2DGPRTEzmode.ipynb

{
 "metadata": {
  "name": "",
  "signature": "sha256:043d95c5606a10f0c176b2361e8d16c694598054312e10bcad736981ae586de1"
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 "nbformat": 3,
 "nbformat_minor": 0,
 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from SimPEG import *\n",
      "from scipy.constants import mu_0, epsilon_0\n",
      "%pylab inline"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Populating the interactive namespace from numpy and matplotlib\n"
       ]
      }
     ],
     "prompt_number": 1
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from SimPEG.Utils import mkvc, sdiag, sdInv"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 2
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "cs = 7.5*1e-2*0.5\n",
      "hx = np.ones(200)*cs\n",
      "hy = np.ones(200)*cs\n",
      "mesh = Mesh.TensorMesh([hx, hy], 'CC')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 3
    },
    {
     "cell_type": "heading",
     "level": 1,
     "metadata": {},
     "source": [
      "2D Geo Penetrating Radar (GPR) modeling: $TE^z$ mode"
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Maxwell's equations in time domain:"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "$ \\nabla \\times \\vec{e} = -\\mu \\frac{\\partial\\vec{h}}{\\partial t}$\n",
      "\n",
      "$ \\nabla \\times \\vec{h} -\\sigma \\vec{e} - \\epsilon \\frac{\\partial\\vec{e}}{\\partial t} = \\vec{j}_s $"
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Assuming TE mode ($e_x$, $e_y$, $h_z$):"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "$\\mathbf{Curl}\\mathbf{e}^{n+1/2} = -\\mathbf{diag}(\\mu)\\triangle t^{-1}(\\mathbf{h}^{n+1}-\\mathbf{h}^{n})$\n",
      "\n",
      "$\\mathbf{Curl}\\mathbf{h}^{n} - \\mathbf{M}^{e}_{\\sigma}\\mathbf{e}^{n-1/2} - \\mathbf{M}^{e}_{\\epsilon}\\triangle t^{-1}(\\mathbf{e}^{n+1/2}-\\mathbf{e}^{n-1/2}) = \\mathbf{j}^{n-1/2}_s$"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "sighalf = 0.\n",
      "mu = mu_0*np.ones(mesh.nC)\n",
      "epsilon = epsilon_0*np.ones(mesh.nC)*25\n",
      "sigma = sighalf*np.ones(mesh.nC)\n",
      "Mmui = sdiag(1./mu)\n",
      "Meeps = sdiag(mesh.aveE2CC.T*epsilon)\n",
      "MeepsI = sdInv(Meeps)\n",
      "Mesig = sdiag(mesh.aveE2CC.T*sigma)\n",
      "curl = mesh.edgeCurl"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 4
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "First compute:"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "$\\mathbf{e}^{n+1/2} = \\mathbf{e}^{n-1/2} - (\\mathbf{M}^{e}_{\\epsilon})^{-1}\\triangle t(-\\mathbf{Curl}^{T}\\mathbf{h}^{n}+\\mathbf{M}^{e}_{\\sigma}\\mathbf{e}^{n}+\\mathbf{j}^{n-1/2}_s)$"
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Then compute:"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "$\\mathbf{h}^{n+1} = \\mathbf{h}^{n} - (\\mathbf{diag}(\\mu))^{-1}\\triangle t\\mathbf{Curl}\\mathbf{e}^{n+1/2}$"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def ricker(fpeak, t, tlag):\n",
      "    \"\"\"\n",
      "        Generating Ricker Wavelet\n",
      "        \n",
      "        .. math ::\n",
      "        \n",
      "        \n",
      "    \"\"\"\n",
      "#     return (1-2*np.pi**2*fpeak**2*(t-tlag)**2)*np.exp(-np.pi**2*fpeak**2*(t-tlag)**2)\n",
      "    return np.exp(-2*fpeak**2*(t-tlag)**2)*np.cos(np.pi*fpeak*(t-tlag))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 5
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "dt = 2e-10\n",
      "time = np.arange(500)*dt\n",
      "wave = ricker(200*1e6, time, 35*dt)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 6
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plt.plot(time, wave, '.-')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 7,
       "text": [
        "[<matplotlib.lines.Line2D at 0xae7a400>]"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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gX4GLCecDas7gl6TyxW3xHwSuAlYQevjcRujRc2X0/hLgu8BI4ObotQOEk8I1U81Vu2Dw\nS0qnuMEPsDx65FuSN3159Og11Vy1C17AJSmdEnHlrqUeSSqfwW/wS0qZVAf/4MGwZ0+48leS0iIR\nwb9jR3Und/v0gYEDQ/hLUlrEHaunlqoeq2fGDNi3D6ZPh6VLK7sga9AgmD07fKbSz0pSo1UzVk8i\ngn/cONi8OUxXOtjaoEGwd291n5WkRmvEIG1Noev7oprB1vr3r/6zktSKatGPv+GmT4eTToJf/rLy\nUs2sWdCvH9x/v2UeSemQiODfvRtuuaW64B4zBr7xDUNfUnokotTz4YcwfHh1nx0+PHxektLC4Df4\nJaVMywd/Z6fBL0mVaPng37sX2trChVjVMPglpU3LB3+c1j4Y/JLSx+A3+CWljMFv8EtKmZYP/o4O\nWLsW5s2Dbdsq//zNN8OTT1b/eUlqNS0f/G+/HVrsy5fDokWVf37TpjCsc7Wfl6RW0/LB3yf6E1Q7\n1k7XcM6O1SMpLWoR/HOB14E1wHVFlrkxen81MLsG2/zI174G06bBypXVDbvws5+FL49qPy9JrSZu\n8PcFbiKE/ynAQuDkgmXmAScA04BFwM0xt3mE/fth4cLqQ3v8+BD8Q4bUcq8kqXnFDf45wFpgPXAA\nWAbML1jmAuDOaPopYAQwNuZ2PxK3V09bG7S327NHUnrEHZ1zArAhb34jcFYZyxwHbI65bSB+8EOu\nS+eYMZV/dtEiuO8+2LIl3j5IUqX6VNl0jxv85d4yq/DuMN1+bvDgDhYtCmWbTCZDJpMpueJaBn+l\nLr8cbr89dyMYSep92egBhw9Xt4a4wb8JmJg3P5HQou9pmeOi146yZ08Ht9wC771Xfs2+UcF/xRVw\n552GvqR6y0SPLosrXkPfmHvwHnA98ACwG/gn4PtAfuHjMHAF8HPgbMIe/1M36+qADg4dCoF6+eXl\nDbz2z/8MX/4yTJhQ/R/ivvvg5JPDXbzK9fWvw549ufmhQ8OX1ZlnhoHjzjijPs/nnANTp4ab0dRr\nm6367LHymCXtWH3607BmzWKoMP3jtvgPAlcBKwhfIrcBrwFXRu8vAR4i9OxZC+wCLi210vfeC7Xz\ncm583ogW/+7dsH17bn7cOHjtNbuDSqq/topusx59pva7UbXO0aM72bo1dK085xy4557SYTpwIJx2\nWlhu6dLqwnfGDNi3L9y7t5x1nHsuPPMMHDwIM2fC448b+pIaoy0kf0VZ3lRX7q5dG769du2CRx6B\nSy7pefnOzhDYTz4Zb8iFnTth3bry1nHFFbBqVQh9gClTDH1JraWpgn/ECBg8ODdf6ifMjh3xh2yA\n3DbLWcdzz+VO6I4cCT/9aXXblKRGaargBzgrugpg8ODQEu9pxMytW8NJ3QUL4g258Nd/DRMnlreO\nN94Iz/36QTZra19S62m64P/FL2DAgHAC9ZFHei69bNkCH/94OAkcJ4AnTQq9ekqto7MznEmHUOr5\n3veq36YkNUrTBf+IEblulaVKL1u3wujR8bc5enRYVykvvQT9+5e3b5LUrJou+AEeeCDU9/v1gwsv\nLF7u2bq1umEWCo0ZU96QC1dcEcb1GTcO7r3XMo+k1tSUwX/88eGCqFWreu5ps2VLfVv8b7wBmzeH\n6wyuvTb+diWpEZoy+PO1t8MPf9j9e7Uq9QwbFrqF7ttXfJlLL8398pg92zKPpNbVtME/MRrdZ/v2\n4q3re++Ff/mX+PfL7SorZTLF1/Xcc7npSZMs80hqXU0b/F1j75x2WvHW9fvvl3/hVSltbT2Xlnbv\nDs9nnGHffUmtrWmD/+674WMfC+WXYid4u66erUUPm0GDel7Xrl2h7GRLX1Kra6qxejoLxjieNAk2\nRLdwWbDg6EHbJk8O/e/vuit+IC9cGIaM6O4irkOHwrUFXWNfd7cvktQI1YzVE3d0zl51zDEh+Ltr\nhXd2hlLPSy+Fk7NxHX88zJrV/RfIK6+EweC6hlv1xK6kVta0pR4Ireq2ttDaLiz37NgRnocOrc22\nxo2Dd9/t/r2/+IswYqj99yUlQVMH/5QpoaX9u98dfdL1vffg2GOrG4u6O8ceG9bZnTVrwq8L++9L\nSoKmDn7I9dMvLLH8zd+EMI7blbPLz34GK1Z0v76uXxeWeSQlQdMH/6RJodRTWF5Zuzb08a9FV04I\nXyLdre/ii0PPorFjLfNISoamD/4DB2D//qNH6jx0KDzXqhU+cmR4Pv30I9f3/POhN8/mzZZ5JCVD\nU/fqgVyp59RTjwzkOXNCv/o44/DnW7YMxo+Hn/zkyPXt2hWeLfNISoq4Lf5RwErgDeA3QHcRPBF4\nDHgFeBn4ViUbuOuucHHVnj1H9ux55x34wQ9qV3oZMSJ8mRQO1rZ9e7gZuyUeSUkRt0/MPwJboufr\ngJHAtwuWGRc9XgCGAv8P+DPgtYLljrqAq8uUKfDWW2G66+KpYcPglFPCL4Jqb7JeaPr00Eto6tSw\nzj59QgnIC7ckNatG3Gz9AuDOaPpOQqAXeo8Q+gA7CYE/vpKNjB0bnrvKLbt3hxLM00/X7uQuhPMJ\nb7yRW+eqVaG1n79tSWp1cYN/LLA5mt4czfdkMjAbeKqSjdx3X2iJ9+0byj1PPJG7WreWgVzYdfS6\n68K9f71wS1KSlHNydyWhVFPo7wrmO6NHMUOBe4GrCS3/o3R0dHw0nclkyGQyQAjeESPgqejrYvNm\nmD8/3P/2xz+uXSAvXQqf/CT85jdhnWvW5E7uXnutZR5JjZfNZslms7HWEbfG/zqQIZRzjiWcxD2p\nm+X6A78ClgM3FFlX0Ro/hFr7tm2hJ8+oUWH8/GnTalff7zJkCMyYEcYI6rqSd/ZsePRRW/ySmk8j\navwPAN+Ipr8B3N/NMm3AbcCrFA/9kqZPD8/bt8P69eECrlrW97sMHw7PPHPk8A3HHmvoS0qOuMH/\nD8B/IXTn/M/RPISTt7+Ops8DLgbOB56PHnMr3VB3t1icNav2J1y7LgzL179/bbchSY3U1OPx59u2\nDU46KdT3u4wfD5s21XYnPvWpcPK4y/Dh4ReGLX5JzagRpZ66GTECXn89jNsDobfN735X++20tx+5\nzdWrDX1JydIyLf4ub78dWuX//u/h5im1tm0bXHJJ6D56xx2GvqTmVk2Lv+WCX5KUk+hSjySpNgx+\nSUoZg1+SUsbgl6SUMfglKWUMfklKGYNfklLG4JeklDH4JSllDH5JShmDX5JSxuCXpJQx+CUpZQx+\nSUoZg1+SUiZO8I8CVhLut/sboKdblvQl3Gv3wRjbkyTVQJzg/zYh+KcDv43mi7kaeBXwTitlyGaz\njd6FpuGxyPFY5Hgs4okT/BcAd0bTdwJ/VmS544B5wE9orjt+NS3/Ued4LHI8Fjkei3jiBP9YYHM0\nvTma787/Ba4FDsfYliSpRvqVeH8lMK6b1/+uYL6T7ss4/xX4A6G+n6l05yRJtRen9PI6IczfA44F\nHgNOKljm+8CfAweBgUA78Avg692sby0wNcb+SFIarQNOqNfG/hG4Lpr+NvAPJZb/DPbqkaSWNgp4\nhKO7c44Hft3N8p8BHqjPrkmSJElqmLmE8wNryJWKCt0Yvb8amF2n/WqEUsfiIsIxeBF4AphVv12r\nq3L+TQCcSThf9KV67FSDlHMsMoQOEy8D2brsVWOUOhZjgIeBFwjH4pK67Vn93U7oPflSD8s0bW72\nJZzEnQz0J/yFnVywzDzgoWj6LGBVvXauzso5FucAw6PpuSTzWJRzHLqWexT4FfDleu1cnZVzLEYA\nrxCuj4EQfklUzrHoAH4QTY8BtlK6p2Kr+hNCmBcL/opys95j9cwh/GWuBw4Ay4D5BcvkXxj2FOEf\nerFrBFpZOcfiSeDDaPopcv/Zk6Sc4wDwl8C9wPt127P6K+dYXEjoGbcxmt9Sr52rs3KOxbuEnoJE\nz1sJvwiT6N+AD3p4v6LcrHfwTwA25M1vjF4rtUwSA6+cY5Hvm+S+0ZOk3H8T84Gbo/mkDv1RzrGY\nRuhY8RjwLKG7dBKVcyxuBWYA7xDKG1fXZ9eaUkW5We+fReX+hy28viCJ/9Er+TOdD1wGnNdL+9JI\n5RyHGwhdhjsJ/zaSOvRHOceiP3Aa8FlgMOFX4SpCbTdJyjkW3yGUgDKEa4BWAqcCO3pvt5pa2blZ\n7+DfBEzMm59I7idrsWWOi15LmnKOBYQTurcSavw9/dRrVeUch9MJP/Uh1HK/QPj5n7TuweUciw2E\n8s6e6PE4IeySFvzlHItzgb+PptcBbwEnEn4JpU1T52Y/wl/QZGAApU/unk0yT2hCecdiEqHOeXZd\n96y+yjkO+e4gub16yjkWJxGun+lLaPG/BJxSv12sm3KOxf8Bro+mxxK+GEbVaf8aYTLlndxtytz8\nAvB7QqD9bfTaldGjy03R+6sJP2uTqtSx+AnhhNXz0ePpeu9gnZTzb6JLkoMfyjsW1xB69rwEfKuu\ne1dfpY7FGMJoAKsJx+LCeu9gHd1FOJexn/Cr7zLSm5uSJEmSJEmSJEmSJElS9coZWK1c55Pr3fc8\n4RqOC2qwXklSDZUaWK1aIwndvAdWu4J6j9UjSWnR3cBqU4HlhKuLHydcaVypBYSLtfbG2jtJUq+Y\nzJEt/t+Suz/uWdF8pR4lXKlbtaSOXS1JzWYo4R4b9+S9NiB6/hKwuJvPbCRcwdzlWOCTwIre2EFJ\nUnyTybX42wnDLsRxNXBLzHVY45ekOtlOGEH0K9F8G5XfTnUhYdweSVITKhxY7VLCL4DlhNFGXwH+\nRwXrm8yRN1uRJEmSJEmSJEmSJEmSJEmSJEmSJDWb/w/9FM++A2kv1QAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x3bf2c18>"
       ]
      }
     ],
     "prompt_number": 7
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "txind = Utils.closestPoints(mesh, [0., 0.], gridLoc='Ex')\n",
      "q = np.zeros(mesh.nE)\n",
      "q[txind] = 1.\n",
      "q = Utils.sdiag(1/mesh.edge)*q"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 8
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "Px = mesh.getInterpolationMat(mesh.gridCC, 'Ex')\n",
      "Py = mesh.getInterpolationMat(mesh.gridCC, 'Ey')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 9
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "h0 = np.zeros(mesh.nC)\n",
      "h1 = np.zeros(mesh.nC)\n",
      "e0 = np.zeros(mesh.nE)\n",
      "e1 = np.zeros(mesh.nE)\n",
      "h = np.zeros((mesh.nC, time.size))\n",
      "ex = np.zeros((mesh.nC, time.size))\n",
      "ey = np.zeros((mesh.nC, time.size))\n",
      "\n",
      "for i in range (time.size):\n",
      "    \n",
      "    js = q*wave[i] \n",
      "    e1 = e0 - MeepsI*dt*(-curl.T*h1+Mesig*e0+js)\n",
      "    e0 = e1.copy()\n",
      "    ex[:,i] = Px*e0\n",
      "    ey[:,i] = Py*e0\n",
      "    h1 = h0 - Mmui*dt*curl*e0\n",
      "    h0 = h1.copy()\n",
      "    h[:,i] = h1\n",
      "    "
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 10
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from JSAnimation import IPython_display\n",
      "from matplotlib import animation\n",
      "extent = [mesh.vectorCCx.min(), mesh.vectorCCx.max(), mesh.vectorCCy.min(), mesh.vectorCCy.max()]\n",
      "fig, ax = plt.subplots(1,3, figsize = (24, 8))\n",
      "for i in range(3):\n",
      "    ax[i].set_xlabel('x (m)', fontsize = 16)\n",
      "    ax[i].set_ylabel('y (m)', fontsize = 16)\n",
      "    ax[i].set_xlim(extent[:2])\n",
      "    ax[i].set_ylim(extent[2:])\n",
      "\n",
      "nskip = 30\n",
      "def animate(i_id):\n",
      "    icount = i_id*nskip\n",
      "    frame1 = ax[0].imshow(np.flipud(h[:,icount].reshape((mesh.nCx, mesh.nCy), order = 'F').T), cmap = 'RdBu', extent=extent)    \n",
      "    frame2 = ax[1].imshow(np.flipud(ex[:,icount].reshape((mesh.nCx, mesh.nCy), order = 'F').T), cmap = 'RdBu', extent=extent, vmin = ex[:,icount].min()*0.05, vmax = ex[:,icount].max()*0.05)\n",
      "    frame3 = ax[2].imshow(np.flipud(ey[:,icount].reshape((mesh.nCx, mesh.nCy), order = 'F').T), cmap = 'RdBu', extent=extent, vmin = ey[:,icount].min()*0.05, vmax = ey[:,icount].max()*0.05)    \n",
      "    return frame1, frame2, frame3\n",
      "animation.FuncAnimation(fig, animate, frames=14, interval=40, blit=True)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "html": [
        "\n",
        "<script language=\"javascript\">\n",
        "  /* Define the Animation class */\n",
        "  function Animation(frames, img_id, slider_id, interval, loop_select_id){\n",
        "    this.img_id = img_id;\n",
        "    this.slider_id = slider_id;\n",
        "    this.loop_select_id = loop_select_id;\n",
        "    this.interval = interval;\n",
        "    this.current_frame = 0;\n",
        "    this.direction = 0;\n",
        "    this.timer = null;\n",
        "    this.frames = new Array(frames.length);\n",
        "\n",
        "    for (var i=0; i<frames.length; i++)\n",
        "    {\n",
        "     this.frames[i] = new Image();\n",
        "     this.frames[i].src = frames[i];\n",
        "    }\n",
        "    document.getElementById(this.slider_id).max = this.frames.length - 1;\n",
        "    this.set_frame(this.current_frame);\n",
        "  }\n",
        "\n",
        "  Animation.prototype.get_loop_state = function(){\n",
        "    var button_group = document[this.loop_select_id].state;\n",
        "    for (var i = 0; i < button_group.length; i++) {\n",
        "        var button = button_group[i];\n",
        "        if (button.checked) {\n",
        "            return button.value;\n",
        "        }\n",
        "    }\n",
        "    return undefined;\n",
        "  }\n",
        "\n",
        "  Animation.prototype.set_frame = function(frame){\n",
        "    this.current_frame = frame;\n",
        "    document.getElementById(this.img_id).src = this.frames[this.current_frame].src;\n",
        "    document.getElementById(this.slider_id).value = this.current_frame;\n",
        "  }\n",
        "\n",
        "  Animation.prototype.next_frame = function()\n",
        "  {\n",
        "    this.set_frame(Math.min(this.frames.length - 1, this.current_frame + 1));\n",
        "  }\n",
        "\n",
        "  Animation.prototype.previous_frame = function()\n",
        "  {\n",
        "    this.set_frame(Math.max(0, this.current_frame - 1));\n",
        "  }\n",
        "\n",
        "  Animation.prototype.first_frame = function()\n",
        "  {\n",
        "    this.set_frame(0);\n",
        "  }\n",
        "\n",
        "  Animation.prototype.last_frame = function()\n",
        "  {\n",
        "    this.set_frame(this.frames.length - 1);\n",
        "  } \n",
        "\n",
        "  Animation.prototype.slower = function()\n",
        "  {\n",
        "    this.interval /= 0.7;\n",
        "    if(this.direction > 0){this.play_animation();}\n",
        "    else if(this.direction < 0){this.reverse_animation();}\n",
        "  }\n",
        "\n",
        "  Animation.prototype.faster = function()\n",
        "  {\n",
        "    this.interval *= 0.7;\n",
        "    if(this.direction > 0){this.play_animation();}\n",
        "    else if(this.direction < 0){this.reverse_animation();}\n",
        "  }\n",
        "\n",
        "  Animation.prototype.anim_step_forward = function()\n",
        "  {\n",
        "    this.current_frame += 1;\n",
        "    if(this.current_frame < this.frames.length){\n",
        "      this.set_frame(this.current_frame);\n",
        "    }else{\n",
        "      var loop_state = this.get_loop_state();\n",
        "      if(loop_state == \"loop\"){\n",
        "        this.first_frame();\n",
        "      }else if(loop_state == \"reflect\"){\n",
        "        this.last_frame();\n",
        "        this.reverse_animation();\n",
        "      }else{\n",
        "        this.pause_animation();\n",
        "        this.last_frame();\n",
        "      }\n",
        "    }\n",
        "  }\n",
        "\n",
        "  Animation.prototype.anim_step_reverse = function()\n",
        "  {\n",
        "    this.current_frame -= 1;\n",
        "    if(this.current_frame >= 0){\n",
        "      this.set_frame(this.current_frame);\n",
        "    }else{\n",
        "      var loop_state = this.get_loop_state();\n",
        "      if(loop_state == \"loop\"){\n",
        "        this.last_frame();\n",
        "      }else if(loop_state == \"reflect\"){\n",
        "        this.first_frame();\n",
        "        this.play_animation();\n",
        "      }else{\n",
        "        this.pause_animation();\n",
        "        this.first_frame();\n",
        "      }\n",
        "    }\n",
        "  }\n",
        "\n",
        "  Animation.prototype.pause_animation = function()\n",
        "  {\n",
        "    this.direction = 0;\n",
        "    if (this.timer){\n",
        "      clearInterval(this.timer);\n",
        "      this.timer = null;\n",
        "    }\n",
        "  }\n",
        "\n",
        "  Animation.prototype.play_animation = function()\n",
        "  {\n",
        "    this.pause_animation();\n",
        "    this.direction = 1;\n",
        "    var t = this;\n",
        "    if (!this.timer) this.timer = setInterval(function(){t.anim_step_forward();}, this.interval);\n",
        "  }\n",
        "\n",
        "  Animation.prototype.reverse_animation = function()\n",
        "  {\n",
        "    this.pause_animation();\n",
        "    this.direction = -1;\n",
        "    var t = this;\n",
        "    if (!this.timer) this.timer = setInterval(function(){t.anim_step_reverse();}, this.interval);\n",
        "  }\n",
        "</script>\n",
        "\n",
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        "    <img id=\"_anim_imgTBHYRORJORJTSFYQ\">\n",
        "    <br>\n",
        "    <input id=\"_anim_sliderTBHYRORJORJTSFYQ\" type=\"range\" style=\"width:350px\" name=\"points\" min=\"0\" max=\"1\" step=\"1\" value=\"0\" onchange=\"animTBHYRORJORJTSFYQ.set_frame(parseInt(this.value));\"></input>\n",
        "    <br>\n",
        "    <button onclick=\"animTBHYRORJORJTSFYQ.slower()\">&#8211;</button>\n",
        "    <button onclick=\"animTBHYRORJORJTSFYQ.first_frame()\"><img class=\"anim_icon\" src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABQAAAAUCAQAAAAngNWGAAAAAXNSR0IArs4c6QAAAAJiS0dEAP+H\n",
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        "    <button onclick=\"animTBHYRORJORJTSFYQ.play_animation()\"><img class=\"anim_icon\" src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABQAAAAUCAQAAAAngNWGAAAAAXNSR0IArs4c6QAAAAJiS0dEAP+H\n",
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        "    <button onclick=\"animTBHYRORJORJTSFYQ.next_frame()\"><img class=\"anim_icon\" src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABQAAAAUCAQAAAAngNWGAAAAAXNSR0IArs4c6QAAAAJiS0dEAP+H\n",
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        "\"></button>\n",
        "    <button onclick=\"animTBHYRORJORJTSFYQ.faster()\">+</button>\n",
        "  <form action=\"#n\" name=\"_anim_loop_selectTBHYRORJORJTSFYQ\" class=\"anim_control\">\n",
        "    <input type=\"radio\" name=\"state\" value=\"once\" > Once </input>\n",
        "    <input type=\"radio\" name=\"state\" value=\"loop\" checked> Loop </input>\n",
        "    <input type=\"radio\" name=\"state\" value=\"reflect\" > Reflect </input>\n",
        "  </form>\n",
        "</div>\n",
        "\n",
        "\n",
        "<script language=\"javascript\">\n",
        "  /* Instantiate the Animation class. */\n",
        "  /* The IDs given should match those used in the template above. */\n",
        "  (function() {\n",
        "    var img_id = \"_anim_imgTBHYRORJORJTSFYQ\";\n",
        "    var slider_id = \"_anim_sliderTBHYRORJORJTSFYQ\";\n",
        "    var loop_select_id = \"_anim_loop_selectTBHYRORJORJTSFYQ\";\n",
        "    var frames = new Array(0);\n",
        "    \n",
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