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simpeg/simpegPF/notebooks/Jacobian.ipynb
T
2014-02-28 16:44:12 -08:00

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{
"metadata": {
"name": ""
},
"nbformat": 3,
"nbformat_minor": 0,
"worksheets": [
{
"cells": [
{
"cell_type": "code",
"collapsed": false,
"input": [
"from SimPEG import Mesh, Problem, Utils, np, sp, Tests\n",
"from simpegPF.Magnetics import BaseMag, MagneticsDiffSecondary\n",
"from scipy.constants import mu_0\n",
"from simpegPF.MagAnalytics import spheremodel, CongruousMagBC\n",
"%pylab inline"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Populating the interactive namespace from numpy and matplotlib\n"
]
}
],
"prompt_number": 15
},
{
"cell_type": "code",
"collapsed": false,
"input": [],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 16
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import matplotlib.pyplot as plt\n",
"# hxind = ((5,25,1.3),(41, 12.5),(5,25,1.3))\n",
"# hyind = ((5,25,1.3),(41, 12.5),(5,25,1.3))\n",
"# hzind = ((5,25,1.3),(40, 12.5),(5,25,1.3))\n",
"\n",
"hxind = ((5,25,1.3),(21, 25.),(5,25,1.3))\n",
"hyind = ((5,25,1.3),(21, 25.),(5,25,1.3))\n",
"hzind = ((5,25,1.3),(20, 25.),(5,25,1.3))\n",
"\n",
"hx, hy, hz = Utils.meshTensors(hxind, hyind, hzind)\n",
"mesh = Mesh.TensorMesh([hx, hy, hz], [-hx.sum()/2,-hy.sum()/2,-hz.sum()/2])\n",
"\n",
"chibkg = 0.001\n",
"chiblk = 0.1\n",
"chi = np.ones(mesh.nC)*chibkg\n",
"sph_ind = spheremodel(mesh, 0., 0., 0., 100)\n",
"chi[sph_ind] = chiblk\n",
"model = BaseMag.BaseMagModel(mesh)\n",
"mu = (1.+chi)*mu_0\n",
"\n",
"data = BaseMag.BaseMagData()\n",
"data.setBackgroundField(x=1., y=1., z=0.)\n",
"xr = np.linspace(-300, 300, 41)\n",
"yr = np.linspace(-300, 300, 41)\n",
"X, Y = np.meshgrid(xr, yr)\n",
"Z = np.ones((xr.size, yr.size))*150\n",
"rxLoc = np.c_[Utils.mkvc(X), Utils.mkvc(Y), Utils.mkvc(Z)]\n",
"data.rxLoc = rxLoc\n",
"\n",
"prob = MagneticsDiffSecondary(mesh, model)\n",
"\n",
"prob.pair(data)\n"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 50
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"fields = prob.fields(chi)\n",
"u = fields['u']\n",
"B = fields['B']\n",
"# mesh.plotSlice(B, 'F', view='vec', showIt=True)\n",
"dpred = data.dpred(chi, fields)"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 51
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## ?? they are different ?"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"MfMui = mesh.getFaceInnerProduct(mu).diagonal()\n",
"MfMui_test = mesh.getFaceMass(mu).diagonal()\n",
"print np.linalg.norm(MfMui - MfMui_test)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"9.55511263546\n"
]
}
],
"prompt_number": 52
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"plot(MfMui/MfMui_test)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "pyout",
"prompt_number": 53,
"text": [
"[<matplotlib.lines.Line2D at 0x3363350>]"
]
},
{
"metadata": {},
"output_type": "display_data",
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RTGFhYYiMjMS///1vAEBtbS2SkpJw9913K/rvBwBVVVXy0NFXH+e7zpSQkID6\n+npMTExACIHa2lpotdo58Tx9/vnnAIDOzk6888472Lhxo7L//2Y8E+JDhw4dEkuWLBExMTGivLzc\nq4+9YcMGER4eLgICAoRGoxGvvvqquHjxosjMzJz2Mq/f/va3IiYmRsTHx4vq6mq5/OplXjExMeIX\nv/iFXD45OSnuv/9+eZlXe3v7jJmOHj0qVCqV0Ov18nK9w4cPK5rr5MmTwmg0Cr1eL5KTk8Xvfvc7\nIYRQ/Ln6MqvVKq8+UjLXp59+KvR6vdDr9SIpKUn+zCr9XLW0tIjU1FSRkpIi8vLyxODgoOKZRkdH\nxaJFi8Tw8LBcpnSmiooKeUnqww8/LOx2u+KZhBBixYoVQqvVCr1eL95//33FnyuPb14jIqLvF37y\nGhERSSwFIiKSWApERCSxFIiISGIpEBGRxFIgIiLpfwGexzRJjCWLBQAAAABJRU5ErkJggg==\n",
"text": [
"<matplotlib.figure.Figure at 0x1fa10d0>"
]
}
],
"prompt_number": 53
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"def MfmuIfun(mu):\n",
" \n",
"# MfMui = mesh.getFaceMass(1./mu)\n",
" \n",
" MfMui = mesh.getFaceInnerProduct(1./mu)*1/3\n",
" # There are scaling issue for Face inner product!! and bit slower than getFaceMass\n",
" \n",
" MfMuI = 1/MfMui.diagonal()\n",
"# dMfMuI = Utils.sdiag(MfMuI**2)*mesh.aveF2CC.T*Utils.sdiag(mesh.vol*1./mu**2)\n",
" dMfMuI = Utils.sdiag(MfMuI**2)*mesh.aveF2CC.T*Utils.sdiag(mesh.vol*1./mu**2)\n",
" \n",
" return MfMuI, dMfMuI"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 54
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"d_mu = 0.8*mu\n",
"# I am not sure why it does not give us second order accuracy\n",
"Tests.checkDerivative(MfmuIfun, mu, dx=d_mu, num=5, plotIt=False)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"==================== checkDerivative ====================\n",
"iter\th\t\t|J0-Jt|\t\t|J0+h*dJ'*dx-Jt|\tOrder\n",
"---------------------------------------------------------\n",
"0\t1.00e-01\t4.299e-09\t\t1.152e-23\t\tnan"
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
"1\t1.00e-02\t4.299e-10\t\t7.723e-24\t\t0.174"
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
"2\t1.00e-03\t4.299e-11\t\t1.170e-23\t\t-0.180"
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
"3\t1.00e-04\t4.299e-12\t\t8.749e-24\t\t0.126"
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
"4\t1.00e-05\t4.299e-13\t\t1.107e-23\t\t-0.102"
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
"========================= PASS! =========================\n",
"Once upon a time, a happy little test passed.\n",
"\n"
]
},
{
"metadata": {},
"output_type": "pyout",
"prompt_number": 55,
"text": [
"True"
]
}
],
"prompt_number": 55
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"def derBbc(chi):\n",
" Bbc, const = CongruousMagBC(mesh, np.array([1., 1., 0.]), chi)\n",
" bc = Utils.sdiag(prob.mesh.vol)*prob.mesh.faceDiv*prob._Pout.T*Bbc \n",
" print const, np.linalg.norm(Bbc)\n",
" dBbc = lambda x: (Utils.sdiag(prob.mesh.vol)*(prob.mesh.faceDiv*prob._Pout.T*const*Bbc))*(np.inner(prob.mesh.vol, x)) \n",
" return bc, dBbc"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 56
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"a, b = derBbc(chi)\n",
"print np.linalg.norm(a), np.linalg.norm(b(chi))\n",
"print np.linalg.norm(chi)\n",
"print np.array([1., 1., 0.])\n",
"print mesh"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"7.65830184557e-07 0.0659506783728\n",
"55.718105908 55.6914561973\n",
"1.6089045963\n",
"[ 1. 1. 0.]\n",
" ---- 3-D TensorMesh ---- \n",
" x0: -488.58\n",
" y0: -488.58\n",
" z0: -476.08\n",
" nCx: 31\n",
" nCy: 31\n",
" nCz: 30\n",
" hx: 71.40, 54.93, 42.25, 32.50, 23*25.00, 32.50, 42.25, 54.93, 71.40\n",
" hy: 71.40, 54.93, 42.25, 32.50, 23*25.00, 32.50, 42.25, 54.93, 71.40\n",
" hz: 71.40, 54.93, 42.25, 32.50, 22*25.00, 32.50, 42.25, 54.93, 71.40\n"
]
}
],
"prompt_number": 57
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"d_chi = 0.8*chi\n",
"# I am not sure why it does not give us second order accuracy\n",
"Tests.checkDerivative(derBbc, chi, dx=d_chi, num=5, plotIt=False)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"==================== checkDerivative ====================\n",
"iter\th\t\t|J0-Jt|\t\t|J0+h*dJ'*dx-Jt|\tOrder\n",
"---------------------------------------------------------\n",
"7.65830184557e-07"
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
" 0.0659506783728\n",
"7.0907489096e-07"
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
" 0.0712240073538\n",
"0\t1.00e-01\t4.455e+00\t\t1.705e-04\t\tnan\n",
"7.59749260143e-07"
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
" 0.0664780294308\n",
"1\t1.00e-02\t4.455e-01\t\t1.705e-06\t\t2.000\n",
"7.65217717349e-07"
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
" 0.0660034136602\n",
"2\t1.00e-03\t4.455e-02\t\t1.706e-08\t\t2.000\n",
"7.65768893742e-07"
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
" 0.0659559519034\n",
"3\t1.00e-04\t4.455e-03\t\t1.749e-10\t\t1.989\n",
"7.65824055034e-07"
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
" 0.0659512057259\n",
"4\t1.00e-05\t4.455e-04\t\t2.506e-12\t\t1.844\n",
"========================= PASS! =========================\n",
"The test be workin!\n",
"\n"
]
},
{
"metadata": {},
"output_type": "pyout",
"prompt_number": 58,
"text": [
"True"
]
}
],
"prompt_number": 58
},
{
"cell_type": "code",
"collapsed": false,
"input": [],
"language": "python",
"metadata": {},
"outputs": []
}
],
"metadata": {}
}
]
}