S2_statistics.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "# # This file is part of Theano Geometry\n",
    "#\n",
    "# Copyright (C) 2017, Stefan Sommer (sommer@di.ku.dk)\n",
    "# https://bitbucket.org/stefansommer/theanogemetry\n",
    "#\n",
    "# Theano Geometry is free software: you can redistribute it and/or modify\n",
    "# it under the terms of the GNU General Public License as published by\n",
    "# the Free Software Foundation, either version 3 of the License, or\n",
    "# (at your option) any later version.\n",
    "#\n",
    "# Theano Geometry is distributed in the hope that it will be useful,\n",
    "# but WITHOUT ANY WARRANTY; without even the implied warranty of\n",
    "# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the\n",
    "# GNU General Public License for more details.\n",
    "#\n",
    "# You should have received a copy of the GNU General Public License\n",
    "# along with Theano Geometry. If not, see <http://www.gnu.org/licenses/>.\n",
    "#"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "# Manifold Statistics - Examples on $\\mathbb{S}^2$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2d sphere (ellipsoid parameters [1. 1. 1.], spherical_coords: True)\n"
     ]
    }
   ],
   "source": [
    "from src.manifolds.S2 import *\n",
    "M = S2(use_spherical_coords=True,chart_center='x')\n",
    "print(M)\n",
    "\n",
    "from src.plotting import *"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO (theano.gof.compilelock): Waiting for existing lock by process '20933' (I am process '20914')\n",
      "INFO (theano.gof.compilelock): To manually release the lock, delete /home/stefan/.theano/compiledir_Linux-4.18--generic-x86_64-with-Ubuntu-18.10-cosmic-x86_64-3.6.6-64/lock_dir\n",
      "INFO (theano.gof.compilelock): Waiting for existing lock by process '20933' (I am process '20914')\n",
      "INFO (theano.gof.compilelock): To manually release the lock, delete /home/stefan/.theano/compiledir_Linux-4.18--generic-x86_64-with-Ubuntu-18.10-cosmic-x86_64-3.6.6-64/lock_dir\n",
      "INFO (theano.gof.compilelock): Waiting for existing lock by process '20933' (I am process '20914')\n",
      "INFO (theano.gof.compilelock): To manually release the lock, delete /home/stefan/.theano/compiledir_Linux-4.18--generic-x86_64-with-Ubuntu-18.10-cosmic-x86_64-3.6.6-64/lock_dir\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "using M.Exp for Logarithm\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO (theano.gof.compilelock): Waiting for existing lock by process '20933' (I am process '20914')\n",
      "INFO (theano.gof.compilelock): To manually release the lock, delete /home/stefan/.theano/compiledir_Linux-4.18--generic-x86_64-with-Ubuntu-18.10-cosmic-x86_64-3.6.6-64/lock_dir\n"
     ]
    }
   ],
   "source": [
    "# Riemannian structure\n",
    "from src.Riemannian import metric\n",
    "metric.initialize(M)\n",
    "\n",
    "# geodesics\n",
    "from src.Riemannian import geodesic\n",
    "geodesic.initialize(M)\n",
    "\n",
    "# Logarithm map\n",
    "from src.Riemannian import Log\n",
    "Log.initialize(M)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Sample Data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 98,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x864 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# coordinate form\n",
    "from src.stochastics import Brownian_coords\n",
    "Brownian_coords.initialize(M)\n",
    "\n",
    "var = .2\n",
    "n_steps.set_value(1000)\n",
    "\n",
    "N_samples = 256\n",
    "x = np.array([np.pi/2,np.pi/2])\n",
    "\n",
    "samples = np.zeros((N_samples,M.dim.eval()))\n",
    "for i in range(N_samples):\n",
    "    (ts,xs) = M.Brownian_coordsf(x,var*dWsf(M.dim.eval()))\n",
    "    samples[i] = xs[-1]\n",
    "\n",
    "# plot\n",
    "newfig()\n",
    "M.plot()\n",
    "for i in range(N_samples):\n",
    "    M.plotx(samples[i])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 99,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
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       "       [1.43062407, 1.57169667],\n",
       "       [1.87640446, 1.70059801],\n",
       "       [1.61302928, 2.09973466],\n",
       "       [1.38436692, 1.68811788],\n",
       "       [1.70588768, 1.61182867],\n",
       "       [1.40087252, 1.5484709 ],\n",
       "       [1.5986604 , 1.82352191],\n",
       "       [1.69453495, 1.3973286 ],\n",
       "       [1.46810447, 1.58823247],\n",
       "       [1.39987518, 1.81964859],\n",
       "       [1.7328667 , 1.92510109],\n",
       "       [1.84867665, 1.28760365],\n",
       "       [1.65420332, 1.49887036],\n",
       "       [1.61433887, 1.12346807],\n",
       "       [1.59938941, 1.59853377],\n",
       "       [1.74652591, 2.01649618],\n",
       "       [1.38974047, 1.62324037],\n",
       "       [1.18046263, 1.58990085],\n",
       "       [1.49951259, 1.16908057],\n",
       "       [1.72302226, 1.26559493],\n",
       "       [1.31588495, 1.52310195],\n",
       "       [1.50317859, 1.68919429],\n",
       "       [1.3508469 , 1.74395494],\n",
       "       [1.8121151 , 1.32176039],\n",
       "       [1.60841862, 1.62480107],\n",
       "       [1.68727817, 1.42977066],\n",
       "       [1.66859398, 2.27747776],\n",
       "       [1.74910334, 1.56795151],\n",
       "       [1.73507591, 1.58123747],\n",
       "       [1.69933393, 1.62902784],\n",
       "       [1.650314  , 1.14190756],\n",
       "       [1.70923751, 1.49983048],\n",
       "       [1.57696267, 1.70005769],\n",
       "       [1.67938409, 1.43987833],\n",
       "       [1.61643927, 1.544937  ],\n",
       "       [1.75154282, 1.95903178],\n",
       "       [1.64292636, 1.05877623],\n",
       "       [1.6209577 , 1.65404536],\n",
       "       [1.20707397, 1.67199556],\n",
       "       [1.80940849, 1.62531577],\n",
       "       [2.16536868, 1.51172418],\n",
       "       [1.42008507, 1.69270745],\n",
       "       [1.5271159 , 1.7058009 ],\n",
       "       [1.72357637, 1.29419297],\n",
       "       [1.29809411, 1.37344511],\n",
       "       [1.94046256, 1.34397013],\n",
       "       [1.59117891, 1.40737993],\n",
       "       [1.36370873, 1.50321427],\n",
       "       [1.41384161, 1.23693667],\n",
       "       [1.20681856, 1.44600128],\n",
       "       [1.78268509, 1.76324198],\n",
       "       [1.6358033 , 1.55697141],\n",
       "       [1.56581369, 1.96009647],\n",
       "       [1.85911651, 1.31070166],\n",
       "       [1.59710845, 1.1354648 ],\n",
       "       [1.47223319, 1.76550476],\n",
       "       [1.50395799, 1.7861092 ],\n",
       "       [1.37857986, 1.60503589],\n",
       "       [1.54995662, 2.08583287],\n",
       "       [1.52285118, 1.81977225],\n",
       "       [1.48148859, 1.80129904],\n",
       "       [1.71482046, 1.62110503],\n",
       "       [1.66022399, 1.38307613],\n",
       "       [1.55195268, 1.59646776],\n",
       "       [1.42196568, 1.37941647],\n",
       "       [1.62157589, 1.41520559],\n",
       "       [1.65116994, 1.13103938],\n",
       "       [1.16888641, 1.74350656],\n",
       "       [1.74632298, 1.19461315],\n",
       "       [1.67633581, 1.35723757],\n",
       "       [1.55461315, 1.46231118],\n",
       "       [1.09300551, 1.4336795 ],\n",
       "       [1.5276607 , 1.62601938],\n",
       "       [1.91583516, 1.69785902],\n",
       "       [1.48603428, 1.77141766],\n",
       "       [1.44944986, 1.66409205],\n",
       "       [1.68189097, 1.35982342],\n",
       "       [1.86758519, 1.52849155],\n",
       "       [1.58402918, 1.47507667],\n",
       "       [1.87731431, 1.25962023],\n",
       "       [1.35303291, 1.51580312],\n",
       "       [1.45740921, 1.71342879],\n",
       "       [1.68897152, 1.83497419],\n",
       "       [1.41640963, 1.61204633],\n",
       "       [1.63567109, 1.60369868],\n",
       "       [1.56795138, 1.71944625],\n",
       "       [1.57741913, 1.58651602],\n",
       "       [2.02468472, 1.35917718],\n",
       "       [1.44050434, 1.50358705],\n",
       "       [1.36433433, 1.42020842],\n",
       "       [1.823989  , 1.63565116],\n",
       "       [1.71101341, 1.43878564],\n",
       "       [1.71999355, 1.47457656],\n",
       "       [1.61309124, 2.05616036],\n",
       "       [1.77414664, 1.42264388],\n",
       "       [1.31439118, 1.76664632],\n",
       "       [1.89757069, 1.48278459],\n",
       "       [1.52309549, 1.46239185],\n",
       "       [1.2678435 , 1.89286707],\n",
       "       [1.68816087, 1.64335315],\n",
       "       [2.00955675, 1.5500968 ],\n",
       "       [1.54497555, 1.37979975],\n",
       "       [1.53630425, 1.57394227],\n",
       "       [1.63076788, 1.69823933],\n",
       "       [1.54058457, 1.86203964],\n",
       "       [1.79832983, 1.80335244],\n",
       "       [2.17933581, 1.16582838],\n",
       "       [1.98505776, 1.50223461],\n",
       "       [1.84150295, 1.69856282],\n",
       "       [1.52363784, 1.52315268],\n",
       "       [1.29742645, 1.67458459],\n",
       "       [1.47396367, 1.70455841],\n",
       "       [1.28593997, 1.578674  ],\n",
       "       [1.72331137, 1.57565976],\n",
       "       [1.59338077, 1.92575741],\n",
       "       [1.49215106, 1.44721716]])"
      ]
     },
     "execution_count": 99,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "samples"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Frechet mean"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "ename": "KeyboardInterrupt",
     "evalue": "",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mIndexError\u001b[0m                                Traceback (most recent call last)",
      "\u001b[0;32m~/projects/theanogeometry/lib/python3.6/site-packages/multiprocess/pool.py\u001b[0m in \u001b[0;36mnext\u001b[0;34m(self, timeout)\u001b[0m\n\u001b[1;32m    719\u001b[0m             \u001b[0;32mtry\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 720\u001b[0;31m                 \u001b[0mitem\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_items\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mpopleft\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    721\u001b[0m             \u001b[0;32mexcept\u001b[0m \u001b[0mIndexError\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mIndexError\u001b[0m: pop from an empty deque",
      "\nDuring handling of the above exception, another exception occurred:\n",
      "\u001b[0;31mKeyboardInterrupt\u001b[0m                         Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-5-3f66fff81b23>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m      1\u001b[0m \u001b[0;32mfrom\u001b[0m \u001b[0msrc\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mstatistics\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mFrechet_mean\u001b[0m \u001b[0;32mimport\u001b[0m \u001b[0;34m*\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      2\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 3\u001b[0;31m \u001b[0mres\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mFrechet_mean\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mM\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;32mlambda\u001b[0m \u001b[0;34m*\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m:\u001b[0m \u001b[0mM\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mLogf\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0msamples\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m      4\u001b[0m \u001b[0mFm\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mres\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      5\u001b[0m \u001b[0mprint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\"loss = \"\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mres\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/projects/theanogeometry/src/statistics/Frechet_mean.py\u001b[0m in \u001b[0;36mFrechet_mean\u001b[0;34m(M, Logf, y, x0, options)\u001b[0m\n\u001b[1;32m     50\u001b[0m     \u001b[0;32mtry\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     51\u001b[0m         \u001b[0mmpu\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mopenPool\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 52\u001b[0;31m         \u001b[0mres\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mminimize\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mfopts\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mx0\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mmethod\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m'BFGS'\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mjac\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;32mTrue\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0moptions\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0moptions\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mcallback\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0msave_step\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     53\u001b[0m     \u001b[0;32mexcept\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     54\u001b[0m         \u001b[0mmpu\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mclosePool\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/projects/theanogeometry/lib/python3.6/site-packages/scipy/optimize/_minimize.py\u001b[0m in \u001b[0;36mminimize\u001b[0;34m(fun, x0, args, method, jac, hess, hessp, bounds, constraints, tol, callback, options)\u001b[0m\n\u001b[1;32m    595\u001b[0m         \u001b[0;32mreturn\u001b[0m \u001b[0m_minimize_cg\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mfun\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mx0\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0margs\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mjac\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mcallback\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0moptions\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    596\u001b[0m     \u001b[0;32melif\u001b[0m \u001b[0mmeth\u001b[0m \u001b[0;34m==\u001b[0m \u001b[0;34m'bfgs'\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 597\u001b[0;31m         \u001b[0;32mreturn\u001b[0m \u001b[0m_minimize_bfgs\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mfun\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mx0\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0margs\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mjac\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mcallback\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0moptions\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    598\u001b[0m     \u001b[0;32melif\u001b[0m \u001b[0mmeth\u001b[0m \u001b[0;34m==\u001b[0m \u001b[0;34m'newton-cg'\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    599\u001b[0m         return _minimize_newtoncg(fun, x0, args, jac, hess, hessp, callback,\n",
      "\u001b[0;32m~/projects/theanogeometry/lib/python3.6/site-packages/scipy/optimize/optimize.py\u001b[0m in \u001b[0;36m_minimize_bfgs\u001b[0;34m(fun, x0, args, jac, callback, gtol, norm, eps, maxiter, disp, return_all, **unknown_options)\u001b[0m\n\u001b[1;32m    981\u001b[0m             \u001b[0malpha_k\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mfc\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mgc\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mold_fval\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mold_old_fval\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mgfkp1\u001b[0m \u001b[0;34m=\u001b[0m\u001b[0;31m \u001b[0m\u001b[0;31m\\\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    982\u001b[0m                      _line_search_wolfe12(f, myfprime, xk, pk, gfk,\n\u001b[0;32m--> 983\u001b[0;31m                                           old_fval, old_old_fval, amin=1e-100, amax=1e100)\n\u001b[0m\u001b[1;32m    984\u001b[0m         \u001b[0;32mexcept\u001b[0m \u001b[0m_LineSearchError\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    985\u001b[0m             \u001b[0;31m# Line search failed to find a better solution.\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/projects/theanogeometry/lib/python3.6/site-packages/scipy/optimize/optimize.py\u001b[0m in \u001b[0;36m_line_search_wolfe12\u001b[0;34m(f, fprime, xk, pk, gfk, old_fval, old_old_fval, **kwargs)\u001b[0m\n\u001b[1;32m    801\u001b[0m     ret = line_search_wolfe1(f, fprime, xk, pk, gfk,\n\u001b[1;32m    802\u001b[0m                              \u001b[0mold_fval\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mold_old_fval\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 803\u001b[0;31m                              **kwargs)\n\u001b[0m\u001b[1;32m    804\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    805\u001b[0m     \u001b[0;32mif\u001b[0m \u001b[0mret\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;32mis\u001b[0m \u001b[0;32mnot\u001b[0m \u001b[0;32mNone\u001b[0m \u001b[0;32mand\u001b[0m \u001b[0mextra_condition\u001b[0m \u001b[0;32mis\u001b[0m \u001b[0;32mnot\u001b[0m \u001b[0;32mNone\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/projects/theanogeometry/lib/python3.6/site-packages/scipy/optimize/linesearch.py\u001b[0m in \u001b[0;36mline_search_wolfe1\u001b[0;34m(f, fprime, xk, pk, gfk, old_fval, old_old_fval, args, c1, c2, amax, amin, xtol)\u001b[0m\n\u001b[1;32m     99\u001b[0m     stp, fval, old_fval = scalar_search_wolfe1(\n\u001b[1;32m    100\u001b[0m             \u001b[0mphi\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mderphi\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mold_fval\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mold_old_fval\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mderphi0\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 101\u001b[0;31m             c1=c1, c2=c2, amax=amax, amin=amin, xtol=xtol)\n\u001b[0m\u001b[1;32m    102\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    103\u001b[0m     \u001b[0;32mreturn\u001b[0m \u001b[0mstp\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mfc\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mgc\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mfval\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mold_fval\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mgval\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/projects/theanogeometry/lib/python3.6/site-packages/scipy/optimize/linesearch.py\u001b[0m in \u001b[0;36mscalar_search_wolfe1\u001b[0;34m(phi, derphi, phi0, old_phi0, derphi0, c1, c2, amax, amin, xtol)\u001b[0m\n\u001b[1;32m    172\u001b[0m         \u001b[0;32mif\u001b[0m \u001b[0mtask\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;36m2\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m==\u001b[0m \u001b[0;34mb'FG'\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    173\u001b[0m             \u001b[0malpha1\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mstp\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 174\u001b[0;31m             \u001b[0mphi1\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mphi\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mstp\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    175\u001b[0m             \u001b[0mderphi1\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mderphi\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mstp\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    176\u001b[0m         \u001b[0;32melse\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/projects/theanogeometry/lib/python3.6/site-packages/scipy/optimize/linesearch.py\u001b[0m in \u001b[0;36mphi\u001b[0;34m(s)\u001b[0m\n\u001b[1;32m     85\u001b[0m     \u001b[0;32mdef\u001b[0m \u001b[0mphi\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0ms\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     86\u001b[0m         \u001b[0mfc\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m+=\u001b[0m \u001b[0;36m1\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 87\u001b[0;31m         \u001b[0;32mreturn\u001b[0m \u001b[0mf\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mxk\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0ms\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0mpk\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m*\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     88\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     89\u001b[0m     \u001b[0;32mdef\u001b[0m \u001b[0mderphi\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0ms\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/projects/theanogeometry/lib/python3.6/site-packages/scipy/optimize/optimize.py\u001b[0m in \u001b[0;36mfunction_wrapper\u001b[0;34m(*wrapper_args)\u001b[0m\n\u001b[1;32m    291\u001b[0m     \u001b[0;32mdef\u001b[0m \u001b[0mfunction_wrapper\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0mwrapper_args\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    292\u001b[0m         \u001b[0mncalls\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m+=\u001b[0m \u001b[0;36m1\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 293\u001b[0;31m         \u001b[0;32mreturn\u001b[0m \u001b[0mfunction\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mwrapper_args\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0margs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    294\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    295\u001b[0m     \u001b[0;32mreturn\u001b[0m \u001b[0mncalls\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mfunction_wrapper\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/projects/theanogeometry/lib/python3.6/site-packages/scipy/optimize/optimize.py\u001b[0m in \u001b[0;36m__call__\u001b[0;34m(self, x, *args)\u001b[0m\n\u001b[1;32m     61\u001b[0m     \u001b[0;32mdef\u001b[0m \u001b[0m__call__\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mx\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m*\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     62\u001b[0m         \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mx\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mnumpy\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0masarray\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mcopy\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 63\u001b[0;31m         \u001b[0mfg\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mfun\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m*\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     64\u001b[0m         \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mjac\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mfg\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     65\u001b[0m         \u001b[0;32mreturn\u001b[0m \u001b[0mfg\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/projects/theanogeometry/src/statistics/Frechet_mean.py\u001b[0m in \u001b[0;36mfopts\u001b[0;34m(x)\u001b[0m\n\u001b[1;32m     34\u001b[0m         \u001b[0mN\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0my\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mshape\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     35\u001b[0m         \u001b[0msol\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mmpu\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mpool\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mimap\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;32mlambda\u001b[0m \u001b[0mpars\u001b[0m\u001b[0;34m:\u001b[0m \u001b[0;34m(\u001b[0m\u001b[0mLogf\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0my\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mpars\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mzeros\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mshape\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mmpu\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0minputArgs\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mrange\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mN\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 36\u001b[0;31m         \u001b[0mres\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mlist\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0msol\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     37\u001b[0m         \u001b[0mLogs\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mmpu\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mgetRes\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mres\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     38\u001b[0m         \u001b[0;31m#Logs = np.zeros((N, M.dim.eval()))\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/projects/theanogeometry/lib/python3.6/site-packages/multiprocess/pool.py\u001b[0m in \u001b[0;36mnext\u001b[0;34m(self, timeout)\u001b[0m\n\u001b[1;32m    722\u001b[0m                 \u001b[0;32mif\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_index\u001b[0m \u001b[0;34m==\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_length\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    723\u001b[0m                     \u001b[0;32mraise\u001b[0m \u001b[0mStopIteration\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 724\u001b[0;31m                 \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_cond\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mwait\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mtimeout\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    725\u001b[0m                 \u001b[0;32mtry\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    726\u001b[0m                     \u001b[0mitem\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_items\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mpopleft\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/usr/lib/python3.6/threading.py\u001b[0m in \u001b[0;36mwait\u001b[0;34m(self, timeout)\u001b[0m\n\u001b[1;32m    293\u001b[0m         \u001b[0;32mtry\u001b[0m\u001b[0;34m:\u001b[0m    \u001b[0;31m# restore state no matter what (e.g., KeyboardInterrupt)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    294\u001b[0m             \u001b[0;32mif\u001b[0m \u001b[0mtimeout\u001b[0m \u001b[0;32mis\u001b[0m \u001b[0;32mNone\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 295\u001b[0;31m                 \u001b[0mwaiter\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0macquire\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    296\u001b[0m                 \u001b[0mgotit\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;32mTrue\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    297\u001b[0m             \u001b[0;32melse\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mKeyboardInterrupt\u001b[0m: "
     ]
    }
   ],
   "source": [
    "from src.statistics.Frechet_mean import *\n",
    "\n",
    "res = Frechet_mean(M,lambda *args: M.Logf(*args), samples)\n",
    "Fm = res[0]\n",
    "print(\"loss = \", res[1])\n",
    "print(\"mean = \", Fm)\n",
    "iterations = res[2]\n",
    "\n",
    "newfig()\n",
    "M.plot(rotate = np.array([50,-45]))\n",
    "M.plotx(Fm)\n",
    "M.plotx(iterations)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Tangent PCA"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "scrolled": false
   },
   "outputs": [],
   "source": [
    "from src.statistics.tangent_PCA import *\n",
    "\n",
    "from src.utils import *\n",
    "from sklearn.decomposition import PCA\n",
    "\n",
    "pca = tangent_PCA(M,lambda *args: M.Logf(*args),x,samples)\n",
    "print(pca.get_covariance())\n",
    "\n",
    "plt.scatter(pca.transformed_Logs[:, 0], pca.transformed_Logs[:, 1])\n",
    "plt.axis('equal')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# ML mean estimation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {},
   "outputs": [],
   "source": [
    "options = {}\n",
    "options['samples_per_obs'] = 1\n",
    "options['epochs'] = 50\n",
    "options['learning_rate'] = .5e0\n",
    "options['varphi_update_rate'] = 1.\n",
    "options['initial'] = [x+.0*np.random.randn(M.dim.eval())]\n",
    "options['verbose'] = True"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Delyon/Hu guided process\n",
    "from src.stochastics.guided_process import *\n",
    "\n",
    "# guide function\n",
    "Cholesky = T.slinalg.Cholesky()\n",
    "# phi = lambda q,v: T.tensordot(T.nlinalg.MatrixInverse()(Cholesky(M.gsharp(q))),-(q-v).flatten(),(1,0))\n",
    "phi = lambda q,v: T.tensordot(Cholesky(M.gsharp(q)).T,-(q-v).flatten(),(1,0))\n",
    "x0 = M.element()\n",
    "(Brownian_coords_guided,Brownian_coords_guidedf) = get_guided_likelihood(M,M.sde_Brownian_coords,phi,lambda x: Cholesky(M.gsharp(x)),x0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "transition density with v constant\n",
      "transition density with v constant\n",
      "transition density with v constant\n",
      "[1.57079633 1.57079633]\n",
      "[1.57079633 1.57079633]\n",
      "-456.89025633932863\n",
      "CPU times: user 109 ms, sys: 128 ms, total: 237 ms\n",
      "Wall time: 60.2 ms\n",
      "0.15954063761026502\n",
      "CPU times: user 105 ms, sys: 72.2 ms, total: 178 ms\n",
      "Wall time: 54.3 ms\n",
      "[array(-1.83467915), array([-1.35336482e-19,  1.26694593e-04])]\n",
      "CPU times: user 650 ms, sys: 331 ms, total: 980 ms\n",
      "Wall time: 489 ms\n"
     ]
    }
   ],
   "source": [
    "# Transition density\n",
    "# transition density etc.\n",
    "q0 = M.element()\n",
    "v = M.element()\n",
    "thetas = (q0,)\n",
    "log_p_Tf = theano.function([q0,v],log_p_T(q0,v,dWs(M.dim),Brownian_coords_guided,phi,options,sde=M.sde_Brownian_coords))\n",
    "dlog_p_Tf = theano.function([q0,v],dlog_p_T(thetas,q0,v,dWs(M.dim),Brownian_coords_guided,phi,options,sde=M.sde_Brownian_coords))\n",
    "p_Tf = theano.function([q0,v],T.exp(log_p_T(q0,v,dWs(M.dim),Brownian_coords_guided,phi,options,sde=M.sde_Brownian_coords)))\n",
    "\n",
    "v = x\n",
    "print(x)\n",
    "print(v)\n",
    "%time print(log_p_Tf(x,v))\n",
    "%time print(p_Tf(x,v))\n",
    "%time print(dlog_p_Tf(x,v))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 103,
   "metadata": {},
   "outputs": [],
   "source": [
    "from src.statistics.mle import *\n",
    "\n",
    "def llog_p_T(thetas,pars):\n",
    "    (v,seed) = pars\n",
    "    if seed:\n",
    "        srng.seed(seed)\n",
    "    q = thetas[0]\n",
    "    ie = 0\n",
    "    while True:\n",
    "        try:\n",
    "            return dlog_p_Tf(q,v)\n",
    "        except ValueError: \n",
    "            if i >= 5:\n",
    "                print(ie,v)\n",
    "            ie += 1\n",
    "            pass    \n",
    "\n",
    "def update_thetas(thetas, dthetas):\n",
    "    q = thetas[0]\n",
    "    \n",
    "    q += options['learning_rate']*np.dot(M.gsharpf(q),dthetas[0]) # use Riemannian g-gradient\n",
    "    \n",
    "    return (q,)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "initial thetas: [[1.57079633 1.57079633]]\n",
      "0 [1.66090014 1.70223809]\n",
      "0 [1.6337426  1.65323112]\n",
      "0 [1.74137839 1.5291286 ]\n",
      "0 [1.27172027 1.53781482]\n",
      "0 [1.89029803 1.06213369]\n",
      "0 [1.7817397  0.59797819]\n",
      "0 [1.15859929 1.62692153]\n",
      "0 [1.81809736 1.77334436]\n",
      "0 [1.57518123 1.44935058]\n",
      "1 [1.57518123 1.44935058]\n",
      "0 [1.50626868 2.26432884]\n",
      "0 [1.57351195 1.49374829]\n",
      "1 [1.57351195 1.49374829]\n",
      "0 [1.28749932 1.6535005 ]\n",
      "0 [1.88215259 1.89243866]\n",
      "0 [1.45122375 1.54715145]\n",
      "0 [1.74461605 2.01758866]\n",
      "0 [1.69453495 1.3973286 ]\n",
      "1 [1.69453495 1.3973286 ]\n",
      "0 [1.8121151  1.32176039]\n",
      "0 [1.74910334 1.56795151]\n",
      "0 [1.72357637 1.29419297]\n",
      "0 [1.29809411 1.37344511]\n",
      "0 [1.55195268 1.59646776]\n",
      "0 [1.09300551 1.4336795 ]\n",
      "0 [1.77414664 1.42264388]\n",
      "0 [1.31439118 1.76664632]\n",
      "0 [1.89757069 1.48278459]\n",
      "0 [1.79832983 1.80335244]\n",
      "0 [1.47396367 1.70455841]\n",
      "iteration:  0 , log-likelihood:  -5.095986785801128\n",
      "thetas: (array([ 3.79536725e+29, -4.58034404e+46]),)\n",
      "0 [1.82033807 1.6211925 ]\n",
      "0 [1.45945072 1.59154888]\n",
      "1 [1.82033807 1.6211925 ]\n",
      "1 [1.45945072 1.59154888]\n",
      "2 [1.82033807 1.6211925 ]\n",
      "2 [1.45945072 1.59154888]\n",
      "3 [1.82033807 1.6211925 ]\n",
      "3 [1.45945072 1.59154888]\n",
      "4 [1.82033807 1.6211925 ]\n",
      "4 [1.45945072 1.59154888]\n",
      "5 [1.82033807 1.6211925 ]\n",
      "5 [1.45945072 1.59154888]\n",
      "6 [1.82033807 1.6211925 ]\n",
      "6 [1.45945072 1.59154888]\n",
      "7 [1.82033807 1.6211925 ]\n",
      "7 [1.45945072 1.59154888]\n",
      "8 [1.82033807 1.6211925 ]\n",
      "8 [1.45945072 1.59154888]\n",
      "9 [1.82033807 1.6211925 ]\n",
      "9 [1.45945072 1.59154888]\n",
      "10 [1.82033807 1.6211925 ]\n",
      "10 [1.45945072 1.59154888]\n",
      "11 [1.82033807 1.6211925 ]\n",
      "11 [1.45945072 1.59154888]\n",
      "12 [1.82033807 1.6211925 ]\n",
      "12 [1.45945072 1.59154888]\n",
      "13 [1.82033807 1.6211925 ]\n",
      "13 [1.45945072 1.59154888]\n",
      "14 [1.82033807 1.6211925 ]\n",
      "14 [1.45945072 1.59154888]\n",
      "15 [1.82033807 1.6211925 ]\n",
      "15 [1.45945072 1.59154888]\n",
      "16 [1.82033807 1.6211925 ]\n",
      "16 [1.45945072 1.59154888]\n",
      "17 [1.82033807 1.6211925 ]\n",
      "17 [1.45945072 1.59154888]\n",
      "18 [1.82033807 1.6211925 ]\n",
      "18 [1.45945072 1.59154888]\n",
      "19 [1.82033807 1.6211925 ]\n",
      "19 [1.45945072 1.59154888]\n",
      "20 [1.82033807 1.6211925 ]\n",
      "20 [1.45945072 1.59154888]\n",
      "21 [1.82033807 1.6211925 ]\n",
      "21 [1.45945072 1.59154888]\n",
      "22 [1.82033807 1.6211925 ]\n",
      "22 [1.45945072 1.59154888]\n",
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      "1985 [1.45945072 1.59154888]\n",
      "1979 [1.82033807 1.6211925 ]\n",
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      "1986 [1.45945072 1.59154888]\n",
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      "1989 [1.45945072 1.59154888]\n",
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      "1984 [1.82033807 1.6211925 ]\n",
      "1991 [1.45945072 1.59154888]\n",
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      "2006 [1.45945072 1.59154888]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1999 [1.82033807 1.6211925 ]\n",
      "2007 [1.45945072 1.59154888]\n",
      "2000 [1.82033807 1.6211925 ]\n",
      "2008 [1.45945072 1.59154888]\n",
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      "2009 [1.45945072 1.59154888]\n",
      "2002 [1.82033807 1.6211925 ]\n",
      "2010 [1.45945072 1.59154888]\n",
      "2003 [1.82033807 1.6211925 ]\n",
      "2011 [1.45945072 1.59154888]\n",
      "2004 [1.82033807 1.6211925 ]\n",
      "2012 [1.45945072 1.59154888]\n",
      "2005 [1.82033807 1.6211925 ]\n",
      "2013 [1.45945072 1.59154888]\n",
      "2006 [1.82033807 1.6211925 ]\n",
      "2014 [1.45945072 1.59154888]\n",
      "2007 [1.82033807 1.6211925 ]\n",
      "2015 [1.45945072 1.59154888]\n",
      "2008 [1.82033807 1.6211925 ]\n",
      "2016 [1.45945072 1.59154888]\n",
      "2009 [1.82033807 1.6211925 ]\n",
      "2017 [1.45945072 1.59154888]\n",
      "2010 [1.82033807 1.6211925 ]\n",
      "2018 [1.45945072 1.59154888]\n",
      "2011 [1.82033807 1.6211925 ]\n",
      "2019 [1.45945072 1.59154888]\n",
      "2012 [1.82033807 1.6211925 ]\n",
      "2020 [1.45945072 1.59154888]\n",
      "2013 [1.82033807 1.6211925 ]\n",
      "2021 [1.45945072 1.59154888]\n",
      "2014 [1.82033807 1.6211925 ]\n",
      "2015 [1.82033807 1.6211925 ]\n",
      "2022 [1.45945072 1.59154888]\n",
      "2016 [1.82033807 1.6211925 ]\n",
      "2023 [1.45945072 1.59154888]\n",
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      "2024 [1.45945072 1.59154888]\n",
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      "2019 [1.82033807 1.6211925 ]\n",
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    },
    {
     "name": "stdout",
     "output_type": "stream",
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     ]
    }
   ],
   "source": [
    "# run MLE\n",
    "(thetas, log_likelihood, log_likelihoods, thetass) = iterative_mle(samples,llog_p_T,update_thetas,options)\n",
    "\n",
    "# plot\n",
    "plt.plot(range(options['epochs']),log_likelihoods)\n",
    "# plt.savefig('ML_likelihoods.pdf')\n",
    "plt.show()\n",
    "plt.plot(range(options['epochs']),thetass[0].reshape((thetass[0].shape[0],-1)))\n",
    "# plt.savefig('ML_thetas.pdf')\n",
    "plt.show()\n",
    "\n",
    "M.newfig()\n",
    "M.plot()\n",
    "M.plotx(thetas[0],s=150)\n",
    "M.plotx(np.vstack((options['initial'][0],thetass[0])),color='blue',linewidth=2.5)\n",
    "M.plotx(Fm,s=150,color='red')\n",
    "M.plotx(np.vstack((np.zeros((1,2)),iterations)),color='red',linewidth=2.5)\n",
    "plt.savefig('MLmean_iterations.pdf')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 101,
   "metadata": {},
   "outputs": [],
   "source": [
    "n_steps.set_value(100)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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