rowanc1/description.md

## description.md

      
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              description.md
            
          
    Playing with anisotropy in SimPEG.

  
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<div class="highlight"><pre><span class="kn">from</span> <span class="nn">SimPEG</span> <span class="kn">import</span> <span class="o">*</span>
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Warning: mumps solver not available.

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<div class="highlight"><pre><span class="n">M</span> <span class="o">=</span> <span class="n">mesh</span><span class="o">.</span><span class="n">TensorMesh</span><span class="p">([</span><span class="mi">30</span><span class="p">,</span><span class="mi">40</span><span class="p">])</span>
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<div class="highlight"><pre><span class="n">D</span> <span class="o">=</span> <span class="n">M</span><span class="o">.</span><span class="n">faceDiv</span>
<span class="n">G</span> <span class="o">=</span> <span class="n">M</span><span class="o">.</span><span class="n">cellGrad</span>
<span class="n">sig1</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">ones</span><span class="p">(</span><span class="n">M</span><span class="o">.</span><span class="n">nC</span><span class="p">)</span>
<span class="n">sig2</span> <span class="o">=</span> <span class="mf">2.</span><span class="o">*</span><span class="n">np</span><span class="o">.</span><span class="n">ones</span><span class="p">(</span><span class="n">M</span><span class="o">.</span><span class="n">nC</span><span class="p">)</span>
<span class="n">sig3</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">(</span><span class="n">M</span><span class="o">.</span><span class="n">nC</span><span class="p">)</span>
<span class="n">xL</span> <span class="o">=</span> <span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">abs</span><span class="p">(</span><span class="n">M</span><span class="o">.</span><span class="n">gridCC</span><span class="p">[:,</span><span class="mi">0</span><span class="p">]</span><span class="o">-</span><span class="mf">0.5</span><span class="p">)</span><span class="o">&lt;</span><span class="mf">0.25</span><span class="p">)</span>
<span class="n">yL</span> <span class="o">=</span> <span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">abs</span><span class="p">(</span><span class="n">M</span><span class="o">.</span><span class="n">gridCC</span><span class="p">[:,</span><span class="mi">1</span><span class="p">]</span><span class="o">-</span><span class="mf">0.5</span><span class="p">)</span><span class="o">&lt;</span><span class="mf">0.25</span><span class="p">)</span>
<span class="n">sig3</span><span class="p">[</span><span class="n">np</span><span class="o">.</span><span class="n">logical_and</span><span class="p">(</span><span class="n">xL</span><span class="p">,</span><span class="n">yL</span><span class="p">)]</span> <span class="o">=</span> <span class="mf">0.25</span>
<span class="n">sig</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">c_</span><span class="p">[</span><span class="n">sig1</span><span class="p">,</span><span class="n">sig2</span><span class="p">,</span><span class="n">sig3</span><span class="p">]</span>

<span class="n">Msig_ani</span> <span class="o">=</span> <span class="n">M</span><span class="o">.</span><span class="n">getFaceInnerProduct</span><span class="p">(</span><span class="n">sig</span><span class="p">)</span>
<span class="n">Msig_iso</span> <span class="o">=</span> <span class="n">M</span><span class="o">.</span><span class="n">getFaceInnerProduct</span><span class="p">(</span><span class="n">sig1</span><span class="p">)</span>

<span class="n">rhs</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">(</span><span class="n">M</span><span class="o">.</span><span class="n">nCv</span><span class="p">)</span>
<span class="n">rhs</span><span class="p">[[</span><span class="mi">3</span><span class="p">,</span><span class="mi">27</span><span class="p">],[</span><span class="mi">10</span><span class="p">,</span><span class="mi">30</span><span class="p">]]</span> <span class="o">=</span> <span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span><span class="mi">1</span><span class="p">]</span>
<span class="n">rhs</span> <span class="o">=</span> <span class="n">utils</span><span class="o">.</span><span class="n">mkvc</span><span class="p">(</span><span class="n">rhs</span><span class="p">)</span>
<span class="n">M</span><span class="o">.</span><span class="n">plotImage</span><span class="p">(</span><span class="n">rhs</span><span class="p">)</span>
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&lt;matplotlib.collections.QuadMesh at 0x111b2a250&gt;
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<div class="highlight"><pre><span class="n">phi_ani</span> <span class="o">=</span> <span class="n">Solver</span><span class="p">(</span><span class="n">D</span><span class="o">*</span><span class="n">Msig_ani</span><span class="o">*</span><span class="n">G</span><span class="p">)</span><span class="o">.</span><span class="n">solve</span><span class="p">(</span><span class="n">rhs</span><span class="p">)</span>
<span class="n">phi_iso</span> <span class="o">=</span> <span class="n">Solver</span><span class="p">(</span><span class="n">D</span><span class="o">*</span><span class="n">Msig_iso</span><span class="o">*</span><span class="n">G</span><span class="p">)</span><span class="o">.</span><span class="n">solve</span><span class="p">(</span><span class="n">rhs</span><span class="p">)</span>
<span class="n">M</span><span class="o">.</span><span class="n">plotImage</span><span class="p">(</span><span class="n">phi_ani</span><span class="p">,</span> <span class="n">figNum</span><span class="o">=</span><span class="mi">1</span><span class="p">)</span>
<span class="n">M</span><span class="o">.</span><span class="n">plotImage</span><span class="p">(</span><span class="n">phi_iso</span><span class="p">,</span><span class="n">figNum</span><span class="o">=</span><span class="mi">2</span><span class="p">)</span>
<span class="n">M</span><span class="o">.</span><span class="n">plotImage</span><span class="p">(</span><span class="n">phi_iso</span> <span class="o">-</span> <span class="n">phi_ani</span><span class="p">,</span><span class="n">figNum</span><span class="o">=</span><span class="mi">3</span><span class="p">)</span>
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<pre>
&lt;matplotlib.collections.QuadMesh at 0x111d90590&gt;
</pre>

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">

</div>
</div>

</div>
</div>

</div>
<div class="cell border-box-sizing code_cell vbox">
<div class="input hbox">
<div class="prompt input_prompt">
In&nbsp;[]:
</div>
<div class="input_area box-flex1">
<div class="highlight"><pre>
</pre></div>

</div>
</div>

</div>

## notebook.ipynb
{
 "metadata": {
  "name": ""
 },
 "nbformat": 3,
 "nbformat_minor": 0,
 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from SimPEG import *"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Warning: mumps solver not available.\n"
       ]
      }
     ],
     "prompt_number": 1
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "M = mesh.TensorMesh([30,40])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 40
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "D = M.faceDiv\n",
      "G = M.cellGrad\n",
      "sig1 = np.ones(M.nC)\n",
      "sig2 = 2.*np.ones(M.nC)\n",
      "sig3 = np.zeros(M.nC)\n",
      "xL = (np.abs(M.gridCC[:,0]-0.5)<0.25)\n",
      "yL = (np.abs(M.gridCC[:,1]-0.5)<0.25)\n",
      "sig3[np.logical_and(xL,yL)] = 0.25\n",
      "sig = np.c_[sig1,sig2,sig3]\n",
      "\n",
      "Msig_ani = M.getFaceInnerProduct(sig)\n",
      "Msig_iso = M.getFaceInnerProduct(sig1)\n",
      "\n",
      "rhs = np.zeros(M.nCv)\n",
      "rhs[[3,27],[10,30]] = [-1,1]\n",
      "rhs = utils.mkvc(rhs)\n",
      "M.plotImage(rhs)\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 51,
       "text": [
        "<matplotlib.collections.QuadMesh at 0x111b2a250>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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RJg324gr24gr24tq5FobBwUFJUlFRkXw+n0pKStTd3W3WdHd3q6qqSrNnz1YgENBbb73l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\ngEEYAADG/wKfDuvXnLtllAAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x1111c0790>"
       ]
      }
     ],
     "prompt_number": 51
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "phi_ani = Solver(D*Msig_ani*G).solve(rhs)\n",
      "phi_iso = Solver(D*Msig_iso*G).solve(rhs)\n",
      "M.plotImage(phi_ani, figNum=1)\n",
      "M.plotImage(phi_iso,figNum=2)\n",
      "M.plotImage(phi_iso - phi_ani,figNum=3)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 52,
       "text": [
        "<matplotlib.collections.QuadMesh at 0x111d90590>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x111b819d0>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x111b816d0>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x111b79450>"
       ]
      }
     ],
     "prompt_number": 52
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": []
    }
   ],
   "metadata": {}
  }
 ]
}

## thumbnail.png

      
    Raw
  

              thumbnail.png