C6_WF_CONV_2TYPES.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "button": false,
    "collapsed": true,
    "deletable": true,
    "new_sheet": false,
    "run_control": {
     "read_only": false
    }
   },
   "outputs": [],
   "source": [
    "# solve the waterfilling problem with one type in 1D, with correct units\n",
    "# 1) compute normalized spatial spectrum of van Hateren image database (in cycles per pixel)\n",
    "# 2) choose a number of neurons\n",
    "# 3) compute corresponding mask (k tild business)\n",
    "# 4) solve water-filling with this mask (obj = VarExpl - FiringRate)\n",
    "# 5) iterate over number of neurons to find sweet spot\n",
    "\n",
    "# => SWEET SPOT FOUND!!\n",
    "# NEXT in C6: TWO TYPES!\n",
    "\n",
    "#Is there a benefit of having two types compared to one type\n",
    "# steps\n",
    "# 1) perform grid search over one type\n",
    "# 2) perform grid serach over two types\n",
    "# 3) conclude\n",
    "\n",
    "# Bonus: Is there mode sharing between the two types?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "button": false,
    "collapsed": false,
    "deletable": true,
    "new_sheet": false,
    "run_control": {
     "read_only": false
    }
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import tensorflow as tf\n",
    "from tqdm import trange\n",
    "\n",
    "\n",
    "%matplotlib inline\n",
    "\n",
    "sess = tf.Session()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "button": false,
    "collapsed": false,
    "deletable": true,
    "new_sheet": false,
    "run_control": {
     "read_only": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(101, 768, 1024)"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# load images fro the Van Hateren DB\n",
    "Is = np.load('Is.npy')\n",
    "\n",
    "Is.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "button": false,
    "collapsed": false,
    "deletable": true,
    "new_sheet": false,
    "run_control": {
     "read_only": false
    }
   },
   "outputs": [],
   "source": [
    "# compute the 1D spectrum of images that are luminance and contrast normalized\n",
    "\n",
    "#for lim in range(300,1000,100):\n",
    "lim = 300\n",
    "\n",
    "pwrs = list()\n",
    "for im in Is:\n",
    "    for l in range(10,760,2):\n",
    "        line = im[l,:lim]\n",
    "        line = (line - np.mean(line))/np.std(line)\n",
    "        pwrs.append(np.abs(np.fft.rfft(line, norm = 'ortho'))**2)\n",
    "\n",
    "pwrs = np.array(pwrs)\n",
    "S = np.mean(pwrs,axis =0)\n",
    "S = S[1:]\n",
    "#S = S/S[0]\n",
    "#plt.plot(np.linspace(0,1,len(S)-1),np.log(S[1:]))\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "button": false,
    "collapsed": false,
    "deletable": true,
    "new_sheet": false,
    "run_control": {
     "read_only": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x7f95bc4fdd30>"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAYQAAAEKCAYAAAASByJ7AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f95bfdef5f8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAYQAAAEKCAYAAAASByJ7AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nAAoEEREJKBBERASA/w+dGWIWyXBNvAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f9618d9da58>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAYgAAAEKCAYAAAAIO8L1AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f95bc0b4d68>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Show spectrum in real units of viewing (look up daytime luminance)\n",
    "\n",
    "plt.figure()\n",
    "plt.plot(np.linspace(0,0.5,len(S)),np.log(S))\n",
    "plt.xlabel('cycles/arcmin')\n",
    "plt.ylabel('Power (a.u.)')\n",
    "\n",
    "plt.figure()\n",
    "plt.plot(np.linspace(0,1024/2,len(S)),np.log(S))\n",
    "plt.xlabel('cycles/images')\n",
    "plt.ylabel('Power (a.u.)')\n",
    "\n",
    "plt.figure()\n",
    "plt.plot(np.cumsum(S))\n",
    "plt.xlabel('cycles/arcmin')\n",
    "plt.ylabel('Cumulated Power (a.u.)')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "button": false,
    "collapsed": false,
    "deletable": true,
    "new_sheet": false,
    "run_control": {
     "read_only": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x7f95bc1461d0>"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXQAAAD8CAYAAABn919SAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f96000966d8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAEMAAAD8CAYAAAAsVhnTAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n8KYwVuH/B9biDeYGhb1lAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f95bfdefef0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Generate pink noise DATASET\n",
    "\n",
    "NSAMPLES = 2000\n",
    "NFREQ = len(S)\n",
    "\n",
    "Ks = np.linspace(0,1024/2,len(S)) # in cycles/image\n",
    "dk = np.mean(np.diff(Ks))\n",
    "\n",
    "# signal\n",
    "X = np.random.randn(NSAMPLES,NFREQ)*np.sqrt(S)\n",
    "\n",
    "plt.figure()\n",
    "plt.plot(Ks,S)\n",
    "\n",
    "plt.figure()\n",
    "plt.imshow(np.log(X**2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "button": false,
    "collapsed": false,
    "deletable": true,
    "new_sheet": false,
    "run_control": {
     "read_only": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f95bc08c940>]"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXYAAAD8CAYAAABjAo9vAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nYhcRiTAqdhGRCKNiFxGJMCp2EZEI839YOIPEUJIgPAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f95bc4847b8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Check that the signal has variance equal to Power\n",
    "\n",
    "Semp = np.mean(X**2,axis = 0)\n",
    "\n",
    "plt.plot(np.log(Semp))\n",
    "plt.plot(np.log(S))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "button": false,
    "collapsed": false,
    "deletable": true,
    "new_sheet": false,
    "run_control": {
     "read_only": false
    }
   },
   "outputs": [],
   "source": [
    "# For a number of neurons, compute the correspoding mask of Ks vs Ktild\n",
    "\n",
    "def create_mask(NCELLS):\n",
    "    skip = int(NCELLS/(dk))\n",
    "\n",
    "    NFREQ_NEURAL = skip\n",
    "\n",
    "    mask = np.zeros((NFREQ,NFREQ_NEURAL))\n",
    "\n",
    "\n",
    "    for freqn in range(NFREQ_NEURAL):\n",
    "        pointer = freqn\n",
    "        while pointer < len(Ks):\n",
    "            mask[pointer,freqn] = 1\n",
    "            pointer += skip\n",
    "            \n",
    "    return mask,NFREQ_NEURAL\n",
    "\n",
    "    #plt.imshow(mask,aspect = 'auto')\n",
    "    #print(np.sum(mask), NFREQ, NFREQ_NEURAL)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "button": false,
    "collapsed": false,
    "deletable": true,
    "new_sheet": false,
    "run_control": {
     "read_only": false
    }
   },
   "outputs": [],
   "source": [
    "# define noise\n",
    "\n",
    "def generate_noise(varNoise, NFREQ_NEURAL, NCELLS):\n",
    "    N = np.sqrt(varNoise)/NFREQ_NEURAL*NCELLS*np.random.randn(NSAMPLES,NFREQ_NEURAL)\n",
    "    return N\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "button": false,
    "collapsed": false,
    "deletable": true,
    "new_sheet": false,
    "run_control": {
     "read_only": false
    }
   },
   "outputs": [],
   "source": [
    "# Set parameters (noise, threshold on total firing rate)\n",
    "\n",
    "varNoise = 1 # noise per cell\n",
    "L1 = 32 # Firing rate per cell\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "button": false,
    "collapsed": false,
    "deletable": true,
    "new_sheet": false,
    "run_control": {
     "read_only": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.06"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "30/500"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "button": false,
    "collapsed": false,
    "deletable": true,
    "new_sheet": false,
    "run_control": {
     "read_only": false
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/user/anaconda/lib/python3.5/site-packages/ipykernel/__main__.py:17: RuntimeWarning: divide by zero encountered in double_scalars\n",
      "/home/user/anaconda/lib/python3.5/site-packages/ipykernel/__main__.py:17: RuntimeWarning: invalid value encountered in double_scalars\n",
      "100%|██████████| 200/200 [00:00<00:00, 760.13it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.0\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 643.78it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.48665595225773806\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 629.23it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.6541540862816457\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 612.30it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.7466513469131645\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 617.27it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.7797977145962783\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 595.41it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.7958928843498037\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 586.73it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.7954009288344576\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 571.38it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.788878109539836\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 558.93it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.7733051190675883\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 561.93it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.7612517667694758\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 509.00it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.7478590490644041\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 515.74it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.7379144416881043\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 513.49it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.7230041371955535\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 479.01it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.7139055351640852\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 460.82it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.7063861639177363\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 444.54it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.6941705084359632\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 420.44it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.6843745749375166\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 625.66it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.48727957102880376\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 586.76it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.6468608990873985\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 575.08it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.734412802520875\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 564.24it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.7763736896437996\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 561.17it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.7899380741777433\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 545.04it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.7904376246497606\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 548.42it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.7873268136295966\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 531.68it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.7751162561324383\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 513.25it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.7597397461488723\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 489.90it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.7498165190958047\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 475.90it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.7526050646599501\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 468.26it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.7431271309569261\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 457.66it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.7414116591339837\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 435.53it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.7273750867801398\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 430.32it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.7226442090776853\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 412.72it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.7246572887575902\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 404.97it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.7086650150608856\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 579.83it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.6574482166669446\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 549.14it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.726515192028245\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 546.55it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.7795670568025758\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 528.43it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.7953219620931765\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 537.01it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.7912979355636649\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 534.30it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.7805323445833479\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 506.42it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.7702699454926302\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 494.66it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.7638260409190384\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 482.45it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.7656298951487241\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 466.22it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.7551089554096752\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 454.93it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.7504421666566661\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 446.34it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.7549828063005799\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 427.57it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.7470548680015159\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 419.19it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.7453565628614607\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 397.02it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.7397094524750906\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 381.66it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.7430195010572485\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 369.32it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.7468194243447055\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 558.18it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.7461833207133581\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 526.27it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.7791286821459383\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 515.92it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.7902954012830528\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 513.90it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.7980615566009679\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 503.45it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.7796105457325567\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00,  9.79it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.7703252950398786\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 476.74it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.7666919405966786\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 464.55it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.757836377178692\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 444.03it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.7659144979428933\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 447.31it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.7741155945808685\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 434.62it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.7532005924953822\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 425.93it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.765125870935106\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 405.68it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.7694501063341388\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 391.34it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.7711527811752925\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 378.16it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.7687581329530313\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 372.04it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.7628048833885063\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 327.94it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.7618545774400722\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 539.10it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.7799772364830774\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 497.55it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.786040196757327\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 499.72it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.7928927204038851\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 487.30it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.7901327339576338\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 487.71it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.7699672916713038\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 464.66it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.7502104684579401\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 444.09it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.7634601824925364\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 443.72it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.7443807669899517\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 442.15it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.7620699412799297\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 431.08it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.7809591187239736\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 409.89it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.7764247735304518\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 380.77it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.7723333807756708\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 386.15it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.7721777361841603\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 374.63it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.7780818266113265\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 344.93it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.7837869915980061\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 332.13it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.7687166207925951\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 312.67it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.7887644973112734\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 504.17it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.7964691126720504\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 485.81it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.7936984100540574\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 484.79it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.7832611708991463\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 470.43it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.7736200496681915\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 445.42it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.7802678216061315\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 448.68it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.7455512226413512\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 438.07it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.7391446686081019\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 420.67it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.7842977264240257\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 415.37it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.7927891480837991\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 401.49it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.7109545823757767\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 375.79it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.8058843619724106\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 368.51it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.7928799754423477\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 351.59it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.8074063704812394\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 345.82it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.7669096453478389\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 331.87it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.8083941310105183\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 308.37it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.804852540290388\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 300.35it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.7929495265181664\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 491.45it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.797923234753098\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 464.53it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.7810701819602287\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 457.79it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.7787698464533448\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 438.12it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.7626706711404792\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 427.08it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.7439596110364526\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 421.57it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.7340836703917015\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 422.12it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.7375649696407219\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 377.25it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.7478383970246884\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 327.51it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.803725781649974\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 301.34it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.759511533306975\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 358.51it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.7834697200861\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 354.63it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.771013679023655\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 342.27it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.7818448155204505\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 315.42it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.7831954173016632\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 306.71it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.7978903579543565\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 293.43it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.8093966652911304\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 278.57it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.7924798356703225\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 466.30it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.7893010862021261\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 439.48it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.7718306050480808\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 433.07it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.7660474617048924\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 413.32it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.7577130371631601\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 409.90it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.7345174152459846\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 404.46it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.7771443176446811\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 391.57it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.7885033556503833\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 385.99it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.786140439781338\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 374.67it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.79547641021891\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 359.93it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.7841200772662689\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 344.00it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.7962403796276414\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 324.26it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.799901252783712\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 309.00it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.7220425428526147\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 305.56it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.80066241309888\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 278.46it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.7841946222862002\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 275.57it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.8030019718751485\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 264.63it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.8030010355106274\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 434.78it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.7732306780881593\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 424.73it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.756191236735336\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 409.14it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.7740141030708294\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 403.40it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.7739833591023859\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 396.33it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.7747843149097015\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 385.66it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.7947232090021716\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 369.57it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.7468268112203721\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 353.64it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.7950878709628966\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 352.44it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.6974251034303703\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 338.02it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.7492048649825089\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 327.13it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.7819222736744476\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 300.28it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.7497063922240708\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 295.24it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.785425785570719\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 287.84it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.7830671353622698\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 268.85it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.7872950292561296\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 260.82it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.7882969392937277\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 253.95it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.7902581547832127\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 415.04it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.7584998434621564\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 401.63it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.7595900838862467\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 387.07it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.7481076538447614\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 381.12it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.7706602534371836\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 378.65it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.7758082815337969\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 365.67it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.7813553569771607\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 356.52it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.8047353386644945\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 343.51it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.7952250483652407\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 332.04it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.7807014103996611\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 317.66it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.7671929476357288\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 297.54it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.7674459221171845\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 291.07it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.6848717324779799\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 275.88it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.7739531353364543\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 265.62it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.7714961148330364\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 260.09it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.7169308248913203\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 250.36it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.775839233583245\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 238.48it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.7708337929950977\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 396.69it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.7487712241687281\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 381.82it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.7540945084915445\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 374.80it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.7636885513951873\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 355.85it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.7674634009215787\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 355.93it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.7600989980034752\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 347.49it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.7987619572627653\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 336.98it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.770465281535786\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 322.37it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.7969982626669854\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 315.54it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.7490338744169022\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 293.73it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.6668219017866174\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 288.32it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.669949983530171\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 267.10it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.699204300061\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 261.52it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.7331092790669742\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 251.13it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.7560129113143138\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 241.36it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.7526018914246285\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 230.82it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.74747269465894\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 218.02it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.7648558858315164\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 384.07it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.7379179270449329\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 367.21it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.7428768615285313\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 349.55it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.7447986976878781\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 349.22it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.7684031987792759\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 336.76it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.767115905643741\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 336.16it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.7734330368652235\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 328.04it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.7972585199836054\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 306.62it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.7998560471854425\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 285.65it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.7809207797988589\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 280.62it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.7107953483869351\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 263.56it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.6912194516071523\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 259.53it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.7481393341777259\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 253.02it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.7494002530459158\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 239.54it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.7483570909491374\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 231.05it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.7505060995453581\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 220.71it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.7063525588354783\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 208.61it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.7140078069778919\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 364.34it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.7229293320743663\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 347.65it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.7356493759115158\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 336.96it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.7462467333995384\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 331.94it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.7647104372092359\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 325.29it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.7821087142546527\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 311.97it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.7845597524291856\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 305.81it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.8081949454687757\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 277.42it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.7990839626175281\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 267.85it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.7747086774644955\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 260.09it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.7715121890906489\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 251.90it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.7113642418537665\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 247.52it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.7368499512883447\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 17.27it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.6808498387787665\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 224.96it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.6329728445506545\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 216.11it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.6293190981689945\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 203.42it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.7070432837305576\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:01<00:00, 191.91it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.68873740936292\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 345.75it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.7114531964832729\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 327.40it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.7369221033767221\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 317.63it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.7416889270727375\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 306.94it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.7646790169775272\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 305.52it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.7844999811605875\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 297.67it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.7632885156636645\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 278.41it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.8078472941301844\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 269.42it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.7904271165590236\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 260.91it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.785046089757405\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 247.87it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.7739698338370808\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 241.92it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.7426291931126952\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 233.47it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.6736726047243845\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 217.02it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.7317871323631533\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 211.30it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.6507596088318336\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 204.21it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.7149071851004273\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:01<00:00, 193.15it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.7107529518822289\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:01<00:00, 185.11it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.6164687436026557\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 330.92it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.7048409543768842\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 314.09it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.7260637082683118\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 305.31it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.747945454701603\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 299.03it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.7704645532522696\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 294.66it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.7769350401742109\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 277.94it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.79382044956331\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 11.62it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.8097095671019379\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 252.80it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.8001855434563742\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 247.24it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.6695854776301996\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 236.92it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.7758810058449372\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 16.09it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.7565162072444156\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 217.42it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.751923391288575\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 211.36it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.7355215101341318\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:01<00:00, 198.38it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.6553828046143594\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:01<00:00, 196.78it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.7186089461739202\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:01<00:00, 186.70it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.6804455373866475\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:01<00:00, 175.76it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.7018742914727214\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 317.26it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.6931946085239518\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 298.76it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.7208590821384219\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 293.03it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.7414273172295869\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 286.55it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.76662904811301\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 271.22it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.7734717919523476\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 263.29it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.8005347033822495\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 254.27it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.8075493221314637\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 240.84it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.8011974934024486\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 231.97it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.7856961348160667\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 229.43it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.7750154408856644\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 215.57it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.7625955538977849\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 207.68it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.7327960651346597\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:01<00:00, 196.85it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.7323443212734706\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:01<00:00, 189.07it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.6640587941252957\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:01<00:00, 183.33it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.722310343105655\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:01<00:00, 177.75it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.7135138746930013\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:01<00:00, 169.41it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.7032399791267744\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 300.51it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.6869286132093727\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 285.14it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.7105991800197606\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 283.42it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.747211865119557\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 261.06it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.760620292940483\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 252.18it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.7880065622516782\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 243.84it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.7900387853840148\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 239.07it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.8100751134069327\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 233.40it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.8023365288221396\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 15.13it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.7624263320207181\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 216.24it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.7769424270498775\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:00<00:00, 204.29it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.7630347088581899\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:01<00:00, 193.60it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.6413413943771565\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:01<00:00, 185.64it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.7374475599338237\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:01<00:00, 183.33it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.7341466669158724\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:01<00:00, 173.73it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.7199260989336286\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:01<00:00, 164.10it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.7066364333461311\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:01<00:00, 157.06it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.7074890972831129\n",
      "16.015342389768644\n"
     ]
    }
   ],
   "source": [
    "grid = range(0,500,30)\n",
    "NG = len(grid)\n",
    "\n",
    "VarExpls = np.zeros((NG,NG))\n",
    "\n",
    "for i1 in range(NG):\n",
    "    for i2 in range(i1,NG):\n",
    "        NCELLS_1 = grid[i1]\n",
    "        NCELLS_2 = grid[i2]\n",
    "\n",
    "        MASK_1,NFREQ_NEURAL_1 = create_mask(NCELLS_1)\n",
    "        MASK_2,NFREQ_NEURAL_2 = create_mask(NCELLS_2)\n",
    "\n",
    "        NFREQ_NEURAL = NFREQ_NEURAL_1+NFREQ_NEURAL_2\n",
    "        NCELLS = NCELLS_1 + NCELLS_2\n",
    "\n",
    "        NOISE = np.sqrt(varNoise)/(NFREQ_NEURAL)*NCELLS*np.random.randn(NSAMPLES,NFREQ_NEURAL)\n",
    "\n",
    "        # data in tensorflow\n",
    "        _X = tf.constant(X, dtype=tf.float32)\n",
    "        _NOISE = tf.constant(NOISE, dtype=tf.float32)\n",
    "\n",
    "        _MASK_1 = tf.constant(MASK_1, dtype=tf.float32)\n",
    "        _MASK_2 = tf.constant(MASK_2, dtype=tf.float32)\n",
    "\n",
    "\n",
    "        # weights\n",
    "        _W1 = tf.Variable(np.random.randn(NFREQ, NFREQ_NEURAL_1), dtype=tf.float32)\n",
    "        _W2 = tf.Variable(np.random.randn(NFREQ, NFREQ_NEURAL_2), dtype=tf.float32)\n",
    "\n",
    "\n",
    "        # mask the weights\n",
    "        _Wm1 = tf.multiply(_W1,_MASK_1)\n",
    "        _Wm2 = tf.multiply(_W2,_MASK_2)\n",
    "\n",
    "\n",
    "        # model estimate\n",
    "        _Rbef1 = tf.matmul(_X,_Wm1)\n",
    "        _Rbef2 = tf.matmul(_X,_Wm2)\n",
    "\n",
    "        _Rbef = tf.concat([_Rbef1, _Rbef2], 1)\n",
    "\n",
    "        # add noise\n",
    "        _R = _Rbef  + _NOISE\n",
    "\n",
    "        _Cxr = tf.matmul(tf.transpose(_X),_R)\n",
    "        #_Cxr = NSAMPLES*tf.transpose(tf.matmul(tf.transpose(_U),_Cxx))\n",
    "\n",
    "        _Crr = tf.matmul(tf.transpose(_R),_R)\n",
    "        #_Crr = NSAMPLES*tf.matmul(tf.matmul(tf.transpose(_U),_Cxx),_U)+NSAMPLES*_Cnn\n",
    "\n",
    "        _Cinv = tf.matrix_inverse(_Crr)\n",
    "\n",
    "        M1 = tf.matmul(_Cxr,_Cinv)\n",
    "\n",
    "        M2 = tf.matmul(M1,tf.transpose(_Cxr))\n",
    "\n",
    "        _loss = -tf.trace(M2)\n",
    "\n",
    "        THRES = L1*NSAMPLES\n",
    "\n",
    "        fr1 = tf.sqrt(NCELLS_1*tf.reduce_sum(tf.square(_Rbef1)))\n",
    "        fr2 = tf.sqrt(NCELLS_2*tf.reduce_sum(tf.square(_Rbef2)))\n",
    "\n",
    "        _regR = 0.03*tf.square(tf.nn.relu(fr1+fr2 - THRES))\n",
    "\n",
    "\n",
    "        # TENSORFLOW BLABLA\n",
    "        opt = tf.train.AdamOptimizer(learning_rate=1e-1)\n",
    "        _objective = _loss + _regR\n",
    "        train_op = opt.minimize(_objective)\n",
    "        uninitialized_vars = []\n",
    "        for var in tf.global_variables():\n",
    "            try:\n",
    "                sess.run(var)\n",
    "            except tf.errors.FailedPreconditionError:\n",
    "                uninitialized_vars.append(var)\n",
    "        sess.run(tf.variables_initializer(uninitialized_vars))\n",
    "\n",
    "\n",
    "        losses = [sess.run([_objective, train_op])[0] for t in trange(200)]\n",
    "\n",
    "        # Variance explained\n",
    "        VarExpl = -sess.run(_loss) / np.sum(X**2)\n",
    "        print(i1,i2,VarExpl)\n",
    "        VarExpls[i1,i2] = VarExpl\n",
    "\n",
    "\n",
    "# Total firing rate across all cells averaged over samples\n",
    "Rbef1 = sess.run(_Rbef1)\n",
    "Rbef2 = sess.run(_Rbef2)\n",
    "fr1 = np.sqrt(NCELLS_1*np.sum(Rbef1**2))/NSAMPLES\n",
    "fr2 = np.sqrt(NCELLS_2*np.sum(Rbef2**2))/NSAMPLES\n",
    "\n",
    "total_firing_rate = fr1+fr2\n",
    "print(total_firing_rate)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "button": false,
    "collapsed": false,
    "deletable": true,
    "new_sheet": false,
    "run_control": {
     "read_only": false
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.7958928843498037 0.8100751134069327\n"
     ]
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAS4AAAD8CAYAAADJwUnTAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nSUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f944a7ae400>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.imshow(VarExpls)\n",
    "plt.colorbar()\n",
    "\n",
    "print(np.max(VarExpls[0,:]),np.max(VarExpls))\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "button": false,
    "collapsed": true,
    "deletable": true,
    "new_sheet": false,
    "run_control": {
     "read_only": false
    }
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "button": false,
    "collapsed": true,
    "deletable": true,
    "new_sheet": false,
    "run_control": {
     "read_only": false
    }
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "button": false,
    "collapsed": true,
    "deletable": true,
    "new_sheet": false,
    "run_control": {
     "read_only": false
    }
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "button": false,
    "collapsed": false,
    "deletable": true,
    "new_sheet": false,
    "run_control": {
     "read_only": false
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-232545.58\n"
     ]
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAZYAAAD8CAYAAABU4IIeAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f95bc0efc50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(losses)\n",
    "print(losses[-1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "button": false,
    "collapsed": false,
    "deletable": true,
    "new_sheet": false,
    "run_control": {
     "read_only": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.colorbar.Colorbar at 0x7f94bae9e470>"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAABAUAAAJCCAYAAAC4dH6aAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nAgAAADBT/x+ShSI6qtf/CwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f94baf6ca20>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Check weights\n",
    "Wm1 =sess.run(_Wm1)\n",
    "plt.figure(figsize = (20,10))\n",
    "plt.imshow(Wm1.T**2, aspect='auto')\n",
    "plt.colorbar()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "button": false,
    "collapsed": false,
    "deletable": true,
    "new_sheet": false,
    "run_control": {
     "read_only": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.colorbar.Colorbar at 0x7f94b9c38898>"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAA/8AAAJCCAYAAACWIXdJAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f95bc1d2e48>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Check weights\n",
    "Wm2 =sess.run(_Wm2)\n",
    "plt.figure(figsize = (20,10))\n",
    "plt.imshow(Wm2.T**2, aspect='auto')\n",
    "plt.colorbar()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "button": false,
    "collapsed": false,
    "deletable": true,
    "new_sheet": false,
    "run_control": {
     "read_only": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f953606ea90>]"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXQAAAD8CAYAAABn919SAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nIioS/x/lyjdeHtXNCQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f94b9c6d550>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(np.diag(Wm1**2),'o-')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "button": false,
    "collapsed": false,
    "deletable": true,
    "new_sheet": false,
    "run_control": {
     "read_only": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f95360386d8>]"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXcAAAD8CAYAAACMwORRAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\ngg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f95366bb630>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(np.diag(Wm2**2),'o-')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "button": false,
    "collapsed": true,
    "deletable": true,
    "new_sheet": false,
    "run_control": {
     "read_only": false
    }
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.5.0"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}