{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Based on a mix of \n",
    "https://github.com/dfm/george/blob/master/docs/_code/model.py\n",
    "and\n",
    "http://dan.iel.fm/george/current/user/hyper/\n",
    "\n",
    "but adapted to do optimization on a model that includes GP and a signal component by Kyle on Aug 14, 2015"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Populating the interactive namespace from numpy and matplotlib\n"
     ]
    }
   ],
   "source": [
    "%pylab inline --no-import-all"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "from __future__ import division, print_function\n",
    "\n",
    "import emcee\n",
    "#import triangle\n",
    "import triangle_plot as triangle\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as pl\n",
    "\n",
    "import george\n",
    "from george import kernels\n",
    "\n",
    "import scipy.optimize as op\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def model(params, t):\n",
    "    amp, loc, sig2 = params\n",
    "    return amp * np.exp(-0.5 * (t - loc) ** 2 / sig2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def generate_data(params, N, rng=(-5, 5)):\n",
    "    gp = george.GP(0.1 * kernels.ExpSquaredKernel(3.3))\n",
    "    t = rng[0] + np.diff(rng) * np.sort(np.random.rand(N))\n",
    "    y = gp.sample(t)\n",
    "    y += model(params, t)\n",
    "    yerr = 0.05 + 0.05 * np.random.rand(N)\n",
    "    y += yerr * np.random.randn(N)\n",
    "    return t, y, yerr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "#we won't use this will use nll instead\n",
    "def lnlike_gp(p, t, y, yerr):\n",
    "    a, tau = np.exp(p[:2])\n",
    "    gp = george.GP(a * kernels.Matern32Kernel(tau))\n",
    "    gp.compute(t, yerr)\n",
    "    return gp.lnlikelihood(y - model(p[2:], t))\n",
    "\n",
    "\n",
    "#we won't use this b/c we aren't using emcee\n",
    "def lnprior_gp(p):\n",
    "    lna, lntau = p[:2]\n",
    "    if not -5 < lna < 5:\n",
    "        return -np.inf\n",
    "    if not -5 < lntau < 5:\n",
    "        return -np.inf\n",
    "    return lnprior_base(p[2:])\n",
    "\n",
    "\n",
    "#we won't use this b/c we aren't using emcee\n",
    "\n",
    "def lnprob_gp(p, t, y, yerr):\n",
    "    lp = lnprior_gp(p)\n",
    "    if not np.isfinite(lp):\n",
    "        return -np.inf\n",
    "    return lp + lnlike_gp(p, t, y, yerr)\n",
    "\n",
    "\n",
    "#we won't use this b/c we aren't using emcee\n",
    "def fit_gp(initial, data, nwalkers=32):\n",
    "    ndim = len(initial)\n",
    "    p0 = [np.array(initial) + 1e-8 * np.random.randn(ndim)\n",
    "          for i in xrange(nwalkers)]\n",
    "    sampler = emcee.EnsembleSampler(nwalkers, ndim, lnprob_gp, args=data)\n",
    "\n",
    "    print(\"Running burn-in\")\n",
    "    p0, lnp, _ = sampler.run_mcmc(p0, 500)\n",
    "    sampler.reset()\n",
    "\n",
    "    print(\"Running second burn-in\")\n",
    "    p = p0[np.argmax(lnp)]\n",
    "    p0 = [p + 1e-8 * np.random.randn(ndim) for i in xrange(nwalkers)]\n",
    "    p0, _, _ = sampler.run_mcmc(p0, 500)\n",
    "    sampler.reset()\n",
    "\n",
    "    print(\"Running production\")\n",
    "    p0, _, _ = sampler.run_mcmc(p0, 5000)\n",
    "\n",
    "    return sampler"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def runToy(plots=False):\n",
    "    truth = [1., 0.1, 0.4] #changed amplitdue to +1 for HEP not exoplanets\n",
    "    t, y, yerr = generate_data(truth, 50)\n",
    "\n",
    "    p = [0.0, 0.0] + truth\n",
    "\n",
    "    a, tau = np.exp(p[:2])\n",
    "    gp = george.GP(a * kernels.Matern32Kernel(tau))\n",
    "    gp.compute(t, yerr)\n",
    "\n",
    "    # Define the objective function (negative log-likelihood in this case).\n",
    "    def nll(p):\n",
    "        # The scipy optimizer doesn't play well with infinities.\n",
    "\n",
    "        # Update the kernel parameters and compute the likelihood.\n",
    "        gp.kernel[:] = p[:2]\n",
    "        ll = gp.lnlikelihood(y - model(p[2:],t), quiet=True)\n",
    "        #ll = gp.lnlikelihood(y , quiet=True)\n",
    "        return -ll if np.isfinite(ll) else 1e25\n",
    "\n",
    "    # And the gradient of the objective function.\n",
    "    # we won't use this either\n",
    "    def grad_nll(p):\n",
    "        # Update the kernel parameters and compute the likelihood.\n",
    "        gp.kernel[:] = p[:2]\n",
    "        return -gp.grad_lnlikelihood(y - model(p[2:],t), quiet=True)\n",
    "        #return -gp.grad_lnlikelihood(y , quiet=True)\n",
    "\n",
    "    # Print the initial ln-likelihood.\n",
    "    print(gp.lnlikelihood(y - model(p[2:],t)))\n",
    "\n",
    "    # Run the optimization routine.\n",
    "    #results = op.minimize(nll, p, jac=grad_nll) \n",
    "    # don't know gradient for other part of model\n",
    "    \n",
    "    results = op.minimize(nll, p)\n",
    "    \n",
    "    print(results.x)\n",
    "    p = results.x\n",
    "    \n",
    "    # Update the kernel and print the final log-likelihood.\n",
    "    gp.kernel[:] = results.x[:2]\n",
    "    print(gp.lnlikelihood(y - model(p[2:],t)))\n",
    "\n",
    "\n",
    "    if plots:\n",
    "        # Plot the samples in data space.\n",
    "        print(\"Making plots\")\n",
    "        x = np.linspace(-5, 5, 500)\n",
    "        pl.figure()\n",
    "        pl.errorbar(t, y, yerr=yerr, fmt=\".k\", capsize=0)\n",
    "        m, cov = gp.predict(y-model(p[2:],t), x)\n",
    "\n",
    "        pl.plot(x, m, color=\"#4682b4\", alpha=0.3)\n",
    "        pl.plot(x, model(p[2:], x), color=\"r\", alpha=0.3)\n",
    "        pl.plot(x, m + model(p[2:], x), color=\"g\", alpha=0.3)\n",
    "\n",
    "        pl.ylabel(r\"$y$\")\n",
    "        pl.xlabel(r\"$t$\")\n",
    "        pl.xlim(-5, 5)\n",
    "        pl.title(\"results with Gaussian process noise model\")\n",
    "        pl.savefig(\"gp-bestfit.png\")\n",
    "    \n",
    "    print( p[2])\n",
    "    return p[2]\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "15.41331803\n",
      "[-1.51625279  3.95584627  0.80565782  0.05470704  0.39135082]\n",
      "47.9155631921\n",
      "Making plots\n",
      "0.805657822905\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "0.80565782290530052"
      ]
     },
     "execution_count": 69,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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       "SimllFJKKaWUUkqp0vD/AQ2edyiLZH07AAAAAElFTkSuQmCC\n"
      ],
      "text/plain": [
       "<matplotlib.figure.Figure at 0x112e9bc50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "runToy(True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "10.5130329837\n",
      "[-1.88152124  3.11820141  1.18211775  0.08629853  0.38843503]\n",
      "39.7604591178\n",
      "1.18211774686\n",
      "9.26494351615\n",
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      "45.8597827147\n",
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      "[ -3.07312949e+00   1.38495825e+00   1.27307178e+00   2.03918480e-03\n",
      "   5.35120622e-01]\n",
      "44.1539038314\n",
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      "46.8050597776\n",
      "1.20813299504\n",
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      "[-2.57334913  1.61418052  0.78846664  0.04361952  0.28590148]\n",
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      "35.5298509639\n",
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      "didnt' work\n",
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      "44.4855193165\n",
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      "19.1361869202\n",
      "didnt' work\n",
      "16.4917669779\n",
      "[-0.79090529  3.48432572  1.14651207  0.15052579  0.4057842 ]\n",
      "39.8646448973\n",
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      "1.08426574062\n",
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      "1.20740396348\n",
      "17.6076623809\n",
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      "51.680722736\n",
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      "43.6490335363\n",
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      "14.4925414235\n",
      "[-2.99021062  1.56902287  1.02196143  0.29262355  0.19509729]\n",
      "38.1957866517\n",
      "1.02196142665\n",
      "20.6784753292\n",
      "[-2.89552398  1.46505407  0.87031631  0.15599494  0.41476334]\n",
      "45.2754551639\n",
      "0.870316309638\n",
      "18.1374601787\n",
      "[-2.07738115  2.52034277  0.93566755  0.15265382  0.39758077]\n",
      "45.7458609881\n",
      "0.935667552236\n",
      "15.4767370564\n",
      "[-1.95700464  2.70620168  0.96030173  0.1271678   0.30387325]"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Library/Python/2.7/site-packages/IPython/kernel/__main__.py:3: RuntimeWarning: overflow encountered in exp\n",
      "  app.launch_new_instance()\n",
      "/System/Library/Frameworks/Python.framework/Versions/2.7/Extras/lib/python/scipy/optimize/linesearch.py:422: RuntimeWarning: invalid value encountered in double_scalars\n",
      "  radical = B * B - 3 * A * C\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
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      "16.9875708086\n",
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      "55.9975556872\n",
      "1.04551581691\n",
      "16.1090079538\n",
      "[-4.06861514  1.09318096  0.89497263  0.08650664  0.46198827]\n",
      "44.8358210203\n",
      "0.894972634211\n",
      "19.4819704024\n",
      "[-2.6801679   1.95351174  0.9078591   0.10333826  0.27216602]\n",
      "49.093669613\n",
      "0.907859101689\n",
      "19.2873329582\n",
      "[-2.12040185  2.28756389  1.11629846  0.03703377  0.4844019 ]\n",
      "42.9864714125\n",
      "1.11629846022\n",
      "23.7242289286\n",
      "[-1.59805546  3.55262392  1.07487121  0.1101012   0.47736249]\n",
      "54.3221893671\n",
      "1.07487120554\n",
      "20.5211056458\n",
      "[-0.41883564  0.37842434  0.99284268  0.10454719  0.38092434]\n",
      "29.0888407\n",
      "0.992842680418\n",
      "17.5627077898\n",
      "[-2.22330776  2.1028349   0.94934709  0.08846255  0.27604143]\n",
      "42.2364155915\n",
      "0.949347091385\n",
      "15.7447588574\n",
      "[-1.89311744  2.98377358  1.12401143  0.06209512  0.43982846]\n",
      "47.4868993755\n",
      "1.12401143011\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/System/Library/Frameworks/Python.framework/Versions/2.7/Extras/lib/python/scipy/optimize/linesearch.py:427: RuntimeWarning: overflow encountered in double_scalars\n",
      "  xmin = a + (-B + np.sqrt(radical)) / (3 * A)\n"
     ]
    }
   ],
   "source": [
    "ampArray = []\n",
    "for i in range(100):\n",
    "    try:\n",
    "        ampArray.append(runToy(False))\n",
    "    except ValueError:\n",
    "        print(\"didnt' work\")\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.02350504175\n"
     ]
    },
    {
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      ],
      "text/plain": [
       "<matplotlib.figure.Figure at 0x115a9e810>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist(ampArray)\n",
    "print(np.mean(ampArray))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 2",
   "language": "python",
   "name": "python2"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}