne8Ut6j7YgLIvJCBe1ZDH9WkT+RkQWeMX2ZonIrLq3zGg4suUGDIpqFlNAj3KwLCYjPNRiQfj9Fj5dtEyBY8e/OUYjMxykDs7eiU4WU3AsJmkWhBEyaslisjGnDaDYxVTGgojIg7F8TSqLQRjhoqqLSURaROR/iMiN3vxKERnPAn7GFKG8iyla2TvZallMJhBGSKglBvF9IAOc4813Af+7bi0yGhanTEe5ZMRKTJQL1qesWJ8RMmoRiBWq+i9AFkBVBwmuuGqEnPKlNvwspmi8ORdcTBG/Dkb4qUUgMiIyDa/ktoisANJ1bZXRkJRzrRSK9UWmo1yZUhtxq8VkhItaspj+AbgLWCIitwDn4pb8NiKGk1NEIF765hyLVqmNbLlSGxFztRnhp5YspntEZB1wNq5r6TpVPVD3lhkNRzafLzwEi0lErNx3WUsqYUFqI1zUksV0n6oeVNXfqupvVPWAiNw3EY0zGgsnYBxmGA7ORq2jXNDASRAdV5sRfspaECLSDLQAc0RkJsOB6Q5g4QS0zWgwnFx+lFsFotgPItiCKGQxOdEQSiP8VHIx/TVwPa4YrGNYIHqBb9W3WUYjks3rqIciDPvioxKcHc5isn4QRrgp62JS1X/1elF/SlWPVdXl3ucUVf3m0R5QRI4XkSeLPr0icn3JNueJSE/RNp872uMZ44eTywe6mKJWYmK4P0iZcTHMxWSEhFqC1N8QkXMYPR7Ej47mgKq6FTgVQETiwC7g9oBNH1RV67HdQDg5HVV/CIrHg4jGm3O2TAyiUKzPXExGSKhlwKB/B1YATzI8HoQCRyUQJVwAPKeqL4zDbxl1xnUxBVgQsWj1IPZjDKkSd5uIkIhJZITSCD+19INYDaxS1Xr8918J3Fpm3etEZAOwG9fNtTloIxG5BrgGYOnSpXVoouHjupgqWBAR8b2XK7XhLpPICKURfmrpSb0JmD/eBxaRFPB23BHrSlkPHKOqpwDfAH5Z7ndU9UZVXa2qqzs7O8e7mUYR2ZyWyWKK1pCj5YoWghuHsCC1ERZqsSDmAE+LyGMUldhQ1be/wmNfDKxX1X2lK1S1t2h6jYh8W0TmWAe9ycXJ5wOzmKI25Gi5NFd/WVSugxF+ai21UQ+uoox7SUTmA/tUVUXkLFxL52Cd2mHUSLmOcrGYEJMoZTEpsYCSI+AGqqNyHYzwU0sW0x/H+6Ai0gK8Bbevhb/sI97xbgCuAD4qIg4wCFxZpxiIMQayueBSG+D64yMzHkQ+OBYDbm/qqPQHMcJPpZ7UfXgVXEtXAaqqHUd7UFU9AswuWXZD0fQ3gaPua2HUByevNCWCH4zJWHTenJ2cjir17ZNKxCJzHYzwU1YgVLV9IhtiND5OLk9rU/CfTCIei0wWUzaXH1Xq2ycRE4tBGKGhliwmwwDc7J1yb87JuESmSF22TIdB8IPUjXkdsrk8v96wOzJCbrxyTCCMmsnlg4PU4Preo/LgcXL5wA6D4Allg16HOzft5eO3PsHXfrdtsptiTBFMIIyaqRicjVD2jlOmaCG4FkSj9qQ+1O9mqX/3jzsYyuaqbG0YJhDGGKgUnE3GY5FxMWXKFC0Erye105jXYW+vKxBOXnnixcOT2xhjSmACYdRMuVIb4AZnI+ViqhSDaFALYm/PYGH64IANK29UxwTCqJlMLrhYH3j9IKLiYirTYRAauyf1np4hju1sBeBgf2aSW2NMBUwgjJrJ5vKjKpj6NHJwdrzJ5IJLjkBj96Te2zvEqxd0EBM42G8WhFEdEwijZjJOnlSZ/P9UA785jzdOFUuqEXtSqyp7eoZYPGMaM1tSHBgwC8KojgmEUTPZXAWBSERIIPL5sv0gUvHG7El9aCBDxskzf3ozs9tSZkEYNWECYdREPq9V0zujMpJatkIMolF7Uu/pGQJgwfRmZrc2ccgsCKMGTCCMmvDdJpUsiHRkBKJCLCbRmMH6/X2uQMzt8C0IEwijOiYQRk0UBKLMgzFSLqZKWUwNakH0DjoAzJiWZE5bEwfMxWTUgAmEURO++6hSkLoRg7P1oFKP8mSDFi3sS7sC0dacYFZrit4hJzIuQePoMYEwaqLSKGrgCUREHjiVXEyN2h+kf8gViPamJLPbUgAWhzCqYgJh1ETBgqjgYoqKQDhlxuYGSMWFbD5Po41v1TeUJRETmpMxZrc2AZibyajKpAiEiOwUkY0i8qSIrA1YLyLydRHZLiJPicjpk9FOY5iCBVFuwKAGfXOuB24WU3kLQtWtfNtI9Kcd2poTiAizWl0L4uUjZkEYlallTOp6cb6qHiiz7mJgpfd5LfAd79uYJNJmQRRw8pXKfce8bZREfCJbVZm+IYc2b7CnjmmJwjLDqESjupguBX6kLo8AM0RkwWQ3Ksr41kEqUX6ozUyu8Vwr9SDrlO8o5wtHowXs+4Yc2puTAIXvvqHsZDbJmAJMlkAocI+IrBORawLWLwJeKprv8paNQkSuEZG1IrK2u7u7Dk01oDgGEfxanPIejFFwM2VyeZqS5V1tQMP1pu5PZ2n3LYhm99tPfTWMckyWQJyrqqfjupI+JiJvLFkf9Joa+B+nqjeq6mpVXd3Z2Tne7TQ8sjV0lIPGe3Meb/J5JZtTmsqNSV0Qysa6Dn1DbgwCoDWVQMQsCKM6kyIQqrrb+94P3A6cVbJJF7CkaH4xsHtiWmcE4VsQ5Xzvfmwi7HEIXwCbygQYfAui0QSiP+3Q7glELCa0NyXotRiEUYUJFwgRaRWRdn8auBDYVLLZHcD7vWyms4EeVd0zwU01ikhX6SjnZzc12oNxvElnfYGoHINoNFdbf1GQGtw4RK9ZEEYVJiOLaR5wu4j4x/8PVb1LRD4CoKo3AGuAS4DtwBHgg5PQTqOIbLVSGxGxINKOO5ZzWaEsxCAa6zoUu5gAOqYlLQZhVGXCBUJVdwCnBCy/oWhagY9NZLuMylQtteEtD3vBPv/8ysYgYo0Xi0k7OTK5PB1e9hJAe3PCYhBGVRo1zdVoMGoptVG8XVjxLYimZJlsLi8NuJGymPwyG8Uupo7mpMUgjKqYQBg1UUu5bwi/i2moSgzCtyAaSSj7AgXCLAijOiYQRk0MZzFFO811OIupcgyikYLU/V4l1/ZRMQgTCKMyJhBGTVR7MEYmSJ2tlubaeP0gChZEc3EWU4K+tEO+wWpGGY2FCYRRE1nHfZCUHXI0IhZEzVlM+ca5Dr4rqb1pOEjd0ZxEFQYyFocwymMCYdREJpcjHhPiZctcR8SCqJbF5NdichrnzTzIxeRPW6DaqIQJhFETGaf8IDkw/MCMikA0l6nFlGpAC6I/PdrF1DHNCvYZ1TGBMGoim9OyZTagcUtMjDfprJfmWiYGkWjA6xCUxdRuBfuMGjCBMGoi7eRJVRjgICpprtWzmBqv1EbfkEMqHqO5qO9Gh5X8NmrABMKoCXcc5vIWRFTSXKtnMTWeBdGfzo5wL0FxDMIEwiiPCYRRExknXzZzB4YfjGG3IKoWLWzA8SD6Sgr1QXEMwlxMRnlMIIyayObyZVNcoShI3UBvzvWgWpprI44H0T/kjMhgguIYhFkQRnlMIIyaMAvCJe2441FXTfdtIIHoS4+2IJoScZoSMbMgjIqYQBg1kaliQfh9JBrpzbkepLP5svEHgESs8Yr19QVYEOCV27AYhFEBEwijJqpZEOC+PYfdgsjkcmUzmMAVSpEGczGls7QXlfr2aW+2UeWMyphAGDWRzeUrPhjB9cuHXSBcC6L8dRARkrFYw6W5lrqYwCv5bTEIowKTMeToEhG5X0S2iMhmEbkuYJvzRKRHRJ70Pp+b6HYaI6nmYgI3DpFpoAdjPUjXYEkl443jalNVd7jRABeTO2iQWRBGeSZjyFEH+FtVXe+NTb1ORO5V1adLtntQVd86Ce0zAqhWagPcTKbQWxBOrmIMAtze1I0y5GjayePktWwMYtfhwUlolTFVmHALQlX3qOp6b7oP2AIsmuh2GGMjm9NCxdZypBKxhsreqQdpJ09TmTpMPo1kSfUWKrkGuZjMgjAqM6kxCBFZBpwGPBqw+nUiskFE7hSR11T4jWtEZK2IrO3u7q5XUyNPLRZEMi5kvH4CYaVaDALc69AoFkR/wFgQPhaDMKoxaQIhIm3Az4HrVbW3ZPV64BhVPQX4BvDLcr+jqjeq6mpVXd3Z2Vm39kadTC5fGG+5HKlEYwVn60EtLqZkPNYwMYhCqe+m4CymtJMvdP4zjFImRSBEJIkrDreo6i9K16tqr6r2e9NrgKSIzJngZhpFDGZyI4q9BdGciDOUDffDJlNDNlciLg0jlEGjyflYuQ2jGpORxSTA94AtqvrVMtvM97ZDRM7CbefBiWulUYyqMpBxAv3YxbQ2JRhIh/thk85Wz2JqScUZbBChDCr17eMHrk0gjHJMRhbTucD7gI0i8qS37L8DSwFU9QbgCuCjIuIAg8CVqtoYr2QR5Egmh6orAJVoa07w0stHJqhVk0PaqW5BtKYSBdfOZOPHGKZPG+1i8kt+WxzCKMeEC4Sq/gmo6MxW1W8C35yYFhnV8B92VQUiFQELooYYRFtTgj09QxPUosocHswAMLM1NWqd72KychtGOawntVGVwpCVNVgQ/SF3V9SS5trWnGAg0xjX4fCRLImY0JoaLWozW1zRODSQmehmGVMEEwijKgM1WhCtTQkGMjny+fB6A9PZ6um+jRSLOTyYZUZLEi+kN4I5ba5AHOw3gTCCMYEwqlKzBdHkvqU2ytvzeOPk8gxmc4EZQcW0NTVODOLwkUxg/AHcGEQiJhwcSE9wq4ypggmEUZWBtJuRU10gkiO2Dxt+5dNyD1yf1lSCoWy+ITrLHT6SZUbL6PgDQCwmzGxNmQVhlMUEwqjKsIupcnDWX9+fDmfQs6dCRlAxvoXRCEJ5+EiWGRXaO7s1xQETCKMMJhBGVfpqdDH5efX9DfBgrAeHj7gP0hktVQTCF0rP1fbVe7byj7/ePCmxmZ7BLNMrtHdOW5O5mIyyTEY/CGOKUXOQOuUJREgzmWq1IPzrNJB2UFW+/vvtgFsw75MXHl/fRpZw+EiGGdOCXUwAs9tSvPhiuPuuGEePWRBGVQbSDiJuD+FKtBUsiLALRPkHLgxbWn1DDvt6h9/O79iwu36NCyDj5BnI5JhZwYKY3drEwX6zIIxgTCCMUWzb18eX7n6Gp3e7NRT70w5tqURgqmQx/oMx/AJRzcU0bEFs3NUDwHnHd7Lz4BH6JrBTmt/eSi6x2W0pBjK50NfQMo4OEwhjBEPZHO/89p/51v3PceMDzwHug66aewlGPhjBfYMNU6XQniNjdzFt2tVDTOCKMxYD8Mzevvo2sogerxf19DJZTFDUF8I6yxkBmEAYI1j3wsv0pR2akzEe3/ky4FoE1TKYYPjB6FsQ1932BCd9/h5ue+zF+jV4Ajk8mKUlFa9arK/Yktq8u4cVnW2sPmYWAJs9i2IiOOwJWuUspiYAczMZgZhAGCP483MHSMSEj533KnYdHmT34UH607mqGUzgDjmajAv9aYehbI47N+0lk8vzz2u2NMz4CK+EnsFsVesBRlpSW/f1ccKCDuZ1NDG7NcXm3SOHPlHVcesvcefGPXzk39cVLLiCQFTKYmp3BWJvg9SOMhoLEwhjBA8/d5CTF0/nvOPnArD2hZcZSAcPel+KiBTKTDy+8xAAV565hN4hh7WeNTKV2HV4kHff8DD3bN4L1C4QviV1aCBD18uDHDunFRFh1cKOEQLx9O5eLvzaA7zzO39+xSmw92/dz0dvWc9dm/fy8/VdAOzuccebntveXHa/YztbAdje3f+Kjm+EExMIo0B/2mFDVw+vWzGbVy9opyUVZ93OQ24MIlVbRnRbk1uw74Ft3aTiMf72wuNJxWPct2VfnVs/vmScPO+76VEe23mIL9z5DLm80nOkNoFIJWKk4jGe3tOL6vBD+DULp/Ps/j4yjmsx/N0vnuLFQ0fY0NXD70quz7Z9fazZuGfUb/cOZXlo+4FRQeVbH32ReR1NnLRoOj94aCf5vPLc/n7amhLM62gq29aO5iQLpjfz7D4TCGM0JhARJZvLc/OfnueZvcNvtI/vPEQur5yzYg6JeIwTF05n464eN4upBhcTDNch+vNzBznjmJl0tjdx9orZ/P6Z/fU6lbrw+2f2s+PAAO88fTHPHxjgns17a7YgwO1V7mcwLZ/jC0QH2ZyybV8fL3nC8IkLVrJ0Vgs3/PG5wr7PHxjgPd99mL+5ZT3fun/7iN/91E828N6bHuX8L/+hkKXUn3b4w7ZuLj5xAVefs4wdBwbY0HWY7d39rOhsrZp9dty8drZOYPDcmDqYQESQfF75xK1P8E+/eZq3feNP3Pu0+/b68HMHScVjnHHMTABOWjydp/f08vJApjB2QDVmtCR5rrufLXt6OWu5G5h986vnsuPAADs8N0bPYJYfP/4id23aW4ezGx9+tq6Lue1NfOHyk5jX0cRvntpDj1cZtRbamhOFPhDLigQCXNfSbz3r4O2nLOS/nL2U9S8eZueBAQA+f8dm8goXnDCXr9yzlZcOuR3Z7t+6n3ue3sfbT1nInp4hvvfgDgDu27KPjJPnkpMW8KYT5iICD2w7wHP7B1gxt61qW4+f38727v6GqB1lNBaTNSb1RSKyVUS2i8hnA9aLiHzdW/+UiJw+Ge2c6vQNZfnKPVv5qx+u5c6Ne/AH5bvt8Ze4c9Nern/zSlZ0tvFPv9lM2snx8HMHOXXpjMLY0ycvns5Q1u1s9fpX1TYk+BtWdvJc9wB5hTOXuQLxphPceMZ9W/aTdnK896ZH+MzPN/KR/28dX7t324j9nVyewczEpsZu2tXDLY++wO7Drs++6+Uj/GHrfi47bRGpRIzzj5/LA9u6OVShMmop8zy//7RkvDBy27LZrbSk4mze3cPP13Vx6pIZLJnVwltPXgjArzfsZtu+Ph7Y1s1/fcNy/vnyk4jHhJse3IGq8tV7tnHM7Ba+/K5TuOSk+dz80E5eHsjw07VdLJoxjdXHzGRWa4qTF01nzcY97O0dYkVndYFYObeNjJPnhUNHUFXWv/gyD20/EKoUZePomPBSGyISB74FvAXoAh4XkTtU9emizS4GVnqf1wLf8b7riqqSyeU5ks6RiAutqQSxmGuep50cPUey5BVamuK0JOMk4jGcXJ7u/jROTumYlqS9yd1HVelLO+zvHSLjKPOnNxd6tB4ayPDCoSNuGYSWFCvnttHenGQom2PTrh62ef7glfPaOH5+O22pBE/t6uF3T+9j1+FBVnS2cvFJC1jR2ca2fX189487+M1Tu2lJxXn3mUu45g3Hsq83zd/cso4XDx2hs72J323Zx4fOXc67Vi/m/971DK9dPovrLljJaUtncvXNj/HJH29g0+4ePvnm4wrX48RF0wE37/+Nx3XWdA0vOnE+X7p7K/GYcOrSGQAsntnCCfPb+cUTu3h2fx+bdvXy9atO48Ft3fzrfc8yt6OJ/3zSAr58z1Z+tq6LvMKlpyzkkxcex/yOZp7q6uGh5w6QzuY5Zcl0Tl86k+nTkuw6PMiz+/oRcds6p60JVaXr5UGe3d9He3OSExdOZ1oqzqGBDL97eh/PHxxg5dw2Lnj1PBIx4Ut3b+UHf94JQGsqzhfeeTIPbusmJsLV5ywD4PwT5nLb4y8BcMGr59V0HT5z8Qm864aHcfLDb+WxmHDiwun84old9A05/MsVJwOwcMY0zlo+i1sfe5G1L7xMczLGX772GGa1prjstEXc+vhLzO1oZuOuHr54+UmkEjGuf/Nx3LlpL//zV5v40/YD/D9vPq7wt/qfjusslPd4VQ0WxGsWuvf51kdfZHfPIGs2upbdstktfO5tqzjfS1g4fCTL7p5BmpNx5rQ20TFtuPOk//JRzZ1lTC0moxbTWcB2Vd0BICK3AZcCxQJxKfAjbxzqR0RkhogsUNXRUbtx4A3/8nsOH8lyJJMjV5RNIuL61J2cBg5Cn0q4AlGagNLWlCCXH72PH7wM6mk8qzVF31CWbG50Nsu0ZJzBbI54TOhsa+KXT+7iy/dsK/j7m5MxLjttEX1DDv/2wA5uevB58qrMbW/ix3/9Ok5bMoP//dst3PzQ89z80PN0tjfxxXeejIjwxpVzePfqxfxkbRdLZ7XwwdcvLxx3+exW5rQ18Z9Pml81999nRWcbJ8xvpykZHxG3+PibVnLtrevZsqeXa89/FW8/ZSGXnDifvb1D/P3tm/jcrzajqlxxxmJSiRg/WdvFz9Z30dGcLPjaRcAfmXxGS7KQxukzr6OJtJMfsTwREzrbm9jbO4Tq8G8k40IiFmMwm+ND5y7n8tMX8Q93bOYTtz4BwAfOWcbCGdMAeP2r5tDWlODiE+dz9rGza7oOZy6bxdfec0qhn4HPf7voeP7y3x5l+rQkb/MsB4DPXHQCV934CLt7uvn821Yxyxsi9DMXncD9W7v50t1bWdHZymWnLwLcuMHbT1nIr57cTXMyxrtWLy781lWvXcp/PPYiB/ozrFrQUbWtqxZ28I5TF3LTn54nERM+/RfHc+ycVr50z1Y+9IO1zG5NMZTNMVBi2SXjwsyWFNlcnp5B9+VJBOIixGJCXIR4TIiJK44xcafF+3bnBRF3v3x+WGhgpNj4k8Uj04v3G6WapAp5VfJ5Ja+gBGeIScDIx6W/FSR3tYpg0GaBywKOUtxm/5y15DT86wYwq7WJX33s3JraNRZES49aZ0TkCuAiVf0rb/59wGtV9dqibX4DfNEbvxoRuQ/4jKquDfi9a4BrAJYuXXrGCy+8MOY2ff5Xm7wUzTgtqQQtqTjZXJ6+IYe+IYdkXJjRkqJjWpK4CEcyDkcyOQYyDk3xGPOmN5OMx+gbcugZzNI3lCUmwvyOZuZ2NJGMx9jbM8Te3iEyTp6ls1o4ZnYLs7xSy9v29bH78CAd05KcumQGJy6ajqry7L5+tuztZX9vmpMXT+fNq+bR0ZxkX+8Qd23ay7P7+1jR2calpy4qPFC27+/nF+u7aE7G+cvXLmVOm/uAUlV+/8x+nurq4fLTF3HM7NbC+Wdzeb59/3P8xYnzOGH+yAfKgf407c2JquMwF+P7zJfMahmx/K5Ne9nbM8jV5ywr/JOlnRw/WdvFS4eOcPnpiwrHf+nQEX62rot9vUOcfsxMLlw1j6ZEnA1dh1m78xAvHRrkNYs6eM3CDpycsqHrMFv39tOUjLFqQQevXtDOywNZ1r/4Mnt7hjhmditvWTWP4+a1sXl3L3dt3stA2uEdpy3i9KUzC2255ZEXaWtKcOlpC0ec896eIea0pUhUGU2uFh57/hBOPs85K0a67e5/Zj/Pdffz4dcvH/EQevKlwzy4rZsPvX75iB7thwYy/P6Z/Zy5bOaI+wmuq25Pz9Coe1CO3qEs/++9z3LZaYs4abFrUWScPL98chePPX+ItqYEi2dOY+GMaWScPAf60xwayHCwP0MqEWP6tCTxmJBXJZdXct4DOpd3H9aq7sM6732788PLVIcf9gKFx6MWP+AVkOEHqqIFMSh9xPqCFA8QEP93Ry0rEZLgbY7ut8rtXLpIVQv3fkSzxf8aPvfiy9LWlOB/vePEgNZVR0TWqerqwHWTIBDvAv6iRCDOUtWPF23zW+ALJQLx31R1XaXfXr16ta5dO0pDDMMwjDJUEojJCFJ3AUuK5hcDpWUua9nGMAzDqCOTIRCPAytFZLmIpIArgTtKtrkDeL+XzXQ20FOv+INhGIYRzIQHqVXVEZFrgbuBOHCzqm4WkY94628A1gCXANuBI8AHJ7qdhmEYUWdSRpRT1TW4IlC87IaiaQU+NtHtMgzDMIaxntSGYRhGICYQhmEYRiAmEIZhGEYgJhCGYRhGIBPeUa6eiEg3MPau1C5zgAPj2JzJJCznEpbzADuXRiQs5wGv7FyOUdXAYmuhEohXgoisLdebcKoRlnMJy3mAnUsjEpbzgPqdi7mYDMMwjEBMIAzDMIxATCCGuXGyGzCOhOVcwnIeYOfSiITlPKBO52IxCMMwDCMQsyAMwzCMQEwgDMMwjEAiJRAicpGIbBWR7SLy2YD1IiJf99Y/JSKnT0Y7a6GGczlPRHpE5Env87nJaGc1RORmEdkvIpvKrJ9K96TauUyVe7JERO4XkS0isllErgvYZkrclxrPZarcl2YReUxENnjn8o8B24zvfVFvOMCwf3BLiz8HHAukgA3AqpJtLgHuxB3g72zg0clu9ys4l/OA30x2W2s4lzcCpwObyqyfEvekxnOZKvdkAXC6N90ObJvC/yu1nMtUuS8CtHnTSeBR4Ox63pcoWRBnAdtVdYeqZoDbgEtLtrkU+JG6PALMEJEFE93QGqjlXKYEqvoAcKjCJlPlntRyLlMCVd2jquu96T5gC7CoZLMpcV9qPJcpgXet+73ZpPcpzTIa1/sSJYFYBLxUNN/F6D+UWrZpBGpt5+s8c/ROEXnNxDRt3Jkq96RWptQ9EZFlwGm4b6vFTLn7UuFcYIrcFxGJi8iTwH7gXlWt632ZlAGDJgkJWFaqvrVs0wjU0s71uDVW+kXkEuCXwMp6N6wOTJV7UgtT6p6ISBvwc+B6Ve0tXR2wS8PelyrnMmXui6rmgFNFZAZwu4icqKrFMa9xvS9RsiC6gCVF84uB3UexTSNQtZ2q2uubo+qO4JcUkTkT18RxY6rck6pMpXsiIkncB+otqvqLgE2mzH2pdi5T6b74qOph4A/ARSWrxvW+REkgHgdWishyEUkBVwJ3lGxzB/B+LxPgbKBHVfdMdENroOq5iMh8ERFv+izce31wwlv6ypkq96QqU+WeeG38HrBFVb9aZrMpcV9qOZcpdF86PcsBEZkGvBl4pmSzcb0vkXExqaojItcCd+NmAd2sqptF5CPe+htwx8m+BNgOHAE+OFntrUSN53IF8FERcYBB4Er10hwaCRG5FTeLZI6IdAGfxw2+Tal7AjWdy5S4J8C5wPuAjZ6/G+C/A0thyt2XWs5lqtyXBcAPRSSOK2I/UdXf1PMZZqU2DMMwjECi5GIyDMMwxoAJhGEYhhGICYRhGIYRiAmEYRiGEYgJhGEYhhFIZNJcjXAhIjlgY9Gid6jqzklqjmGEEktzNaYkItKvqm1l1gnu33Z+gptlGKHCXExGKBCRZV7N/2/j1tZZIiKfFpHHvbr4/1i07d+LO5bG70TkVhH5lLf8DyKy2pueIyI7vem4iHyp6Lf+2lt+nrfPz0TkGRG5pahH7pki8mevANxjItIuIg+KyKlF7XhIRE4uOY9mEfm+iGwUkSdE5Hxv+QdE5Jci8msReV5ErhWRT3rbPCIis7ztVojIXSKyzjveCUXLH/HO4Z9EpN9b3iYi94nIeu+YU7IqsFEfTCCMqco0GR7g5XZv2fG4pY5P86ZX4pZGPxU4Q0TeKCJn4JYmOQ24HDizhmN9GLdkwZne9v9VRJZ7604DrgdW4Y7Pca5X/uTHwHWqegpuSYRB4CbgAwAichzQpKpPlRzrYwCqehJwFW7P2WZv3YnAX3rn9H+AI965Pgy839vmRuDjqnoG8Cng297yfwX+1TuH4to8Q8Blqno6cD7wFV/kDMNiEMZUZVBVT/VnxC3l/IJXAx/gQu/zhDffhisY7cDtqnrE26+0HlcQFwIni8gV3vx077cywGOq2uX91pPAMqAH2KOqj4NbDM5b/1Pgf4rIp4EPAT8IONbrgW94+z0jIi8Ax3nr7vfGNOgTkR7g197yjV772oBzgJ8WPeObvO/XAe/wpv8D+LI3LcA/i8gbgTxuaeh5wN4arosRckwgjDAxUDQtwBdU9bvFG4jI9ZQvf+wwbFU3Fy0X3Lfyu0t+6zwgXbQoh/s/JUHHUNUjInIv7qAu7wZWB7Sh0tt78bHyRfN577gx4HCxcNbAe4FO4AxVzXputebKuxhRwVxMRli5G/iQ91aNiCwSkbnAA8BlIjJNRNqBtxXtsxM4w5u+ouS3Pipu2WhE5DgRaa1w7GeAhSJyprd9u4j4L2M3AV8HHlfVoNHnHsB9aPtuqKXA1lpO2LNUnheRd3n7i4ic4q1+BHinN31l0W7Tgf2eOJwPHFPLsYxoYAJhhBJVvQfXlfKwiGwEfga0e8NP/hh4EneMgAeLdvsyrhD8GSgeD+Am4GlgvYhsAr5LBevbGwb2PcA3RGQDcC/eW7mqrgN6ge+X2f3bQNxr84+BD6hqusy2QbwX+LB33M0MD0V7PfBJEXkMtypoj7f8FmC1iKz19i0tH21EGEtzNSKNiPwD0K+qX6627TgdbyHuQC8nTGQaroi04MZtVESuBK5SVctYMipiMQjDmCBE5P242UefnIQ+GmcA3/QylA7jBskNoyJmQRiGYRiBWAzCMAzDCMQEwjAMwwjEBMIwDMMIxATCMAzDCMQEwjAMwwjk/wfovJDJlMBZPQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.xlabel('Frequency omega')\n",
    "plt.ylabel('Intensity FT')\n",
    "plt.plot(ft[0,:,0].real, abs(ft[0,:,1])**2 )\n",
    "plt.show()\n",
    "\n",
    "plt.xlabel('Frequency omega')\n",
    "plt.ylabel('Intensity FT')\n",
    "plt.plot(ft[1,:,0].real, abs(ft[1,:,1])**2 )\n",
    "plt.show()\n",
    "\n",
    "plt.xlabel('Frequency omega')\n",
    "plt.ylabel('Intensity FT')\n",
    "plt.plot(ft[2,:,0].real, abs(ft[2,:,1])**2 )\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a5999d83",
   "metadata": {},
   "source": [
    "Eigenvalues:\n",
    "\n",
    "\\begin{align} \n",
    "\\omega_1 = \\sqrt{\\frac{k}{m}}\\sqrt{2+\\sqrt{2}}, \\quad \\omega_2 = \\sqrt{\\frac{k}{m}}\\sqrt{2}, \\quad \\omega_3 = \\sqrt{\\frac{k}{m}}\\sqrt{2-\\sqrt{2}}\n",
    "\\end{align}\n",
    "\n",
    "Eigenvectors:\n",
    "\n",
    "\\begin{align}\n",
    "\\begin{pmatrix}-\\frac{1}{2}\\\\-\\frac{\\sqrt{3}}{2}\\\\\\frac{1}{2}\\end{pmatrix},\\quad\\quad\n",
    "\\begin{pmatrix}\\frac{\\sqrt{3}}{2}\\\\0\\\\\\frac{\\sqrt{3}}{2}\\end{pmatrix},\\quad\\quad\n",
    "\\begin{pmatrix}-\\frac{1}{2}\\\\\\frac{\\sqrt{3}}{2}\\\\\\frac{1}{2}\\end{pmatrix}\n",
    "\\end{align}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "8c1f3be2",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.8477590650225735\n",
      "1.4142135623730951\n",
      "0.7653668647301795\n"
     ]
    }
   ],
   "source": [
    "omega1 = np.sqrt(k/m) * np.sqrt( 2+np.sqrt(2) )\n",
    "omega2 = np.sqrt(k/m) * np.sqrt( 2 )\n",
    "omega3 = np.sqrt(k/m) * np.sqrt( 2-np.sqrt(2) )\n",
    "\n",
    "print( omega1 ) \n",
    "print( omega2 ) \n",
    "print( omega3 ) "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d4b025b0",
   "metadata": {},
   "source": [
    "## 4. Fit harmonic functions with the eigenfrequency to the numerical solution"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "6ec0ba6a",
   "metadata": {},
   "outputs": [],
   "source": [
    "data1 = np.array( [ solution_3osc.t, solution_3osc.y[0] ] )\n",
    "data2 = np.array( [ solution_3osc.t, solution_3osc.y[1] ] )\n",
    "data3 = np.array( [ solution_3osc.t, solution_3osc.y[2] ] )"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "17ef80b2",
   "metadata": {},
   "source": [
    "We consider the model function \n",
    "\n",
    "\\\\( f(t) = A_1\\cos(\\omega_1t+\\phi_1) + A_2\\cos(\\omega_2t+\\phi_2) + A_3\\cos(\\omega_3t+\\phi_3)\\\\)\n",
    "\n",
    "The fitting parameters are\n",
    "\n",
    "\\\\( \\vec{a} = (A_1, \\phi_1, A_2, \\phi_2, A_3, \\phi_3)\\\\)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "a65fab92",
   "metadata": {},
   "outputs": [],
   "source": [
    "def functionModel(t, a):\n",
    "    return a[0]*np.cos(omega1*t+a[1]) + a[2]*np.cos(omega2*t+a[3]) + a[4]*np.cos(omega3*t+a[5])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ee572618",
   "metadata": {},
   "source": [
    "There are many reasonable definitions of an error function but a very common choice is: \\\\( \\Delta = \\sum_{i=1}^n \\left(y_i-f(x_i)\\right)^2\\\\)\n",
    "\n",
    "\\\\( f \\\\) is the fit function that is determined by the coefficients \\\\( a_i \\\\) in our case.\n",
    "\n",
    "\\\\( (x_i, y_i) \\\\) are the data points that we try to fit."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "562af681",
   "metadata": {},
   "outputs": [],
   "source": [
    "def errorFit(f, coefficients, data):\n",
    "    error = 0\n",
    "    for i in range(len(data[0])):\n",
    "        error = error + ( data[1,i] - f( data[0,i], coefficients ) )**2\n",
    "    return error"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "cc49f7f4",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "362.54089950595693"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a = np.array( [0.1, 0.2, 0.3, 0.4, 0.5, 0.6] )\n",
    "\n",
    "errorFit( functionModel, a, data1)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a74ea56d",
   "metadata": {},
   "source": [
    "We can use several different methods to minimize the error, e. g. a Monte-Carlo algorithm. Here, we will use the gradient descent method. The coefficients \\\\( a_i \\\\) will be updated along the gradient direction of the error function \\\\( \\nabla_{\\vec{a}} \\Delta\\\\). The gradient consists of elements \\\\( \\frac{\\partial}{\\partial a_k} \\Delta = -2 \\sum_{i=1}^n \\left(y_i-f(x_i)\\right) \\frac{\\partial}{\\partial a_k}f(x_i) \\\\)\n",
    "\n",
    "\\\\( \\nabla_{\\vec{a}} \\Delta = \\begin{pmatrix}\n",
    "\\cos(\\omega_1t+\\phi_1)\\\\\n",
    "-A_1\\sin(\\omega_1t+\\phi_1)\\\\\n",
    "\\cos(\\omega_2t+\\phi_2)\\\\\n",
    "-A_2\\sin(\\omega_2t+\\phi_2)\\\\\n",
    "\\cos(\\omega_3t+\\phi_3)\\\\\n",
    "-A_3\\sin(\\omega_3t+\\phi_3)\n",
    "\\end{pmatrix}\\\\)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "be90b0f2",
   "metadata": {},
   "outputs": [],
   "source": [
    "def errorFitGradient(f, coefficients, data):\n",
    "    total = 0\n",
    "    for i in range(len(data[0])):\n",
    "        dfda = np.array([ np.cos(omega1*data[0,i]+a[1]), -a[0]*np.sin(omega1*data[0,i]+a[1]), np.cos(omega2*data[0,i]+a[3]), -a[2]*np.sin(omega2*data[0,i]+a[3]), np.cos(omega3*data[0,i]+a[5]), -a[4]*np.sin(omega3*data[0,i]+a[5]) ])\n",
    "        total = total + (data[1,i] - f(data[0,i],coefficients)) * dfda\n",
    "    return -2*total"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "1402df0e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-20.12441742,   4.27645297, 513.82306356, -23.12844482,\n",
       "       658.71314821,  81.2522938 ])"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "errorFitGradient( functionModel, a, data1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "a8adc4ff",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "134.98227477612102\n"
     ]
    }
   ],
   "source": [
    "h = 0.0001\n",
    "\n",
    "# One test step\n",
    "a = a - h * errorFitGradient( functionModel, a, data1)\n",
    "print(errorFit( functionModel, a, data1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "953b547c",
   "metadata": {},
   "outputs": [],
   "source": [
    "iterations = 1000\n",
    "\n",
    "for i in range(iterations):\n",
    "    a = a - h * errorFitGradient( functionModel, a, data1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "18a78b38",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.04989249923405641"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "errorFit( functionModel, a, data1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "f44748a1",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-1.05607069e-02,  1.20850838e+00,  1.47018148e-03,  2.15765429e-01,\n",
       "       -8.81130229e-04, -3.93025573e-01])"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "errorFitGradient( functionModel, a, data1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "id": "e42ac50d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x16df6314130>"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.xlabel('Time t')\n",
    "plt.ylabel('Coordinates')\n",
    "\n",
    "t_eval = np.linspace(tStart, tEnd, 1001)\n",
    "\n",
    "plt.plot(t_eval, functionModel(t_eval,a),'red')\n",
    "plt.scatter(data1[0], data1[1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "id": "23ce1db3",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0.1263005 , -0.10453525, -0.21310431,  0.08474101, -0.22367036,\n",
       "        1.37524734])"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "147b339e",
   "metadata": {},
   "source": [
    "## Oscillator 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "id": "2357783b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x16df637ad60>"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "a = np.array( [0.1, 0.2, 0.3, 0.4, 0.5, 0.6] )\n",
    "\n",
    "for i in range(iterations):\n",
    "    a = a - h * errorFitGradient(functionModel, a, data2)\n",
    "    \n",
    "plt.xlabel('Time t')\n",
    "plt.ylabel('Coordinate')\n",
    "\n",
    "t_eval=np.linspace(tStart,tEnd,1001)\n",
    "\n",
    "plt.plot(t_eval, functionModel(t_eval, a), 'red')\n",
    "plt.scatter(data2[0], data2[1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "id": "d1bc8909",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-1.79024309e-01, -1.62396250e-01, -2.16291736e-04,  4.00511893e-01,\n",
       "       -3.16246581e-01,  1.38189295e+00])"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c622375b",
   "metadata": {},
   "source": [
    "## 5. Generalization to n oscillators"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "id": "424c4358",
   "metadata": {},
   "outputs": [],
   "source": [
    "n = 20\n",
    "\n",
    "def f_nosc(t,y):\n",
    "    r = y[0:n]\n",
    "    v = y[n:2*n]\n",
    "    eq = np.zeros(n)\n",
    "    eq[0] = 2*r[0] -r[1]\n",
    "    eq[1:-1] = -r[:-2] + 2*r[1:-1] -r[2:]\n",
    "    eq[n-1] = -r[n-2] + 2*r[n-1]\n",
    "    return np.concatenate([v, -k/m*eq])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6b0e121f",
   "metadata": {},
   "source": [
    "### 5.1 Numerical solution"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "id": "6c2062fb",
   "metadata": {},
   "outputs": [],
   "source": [
    "a = 1\n",
    "yStart = 0.3 * (2*np.random.rand(2*n)-1) * a\n",
    "\n",
    "solution_nosc = integrate.solve_ivp(f_nosc, [tStart, tEnd], yStart, method='RK45', t_eval=np.linspace(tStart,tEnd,501))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "id": "0f53fb65",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.xlabel('Time t')\n",
    "plt.ylabel('Coordinates')\n",
    "\n",
    "for i in range(n):\n",
    "    plt.plot(solution_nosc.t, solution_nosc.y[i] + (i+1)*a)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7ec3537d",
   "metadata": {},
   "source": [
    "### 5.2 Eigenfrequencies"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "id": "a25deb84",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[-1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1]"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "[-1]*(n-1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "id": "86cb0e3a",
   "metadata": {},
   "outputs": [],
   "source": [
    "A = np.diag([-1]*(n-1), k = 1) + np.diag([2]*(n), k = 0) + np.diag([-1]*(n-1), k = -1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "id": "5a97565c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 2, -1,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,\n",
       "         0,  0,  0,  0],\n",
       "       [-1,  2, -1,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,\n",
       "         0,  0,  0,  0],\n",
       "       [ 0, -1,  2, -1,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,\n",
       "         0,  0,  0,  0],\n",
       "       [ 0,  0, -1,  2, -1,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,\n",
       "         0,  0,  0,  0],\n",
       "       [ 0,  0,  0, -1,  2, -1,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,\n",
       "         0,  0,  0,  0],\n",
       "       [ 0,  0,  0,  0, -1,  2, -1,  0,  0,  0,  0,  0,  0,  0,  0,  0,\n",
       "         0,  0,  0,  0],\n",
       "       [ 0,  0,  0,  0,  0, -1,  2, -1,  0,  0,  0,  0,  0,  0,  0,  0,\n",
       "         0,  0,  0,  0],\n",
       "       [ 0,  0,  0,  0,  0,  0, -1,  2, -1,  0,  0,  0,  0,  0,  0,  0,\n",
       "         0,  0,  0,  0],\n",
       "       [ 0,  0,  0,  0,  0,  0,  0, -1,  2, -1,  0,  0,  0,  0,  0,  0,\n",
       "         0,  0,  0,  0],\n",
       "       [ 0,  0,  0,  0,  0,  0,  0,  0, -1,  2, -1,  0,  0,  0,  0,  0,\n",
       "         0,  0,  0,  0],\n",
       "       [ 0,  0,  0,  0,  0,  0,  0,  0,  0, -1,  2, -1,  0,  0,  0,  0,\n",
       "         0,  0,  0,  0],\n",
       "       [ 0,  0,  0,  0,  0,  0,  0,  0,  0,  0, -1,  2, -1,  0,  0,  0,\n",
       "         0,  0,  0,  0],\n",
       "       [ 0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0, -1,  2, -1,  0,  0,\n",
       "         0,  0,  0,  0],\n",
       "       [ 0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0, -1,  2, -1,  0,\n",
       "         0,  0,  0,  0],\n",
       "       [ 0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0, -1,  2, -1,\n",
       "         0,  0,  0,  0],\n",
       "       [ 0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0, -1,  2,\n",
       "        -1,  0,  0,  0],\n",
       "       [ 0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0, -1,\n",
       "         2, -1,  0,  0],\n",
       "       [ 0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,\n",
       "        -1,  2, -1,  0],\n",
       "       [ 0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,\n",
       "         0, -1,  2, -1],\n",
       "       [ 0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,\n",
       "         0,  0, -1,  2]])"
      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "id": "76fe5bcb",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1.99440759, 1.97766165, 1.94985582, 1.91114561, 1.8617475 ,\n",
       "       1.80193774, 1.73205081, 1.65247755, 1.56366296, 1.46610374,\n",
       "       1.36034548, 1.2469796 , 1.12664012, 0.14946019, 0.29808453,\n",
       "       0.44504187, 0.58951035, 0.73068205, 0.86776748, 1.        ])"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.sqrt(k/m) * np.sqrt( np.linalg.eigvals(A) )"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e7fb7035",
   "metadata": {},
   "source": [
    "### 5.3 Fourier transform"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "id": "825038ef",
   "metadata": {},
   "outputs": [],
   "source": [
    "ft = np.array(\n",
    "    [[[om, \n",
    "    integralTrapezoidal( np.array([solution_nosc.t, 1/np.sqrt(2*np.pi) * solution_nosc.y[i] * np.exp(1j*om*solution_nosc.t)]) )] for om in np.linspace(0,2.5,251)\n",
    "    ] for i in range(n)]\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "id": "d6e2ae4b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.xlabel('Frequency omega')\n",
    "plt.ylabel('Intensity')\n",
    "plt.plot(ft[0,:,0].real, abs(ft[0,:,1])**2 ) \n",
    "plt.show()\n",
    "\n",
    "plt.xlabel('Frequency omega')\n",
    "plt.ylabel('Intensity')\n",
    "for i in range(n):\n",
    "    plt.plot(ft[i,:,0].real, abs(ft[i,:,1])**2 ) \n",
    "plt.show()\n",
    "\n",
    "plt.xlabel('Frequency omega')\n",
    "plt.ylabel('Intensity')\n",
    "plt.xlim([0,0.6])\n",
    "for i in range(n):\n",
    "    plt.plot(ft[i,:,0].real, abs(ft[i,:,1])**2 ) \n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e33a2996",
   "metadata": {},
   "source": [
    "## 6. Alternative geometry: Periodic boundary conditions"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "id": "3d3109d6",
   "metadata": {},
   "source": [
    "![Coupled_oscillators_circle](figure_08_coupled_oscillators_circle.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "38f94aae",
   "metadata": {},
   "source": [
    "\\\\( \n",
    "\\begin{pmatrix}\\ddot{r}_1\\\\\\ddot{r}_2\\\\\\ddot{r}_3\\\\\\ddot{r}_4\\\\\\ddot{r}_5\\\\\\ddot{r}_6\\end{pmatrix}=-\\frac{k}{m}\n",
    "\\begin{pmatrix}2&-1&0&0&0&-1\\\\-1&2&-1&0&0&0\\\\0&-1&2&-1&0&0\\\\0&0&-1&2&-1&0\\\\0&0&0&-1&2&-1\\\\-1&0&0&0&-1&2&\\end{pmatrix}\n",
    "\\begin{pmatrix}r_1\\\\ r_2\\\\ r_3\\\\r_4\\\\ r_5\\\\ r_6\\end{pmatrix}\n",
    "\\\\)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "id": "3e42f950",
   "metadata": {},
   "outputs": [],
   "source": [
    "n = 20\n",
    "\n",
    "def f_nosc_periodic(t,y):\n",
    "    r = y[0:n]\n",
    "    v = y[n:2*n]\n",
    "    eq = np.zeros(n)\n",
    "    eq[0] = -r[n-1] +2*r[0] -r[1]\n",
    "    eq[1:-1] = -r[:-2] + 2*r[1:-1] -r[2:]\n",
    "    eq[n-1] = -r[n-2] + 2*r[n-1] -r[0]\n",
    "    return np.concatenate( [v, -k/m*eq] )"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9d476ab4",
   "metadata": {},
   "source": [
    "### 6.1 Numerical solution"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "id": "26494795",
   "metadata": {},
   "outputs": [],
   "source": [
    "yStart = 0.3 * (2*np.random.rand(2*n)-1) * a\n",
    "\n",
    "solution_nosc_periodic = integrate.solve_ivp(f_nosc_periodic, [tStart, tEnd], yStart, method='RK45', t_eval=np.linspace(tStart,tEnd,501))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "id": "43089e9f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.xlabel('Time t')\n",
    "plt.ylabel('Coordinates')\n",
    "\n",
    "for i in range(n):\n",
    "    plt.plot(solution_nosc_periodic.t, solution_nosc_periodic.y[i] + (i+1)*a)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "24971161",
   "metadata": {},
   "source": [
    "### 6.2 Eigenfrequencies"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "id": "4726b4d5",
   "metadata": {},
   "outputs": [],
   "source": [
    "A = np.diag([-1]*(n-1), k=1) + np.diag([2]*n, k=0) + np.diag([-1]*(n-1), k=-1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "id": "9d948687",
   "metadata": {},
   "outputs": [],
   "source": [
    "A[0,-1] = -1\n",
    "A[-1,0] = -1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "id": "fa91268d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-1.11022302e-16,  9.78869674e-02,  3.81966011e-01,  8.24429495e-01,\n",
       "        1.38196601e+00,  2.00000000e+00,  2.61803399e+00,  3.17557050e+00,\n",
       "        4.00000000e+00,  3.90211303e+00,  3.61803399e+00,  3.90211303e+00,\n",
       "        3.61803399e+00,  3.17557050e+00,  2.61803399e+00,  9.78869674e-02,\n",
       "        3.81966011e-01,  1.38196601e+00,  8.24429495e-01,  2.00000000e+00])"
      ]
     },
     "execution_count": 57,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.linalg.eigvals(A)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "id": "e6998031",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\boerg\\AppData\\Local\\Temp/ipykernel_10580/3856773907.py:1: RuntimeWarning: invalid value encountered in sqrt\n",
      "  np.sqrt(k/m) * np.sqrt( np.linalg.eigvals(A) )\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "array([       nan, 0.31286893, 0.61803399, 0.907981  , 1.1755705 ,\n",
       "       1.41421356, 1.61803399, 1.78201305, 2.        , 1.97537668,\n",
       "       1.90211303, 1.97537668, 1.90211303, 1.78201305, 1.61803399,\n",
       "       0.31286893, 0.61803399, 1.1755705 , 0.907981  , 1.41421356])"
      ]
     },
     "execution_count": 58,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.sqrt(k/m) * np.sqrt( np.linalg.eigvals(A) )"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9a48308a",
   "metadata": {},
   "source": [
    "The first eigenvalue is zero. The corresponding mode is the translation that is allowed due to the periodic boundary conditions. It was forbidden before, since the system had fixed edges.\n",
    "\n",
    "Numerically, this value will be a very small number. Here it is negative which gives an error when calculating the square root. The correct value for the square root (and the frequency) is zero: The eigenmode is not an oscillation but a translation."
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.9.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}
