simpeg/notebooks/BFGS.ipynb

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     "cell_type": "code",
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     "input": [
      "import SimPEG\n",
      "from SimPEG import Solver\n",
      "from SimPEG.mesh import TensorMesh\n",
      "from SimPEG.regularization import Regularization\n",
      "import SimPEG.inverse as inverse\n",
      "from SimPEG.inverse import Minimize, Remember, IterationPrinters\n",
      "import numpy as np\n",
      "import scipy.sparse as sp"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 2
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "FUN = SimPEG.tests.Rosenbrock\n",
      "FUN = SimPEG.tests.getQuadratic(sp.csr_matrix(([100,1],([0,1],[0,1])),shape=(2,2)),np.array([-5,-5]),100)\n",
      "\n",
      "x0 = np.array([1,0])\n",
      "opt = inverse.BFGS()\n",
      "xopt = opt.minimize(FUN,x0)\n",
      "print xopt\n",
      "opt = inverse.GaussNewton()\n",
      "xopt = opt.minimize(FUN,x0)\n",
      "print xopt\n",
      "opt = inverse.SteepestDescent()\n",
      "xopt = opt.minimize(FUN,x0)\n",
      "print xopt"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "===================== BFGS =====================\n",
        "  #      f      |proj(x-g)-x|  LS    Comment   \n",
        "-----------------------------------------------\n",
        "   0  1.45e+02    9.51e+01      0              \n",
        "   1  1.14e+02    5.37e+01      6              \n",
        "   2  1.04e+02    3.04e+01      6              \n",
        "   3  8.83e+01    1.37e+01      0              \n",
        "   4  8.76e+01    5.97e+00      0   Skip BFGS  \n",
        "   5  8.74e+01    2.61e+00      0   Skip BFGS  \n",
        "   6  8.74e+01    1.14e+00      0   Skip BFGS  \n",
        "   7  8.74e+01    5.01e-01      0   Skip BFGS  \n",
        "   8  8.74e+01    2.19e-01      0   Skip BFGS  \n",
        "   9  8.74e+01    9.60e-02      0   Skip BFGS  \n",
        "------------------------- STOP! -------------------------\n",
        "1 : |fc-fOld| = 1.9437e-04 <= tolF*(1+|f0|) = 1.4600e+01\n",
        "1 : |xc-x_last| = 1.2663e-03 <= tolX*(1+|x0|) = 2.0000e-01\n",
        "1 : |proj(x-g)-x|    = 9.5952e-02 <= tolG          = 1.0000e-01\n",
        "0 : |proj(x-g)-x|    = 9.5952e-02 <= 1e3*eps       = 1.0000e-02\n",
        "0 : maxIter   =      20    <= iter          =      9\n",
        "------------------------- DONE! -------------------------\n",
        "[ 0.05095952  4.99977449]\n",
        "=========== Gauss Newton ===========\n",
        "  #      f      |proj(x-g)-x|  LS  \n",
        "-----------------------------------\n",
        "   0  1.45e+02    9.51e+01      0  \n",
        "   1  8.74e+01    4.44e-15      0  \n",
        "------------------------- STOP! -------------------------\n",
        "0 : |fc-fOld| = 5.7625e+01 <= tolF*(1+|f0|) = 1.4600e+01\n",
        "0 : |xc-x_last| = 5.0894e+00 <= tolX*(1+|x0|) = 2.0000e-01\n",
        "1 : |proj(x-g)-x|    = 4.4409e-15 <= tolG          = 1.0000e-01\n",
        "1 : |proj(x-g)-x|    = 4.4409e-15 <= 1e3*eps       = 1.0000e-02\n",
        "0 : maxIter   =      20    <= iter          =      1\n",
        "------------------------- DONE! -------------------------\n",
        "[ 0.05  5.  ]\n",
        "========= Steepest Descent =========\n",
        "  #      f      |proj(x-g)-x|  LS  \n",
        "-----------------------------------\n",
        "   0  1.45e+02    9.51e+01      0  \n",
        "   1  1.14e+02    5.37e+01      6  \n",
        "   2  1.04e+02    3.04e+01      6  \n",
        "   3  1.00e+02    1.76e+01      6  \n",
        "   4  9.88e+01    1.06e+01      6  \n",
        "   5  9.82e+01    7.07e+00      6  \n",
        "   6  9.80e+01    1.22e+01      5  \n",
        "   7  9.73e+01    7.77e+00      6  \n",
        "   8  9.68e+01    5.64e+00      6  \n",
        "   9  9.65e+01    8.72e+00      5  \n",
        "  10  9.60e+01    5.97e+00      6  \n",
        "  11  9.58e+01    9.98e+00      5  \n",
        "  12  9.53e+01    6.48e+00      6  \n",
        "  13  9.53e+01    1.16e+01      5  \n",
        "  14  9.46e+01    7.20e+00      6  \n",
        "  15  9.43e+01    5.07e+00      6  \n",
        "  16  9.41e+01    8.17e+00      5  \n",
        "  17  9.37e+01    5.43e+00      6  \n",
        "  18  9.36e+01    9.42e+00      5  \n",
        "  19  9.32e+01    5.98e+00      6  \n",
        "  20  9.29e+01    4.32e+00      6  \n",
        "------------------------- STOP! -------------------------\n",
        "1 : |fc-fOld| = 2.5913e-01 <= tolF*(1+|f0|) = 1.4600e+01\n",
        "1 : |xc-x_last| = 9.3379e-02 <= tolX*(1+|x0|) = 2.0000e-01\n",
        "0 : |proj(x-g)-x|    = 4.3246e+00 <= tolG          = 1.0000e-01\n",
        "0 : |proj(x-g)-x|    = 4.3246e+00 <= 1e3*eps       = 1.0000e-02\n",
        "1 : maxIter   =      20    <= iter          =     20\n",
        "------------------------- DONE! -------------------------\n",
        "[ 0.07777107  1.6849632 ]\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stderr",
       "text": [
        "/Users/rowan/git/simpeg/SimPEG/inverse/Optimize.py:664: RuntimeWarning: divide by zero encountered in remainder\n",
        "  khat    = np.mod(n-nn+k,nn)\n"
       ]
      }
     ],
     "prompt_number": 3
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "A = sp.identity(2)\n",
      "S = Solver(A)\n",
      "\n",
      "assert type(S) is Solver"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 6
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": []
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