{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Populating the interactive namespace from numpy and matplotlib\n"
     ]
    }
   ],
   "source": [
    "# Test 1D solution of MT problem and compare to a analytic solution\n",
    "%pylab inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# import the simpegMT module\n",
    "from simpegMT.Utils import MT1Danalytic, MT1Dsolutions\n",
    "import SimPEG as simpeg\n",
    "from scipy.constants import mu_0\n",
    "def omega(freq):\n",
    "    \"\"\"Change frequency to angular frequency, omega\"\"\"\n",
    "    return 2.*np.pi*freq"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# Set up the mesh.\n",
    "freq = 10\n",
    "z = 100.\n",
    "hz = [(z,10,-1.5),(z,10),(z,10,1.5)]\n",
    "M = simpeg.Mesh.TensorMesh([hz],'C')\n",
    "sig = np.zeros(M.nC) + 1e-8\n",
    "sig[M.vectorCCx<=300] = 0.01\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-17499.51171875, -11733.0078125 ,  -7888.671875  ,  -5325.78125   ,\n",
       "        -3617.1875    ,  -2478.125     ,  -1718.75      ,  -1212.5       ,\n",
       "         -875.        ,   -650.        ,   -500.        ,   -400.        ,\n",
       "         -300.        ,   -200.        ,   -100.        ,      0.        ,\n",
       "          100.        ,    200.        ,    300.        ,    400.        ,\n",
       "          500.        ,    650.        ,    875.        ,   1212.5       ,\n",
       "         1718.75      ,   2478.125     ,   3617.1875    ,   5325.78125   ,\n",
       "         7888.671875  ,  11733.0078125 ,  17499.51171875])"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "M.vectorNx"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# Get the fields\n",
    "anaEd, anaEu, anaHd, anaHu = MT1Danalytic.getEHfields(M,sig,freq,M.vectorNx)\n",
    "anaEtemp = (anaEd+anaEu)\n",
    "anaHtemp = (anaHd+anaHu)\n",
    "# Scale the solution\n",
    "anaZ = (anaEtemp/anaHtemp)[np.argmin(M.vectorNx**2)]\n",
    "anaEcor = anaEtemp/anaEtemp[-1] #.real/np.abs(anaEtemp[-1].real)+1j*anaEtemp.imag/np.abs(anaEtemp[-1].imag)\n",
    "anaHcor = anaHtemp/anaEtemp[-1] # .real/np.abs(anaEtemp[-1].real)+1j*anaHtemp.imag/np.abs(anaEtemp[-1].imag)\n",
    "\n",
    "solE = MT1Dsolutions.get1DEfields(M,sig,freq,sourceAmp=1).conj()\n",
    "solH = -M.nodalGrad*solE/(1j*omega(freq)*mu_0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(922807.04800415318-689021.35510797054j)"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "anaEtemp[-1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[  6.95763292e-07 +5.19497296e-07j,\n",
       "          6.95763292e-07 -5.19497296e-07j],\n",
       "       [ -1.40834457e-05 -2.93173032e-05j,\n",
       "          9.74760218e-06 -1.09092785e-05j],\n",
       "       [  3.35815988e-04 +1.40732501e-04j,\n",
       "          1.74907169e-04 +1.24344756e-04j],\n",
       "       [ -7.70118008e-04 +1.65141317e-03j,\n",
       "         -5.21083562e-04 +1.34839517e-03j],\n",
       "       [ -5.32123445e-03 +3.24450003e-04j,\n",
       "         -4.87010903e-03 +6.63069113e-04j],\n",
       "       [ -8.64982593e-03 -6.64134560e-03j,\n",
       "         -8.61854919e-03 -6.03020882e-03j],\n",
       "       [ -7.46721859e-03 -1.59079740e-02j,\n",
       "         -7.68552978e-03 -1.53974787e-02j],\n",
       "       [ -2.91038457e-03 -2.39785146e-02j,\n",
       "         -3.16876824e-03 -2.35863583e-02j],\n",
       "       [  2.72167021e-03 -2.97359468e-02j,\n",
       "          2.49400722e-03 -2.94018473e-02j],\n",
       "       [  7.92975642e-03 -3.34680056e-02j,\n",
       "          7.73825040e-03 -3.31542272e-02j],\n",
       "       [  1.21356998e-02 -3.57924928e-02j,\n",
       "          1.19706555e-02 -3.54839735e-02j],\n",
       "       [  1.52903430e-02 -3.72269264e-02j,\n",
       "          1.51424717e-02 -3.69189921e-02j],\n",
       "       [  1.87388388e-02 -3.85404390e-02j,\n",
       "          1.86057886e-02 -3.82344505e-02j],\n",
       "       [  2.24915402e-02 -3.97057953e-02j,\n",
       "          2.23709926e-02 -3.94030035e-02j],\n",
       "       [  2.65576291e-02 -4.06933593e-02j,\n",
       "          2.64473102e-02 -4.03949222e-02j],\n",
       "       [  3.09448819e-02 -4.14710213e-02j,\n",
       "          3.08425733e-02 -4.11780213e-02j],\n",
       "       [  3.56594159e-02 -4.20041369e-02j,\n",
       "          3.55629651e-02 -4.17175972e-02j],\n",
       "       [  4.07054159e-02 -4.22554788e-02j,\n",
       "          4.06127458e-02 -4.19763792e-02j],\n",
       "       [  4.60848403e-02 -4.21852042e-02j,\n",
       "          4.59939588e-02 -4.19144958e-02j],\n",
       "       [  5.16310109e-02 -4.19401825e-02j,\n",
       "          5.15406437e-02 -4.16710354e-02j],\n",
       "       [  5.71771819e-02 -4.16951603e-02j,\n",
       "          5.70873289e-02 -4.14275746e-02j],\n",
       "       [  6.54964388e-02 -4.13276262e-02j,\n",
       "          6.54073573e-02 -4.10623825e-02j],\n",
       "       [  7.79753255e-02 -4.07763228e-02j,\n",
       "          7.78874014e-02 -4.05145921e-02j],\n",
       "       [  9.66936582e-02 -3.99493614e-02j,\n",
       "          9.66074704e-02 -3.96929008e-02j],\n",
       "       [  1.24771163e-01 -3.87089021e-02j,\n",
       "          1.24687581e-01 -3.84603474e-02j],\n",
       "       [  1.66887432e-01 -3.68481633e-02j,\n",
       "          1.66807761e-01 -3.66114701e-02j],\n",
       "       [  2.30061859e-01 -3.40569049e-02j,\n",
       "          2.29988062e-01 -3.38380118e-02j],\n",
       "       [  3.24823538e-01 -2.98695515e-02j,\n",
       "          3.24758579e-01 -2.96773825e-02j],\n",
       "       [  4.66966101e-01 -2.35870424e-02j,\n",
       "          4.66914483e-01 -2.34350351e-02j],\n",
       "       [  6.80179899e-01 -1.41584953e-02j,\n",
       "          6.80148567e-01 -1.40669735e-02j],\n",
       "       [  1.00000000e+00 +0.00000000e+00j,\n",
       "          1.00000000e+00 -0.00000000e+00j]])"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.hstack((simpeg.mkvc(anaEcor,2),simpeg.mkvc(solE,2)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7feb9a686510>,\n",
       " <matplotlib.lines.Line2D at 0x7feb9a686790>]"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
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       "7HBwAAAAAElFTkSuQmCC\n"
      ],
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7feb9a72ad50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(solE.real,M.vectorNx,'r*--',anaEcor.real,M.vectorNx,'b+:')\n",
    "#axis([-.2,.2,-10000,10000])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7feb9981fad0>]"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": [
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       "u8W/v1cB3y+/v7uBD3S63i2+v9dR9U3dSZUQ7wDmdbrurbq/El8JPAT8hqqN/X92uu6buKc3Aj+i\n",
       "ms37zFL2DuAdtWM+V/bfBRzS6Tq38v6omiUfBB6neqHhp8B2I10vAwAjImJMerWpKiIiOiSJIyIi\n",
       "xiSJIyIixiSJIyIixiSJIyIixiSJIyIixiSJIyIixiSJIyIixuT/A4kEhS0tjZoYAAAAAElFTkSu\n",
       "QmCC\n"
      ],
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7feb9a5f5ed0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot((abs(solE.real)-abs(anaEcor.real))/abs(anaEcor.real),M.vectorNx,'b+:')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7feb997604d0>,\n",
       " <matplotlib.lines.Line2D at 0x7feb99760750>]"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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       "ScTMzKrMScTMzKrMScTMzKrs/wPsAamFgCvYggAAAABJRU5ErkJggg==\n"
      ],
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7feb9a57e510>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(solE.imag,M.vectorNx,'r*--',anaEcor.imag,M.vectorNx,'b+:')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/gudni/anaconda/lib/python2.7/site-packages/IPython/kernel/__main__.py:1: RuntimeWarning: invalid value encountered in divide\n",
      "  if __name__ == '__main__':\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7feb9970fad0>]"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
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       "3hNZABg91tKJAAAAOklEQVQREW0ZhK6qiIjooiSOiIhoSxJHRES0JYkjIiLaksQRERFtSeKIiIi2\n",
       "JHFERERbkjgiIqIt/x+4vI9l3pPo8wAAAABJRU5ErkJggg==\n"
      ],
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7febc43946d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot((abs(solE.imag)-abs(anaEcor.imag))/abs(anaEcor.imag),M.vectorNx,'b+:')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7feb9967c590>,\n",
       " <matplotlib.lines.Line2D at 0x7feb99638890>]"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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       "M7M2+f/DvAf0HfArswAAAABJRU5ErkJggg==\n"
      ],
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7feb996d74d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "semilogx(abs(solE),M.vectorNx,'r*--',abs(anaEcor),M.vectorNx,'b+:')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7feb993ce610>]"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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       "PtcBbwBQ9fTm+trtuKaNJv+W0U2kbnrgps3Bnn2oBl3vpZpdPr20HwB8pdbv5VSDmncDX6BaymRS\n",
       "5A88D7irvH4InNN03mP9/tf6Hwtc13TeY/z+vwz4fvn+/wB4T9N5jzH/11CNLd1FVfDuBOY2nftY\n",
       "/v0AVwIPAE9S3aP/kwZzfj3w71SrfZ9T2s4Czqr1+fty/m7gqKa/z2PJn+q24v3ABuAR4D+APbf2\n",
       "eZkAGBERYzJZb1VFRERDUjgiImJMUjgiImJMUjgiImJMUjgiImJMUjgiImJMUjgiImJMUjgiImJM\n",
       "/j93KY9Nb6nlqgAAAABJRU5ErkJggg==\n"
      ],
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7feb9954b1d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot((abs(solE)-abs(anaEcor))/abs(anaEcor),M.vectorNx,'b+:')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "100.0 44.999998407\n",
      "91.3634893888 -137.014649098\n"
     ]
    }
   ],
   "source": [
    "def appResPhs(freq,z):\n",
    "    app_res = ((1./(8e-7*np.pi**2))/freq)*np.abs(z)**2\n",
    "    app_phs = np.arctan2(z.imag,z.real)*(180/np.pi)\n",
    "    return app_res, app_phs\n",
    "app_rAna, app_pAna = appResPhs(freq,anaZ)\n",
    "app_rSol, app_pSol = appResPhs(freq,solE[np.argmin(M.hx**2)]/solH[np.argmin(M.hx**2)])\n",
    "print app_rAna, app_pAna\n",
    "print app_rSol, app_pSol"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(30,)"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "M.nodalGrad.dot(solE).shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "31"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "M.nN\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7feb99304550>,\n",
       " <matplotlib.lines.Line2D at 0x7feb993047d0>]"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
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       "MDOzRvn/0De/+koUcWoAAAAASUVORK5CYII=\n"
      ],
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7feb9936d610>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(-solH.imag,M.vectorCCx,'r*--',anaHcor.imag,M.vectorNx,'b+:')\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-14616.25976562,  -9810.83984375,  -6607.2265625 ,  -4471.484375  ,\n",
       "        -3047.65625   ,  -2098.4375    ,  -1465.625     ,  -1043.75      ,\n",
       "         -762.5       ,   -575.        ,   -450.        ,   -350.        ,\n",
       "         -250.        ,   -150.        ,    -50.        ,     50.        ,\n",
       "          150.        ,    250.        ,    350.        ,    450.        ,\n",
       "          575.        ,    762.5       ,   1043.75      ,   1465.625     ,\n",
       "         2098.4375    ,   3047.65625   ,   4471.484375  ,   6607.2265625 ,\n",
       "         9810.83984375,  14616.25976562])"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "M.vectorCCx"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": []
  },
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