{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "import GPy\n",
    "from GPy.inference.optimization import Optimizer\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import climin"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In Paramz/GPy we can implement an own optimizer in a really simple way. We need to supply GPy with an implementation of the Optimizer class.\n",
    "The Optimizer has a name, which is the most important. \n",
    "\n",
    "It also provides an opt() method, which opitmizes the result given an optimization function and a starting point."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Get the parameters for Rprop of climin:\n",
    "climin.Rprop?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "class RProp(Optimizer):\n",
    "    # We want the optimizer to know some things in the Optimizer implementation:\n",
    "    def __init__(self, step_shrink=0.5, step_grow=1.2, min_step=1e-06, max_step=1, changes_max=0.1, *args, **kwargs):\n",
    "        super(RProp, self).__init__(*args, **kwargs)\n",
    "        self.opt_name = 'RProp (climin)'\n",
    "        self.step_shrink = step_shrink\n",
    "        self.step_grow = step_grow\n",
    "        self.min_step = min_step\n",
    "        self.max_step = max_step\n",
    "        self.changes_max = changes_max\n",
    "        \n",
    "    def opt(self, x_init, f_fp=None, f=None, fp=None):\n",
    "        # We only need the gradient of the \n",
    "        assert not fp is None\n",
    "\n",
    "        # Do the optimization, giving previously stored parameters\n",
    "        opt = climin.rprop.Rprop(x_init, fp, \n",
    "                                 step_shrink=self.step_shrink, step_grow=self.step_grow, \n",
    "                                 min_step=self.min_step, max_step=self.max_step, \n",
    "                                 changes_max=self.changes_max)\n",
    "\n",
    "        # Get the optimized state and transform it into Paramz readable format by setting\n",
    "        # values on this object:\n",
    "        # Important ones are x_opt and status:\n",
    "        for info in opt:\n",
    "            if info['n_iter']>=self.max_iters:\n",
    "                self.x_opt =  opt.wrt\n",
    "                self.status = 'maximum number of function evaluations exceeded'\n",
    "                break"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This is all we need, GPy/Paramz will handle the rest for you : )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "m = GPy.examples.regression.toy_rbf_1d_50(optimize=False, plot=False)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This is the model plot before optimization:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<style type=\"text/css\">\n",
       ".pd{\n",
       "    font-family: \"Courier New\", Courier, monospace !important;\n",
       "    width: 100%;\n",
       "    padding: 3px;\n",
       "}\n",
       "</style>\n",
       "\n",
       "<p class=pd>\n",
       "<b>Model</b>: GP regression<br>\n",
       "<b>Objective</b>: 71.7157240818<br>\n",
       "<b>Number of Parameters</b>: 3<br>\n",
       "<b>Number of Optimization Parameters</b>: 3<br>\n",
       "<b>Updates</b>: True<br>\n",
       "</p>\n",
       "<style type=\"text/css\">\n",
       ".tg  {font-family:\"Courier New\", Courier, monospace !important;padding:2px 3px;word-break:normal;border-collapse:collapse;border-spacing:0;border-color:#DCDCDC;margin:0px auto;width:100%;}\n",
       ".tg td{font-family:\"Courier New\", Courier, monospace !important;font-weight:bold;color:#444;background-color:#F7FDFA;border-style:solid;border-width:1px;overflow:hidden;word-break:normal;border-color:#DCDCDC;}\n",
       ".tg th{font-family:\"Courier New\", Courier, monospace !important;font-weight:normal;color:#fff;background-color:#26ADE4;border-style:solid;border-width:1px;overflow:hidden;word-break:normal;border-color:#DCDCDC;}\n",
       ".tg .tg-left{font-family:\"Courier New\", Courier, monospace !important;font-weight:normal;text-align:left;}\n",
       ".tg .tg-center{font-family:\"Courier New\", Courier, monospace !important;font-weight:normal;text-align:center;}\n",
       ".tg .tg-right{font-family:\"Courier New\", Courier, monospace !important;font-weight:normal;text-align:right;}\n",
       "</style>\n",
       "<table class=\"tg\"><tr><th><b>  GP_regression.         </b></th><th><b>value</b></th><th><b>constraints</b></th><th><b>priors</b></th></tr>\n",
       "<tr><td class=tg-left>  rbf.variance           </td><td class=tg-right>  1.0</td><td class=tg-center>    +ve    </td><td class=tg-center>      </td></tr>\n",
       "<tr><td class=tg-left>  rbf.lengthscale        </td><td class=tg-right>  1.0</td><td class=tg-center>    +ve    </td><td class=tg-center>      </td></tr>\n",
       "<tr><td class=tg-left>  Gaussian_noise.variance</td><td class=tg-right>  1.0</td><td class=tg-center>    +ve    </td><td class=tg-center>      </td></tr>\n",
       "</table>"
      ],
      "text/plain": [
       "<GPy.models.gp_regression.GPRegression at 0x7f2be43820d0>"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "m"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x7f2be4307d90>"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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qKqStzcNb+/dy552X8fLe1+l0L8RRNJueyFQ+Pv8y/v7vb07K3yAyx8nmDv6/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\nAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f2be4311190>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "m.plot()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "m.optimize(RProp(), messages=1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And then the optimized state after running RProp:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<style type=\"text/css\">\n",
       ".pd{\n",
       "    font-family: \"Courier New\", Courier, monospace !important;\n",
       "    width: 100%;\n",
       "    padding: 3px;\n",
       "}\n",
       "</style>\n",
       "\n",
       "<p class=pd>\n",
       "<b>Model</b>: GP regression<br>\n",
       "<b>Objective</b>: -15.5366629083<br>\n",
       "<b>Number of Parameters</b>: 3<br>\n",
       "<b>Number of Optimization Parameters</b>: 3<br>\n",
       "<b>Updates</b>: True<br>\n",
       "</p>\n",
       "<style type=\"text/css\">\n",
       ".tg  {font-family:\"Courier New\", Courier, monospace !important;padding:2px 3px;word-break:normal;border-collapse:collapse;border-spacing:0;border-color:#DCDCDC;margin:0px auto;width:100%;}\n",
       ".tg td{font-family:\"Courier New\", Courier, monospace !important;font-weight:bold;color:#444;background-color:#F7FDFA;border-style:solid;border-width:1px;overflow:hidden;word-break:normal;border-color:#DCDCDC;}\n",
       ".tg th{font-family:\"Courier New\", Courier, monospace !important;font-weight:normal;color:#fff;background-color:#26ADE4;border-style:solid;border-width:1px;overflow:hidden;word-break:normal;border-color:#DCDCDC;}\n",
       ".tg .tg-left{font-family:\"Courier New\", Courier, monospace !important;font-weight:normal;text-align:left;}\n",
       ".tg .tg-center{font-family:\"Courier New\", Courier, monospace !important;font-weight:normal;text-align:center;}\n",
       ".tg .tg-right{font-family:\"Courier New\", Courier, monospace !important;font-weight:normal;text-align:right;}\n",
       "</style>\n",
       "<table class=\"tg\"><tr><th><b>  GP_regression.         </b></th><th><b>          value</b></th><th><b>constraints</b></th><th><b>priors</b></th></tr>\n",
       "<tr><td class=tg-left>  rbf.variance           </td><td class=tg-right>  2.09912029816</td><td class=tg-center>    +ve    </td><td class=tg-center>      </td></tr>\n",
       "<tr><td class=tg-left>  rbf.lengthscale        </td><td class=tg-right> 0.275423851372</td><td class=tg-center>    +ve    </td><td class=tg-center>      </td></tr>\n",
       "<tr><td class=tg-left>  Gaussian_noise.variance</td><td class=tg-right>0.0106782996505</td><td class=tg-center>    +ve    </td><td class=tg-center>      </td></tr>\n",
       "</table>"
      ],
      "text/plain": [
       "<GPy.models.gp_regression.GPRegression at 0x7f2be43820d0>"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "m"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x7f2be42fd050>"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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WHTnnmcth5QvjTuCME0exq64Zd0EhDz74IACXXPJVAPY3NPLmplrsg45j0BlT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\npo7Haun8bwkEglQMcffZk6C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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f2be427d510>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "m.plot()"
   ]
  }
 ],
 "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": "2.7.11"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}