Fix examples folder

docs/api_PF.rst

@@ -100,7 +100,7 @@ Since most materials in the earth  have lower permeability than \\(\\mu_0\\), us
 Since we compute secondary field based on the earth field, which can be different from different locations in the world, we can expect different anomalous responses in different locations in the earth. For instance, assume we have two susceptible spheres, which are exactly same. However, anomalous responses in Seoul and Vancouver are going to be different.
 
 
-.. plot :: /home/seogi/Documents/simpegpf/docs/figures/figure1.py
+.. plot :: examples/Mag_back_1.py
 
 Since we can measure total fields ( \\(\\vec{B}\\)), and usually have reasonably accurate earth field (\\(\\vec{B}_0\\)), we can compute anmalous fields, \\(\\vec{B}_s\\) from our observed data. If you want to download earth magnetic fields at specific location see this website (`noaa <http://www.ngdc.noaa.gov/geomag-web/>`_).
 

docs/examples/Mag_back_1.py

@@ -0,0 +1,47 @@
+from simpegPF.MagAnalytics import MagSphereAnalFunA, IDTtoxyz
+from SimPEG import *
+import matplotlib.pyplot as plt
+from mpl_toolkits.axes_grid1 import make_axes_locatable
+
+xr = np.linspace(-300, 300, 41)
+yr = np.linspace(-300, 300, 41)
+X, Y = np.meshgrid(xr, yr)
+Z = np.ones((np.size(xr), np.size(yr)))*150
+
+
+# Bz component at Korea
+inckr = -8. + 3/60
+deckr = 54. + 9/60
+btotkr = 50898.6
+Bokr = IDTtoxyz(inckr, deckr, btotkr)
+
+bx,by,bz = MagSphereAnalFunA(X, Y, Z,100.,0.,0.,0.,0.01,Bokr,'secondary')
+Bzkr = np.reshape(bz, (np.size(xr), np.size(yr)), order='F')
+
+# Bz component at Canada
+incca = 16. + 49/60
+decca = 70. + 19/60
+btotca = 54692.1
+Boca = IDTtoxyz(incca, decca, btotca)
+
+bx,by,bz = MagSphereAnalFunA(X, Y, Z,100.,0.,0.,0.,0.01,Boca,'secondary')
+Bzca = np.reshape(bz, (np.size(xr), np.size(yr)), order='F')
+
+fig = plt.figure( figsize = (14,5) )
+
+ax1 = plt.subplot(121)
+dat1 = plt.imshow(Bzkr, extent=[min(xr), max(xr), min(yr), max(yr)]); 
+divider = make_axes_locatable(ax1)
+cax1 = divider.append_axes("right", size="5%", pad=0.05)
+ax1.set_xlabel('East-West (m)'); ax1.set_ylabel('South-North (m)')
+plt.colorbar(dat1, cax=cax1)
+ax1.set_title('$B_z$ field at Seoul, South Korea')
+
+ax2 = plt.subplot(122)
+dat2 = plt.imshow(Bzca, extent=[min(xr), max(xr), min(yr), max(yr)]); 
+divider = make_axes_locatable(ax2)
+cax2 = divider.append_axes("right", size="5%", pad=0.05)
+ax2.set_xlabel('East-West (m)'); ax2.set_ylabel('South-North (m)')
+plt.colorbar(dat2, cax=cax2)
+ax2.set_title('$B_z$ field at Vancouver, Canada')
+plt.show()

simpegPF/Tests/test_forward_PFproblem.py

@@ -1,23 +1,55 @@
 import unittest
 from SimPEG import *
+import matplotlib.pyplot as plt
 import simpegPF as PF
 
 
 class MagProblemTests(unittest.TestCase):
 
     def setUp(self):
-        M = Mesh.TensorMesh([10,10])
-        mod = Model.LogModel(M)
-        prob = PF.Mag.MagProblem(M, mod, None)
 
+        hxind = ((5,25,1.3),(41, 12.5),(5,25,1.3))
+        hyind = ((5,25,1.3),(41, 12.5),(5,25,1.3))
+        hzind = ((5,25,1.3),(40, 12.5),(5,25,1.3))
+        hx, hy, hz = Utils.meshTensors(hxind, hyind, hzind)
+        M = Mesh.TensorMesh([hx, hy, hz], [-hx.sum()/2,-hy.sum()/2,-hz.sum()/2])
+
+        chibkg = 0.
+        chiblk = 0.01
+        chi = np.ones(M.nC)*chibkg
+        sph_ind = PF.MagAnalytics.spheremodel(M, 0., 0., 0., 100)
+        chi[sph_ind] = chiblk
+        model = PF.BaseMag.BaseMagModel(M)
+        prob = PF.Magnetics.MagneticsDiffSecondary(M, model)
         self.prob = prob
         self.M = M
+        self.chi = chi
 
-    def test_forward(self):
 
-        passed = True
-        self.assertTrue(passed)
+    def test_anal_forward(self):
 
+        data = PF.BaseMag.BaseMagData()
+        data.setBackgroundField(x=1., y=1., z=0.)
+        xr = np.linspace(-300, 300, 41)
+        yr = np.linspace(-300, 300, 41)
+        X, Y = np.meshgrid(xr, yr)
+        Z = np.ones((xr.size, yr.size))*150
+        rxLoc = np.c_[Utils.mkvc(X), Utils.mkvc(Y), Utils.mkvc(Z)]
+        data.rxLoc = rxLoc
+            
+        self.prob.pair(data)
+        B = self.prob.fields(self.chi)
+
+        bxa,bya,bza = PF.MagAnalytics.MagSphereAnalFunA(rxLoc[:,0],rxLoc[:,1],rxLoc[:,2],100.,0.,0.,0.,0.01,np.array([1.,1.,0.]),'secondary') 
+       
+        dpred = data.projectFieldsAsVector(B)
+        err = np.linalg.norm(dpred-np.r_[bxa, bya, bza])/np.linalg.norm(np.r_[bxa, bya, bza])
+
+        if err > 0.05:
+            raise Exception('Anaytic test is failed T.T')
+        else:
+            print "Anaytic test is passed"
+            pass
 
 if __name__ == '__main__':
     unittest.main()

simpegPF/notebooks/Jacobian.ipynb

@@ -0,0 +1,400 @@
+{
+ "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": 3
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "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",
+      "hx, hy, hz = Utils.meshTensors(hxind, hyind, hzind)\n",
+      "M3 = Mesh.TensorMesh([hx, hy, hz], [-sum(hx)/2,-sum(hy)/2,-sum(hz)/2])"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [],
+     "prompt_number": 4
+    },
+    {
+     "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",
+      "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": 5
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "phi, B = prob.fields(chi)\n",
+      "# mesh.plotSlice(B, 'F', view='vec', showIt=True)\n",
+      "dpred = data.dpred(chi, u=B)"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [],
+     "prompt_number": 4
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "test = {'B': B, 'u': phi}"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [],
+     "prompt_number": 5
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "print test['B']"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "output_type": "stream",
+       "stream": "stdout",
+       "text": [
+        "[ 0.001       0.00032989  0.00039923 ...,  0.          0.          0.        ]\n"
+       ]
+      }
+     ],
+     "prompt_number": 7
+    },
+    {
+     "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": [
+        "6.99232804893\n"
+       ]
+      }
+     ],
+     "prompt_number": 6
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "plot(MfMui/MfMui_test)"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "metadata": {},
+       "output_type": "pyout",
+       "prompt_number": 7,
+       "text": [
+        "[<matplotlib.lines.Line2D at 0x301f910>]"
+       ]
+      },
+      {
+       "metadata": {},
+       "output_type": "display_data",
+       "png": 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truncated
+       "text": [
+        "<matplotlib.figure.Figure at 0x2d7f0d0>"
+       ]
+      }
+     ],
+     "prompt_number": 7
+    },
+    {
+     "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": 8
+    },
+    {
+     "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\t7.240e-08\t\t1.904e-22\t\tnan"
+       ]
+      },
+      {
+       "output_type": "stream",
+       "stream": "stdout",
+       "text": [
+        "\n",
+        "1\t1.00e-02\t7.240e-09\t\t1.009e-22\t\t0.276"
+       ]
+      },
+      {
+       "output_type": "stream",
+       "stream": "stdout",
+       "text": [
+        "\n",
+        "2\t1.00e-03\t7.240e-10\t\t2.166e-22\t\t-0.332"
+       ]
+      },
+      {
+       "output_type": "stream",
+       "stream": "stdout",
+       "text": [
+        "\n",
+        "3\t1.00e-04\t7.240e-11\t\t9.316e-23\t\t0.366"
+       ]
+      },
+      {
+       "output_type": "stream",
+       "stream": "stdout",
+       "text": [
+        "\n",
+        "4\t1.00e-05\t7.240e-12\t\t2.209e-22\t\t-0.375"
+       ]
+      },
+      {
+       "output_type": "stream",
+       "stream": "stdout",
+       "text": [
+        "\n",
+        "========================= PASS! =========================\n",
+        "You are awesome.\n",
+        "\n"
+       ]
+      },
+      {
+       "metadata": {},
+       "output_type": "pyout",
+       "prompt_number": 9,
+       "text": [
+        "True"
+       ]
+      }
+     ],
+     "prompt_number": 9
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "def derBbc(chi):\n",
+      "    Bbc, const = CongruousMagBC(mesh, np.array([1., 0., 0.]), chi)\n",
+      "    bc = Utils.sdiag(prob.mesh.vol)*prob.mesh.faceDiv*prob._Pout.T*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": 8
+    },
+    {
+     "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",
+        "0\t1.00e-01\t2.212e+00\t\t8.604e-05\t\tnan"
+       ]
+      },
+      {
+       "output_type": "stream",
+       "stream": "stdout",
+       "text": [
+        "\n",
+        "1\t1.00e-02\t2.212e-01\t\t8.604e-07\t\t2.000"
+       ]
+      },
+      {
+       "output_type": "stream",
+       "stream": "stdout",
+       "text": [
+        "\n",
+        "2\t1.00e-03\t2.212e-02\t\t8.574e-09\t\t2.001"
+       ]
+      },
+      {
+       "output_type": "stream",
+       "stream": "stdout",
+       "text": [
+        "\n",
+        "3\t1.00e-04\t2.212e-03\t\t9.857e-11\t\t1.939"
+       ]
+      },
+      {
+       "output_type": "stream",
+       "stream": "stdout",
+       "text": [
+        "\n",
+        "4\t1.00e-05\t2.212e-04\t\t1.424e-11\t\t0.840"
+       ]
+      },
+      {
+       "output_type": "stream",
+       "stream": "stdout",
+       "text": [
+        "\n",
+        "========================= PASS! =========================\n",
+        "Awesome, Seogi, just awesome.\n",
+        "\n"
+       ]
+      },
+      {
+       "metadata": {},
+       "output_type": "pyout",
+       "prompt_number": 9,
+       "text": [
+        "True"
+       ]
+      }
+     ],
+     "prompt_number": 9
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "##################\n",
+      "# Test J\n",
+      "##################\n",
+      "\n",
+      "d_chi = 0.8*chi #np.random.rand(mesh.nCz)\n",
+      "d_sph_ind = spheremodel(mesh, 0., 0., -100., 50)\n",
+      "d_chi[d_sph_ind] = 0.02\n",
+      "\n",
+      "from SimPEG.Tests import checkDerivative\n",
+      "\n",
+      "derChk = lambda m: [prob.data.dpred(m), lambda mx: -prob.Jvec(chi, mx)]\n",
+      "print '\\n'\n",
+      "passed = checkDerivative(derChk, chi, plotIt=False, dx=d_chi, num=2)\n",
+      "\n",
+      "\n",
+      "# plt.pcolor(X, Y, dpred.reshape(X.shape, order='F'))\n",
+      "\n",
+      "# plt.show()"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": []
+    }
+   ],
+   "metadata": {}
+  }
+ ]
+}