Heat Equation.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Heat equation: \n",
    " \n",
    "\\begin{align}\n",
    "\\frac{\\partial u}{\\partial t} &= \\nabla^2u + f\n",
    "\\end{align}\n",
    "\n",
    "In this example, we use $f = \\beta - 2 - 2\\alpha$, where $\\beta$ and $\\alpha$ are constants.\n",
    "\n",
    "The solution is known to be $u = 1 + x^2 + \\alpha y^2 + \\beta t$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\u001b[33mWARNING: The directory '/home/fenics/.cache/pip/http' or its parent directory is not owned by the current user and the cache has been disabled. Please check the permissions and owner of that directory. If executing pip with sudo, you may want sudo's -H flag.\u001b[0m\n",
      "\u001b[33mWARNING: The directory '/home/fenics/.cache/pip' or its parent directory is not owned by the current user and caching wheels has been disabled. check the permissions and owner of that directory. If executing pip with sudo, you may want sudo's -H flag.\u001b[0m\n",
      "Requirement already satisfied: sklearn in /usr/local/lib/python3.6/dist-packages (0.0)\n",
      "Requirement already satisfied: scikit-learn in /usr/local/lib/python3.6/dist-packages (from sklearn) (0.21.2)\n",
      "Requirement already satisfied: scipy>=0.17.0 in /usr/lib/python3/dist-packages (from scikit-learn->sklearn) (0.19.1)\n",
      "Requirement already satisfied: joblib>=0.11 in /usr/local/lib/python3.6/dist-packages (from scikit-learn->sklearn) (0.13.2)\n",
      "Requirement already satisfied: numpy>=1.11.0 in /usr/lib/python3/dist-packages (from scikit-learn->sklearn) (1.13.3)\n",
      "\u001b[33mWARNING: You are using pip version 19.1, however version 19.2.2 is available.\n",
      "You should consider upgrading via the 'pip install --upgrade pip' command.\u001b[0m\n",
      "Done!\n"
     ]
    }
   ],
   "source": [
    "!sudo pip install sklearn\n",
    "print(\"Done!\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "from fenics import *\n",
    "import numpy as np\n",
    "from IPython.display import HTML\n",
    "import matplotlib.pyplot as plt\n",
    "from sklearn.linear_model import Ridge\n",
    "from sklearn.linear_model import LinearRegression\n",
    "from sklearn.model_selection import train_test_split"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x806.4 with 22 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "def calculate_simulation(nx, ny, nt, dt=None, tmax=None, alpha=6, beta=1.2):\n",
    "    if dt is not None and tmax is not None:\n",
    "        raise ValueError(\"For a given number of points, dt and tmax cannot both be defined.\")\n",
    "    elif dt is None and tmax is None:\n",
    "        raise ValueError(\"For a given number of points, either dt or tmax should be set.\")\n",
    "    elif dt is None:\n",
    "        dt = tmax/nt\n",
    "    elif tmax is None:\n",
    "        tmax = dt*nt\n",
    "    \n",
    "    # Mesh setup\n",
    "    mesh = UnitSquareMesh(nx, ny)\n",
    "    mesh_info = {'mesh':mesh, 'nx':nx, 'ny':ny, 'nt':nt, 'dt':dt, 'tmax':tmax}\n",
    "    \n",
    "    # Simulation setup\n",
    "    sim_info = {'alpha':alpha, 'beta':beta, 'f':beta-2-2*alpha}\n",
    "\n",
    "    # Functions setup\n",
    "    V = FunctionSpace(mesh, 'P', 1)\n",
    "    u = TrialFunction(V)\n",
    "    v = TestFunction(V)\n",
    "\n",
    "    # Boundary setup\n",
    "    def boundary(x, on_boundary):\n",
    "        return on_boundary\n",
    "    u_D = Expression('1 + x[0]*x[0] + alpha*x[1]*x[1] + beta*t', degree=2, alpha=alpha, beta=beta, t=0)\n",
    "    bc = DirichletBC(V, u_D, boundary)\n",
    "\n",
    "    # Initial values\n",
    "    t = 0\n",
    "    u_n = interpolate(u_D, V)\n",
    "\n",
    "    # Variational problem\n",
    "    f = Constant(beta - 2 - 2*alpha)\n",
    "    a = u*v*dx + dt*dot(grad(u), grad(v))*dx\n",
    "    L = (dt*f+u_n)*v*dx\n",
    "    \n",
    "    # Logs\n",
    "    logs = {'t':[], 'u':[], 'error_L2':[], 'error_max':[]}\n",
    "    \n",
    "    #Log initial values\n",
    "    logs['t'].append(t)\n",
    "    logs['u'].append(u_n.copy(deepcopy=True))\n",
    "    logs['error_L2'].append(0)\n",
    "    logs['error_max'].append(0)\n",
    "    \n",
    "    # Solving\n",
    "    u = Function(V)\n",
    "    for i in range(nt):\n",
    "        t += dt\n",
    "        u_D.t = t\n",
    "        solve(a == L, u, bc)\n",
    "        u_n.assign(u)\n",
    "\n",
    "        #Get error\n",
    "        vertex_values_u_D = u_D.compute_vertex_values(mesh)\n",
    "        vertex_values_u = u.compute_vertex_values(mesh)\n",
    "        error_L2 = errornorm(u_D, u_n, norm_type='L2')\n",
    "        error_max = np.max(np.abs(vertex_values_u_D - vertex_values_u))\n",
    "\n",
    "        # Log current values\n",
    "        logs['t'].append(t)\n",
    "        logs['u'].append(u_n.copy(deepcopy=True))\n",
    "        logs['error_L2'].append(error_L2)\n",
    "        logs['error_max'].append(error_max)\n",
    "        \n",
    "    return mesh_info, sim_info, logs\n",
    "\n",
    "\n",
    "def display_simulation(mesh_info, logs, nplots_max=None, nrows_max=None, show_bounds=False, square=True, scalemin=1, scalemax=8):\n",
    "#If square is false, each image becomes a rectangle so that each pixel/vertex is of equal aspect\n",
    "#Scalemin and scalemax are decided arbitrarily to scale the colour of all images to the same standard\n",
    "#Ideally, we would scale everything based on the absolute min and max values of u over across all time points,\n",
    "#but here we are plotting the first  before doing the entire calculation.\n",
    "\n",
    "    # Retrieve variables\n",
    "    mesh = mesh_info['mesh']\n",
    "    nx = mesh_info['nx']\n",
    "    ny = mesh_info['ny']\n",
    "    nt = mesh_info['nt']\n",
    "    u_hist = logs['u']\n",
    "    t_hist = logs['t']\n",
    "\n",
    "    # Default values\n",
    "    if nplots_max is None: \n",
    "        nplots_max = 1e19\n",
    "    if nrows_max is None:\n",
    "        nrows_max = 1e19\n",
    "    nplots = min(nt+1, nplots_max)\n",
    "\n",
    "    #Figure values\n",
    "    ncols = int(np.ceil(nplots/nrows_max))\n",
    "    nrows = int(np.ceil(nplots/ncols))\n",
    "    figsize = np.array([ncols, 0.8*nrows])*2 #inches\n",
    "    aspect = 1 if square else ny/nx\n",
    "\n",
    "    fig, axes = plt.subplots(nrows=nrows, ncols=ncols, figsize=figsize)\n",
    "\n",
    "    #Draw plots one at a time\n",
    "    for i in range(nplots):\n",
    "        ax = axes.flat[i]\n",
    "        \n",
    "        vertex_values_u = u_hist[i].compute_vertex_values(mesh).reshape(ny+1, nx+1) #get values\n",
    "        img = ax.imshow(vertex_values_u, \n",
    "                        origin='lower', extent=(-0.05, 1.05, -0.05, 1.05), #center the pixels\n",
    "                        aspect=aspect,\n",
    "                        cmap='cividis', vmin=scalemin, vmax=scalemax) #colour\n",
    "        ax.set_title(f'Time: {t_hist[i]:.2f}')\n",
    "        \n",
    "        #Tickmarks\n",
    "        if show_bounds:\n",
    "            maj_locator = plt.FixedLocator([0, 1])\n",
    "        if not show_bounds:\n",
    "            maj_locator = plt.NullLocator()\n",
    "        ax.xaxis.set_major_locator(maj_locator)\n",
    "        ax.yaxis.set_major_locator(maj_locator)\n",
    "        ax.xaxis.set_minor_locator(plt.NullLocator())\n",
    "        ax.yaxis.set_minor_locator(plt.NullLocator())\n",
    "\n",
    "    plt.tight_layout(True)\n",
    "\n",
    "    #Add colorbar\n",
    "    fig.subplots_adjust(right=0.8)\n",
    "    cbar_ax = fig.add_axes([0.85, 0.15, 0.05, 0.7])\n",
    "    fig.colorbar(img, cax=cbar_ax)\n",
    "\n",
    "    plt.show()\n",
    "    \n",
    "#Test\n",
    "mesh_info, sim_info, logs = calculate_simulation(10, 15, 20, tmax=4.0, alpha=6, beta=1.2)\n",
    "display_simulation(mesh_info, logs, nrows_max=7, show_bounds=True, scalemin=0, scalemax=7)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "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": {
      "text/plain": [
       "(<matplotlib.axes._subplots.AxesSubplot at 0x7f4dda5dcf98>,\n",
       " <matplotlib.lines.Line2D at 0x7f4dd64edb00>)"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def display_error(error_type, mesh_info, logs, prev_ax=None, major_ticks_period=1, show=True):\n",
    "    #the simulation time is displayed every 'major_ticks_period' times the timestep dt\n",
    "    #'show' is false when the function is used as an intermediate step (if the axis will be used for further plotting)\n",
    "    \n",
    "    #Initialize figure and axis\n",
    "    if prev_ax is None:\n",
    "        fig = plt.figure()\n",
    "        ax = fig.add_subplot(111)\n",
    "    else:\n",
    "        ax = prev_ax\n",
    "    \n",
    "    #Plot, and keep artist to be later used when creating a legend when displaying multiple legends at once\n",
    "    artist, = ax.plot(logs['t'], logs['error_'+error_type])\n",
    "    \n",
    "    #Display settings\n",
    "    ax.margins(x=0)\n",
    "    ax.set_title('Error analysis')\n",
    "    ax.set_xlabel('Simulation time')\n",
    "    ax.set_ylabel('Error '+str(error_type)+'of u across all vertices')\n",
    "    \n",
    "    if show: #if display for only on simulation\n",
    "        ax.xaxis.set_major_locator(plt.MultipleLocator(mesh_info['dt']*major_ticks_period))\n",
    "        ax.xaxis.set_minor_locator(plt.MultipleLocator(mesh_info['dt']))\n",
    "        plt.show()\n",
    "        \n",
    "    return ax, artist\n",
    "\n",
    "mesh_info, sim_info, logs = calculate_simulation(10, 15, 20, tmax=4.0, alpha=6, beta=1.2)\n",
    "display_error('max', mesh_info, logs, major_ticks_period=5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "scrolled": true
   },
   "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": [
    "from matplotlib.patches import Patch\n",
    "\n",
    "def display_errors(error_type, nxs, nys, nts, tmax):\n",
    "    nxs, nys, nts = np.sort(nxs), np.sort(nys), np.sort(nts) #Sort number of points into ascending order\n",
    "    \n",
    "    # Display setup\n",
    "    prev_ax = None\n",
    "    artists = []\n",
    "    \n",
    "    # Reuse smallest value of n_s if their are smaller values of a different n_s to get through\n",
    "    len_max = max(len(nxs), len(nys), len(nts))\n",
    "    for n_s in [nxs, nys, nts]:\n",
    "        if len(n_s) < len_max:\n",
    "            n_missing = len_max - len(n_s)\n",
    "            n_s = n_s + [n_s]*n_missing\n",
    "    \n",
    "    # Iteration\n",
    "    for i in range(len_max):\n",
    "            \n",
    "        # calculation step\n",
    "        mesh_info, sim_info, logs = calculate_simulation(nxs[i], nys[i], nts[i], tmax=tmax)\n",
    "        \n",
    "        # display step\n",
    "        prev_ax, prev_art = display_error(error_type, mesh_info, logs, prev_ax=prev_ax, show=False)\n",
    "        artists.append(prev_art)\n",
    "        \n",
    "    # Add legend\n",
    "    empty_artist = Patch(color='white', label=str((nxs, nys, nts)))\n",
    "    prev_ax.legend([empty_artist]+artists, ['(nx, ny, nt)']+list(zip(nxs, nys, nts)), \n",
    "                   bbox_to_anchor=(1.05, 1), loc='upper left', borderaxespad=0.)\n",
    "    plt.show()\n",
    "            \n",
    "display_errors('L2', [10, 15, 20, 30], [10, 15, 20, 30], [20, 30, 40, 60], 4.0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "n=4\t(1 of 6)\n",
      "n=8\t(2 of 6)\n",
      "n=16\t(3 of 6)\n",
      "n=32\t(4 of 6)\n",
      "n=64\t(5 of 6)\n",
      "n=128\t(6 of 6)\n"
     ]
    },
    {
     "data": {
      "image/png": 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sWb/JTyhmNmQ5odRIa5u7DJvZ0OaEUiP5UfKu8jKzocoJpUZa8wnFVV5mNkQ5odRI87r8a1dc5WVmQ5MTSo20tHUwoklMrvIUnGZm9eKEUiMtuXZmjB/NsGGejdDMhiYnlBppzXliLTMb2pxQaqTZU/+a2RDnhFIjLU4oZjbEOaHUwMZNnbS1dzqhmNmQ5oRSAy05j5I3s6GvrglF0gmSHpG0XNJ53Wy/SNLi9HlU0gsF27oKti2obeR9s3WUvJ9QzGwIG16vC0tqAi4BjgNWAvdKWhARD+X3iYj/U7D/R4CDCk7xYkQcWKt4+8MJxcwaQT2fUA4DlkfEiojYBFwHnNzD/qcD19YksgprdZWXmTWAeiaUXYCnC9ZXprKXkTQH2A34fUHxaEkLJf1V0imlLiLpnLTfwtWrV1ci7j5rzrUzZmQT40bV7YHQzKzqBkuj/GnADRHRVVA2JyLmA+8CviVpj+4OjIjLImJ+RMyfPn16LWJ9mXyXYcmj5M1s6KpnQlkF7FqwPiuVdec0iqq7ImJV+roCuJ2Xtq8MKB4lb2aNoJ4J5V5gnqTdJI0kSxov660laW9gMvCXgrLJkkal5WnAEcBDxccOFB4lb2aNoG6V+hHRKenDwC1AE3BFRCyV9EVgYUTkk8tpwHUREQWH7wNcKmkLWVK8oLB32EASER4lb2YNoa6txBFxM3BzUdnnita/0M1xfwZeVdXgKiT3YicdnVucUMxsyBssjfKDVkubJ9Yys8bghFJl22Zq9BOKmQ1tTihV1uK55M2sQTihVFlrWzZKfoarvMxsiHNCqbLmde1MGjOC0SOa6h2KmVlVOaFUWUuu3dVdZtYQnFCqrKWtg5kTnVDMbOhzQqmy1lw7M8e7/cTMhj4nlCrq2hK0tnW4y7CZNQQnlCpau6GDri3hQY1m1hCcUKpo28RafkIxs6GvrIQiaY6kY9PyDpLGVzesocFT/5pZI+k1oUj6IHADcGkqmgX8vJpBDRXNTihm1kDKeUI5l2y+kRxARCwDZlQzqKGiJdfBMMG0cSPrHYqZWdWVk1A6ImJTfkXScCB62N+S1lw708aNYniTm6rMbOgr5zfdHyV9GthB0nHAT4CbqhvW0OCZGs2skZSTUM4DVgMPAP8M3BwR51c1qiGixXPJm1kDKWfGxo9ExMXA9/MFkj6ayqwHrbl2Dp49qd5hmJnVRDlPKGd2U/a+Cscx5Gzq3MLaDZtc5WVmDaNkQpF0uqSbgN0kLSj4/AF4rhIXl3SCpEckLZd0Xjfb3ydptaTF6fOBgm1nSlqWPt0lvbpq9dS/ZtZgeqry+jPwLDAN+EZBeRuwpL8XltQEXAIcB6wE7pW0ICIeKtr1+oj4cNGxU4DPA/PJepwtSsc+39+4KqUll59Yy08oZtYYSiaUiHgSeBJ4TZWufRiwPCJWAEi6DjgZKE4o3XkjcGtEPJeOvRU4Abi2SrH2WWsa1LijE4qZNYhyRsq/WtK9ktZL2iSpS1KuAtfeBXi6YH1lKiv2NklLJN0gadc+Hls3HiVvZo2mnEb57wCnA8uAHYAPkFVV1cJNwNyI2B+4Fbi6ryeQdI6khZIWrl69uuIBltKS62Bk0zAmjxlRs2uamdVTWUO4I2I50BQRXRFxJVn1Un+tAnYtWJ+VygqvuzYiOtLq5cAh5R5bcI7LImJ+RMyfPn16BcIuT2uunRkTRiGpZtc0M6unchLKRkkjgcWSLpT0f8o8rjf3AvMk7ZbOfxqwoHAHSTsVrJ4EPJyWbwGOlzRZ0mTg+FQ2YLS0eZS8mTWWchLDe9N+HwY2kD0ZvK2/F46IznTOW8gSxf9GxFJJX5R0Utrt3yQtlXQ/8G+k8S+pMf5LZEnpXuCL+Qb6gaJ5Xbu7DJtZQ+lxpHzq2vvViHg30A78ZyUvHhE3AzcXlX2uYPlTwKdKHHsFcEUl46mk1lwHR82rXRWbmVm99fiEEhFdwJxUJWVl2tDRSVtHJztOdJWXmTWOct7ltQL4k6QFZFVeAETEN6sW1SC3baZGV3mZWeMoJ6E8lj7DAE/9W4b8KPmZ4/2EYmaNo9eEEhEVbTdpBPn3ePm1K2bWSDyVYBXkq7zchmJmjcQJpQqa13UwdmQT40aVU6NoZjY0OKFUgQc1mlkjKuflkHtJuk3Sg2l9f0mfqX5og1er55I3swZUzhPK98kGF24GiIglZK9JsRKacx4lb2aNp5yEMiYi7ikq66xGMENBRNCS6/ATipk1nHISyhpJe5DNjIikU8lmcrRurHtxM5s6t7jLsJk1nHK6IZ0LXAbsLWkV8DjwnqpGNYjlBzV6pkYzazTlDGxcARwraSwwLCLaqh/W4NXs166YWYMqp5fXVyVNiogNEdGW5iD5ci2CG4xaPPWvmTWoctpQToyIF/IrEfE88KbqhTS4tebyr13xE4qZNZZyEkqTpK2/HSXtAPi3ZQnNuXYmjxnBqOFN9Q7FzKymymmU/xFwm6Qr0/pZwNXVC2lwc5dhM2tU5TTKf03SEuCYVPSliBhQ87cPJK25dncZNrOGVNbbCyPi18CvqxzLkNCS6+AVO3raGDNrPOX08nqrpGWS1knKSWqTlKtFcINN15Zg9XpXeZlZYyqnUf5C4KSImBgREyJifERMqMTFJZ0g6RFJyyWd1832j0l6SNKS9ILKOQXbuiQtTp8FlYinv9au76BrS7jKy8waUjlVXi0R8XClLyypCbgEOA5YCdwraUFEPFSw29+A+RGxUdKHyJLbO9O2FyPiwErH1R/bpv51JzgzazzlJJSFkq4Hfg505Asj4mf9vPZhwPI0Eh9J1wEnA1sTSkT8oWD/vzLAX/nS7JkazayBlZNQJgAbgeMLygLob0LZBXi6YH0lcHgP+5/NSzsGjJa0kOzNxxdExM+7O0jSOcA5ALNnz+5XwL3xKHkza2TldBs+qxaB9ETSe4D5wOsLiudExCpJuwO/l/RARDxWfGxEXEb2ckvmz58f1YyzNdfOMMHUsSOreRkzswGpnjM2rgJ2LViflcqKr38scD5Zx4DCKrdV6esK4HbgoArE1C8tuQ6mjx/F8CbPrGxmjaeeMzbeC8yTtJukkemcL+mtJekg4FKyZNJaUD45/zoYSdOAIyhoe6mXZk/9a2YNrJw2lDERcY+kwrJ+z9gYEZ2SPgzcAjQBV0TEUklfBBZGxALgv4BxwE/S9Z+KiJOAfYBLJW0hS4oXFPUOq4uWXDuzJo+pdxhmZnVRTkKp2oyNEXEzcHNR2ecKlo8tcdyfgVdVIoZKam3r4JA5k+sdhplZXXjGxgrp6OziuQ2bPFOjmTUsz9hYIa35QY1OKGbWoHpNKJI+VrQOsA5YFBGLqxTXoNPa5om1zKyxldPLaz7wL2QDEXcB/hk4Afi+pP+oYmyDSv61Kx4lb2aNqpw2lFnAwRGxHkDS54FfAa8DFpG9X6vhNa9Lo+THO6GYWWMq5wllBgXv8CIbjzIzIl4sKm9oLW3tjGwaxqQxI+odiplZXZQ7BfDdkn6R1t8C/Dg10td97MdA0ZrrYMaEURSN1zEzaxjl9PL6kqRfk41GB/iXiFiYlt9dtcgGmZZcu7sMm1lD6zGhpDlLlkbE3sDCnvZtdM25dvbZsSLzjpmZDUo9tqFERBfwiKTqvvd9CMhXeZmZNapy2lAmA0sl3QNsyBemd2oZsL6jk/UdnR7UaGYNrZyE8tmqRzHI5SfWchuKmTWychrl/yhpDjAvIn4naQzZ24EtyScUV3mZWSMrZ4KtDwI3kM1LAtlo+W6n221Ufo+XmVl5AxvPJesynAOIiGVkgx0t8VzyZmblJZSOiNiUX5E0nDQ3imWac+2MGzWccaPKaZIyMxuaykkof5T0aWAHSccBPwFuqm5Yg4u7DJuZlZdQzgNWAw+QvWn4ZuAz1QxqsGnJtfulkGbW8MqpozkFuCYivl/tYAar5lw7h86dUu8wzMzqqpwnlLcAj0r6gaQ3pzYUSyLCVV5mZpSRUCLiLGBPsraT04HHJF1eiYtLOkHSI5KWSzqvm+2jJF2ftt8taW7Btk+l8kckvbES8WyPFzZuZlPXFld5mVnDK+cJhYjYDPwauI5sUq1T+nvh9OLJS4ATgX2B0yXtW7Tb2cDzEbEncBHwtXTsvsBpwCvJZo/8bjpfzbWkqX89U6OZNbpyBjaeKOkqYBnwNuByYMcKXPswYHlErEjdkq8DTi7a52Tg6rR8A3CMsglHTgaui4iOiHgcWJ7OV3NbZ2p0lZeZNbhy2kPOAK4H/jkiKjlD4y7A0wXrK4HDS+0TEZ2S1gFTU/lfi47dpbuLSDoHOAdg9uzKvzQ5P0p+hqu8zKzBlfMur9NrEUi1RMRlwGUA8+fPr/iATL/Hy8wsU06V11slLZO0TlJOUpukXAWuvQrYtWB9Virrdp/Uu2wisLbMY2uiOdfOlLEjGTXc78s0s8ZWTqP8hcBJETExIiZExPiIqMTUhPcC8yTtJmkkWSP7gqJ9FgBnpuVTgd9HRKTy01IvsN2AecA9FYipz1pyHcwY76cTM7Ny2lBaIuLhSl84tYl8GLiF7HX4V0TEUklfBBZGxALgf4AfSFoOPEeWdEj7/S/wENAJnJtml6y51rZ2vxTSzIzyEspCSdeTvbJ+a6N8RPysvxePiJvJXuVSWPa5guV24O0ljv0K8JX+xtBfLbl29t5xfL3DMDOru3ISygRgI3B8QVkA/U4og11n1xZWt3V4pkYzM8rr5XVWLQIZjNZu2MSWgBlOKGZmZfXymiXpRkmt6fNTSbNqEdxA54m1zMy2KaeX15Vkvap2Tp+bUlnDy4+Sd5WXmVl5CWV6RFwZEZ3pcxUwvcpxDQotbfm55N1t2MysnISyVtJ7JDWlz3vIBhc2vNZcO8MEU8c5oZiZlZNQ3g+8A2gGniUbYOiGerI2lOnjR9E0TPUOxcys7srp5fUkcFINYhl0mnPuMmxmlldOL6+rJU0qWJ8s6YrqhjU4tOba3WXYzCwpp8pr/4h4Ib8SEc8DB1UvpMGjJdfuBnkzs6SchDJM0uT8iqQplDfCfkhr39zF8xs3u8rLzCwpJzF8A/iLpJ+k9bczAN6hVW+rU5dhV3mZmWXKaZS/RtJC4OhU9NaIeKi6YQ18HiVvZvZSZVVdpQTS8EmkUEvOgxrNzAqV04Zi3WjO+bUrZmaFnFC2U2uunZHDhzFxhxH1DsXMbEBwQtlO+S7DkkfJm5mBE8p2a861M3O8q7vMzPKcULZTa66DmROdUMzM8uqSUCRNkXSrpGXp6+Ru9jlQ0l8kLZW0RNI7C7ZdJelxSYvT58Da3kGq8vITipnZVvV6QjkPuC0i5gG3pfViG4EzIuKVwAnAtwrfKQZ8IiIOTJ/F1Q95m/UdnWzY1OUuw2ZmBeqVUE4Grk7LVwOnFO8QEY9GxLK0/AzQygCZ2GvrTI2u8jIz26peCWVmRDyblpuBmT3tLOkwYCTwWEHxV1JV2EWSSj4qSDpH0kJJC1evXt3vwCHrMgwww1VeZmZbVS2hSPqdpAe7+ZxcuF9EBBA9nGcn4AfAWRGxJRV/CtgbOBSYAnyy1PERcVlEzI+I+dOnV+YBp6Ut/9oVV3mZmeVV7a3BEXFsqW2SWiTtFBHPpoTRWmK/CcCvgPMj4q8F584/3XRIuhL4eAVD71XzuvxrV/yEYmaWV68qrwXAmWn5TOAXxTtIGgncCFwTETcUbdspfRVZ+8uDVY22SEuunfGjhjN2VMO/xd/MbKt6JZQLgOMkLQOOTetImi/p8rTPO4DXAe/rpnvwjyQ9ADwATAO+XMvgW9vameHqLjOzl6jLn9gRsRY4ppvyhcAH0vIPgR+WOP7o7sprpSXX4eouM7MiHim/HZrXtfstw2ZmRZxQ+igiUpWXE4qZWSEnlD56fuNmNneFuwybmRVxQukjT/1rZtY9J5Q+anZCMTPrlhNKH7XmPErezKw7Tih91JLLRslPH++EYmZWyAmlj5pz7UwZO5JRw5vqHYqZ2YDihNJHrbl2t5+YmXXDCaWPslHyru4yMyvmhNJHnvrXzKx7Tih90Nm1hTXrO5jpmRrNzF7GCaUP1qzfxJZwl2Ezs+44ofTB1lHyrvIyM3sZJ5Q+8Ch5M7PSnFD6YOso+Ymu8jKaJNL3AAAJsElEQVQzK+aE0gctuQ6ahompY51QzMyKOaH0QUuunenjRtE0TPUOxcxswHFC6YPmXLu7DJuZleCE0getuQ5m+qWQZmbdqktCkTRF0q2SlqWvk0vs1yVpcfosKCjfTdLdkpZLul7SyFrE3dLm93iZmZVSryeU84DbImIecFta786LEXFg+pxUUP414KKI2BN4Hji7uuFC++YuXti42YMazcxKqFdCORm4Oi1fDZxS7oGSBBwN3LA9x2+v1jQPip9QzMy6V6+EMjMink3LzcDMEvuNlrRQ0l8l5ZPGVOCFiOhM6yuBXUpdSNI56RwLV69evd0Bt7R5UKOZWU+GV+vEkn4H7NjNpvMLVyIiJEWJ08yJiFWSdgd+L+kBYF1f4oiIy4DLAObPn1/qOr1q8Sh5M7MeVS2hRMSxpbZJapG0U0Q8K2knoLXEOValrysk3Q4cBPwUmCRpeHpKmQWsqvgNFGle57nkzcx6Uq8qrwXAmWn5TOAXxTtImixpVFqeBhwBPBQRAfwBOLWn4yutta2DUcOHMXGHEdW+lJnZoFSvhHIBcJykZcCxaR1J8yVdnvbZB1go6X6yBHJBRDyUtn0S+Jik5WRtKv9T7YBb0tS/WZ8AMzMrVrUqr55ExFrgmG7KFwIfSMt/Bl5V4vgVwGHVjLFY87p2V3eZmfXAI+XL1NrW4QZ5M7MeOKGUISK2VnmZmVn3nFDKsL6jk42bulzlZWbWAyeUMngMiplZ75xQytDi166YmfXKCaUMfkIxM+udE0oZmnMeJW9m1hsnlDK05joYP3o4Y0bWZdiOmdmg4IRSBncZNjPrnf/kLsN+u0xk7rSx9Q7DzGxAc0Ipw7n/sGe9QzAzG/Bc5WVmZhXhhGJmZhXhhGJmZhXhhGJmZhXhhGJmZhXhhGJmZhXhhGJmZhXhhGJmZhWhiKh3DDUjaTXwZL3j2E7TgDX1DqKCfD8D21C6n6F0L1Cf+5kTEdN726mhEspgJmlhRMyvdxyV4vsZ2IbS/Qyle4GBfT+u8jIzs4pwQjEzs4pwQhk8Lqt3ABXm+xnYhtL9DKV7gQF8P25DMTOzivATipmZVYQTipmZVYQTSp1JOkHSI5KWSzqvm+2jJF2ftt8taW4qP07SIkkPpK9H1zr27mzv/RRsny1pvaSP1yrmnvTnfiTtL+kvkpamf6e6zyPdj5+3EZKuTvfxsKRP1Tr27pRxP6+TdJ+kTkmnFm07U9Ky9DmzdlGXtr33I+nAgp+1JZLeWdvIk4jwp04foAl4DNgdGAncD+xbtM+/At9Ly6cB16flg4Cd0/J+wKrBfD8F228AfgJ8fDDfD9lsqEuAA9L6VKBpEN/Pu4Dr0vIY4Alg7iC4n7nA/sA1wKkF5VOAFenr5LQ8eRDfz17AvLS8M/AsMKnW9+AnlPo6DFgeESsiYhNwHXBy0T4nA1en5RuAYyQpIv4WEc+k8qXADpJG1STq0rb7fgAknQI8TnY/A0F/7ud4YElE3A8QEWsjoqtGcZfSn/sJYKyk4cAOwCYgV5uwS+r1fiLiiYhYAmwpOvaNwK0R8VxEPA/cCpxQi6B7sN33ExGPRsSytPwM0Ar0OrK90pxQ6msX4OmC9ZWprNt9IqITWEf2126htwH3RURHleIs13bfj6RxwCeB/6xBnOXqz7/PXkBIuiVVUfxHDeLtTX/u5wZgA9lfvk8BX4+I56odcC/KuZ9qHFstFYlJ0mFkTziPVSiusg2v9QWtsiS9Evga2V/Eg9kXgIsiYn16YBnshgNHAocCG4HbJC2KiNvqG9Z2OwzoIqtOmQzcKel3EbGivmFZIUk7AT8AzoyI4qeyqvMTSn2tAnYtWJ+VyrrdJ1U3TATWpvVZwI3AGRFR879GutGf+zkcuFDSE8C/A5+W9OFqB9yL/tzPSuCOiFgTERuBm4GDqx5xz/pzP+8CfhMRmyOiFfgTUO/3SZVzP9U4tlr6FZOkCcCvgPMj4q8Vjq0sTij1dS8wT9JukkaSNYIuKNpnAZDvgXIq8PuICEmTyH54zouIP9Us4p5t9/1ExFERMTci5gLfAr4aEd+pVeAlbPf9ALcAr5I0Jv1ifj3wUI3iLqU/9/MUcDSApLHAq4G/1yTq0sq5n1JuAY6XNFnSZLIn/FuqFGe5tvt+0v43AtdExA1VjLFn9ezV4E8AvAl4lKy+8/xU9kXgpLQ8mqzX03LgHmD3VP4ZsjrtxQWfGYP1forO8QUGQC+v/t4P8B6yDgYPAhfW+176+fM2LpUvJUuMn6j3vZR5P4eSPS1uIHvSWlpw7PvTfS4Hzqr3vfTnftLP2uai3wcH1jp+v3rFzMwqwlVeZmZWEU4oZmZWEU4oZmZWEU4oZmZWEU4oZmZWEU4oZttB0r9IOqOb8rmSHqxDPH+u9TXNirnbsFkfSRoe2Xuuuts2F/hlROxX06DMBgA/oZgVkPTZNB/FXZKuzc/LIul2Sd+StBD4qKQvFGw7RNL9ku4Hzi1x3p0k3SFpsaQHJR2VytdLuijNY3GbpOmp/IOS7k3n/amkMal8pqQb89eT9Nr8edLXN6RYb5D0d0k/Knib85tS2SJJ35b0y+p+N63ROKGYJZIOJXtz8wHAibz8XVUjI2J+RHyjqPxK4CMRcUAPp38XcEtEHJjOvziVjwUWRsQrgT8Cn0/lP4uIQ9M5HwbOTuXfBv6Yyg+m+1f9H0T2PrR9yebWOELZ5F6XAidGxCHU4dXmNvQ5oZhtcwTwi4hoj4g24Kai7dcXH5DeqTYpIu5IRT8oce57gbMkfQF4VTo/ZPNa5M/7Q7I3FAPsJ+lOSQ8A7wZemcqPBv4bICK6ImJdN9e6JyJWRva22cVkkzLtDayIiMfTPteWiNNsuzmhmJVvw/YemBLO68jeHntVdw36+V3T16uAD0fEq8jmiOnL9MGF8+J04WkqrEacUMy2+RPwFkmj04Rfb+7tgIh4AXhBUv7J4t3d7SdpDtASEd8HLmfbq+yHkb3VF7JqsbvS8njgWUkjis55G/ChdM4mSRPLvLdHgN21bc77+sw5bkOaE4pZEhH3kr0ufAnwa+ABshkLe3MWcImkxUCp2cHeANwv6W9kv8wvTuUbgMNSV+Ojyd4sC/BZ4G6yJFf4mviPAv+QqsIWkbWTlHNvL5LNF/8bSYuAtjLvzaxs7jZsVkDSuMhmjRwD3AGcExH3VfF66yNiXLXOX3St/L0JuARYFhEX1eLa1hj8hGL2UpelJ437gJ9WM5nUwQfTvS0lm4nx0jrHY0OMn1DMzKwi/IRiZmYV4YRiZmYV4YRiZmYV4YRiZmYV4YRiZmYV8f8BhpSIrjAgNlwAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "def calculate_convergence(initial_n, increase_factor_n, iterations, tmax=1.0, error_type='L2'):\n",
    "    #increase_factor_n is decides how many more points are in the nest mesh\n",
    "    if type(increase_factor_n) is not int:\n",
    "        raise ValueError(\"increase_factor_n should be an integer\")\n",
    "    if type(initial_n) is not int or initial_n <= 0:\n",
    "        raise ValuError(\"initial_n should be a positive integer\")\n",
    "    \n",
    "    # Logs\n",
    "    hs = [] #spacing between points in interval, h = 1/n\n",
    "    errors_L2 = []\n",
    "    \n",
    "    # Simulations\n",
    "    for i in range(iterations):\n",
    "        #Set n\n",
    "        if i == 0:\n",
    "            n = initial_n\n",
    "        else:\n",
    "            n *= increase_factor_n\n",
    "        # Calculate simulation\n",
    "        mesh_info, sim_info, logs = calculate_simulation(n, n, n, tmax=tmax)\n",
    "        print(f'n={n}\\t({i+1} of {iterations})')\n",
    "        # Log\n",
    "        hs.append(1/n)\n",
    "        errors_L2.append(logs['error_'+error_type][-1])\n",
    "        \n",
    "    #Calculate convergence rates\n",
    "    hs = np.array(hs)\n",
    "    errors_L2 = np.array(errors_L2)\n",
    "    convergence_rates = np.log(errors_L2[1:]/errors_L2[:-1])/np.log(hs[1:]/hs[:-1])\n",
    "    \n",
    "    return hs[1:], convergence_rates\n",
    "\n",
    "\n",
    "def display_convergence(hs, convergence_rates):\n",
    "    fig = plt.figure()\n",
    "    ax = fig.add_subplot(111)\n",
    "    \n",
    "    ax.plot(hs, convergence_rates)\n",
    "    \n",
    "    ax.set_title(\"Convergence\")\n",
    "    ax.set_xlabel(\"grid spacing\")\n",
    "    ax.set_ylabel(\"convergence rate\")\n",
    "    \n",
    "    plt.show()\n",
    "    \n",
    "\n",
    "hs, convergence_rates = calculate_convergence(initial_n=4, increase_factor_n=2, iterations=6, tmax=1.0)\n",
    "display_convergence(hs, convergence_rates)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "### Cross-sections"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x720 with 9 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Note: The nth spatial partial derivatives have n endpoints that should be removed in further analysis\n"
     ]
    }
   ],
   "source": [
    "#Comparing numerical derivatives with true analytical values and displaying\n",
    "\n",
    "from matplotlib.patches import Patch\n",
    "\n",
    "def display_derivatives_comparison(mesh_info, sim_info, t_section = 8, x_section = 8, y_section = 8):\n",
    "    #xyz_sections determine where to take the cross section when displaying\n",
    "\n",
    "    #Renaming for simplicity\n",
    "    nx = mesh_info['nx']\n",
    "    ny = mesh_info['ny']\n",
    "    nt = mesh_info['nt']\n",
    "    alpha = sim_info['alpha']\n",
    "    beta = sim_info['beta']\n",
    "    blue = '#1f77b4'\n",
    "    orange = '#ff7f0e'\n",
    "    \n",
    "    #Get coordinates in a similar format to np.linspace()\n",
    "    coords = mesh_info['mesh'].coordinates().reshape(ny+1, nx+1, 2).transpose(1, 0, 2) #some sort of meshgrid, intermediate step\n",
    "    xcoords = coords[:, 0, 0]\n",
    "    ycoords = coords[0, :, 1]\n",
    "    tcoords = logs['t']\n",
    "    \n",
    "    #Get function values from simulation\n",
    "    u_vals = np.array([u_at_t.compute_vertex_values().reshape(ny+1, nx+1) for u_at_t in logs['u']]).transpose(0, 2, 1) #converted to array in the right shape\n",
    "    du_vals = np.gradient(u_vals, tcoords, xcoords, ycoords) #[u_t, u_x, u_y]\n",
    "    ddu_vals = np.array([np.gradient(du_vals_dim, tcoords, xcoords, ycoords) for du_vals_dim in du_vals]) #[[u_tt, u_tx,..], ...]\n",
    "    laplaceu_vals = ddu_vals.trace() #laplace(u) = u_tt + u_xx + u_yy\n",
    "\n",
    "    #which cross-sections do we plot? choose the _th point in each dimension\n",
    "    t_section = 8\n",
    "    x_section = 8\n",
    "    y_section = 8\n",
    "\n",
    "    #Plot setup\n",
    "    fig, axes = plt.subplots(3, 3, figsize=(15, 10), constrained_layout=True)\n",
    "    blue_legend_artist = Patch(color=blue, label='numerical result')\n",
    "    orange_legend_artist = Patch(color=orange, label='analytical result')\n",
    "\n",
    "    #Plot along t\n",
    "    #Plot u\n",
    "    axes[0, 0].plot(tcoords, u_vals[:, x_section, y_section], blue)\n",
    "    axes[0, 0].set_title(f'u at at (:, {x_section}, {y_section})')\n",
    "    #Plot u_t\n",
    "    axes[0, 1].plot(tcoords, du_vals[0][:, x_section, y_section], blue)\n",
    "    axes[0, 1].plot(tcoords, np.full_like(tcoords, beta), orange)       #ground truth\n",
    "    axes[0, 1].set_title(f'u_t at (:, {x_section}, {y_section})')\n",
    "    axes[0, 1].set_ylim(1.2-1e-12, 1.2+1e-12)\n",
    "    #Plot u_tt\n",
    "    axes[0, 2].plot(tcoords, ddu_vals[0, 0][:, x_section, y_section], blue)\n",
    "    axes[0, 2].set_title(f'u_tt at (:, {x_section}, {y_section})')\n",
    "    axes[0, 2].set_ylim(-1e-12, +1e-12)\n",
    "\n",
    "    #Plot along x\n",
    "    #Plot u\n",
    "    axes[1, 0].plot(xcoords, u_vals[t_section, :, y_section], blue)\n",
    "    axes[1, 0].set_title(f'u at ({t_section}, :, {y_section})')\n",
    "    #Plot u_x\n",
    "    axes[1, 1].plot(xcoords, du_vals[1][t_section, :, y_section], blue)\n",
    "    axes[1, 1].set_title(f'u_x at at ({t_section}, :, {y_section})')\n",
    "    #Plot u_xx\n",
    "    axes[1, 2].plot(xcoords, ddu_vals[1, 1][t_section, :, y_section], blue)\n",
    "    axes[1, 2].plot(xcoords, np.full_like(xcoords, 2*1), orange)          #ground truth\n",
    "    axes[1, 2].set_title(f'u_xx at ({t_section}, :, {y_section})')\n",
    "    #Legend\n",
    "    fig.legend(handles=[blue_legend_artist, orange_legend_artist], \n",
    "                      bbox_to_anchor=(1.15, 0.5), loc='center right', borderaxespad=0.)\n",
    "\n",
    "    #Plot along y\n",
    "    #Plot u\n",
    "    axes[2, 0].plot(ycoords, u_vals[t_section, x_section, :], blue)\n",
    "    axes[2, 0].set_title(f'u at at ({t_section}, {x_section}, :)')\n",
    "    #Plot u_y\n",
    "    axes[2, 1].plot(ycoords, du_vals[2][t_section, x_section, :], blue)\n",
    "    axes[2, 1].set_title(f'u_y at ({t_section}, {x_section}, :)')\n",
    "    #Plot u_yy\n",
    "    axes[2, 2].plot(ycoords, ddu_vals[2, 2][t_section, x_section, :], blue)\n",
    "    axes[2, 2].plot(ycoords, np.full_like(ycoords, 2*alpha), orange)      #ground truth\n",
    "    axes[2, 2].set_title(f'u_yy at ({t_section}, {x_section}, :)')\n",
    "    \n",
    "    #Display\n",
    "    fig.suptitle('Cross-sections of u and its partial derivatives, occasionnaly compared to its ground truth analytical values\\n', fontsize=16)\n",
    "    plt.show()\n",
    "    \n",
    "mesh_info, sim_info, logs = calculate_simulation(16, 17, 18, tmax=1.0)\n",
    "display_derivatives_comparison(mesh_info, sim_info)\n",
    "print(\"Note: The nth spatial partial derivatives have n endpoints that should be removed in further analysis\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x576 with 6 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Comparing left and right side of the numerical PDE\n",
    "\n",
    "def display_pde_sides_comparison(mesh_info, sim_info, t_section = 8, x_section = 8, y_section = 8):\n",
    "    #xyz_sections determine where to take the cross section when displaying\n",
    "\n",
    "    #Renaming for simplicity\n",
    "    nx = mesh_info['nx']\n",
    "    ny = mesh_info['ny']\n",
    "    nt = mesh_info['nt']\n",
    "    alpha = sim_info['alpha']\n",
    "    beta = sim_info['beta']\n",
    "    blue = '#1f77b4'\n",
    "    orange = '#ff7f0e'\n",
    "    \n",
    "    #Get coordinates in a similar format to np.linspace()\n",
    "    coords = mesh_info['mesh'].coordinates().reshape(ny+1, nx+1, 2).transpose(1, 0, 2) #some sort of meshgrid, intermediate step\n",
    "    xcoords = coords[:, 0, 0]\n",
    "    ycoords = coords[0, :, 1]\n",
    "    tcoords = logs['t']\n",
    "    \n",
    "    #Get function values from simulation\n",
    "    u_vals = np.array([u_at_t.compute_vertex_values().reshape(ny+1, nx+1) for u_at_t in logs['u']]).transpose(0, 2, 1) #converted to array in the right shape\n",
    "    du_vals = np.gradient(u_vals, tcoords, xcoords, ycoords) #[u_t, u_x, u_y]\n",
    "    ddu_vals = np.array([np.gradient(du_vals_dim, tcoords, xcoords, ycoords) for du_vals_dim in du_vals]) #[[u_tt, u_tx,..], ...]\n",
    "    laplaceu_vals = ddu_vals.trace() #laplace(u) = u_tt + u_xx + u_yy\n",
    "    f_vals = sim_info['f']\n",
    "\n",
    "    #which cross-sections do we plot? choose the _th point in each dimension\n",
    "    t_section = 8\n",
    "    x_section = 8\n",
    "    y_section = 8\n",
    "\n",
    "    #Plot setup\n",
    "    fig, axes = plt.subplots(nrows=3, ncols=2, sharey='all', figsize=(8, 8), constrained_layout=True)\n",
    "\n",
    "    #Plot along t\n",
    "    axes[0, 0].plot(tcoords, du_vals[0][:, x_section, y_section])\n",
    "    axes[0, 0].set_title(f'u_t at (:, {x_section}, {y_section})')\n",
    "    axes[0, 1].plot(tcoords, laplaceu_vals[:, x_section, y_section]+f_vals)\n",
    "    axes[0, 1].set_title(f'Laplace(u) + f at (:, {x_section}, {y_section})')\n",
    "\n",
    "    #Plot along x\n",
    "    axes[1, 0].plot(xcoords, du_vals[0][t_section, :, y_section])\n",
    "    axes[1, 0].set_title(f'u_t at ({t_section}, :, {y_section})')\n",
    "    axes[1, 1].plot(xcoords, laplaceu_vals[t_section, :, y_section]+f_vals)\n",
    "    axes[1, 1].set_title(f'Laplace(u) + f at ({t_section}, :, {y_section})')\n",
    "\n",
    "    #Plot along y\n",
    "    axes[2, 0].plot(ycoords, du_vals[0][t_section, x_section, :])\n",
    "    axes[2, 0].set_title(f'u_t at ({t_section}, {x_section}, :)')\n",
    "    axes[2, 1].plot(ycoords, laplaceu_vals[t_section, x_section, :]+f_vals)\n",
    "    axes[2, 1].set_title(f'Laplace(u) + f at ({t_section}, {x_section}, :)')\n",
    "\n",
    "    #Display\n",
    "    plt.suptitle(\"Comparing numerical values of left side (u_t) to the right side (Laplace(u)+f) of the PDE\\n\", fontsize=16)\n",
    "    #plt.tight_layout()\n",
    "    plt.show()\n",
    "                 \n",
    "mesh_info, sim_info, logs = calculate_simulation(16, 17, 18, tmax=1.0)\n",
    "display_pde_sides_comparison(mesh_info, sim_info)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "''"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Ignore, notes that might be reused later\n",
    "\n",
    "\"\"\"uvals = logs['u'][0].compute_vertex_values()\n",
    "xyvals = mesh_info['mesh'].coordinates()\n",
    "xvals = xyvals[:,0]\n",
    "yvals=xyvals[:,1]\n",
    "\n",
    "xx = np.linspace(0,1)\n",
    "yy = np.linspace(0,1)\n",
    "\n",
    "XX, YY = np.meshgrid(xx,yy)\n",
    "\n",
    "plt.figure()\n",
    "from scipy.interpolate import griddata\n",
    "uu = griddata(xyvals, uvals, (XX, YY), method='linear')\n",
    "plt.imshow(uu, origin='lower', extent=(-5e-3, 1+5e-3, -5e-3, 1+5e-3))\"\"\"\n",
    "\"\"\"skipper = int(np.ceil((nt+1)/nplots))\"\"\"\n",
    "\"\"\"\"\"\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### PDE-FIND methods"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Define simulation\n",
    "mesh_info, sim_info, logs = calculate_simulation(16, 17, 18, tmax=1.0,  alpha=1, beta=1.2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [],
   "source": [
    "def build_system(mesh_info, sim_info, logs, max_order=2, max_degree=2):\n",
    "    #max_order: calculate only up to d^(max_order)u/dx^(max_order) inclusive\n",
    "    #max_degree: calculate only up to u^(max_degree)\n",
    "\n",
    "    #Renaming for simplicity\n",
    "    nt = mesh_info['nt']\n",
    "    nx = mesh_info['nx']\n",
    "    ny = mesh_info['ny']\n",
    "    \n",
    "    #Get coordinates in a similar format to np.linspace()\n",
    "    coordinates = mesh_info['mesh'].coordinates().reshape(ny+1, nx+1, 2).transpose(1, 0, 2)\n",
    "    xcoords = coordinates[:, 0, 0]\n",
    "    ycoords = coordinates[0, :, 1]\n",
    "    tcoords = logs['t']\n",
    "\n",
    "    #calculate derivatives\n",
    "    u_vals = np.array([u_at_t.compute_vertex_values().reshape(ny+1, nx+1) for u_at_t in logs['u']]).transpose(0, 2, 1) #order: t, x, y\n",
    "    u_derivs_unmixed = [] #(unmixed means only u_xx or u_yy but not u_xy nor u_yx)\n",
    "    for i in range(max_order):\n",
    "        if i == 0: #partial derivatives of u\n",
    "            derivs = np.array(np.gradient(u_vals, tcoords, xcoords, ycoords))\n",
    "            u_derivs_unmixed.append(derivs)\n",
    "        else: #partial derivatives of other partial derivatives\n",
    "            functions_to_derive = u_derivs_unmixed[-1]\n",
    "            derivs_all = np.array([np.gradient(function, tcoords, xcoords, ycoords) for function in functions_to_derive])\n",
    "            derivs_unmixed = derivs_all.diagonal().transpose(3, 0, 1, 2) #retrieve only unmixed derivatives\n",
    "            #alternatively: derivs_unmixed = np.array([np.gradient(functions_to_derive[dim], tcoords, xcoords, ycoords)[dim] for dim in range(len(functions_to_derive))])\n",
    "            u_derivs_unmixed.append(derivs_unmixed)\n",
    "    u_derivs_unmixed = np.array(u_derivs_unmixed) #shape is (order(1..n), dimension(t,x,y), tpos, xpos, ypos)\n",
    "\n",
    "    #flattening to make vector\n",
    "    u_t = u_derivs_unmixed[0, 0, 2:-2, 2:-2, 2:-2].flatten() #removing endpoints where derivatives are wrong\n",
    "\n",
    "    #flattening and stacking to make theta matrix\n",
    "    theta = []\n",
    "    for order in range(max_order+1):\n",
    "        for deg in range(max_degree+1):\n",
    "            u_power_flat = u_vals[2:-2, 2:-2, 2:-2].flatten()**deg #u^deg\n",
    "            for dim in range(1, 3): #spacial dimensions only\n",
    "                if order == 0:\n",
    "                    if dim == 1:\n",
    "                        u_deriv_flat = np.ones_like(u_power_flat) #to have rows of u^exponent without multiplying with a derivative\n",
    "                    else:\n",
    "                        u_deriv_flat = np.zeros_like(u_power_flat) #to conserve shape for when we declare xi (before flattening)\n",
    "                else:\n",
    "                    u_deriv_flat = u_derivs_unmixed[order-1, dim, 2:-2, 2:-2, 2:-2].flatten() #d^order u / d(dim)^order\n",
    "                theta.append(u_power_flat*u_deriv_flat)\n",
    "    theta = np.array(theta).T\n",
    "\n",
    "#In this linear system, rows are ordered (t0,x0,y0)...(t0,x0,yn),(t0,x1,y0)......(t0,xm,yn),(t1,x0,y0).........(tl,xm,yn)\n",
    "#                       cols are ordered u^0, 0, u^1, 0, ...u^n, 0, u^0*u_x, u^0*u_y, u^1*u_x, u^1*u_y ... u^n*u_x, u^n*u_y, u^0*u_xx, u^0*u_yy, ......u^n*u_xxx, u^n*u_yyy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [],
   "source": [
    "def stridge(theta, u_t, alpha, tol, iters, random_state=0): #alpha is this implementation's name for the paper's lambda\n",
    "    if iters == 0: #recursion end, final guess\n",
    "        model = Ridge(alpha=alpha, fit_intercept=True, normalize=False, copy_X=True) #SHOULD IT BE RIDGE OR OLS?\n",
    "        model.fit(theta, u_t)\n",
    "        xi_guess = model.coef_\n",
    "        return xi_guess\n",
    "    else:\n",
    "        model = Ridge(alpha=alpha, fit_intercept=False, normalize=False, copy_X=True)\n",
    "        model.fit(theta, u_t)\n",
    "        xi_guess = model.coef_\n",
    "        print(f\"{iters}: {xi_guess}\")\n",
    "        selected_features, = np.where(np.abs(xi_guess) < tol) #unpacked the tuple, because indexing the 2d array theta with a tuple selects the wrong axis\n",
    "        new_theta = theta.copy()\n",
    "        new_theta[:, selected_features] = 0\n",
    "        xi_guess[selected_features] = 0\n",
    "        print(f\"{iters}: {xi_guess}\")\n",
    "        print()\n",
    "        return stridge(new_theta, u_t, alpha, tol, iters-1) #recursion step\n",
    "    \n",
    "def calculate_error(theta_test, u_t_test, xi_guess, l0_penalty):\n",
    "    return np.linalg.norm(np.dot(theta_test, xi_guess) - u_t_test, 2) + l0_penalty*np.linalg.norm(xi_guess, 0)\n",
    "\n",
    "def train_stridge(theta, u_t, alpha, dtol, tol_iters, stridge_iters): #alpha is this implementation's name for the paper's lambda\n",
    "    theta_train, theta_test, u_t_train, u_t_test = train_test_split(theta, u_t, test_size=0.20, shuffle=True)\n",
    "    l0_penalty = 1e-3*np.linalg.cond(theta) \n",
    "    \n",
    "    model_baseline = LinearRegression(fit_intercept=True, normalize=True, copy_X=True)\n",
    "    model_baseline.fit(theta_train, u_t_train)\n",
    "    xi_guess_best = model_baseline.coef_\n",
    "    error_best = calculate_error(theta_test, u_t_test, xi_guess_best, l0_penalty)\n",
    "    print(f\"best: {xi_guess_best}\")\n",
    "    print(f\"best: {error_best}\")\n",
    "    \n",
    "    tol = dtol\n",
    "    for i in range(1, tol_iters+1):\n",
    "        xi_guess = stridge(theta_train, u_t_train, alpha, tol, stridge_iters)\n",
    "        error = calculate_error(theta_test, u_t_test, xi_guess, l0_penalty)\n",
    "        print(f\"{i}: {xi_guess}\")\n",
    "        print(f\"{i}: {error}\")\n",
    "        \n",
    "        if error <= error_best:\n",
    "            error_best = error\n",
    "            xi_best = xi_guess\n",
    "            tol = tol + dtol\n",
    "        else:\n",
    "            tol = np.max([0, tol - 2*dtol])\n",
    "            dtol = 2*dtol/(tol_iters - i)\n",
    "            tol = tol + dtol\n",
    "    return xi_best"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
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7juLOz5aiXZN6WJZ32MAlmycZv514b2IvyD2IZ35aiymP90OdmukGlarS2S+4L7/1tmdfsfMwKhwu9O7QNOi94nIH/vbtat9rM56DMKoFV6iinyhzwKUUGtapiU/nb8fLv23ULofO9bhcSvMmZjRlCl539TkrMC3jFcdv7b9ztmH/0TLbBHZ/iQxC8S75xV/WI6+wGHkxPl3ob2bOfmzZH12KJdANHy7ELSFq4c6AttUrLJCGue+LZfhkXvjuf6MJhVkvT/edEOdtORhHydz+2LAfIydVTePx4UD9qm1wrz7n79gkc4Sq0goXBr4zNygARuLrRMqAvXnP59m4Iobmhnorw4Fb9qaJfQV5yzJ9Y0HI2rWezwcqqYivBUngw03h2vbz9xtZtQ3uwa1ljI1iqZ4T1BMwf1ieH9c6/E8cOfuOxXzzLpnftdEPpyUyLx3IqJInqvb80Dj2WGqkahvc41VwtBQXvjoTeSEe8rHL1WO4zVi8LfIoNNEsPNqgYcZXbFRgU1BYkHuwShNBK4r1XBZvLV7LV4vy4Azx/dvk52YoBnePaH+zk1bvwe6iEnyxKC8RxTGd1o+6pNyJsYt3+AJcvDXBeK+WjCqHWdbkJ2Y4vYjijIR6Pr50+6GQ78V6wnju5/X4cfluzzIiL+R4mQMlSXzYSCmFg8eTdyUWCYO7R7THe6SDy0ppmYkrdxty0L02JQfPTlyHGRtDP8kXjcAT6rfZu3Ashr4/rPRd62X0ld2Rkgpc8sYsrN+jfcI4UeZAqac2nVd4AlPXV+1nfM7mA0E3lI+VVgT1wZQsA9+Zi4Vbg68Mo7ki6DpyKrJeTk6bcgD4fGEesl6ejtyC40lbZzjVtilkdbH/aCke/3YVerRrHNPn/YNQoefR8RMGdGKl5fUpm7Bhz1G8f1sPXfPriY9WafqW6DTdoq2FyCssxjsheug8a+RU39/r9xzF/V9V7Wf8zs+WAqja7NPb8iVQMlKOOfuOIWdf6NZLi7cVIivjZJzVqlHY5SS6t8cl2w5h3e4j6Nq6EeZudvcYuqPwBM5o0SCh69WDNXePaHOp3pBh9dx6ucM9nNv+o/HX3AO/o3hrzFpfXeHxKPoe8S3AGgE8GgrGXnEk8+rF6MYH+YdLgq4kIvl93T5c9d58OF0K136wwHecayk8Xlbld2rkd1VS4fQNaO69mrdKTNBVcxeRgQDeBZAO4BOl1Ksh5vsTgB8A9FJKZRtWSgvyP0DMCi0v/7oBNWuk4R8DOyd1vd6DON5asdYJNZoWM95Pp0RaJs6bx3YSuLviGULySEkFVu8K/8xAz5cTf9N67OIdUTXlVUolvFvwiDV3EUkH8AGAQQC6ABgqIkE9/4hIQwCPAVhidCGTIdJueWjccoxbov20nFk/00/mb8fo2Vtj/vxhHT30adXSjGsxEswVxbLNuKGazJ6hK5wuw/sfN0SEwg9IYvfEoY7FZ35aqz1/gn6tz05chzmetIyeNSTj3K4nLXMegFyl1DalVDmA8QCu1ZjvJQCvASjVeC/lTV67D8/8tE73/FapTYYbLb77S9Ow61Cx5ueScYkZz7L9T0zx1IDmbD6AP41eGHtBYqVj2x8etwLn+OW9jxRXwKVROyytcPpuls4K022tXmUOJ4a8Pz/k+0HPiChVZX9sivNJ32iE+hrHLdHuqjrSMffTyvie3XCvQ0ffO3GvJTI9wb01gF1+r/M903xEpAeAtkqp38ItSESGiUi2iGQfOGDMcGVGiTbQVObcrX157a2phIp/uw6HCO5hlikiqHC6cLws9I3VNflFWL4j+u4Y9Abq7i9NQ16hdtmj8bdvV8VUznCueGsOflm9Bxv3HsXxMgfKHa6gGqOeo+aPDVW72u026g/8e1pwCqPXy9Px2PhVALSHkIvWtgMnwjbT/OeEtRgzt/KK8ZN529E9ip4OiwzsaTLan59C+GPbv/+fWOmruSc+bsR9Q1VE0gC8BeD/Is2rlBqjlMpSSmU1b9483lWbylezRWrczguZHw9xjGn3Blhp+Ncr8FuYsTCHvL8gYo1Y6xJ5496j+CbKAULi+f6jf3Aq8vxbCo7jkW9WYtC789B15FTc/flSzfliKfeUdcE3Ho+FOckmwoycArwyOQdHPD1chhs5SUuoFj2xiDbNkqzKWEm5E98t2xXyfavU3HcDaOv3uo1nmldDAF0BzBaRPAB9AEwSkSyjCpkIgTvZqt3OJlosWy0Apq7fH3G+WFf+9ATtfGkiJGOvL8gNbq8dzb0Ff1Yam7fbqD+wp6gE6WkmlinamnsSdrhSwL8mb8Dffww9IliRRtfPRtMT3JcByBSR9iJSC8CtACZ531RKHVFKNVNKZSilMgAsBjDE7q1l/Fn5tBAu567v8xo3VOMoTyKWY6F4F1Lg12jVbN7C3INRPYSz81CxqcF9aV7oJ2HNE7kv+5k5BlSOIogY3JVSDgDDAUwFsBHAd0qp9SIySkSGJLqASRPjj82qP1K9QpU/Of25G7OceJpkBpbh9k+WhHxKttzhinnsTKM6qit3uHw3TxPhtk+W4JFvVuqe3+FUpgb34V/rLyvg3t+JvvpRKvIxmYyH63Tl3JVSk5VSHZVSpyul/uWZ9rxSapLGvJekQq09qCYV5ed9XeJCWTrnrne7Hh+/Ej/q7OUx2u3dXVSCwe/O872+7oMFhvb5YeRvdX7uQVz46kzN94a8Pz/kQNWx9GgZS7l3HirGmc9Pif6DCVLhdJmblolSspqWRty3SfjK+IRqjCLvu/j23vEyR9T9m2vR2xZ84qo9+L/vg1sKGFG5/mJhHjbsPep7vWpXEVbuOmzKfY4p6/ZV6WdHK+10NER/KqEeh8/ZdxTdXtR+VD8UV+gHKiOy0tViflEJpm1IfIrBKFf/Z74hv6twFIC0SH1PJbQEbgzuHrH+YJTSFwAdTheGjlmMJWG6yS0ud6DC6UKF04WuI6di5CT97epDls/zf6hL0VABVrOdu+fvt6dvjqoMoQ7kZASpwM1+YOxyXz8qgDEnr01h+kDxrSfwBr6VInQcnpsY/zFqN+7Uj9mlqMbBPe7fVpR7b++RUizaVognvgvdjrbL81Nx9/+WocLprtZ5uzc1QrQBNtzmbTsQ5bB20bXCjFq0P6Sdfg9uJavXQ3uEctIrcq+xFsm5Vwexpgj0tnOvHLYu/Hrm58Y/9qS/eE9iCUudKHvUXmPdhDKHCxXO1N9+CqbnPhzTMgmkJ2iFewLTu3NyC45j2Y7IzbG8Obho0316A+Af6/fhoXHLg6b7Ph9l7dmog+9Poxdia0HyR6vyXv1s3BucMjHyh6X35Be4rYUnyuPqMIusi2kZg01Ztw+PjdffLCpSu+OFuQfRdeRUzI8wivvS7Yew61BwC4rAnVsZ3PVHNJdSuvujHvbVckxeG/z0Yrz3juINwMt3HMb0jdo33MaG6IjNq7TCiZ9W5mNmzn7sPxq+y6LtB09UGfZvwDvuzqtCrdsoer+fWJ6kNKoRSqSWSS/9usGYFREAdwOCn1ftMbsY9hms44Gx7lrru7d2rzJ99a4ivDF1Ez67qxdq1ag8l0X6qXkfjli6vRB9M5sFvR/tmbmy6aR+ZQ73jdV4uHS2lgmisYHhmpEdKalAo7o1o1rFtAhPuX44KxfvzcwFALRuXBcLRlymOZ9SwKVvzq4yLdx9gVRIhszMKXDnZQ24vInUdPLT+dvjXgdVyja4r6JY2abmHsrff1iD+bkHse1g+KfuAn9CoZoyTliRj3KHC2UV0bVlq8y5R/WxuEVaX2Dap7TCiaFjFmPTvqNB8+YVhg6Yj49fidGzt+K9Gfr6DVEIH2QfHLscv/v1o7K7SLt9udl0788o93ss7eYpdSTj2QDb1NwjCU7DxBZln/huddgWL1ryDp7ARk87b13dgYaY5aaPFuI/Q3vglEZ1dK87Ujog8N0VOw9j0bZCLPKkOPzfD9d2P/9wCWZtygEAPNo/U1/ZwnwXv2t0kGWUaH9WJeVO1K2Vrvme7px7lOsEUqNDOopN2yb1Er4O29fcQ6VPtPqk1jNfLC55czYeHLcCgLtL1kiPj4da57K8w/hk3rag6f451eD21O7/9Ta9CgzgiRqezMzApWefbvR76OrM56fgy0V52stS+mrvUXdNmwq5I4pDCnT5a1eJutt9pKQCnZ+bggW5B7EnRKqhIsx4kFqHhH9ONXAsyohBIqgbhuRElS0Fx6Puj/3nVdG1+8/RSC3pNcivuwQAeP7n9Zrz6f22yhzRdbcQabmrdxUhY8RvyDsY5TMHZAnJOHlXm7RMoMAv953pW3Bu28a4vc9pSVn/nz9Zgnq10rFh1MCg98INfBCptc3hgK5EI83/8bxtYTvDWrmz8uZQuPPdFr+eBG/7eHHYdQLAC79oB8twvANSBAq1iQPfmaf9hoF2FJ5Ato6msBe/MTuq5brH2Az9/o8r3P0AzdoU/8hLlHxW6c89pdz3xTKs2x16FJlKVb/eH5bn41nPo9Rb9h8LOxKNUWLpYdDpUmFHeo+2Q7SFWwvx8NcrfK8D0zKh+lOJtMzq4rHxqzB2cXSDi+ih98ev1Vc8WZ9VxlBNKdM3FuBJjQ6wvLz57nBf7hVvz/W1j7Za7vPLRTvQ8dnfQ76vUDWnH3NTSA1GPjJt5Pdqx4FWyiLdl/FscqjuicnaUmKYPSsKVbOdvmE/Oj83BWvyi5JcouTJ2XsMnZ+bgsmeIfCMPIbs1npjyrrQwwSa7bmf14ftnuBwsXtA6ki9D5I1MS0TozKN4K4UMHuzOz+5aleRZep6d3y6pMrI8fFa40lJjfrF+9RhdFuairEiXJpKy7FSB/4zYwseGLsi8swW9esa656YKDKmZWJU7oz8Yw/15WY+M7nqfAk+DczbchDfLDM+Z7vP87i+t/uBLVEMnZZqrnh7btSf+fe06LottqpFYbqQJutKRirRlsE99NBxkaulZvTUl8izeLS1WiKyh5QN7hVOF5wuBYdmLV3HU6Ax9uaXSmblFODPnyyJ6jNPfKvd3JCIDMR27tpcLoXMZypbjOS9elWV97UCsoKCwzO22X/nbEOvjCa61qVQ2X1sorgSNOxXLG2g9xwJ0/tiCubjiayIN1RDqAgYgPLez5dVea31xX02Pw/fLN0FwN0Jld4uOUfP3lrlRKLX8TIHZubo627WyB292a9deqjBnKPlHUaOsZ3IGLyhGkLgFzMjpyDg/eBvzvtEn9dHc7YaXi5/z/y0Dvd8no2dOh6xD51eCrf8tZrTS/zaR8/MMebpRW/f6ERkjGTcUE3JtEyk0csDH8E3U0mEh1EA4N0ZW/Cuzq5yvcYtMb6FTTgjf16HrdGOnUpEmlhzD8GZQnc5U7HduJYvFoUfNYmI9GPOPYRobkCafR5IQp/8RJRi2P1ACJHSMv7CjR6UDMO/1j+uKxFVD6y5hxBNcDc7LRJLr4pEZHPMuWuLJufOjpWIqDrSFdxFZKCIbBKRXBEZofH+EyKyQUTWiMgMEUnoiBdR1dwTWA4iolhYom8ZEUkH8AGAQQC6ABgqIl0CZlsJIEspdQ6AHwC8bnRB/e0L9xRlACP7ICciMoJVmkKeByBXKbVNKVUOYDyAa/1nUErNUkp5n9ZZDKCNscWs6saPFumar9Ozv+N4mSORRSEiippVgntrALv8Xud7poVyLwDN5/VFZJiIZItI9oEDB/SXMkZa/boTEZkt5VrLiMjtALIAvKH1vlJqjFIqSymV1bx5cyNXTUSUMpLRzl1P9wO7AbT1e93GM60KEbkcwDMALlZKlRlTPCIi+7FKzX0ZgEwRaS8itQDcCmCS/wwi0h3AfwEMUUoZ01tVnGYZ1GkWEZHRLJFzV0o5AAwHMBXARgDfKaXWi8goERnime0NAA0AfC8iq0RkUojFJc3dAd0AExFZhzXSMlBKTQYwOWDa835/X25wuYiIbMsSNXciIko9DO5ERElmlRuqRERkIKZlNCSjfSgRUSJZom8Zq6lwMrgTUWpjzV2DizV3IkpxzLlrYHAnolTHYfY0RNOXOxFRdZVywZ2xnYhSHXPuGlyM7kREEaVccI9m/FQiIitiU0gNrLkTUapjWkYDa+5ElOoY3DV8tWiH2UUgIooL27lrOFbKAa8y3CeGAAAROklEQVSJKLWxnbuGZNyIICJKJNbcNTDlTkQpjzn3YIztRJTq2BSSiMiG2FpGA9MyRESRpVxwt1piZsBZLc0ugq0NPvsUs4ugW5qYXYLE6dSyodlFsBXeUNUQa839z73bGVsQjxppxn6FC0ZcZujyUp0R32+9WukYc0fPuJZxaqM6EeexVrXDWDXS4z9zfXZXFp6/uosBpUl9TMtoiPVLefCS040tiIcRXRC/dXM3NKxTAwBQr2a6rs/8c3DnuNcbj+GXnmHo8h7rn4k+HZoETTciqNSvXSPuZRhRDqMNPCs5VzUtT6ptyHIu69zS1idALZktGmhO5w3VFGBEdwiDup7q6zNHbxARmBtshl92BurqPBHpcVark1AzPfhwrF3DmJq7SHzfl9nft5aP4rwa0WPsvb0xaXjfmD/f94xm6Na2se+10Q/vnFQn/hN3ItWrpf0bYc1dQ6wjMSXqyzSi5i4C3NLLnTaqY2DATKR0gxPM6WmCNI0A3MCAWvcZzRvEHZr1nBuMOsZ6ZZwc1+f9g2m8+mY2Q8uTIqekQhl7X29MePACbHp5YMzL+PvATiHfi/Y47HnayfjX9V1jLgsAtGio/0om1CFxroH7KJSUC+4Oi/UKWeF0xb0MEeDZq85EzksDNWuvQPClcSIv6z7+S1bEebQCcTy6tW2MGho/1C6tTop72W/c1C3qz7RvVr/K68CSzX3q0qiX+eU954V874krOvr+jiWNdEtWW7x07Vn49ZG+6HtGU9/0V64/W/cyRIA2J9fVfC+eE1d6mqB2jfSYl/PQJWdg9pOX4IYerYPeu7lX26iXVyvEb0yPj/+ShQkPXaB7/pJyp+b0rq0bxVwGvVIuuOsJpvf1bZ+Ekrhd3LF53MsQCNLSJKpae92a6bimW6u4162Vty13RP6OQ1WYtPLm79xybthl5b16FZo1qI1nrjoTF57RFG/6BePrzm0dVU1JS5P6tXTVvP1dfmYLzem92zdB+2b1UcuTLmp5Um28fF1X/PZo36jX4e/R/pm+v2M5cXY8pSHuOD8DXVs3QrMGld/X9d2DA2Iof+rRRnfgCzz5dQh4HcqNPdvovjLp3q4xnhrgrrVnNKuPhgEnva//2hv/GNA55L4KJfDq/6kBnVCnpr7tbnNyXTSsU1P3upJRQw8l5YK7w+neMUO6tcKyZy7XnKd7u+CDJ1EDa199TvwBNtrf8v0Xd8B13VvjP0O7x71urbxtcXnkztlEBCUVwbWS8cPOD5p2nc4A06F5A4y7rw9u7NmmynqG9etQZb5Ybo5H+x375+jr++Xs/98NZ2PWk5f47rWkieD2PqfhrFaVNbG7LsjQbF0jAvzxt35VUk1XdgluSnv5mfE1r/3L+RkxfS7UVaMW/xuFm14eiCmP99P1uZPr18J39wcfI1omPHgBHva7cR9436R2jXSkpQk+ubMX8l69Ci9cE7kljlIq6Or/4UvPQM5Lg3Bv3/Z4rH8mnh5U2VjhlICUlNOlomoW9dJ18aWA4pFywf0yz1n6scsz0dyvRudfk9S6yWlEbP/54QuDphmRe452CU8POjOq2kO0ijUuJTeOGlgldQAAzww+s8rrXx+J/cZbOEPPa4ebsyoD/s1Z2pfirRtrpxQAoE+HpiHf09K4XuX3+82wPr595D2MvDfA/WvZ3mPs+au7YNHT/YPuF2Q0rY+OLRvi2/v7+KaNvr0ncl6qmo++tVdbbBg1APdc2B73XBj+KlSrNUZ6muiuiVb9nP64lSaCs1s3wvXdW6N2jXTflYxRPr0zK+JN8MAb+ndd2L7KFVAooQb8ee7qLvjbFR1x4RnNAABnnnoS7g3IAigVPiXqHw7eurkb6tRMjyqNYyRde0REBorIJhHJFZERGu/XFpFvPe8vEZEMowvqdVPPNlj/4gCc3tx9UPfv7A7279/WwzdP4OUbEF0b5Ecv027m53+jqlPLhvjvHT2rnGD0eu1PZ2PS8MoTReBluH8gA9xtrCO11njgYuOaerbSCJJ1a6UH/XD+2q9DlbJ684gPGdzstH7tGnj9xm7oeZr7iixcIAmVhqhXK7o89pBurfDWzd2w5V+DcE4b/9Ye7v+9V4L+zfCHnuc+6Xh3p//N9vMymqBtk3oA4Dt2a6WneQJx1SCVliaoV6sGnr+mC4ZrHIv1/Vpg9M1sFnY7/ANRk/q1ALhPynOeuiRoP6WJ4NH++pq4pqcJfnmkL972S7l5l+/17q3a6Tg9LZcyWwQ/NOX92BNXdMT7t3XXvB8TackKwNltwqdKSj1XpHVrpuG+i6oGd6dSYSuKvds3xaCu7lSn9z5Dj3YnY/2LAyKUzHgRg7uIpAP4AMAgAF0ADBWRwOufewEcVkqdAeBtAK8ZXVC/8lS54eT9oft/4Zd0qpoHr18r3Xd5paem3bRB1YDdo11j3H9x1dTAb4/2xQCNfPX3D5yv2fypU8uGWPLP/ni0fyZuzmpbJWCkBZTJ/705T12CKY/1i3gDdYTfpeQr15+NjaMGokXD2vjxwfNx1wUZAIAP/E6AoTw9qDOu6NLSlzsfP6xPUM3Sn/cA9ve3KzripWvPqjLNP/3wv7t7+U7K0fjszl4Y/eceIWvoaWnA27eci6cHdcaj/TNxXvuq+f8e7RrjqnNOxbj7emPiwxfi7gszAGjfJ0gTwQ092lSmKny7yL0fvMdgr4zKz758nft79wavm/xOfA9eWhlIa9dIwxVdWuLTu4JvXHtPYF5N6tfCwhGXoVfGyRj95x54/PJMrBp5ZdA+CWxieMHp7qDvf7x/+OceuKxzC9zTtz1Oa1o/6Pi9/+LTcX33Nvjf3b2CyhVIKz6PCtjn154bOh3nfa6jQ7P6eCyg0nBxx+Zo17Re0Ge8FanWjeuGTId6K0rD+nXAH38LThUNu6gDzm3bGOteHICrzjlVcxlHSioAACfVrRl0InK6VFDlIrNFA7z2J/eNaxHg0k7uY7vTKZUnKCOetYiWnjWeByBXKbUNAERkPIBrAWzwm+daAC94/v4BwPsiIioJPdL3P7Mlfl+3Dx1bNsCTV3ZE/do1ICK4uGNzzNl8AJ1PaYj/3d0LdWulI+/Vq+B0KZQ5nOjy/FQAwPJnL8eDY1fglRvOxuVvzQEA3N7nNNSvXQO92zdB7ZppaNGwMu/2wW09MG3DPtTwy0/+6/qumL/lIG7p1Ra9Mppg/j8uw9Lth/DA2OV4b2h3XNmlJdLTBDXT04JSGx2aB9+IGnpeOzw7cR2aNaiN05q633/v1u64ZczioHmnP3ExDp0oBwCMvKYLerdv6qvRLPXckzinTWPclNUGZ7VqhFMaXYBnflqLnH3HfMu4sWcbXJTZDO2a1PPdAPr6vj4oqXAGHZSDup6C39ft871+amAnfLW46uhYNdPTcMf5GZiZU4CjnsFVRt/eE6f/czIA98F/aacWyBjxG1qFePLz54cvDMoBN6pXE4PO1v5BXpTZzBck7vdcxTicrir51QkPVU2rNaidjv8tyMM5bRpj8bZD7s/264D/zt0WVAsd0q0V3pm+BU3ruwNMswa1MeXxi6rcWExPE9T1O7GPvOYsjBjUOeiqQUQ0WyTlvDRQs/LRqnFdfP+A+9Leu/3eyr434DWuV7W879/WHfmHS1C7RjqG9euA8Ut3ok+HplXSU+e0aYRH+2fii4V5OFJS4TtpXtqpBV65/mxs2nfUN+9V55yKDXuPYvDZp2Dz/uNBxzEA38n00f6ZEbuNeHHIWXjiu9UYfXtPdDqlIbq0OgnvTt+CF4acFXRS9hp2UQe0aFgn7E3i23q3w6xNBbivb3u0OKkOHr3sDExZvw+b9x/HiEGdfd9fg9o18N6t3fHmjcEtqbz3T7z3erJOOxnZOw4DAFo1roP6tWtg6uP9sPNQMf76ZTZeHHIW6nl+J6c0qoObstpg8DmnBqXlaqQJHC4VtmmnoZRSYf8BuBHAJ36v7wDwfsA86wC08Xu9FUAzjWUNA5ANILtdu3bKKEdLyoOmuVwu9X32LlVW4dT8zP4jJWpPUXGVaV8uylOrdh5OaLn8bS04poqKtecpKXcElX1B7gG1/cDxuMvlcrlU4fEyVVLuiPqzFQ6nOlFWUWXakm2FKrfgWMTP5h08rhZsOeB7rbWNei3MPai+XbpT7TtSovYWlcS0DKWUWptfpCocTrVmV5H6cFZuyPmcTpc6VloR8n2zVDic6vvsXcrpdMW8jCMl5RH3n8tl/PZH+n0Yxel0qe+W7VQVjtiOtXKHUxWXOTS3338bJq7MD/pt+CutcKjSiuh/c4EAZKsIcVspBVERKtciciOAgUqp+zyv7wDQWyk13G+edZ558j2vt3rmORhquVlZWSo7Ozv6sxERUTUmIsuVUhEfRtFzQ3U3AP/mCW080zTnEZEaABoBKNRXVCIiMpqe4L4MQKaItBeRWgBuBTApYJ5JAO70/H0jgJkq0iUBERElTMQbqkoph4gMBzAVQDqAz5RS60VkFNy5n0kAPgXwlYjkAjgE9wmAiIhMoqt9jlJqMoDJAdOe9/u7FMBNxhaNiIhilXJPqBIRUWQM7kRENsTgTkRkQwzuREQ2FPEhpoStWOQAgB0RZ9TWDEDIB6RsgNuX2uy8fXbeNiA1tu80pVTEgSRMC+7xEJFsPU9opSpuX2qz8/bZedsAe20f0zJERDbE4E5EZEOpGtzHmF2ABOP2pTY7b5+dtw2w0falZM6diIjCS9WaOxERhcHgTkRkQykX3CMN1p0KRCRPRNaKyCoRyfZMayIi00Rki+f/kz3TRUTe82zvGhGJPBBqkonIZyJS4Bm0xTst6u0RkTs9828RkTu11mWGENv3gojs9uzDVSIy2O+9pz3bt0lEBvhNt+SxKyJtRWSWiGwQkfUi8phnesrvwzDbZpv9F5Ke4Zqs8g/uLoe3AugAoBaA1QC6mF2uGLYjDwHDEAJ4HcAIz98jALzm+XswgN/hHqK5D4AlZpdfY3v6AegBYF2s2wOgCYBtnv9P9vx9stnbFmb7XgDwpMa8XTzHZW0A7T3Ha7qVj10ApwLo4fm7IYDNnu1I+X0YZttss/9C/Uu1mrtvsG6lVDkA72DddnAtgC88f38B4Dq/6V8qt8UAGouI9ijRJlFKzYW7H39/0W7PAADTlFKHlFKHAUwDMDDxpY8sxPaFci2A8UqpMqXUdgC5cB+3lj12lVJ7lVIrPH8fA7ARQGvYYB+G2bZQUm7/hZJqwb01gF1+r/MRfkdZlQLwh4gsF5FhnmktlVJ7PX/vA9DS83eqbnO025OK2znck5b4zJuyQIpvn4hkAOgOYAlstg8Dtg2w4f7zl2rB3S76KqV6ABgE4GER6ef/pnJfH9qmjardtsdjNIDTAZwLYC+Af5tbnPiJSAMAPwJ4XCl11P+9VN+HGttmu/0XKNWCu57Bui1PKbXb838BgJ/gvuTb7023eP4v8Myeqtsc7fak1HYqpfYrpZxKKReAj+Heh0CKbp+I1IQ7+I1TSk3wTLbFPtTaNrvtPy2pFtz1DNZtaSJSX0Qaev8GcCWAdag6yPidAH72/D0JwF88LRT6ADjid6lsZdFuz1QAV4rIyZ5L5Cs90ywp4L7H9XDvQ8C9fbeKSG0RaQ8gE8BSWPjYFRGBexzkjUqpt/zeSvl9GGrb7LT/QjL7jm60/+C+U78Z7jvXz5hdnhjK3wHuO+2rAaz3bgOApgBmANgCYDqAJp7pAuADz/auBZBl9jZobNM3cF/aVsCdi7w3lu0BcA/cN7ByAdxt9nZF2L6vPOVfA/eP/FS/+Z/xbN8mAIOsfuwC6At3ymUNgFWef4PtsA/DbJtt9l+of+x+gIjIhlItLUNERDowuBMR2RCDOxGRDTG4ExHZEIM7EZENMbgTEdkQgzsRkQ39fxbJiL/d6rpWAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "theta shape: (2730, 18)\n"
     ]
    }
   ],
   "source": [
    "#Check that the solution exists\n",
    "xi = np.zeros((max_order+1, max_degree+1, 2)) #last axis is dims\n",
    "xi[0, 0, 0] = f_vals #constant column\n",
    "xi[2, 0] = 1 #laplace operator columns, i.e. u^0*u_xx, u^0*u_yy columns\n",
    "xi_flat = xi.flatten()\n",
    "u_t_reconstructed = np.dot(theta, xi_flat)\n",
    "\n",
    "fig = plt.figure()\n",
    "\n",
    "ax = fig.add_subplot(111)\n",
    "ax.plot(np.abs(u_t - u_t_reconstructed))\n",
    "\n",
    "plt.show()\n",
    "print(f\"theta shape: {theta.shape}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[-2.8  0.   0.   0.   0.   0.   0.   0.   0.   0.   0.   0.   1.   1.   0.\n",
      "  0.   0.   0. ]\n",
      "[ 0.13333625  0.          0.          0.          0.          0.          0.\n",
      "  0.          0.          0.          0.          0.          0.26666411\n",
      "  0.26666777  0.          0.          0.          0.        ] 0.0\n",
      "error: 1.0982467542643632e-11\n",
      "error: 2.5518567498977467e-08\n"
     ]
    }
   ],
   "source": [
    "#once identified which are nonzero, can it get the right values?\n",
    "#Set zero columns:\n",
    "theta_ish, u_t_ish = theta.copy(), u_t.copy()\n",
    "theta_ish[:, 1:-6] = 0\n",
    "theta_ish[:, -4:] = 0\n",
    "#Set ground truth\n",
    "xi_true = np.zeros((max_order+1, max_degree+1, 2)) #last axis is dims\n",
    "xi_true[0, 0, 0] = f_vals #constant column\n",
    "xi_true[2, 0] = 1 #laplace operator columns, i.e. u^0*u_xx, u^0*u_yy columns\n",
    "xi_true = xi_true.flatten()\n",
    "print(f\"{xi_true}\")\n",
    "#Test\n",
    "model = Ridge(alpha=1e-5, fit_intercept=False, normalize=False, copy_X=True) #SHOULD IT BE RIDGE OR OLS?\n",
    "model.fit(theta_ish, u_t_ish)\n",
    "xi_guess = model.coef_\n",
    "print(xi_guess, model.intercept_)\n",
    "print(f\"error: {calculate_error(theta_ish, u_t_ish, xi_true, 0):}\")\n",
    "print(f\"error: {calculate_error(theta_ish, u_t_ish, xi_guess, 0):}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0: [-2.8  0.   0.   0.   0.   0.   0.   0.   0.   0.   0.   0.   1.   1.   0.\n",
      "  0.   0.   0. ]\n",
      "\n",
      "10: [ 0.1236018   0.          0.01031754  0.         -0.00261913  0.\n",
      "  0.02214666  0.02182897 -0.02530551 -0.02507521  0.00674301  0.00670713\n",
      "  0.2472036   0.2472036   0.02063508  0.02063508 -0.00523826 -0.00523826]\n",
      "10: [ 0.1236018  0.         0.         0.         0.         0.         0.         0.\n",
      "  0.         0.         0.         0.         0.2472036  0.2472036  0.         0.\n",
      "  0.         0.       ]\n",
      "\n",
      "9: [ 0.13332791  0.          0.          0.          0.          0.          0.\n",
      "  0.          0.          0.          0.          0.          0.26665581\n",
      "  0.26665581  0.          0.          0.          0.        ]\n",
      "9: [ 0.13332791  0.          0.          0.          0.          0.          0.\n",
      "  0.          0.          0.          0.          0.          0.26665581\n",
      "  0.26665581  0.          0.          0.          0.        ]\n",
      "\n",
      "8: [ 0.13332791  0.          0.          0.          0.          0.          0.\n",
      "  0.          0.          0.          0.          0.          0.26665581\n",
      "  0.26665581  0.          0.          0.          0.        ]\n",
      "8: [ 0.13332791  0.          0.          0.          0.          0.          0.\n",
      "  0.          0.          0.          0.          0.          0.26665581\n",
      "  0.26665581  0.          0.          0.          0.        ]\n",
      "\n",
      "7: [ 0.13332791  0.          0.          0.          0.          0.          0.\n",
      "  0.          0.          0.          0.          0.          0.26665581\n",
      "  0.26665581  0.          0.          0.          0.        ]\n",
      "7: [ 0.13332791  0.          0.          0.          0.          0.          0.\n",
      "  0.          0.          0.          0.          0.          0.26665581\n",
      "  0.26665581  0.          0.          0.          0.        ]\n",
      "\n",
      "6: [ 0.13332791  0.          0.          0.          0.          0.          0.\n",
      "  0.          0.          0.          0.          0.          0.26665581\n",
      "  0.26665581  0.          0.          0.          0.        ]\n",
      "6: [ 0.13332791  0.          0.          0.          0.          0.          0.\n",
      "  0.          0.          0.          0.          0.          0.26665581\n",
      "  0.26665581  0.          0.          0.          0.        ]\n",
      "\n",
      "5: [ 0.13332791  0.          0.          0.          0.          0.          0.\n",
      "  0.          0.          0.          0.          0.          0.26665581\n",
      "  0.26665581  0.          0.          0.          0.        ]\n",
      "5: [ 0.13332791  0.          0.          0.          0.          0.          0.\n",
      "  0.          0.          0.          0.          0.          0.26665581\n",
      "  0.26665581  0.          0.          0.          0.        ]\n",
      "\n",
      "4: [ 0.13332791  0.          0.          0.          0.          0.          0.\n",
      "  0.          0.          0.          0.          0.          0.26665581\n",
      "  0.26665581  0.          0.          0.          0.        ]\n",
      "4: [ 0.13332791  0.          0.          0.          0.          0.          0.\n",
      "  0.          0.          0.          0.          0.          0.26665581\n",
      "  0.26665581  0.          0.          0.          0.        ]\n",
      "\n",
      "3: [ 0.13332791  0.          0.          0.          0.          0.          0.\n",
      "  0.          0.          0.          0.          0.          0.26665581\n",
      "  0.26665581  0.          0.          0.          0.        ]\n",
      "3: [ 0.13332791  0.          0.          0.          0.          0.          0.\n",
      "  0.          0.          0.          0.          0.          0.26665581\n",
      "  0.26665581  0.          0.          0.          0.        ]\n",
      "\n",
      "2: [ 0.13332791  0.          0.          0.          0.          0.          0.\n",
      "  0.          0.          0.          0.          0.          0.26665581\n",
      "  0.26665581  0.          0.          0.          0.        ]\n",
      "2: [ 0.13332791  0.          0.          0.          0.          0.          0.\n",
      "  0.          0.          0.          0.          0.          0.26665581\n",
      "  0.26665581  0.          0.          0.          0.        ]\n",
      "\n",
      "1: [ 0.13332791  0.          0.          0.          0.          0.          0.\n",
      "  0.          0.          0.          0.          0.          0.26665581\n",
      "  0.26665581  0.          0.          0.          0.        ]\n",
      "1: [ 0.13332791  0.          0.          0.          0.          0.          0.\n",
      "  0.          0.          0.          0.          0.          0.26665581\n",
      "  0.26665581  0.          0.          0.          0.        ]\n",
      "\n",
      "\n",
      "best: [  0.00000000e+00   0.00000000e+00   0.00000000e+00   0.00000000e+00\n",
      "   0.00000000e+00   0.00000000e+00   0.00000000e+00   0.00000000e+00\n",
      "   0.00000000e+00   0.00000000e+00   0.00000000e+00   0.00000000e+00\n",
      "   1.17385757e-25   8.70736779e-26   0.00000000e+00   0.00000000e+00\n",
      "   0.00000000e+00   0.00000000e+00]\n"
     ]
    }
   ],
   "source": [
    "xi_true = np.zeros((max_order+1, max_degree+1, 2)) #last axis is dims\n",
    "xi_true[0, 0, 0] = f_vals #constant column\n",
    "xi_true[2, 0] = 1 #laplace operator columns, i.e. u^0*u_xx, u^0*u_yy columns\n",
    "xi_true = xi_true.flatten()\n",
    "print(f\"0: {xi_true}\")\n",
    "print()\n",
    "xi_best = stridge(theta, u_t, alpha=1e5*1e-5, tol=1e4*1e-5, iters=10)\n",
    "print()\n",
    "print(f\"best: {xi_best}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "best: [  0.00000000e+00  -2.82025666e-04   3.67561351e-03  -4.33129104e-04\n",
      "   1.68996404e-04  -1.90955646e-04   2.68022598e-14   3.14518460e-14\n",
      "  -1.07238180e-14  -1.69225500e-14   4.60506820e-16   2.37106943e-15\n",
      "  -1.85423101e-02   2.21884225e-02   1.86916881e-02  -2.05294949e-02\n",
      "  -4.51752738e-03   4.43302918e-03]\n",
      "best: 4.050823412334599e+17\n",
      "10: [  1.05027673e+00  -1.38727734e+00   1.21036607e-01  -8.68730720e-01\n",
      "  -2.33969022e-02  -1.43550632e-01   2.60381994e-14   3.23838178e-14\n",
      "  -1.15463195e-14  -1.78190795e-14   8.32667268e-16   2.32106001e-15\n",
      "   5.50707091e-02   1.97909237e-02  -4.41281400e-02  -1.63901637e-02\n",
      "   8.47027563e-03   3.22817548e-03]\n",
      "10: [ 1.05027673 -1.38727734  0.12103661 -0.86873072 -0.0233969  -0.14355063\n",
      "  0.          0.          0.          0.          0.          0.\n",
      "  0.05507071  0.01979092 -0.04412814 -0.01639016  0.00847028  0.00322818]\n",
      "\n",
      "9: [  9.07110006e-01   6.08211818e-01   2.43208194e-01   1.54202407e-13\n",
      "  -4.81817128e-02  -2.28755409e-14  -1.02648883e-14   6.22123011e-16\n",
      "   4.65368581e-16  -6.73926950e-17   0.00000000e+00   0.00000000e+00\n",
      "   1.79100530e-02   1.28534944e-01  -1.27590200e-02  -1.08845077e-01\n",
      "   2.00979079e-03   2.20810656e-02]\n",
      "9: [ 0.90711001  0.60821182  0.24320819  0.         -0.04818171  0.          0.\n",
      "  0.          0.          0.          0.          0.          0.01791005\n",
      "  0.12853494 -0.01275902 -0.10884508  0.00200979  0.02208107]\n",
      "\n",
      "8: [  9.07110006e-01   6.08211818e-01   2.43208194e-01   1.54202407e-13\n",
      "  -4.81817128e-02  -2.28755409e-14  -1.02648883e-14   6.22123011e-16\n",
      "   4.65368581e-16  -6.73926950e-17   0.00000000e+00   0.00000000e+00\n",
      "   1.79100530e-02   1.28534944e-01  -1.27590200e-02  -1.08845077e-01\n",
      "   2.00979079e-03   2.20810656e-02]\n",
      "8: [ 0.90711001  0.60821182  0.24320819  0.         -0.04818171  0.          0.\n",
      "  0.          0.          0.          0.          0.          0.01791005\n",
      "  0.12853494 -0.01275902 -0.10884508  0.00200979  0.02208107]\n",
      "\n",
      "7: [  9.07110006e-01   6.08211818e-01   2.43208194e-01   1.54202407e-13\n",
      "  -4.81817128e-02  -2.28755409e-14  -1.02648883e-14   6.22123011e-16\n",
      "   4.65368581e-16  -6.73926950e-17   0.00000000e+00   0.00000000e+00\n",
      "   1.79100530e-02   1.28534944e-01  -1.27590200e-02  -1.08845077e-01\n",
      "   2.00979079e-03   2.20810656e-02]\n",
      "7: [ 0.90711001  0.60821182  0.24320819  0.         -0.04818171  0.          0.\n",
      "  0.          0.          0.          0.          0.          0.01791005\n",
      "  0.12853494 -0.01275902 -0.10884508  0.00200979  0.02208107]\n",
      "\n",
      "6: [  9.07110006e-01   6.08211818e-01   2.43208194e-01   1.54202407e-13\n",
      "  -4.81817128e-02  -2.28755409e-14  -1.02648883e-14   6.22123011e-16\n",
      "   4.65368581e-16  -6.73926950e-17   0.00000000e+00   0.00000000e+00\n",
      "   1.79100530e-02   1.28534944e-01  -1.27590200e-02  -1.08845077e-01\n",
      "   2.00979079e-03   2.20810656e-02]\n",
      "6: [ 0.90711001  0.60821182  0.24320819  0.         -0.04818171  0.          0.\n",
      "  0.          0.          0.          0.          0.          0.01791005\n",
      "  0.12853494 -0.01275902 -0.10884508  0.00200979  0.02208107]\n",
      "\n",
      "5: [  9.07110006e-01   6.08211818e-01   2.43208194e-01   1.54202407e-13\n",
      "  -4.81817128e-02  -2.28755409e-14  -1.02648883e-14   6.22123011e-16\n",
      "   4.65368581e-16  -6.73926950e-17   0.00000000e+00   0.00000000e+00\n",
      "   1.79100530e-02   1.28534944e-01  -1.27590200e-02  -1.08845077e-01\n",
      "   2.00979079e-03   2.20810656e-02]\n",
      "5: [ 0.90711001  0.60821182  0.24320819  0.         -0.04818171  0.          0.\n",
      "  0.          0.          0.          0.          0.          0.01791005\n",
      "  0.12853494 -0.01275902 -0.10884508  0.00200979  0.02208107]\n",
      "\n",
      "4: [  9.07110006e-01   6.08211818e-01   2.43208194e-01   1.54202407e-13\n",
      "  -4.81817128e-02  -2.28755409e-14  -1.02648883e-14   6.22123011e-16\n",
      "   4.65368581e-16  -6.73926950e-17   0.00000000e+00   0.00000000e+00\n",
      "   1.79100530e-02   1.28534944e-01  -1.27590200e-02  -1.08845077e-01\n",
      "   2.00979079e-03   2.20810656e-02]\n",
      "4: [ 0.90711001  0.60821182  0.24320819  0.         -0.04818171  0.          0.\n",
      "  0.          0.          0.          0.          0.          0.01791005\n",
      "  0.12853494 -0.01275902 -0.10884508  0.00200979  0.02208107]\n",
      "\n",
      "3: [  9.07110006e-01   6.08211818e-01   2.43208194e-01   1.54202407e-13\n",
      "  -4.81817128e-02  -2.28755409e-14  -1.02648883e-14   6.22123011e-16\n",
      "   4.65368581e-16  -6.73926950e-17   0.00000000e+00   0.00000000e+00\n",
      "   1.79100530e-02   1.28534944e-01  -1.27590200e-02  -1.08845077e-01\n",
      "   2.00979079e-03   2.20810656e-02]\n",
      "3: [ 0.90711001  0.60821182  0.24320819  0.         -0.04818171  0.          0.\n",
      "  0.          0.          0.          0.          0.          0.01791005\n",
      "  0.12853494 -0.01275902 -0.10884508  0.00200979  0.02208107]\n",
      "\n",
      "2: [  9.07110006e-01   6.08211818e-01   2.43208194e-01   1.54202407e-13\n",
      "  -4.81817128e-02  -2.28755409e-14  -1.02648883e-14   6.22123011e-16\n",
      "   4.65368581e-16  -6.73926950e-17   0.00000000e+00   0.00000000e+00\n",
      "   1.79100530e-02   1.28534944e-01  -1.27590200e-02  -1.08845077e-01\n",
      "   2.00979079e-03   2.20810656e-02]\n",
      "2: [ 0.90711001  0.60821182  0.24320819  0.         -0.04818171  0.          0.\n",
      "  0.          0.          0.          0.          0.          0.01791005\n",
      "  0.12853494 -0.01275902 -0.10884508  0.00200979  0.02208107]\n",
      "\n",
      "1: [  9.07110006e-01   6.08211818e-01   2.43208194e-01   1.54202407e-13\n",
      "  -4.81817128e-02  -2.28755409e-14  -1.02648883e-14   6.22123011e-16\n",
      "   4.65368581e-16  -6.73926950e-17   0.00000000e+00   0.00000000e+00\n",
      "   1.79100530e-02   1.28534944e-01  -1.27590200e-02  -1.08845077e-01\n",
      "   2.00979079e-03   2.20810656e-02]\n",
      "1: [ 0.90711001  0.60821182  0.24320819  0.         -0.04818171  0.          0.\n",
      "  0.          0.          0.          0.          0.          0.01791005\n",
      "  0.12853494 -0.01275902 -0.10884508  0.00200979  0.02208107]\n",
      "\n",
      "1: [  0.00000000e+00  -4.90804007e-06   2.11512041e-02  -6.56657899e-17\n",
      "  -3.31445941e-03  -2.43035600e-17   6.11573638e-18  -1.15824563e-17\n",
      "   1.15824563e-17   0.00000000e+00   1.19159785e-49   4.73131773e-45\n",
      "  -4.80411563e-02   6.15658343e-02   4.01965764e-02  -5.07721784e-02\n",
      "  -8.16513718e-03   9.82236688e-03]\n",
      "1: 3.81253968219727e+17\n",
      "10: [  1.05027673e+00  -1.38727734e+00   1.21036607e-01  -8.68730720e-01\n",
      "  -2.33969022e-02  -1.43550632e-01   2.60381994e-14   3.23838178e-14\n",
      "  -1.15463195e-14  -1.78190795e-14   8.32667268e-16   2.32106001e-15\n",
      "   5.50707091e-02   1.97909237e-02  -4.41281400e-02  -1.63901637e-02\n",
      "   8.47027563e-03   3.22817548e-03]\n",
      "10: [ 1.05027673 -1.38727734  0.12103661 -0.86873072 -0.0233969  -0.14355063\n",
      "  0.          0.          0.          0.          0.          0.\n",
      "  0.05507071  0.01979092 -0.04412814 -0.01639016  0.00847028  0.00322818]\n",
      "\n",
      "9: [  9.07110006e-01   6.08211818e-01   2.43208194e-01   1.54202407e-13\n",
      "  -4.81817128e-02  -2.28755409e-14  -1.02648883e-14   6.22123011e-16\n",
      "   4.65368581e-16  -6.73926950e-17   0.00000000e+00   0.00000000e+00\n",
      "   1.79100530e-02   1.28534944e-01  -1.27590200e-02  -1.08845077e-01\n",
      "   2.00979079e-03   2.20810656e-02]\n",
      "9: [ 0.90711001  0.60821182  0.24320819  0.         -0.04818171  0.          0.\n",
      "  0.          0.          0.          0.          0.          0.01791005\n",
      "  0.12853494 -0.01275902 -0.10884508  0.00200979  0.02208107]\n",
      "\n",
      "8: [  9.07110006e-01   6.08211818e-01   2.43208194e-01   1.54202407e-13\n",
      "  -4.81817128e-02  -2.28755409e-14  -1.02648883e-14   6.22123011e-16\n",
      "   4.65368581e-16  -6.73926950e-17   0.00000000e+00   0.00000000e+00\n",
      "   1.79100530e-02   1.28534944e-01  -1.27590200e-02  -1.08845077e-01\n",
      "   2.00979079e-03   2.20810656e-02]\n",
      "8: [ 0.90711001  0.60821182  0.24320819  0.         -0.04818171  0.          0.\n",
      "  0.          0.          0.          0.          0.          0.01791005\n",
      "  0.12853494 -0.01275902 -0.10884508  0.00200979  0.02208107]\n",
      "\n",
      "7: [  9.07110006e-01   6.08211818e-01   2.43208194e-01   1.54202407e-13\n",
      "  -4.81817128e-02  -2.28755409e-14  -1.02648883e-14   6.22123011e-16\n",
      "   4.65368581e-16  -6.73926950e-17   0.00000000e+00   0.00000000e+00\n",
      "   1.79100530e-02   1.28534944e-01  -1.27590200e-02  -1.08845077e-01\n",
      "   2.00979079e-03   2.20810656e-02]\n",
      "7: [ 0.90711001  0.60821182  0.24320819  0.         -0.04818171  0.          0.\n",
      "  0.          0.          0.          0.          0.          0.01791005\n",
      "  0.12853494 -0.01275902 -0.10884508  0.00200979  0.02208107]\n",
      "\n",
      "6: [  9.07110006e-01   6.08211818e-01   2.43208194e-01   1.54202407e-13\n",
      "  -4.81817128e-02  -2.28755409e-14  -1.02648883e-14   6.22123011e-16\n",
      "   4.65368581e-16  -6.73926950e-17   0.00000000e+00   0.00000000e+00\n",
      "   1.79100530e-02   1.28534944e-01  -1.27590200e-02  -1.08845077e-01\n",
      "   2.00979079e-03   2.20810656e-02]\n",
      "6: [ 0.90711001  0.60821182  0.24320819  0.         -0.04818171  0.          0.\n",
      "  0.          0.          0.          0.          0.          0.01791005\n",
      "  0.12853494 -0.01275902 -0.10884508  0.00200979  0.02208107]\n",
      "\n",
      "5: [  9.07110006e-01   6.08211818e-01   2.43208194e-01   1.54202407e-13\n",
      "  -4.81817128e-02  -2.28755409e-14  -1.02648883e-14   6.22123011e-16\n",
      "   4.65368581e-16  -6.73926950e-17   0.00000000e+00   0.00000000e+00\n",
      "   1.79100530e-02   1.28534944e-01  -1.27590200e-02  -1.08845077e-01\n",
      "   2.00979079e-03   2.20810656e-02]\n",
      "5: [ 0.90711001  0.60821182  0.24320819  0.         -0.04818171  0.          0.\n",
      "  0.          0.          0.          0.          0.          0.01791005\n",
      "  0.12853494 -0.01275902 -0.10884508  0.00200979  0.02208107]\n",
      "\n",
      "4: [  9.07110006e-01   6.08211818e-01   2.43208194e-01   1.54202407e-13\n",
      "  -4.81817128e-02  -2.28755409e-14  -1.02648883e-14   6.22123011e-16\n",
      "   4.65368581e-16  -6.73926950e-17   0.00000000e+00   0.00000000e+00\n",
      "   1.79100530e-02   1.28534944e-01  -1.27590200e-02  -1.08845077e-01\n",
      "   2.00979079e-03   2.20810656e-02]\n",
      "4: [ 0.90711001  0.60821182  0.24320819  0.         -0.04818171  0.          0.\n",
      "  0.          0.          0.          0.          0.          0.01791005\n",
      "  0.12853494 -0.01275902 -0.10884508  0.00200979  0.02208107]\n",
      "\n",
      "3: [  9.07110006e-01   6.08211818e-01   2.43208194e-01   1.54202407e-13\n",
      "  -4.81817128e-02  -2.28755409e-14  -1.02648883e-14   6.22123011e-16\n",
      "   4.65368581e-16  -6.73926950e-17   0.00000000e+00   0.00000000e+00\n",
      "   1.79100530e-02   1.28534944e-01  -1.27590200e-02  -1.08845077e-01\n",
      "   2.00979079e-03   2.20810656e-02]\n",
      "3: [ 0.90711001  0.60821182  0.24320819  0.         -0.04818171  0.          0.\n",
      "  0.          0.          0.          0.          0.          0.01791005\n",
      "  0.12853494 -0.01275902 -0.10884508  0.00200979  0.02208107]\n",
      "\n",
      "2: [  9.07110006e-01   6.08211818e-01   2.43208194e-01   1.54202407e-13\n",
      "  -4.81817128e-02  -2.28755409e-14  -1.02648883e-14   6.22123011e-16\n",
      "   4.65368581e-16  -6.73926950e-17   0.00000000e+00   0.00000000e+00\n",
      "   1.79100530e-02   1.28534944e-01  -1.27590200e-02  -1.08845077e-01\n",
      "   2.00979079e-03   2.20810656e-02]\n",
      "2: [ 0.90711001  0.60821182  0.24320819  0.         -0.04818171  0.          0.\n",
      "  0.          0.          0.          0.          0.          0.01791005\n",
      "  0.12853494 -0.01275902 -0.10884508  0.00200979  0.02208107]\n",
      "\n",
      "1: [  9.07110006e-01   6.08211818e-01   2.43208194e-01   1.54202407e-13\n",
      "  -4.81817128e-02  -2.28755409e-14  -1.02648883e-14   6.22123011e-16\n",
      "   4.65368581e-16  -6.73926950e-17   0.00000000e+00   0.00000000e+00\n",
      "   1.79100530e-02   1.28534944e-01  -1.27590200e-02  -1.08845077e-01\n",
      "   2.00979079e-03   2.20810656e-02]\n",
      "1: [ 0.90711001  0.60821182  0.24320819  0.         -0.04818171  0.          0.\n",
      "  0.          0.          0.          0.          0.          0.01791005\n",
      "  0.12853494 -0.01275902 -0.10884508  0.00200979  0.02208107]\n",
      "\n",
      "2: [  0.00000000e+00  -4.90804007e-06   2.11512041e-02  -6.56657899e-17\n",
      "  -3.31445941e-03  -2.43035600e-17   6.11573638e-18  -1.15824563e-17\n",
      "   1.15824563e-17   0.00000000e+00   1.19159785e-49   4.73131773e-45\n",
      "  -4.80411563e-02   6.15658343e-02   4.01965764e-02  -5.07721784e-02\n",
      "  -8.16513718e-03   9.82236688e-03]\n",
      "2: 3.81253968219727e+17\n",
      "10: [  1.05027673e+00  -1.38727734e+00   1.21036607e-01  -8.68730720e-01\n",
      "  -2.33969022e-02  -1.43550632e-01   2.60381994e-14   3.23838178e-14\n",
      "  -1.15463195e-14  -1.78190795e-14   8.32667268e-16   2.32106001e-15\n",
      "   5.50707091e-02   1.97909237e-02  -4.41281400e-02  -1.63901637e-02\n",
      "   8.47027563e-03   3.22817548e-03]\n",
      "10: [ 1.05027673 -1.38727734  0.12103661 -0.86873072 -0.0233969  -0.14355063\n",
      "  0.          0.          0.          0.          0.          0.\n",
      "  0.05507071  0.01979092 -0.04412814 -0.01639016  0.00847028  0.00322818]\n",
      "\n",
      "9: [  9.07110006e-01   6.08211818e-01   2.43208194e-01   1.54202407e-13\n",
      "  -4.81817128e-02  -2.28755409e-14  -1.02648883e-14   6.22123011e-16\n",
      "   4.65368581e-16  -6.73926950e-17   0.00000000e+00   0.00000000e+00\n",
      "   1.79100530e-02   1.28534944e-01  -1.27590200e-02  -1.08845077e-01\n",
      "   2.00979079e-03   2.20810656e-02]\n",
      "9: [ 0.90711001  0.60821182  0.24320819  0.         -0.04818171  0.          0.\n",
      "  0.          0.          0.          0.          0.          0.01791005\n",
      "  0.12853494 -0.01275902 -0.10884508  0.00200979  0.02208107]\n",
      "\n",
      "8: [  9.07110006e-01   6.08211818e-01   2.43208194e-01   1.54202407e-13\n",
      "  -4.81817128e-02  -2.28755409e-14  -1.02648883e-14   6.22123011e-16\n",
      "   4.65368581e-16  -6.73926950e-17   0.00000000e+00   0.00000000e+00\n",
      "   1.79100530e-02   1.28534944e-01  -1.27590200e-02  -1.08845077e-01\n",
      "   2.00979079e-03   2.20810656e-02]\n",
      "8: [ 0.90711001  0.60821182  0.24320819  0.         -0.04818171  0.          0.\n",
      "  0.          0.          0.          0.          0.          0.01791005\n",
      "  0.12853494 -0.01275902 -0.10884508  0.00200979  0.02208107]\n",
      "\n",
      "7: [  9.07110006e-01   6.08211818e-01   2.43208194e-01   1.54202407e-13\n",
      "  -4.81817128e-02  -2.28755409e-14  -1.02648883e-14   6.22123011e-16\n",
      "   4.65368581e-16  -6.73926950e-17   0.00000000e+00   0.00000000e+00\n",
      "   1.79100530e-02   1.28534944e-01  -1.27590200e-02  -1.08845077e-01\n",
      "   2.00979079e-03   2.20810656e-02]\n",
      "7: [ 0.90711001  0.60821182  0.24320819  0.         -0.04818171  0.          0.\n",
      "  0.          0.          0.          0.          0.          0.01791005\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "  0.12853494 -0.01275902 -0.10884508  0.00200979  0.02208107]\n",
      "\n",
      "6: [  9.07110006e-01   6.08211818e-01   2.43208194e-01   1.54202407e-13\n",
      "  -4.81817128e-02  -2.28755409e-14  -1.02648883e-14   6.22123011e-16\n",
      "   4.65368581e-16  -6.73926950e-17   0.00000000e+00   0.00000000e+00\n",
      "   1.79100530e-02   1.28534944e-01  -1.27590200e-02  -1.08845077e-01\n",
      "   2.00979079e-03   2.20810656e-02]\n",
      "6: [ 0.90711001  0.60821182  0.24320819  0.         -0.04818171  0.          0.\n",
      "  0.          0.          0.          0.          0.          0.01791005\n",
      "  0.12853494 -0.01275902 -0.10884508  0.00200979  0.02208107]\n",
      "\n",
      "5: [  9.07110006e-01   6.08211818e-01   2.43208194e-01   1.54202407e-13\n",
      "  -4.81817128e-02  -2.28755409e-14  -1.02648883e-14   6.22123011e-16\n",
      "   4.65368581e-16  -6.73926950e-17   0.00000000e+00   0.00000000e+00\n",
      "   1.79100530e-02   1.28534944e-01  -1.27590200e-02  -1.08845077e-01\n",
      "   2.00979079e-03   2.20810656e-02]\n",
      "5: [ 0.90711001  0.60821182  0.24320819  0.         -0.04818171  0.          0.\n",
      "  0.          0.          0.          0.          0.          0.01791005\n",
      "  0.12853494 -0.01275902 -0.10884508  0.00200979  0.02208107]\n",
      "\n",
      "4: [  9.07110006e-01   6.08211818e-01   2.43208194e-01   1.54202407e-13\n",
      "  -4.81817128e-02  -2.28755409e-14  -1.02648883e-14   6.22123011e-16\n",
      "   4.65368581e-16  -6.73926950e-17   0.00000000e+00   0.00000000e+00\n",
      "   1.79100530e-02   1.28534944e-01  -1.27590200e-02  -1.08845077e-01\n",
      "   2.00979079e-03   2.20810656e-02]\n",
      "4: [ 0.90711001  0.60821182  0.24320819  0.         -0.04818171  0.          0.\n",
      "  0.          0.          0.          0.          0.          0.01791005\n",
      "  0.12853494 -0.01275902 -0.10884508  0.00200979  0.02208107]\n",
      "\n",
      "3: [  9.07110006e-01   6.08211818e-01   2.43208194e-01   1.54202407e-13\n",
      "  -4.81817128e-02  -2.28755409e-14  -1.02648883e-14   6.22123011e-16\n",
      "   4.65368581e-16  -6.73926950e-17   0.00000000e+00   0.00000000e+00\n",
      "   1.79100530e-02   1.28534944e-01  -1.27590200e-02  -1.08845077e-01\n",
      "   2.00979079e-03   2.20810656e-02]\n",
      "3: [ 0.90711001  0.60821182  0.24320819  0.         -0.04818171  0.          0.\n",
      "  0.          0.          0.          0.          0.          0.01791005\n",
      "  0.12853494 -0.01275902 -0.10884508  0.00200979  0.02208107]\n",
      "\n",
      "2: [  9.07110006e-01   6.08211818e-01   2.43208194e-01   1.54202407e-13\n",
      "  -4.81817128e-02  -2.28755409e-14  -1.02648883e-14   6.22123011e-16\n",
      "   4.65368581e-16  -6.73926950e-17   0.00000000e+00   0.00000000e+00\n",
      "   1.79100530e-02   1.28534944e-01  -1.27590200e-02  -1.08845077e-01\n",
      "   2.00979079e-03   2.20810656e-02]\n",
      "2: [ 0.90711001  0.60821182  0.24320819  0.         -0.04818171  0.          0.\n",
      "  0.          0.          0.          0.          0.          0.01791005\n",
      "  0.12853494 -0.01275902 -0.10884508  0.00200979  0.02208107]\n",
      "\n",
      "1: [  9.07110006e-01   6.08211818e-01   2.43208194e-01   1.54202407e-13\n",
      "  -4.81817128e-02  -2.28755409e-14  -1.02648883e-14   6.22123011e-16\n",
      "   4.65368581e-16  -6.73926950e-17   0.00000000e+00   0.00000000e+00\n",
      "   1.79100530e-02   1.28534944e-01  -1.27590200e-02  -1.08845077e-01\n",
      "   2.00979079e-03   2.20810656e-02]\n",
      "1: [ 0.90711001  0.60821182  0.24320819  0.         -0.04818171  0.          0.\n",
      "  0.          0.          0.          0.          0.          0.01791005\n",
      "  0.12853494 -0.01275902 -0.10884508  0.00200979  0.02208107]\n",
      "\n",
      "3: [  0.00000000e+00  -4.90804007e-06   2.11512041e-02  -6.56657899e-17\n",
      "  -3.31445941e-03  -2.43035600e-17   6.11573638e-18  -1.15824563e-17\n",
      "   1.15824563e-17   0.00000000e+00   1.19159785e-49   4.73131773e-45\n",
      "  -4.80411563e-02   6.15658343e-02   4.01965764e-02  -5.07721784e-02\n",
      "  -8.16513718e-03   9.82236688e-03]\n",
      "3: 3.81253968219727e+17\n",
      "10: [  1.05027673e+00  -1.38727734e+00   1.21036607e-01  -8.68730720e-01\n",
      "  -2.33969022e-02  -1.43550632e-01   2.60381994e-14   3.23838178e-14\n",
      "  -1.15463195e-14  -1.78190795e-14   8.32667268e-16   2.32106001e-15\n",
      "   5.50707091e-02   1.97909237e-02  -4.41281400e-02  -1.63901637e-02\n",
      "   8.47027563e-03   3.22817548e-03]\n",
      "10: [ 1.05027673 -1.38727734  0.12103661 -0.86873072 -0.0233969  -0.14355063\n",
      "  0.          0.          0.          0.          0.          0.\n",
      "  0.05507071  0.01979092 -0.04412814 -0.01639016  0.00847028  0.00322818]\n",
      "\n",
      "9: [  9.07110006e-01   6.08211818e-01   2.43208194e-01   1.54202407e-13\n",
      "  -4.81817128e-02  -2.28755409e-14  -1.02648883e-14   6.22123011e-16\n",
      "   4.65368581e-16  -6.73926950e-17   0.00000000e+00   0.00000000e+00\n",
      "   1.79100530e-02   1.28534944e-01  -1.27590200e-02  -1.08845077e-01\n",
      "   2.00979079e-03   2.20810656e-02]\n",
      "9: [ 0.90711001  0.60821182  0.24320819  0.         -0.04818171  0.          0.\n",
      "  0.          0.          0.          0.          0.          0.01791005\n",
      "  0.12853494 -0.01275902 -0.10884508  0.00200979  0.02208107]\n",
      "\n",
      "8: [  9.07110006e-01   6.08211818e-01   2.43208194e-01   1.54202407e-13\n",
      "  -4.81817128e-02  -2.28755409e-14  -1.02648883e-14   6.22123011e-16\n",
      "   4.65368581e-16  -6.73926950e-17   0.00000000e+00   0.00000000e+00\n",
      "   1.79100530e-02   1.28534944e-01  -1.27590200e-02  -1.08845077e-01\n",
      "   2.00979079e-03   2.20810656e-02]\n",
      "8: [ 0.90711001  0.60821182  0.24320819  0.         -0.04818171  0.          0.\n",
      "  0.          0.          0.          0.          0.          0.01791005\n",
      "  0.12853494 -0.01275902 -0.10884508  0.00200979  0.02208107]\n",
      "\n",
      "7: [  9.07110006e-01   6.08211818e-01   2.43208194e-01   1.54202407e-13\n",
      "  -4.81817128e-02  -2.28755409e-14  -1.02648883e-14   6.22123011e-16\n",
      "   4.65368581e-16  -6.73926950e-17   0.00000000e+00   0.00000000e+00\n",
      "   1.79100530e-02   1.28534944e-01  -1.27590200e-02  -1.08845077e-01\n",
      "   2.00979079e-03   2.20810656e-02]\n",
      "7: [ 0.90711001  0.60821182  0.24320819  0.         -0.04818171  0.          0.\n",
      "  0.          0.          0.          0.          0.          0.01791005\n",
      "  0.12853494 -0.01275902 -0.10884508  0.00200979  0.02208107]\n",
      "\n",
      "6: [  9.07110006e-01   6.08211818e-01   2.43208194e-01   1.54202407e-13\n",
      "  -4.81817128e-02  -2.28755409e-14  -1.02648883e-14   6.22123011e-16\n",
      "   4.65368581e-16  -6.73926950e-17   0.00000000e+00   0.00000000e+00\n",
      "   1.79100530e-02   1.28534944e-01  -1.27590200e-02  -1.08845077e-01\n",
      "   2.00979079e-03   2.20810656e-02]\n",
      "6: [ 0.90711001  0.60821182  0.24320819  0.         -0.04818171  0.          0.\n",
      "  0.          0.          0.          0.          0.          0.01791005\n",
      "  0.12853494 -0.01275902 -0.10884508  0.00200979  0.02208107]\n",
      "\n",
      "5: [  9.07110006e-01   6.08211818e-01   2.43208194e-01   1.54202407e-13\n",
      "  -4.81817128e-02  -2.28755409e-14  -1.02648883e-14   6.22123011e-16\n",
      "   4.65368581e-16  -6.73926950e-17   0.00000000e+00   0.00000000e+00\n",
      "   1.79100530e-02   1.28534944e-01  -1.27590200e-02  -1.08845077e-01\n",
      "   2.00979079e-03   2.20810656e-02]\n",
      "5: [ 0.90711001  0.60821182  0.24320819  0.         -0.04818171  0.          0.\n",
      "  0.          0.          0.          0.          0.          0.01791005\n",
      "  0.12853494 -0.01275902 -0.10884508  0.00200979  0.02208107]\n",
      "\n",
      "4: [  9.07110006e-01   6.08211818e-01   2.43208194e-01   1.54202407e-13\n",
      "  -4.81817128e-02  -2.28755409e-14  -1.02648883e-14   6.22123011e-16\n",
      "   4.65368581e-16  -6.73926950e-17   0.00000000e+00   0.00000000e+00\n",
      "   1.79100530e-02   1.28534944e-01  -1.27590200e-02  -1.08845077e-01\n",
      "   2.00979079e-03   2.20810656e-02]\n",
      "4: [ 0.90711001  0.60821182  0.24320819  0.         -0.04818171  0.          0.\n",
      "  0.          0.          0.          0.          0.          0.01791005\n",
      "  0.12853494 -0.01275902 -0.10884508  0.00200979  0.02208107]\n",
      "\n",
      "3: [  9.07110006e-01   6.08211818e-01   2.43208194e-01   1.54202407e-13\n",
      "  -4.81817128e-02  -2.28755409e-14  -1.02648883e-14   6.22123011e-16\n",
      "   4.65368581e-16  -6.73926950e-17   0.00000000e+00   0.00000000e+00\n",
      "   1.79100530e-02   1.28534944e-01  -1.27590200e-02  -1.08845077e-01\n",
      "   2.00979079e-03   2.20810656e-02]\n",
      "3: [ 0.90711001  0.60821182  0.24320819  0.         -0.04818171  0.          0.\n",
      "  0.          0.          0.          0.          0.          0.01791005\n",
      "  0.12853494 -0.01275902 -0.10884508  0.00200979  0.02208107]\n",
      "\n",
      "2: [  9.07110006e-01   6.08211818e-01   2.43208194e-01   1.54202407e-13\n",
      "  -4.81817128e-02  -2.28755409e-14  -1.02648883e-14   6.22123011e-16\n",
      "   4.65368581e-16  -6.73926950e-17   0.00000000e+00   0.00000000e+00\n",
      "   1.79100530e-02   1.28534944e-01  -1.27590200e-02  -1.08845077e-01\n",
      "   2.00979079e-03   2.20810656e-02]\n",
      "2: [ 0.90711001  0.60821182  0.24320819  0.         -0.04818171  0.          0.\n",
      "  0.          0.          0.          0.          0.          0.01791005\n",
      "  0.12853494 -0.01275902 -0.10884508  0.00200979  0.02208107]\n",
      "\n",
      "1: [  9.07110006e-01   6.08211818e-01   2.43208194e-01   1.54202407e-13\n",
      "  -4.81817128e-02  -2.28755409e-14  -1.02648883e-14   6.22123011e-16\n",
      "   4.65368581e-16  -6.73926950e-17   0.00000000e+00   0.00000000e+00\n",
      "   1.79100530e-02   1.28534944e-01  -1.27590200e-02  -1.08845077e-01\n",
      "   2.00979079e-03   2.20810656e-02]\n",
      "1: [ 0.90711001  0.60821182  0.24320819  0.         -0.04818171  0.          0.\n",
      "  0.          0.          0.          0.          0.          0.01791005\n",
      "  0.12853494 -0.01275902 -0.10884508  0.00200979  0.02208107]\n",
      "\n",
      "4: [  0.00000000e+00  -4.90804007e-06   2.11512041e-02  -6.56657899e-17\n",
      "  -3.31445941e-03  -2.43035600e-17   6.11573638e-18  -1.15824563e-17\n",
      "   1.15824563e-17   0.00000000e+00   1.19159785e-49   4.73131773e-45\n",
      "  -4.80411563e-02   6.15658343e-02   4.01965764e-02  -5.07721784e-02\n",
      "  -8.16513718e-03   9.82236688e-03]\n",
      "4: 3.81253968219727e+17\n",
      "10: [  1.05027673e+00  -1.38727734e+00   1.21036607e-01  -8.68730720e-01\n",
      "  -2.33969022e-02  -1.43550632e-01   2.60381994e-14   3.23838178e-14\n",
      "  -1.15463195e-14  -1.78190795e-14   8.32667268e-16   2.32106001e-15\n",
      "   5.50707091e-02   1.97909237e-02  -4.41281400e-02  -1.63901637e-02\n",
      "   8.47027563e-03   3.22817548e-03]\n",
      "10: [ 1.05027673 -1.38727734  0.12103661 -0.86873072 -0.0233969  -0.14355063\n",
      "  0.          0.          0.          0.          0.          0.\n",
      "  0.05507071  0.01979092 -0.04412814 -0.01639016  0.00847028  0.00322818]\n",
      "\n",
      "9: [  9.07110006e-01   6.08211818e-01   2.43208194e-01   1.54202407e-13\n",
      "  -4.81817128e-02  -2.28755409e-14  -1.02648883e-14   6.22123011e-16\n",
      "   4.65368581e-16  -6.73926950e-17   0.00000000e+00   0.00000000e+00\n",
      "   1.79100530e-02   1.28534944e-01  -1.27590200e-02  -1.08845077e-01\n",
      "   2.00979079e-03   2.20810656e-02]\n",
      "9: [ 0.90711001  0.60821182  0.24320819  0.         -0.04818171  0.          0.\n",
      "  0.          0.          0.          0.          0.          0.01791005\n",
      "  0.12853494 -0.01275902 -0.10884508  0.00200979  0.02208107]\n",
      "\n",
      "8: [  9.07110006e-01   6.08211818e-01   2.43208194e-01   1.54202407e-13\n",
      "  -4.81817128e-02  -2.28755409e-14  -1.02648883e-14   6.22123011e-16\n",
      "   4.65368581e-16  -6.73926950e-17   0.00000000e+00   0.00000000e+00\n",
      "   1.79100530e-02   1.28534944e-01  -1.27590200e-02  -1.08845077e-01\n",
      "   2.00979079e-03   2.20810656e-02]\n",
      "8: [ 0.90711001  0.60821182  0.24320819  0.         -0.04818171  0.          0.\n",
      "  0.          0.          0.          0.          0.          0.01791005\n",
      "  0.12853494 -0.01275902 -0.10884508  0.00200979  0.02208107]\n",
      "\n",
      "7: [  9.07110006e-01   6.08211818e-01   2.43208194e-01   1.54202407e-13\n",
      "  -4.81817128e-02  -2.28755409e-14  -1.02648883e-14   6.22123011e-16\n",
      "   4.65368581e-16  -6.73926950e-17   0.00000000e+00   0.00000000e+00\n",
      "   1.79100530e-02   1.28534944e-01  -1.27590200e-02  -1.08845077e-01\n",
      "   2.00979079e-03   2.20810656e-02]\n",
      "7: [ 0.90711001  0.60821182  0.24320819  0.         -0.04818171  0.          0.\n",
      "  0.          0.          0.          0.          0.          0.01791005\n",
      "  0.12853494 -0.01275902 -0.10884508  0.00200979  0.02208107]\n",
      "\n",
      "6: [  9.07110006e-01   6.08211818e-01   2.43208194e-01   1.54202407e-13\n",
      "  -4.81817128e-02  -2.28755409e-14  -1.02648883e-14   6.22123011e-16\n",
      "   4.65368581e-16  -6.73926950e-17   0.00000000e+00   0.00000000e+00\n",
      "   1.79100530e-02   1.28534944e-01  -1.27590200e-02  -1.08845077e-01\n",
      "   2.00979079e-03   2.20810656e-02]\n",
      "6: [ 0.90711001  0.60821182  0.24320819  0.         -0.04818171  0.          0.\n",
      "  0.          0.          0.          0.          0.          0.01791005\n",
      "  0.12853494 -0.01275902 -0.10884508  0.00200979  0.02208107]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "5: [  9.07110006e-01   6.08211818e-01   2.43208194e-01   1.54202407e-13\n",
      "  -4.81817128e-02  -2.28755409e-14  -1.02648883e-14   6.22123011e-16\n",
      "   4.65368581e-16  -6.73926950e-17   0.00000000e+00   0.00000000e+00\n",
      "   1.79100530e-02   1.28534944e-01  -1.27590200e-02  -1.08845077e-01\n",
      "   2.00979079e-03   2.20810656e-02]\n",
      "5: [ 0.90711001  0.60821182  0.24320819  0.         -0.04818171  0.          0.\n",
      "  0.          0.          0.          0.          0.          0.01791005\n",
      "  0.12853494 -0.01275902 -0.10884508  0.00200979  0.02208107]\n",
      "\n",
      "4: [  9.07110006e-01   6.08211818e-01   2.43208194e-01   1.54202407e-13\n",
      "  -4.81817128e-02  -2.28755409e-14  -1.02648883e-14   6.22123011e-16\n",
      "   4.65368581e-16  -6.73926950e-17   0.00000000e+00   0.00000000e+00\n",
      "   1.79100530e-02   1.28534944e-01  -1.27590200e-02  -1.08845077e-01\n",
      "   2.00979079e-03   2.20810656e-02]\n",
      "4: [ 0.90711001  0.60821182  0.24320819  0.         -0.04818171  0.          0.\n",
      "  0.          0.          0.          0.          0.          0.01791005\n",
      "  0.12853494 -0.01275902 -0.10884508  0.00200979  0.02208107]\n",
      "\n",
      "3: [  9.07110006e-01   6.08211818e-01   2.43208194e-01   1.54202407e-13\n",
      "  -4.81817128e-02  -2.28755409e-14  -1.02648883e-14   6.22123011e-16\n",
      "   4.65368581e-16  -6.73926950e-17   0.00000000e+00   0.00000000e+00\n",
      "   1.79100530e-02   1.28534944e-01  -1.27590200e-02  -1.08845077e-01\n",
      "   2.00979079e-03   2.20810656e-02]\n",
      "3: [ 0.90711001  0.60821182  0.24320819  0.         -0.04818171  0.          0.\n",
      "  0.          0.          0.          0.          0.          0.01791005\n",
      "  0.12853494 -0.01275902 -0.10884508  0.00200979  0.02208107]\n",
      "\n",
      "2: [  9.07110006e-01   6.08211818e-01   2.43208194e-01   1.54202407e-13\n",
      "  -4.81817128e-02  -2.28755409e-14  -1.02648883e-14   6.22123011e-16\n",
      "   4.65368581e-16  -6.73926950e-17   0.00000000e+00   0.00000000e+00\n",
      "   1.79100530e-02   1.28534944e-01  -1.27590200e-02  -1.08845077e-01\n",
      "   2.00979079e-03   2.20810656e-02]\n",
      "2: [ 0.90711001  0.60821182  0.24320819  0.         -0.04818171  0.          0.\n",
      "  0.          0.          0.          0.          0.          0.01791005\n",
      "  0.12853494 -0.01275902 -0.10884508  0.00200979  0.02208107]\n",
      "\n",
      "1: [  9.07110006e-01   6.08211818e-01   2.43208194e-01   1.54202407e-13\n",
      "  -4.81817128e-02  -2.28755409e-14  -1.02648883e-14   6.22123011e-16\n",
      "   4.65368581e-16  -6.73926950e-17   0.00000000e+00   0.00000000e+00\n",
      "   1.79100530e-02   1.28534944e-01  -1.27590200e-02  -1.08845077e-01\n",
      "   2.00979079e-03   2.20810656e-02]\n",
      "1: [ 0.90711001  0.60821182  0.24320819  0.         -0.04818171  0.          0.\n",
      "  0.          0.          0.          0.          0.          0.01791005\n",
      "  0.12853494 -0.01275902 -0.10884508  0.00200979  0.02208107]\n",
      "\n",
      "5: [  0.00000000e+00  -4.90804007e-06   2.11512041e-02  -6.56657899e-17\n",
      "  -3.31445941e-03  -2.43035600e-17   6.11573638e-18  -1.15824563e-17\n",
      "   1.15824563e-17   0.00000000e+00   1.19159785e-49   4.73131773e-45\n",
      "  -4.80411563e-02   6.15658343e-02   4.01965764e-02  -5.07721784e-02\n",
      "  -8.16513718e-03   9.82236688e-03]\n",
      "5: 3.81253968219727e+17\n",
      "10: [  1.05027673e+00  -1.38727734e+00   1.21036607e-01  -8.68730720e-01\n",
      "  -2.33969022e-02  -1.43550632e-01   2.60381994e-14   3.23838178e-14\n",
      "  -1.15463195e-14  -1.78190795e-14   8.32667268e-16   2.32106001e-15\n",
      "   5.50707091e-02   1.97909237e-02  -4.41281400e-02  -1.63901637e-02\n",
      "   8.47027563e-03   3.22817548e-03]\n",
      "10: [ 1.05027673 -1.38727734  0.12103661 -0.86873072 -0.0233969  -0.14355063\n",
      "  0.          0.          0.          0.          0.          0.\n",
      "  0.05507071  0.01979092 -0.04412814 -0.01639016  0.00847028  0.00322818]\n",
      "\n",
      "9: [  9.07110006e-01   6.08211818e-01   2.43208194e-01   1.54202407e-13\n",
      "  -4.81817128e-02  -2.28755409e-14  -1.02648883e-14   6.22123011e-16\n",
      "   4.65368581e-16  -6.73926950e-17   0.00000000e+00   0.00000000e+00\n",
      "   1.79100530e-02   1.28534944e-01  -1.27590200e-02  -1.08845077e-01\n",
      "   2.00979079e-03   2.20810656e-02]\n",
      "9: [ 0.90711001  0.60821182  0.24320819  0.         -0.04818171  0.          0.\n",
      "  0.          0.          0.          0.          0.          0.01791005\n",
      "  0.12853494 -0.01275902 -0.10884508  0.00200979  0.02208107]\n",
      "\n",
      "8: [  9.07110006e-01   6.08211818e-01   2.43208194e-01   1.54202407e-13\n",
      "  -4.81817128e-02  -2.28755409e-14  -1.02648883e-14   6.22123011e-16\n",
      "   4.65368581e-16  -6.73926950e-17   0.00000000e+00   0.00000000e+00\n",
      "   1.79100530e-02   1.28534944e-01  -1.27590200e-02  -1.08845077e-01\n",
      "   2.00979079e-03   2.20810656e-02]\n",
      "8: [ 0.90711001  0.60821182  0.24320819  0.         -0.04818171  0.          0.\n",
      "  0.          0.          0.          0.          0.          0.01791005\n",
      "  0.12853494 -0.01275902 -0.10884508  0.00200979  0.02208107]\n",
      "\n",
      "7: [  9.07110006e-01   6.08211818e-01   2.43208194e-01   1.54202407e-13\n",
      "  -4.81817128e-02  -2.28755409e-14  -1.02648883e-14   6.22123011e-16\n",
      "   4.65368581e-16  -6.73926950e-17   0.00000000e+00   0.00000000e+00\n",
      "   1.79100530e-02   1.28534944e-01  -1.27590200e-02  -1.08845077e-01\n",
      "   2.00979079e-03   2.20810656e-02]\n",
      "7: [ 0.90711001  0.60821182  0.24320819  0.         -0.04818171  0.          0.\n",
      "  0.          0.          0.          0.          0.          0.01791005\n",
      "  0.12853494 -0.01275902 -0.10884508  0.00200979  0.02208107]\n",
      "\n",
      "6: [  9.07110006e-01   6.08211818e-01   2.43208194e-01   1.54202407e-13\n",
      "  -4.81817128e-02  -2.28755409e-14  -1.02648883e-14   6.22123011e-16\n",
      "   4.65368581e-16  -6.73926950e-17   0.00000000e+00   0.00000000e+00\n",
      "   1.79100530e-02   1.28534944e-01  -1.27590200e-02  -1.08845077e-01\n",
      "   2.00979079e-03   2.20810656e-02]\n",
      "6: [ 0.90711001  0.60821182  0.24320819  0.         -0.04818171  0.          0.\n",
      "  0.          0.          0.          0.          0.          0.01791005\n",
      "  0.12853494 -0.01275902 -0.10884508  0.00200979  0.02208107]\n",
      "\n",
      "5: [  9.07110006e-01   6.08211818e-01   2.43208194e-01   1.54202407e-13\n",
      "  -4.81817128e-02  -2.28755409e-14  -1.02648883e-14   6.22123011e-16\n",
      "   4.65368581e-16  -6.73926950e-17   0.00000000e+00   0.00000000e+00\n",
      "   1.79100530e-02   1.28534944e-01  -1.27590200e-02  -1.08845077e-01\n",
      "   2.00979079e-03   2.20810656e-02]\n",
      "5: [ 0.90711001  0.60821182  0.24320819  0.         -0.04818171  0.          0.\n",
      "  0.          0.          0.          0.          0.          0.01791005\n",
      "  0.12853494 -0.01275902 -0.10884508  0.00200979  0.02208107]\n",
      "\n",
      "4: [  9.07110006e-01   6.08211818e-01   2.43208194e-01   1.54202407e-13\n",
      "  -4.81817128e-02  -2.28755409e-14  -1.02648883e-14   6.22123011e-16\n",
      "   4.65368581e-16  -6.73926950e-17   0.00000000e+00   0.00000000e+00\n",
      "   1.79100530e-02   1.28534944e-01  -1.27590200e-02  -1.08845077e-01\n",
      "   2.00979079e-03   2.20810656e-02]\n",
      "4: [ 0.90711001  0.60821182  0.24320819  0.         -0.04818171  0.          0.\n",
      "  0.          0.          0.          0.          0.          0.01791005\n",
      "  0.12853494 -0.01275902 -0.10884508  0.00200979  0.02208107]\n",
      "\n",
      "3: [  9.07110006e-01   6.08211818e-01   2.43208194e-01   1.54202407e-13\n",
      "  -4.81817128e-02  -2.28755409e-14  -1.02648883e-14   6.22123011e-16\n",
      "   4.65368581e-16  -6.73926950e-17   0.00000000e+00   0.00000000e+00\n",
      "   1.79100530e-02   1.28534944e-01  -1.27590200e-02  -1.08845077e-01\n",
      "   2.00979079e-03   2.20810656e-02]\n",
      "3: [ 0.90711001  0.60821182  0.24320819  0.         -0.04818171  0.          0.\n",
      "  0.          0.          0.          0.          0.          0.01791005\n",
      "  0.12853494 -0.01275902 -0.10884508  0.00200979  0.02208107]\n",
      "\n",
      "2: [  9.07110006e-01   6.08211818e-01   2.43208194e-01   1.54202407e-13\n",
      "  -4.81817128e-02  -2.28755409e-14  -1.02648883e-14   6.22123011e-16\n",
      "   4.65368581e-16  -6.73926950e-17   0.00000000e+00   0.00000000e+00\n",
      "   1.79100530e-02   1.28534944e-01  -1.27590200e-02  -1.08845077e-01\n",
      "   2.00979079e-03   2.20810656e-02]\n",
      "2: [ 0.90711001  0.60821182  0.24320819  0.         -0.04818171  0.          0.\n",
      "  0.          0.          0.          0.          0.          0.01791005\n",
      "  0.12853494 -0.01275902 -0.10884508  0.00200979  0.02208107]\n",
      "\n",
      "1: [  9.07110006e-01   6.08211818e-01   2.43208194e-01   1.54202407e-13\n",
      "  -4.81817128e-02  -2.28755409e-14  -1.02648883e-14   6.22123011e-16\n",
      "   4.65368581e-16  -6.73926950e-17   0.00000000e+00   0.00000000e+00\n",
      "   1.79100530e-02   1.28534944e-01  -1.27590200e-02  -1.08845077e-01\n",
      "   2.00979079e-03   2.20810656e-02]\n",
      "1: [ 0.90711001  0.60821182  0.24320819  0.         -0.04818171  0.          0.\n",
      "  0.          0.          0.          0.          0.          0.01791005\n",
      "  0.12853494 -0.01275902 -0.10884508  0.00200979  0.02208107]\n",
      "\n",
      "6: [  0.00000000e+00  -4.90804007e-06   2.11512041e-02  -6.56657899e-17\n",
      "  -3.31445941e-03  -2.43035600e-17   6.11573638e-18  -1.15824563e-17\n",
      "   1.15824563e-17   0.00000000e+00   1.19159785e-49   4.73131773e-45\n",
      "  -4.80411563e-02   6.15658343e-02   4.01965764e-02  -5.07721784e-02\n",
      "  -8.16513718e-03   9.82236688e-03]\n",
      "6: 3.81253968219727e+17\n",
      "10: [  1.05027673e+00  -1.38727734e+00   1.21036607e-01  -8.68730720e-01\n",
      "  -2.33969022e-02  -1.43550632e-01   2.60381994e-14   3.23838178e-14\n",
      "  -1.15463195e-14  -1.78190795e-14   8.32667268e-16   2.32106001e-15\n",
      "   5.50707091e-02   1.97909237e-02  -4.41281400e-02  -1.63901637e-02\n",
      "   8.47027563e-03   3.22817548e-03]\n",
      "10: [ 1.05027673 -1.38727734  0.12103661 -0.86873072 -0.0233969  -0.14355063\n",
      "  0.          0.          0.          0.          0.          0.\n",
      "  0.05507071  0.01979092 -0.04412814 -0.01639016  0.00847028  0.00322818]\n",
      "\n",
      "9: [  9.07110006e-01   6.08211818e-01   2.43208194e-01   1.54202407e-13\n",
      "  -4.81817128e-02  -2.28755409e-14  -1.02648883e-14   6.22123011e-16\n",
      "   4.65368581e-16  -6.73926950e-17   0.00000000e+00   0.00000000e+00\n",
      "   1.79100530e-02   1.28534944e-01  -1.27590200e-02  -1.08845077e-01\n",
      "   2.00979079e-03   2.20810656e-02]\n",
      "9: [ 0.90711001  0.60821182  0.24320819  0.         -0.04818171  0.          0.\n",
      "  0.          0.          0.          0.          0.          0.01791005\n",
      "  0.12853494 -0.01275902 -0.10884508  0.00200979  0.02208107]\n",
      "\n",
      "8: [  9.07110006e-01   6.08211818e-01   2.43208194e-01   1.54202407e-13\n",
      "  -4.81817128e-02  -2.28755409e-14  -1.02648883e-14   6.22123011e-16\n",
      "   4.65368581e-16  -6.73926950e-17   0.00000000e+00   0.00000000e+00\n",
      "   1.79100530e-02   1.28534944e-01  -1.27590200e-02  -1.08845077e-01\n",
      "   2.00979079e-03   2.20810656e-02]\n",
      "8: [ 0.90711001  0.60821182  0.24320819  0.         -0.04818171  0.          0.\n",
      "  0.          0.          0.          0.          0.          0.01791005\n",
      "  0.12853494 -0.01275902 -0.10884508  0.00200979  0.02208107]\n",
      "\n",
      "7: [  9.07110006e-01   6.08211818e-01   2.43208194e-01   1.54202407e-13\n",
      "  -4.81817128e-02  -2.28755409e-14  -1.02648883e-14   6.22123011e-16\n",
      "   4.65368581e-16  -6.73926950e-17   0.00000000e+00   0.00000000e+00\n",
      "   1.79100530e-02   1.28534944e-01  -1.27590200e-02  -1.08845077e-01\n",
      "   2.00979079e-03   2.20810656e-02]\n",
      "7: [ 0.90711001  0.60821182  0.24320819  0.         -0.04818171  0.          0.\n",
      "  0.          0.          0.          0.          0.          0.01791005\n",
      "  0.12853494 -0.01275902 -0.10884508  0.00200979  0.02208107]\n",
      "\n",
      "6: [  9.07110006e-01   6.08211818e-01   2.43208194e-01   1.54202407e-13\n",
      "  -4.81817128e-02  -2.28755409e-14  -1.02648883e-14   6.22123011e-16\n",
      "   4.65368581e-16  -6.73926950e-17   0.00000000e+00   0.00000000e+00\n",
      "   1.79100530e-02   1.28534944e-01  -1.27590200e-02  -1.08845077e-01\n",
      "   2.00979079e-03   2.20810656e-02]\n",
      "6: [ 0.90711001  0.60821182  0.24320819  0.         -0.04818171  0.          0.\n",
      "  0.          0.          0.          0.          0.          0.01791005\n",
      "  0.12853494 -0.01275902 -0.10884508  0.00200979  0.02208107]\n",
      "\n",
      "5: [  9.07110006e-01   6.08211818e-01   2.43208194e-01   1.54202407e-13\n",
      "  -4.81817128e-02  -2.28755409e-14  -1.02648883e-14   6.22123011e-16\n",
      "   4.65368581e-16  -6.73926950e-17   0.00000000e+00   0.00000000e+00\n",
      "   1.79100530e-02   1.28534944e-01  -1.27590200e-02  -1.08845077e-01\n",
      "   2.00979079e-03   2.20810656e-02]\n",
      "5: [ 0.90711001  0.60821182  0.24320819  0.         -0.04818171  0.          0.\n",
      "  0.          0.          0.          0.          0.          0.01791005\n",
      "  0.12853494 -0.01275902 -0.10884508  0.00200979  0.02208107]\n",
      "\n",
      "4: [  9.07110006e-01   6.08211818e-01   2.43208194e-01   1.54202407e-13\n",
      "  -4.81817128e-02  -2.28755409e-14  -1.02648883e-14   6.22123011e-16\n",
      "   4.65368581e-16  -6.73926950e-17   0.00000000e+00   0.00000000e+00\n",
      "   1.79100530e-02   1.28534944e-01  -1.27590200e-02  -1.08845077e-01\n",
      "   2.00979079e-03   2.20810656e-02]\n",
      "4: [ 0.90711001  0.60821182  0.24320819  0.         -0.04818171  0.          0.\n",
      "  0.          0.          0.          0.          0.          0.01791005\n",
      "  0.12853494 -0.01275902 -0.10884508  0.00200979  0.02208107]\n",
      "\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "3: [  9.07110006e-01   6.08211818e-01   2.43208194e-01   1.54202407e-13\n",
      "  -4.81817128e-02  -2.28755409e-14  -1.02648883e-14   6.22123011e-16\n",
      "   4.65368581e-16  -6.73926950e-17   0.00000000e+00   0.00000000e+00\n",
      "   1.79100530e-02   1.28534944e-01  -1.27590200e-02  -1.08845077e-01\n",
      "   2.00979079e-03   2.20810656e-02]\n",
      "3: [ 0.90711001  0.60821182  0.24320819  0.         -0.04818171  0.          0.\n",
      "  0.          0.          0.          0.          0.          0.01791005\n",
      "  0.12853494 -0.01275902 -0.10884508  0.00200979  0.02208107]\n",
      "\n",
      "2: [  9.07110006e-01   6.08211818e-01   2.43208194e-01   1.54202407e-13\n",
      "  -4.81817128e-02  -2.28755409e-14  -1.02648883e-14   6.22123011e-16\n",
      "   4.65368581e-16  -6.73926950e-17   0.00000000e+00   0.00000000e+00\n",
      "   1.79100530e-02   1.28534944e-01  -1.27590200e-02  -1.08845077e-01\n",
      "   2.00979079e-03   2.20810656e-02]\n",
      "2: [ 0.90711001  0.60821182  0.24320819  0.         -0.04818171  0.          0.\n",
      "  0.          0.          0.          0.          0.          0.01791005\n",
      "  0.12853494 -0.01275902 -0.10884508  0.00200979  0.02208107]\n",
      "\n",
      "1: [  9.07110006e-01   6.08211818e-01   2.43208194e-01   1.54202407e-13\n",
      "  -4.81817128e-02  -2.28755409e-14  -1.02648883e-14   6.22123011e-16\n",
      "   4.65368581e-16  -6.73926950e-17   0.00000000e+00   0.00000000e+00\n",
      "   1.79100530e-02   1.28534944e-01  -1.27590200e-02  -1.08845077e-01\n",
      "   2.00979079e-03   2.20810656e-02]\n",
      "1: [ 0.90711001  0.60821182  0.24320819  0.         -0.04818171  0.          0.\n",
      "  0.          0.          0.          0.          0.          0.01791005\n",
      "  0.12853494 -0.01275902 -0.10884508  0.00200979  0.02208107]\n",
      "\n",
      "7: [  0.00000000e+00  -4.90804007e-06   2.11512041e-02  -6.56657899e-17\n",
      "  -3.31445941e-03  -2.43035600e-17   6.11573638e-18  -1.15824563e-17\n",
      "   1.15824563e-17   0.00000000e+00   1.19159785e-49   4.73131773e-45\n",
      "  -4.80411563e-02   6.15658343e-02   4.01965764e-02  -5.07721784e-02\n",
      "  -8.16513718e-03   9.82236688e-03]\n",
      "7: 3.81253968219727e+17\n",
      "10: [  1.05027673e+00  -1.38727734e+00   1.21036607e-01  -8.68730720e-01\n",
      "  -2.33969022e-02  -1.43550632e-01   2.60381994e-14   3.23838178e-14\n",
      "  -1.15463195e-14  -1.78190795e-14   8.32667268e-16   2.32106001e-15\n",
      "   5.50707091e-02   1.97909237e-02  -4.41281400e-02  -1.63901637e-02\n",
      "   8.47027563e-03   3.22817548e-03]\n",
      "10: [ 1.05027673 -1.38727734  0.12103661 -0.86873072 -0.0233969  -0.14355063\n",
      "  0.          0.          0.          0.          0.          0.\n",
      "  0.05507071  0.01979092 -0.04412814 -0.01639016  0.00847028  0.00322818]\n",
      "\n",
      "9: [  9.07110006e-01   6.08211818e-01   2.43208194e-01   1.54202407e-13\n",
      "  -4.81817128e-02  -2.28755409e-14  -1.02648883e-14   6.22123011e-16\n",
      "   4.65368581e-16  -6.73926950e-17   0.00000000e+00   0.00000000e+00\n",
      "   1.79100530e-02   1.28534944e-01  -1.27590200e-02  -1.08845077e-01\n",
      "   2.00979079e-03   2.20810656e-02]\n",
      "9: [ 0.90711001  0.60821182  0.24320819  0.         -0.04818171  0.          0.\n",
      "  0.          0.          0.          0.          0.          0.01791005\n",
      "  0.12853494 -0.01275902 -0.10884508  0.00200979  0.02208107]\n",
      "\n",
      "8: [  9.07110006e-01   6.08211818e-01   2.43208194e-01   1.54202407e-13\n",
      "  -4.81817128e-02  -2.28755409e-14  -1.02648883e-14   6.22123011e-16\n",
      "   4.65368581e-16  -6.73926950e-17   0.00000000e+00   0.00000000e+00\n",
      "   1.79100530e-02   1.28534944e-01  -1.27590200e-02  -1.08845077e-01\n",
      "   2.00979079e-03   2.20810656e-02]\n",
      "8: [ 0.90711001  0.60821182  0.24320819  0.         -0.04818171  0.          0.\n",
      "  0.          0.          0.          0.          0.          0.01791005\n",
      "  0.12853494 -0.01275902 -0.10884508  0.00200979  0.02208107]\n",
      "\n",
      "7: [  9.07110006e-01   6.08211818e-01   2.43208194e-01   1.54202407e-13\n",
      "  -4.81817128e-02  -2.28755409e-14  -1.02648883e-14   6.22123011e-16\n",
      "   4.65368581e-16  -6.73926950e-17   0.00000000e+00   0.00000000e+00\n",
      "   1.79100530e-02   1.28534944e-01  -1.27590200e-02  -1.08845077e-01\n",
      "   2.00979079e-03   2.20810656e-02]\n",
      "7: [ 0.90711001  0.60821182  0.24320819  0.         -0.04818171  0.          0.\n",
      "  0.          0.          0.          0.          0.          0.01791005\n",
      "  0.12853494 -0.01275902 -0.10884508  0.00200979  0.02208107]\n",
      "\n",
      "6: [  9.07110006e-01   6.08211818e-01   2.43208194e-01   1.54202407e-13\n",
      "  -4.81817128e-02  -2.28755409e-14  -1.02648883e-14   6.22123011e-16\n",
      "   4.65368581e-16  -6.73926950e-17   0.00000000e+00   0.00000000e+00\n",
      "   1.79100530e-02   1.28534944e-01  -1.27590200e-02  -1.08845077e-01\n",
      "   2.00979079e-03   2.20810656e-02]\n",
      "6: [ 0.90711001  0.60821182  0.24320819  0.         -0.04818171  0.          0.\n",
      "  0.          0.          0.          0.          0.          0.01791005\n",
      "  0.12853494 -0.01275902 -0.10884508  0.00200979  0.02208107]\n",
      "\n",
      "5: [  9.07110006e-01   6.08211818e-01   2.43208194e-01   1.54202407e-13\n",
      "  -4.81817128e-02  -2.28755409e-14  -1.02648883e-14   6.22123011e-16\n",
      "   4.65368581e-16  -6.73926950e-17   0.00000000e+00   0.00000000e+00\n",
      "   1.79100530e-02   1.28534944e-01  -1.27590200e-02  -1.08845077e-01\n",
      "   2.00979079e-03   2.20810656e-02]\n",
      "5: [ 0.90711001  0.60821182  0.24320819  0.         -0.04818171  0.          0.\n",
      "  0.          0.          0.          0.          0.          0.01791005\n",
      "  0.12853494 -0.01275902 -0.10884508  0.00200979  0.02208107]\n",
      "\n",
      "4: [  9.07110006e-01   6.08211818e-01   2.43208194e-01   1.54202407e-13\n",
      "  -4.81817128e-02  -2.28755409e-14  -1.02648883e-14   6.22123011e-16\n",
      "   4.65368581e-16  -6.73926950e-17   0.00000000e+00   0.00000000e+00\n",
      "   1.79100530e-02   1.28534944e-01  -1.27590200e-02  -1.08845077e-01\n",
      "   2.00979079e-03   2.20810656e-02]\n",
      "4: [ 0.90711001  0.60821182  0.24320819  0.         -0.04818171  0.          0.\n",
      "  0.          0.          0.          0.          0.          0.01791005\n",
      "  0.12853494 -0.01275902 -0.10884508  0.00200979  0.02208107]\n",
      "\n",
      "3: [  9.07110006e-01   6.08211818e-01   2.43208194e-01   1.54202407e-13\n",
      "  -4.81817128e-02  -2.28755409e-14  -1.02648883e-14   6.22123011e-16\n",
      "   4.65368581e-16  -6.73926950e-17   0.00000000e+00   0.00000000e+00\n",
      "   1.79100530e-02   1.28534944e-01  -1.27590200e-02  -1.08845077e-01\n",
      "   2.00979079e-03   2.20810656e-02]\n",
      "3: [ 0.90711001  0.60821182  0.24320819  0.         -0.04818171  0.          0.\n",
      "  0.          0.          0.          0.          0.          0.01791005\n",
      "  0.12853494 -0.01275902 -0.10884508  0.00200979  0.02208107]\n",
      "\n",
      "2: [  9.07110006e-01   6.08211818e-01   2.43208194e-01   1.54202407e-13\n",
      "  -4.81817128e-02  -2.28755409e-14  -1.02648883e-14   6.22123011e-16\n",
      "   4.65368581e-16  -6.73926950e-17   0.00000000e+00   0.00000000e+00\n",
      "   1.79100530e-02   1.28534944e-01  -1.27590200e-02  -1.08845077e-01\n",
      "   2.00979079e-03   2.20810656e-02]\n",
      "2: [ 0.90711001  0.60821182  0.24320819  0.         -0.04818171  0.          0.\n",
      "  0.          0.          0.          0.          0.          0.01791005\n",
      "  0.12853494 -0.01275902 -0.10884508  0.00200979  0.02208107]\n",
      "\n",
      "1: [  9.07110006e-01   6.08211818e-01   2.43208194e-01   1.54202407e-13\n",
      "  -4.81817128e-02  -2.28755409e-14  -1.02648883e-14   6.22123011e-16\n",
      "   4.65368581e-16  -6.73926950e-17   0.00000000e+00   0.00000000e+00\n",
      "   1.79100530e-02   1.28534944e-01  -1.27590200e-02  -1.08845077e-01\n",
      "   2.00979079e-03   2.20810656e-02]\n",
      "1: [ 0.90711001  0.60821182  0.24320819  0.         -0.04818171  0.          0.\n",
      "  0.          0.          0.          0.          0.          0.01791005\n",
      "  0.12853494 -0.01275902 -0.10884508  0.00200979  0.02208107]\n",
      "\n",
      "8: [  0.00000000e+00  -4.90804007e-06   2.11512041e-02  -6.56657899e-17\n",
      "  -3.31445941e-03  -2.43035600e-17   6.11573638e-18  -1.15824563e-17\n",
      "   1.15824563e-17   0.00000000e+00   1.19159785e-49   4.73131773e-45\n",
      "  -4.80411563e-02   6.15658343e-02   4.01965764e-02  -5.07721784e-02\n",
      "  -8.16513718e-03   9.82236688e-03]\n",
      "8: 3.81253968219727e+17\n",
      "10: [  1.05027673e+00  -1.38727734e+00   1.21036607e-01  -8.68730720e-01\n",
      "  -2.33969022e-02  -1.43550632e-01   2.60381994e-14   3.23838178e-14\n",
      "  -1.15463195e-14  -1.78190795e-14   8.32667268e-16   2.32106001e-15\n",
      "   5.50707091e-02   1.97909237e-02  -4.41281400e-02  -1.63901637e-02\n",
      "   8.47027563e-03   3.22817548e-03]\n",
      "10: [ 1.05027673 -1.38727734  0.12103661 -0.86873072 -0.0233969  -0.14355063\n",
      "  0.          0.          0.          0.          0.          0.\n",
      "  0.05507071  0.01979092 -0.04412814 -0.01639016  0.00847028  0.00322818]\n",
      "\n",
      "9: [  9.07110006e-01   6.08211818e-01   2.43208194e-01   1.54202407e-13\n",
      "  -4.81817128e-02  -2.28755409e-14  -1.02648883e-14   6.22123011e-16\n",
      "   4.65368581e-16  -6.73926950e-17   0.00000000e+00   0.00000000e+00\n",
      "   1.79100530e-02   1.28534944e-01  -1.27590200e-02  -1.08845077e-01\n",
      "   2.00979079e-03   2.20810656e-02]\n",
      "9: [ 0.90711001  0.60821182  0.24320819  0.         -0.04818171  0.          0.\n",
      "  0.          0.          0.          0.          0.          0.01791005\n",
      "  0.12853494 -0.01275902 -0.10884508  0.00200979  0.02208107]\n",
      "\n",
      "8: [  9.07110006e-01   6.08211818e-01   2.43208194e-01   1.54202407e-13\n",
      "  -4.81817128e-02  -2.28755409e-14  -1.02648883e-14   6.22123011e-16\n",
      "   4.65368581e-16  -6.73926950e-17   0.00000000e+00   0.00000000e+00\n",
      "   1.79100530e-02   1.28534944e-01  -1.27590200e-02  -1.08845077e-01\n",
      "   2.00979079e-03   2.20810656e-02]\n",
      "8: [ 0.90711001  0.60821182  0.24320819  0.         -0.04818171  0.          0.\n",
      "  0.          0.          0.          0.          0.          0.01791005\n",
      "  0.12853494 -0.01275902 -0.10884508  0.00200979  0.02208107]\n",
      "\n",
      "7: [  9.07110006e-01   6.08211818e-01   2.43208194e-01   1.54202407e-13\n",
      "  -4.81817128e-02  -2.28755409e-14  -1.02648883e-14   6.22123011e-16\n",
      "   4.65368581e-16  -6.73926950e-17   0.00000000e+00   0.00000000e+00\n",
      "   1.79100530e-02   1.28534944e-01  -1.27590200e-02  -1.08845077e-01\n",
      "   2.00979079e-03   2.20810656e-02]\n",
      "7: [ 0.90711001  0.60821182  0.24320819  0.         -0.04818171  0.          0.\n",
      "  0.          0.          0.          0.          0.          0.01791005\n",
      "  0.12853494 -0.01275902 -0.10884508  0.00200979  0.02208107]\n",
      "\n",
      "6: [  9.07110006e-01   6.08211818e-01   2.43208194e-01   1.54202407e-13\n",
      "  -4.81817128e-02  -2.28755409e-14  -1.02648883e-14   6.22123011e-16\n",
      "   4.65368581e-16  -6.73926950e-17   0.00000000e+00   0.00000000e+00\n",
      "   1.79100530e-02   1.28534944e-01  -1.27590200e-02  -1.08845077e-01\n",
      "   2.00979079e-03   2.20810656e-02]\n",
      "6: [ 0.90711001  0.60821182  0.24320819  0.         -0.04818171  0.          0.\n",
      "  0.          0.          0.          0.          0.          0.01791005\n",
      "  0.12853494 -0.01275902 -0.10884508  0.00200979  0.02208107]\n",
      "\n",
      "5: [  9.07110006e-01   6.08211818e-01   2.43208194e-01   1.54202407e-13\n",
      "  -4.81817128e-02  -2.28755409e-14  -1.02648883e-14   6.22123011e-16\n",
      "   4.65368581e-16  -6.73926950e-17   0.00000000e+00   0.00000000e+00\n",
      "   1.79100530e-02   1.28534944e-01  -1.27590200e-02  -1.08845077e-01\n",
      "   2.00979079e-03   2.20810656e-02]\n",
      "5: [ 0.90711001  0.60821182  0.24320819  0.         -0.04818171  0.          0.\n",
      "  0.          0.          0.          0.          0.          0.01791005\n",
      "  0.12853494 -0.01275902 -0.10884508  0.00200979  0.02208107]\n",
      "\n",
      "4: [  9.07110006e-01   6.08211818e-01   2.43208194e-01   1.54202407e-13\n",
      "  -4.81817128e-02  -2.28755409e-14  -1.02648883e-14   6.22123011e-16\n",
      "   4.65368581e-16  -6.73926950e-17   0.00000000e+00   0.00000000e+00\n",
      "   1.79100530e-02   1.28534944e-01  -1.27590200e-02  -1.08845077e-01\n",
      "   2.00979079e-03   2.20810656e-02]\n",
      "4: [ 0.90711001  0.60821182  0.24320819  0.         -0.04818171  0.          0.\n",
      "  0.          0.          0.          0.          0.          0.01791005\n",
      "  0.12853494 -0.01275902 -0.10884508  0.00200979  0.02208107]\n",
      "\n",
      "3: [  9.07110006e-01   6.08211818e-01   2.43208194e-01   1.54202407e-13\n",
      "  -4.81817128e-02  -2.28755409e-14  -1.02648883e-14   6.22123011e-16\n",
      "   4.65368581e-16  -6.73926950e-17   0.00000000e+00   0.00000000e+00\n",
      "   1.79100530e-02   1.28534944e-01  -1.27590200e-02  -1.08845077e-01\n",
      "   2.00979079e-03   2.20810656e-02]\n",
      "3: [ 0.90711001  0.60821182  0.24320819  0.         -0.04818171  0.          0.\n",
      "  0.          0.          0.          0.          0.          0.01791005\n",
      "  0.12853494 -0.01275902 -0.10884508  0.00200979  0.02208107]\n",
      "\n",
      "2: [  9.07110006e-01   6.08211818e-01   2.43208194e-01   1.54202407e-13\n",
      "  -4.81817128e-02  -2.28755409e-14  -1.02648883e-14   6.22123011e-16\n",
      "   4.65368581e-16  -6.73926950e-17   0.00000000e+00   0.00000000e+00\n",
      "   1.79100530e-02   1.28534944e-01  -1.27590200e-02  -1.08845077e-01\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "   2.00979079e-03   2.20810656e-02]\n",
      "2: [ 0.90711001  0.60821182  0.24320819  0.         -0.04818171  0.          0.\n",
      "  0.          0.          0.          0.          0.          0.01791005\n",
      "  0.12853494 -0.01275902 -0.10884508  0.00200979  0.02208107]\n",
      "\n",
      "1: [  9.07110006e-01   6.08211818e-01   2.43208194e-01   1.54202407e-13\n",
      "  -4.81817128e-02  -2.28755409e-14  -1.02648883e-14   6.22123011e-16\n",
      "   4.65368581e-16  -6.73926950e-17   0.00000000e+00   0.00000000e+00\n",
      "   1.79100530e-02   1.28534944e-01  -1.27590200e-02  -1.08845077e-01\n",
      "   2.00979079e-03   2.20810656e-02]\n",
      "1: [ 0.90711001  0.60821182  0.24320819  0.         -0.04818171  0.          0.\n",
      "  0.          0.          0.          0.          0.          0.01791005\n",
      "  0.12853494 -0.01275902 -0.10884508  0.00200979  0.02208107]\n",
      "\n",
      "9: [  0.00000000e+00  -4.90804007e-06   2.11512041e-02  -6.56657899e-17\n",
      "  -3.31445941e-03  -2.43035600e-17   6.11573638e-18  -1.15824563e-17\n",
      "   1.15824563e-17   0.00000000e+00   1.19159785e-49   4.73131773e-45\n",
      "  -4.80411563e-02   6.15658343e-02   4.01965764e-02  -5.07721784e-02\n",
      "  -8.16513718e-03   9.82236688e-03]\n",
      "9: 3.81253968219727e+17\n",
      "10: [  1.05027673e+00  -1.38727734e+00   1.21036607e-01  -8.68730720e-01\n",
      "  -2.33969022e-02  -1.43550632e-01   2.60381994e-14   3.23838178e-14\n",
      "  -1.15463195e-14  -1.78190795e-14   8.32667268e-16   2.32106001e-15\n",
      "   5.50707091e-02   1.97909237e-02  -4.41281400e-02  -1.63901637e-02\n",
      "   8.47027563e-03   3.22817548e-03]\n",
      "10: [ 1.05027673 -1.38727734  0.12103661 -0.86873072 -0.0233969  -0.14355063\n",
      "  0.          0.          0.          0.          0.          0.\n",
      "  0.05507071  0.01979092 -0.04412814 -0.01639016  0.00847028  0.00322818]\n",
      "\n",
      "9: [  9.07110006e-01   6.08211818e-01   2.43208194e-01   1.54202407e-13\n",
      "  -4.81817128e-02  -2.28755409e-14  -1.02648883e-14   6.22123011e-16\n",
      "   4.65368581e-16  -6.73926950e-17   0.00000000e+00   0.00000000e+00\n",
      "   1.79100530e-02   1.28534944e-01  -1.27590200e-02  -1.08845077e-01\n",
      "   2.00979079e-03   2.20810656e-02]\n",
      "9: [ 0.90711001  0.60821182  0.24320819  0.         -0.04818171  0.          0.\n",
      "  0.          0.          0.          0.          0.          0.01791005\n",
      "  0.12853494 -0.01275902 -0.10884508  0.00200979  0.02208107]\n",
      "\n",
      "8: [  9.07110006e-01   6.08211818e-01   2.43208194e-01   1.54202407e-13\n",
      "  -4.81817128e-02  -2.28755409e-14  -1.02648883e-14   6.22123011e-16\n",
      "   4.65368581e-16  -6.73926950e-17   0.00000000e+00   0.00000000e+00\n",
      "   1.79100530e-02   1.28534944e-01  -1.27590200e-02  -1.08845077e-01\n",
      "   2.00979079e-03   2.20810656e-02]\n",
      "8: [ 0.90711001  0.60821182  0.24320819  0.         -0.04818171  0.          0.\n",
      "  0.          0.          0.          0.          0.          0.01791005\n",
      "  0.12853494 -0.01275902 -0.10884508  0.00200979  0.02208107]\n",
      "\n",
      "7: [  9.07110006e-01   6.08211818e-01   2.43208194e-01   1.54202407e-13\n",
      "  -4.81817128e-02  -2.28755409e-14  -1.02648883e-14   6.22123011e-16\n",
      "   4.65368581e-16  -6.73926950e-17   0.00000000e+00   0.00000000e+00\n",
      "   1.79100530e-02   1.28534944e-01  -1.27590200e-02  -1.08845077e-01\n",
      "   2.00979079e-03   2.20810656e-02]\n",
      "7: [ 0.90711001  0.60821182  0.24320819  0.         -0.04818171  0.          0.\n",
      "  0.          0.          0.          0.          0.          0.01791005\n",
      "  0.12853494 -0.01275902 -0.10884508  0.00200979  0.02208107]\n",
      "\n",
      "6: [  9.07110006e-01   6.08211818e-01   2.43208194e-01   1.54202407e-13\n",
      "  -4.81817128e-02  -2.28755409e-14  -1.02648883e-14   6.22123011e-16\n",
      "   4.65368581e-16  -6.73926950e-17   0.00000000e+00   0.00000000e+00\n",
      "   1.79100530e-02   1.28534944e-01  -1.27590200e-02  -1.08845077e-01\n",
      "   2.00979079e-03   2.20810656e-02]\n",
      "6: [ 0.90711001  0.60821182  0.24320819  0.         -0.04818171  0.          0.\n",
      "  0.          0.          0.          0.          0.          0.01791005\n",
      "  0.12853494 -0.01275902 -0.10884508  0.00200979  0.02208107]\n",
      "\n",
      "5: [  9.07110006e-01   6.08211818e-01   2.43208194e-01   1.54202407e-13\n",
      "  -4.81817128e-02  -2.28755409e-14  -1.02648883e-14   6.22123011e-16\n",
      "   4.65368581e-16  -6.73926950e-17   0.00000000e+00   0.00000000e+00\n",
      "   1.79100530e-02   1.28534944e-01  -1.27590200e-02  -1.08845077e-01\n",
      "   2.00979079e-03   2.20810656e-02]\n",
      "5: [ 0.90711001  0.60821182  0.24320819  0.         -0.04818171  0.          0.\n",
      "  0.          0.          0.          0.          0.          0.01791005\n",
      "  0.12853494 -0.01275902 -0.10884508  0.00200979  0.02208107]\n",
      "\n",
      "4: [  9.07110006e-01   6.08211818e-01   2.43208194e-01   1.54202407e-13\n",
      "  -4.81817128e-02  -2.28755409e-14  -1.02648883e-14   6.22123011e-16\n",
      "   4.65368581e-16  -6.73926950e-17   0.00000000e+00   0.00000000e+00\n",
      "   1.79100530e-02   1.28534944e-01  -1.27590200e-02  -1.08845077e-01\n",
      "   2.00979079e-03   2.20810656e-02]\n",
      "4: [ 0.90711001  0.60821182  0.24320819  0.         -0.04818171  0.          0.\n",
      "  0.          0.          0.          0.          0.          0.01791005\n",
      "  0.12853494 -0.01275902 -0.10884508  0.00200979  0.02208107]\n",
      "\n",
      "3: [  9.07110006e-01   6.08211818e-01   2.43208194e-01   1.54202407e-13\n",
      "  -4.81817128e-02  -2.28755409e-14  -1.02648883e-14   6.22123011e-16\n",
      "   4.65368581e-16  -6.73926950e-17   0.00000000e+00   0.00000000e+00\n",
      "   1.79100530e-02   1.28534944e-01  -1.27590200e-02  -1.08845077e-01\n",
      "   2.00979079e-03   2.20810656e-02]\n",
      "3: [ 0.90711001  0.60821182  0.24320819  0.         -0.04818171  0.          0.\n",
      "  0.          0.          0.          0.          0.          0.01791005\n",
      "  0.12853494 -0.01275902 -0.10884508  0.00200979  0.02208107]\n",
      "\n",
      "2: [  9.07110006e-01   6.08211818e-01   2.43208194e-01   1.54202407e-13\n",
      "  -4.81817128e-02  -2.28755409e-14  -1.02648883e-14   6.22123011e-16\n",
      "   4.65368581e-16  -6.73926950e-17   0.00000000e+00   0.00000000e+00\n",
      "   1.79100530e-02   1.28534944e-01  -1.27590200e-02  -1.08845077e-01\n",
      "   2.00979079e-03   2.20810656e-02]\n",
      "2: [ 0.90711001  0.60821182  0.24320819  0.         -0.04818171  0.          0.\n",
      "  0.          0.          0.          0.          0.          0.01791005\n",
      "  0.12853494 -0.01275902 -0.10884508  0.00200979  0.02208107]\n",
      "\n",
      "1: [  9.07110006e-01   6.08211818e-01   2.43208194e-01   1.54202407e-13\n",
      "  -4.81817128e-02  -2.28755409e-14  -1.02648883e-14   6.22123011e-16\n",
      "   4.65368581e-16  -6.73926950e-17   0.00000000e+00   0.00000000e+00\n",
      "   1.79100530e-02   1.28534944e-01  -1.27590200e-02  -1.08845077e-01\n",
      "   2.00979079e-03   2.20810656e-02]\n",
      "1: [ 0.90711001  0.60821182  0.24320819  0.         -0.04818171  0.          0.\n",
      "  0.          0.          0.          0.          0.          0.01791005\n",
      "  0.12853494 -0.01275902 -0.10884508  0.00200979  0.02208107]\n",
      "\n",
      "10: [  0.00000000e+00  -4.90804007e-06   2.11512041e-02  -6.56657899e-17\n",
      "  -3.31445941e-03  -2.43035600e-17   6.11573638e-18  -1.15824563e-17\n",
      "   1.15824563e-17   0.00000000e+00   1.19159785e-49   4.73131773e-45\n",
      "  -4.80411563e-02   6.15658343e-02   4.01965764e-02  -5.07721784e-02\n",
      "  -8.16513718e-03   9.82236688e-03]\n",
      "10: 3.81253968219727e+17\n",
      "best: [  0.00000000e+00  -4.90804007e-06   2.11512041e-02  -6.56657899e-17\n",
      "  -3.31445941e-03  -2.43035600e-17   6.11573638e-18  -1.15824563e-17\n",
      "   1.15824563e-17   0.00000000e+00   1.19159785e-49   4.73131773e-45\n",
      "  -4.80411563e-02   6.15658343e-02   4.01965764e-02  -5.07721784e-02\n",
      "  -8.16513718e-03   9.82236688e-03]\n"
     ]
    }
   ],
   "source": [
    "xi_best = train_stridge(theta, u_t, alpha=0*1e-5, dtol=1e-5, tol_iters=10, stridge_iters=10)\n",
    "print(f\"best: {xi_best}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0 1 2 3 4 5 6 7 8 9]\n",
      "(10, 4)\n",
      "[[ 4 14 24 34]\n",
      " [ 9 19 29 39]\n",
      " [ 1 11 21 31]\n",
      " [ 6 16 26 36]\n",
      " [ 7 17 27 37]\n",
      " [ 3 13 23 33]\n",
      " [ 0 10 20 30]\n",
      " [ 5 15 25 35]]\n"
     ]
    }
   ],
   "source": [
    "d = np.arange(10)\n",
    "t = np.arange(4*10).reshape(4, 10).T\n",
    "print(d)\n",
    "print(t.shape)\n",
    "d_train, d_test, t_train, t_test = train_test_split(d, t, test_size=0.2, random_state=0, shuffle=True)\n",
    "print(t_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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