A trial implementation for the refactor of the fatiando.inversion package

trial_inversion_refactor.ipynb

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  "name": "trial_inversion_refactor"
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  {
   "cells": [
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "# Sample implementation for the fatiando.inversion package refactor"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%pylab inline\n",
      "import numpy\n",
      "import matplotlib.pyplot as plt\n",
      "import scipy.sparse"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Welcome to pylab, a matplotlib-based Python environment [backend: module://IPython.kernel.zmq.pylab.backend_inline].\n",
        "For more information, type 'help(pylab)'.\n"
       ]
      }
     ],
     "prompt_number": 1
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def safe_solve(matrix, vector):\n",
      "    if scipy.sparse.issparse(matrix) or scipy.sparse.issparse(vector):\n",
      "        estimate, status = scipy.sparse.linalg.cgs(matrix, vector)\n",
      "        if status >= 0:\n",
      "            return estimate\n",
      "        else:\n",
      "            raise ValueError('CGS exited with input error')\n",
      "    else:\n",
      "        return numpy.linalg.solve(matrix, vector)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 2
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## Non-linear optimizer\n",
      "\n",
      "Optimizers receive a list of goal functions, initial estimate and auxiliary variables.\n",
      "Goal functions know how to compute their value, gradient and Hessian at a given point in parameter space `p`.\n",
      "Goal functions need to be \"moved\" to the computation point before getting these values using the `.at(p)` method call.\n",
      "The `.precompute(p)` method call is when the goal functions can compute intensive tasks (like Jacobian matrix building) in order to not repeat the computation when calculating gradient and Hessian."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def levmarq(goals, initial, maxit=30, maxsteps=10, lamb=10, dlamb=2, tol=10**-5, precondition=True):\n",
      "    nparams = len(initial)\n",
      "    diag = range(len(initial))\n",
      "    p = initial\n",
      "    misfit = sum(g.mu*g.at(p).value() for g in goals)\n",
      "    for iteration in xrange(maxit):\n",
      "        [g.precompute() for g in goals]\n",
      "        if precondition:\n",
      "            hessian = numpy.zeros((nparams, nparams))\n",
      "            minus_gradient = numpy.zeros(nparams)\n",
      "            for g in goals:\n",
      "                h = g.hessian()\n",
      "                precond = numpy.abs(h[diag,diag])\n",
      "                precond[precond < 10**-10] = 10**-10\n",
      "                hessian += g.mu*(h.T/precond).T\n",
      "                minus_gradient -= g.mu*g.gradient()/precond\n",
      "        else:\n",
      "            hessian = sum(g.mu*g.hessian() for g in goals)\n",
      "            minus_gradient = -sum(g.mu*g.gradient() for g in goals)\n",
      "        stagnation = True\n",
      "        for step in xrange(maxsteps):\n",
      "            damping = lamb*hessian[diag,diag]\n",
      "            hessian[diag,diag] += damping\n",
      "            newp = p + safe_solve(hessian, minus_gradient)\n",
      "            newmisfit = sum(g.mu*g.at(newp).value() for g in goals)\n",
      "            if newmisfit >= misfit:\n",
      "                hessian[diag,diag] -= damping\n",
      "                if lamb < 10**15:\n",
      "                    lamb *= dlamb\n",
      "            else:\n",
      "                if lamb > 10**-15:\n",
      "                    lamb /= float(dlamb)\n",
      "                stagnation = False\n",
      "                break\n",
      "        if stagnation:       \n",
      "            [g.at(p) for g in goals]\n",
      "            stop = True\n",
      "        else:\n",
      "            p = newp\n",
      "            stop = newmisfit < misfit and abs((newmisfit - misfit)/float(misfit)) < tol\n",
      "            misfit = newmisfit            \n",
      "        yield p, misfit, {'steps':step + 1, 'stagnation':stagnation, 'lambda':lamb}\n",
      "        if stop:\n",
      "            break"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 3
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## Linear solver\n",
      "\n",
      "The linear overdetermined solver asks for the hessian and the gradient calculated at the null vector:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def overdetermined(goals):\n",
      "    [g.precompute() for g in goals]\n",
      "    hessian = None\n",
      "    gradient = None\n",
      "    for g in goals:\n",
      "        h = g.hessian()\n",
      "        if hessian is None and gradient is None:\n",
      "            nparams = len(h)\n",
      "            hessian = numpy.zeros((nparams, nparams))\n",
      "            gradient = numpy.zeros(nparams)\n",
      "            diag = range(nparams)\n",
      "        precond = numpy.abs(h[diag,diag])\n",
      "        precond[precond < 10**-10] = 10**-10\n",
      "        hessian += g.mu*(h.T/precond).T\n",
      "        gradient += g.mu*g.gradient_at_null()/precond\n",
      "    p = safe_solve(hessian, -gradient)\n",
      "    [g.at(p) for g in goals]\n",
      "    return p    "
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 4
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## Goal functions\n",
      "\n",
      "An $\\ell_2$-norm goal function. This is a generic goal function and needs to be subclassed in order to be used."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "class L2Norm(object):\n",
      "    def __init__(self, data, weights=None):\n",
      "        super(L2Norm, self).__init__()\n",
      "        self.data = data\n",
      "        self.size = len(data)\n",
      "        self.mu = 1.\n",
      "        self._p = None\n",
      "        self._predicted = None\n",
      "        self._jacobian = None\n",
      "        self.weights = weights\n",
      "        \n",
      "    def at(self, p):\n",
      "        self._predicted = self.predicted(p)\n",
      "        self._p = p\n",
      "        self._jacobian = None\n",
      "        return self\n",
      "        \n",
      "    def precompute(self):\n",
      "        self._jacobian = self.jacobian(self._p)\n",
      "        \n",
      "    def residuals(self):\n",
      "        return self.data - self._predicted\n",
      "\n",
      "    def value(self):\n",
      "        if self.weights is None:            \n",
      "            return numpy.linalg.norm(self.residuals())**2/self.size\n",
      "        else:\n",
      "            return numpy.sum(self.weights*(self.residuals()**2))/self.size \n",
      "    \n",
      "    def hessian(self):\n",
      "        if self.weights is None:\n",
      "            return 2*numpy.dot(self._jacobian.T, self._jacobian)/self.size\n",
      "        else:\n",
      "            return 2*numpy.dot(self._jacobian.T, (self.weights*self._jacobian.T).T)/self.size\n",
      "    \n",
      "    def gradient(self):\n",
      "        if self.weights is None:\n",
      "            return -2*numpy.dot(self._jacobian.T, self.residuals())/self.size\n",
      "        else:\n",
      "            return -2*numpy.dot(self._jacobian.T, self.weights*self.residuals())/self.size\n",
      "    \n",
      "    def gradient_at_null(self):\n",
      "        if self.weights is None:\n",
      "            return -2*numpy.dot(self._jacobian.T, self.data)/self.size\n",
      "        else:\n",
      "            return -2*numpy.dot(self._jacobian.T, self.weights*self.data)/self.size\n",
      "    \n",
      "    def jacobian(self, p):\n",
      "        raise NotImplementedError(\"Jacobian matrix not implemented\")\n",
      "    \n",
      "    def predicted(self, p):\n",
      "        raise NotImplementedError(\"Predicted data not implemented\") \n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 5
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Regularizing functions are also goal functions:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "class Damping(object):\n",
      "    def __init__(self, mu, size):\n",
      "        super(Damping, self).__init__()\n",
      "        self.size = size\n",
      "        self._stored_hessian = 2*numpy.identity(size)\n",
      "        self.mu = mu\n",
      "        self._p = None\n",
      "        \n",
      "    def at(self, p):\n",
      "        self._p = p\n",
      "        return self\n",
      "        \n",
      "    def precompute(self):\n",
      "        pass\n",
      "        \n",
      "    def value(self):\n",
      "        return numpy.linalg.norm(self._p)**2\n",
      "    \n",
      "    def hessian(self):\n",
      "        return self._stored_hessian\n",
      "    \n",
      "    def gradient(self):\n",
      "        return 2*self._p\n",
      "    \n",
      "    def gradient_at_null(self):\n",
      "        return 0\n",
      "    \n",
      "class Smoothness(object):    \n",
      "    def __init__(self, mu, hessian):\n",
      "        super(Smoothness, self).__init__()\n",
      "        self.mu = mu\n",
      "        self._p = None\n",
      "        self._stored_hessian = hessian\n",
      "    \n",
      "    def at(self, p):\n",
      "        self._p = p\n",
      "        return self\n",
      "        \n",
      "    def precompute(self):\n",
      "        pass\n",
      "        \n",
      "    def value(self):\n",
      "        # Need to divide by 2 because the hessian is 2*R.T*R\n",
      "        return numpy.sum(self._p*numpy.dot(self._stored_hessian, self._p))/2.\n",
      "    \n",
      "    def hessian(self):\n",
      "        return self._stored_hessian\n",
      "    \n",
      "    def gradient(self):\n",
      "        return 2*self._p\n",
      "    \n",
      "    def gradient_at_null(self):\n",
      "        return 0\n",
      "    \n",
      "class Smoothness1D(Smoothness):\n",
      "    def __init__(self, mu, size):\n",
      "        super(Smoothness1D, self).__init__(mu, self._calculate_hessian(size))\n",
      "        self.size = size\n",
      "    \n",
      "    def _calculate_hessian(self, size):\n",
      "        fd = numpy.zeros((size - 1, size), dtype='f')\n",
      "        fd[xrange(size - 1),xrange(size - 1)] = 1\n",
      "        fd[xrange(size - 1),xrange(1, size)] = -1        \n",
      "        return 2*numpy.dot(fd.T, fd)\n",
      "    "
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 6
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## Example use: polynomial regression\n",
      "\n",
      "This is a problem specific goal function that wraps the data and auxiliary values. It also knows how to compute the Jacobian matrix and predicted data for the case of a second order regression. Since this is a linear problem, the Jacobian can be computed only once."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "class PolyData(L2Norm):\n",
      "    def __init__(self, x, y, weights=None):\n",
      "        super(PolyData, self).__init__(y, weights)\n",
      "        self.x = x\n",
      "        self._stored_jacobian = None\n",
      "        \n",
      "    def _calculate_jacobian(self):\n",
      "        self._stored_jacobian = numpy.transpose([self.x**2, self.x, numpy.ones_like(x)])\n",
      "                \n",
      "    def jacobian(self, p):\n",
      "        if self._stored_jacobian is None:\n",
      "            self._calculate_jacobian()\n",
      "        return self._stored_jacobian\n",
      "\n",
      "    def predicted(self, p):\n",
      "        return numpy.dot(self._stored_jacobian, p)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 7
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Testing this on some synthetic data:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def fit(data, initial, log=True, **kwargs):\n",
      "    for i, step in enumerate(levmarq([data], initial, **kwargs)):\n",
      "        p, misfit, report = step\n",
      "    if log:\n",
      "        print 'estimate:', p.tolist(), misfit, report, 'iterations:', i\n",
      "    return p"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 8
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "x = numpy.linspace(0, 10, 100)\n",
      "numpy.random.seed(1)\n",
      "a, b, c = 10, -100, 30000\n",
      "y = a*x**2 + b*x + c + numpy.random.normal(scale=20, size=len(x))\n",
      "data = PolyData(x, y)\n",
      "plt.figure()\n",
      "# Use the linear solver\n",
      "print \"LINEAR:\"\n",
      "print 'estimated:', overdetermined([data]).tolist(), data.value()\n",
      "print 'true:', [a, b, c]\n",
      "plt.plot(x, y, '.k', x, data._predicted, '-r')\n",
      "# Run through the non-linear optimizer\n",
      "print \"NON-LINEAR:\"\n",
      "fit(data, numpy.array([0, 0, 0])).tolist()\n",
      "print 'true:', [a, b, c]\n",
      "plt.plot(x, data._predicted, '--b')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "LINEAR:\n",
        "estimated: [9.837849810927692, -97.7168087836429, 29995.228005273766] 308.15843054\n",
        "true: [10, -100, 30000]\n",
        "NON-LINEAR:\n",
        "estimate: [9.83784561494896, -97.71676464332248, 29995.22792434797] 308.158430541 {'stagnation': False, 'steps': 1, 'lambda': 7.62939453125e-05} iterations: 16\n",
        "true: [10, -100, 30000]\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 9,
       "text": [
        "[<matplotlib.lines.Line2D at 0x30f3110>]"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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cSc7OzjR8+HBat26d/Fqenp40bNgwcnV1JVdXV7p9+zYRET169IhmzJhBQ4cO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\nAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x2fe9f50>"
       ]
      }
     ],
     "prompt_number": 9
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## Example: Gaussian fit\n",
      "\n",
      "Fit an equation of the form:\n",
      "\n",
      "$$ f(x) = a\\exp(-b(x + c)^{2}) + d\\exp(-e(x + f)^{2}) $$"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "class ExpData(L2Norm):\n",
      "    def __init__(self, x, y):\n",
      "        super(ExpData, self).__init__(y)\n",
      "        self.x = x\n",
      "    \n",
      "    def jacobian(self, p):\n",
      "        jac = numpy.transpose(self._derivs(p[:3]) + self._derivs(p[3:]))\n",
      "        return jac\n",
      "    \n",
      "    def _derivs(self, coefs):\n",
      "        a, b, c = coefs\n",
      "        derivs = [\n",
      "            numpy.exp(-b*(self.x + c)**2),\n",
      "            # Do a numerical derivative for these two because I'm too lazy to do it by hand\n",
      "            (a*numpy.exp(-(b + 0.005)*(self.x + c)**2) - a*numpy.exp(-(b - 0.005)*(self.x + c)**2))/0.01,\n",
      "            (a*numpy.exp(-(b)*(self.x + c + 0.05)**2) - a*numpy.exp(-(b)*(self.x + c - 0.05)**2))/0.1]\n",
      "        return derivs\n",
      "    \n",
      "    def predicted(self, p):\n",
      "        a, b, c, d, e, f = p\n",
      "        return a*numpy.exp(-b*(self.x + c)**2) + d*numpy.exp(-e*(self.x + f)**2)\n",
      "            "
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 10
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "x = numpy.linspace(0, 10, 100)\n",
      "numpy.random.seed(1)\n",
      "a, b, c = 100, 0.1, -2\n",
      "d, e, f = 30, 2, -7\n",
      "y = a*numpy.exp(-b*(x + c)**2) + d*numpy.exp(-e*(x + f)**2) + numpy.random.normal(scale=5, size=len(x))\n",
      "data = ExpData(x, y)\n",
      "coefs = fit(data, numpy.array([1, 1, 1, 1, 1, -9]), lamb=10**5, maxit=100, tol=10**-8)\n",
      "print 'true:', [a, b, c, d, e, f]\n",
      "plt.figure()\n",
      "plt.plot(x, y, '.k', x, data._predicted, '-')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "estimate: [99.11974087126981, 0.09720867295485668, -2.0037337226897325, 29.95772769502588, 1.879659155339882, -6.948228224563931] 18.6717544304 {'stagnation': False, 'steps': 1, 'lambda': 4.6566128730773926e-05} iterations: 34\n",
        "true: [100, 0.1, -2, 30, 2, -7]\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 11,
       "text": [
        "[<matplotlib.lines.Line2D at 0x312a250>,\n",
        " <matplotlib.lines.Line2D at 0x312a490>]"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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WKL4sZxco2bsQ6dZboUMHa8tA8TyteBXxQf37D+Tjj78HmtC/fyx//3s8nTrB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\nRLSVAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x30036d0>"
       ]
      }
     ],
     "prompt_number": 11
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## Example: Using weights"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "x = numpy.linspace(0, 10, 150)\n",
      "numpy.random.seed(1)\n",
      "d, e, f = 300, 10, -7\n",
      "a, b, c = -10, 80, 1000\n",
      "y = a*x**2 + b*x + c + d*numpy.exp(-e*(x + f)**2) + numpy.random.normal(scale=20, size=len(x))\n",
      "data = PolyData(x, y)\n",
      "coefs = overdetermined([data])\n",
      "print [a, b, c]\n",
      "print coefs.tolist()\n",
      "plt.figure()\n",
      "plt.plot(x, y, '.k', x, data._predicted, '-')\n",
      "# Iteratively re-weight based on the residuals\n",
      "for k in xrange(100):\n",
      "    residuals = numpy.abs(data.residuals())\n",
      "    residuals[residuals < 10**-8] = 10**-8\n",
      "    data.weights = 1./residuals\n",
      "    coefs = overdetermined([data])\n",
      "print coefs.tolist()\n",
      "plt.plot(x, data._predicted, '--r')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "[-10, 80, 1000]\n",
        "[-11.374210598582058, 98.14592854854794, 973.3061300816588]\n",
        "[-10.2954807027229, 84.96441200274532, 989.7157319402121]\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 12,
       "text": [
        "[<matplotlib.lines.Line2D at 0x3109f90>]"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x2fd24d0>"
       ]
      }
     ],
     "prompt_number": 12
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## Example: 2D gravity inversion for the relief of a basin"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from fatiando import gravmag, mesher, utils\n",
      "from fatiando.vis import mpl"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 13
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "class Gz(L2Norm):\n",
      "    def __init__(self, x, z, gz, height, npoints, density):\n",
      "        super(Gz, self).__init__(gz)\n",
      "        self.x, self.z = x, z\n",
      "        self.height = height\n",
      "        self.nparams = npoints\n",
      "        self.shape = (self.size, self.nparams)\n",
      "        self.props = {'density':density}\n",
      "        self._left, self._right = [[x.min(), -height]], [[x.max(), -height]]\n",
      "        self._xs = numpy.linspace(x.min(), x.max(), npoints + 2)[::-1][1:-1]\n",
      "        \n",
      "    def p2vertices(self, p):\n",
      "        return self._right + numpy.transpose([self._xs, p]).tolist() + self._left\n",
      "        \n",
      "    def jacobian(self, p):\n",
      "        verts = self.p2vertices(p)\n",
      "        x, z = self.x, self.z\n",
      "        xs = self._xs\n",
      "        dz = 10.\n",
      "        jac = numpy.zeros(self.shape)\n",
      "        for i in xrange(self.nparams):\n",
      "            difference = mesher.Polygon([verts[i+2],[xs[i],p[i]-dz],verts[i],[xs[i],p[i]+dz]], self.props)\n",
      "            jac[:,i] = numpy.nan_to_num(gravmag.talwani.gz(x, z, [difference]))/(2.*dz)\n",
      "        return jac\n",
      "        \n",
      "    def predicted(self, p):\n",
      "        vertices = self.p2vertices(p)\n",
      "        return gravmag.talwani.gz(self.x, self.z, [mesher.Polygon(vertices, self.props)])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 14
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def basin2d(data, damp, smooth, **kwargs):\n",
      "    goals = [data]\n",
      "    if damp > 0:\n",
      "        goals.append(Damping(damp, data.nparams))\n",
      "    if smooth > 0:\n",
      "        goals.append(Smoothness1D(smooth, data.nparams))\n",
      "    initial = 5000*numpy.ones(data.nparams)\n",
      "    for i, step in enumerate(levmarq(goals, initial, **kwargs)):\n",
      "        p, misfit, report = step\n",
      "    print 'iterations:', i+1, report    \n",
      "    return mesher.Polygon(data.p2vertices(p), data.props)\n",
      "    "
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 15
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def mean_polygon(polygons):\n",
      "    x = numpy.mean([p.x for p in polygons], axis=0)\n",
      "    y = numpy.mean([p.y for p in polygons], axis=0)\n",
      "    return mesher.Polygon(numpy.transpose([x, y]).tolist())    "
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 16
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "x = numpy.linspace(0, 10000, 100)\n",
      "z = -10*numpy.ones_like(x)\n",
      "xs = numpy.linspace(0, 10000, 100)[::-1]\n",
      "depths = -10**-11*(xs - 5000)**4 + 6000 - 5000*numpy.exp(-(xs - 7000)**2/(1000**2))\n",
      "depths -= depths.min()\n",
      "density = -500\n",
      "model = mesher.Polygon(numpy.transpose([xs, depths]), {'density':density})\n",
      "gz = utils.contaminate(gravmag.talwani.gz(x, z, [model]), 0.5)\n",
      "data = Gz(x, z, gz, 0, 50, density)\n",
      "estimate = basin2d(data, 10**-10, 10**-9)\n",
      "mpl.figure(figsize=(10,6))\n",
      "mpl.subplot(2, 1, 2)\n",
      "mpl.polygon(model, fill='gray', alpha=0.5)\n",
      "npoints = 50\n",
      "estimates = [basin2d(Gz(x, z, utils.contaminate(gz, 0.5), 0, npoints, density), 10**-10, 10**-8)\n",
      "             for i in xrange(10)]\n",
      "mean = mean_polygon(estimates)\n",
      "mean.addprop('density', density)\n",
      "predicted = gravmag.talwani.gz(x, z, [mean])\n",
      "for estimate in estimates:\n",
      "    mpl.polygon(estimate, '-r')\n",
      "mpl.polygon(mean, '-b', linewidth=3) \n",
      "mpl.ylim(depths.max() + 1000, depths.min())\n",
      "mpl.xlim(x.min(), x.max())\n",
      "mpl.m2km()\n",
      "mpl.subplot(2, 1, 1)\n",
      "mpl.plot(x*0.001, gz, '.k')\n",
      "mpl.plot(x*0.001, predicted, '-r')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "iterations: 15 {'stagnation': True, 'steps': 10, 'lambda': 80.0}\n",
        "iterations:"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 11 {'stagnation': True, 'steps': 10, 'lambda': 160.0}\n",
        "iterations:"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 11 {'stagnation': True, 'steps': 10, 'lambda': 320.0}\n",
        "iterations:"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 12 {'stagnation': True, 'steps': 10, 'lambda': 10240.0}\n",
        "iterations:"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 12 {'stagnation': True, 'steps': 10, 'lambda': 2560.0}\n",
        "iterations:"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 11 {'stagnation': True, 'steps': 10, 'lambda': 320.0}\n",
        "iterations:"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 11 {'stagnation': False, 'steps': 9, 'lambda': 10.0}\n",
        "iterations:"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 11 {'stagnation': False, 'steps': 8, 'lambda': 5.0}\n",
        "iterations:"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 11 {'stagnation': True, 'steps': 10, 'lambda': 320.0}\n",
        "iterations:"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 11 {'stagnation': True, 'steps': 10, 'lambda': 80.0}\n",
        "iterations:"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 11 {'stagnation': True, 'steps': 10, 'lambda': 320.0}\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 17,
       "text": [
        "[<matplotlib.lines.Line2D at 0x395ce50>]"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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K7joiIiKlXGBgIJGRkdS0s2Nh9eo4bt0KM2di+uADwsLCgOK/hEeVrFt99BFUqwbPPAPp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\ngg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x31140d0>"
       ]
      }
     ],
     "prompt_number": 17
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%timeit basin2d(Gz(x, z, utils.contaminate(gz, 0.5), 0, npoints, density), 10**-10, 10**-8)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "iterations: 11 {'stagnation': True, 'steps': 10, 'lambda': 80.0}\n",
        "iterations:"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 12 {'stagnation': True, 'steps': 10, 'lambda': 20480.0}\n",
        "iterations:"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 11 {'stagnation': True, 'steps': 10, 'lambda': 160.0}\n",
        "iterations:"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 11 {'stagnation': True, 'steps': 10, 'lambda': 160.0}\n",
        "1 loops, best of 3: 1.21 s per loop\n"
       ]
      }
     ],
     "prompt_number": 20
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%prun -T inversion.profile basin2d(Gz(x, z, utils.contaminate(gz, 0.5), 0, npoints, density), 10**-10, 10**-8)\n",
      "!cat inversion.profile"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "iterations: 11 {'stagnation': False, 'steps': 10, 'lambda': 20.0}\n",
        " \n",
        "*** Profile printout saved to text file u'inversion.profile'. \n",
        "         53414 function calls (53390 primitive calls) in 1.218 seconds\r\n",
        "\r\n",
        "   Ordered by: internal time\r\n",
        "\r\n",
        "   ncalls  tottime  percall  cumtime  percall filename:lineno(function)\r\n",
        "      574    0.953    0.002    1.148    0.002 talwani.py:29(gz)\r\n",
        "    37928    0.192    0.000    0.192    0.000 talwani.py:59(<lambda>)\r\n",
        "     1806    0.017    0.000    0.017    0.000 {numpy.core.multiarray.array}\r\n",
        "       11    0.011    0.001    0.786    0.071 <ipython-input-14-a30b6bf021a5>:15(jacobian)\r\n",
        "      550    0.007    0.000    0.024    0.000 type_check.py:310(nan_to_num)\r\n",
        "       12    0.006    0.000    1.217    0.101 <ipython-input-3-0c488aa3c723>:1(levmarq)\r\n",
        "      550    0.005    0.000    0.007    0.000 ufunclike.py:51(isposinf)\r\n",
        "      550    0.003    0.000    0.004    0.000 ufunclike.py:113(isneginf)\r\n",
        "      575    0.003    0.000    0.019    0.000 mesher.py:86(__init__)\r\n",
        "      550    0.003    0.000    0.005    0.000 type_check.py:305(_getmaxmin)\r\n",
        "       47    0.002    0.000    0.002    0.000 {numpy.core._dotblas.dot}\r\n",
        "       23    0.001    0.000    0.001    0.000 {numpy.linalg.lapack_lite.dgesv}\r\n",
        "      596    0.001    0.000    0.001    0.000 {method 'get' of 'dict' objects}\r\n",
        "     1101    0.001    0.000    0.001    0.000 {numpy.core.multiarray.empty}\r\n",
        "     1230    0.001    0.000    0.003    0.000 numeric.py:167(asarray)\r\n",
        "      574    0.001    0.000    0.001    0.000 {numpy.core.multiarray.empty_like}\r\n",
        "      550    0.001    0.000    0.002    0.000 getlimits.py:91(__new__)\r\n",
        "      574    0.001    0.000    0.002    0.000 numeric.py:65(zeros_like)\r\n",
        "      575    0.001    0.000    0.001    0.000 mesher.py:47(__init__)\r\n",
        "      575    0.001    0.000    0.001    0.000 {method 'fill' of 'numpy.ndarray' objects}\r\n",
        "      550    0.001    0.000    0.001    0.000 {method 'copy' of 'numpy.ndarray' objects}\r\n",
        "       48    0.000    0.000    0.001    0.000 linalg.py:1840(norm)\r\n",
        "     1215    0.000    0.000    0.000    0.000 {issubclass}\r\n",
        "       23    0.000    0.000    0.003    0.000 linalg.py:244(solve)\r\n",
        "       11    0.000    0.000    0.002    0.000 <ipython-input-5-b05f5f62e4f1>:30(hessian)\r\n",
        "       46    0.000    0.000    0.000    0.000 {numpy.core.multiarray._fastCopyAndTranspose}\r\n",
        "       92    0.000    0.000    0.399    0.004 <ipython-input-3-0c488aa3c723>:25(<genexpr>)\r\n",
        "       36    0.000    0.000    0.001    0.000 fromnumeric.py:445(transpose)\r\n",
        "       46    0.000    0.000    0.000    0.000 sputils.py:116(_isinstance)\r\n",
        "       24    0.000    0.000    0.417    0.017 <ipython-input-14-a30b6bf021a5>:26(predicted)\r\n",
        "       58    0.000    0.000    0.000    0.000 {numpy.core.multiarray.zeros}\r\n",
        "       24    0.000    0.000    0.417    0.017 <ipython-input-5-b05f5f62e4f1>:12(at)\r\n",
        "       24    0.000    0.000    0.001    0.000 <ipython-input-6-ea9f059183fa>:42(value)\r\n",
        "       36    0.000    0.000    0.001    0.000 <ipython-input-14-a30b6bf021a5>:12(p2vertices)\r\n",
        "       24    0.000    0.000    0.001    0.000 <ipython-input-5-b05f5f62e4f1>:24(value)\r\n",
        "       36    0.000    0.000    0.000    0.000 {method 'tolist' of 'numpy.ndarray' objects}\r\n",
        "       36    0.000    0.000    0.001    0.000 fromnumeric.py:32(_wrapit)\r\n",
        "        1    0.000    0.000    0.000    0.000 utils.py:494(contaminate)\r\n",
        "       11    0.000    0.000    0.000    0.000 <ipython-input-5-b05f5f62e4f1>:36(gradient)\r\n",
        "       23    0.000    0.000    0.000    0.000 linalg.py:99(_commonType)\r\n",
        "       35    0.000    0.000    0.000    0.000 <ipython-input-5-b05f5f62e4f1>:21(residuals)\r\n",
        "       11    0.000    0.000    0.786    0.071 <ipython-input-5-b05f5f62e4f1>:18(precompute)\r\n",
        "       48    0.000    0.000    0.000    0.000 {method 'reduce' of 'numpy.ufunc' objects}\r\n",
        "       23    0.000    0.000    0.003    0.000 <ipython-input-2-1bc112e6e8bc>:1(safe_solve)\r\n",
        "      693    0.000    0.000    0.000    0.000 {len}\r\n",
        "       24    0.000    0.000    0.419    0.017 {sum}\r\n",
        "       24    0.000    0.000    0.000    0.000 {method 'sum' of 'numpy.ndarray' objects}\r\n",
        "        1    0.000    0.000    0.000    0.000 <ipython-input-6-ea9f059183fa>:60(_calculate_hessian)\r\n",
        "    48/24    0.000    0.000    0.419    0.017 fromnumeric.py:1379(sum)\r\n",
        "       23    0.000    0.000    0.000    0.000 linalg.py:139(_fastCopyAndTranspose)\r\n",
        "      100    0.000    0.000    0.000    0.000 {isinstance}\r\n",
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