Figure-5.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The autoreload extension is already loaded. To reload it, use:\n",
      "  %reload_ext autoreload\n",
      "The jupyternotify extension is already loaded. To reload it, use:\n",
      "  %reload_ext jupyternotify\n"
     ]
    }
   ],
   "source": [
    "%load_ext autoreload\n",
    "%autoreload 2\n",
    "%load_ext jupyternotify\n",
    "import numpy as np \n",
    "import pickle\n",
    "from sets import Set\n",
    "from conf_ope_rl import * \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Generate gridworld"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(2, 2)\n",
      "(2, 2)\n",
      "(9, 4)\n"
     ]
    }
   ],
   "source": [
    "\n",
    "#'up':2, 'down':3, 'left':0, 'right':1\n",
    "# indexing is j,i; j increasing goes downwards \n",
    "# (0,0), (0,1), (0,2)\n",
    "# (1,0), (1,1), (1,2)... \n",
    "# (2,0), (2,1), (2,2) \n",
    "\n",
    "# The bad states are\n",
    "# (0,0), (0,1) X, (0,2) X\n",
    "# (1,0), (1,1),  (1,2) X... \n",
    "# (2,0) X, (2,1), (2,2) \n",
    "\n",
    "\n",
    "\n",
    "P_u0, R_u0 = grid_world_example()\n",
    "[nA, nS,nS] = P_u0.shape\n",
    "nU = 2\n",
    "# make reward array\n",
    "bad_Rwd = -0.3\n",
    "living_Rwd = -0.1\n",
    "R_u0_vec = np.asarray([living_Rwd, bad_Rwd, bad_Rwd, \n",
    "      living_Rwd  , living_Rwd, bad_Rwd, \n",
    "       bad_Rwd, bad_Rwd, 1])\n",
    "R_u0 = np.zeros([nS,nA]); \n",
    "for a in range(nA): \n",
    "    R_u0[:,a] = R_u0_vec\n",
    "\n",
    "# repeat for all actions\n",
    "\n",
    "P_u1, R_u1 = westward_wind_grid_world_example()\n",
    "\n",
    "P_u1\n",
    "print R_u1.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "# build S,U transition matrix \n",
    "nU = 2\n",
    "nS = 3*3\n",
    "P_su = np.zeros([nS*nU, nA ,nS*nU])\n",
    "P_su_mdptoolbox = np.zeros([nA , nS*nU, nS*nU])\n",
    "Ps = [P_u0, P_u1]\n",
    "for a_ind in range(nA): \n",
    "    for i_s in range(nS): \n",
    "        for i_sprime in range(nS): \n",
    "            for i_u in range(nU): \n",
    "                P_su[ i_s*nU + i_u,a_ind, i_sprime*nU:(i_sprime*nU+nU)] = Ps[i_u][a_ind, i_s, i_sprime]/nU\n",
    "                P_su_mdptoolbox[ a_ind, i_s*nU + i_u, i_sprime*nU:(i_sprime*nU+nU)] = Ps[i_u][a_ind, i_s, i_sprime]/nU\n",
    "\n",
    "# print [(P_su[:,a,:].sum(axis=1)) for a in range(nA)]\n",
    "# print [(P_su_mdptoolbox[a,:,:].sum(axis=1)) for a in range(nA)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "import mdptoolbox.example\n",
    "# P, R = mdptoolbox.example.forest()\n",
    "vi = mdptoolbox.mdp.ValueIteration(P_u0, R_u0, 0.99)\n",
    "vi.run()\n",
    "pi_opt_s = vi.policy # result is (0, 0, 0)\n",
    "pi_opt_s\n",
    "pi_opt_s_ = np.zeros([nA, nS*nU])\n",
    "for s in range(nS): \n",
    "    pi_opt_s_[pi_opt_s[s],s*nU] = 1\n",
    "    pi_opt_s_[pi_opt_s[s],s*nU+1 ] = 1\n",
    "# print pi_opt_s\n",
    "uniform_pi = np.ones([nA, nS*nU])*1.0 / (nA)\n",
    "# print uniform_pi\n",
    "# print pi_opt_s_\n",
    "\n",
    "# print np.round(pi_opt_s_,2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-0.1, -0.1, -0.1, -0.1],\n",
       "       [-0.3, -0.3, -0.3, -0.3],\n",
       "       [-0.3, -0.3, -0.3, -0.3],\n",
       "       [-0.1, -0.1, -0.1, -0.1],\n",
       "       [-0.1, -0.1, -0.1, -0.1],\n",
       "       [-0.3, -0.3, -0.3, -0.3],\n",
       "       [-0.3, -0.3, -0.3, -0.3],\n",
       "       [-0.3, -0.3, -0.3, -0.3],\n",
       "       [ 1. ,  1. ,  1. ,  1. ]])"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Reward matrix\n",
    "R_u0"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Compute optimal full-information policy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "vi = mdptoolbox.mdp.ValueIteration(P_u0*0.5+0.5*P_u1, R_u0, 0.99)\n",
    "vi.run()\n",
    "pi_opt_smarg = vi.policy # result is (0, 0, 0)\n",
    "pi_opt_smarg_ = np.zeros([nA, nS*nU])\n",
    "for s in range(nS): \n",
    "    pi_opt_smarg_[pi_opt_smarg[s],s*nU] = 1\n",
    "    pi_opt_smarg_[pi_opt_smarg[s],s*nU+1 ] = 1\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "R_su = np.repeat(R_u0, 2 ).reshape([nS*nU, nA])\n",
    "vi = mdptoolbox.mdp.ValueIteration(P_su_mdptoolbox, R_su, 0.99)\n",
    "vi.run()\n",
    "pi_opt_su = vi.policy # result is (0, 0, 0)\n",
    "pi_opt_su\n",
    "pi_opt_su_ = np.zeros([nA, nS*nU])\n",
    "for su in range(nS*nU): \n",
    "    pi_opt_su_[pi_opt_su[su],su] = 1\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Rename some quantities"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "# pi_opt_s_ optimal on state space s \n",
    "# pi_opt_su optimal on state space, unobserved state space U \n",
    "\n",
    "# Assume Suboptimal behavior policy \n",
    "mu_mix_behavior = 0.15\n",
    "Pi = mu_mix_behavior*pi_opt_su_ + (1-mu_mix_behavior)*uniform_pi\n",
    "nS = pi_opt_su_.shape[1] \n",
    "P = np.zeros([nS, nA, nS ])\n",
    "# print p_e_su\n",
    "P = P_su\n",
    "state_dist = np.ones(nS)/nS\n",
    "n = 40000\n",
    "# get evaluation policy "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Generate data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0.05555556 0.05555556 0.05555556 0.05555556 0.05555556 0.05555556\n",
      " 0.05555556 0.05555556 0.05555556 0.05555556 0.05555556 0.05555556\n",
      " 0.05555556 0.05555556 0.05555556 0.05555556 0.05555556 0.05555556]\n"
     ]
    }
   ],
   "source": [
    "tight = False\n",
    "nSmarg = nS / nU\n",
    "[ stateChangeHist, stateHist, a_s, s_a_sprime, p_infty_b_su, distr_hist ] =  simulate_rollouts( \n",
    "    nS, nA, P, Pi, state_dist, n )\n",
    "p_infty_b_s = (reshape_byxrow(p_infty_b_su.T, nU).T).flatten()\n",
    "p_infty_b_su = p_infty_b_su.flatten()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "stationary state occupancy s [0.11562211 0.13694658 0.30951726 0.03804905 0.08649784 0.22569436\n",
      " 0.01269968 0.02594935 0.04902377]\n",
      "('stationary distn on s,u: ', array([0.05784855, 0.05777356, 0.06862328, 0.06832329, 0.15497113,\n",
      "       0.15454614, 0.01909952, 0.01894953, 0.04297393, 0.04352391,\n",
      "       0.11347216, 0.11222219, 0.00637484, 0.00632484, 0.01284968,\n",
      "       0.01309967, 0.02494938, 0.0240744 ]))\n",
      "1.0\n"
     ]
    }
   ],
   "source": [
    "print 'stationary state occupancy s',  p_infty_b_s\n",
    "print('stationary distn on s,u: ', p_infty_b_su)\n",
    "\n",
    "print sum(p_infty_b_su)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Change evaluation policy "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25\n",
      "  0.25 0.25 0.25 0.25]\n",
      " [0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25\n",
      "  0.25 0.25 0.25 0.25]\n",
      " [0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25\n",
      "  0.25 0.25 0.25 0.25]\n",
      " [0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25\n",
      "  0.25 0.25 0.25 0.25]]\n"
     ]
    }
   ],
   "source": [
    "# Closer to optimal evaluation policy\n",
    "mumix = 0 # mixing coef for policies\n",
    "p_e_su = pi_opt_su_*mumix + uniform_pi*(1-mumix)\n",
    "p_e_s = reshape_byxrow(p_e_su.T,nU).T / nU \n",
    "print p_e_su\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "True\n",
      "pi_e_s [[0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25]\n",
      " [0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25]\n",
      " [0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25]\n",
      " [0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25]]\n"
     ]
    }
   ],
   "source": [
    "# process history \n",
    "print np.isclose(sum(p_infty_b_s),1)\n",
    "[ p_a1_su, joint_s_a_sprime, s_a_giv_sprime ] = get_auxiliary_info_from_traj(stateChangeHist, \n",
    "                                        stateHist, a_s, s_a_sprime, p_infty_b_su, distr_hist, nA,nS)\n",
    "# agg history and process\n",
    "[aggStateHist, p_a1_s, p_e_s, agg_s_a_sprime, joint_s_a_sprime_agg, s_a_giv_sprime_agg] = agg_history(\n",
    "            stateHist, s_a_sprime, p_infty_b_s, a_s, p_e_su, nA, nS, nSmarg, nU)\n",
    "# # Simulate from evaluation policy: \n",
    "# [ stateChangeHist_e, stateHist_e, a_s_e, s_a_sprime_e, p_infty_e, distr_hist_e ] =  simulate_rollouts( \n",
    "#     nS, nA, P, p_e_su, state_dist, n )\n",
    "\n",
    "print 'pi_e_s', p_e_s"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "# intermediate data save\n",
    "# \n",
    "# data = {'p_a1_su': p_a1_su, 'joint_s_a_sprime': joint_s_a_sprime, 's_a_giv_sprime':s_a_giv_sprime,'aggStateHist':aggStateHist,'p_a1_s':p_a1_s,'p_e_s':p_e_s,'agg_s_a_sprime':agg_s_a_sprime,'joint_s_a_sprime_agg':joint_s_a_sprime_agg,'s_a_giv_sprime_agg':s_a_giv_sprime_agg   } \n",
    "# pickle.dump(data, open('data-0.15behaviormixture.p','wb'))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Simulate to get real policy evaluation value"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "# [ stateChangeHist, stateHist, a_s, s_a_sprime, p_infty_b_su_long, distr_hist ] =  simulate_rollouts( \n",
    "#     nS, nA, P, Pi, state_dist, 10000 )\n",
    "# [ stateChangeHist_e, stateHist_e, a_s, s_a_sprime_e, p_infty_e_long, distr_hist_e ] =  simulate_rollouts( \n",
    "#     nS, nA, P, p_e_su, state_dist, 10000 )\n",
    "\n",
    "# print p_infty_b_su_long\n",
    "# print p_infty_e_long\n",
    "# w_su_oracle_norm = p_infty_b_su_long/p_infty_e_long\n",
    "# w_s_oracle_norm = reshape_byxrow(w_su_oracle_norm.T,nU).T.flatten()\n",
    "# w_s_oracle_normalized = w_s_oracle_norm / np.dot(w_s_oracle_norm, p_infty_b_s)\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [],
   "source": [
    "# pickle.dump({'min_bnds':min_bnds, 'max_bnds':max_bnds}, open('bnds-pi-smarg.p','w'))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Generate figure"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "4 18\n",
      "9\n",
      "\n",
      "--------------------------------------------\n",
      "Warning: your license will expire in 5 days\n",
      "--------------------------------------------\n",
      "\n",
      "Using license file /Users/az/gurobi.lic\n",
      "Academic license - for non-commercial use only\n",
      "None\n",
      "None\n",
      "9\n",
      "None\n",
      "None\n",
      "9\n",
      "None\n",
      "None\n",
      "9\n",
      "None\n",
      "None\n",
      "9\n",
      "None\n",
      "None\n",
      "9\n",
      "None\n",
      "None\n",
      "9\n",
      "-0.135954722347\n",
      "[1.1692936507725635, 0.8561677924782077, 0.6643508585563435, 1.42313840472535, 1.2779154352913062, 1.0664690842298805, 1.0937338592803545, 1.6417145727643752, 1.6329414791555739]\n",
      "9\n",
      "-0.153751415515\n",
      "[1.1718596314836431, 0.9438790284223699, 0.7817810521688991, 1.3357139765683226, 1.1556039945840433, 1.0134705324743238, 0.9198488554799368, 1.295530554635972, 1.396403000874729]\n",
      "9\n",
      "-0.132715347486\n",
      "[1.170178051594183, 0.8385836828406907, 0.6474374386585104, 1.4348191173570446, 1.2927101803581018, 1.0751145168678518, 1.1192523666747958, 1.6929885433742713, 1.6780387962834606]\n",
      "9\n",
      "-0.156692112939\n",
      "[1.175095737831451, 0.9542315392814088, 0.7955488245528787, 1.3267687966724218, 1.142021667383416, 1.0096716197437563, 0.8956206629709446, 1.245954864787463, 1.3538413750073892]\n",
      "9\n",
      "-0.129422185628\n",
      "[1.1712557866083464, 0.8222638254055818, 0.631122220344453, 1.4470436726117788, 1.3082086986790404, 1.0812054165455758, 1.145977827028209, 1.7470995420203765, 1.723653958599904]\n",
      "9\n",
      "-0.159514700635\n",
      "[1.1771483578102075, 0.962770485883514, 0.808513173689489, 1.3161637381548528, 1.127772352666174, 1.0085635126564731, 0.8706731997579567, 1.1973833936194482, 1.3139416777129085]\n",
      "9\n",
      "-0.12591587707\n",
      "[1.1731374097261034, 0.8053224187678928, 0.6144477622036406, 1.4612789848505452, 1.324934138480869, 1.0857919850931408, 1.1750456440318104, 1.8054086868347745, 1.7717487743769063]\n",
      "9\n",
      "-0.162286720889\n",
      "[1.1797845468786388, 0.9706085070368424, 0.8210738467345243, 1.3048198917039648, 1.1127931113290963, 1.0083169532698382, 0.8448810006028068, 1.1495222951766932, 1.2749100395341597]\n",
      "9\n",
      "-0.122206934868\n",
      "[1.1754755089891402, 0.787368136498078, 0.5974033314212254, 1.4766839072611122, 1.3429470085395965, 1.0898384281681273, 1.2052849540244575, 1.8647904536456512, 1.8223683525923926]\n",
      "9\n",
      "-0.165025587982\n",
      "[1.1825377161920334, 0.9780044393718264, 0.8333849911580583, 1.2921981847160295, 1.0970229196562282, 1.0089374670348954, 0.8180872032266416, 1.1023119466790745, 1.2367234455755522]\n",
      "9\n",
      "-0.118483026786\n",
      "[1.1771415974974766, 0.7684335489323145, 0.5804284602221025, 1.4919636770608542, 1.3607841191173704, 1.0961511197401934, 1.2327017492132617, 1.9129276890765627, 1.873529248854717]\n",
      "9\n",
      "-0.167180631716\n",
      "[1.1844964720963251, 0.9843409015120207, 0.8449070861459023, 1.2778970698930732, 1.0811641875061209, 1.0099002517087368, 0.7908714749583589, 1.0553559504305774, 1.2082104217738596]\n",
      "9\n",
      "-0.114865791851\n",
      "[1.1782535379773247, 0.7539094469105017, 0.5654445740459921, 1.5078536071924644, 1.3792428429883195, 1.0971764756142248, 1.260960123767154, 1.962356642807105, 1.9229758177340592]\n",
      "9\n",
      "-0.169165231287\n",
      "[1.186174101303381, 0.9900595434226251, 0.8560068717100144, 1.2620933263046008, 1.0653457122561363, 1.0115056195198588, 0.7627603956262634, 1.0093050953065419, 1.1826423324770883]\n",
      "9\n",
      "-0.11106950446\n",
      "[1.1797353260091363, 0.7394687523703743, 0.5505651150899119, 1.5248511512828224, 1.3985196830865692, 1.0965945913935302, 1.2903006337356078, 2.013165328699193, 1.9747433665652248]\n",
      "9\n",
      "-0.171071390777\n",
      "[1.1889353044086108, 0.9959042606745986, 0.8661973436346535, 1.2454391532907407, 1.049164889658297, 1.0130677665370627, 0.7351924327655098, 0.9692116615119161, 1.1581117793355513]\n",
      "9\n",
      "-0.106998234261\n",
      "[1.1791612987152753, 0.7241712044813087, 0.5354994355849138, 1.5427195551380883, 1.4192447916394215, 1.0958091271494153, 1.320941627154892, 2.0662854110450772, 2.031074491667243]\n",
      "9\n",
      "-0.172949378249\n",
      "[1.1924907981398924, 1.0018259673173913, 0.875771359816464, 1.2280298951553885, 1.0327437599451184, 1.014778587534839, 0.7075347143614116, 0.9326005569478865, 1.1338904602967863]\n",
      "9\n",
      "-0.1026242262\n",
      "[1.1762169318014655, 0.7079521085058742, 0.520259203479437, 1.5603970024433143, 1.4414193916621454, 1.0950709635980775, 1.3524348193973217, 2.1216335040292384, 2.092645274897883]\n",
      "9\n",
      "-0.174748045328\n",
      "[1.197681218799067, 1.0083439916419368, 0.8835469847178028, 1.2120954327396996, 1.0192162647477392, 1.0160202877516904, 0.6807133265426613, 0.8994573974953001, 1.1093589638376382]\n",
      "9\n",
      "-0.0989881083664\n",
      "[1.1662926964879476, 0.6896231509641393, 0.505050015107001, 1.5757958681152942, 1.4659604398808785, 1.1003153532034646, 1.3841499166946405, 2.1799457692644486, 2.14480015939028]\n",
      "9\n",
      "-0.176692518745\n",
      "[1.205822421790005, 1.0168746262868524, 0.8918782682446709, 1.1952066775509853, 1.0040731907467757, 1.0152580469026216, 0.6526896419125395, 0.866020640448243, 1.0820214399563595]\n",
      "9\n",
      "-0.0958448236318\n",
      "[1.1516793727681338, 0.6701161636716847, 0.49024651589607177, 1.589046612522701, 1.4885661007899353, 1.110654069121905, 1.4147090459140435, 2.236305985481118, 2.191705275760132]\n",
      "9\n",
      "-0.1788014953\n",
      "[1.2150781557600692, 1.0263783298035498, 0.9012296452038129, 1.175205680241944, 0.9859365811966752, 1.014171067890532, 0.623925098471438, 0.8314472473930381, 1.0528825046789927]\n",
      "9\n",
      "-0.0926433372795\n",
      "[1.1349569883715038, 0.650195230933032, 0.4755306737838447, 1.6040954702569965, 1.5125761258357586, 1.120622442692086, 1.4475619635915364, 2.2959380142706967, 2.2396929788619855]\n",
      "9\n",
      "-0.18067263523\n",
      "[1.216870604137699, 1.0301490960258168, 0.9074992346673766, 1.1494981169654799, 0.9677210135275375, 1.0240028795386154, 0.5944472798349216, 0.7976614607874929, 1.030886298654772]\n",
      "9\n",
      "-0.0893850327874\n",
      "[1.1169422303951264, 0.6301421134468507, 0.46093694846888306, 1.6221373731692235, 1.5381336797224225, 1.1293051822379747, 1.4835423137530652, 2.359572199495604, 2.2882636871274276]\n",
      "9\n",
      "-0.182503462712\n",
      "[1.2142381002003735, 1.0304749495116066, 0.9125996909738788, 1.1200460718719578, 0.9476919835285313, 1.0400453107929923, 0.569054109639644, 0.7652338988882901, 1.0120675748195516]\n",
      "9\n",
      "-0.0860589642727\n",
      "[1.0979934161472558, 0.6100589781938772, 0.4464487434051354, 1.644205301290746, 1.5654648907014144, 1.1361143418327735, 1.5234208558038942, 2.428008947751173, 2.337274413412603]\n",
      "9\n",
      "-0.184470129642\n",
      "[1.2098053969838178, 1.0293846306734094, 0.9178678105155644, 1.0937082697639187, 0.9265633366753794, 1.0576250932223084, 0.5458148348723679, 0.7339065610719835, 0.9916972210766604]\n",
      "9\n",
      "-0.0826334825325\n",
      "[1.0775600263249852, 0.58976253128403, 0.4319805012300795, 1.6709396654540967, 1.5949598327968577, 1.1410378965555361, 1.5679263697263466, 2.5022266147098597, 2.387239164636384]\n",
      "9\n",
      "-0.186579307293\n",
      "[1.2034990137936334, 1.0267544316086132, 0.9232143082158163, 1.0649876122006814, 0.9030783143010773, 1.0785142587258068, 0.5222443418156183, 0.7020410108669968, 0.9706947470078645]\n",
      "9\n",
      "-0.0790841923623\n",
      "[1.0555742438075535, 0.5692227882313332, 0.4174756925928185, 1.7033806957277169, 1.626993837649637, 1.143678789245611, 1.6179083229937345, 2.5832786636452174, 2.4383392407179314]\n",
      "9\n",
      "-0.1888935063\n",
      "[1.1936758342102727, 1.0213762581326318, 0.9287463479926402, 1.0320156475712914, 0.8753978885448259, 1.105291336132484, 0.49744792956828665, 0.6682989094559739, 0.9493977977671585]\n",
      "9\n",
      "-0.0753815282175\n",
      "[1.0319978455625587, 0.5484100198127623, 0.4028637363688949, 1.7428547424449998, 1.6620201911326649, 1.1435176289877973, 1.6744928173712659, 2.6724737254775897, 2.4907710064574613]\n",
      "9\n",
      "-0.191439055672\n",
      "[1.1798433573756195, 1.0129243052820058, 0.9345256681707907, 0.9958087248015229, 0.8451928320508346, 1.1375138264996343, 0.47203972978455166, 0.633875243834275, 0.9269970630634049]\n",
      "9\n",
      "-0.0709168437989\n",
      "[1.7683921409445174, 0.712645615723781, 0.4121682233024096, 2.1984119034457024, 1.642039039942238, 0.6123738868247194, 1.9061597713990834, 2.783436613515979, 2.2446573576191833]\n",
      "9\n",
      "-0.193430609285\n",
      "[1.1709452991614682, 1.0079013509494903, 0.9411632516903432, 0.9624040942475266, 0.815657216160999, 1.1614738675460654, 0.44879724304019947, 0.6015296645022639, 0.9109823074519746]\n",
      "9\n",
      "-0.0659048758465\n",
      "[1.7812173943577714, 0.6941161920273606, 0.3969977152685346, 2.2273505123018027, 1.6741911850508575, 0.594748601760291, 1.9558070057361963, 2.86765729523464, 2.3064634117138865]\n",
      "9\n",
      "-0.19637499265\n",
      "[0.6251804571637518, 0.8381106348334809, 1.0012810979700102, 0.6665612645222729, 0.9372596513671215, 1.4376014188724213, 0.3320334331720005, 0.6050411295594508, 1.0651265321701657]\n",
      "9\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-0.0607977390574\n",
      "[1.7896745660080955, 0.6757600197661446, 0.3823552523389503, 2.252440169053601, 1.707154967029841, 0.5776979724373357, 2.0063094670998805, 2.955382182009981, 2.371586961817879]\n",
      "9\n",
      "-0.19930096438\n",
      "[0.6089576615012506, 0.8484992774150792, 1.0241992906252757, 0.6360406963409754, 0.8819892857932412, 1.4452683588699549, 0.31081674514087415, 0.5622103717284667, 1.0437488381979236]\n",
      "9\n",
      "-0.0553956232835\n",
      "[1.795307893101006, 0.6560734482048436, 0.36746093459950996, 2.2757954756908534, 1.7423370318391336, 0.5606072891777129, 2.0599575235621024, 3.0497384913746557, 2.4419685808197165]\n",
      "9\n",
      "-0.202484321565\n",
      "[0.5922546717597423, 0.8599327795239111, 1.0473161047283663, 0.6054967084370696, 0.8265790114532414, 1.452925107067462, 0.2904096287035183, 0.5210526571496018, 1.0185475258848276]\n",
      "9\n",
      "None\n",
      "None\n",
      "9\n",
      "None\n",
      "None\n",
      "9\n",
      "None\n",
      "None\n",
      "9\n",
      "None\n",
      "None\n",
      "9\n",
      "None\n",
      "None\n",
      "9\n",
      "None\n",
      "None\n",
      "9\n",
      "-0.107287093202\n",
      "[1.2427349379145776, 0.7876067219854749, 0.5240830830525822, 1.6532040116866318, 1.4074802217669489, 1.0537561905039918, 1.088611027385023, 2.0121189453146826, 1.9934756806301175]\n",
      "9\n",
      "-0.134377689142\n",
      "[1.2636406556114173, 0.9171299475675774, 0.6757703904398351, 1.5480067604881593, 1.241320657465351, 0.9916772795323593, 0.8836873948411521, 1.482915380396141, 1.618476953413909]\n",
      "9\n",
      "-0.102428634685\n",
      "[1.2429453457003186, 0.7649129103084701, 0.5040966741782017, 1.6684734576139737, 1.4262230531184745, 1.059344877022276, 1.1190174519186102, 2.0901643897744906, 2.062722341800019]\n",
      "9\n",
      "-0.138975460518\n",
      "[1.2714056226066588, 0.9326617537313117, 0.694469562552324, 1.5384499685642081, 1.2221672177538947, 0.9864709745025606, 0.856692058957005, 1.4092998213782637, 1.5498562420248088]\n",
      "9\n",
      "-0.097416081195\n",
      "[1.2438184017276768, 0.7433447962216594, 0.48479751839188834, 1.6854786476000025, 1.4459759673279502, 1.0612319281881424, 1.15142448724683, 2.1732187629154414, 2.1336650236538466]\n",
      "9\n",
      "-0.143363005961\n",
      "[1.2762617836514245, 0.9457814212617828, 0.7123066319407053, 1.5248579041376131, 1.2013479439159334, 0.9855709190247509, 0.8276074629394149, 1.3367060548740082, 1.4865236439305287]\n",
      "9\n",
      "-0.0920781725372\n",
      "[1.2461226133406051, 0.72109459482293, 0.46536679856070595, 1.7049348962569078, 1.4669844598259116, 1.0603635852860633, 1.1864601113855218, 2.262497855732122, 2.2085600652639266]\n",
      "9\n",
      "-0.147625554788\n",
      "[1.2818218510015955, 0.9577760660794834, 0.7295730802789966, 1.5098983889037298, 1.1790479965939995, 0.9857991482177746, 0.7992821893026252, 1.2661845526872268, 1.4254621611973959]\n",
      "9\n",
      "-0.0864086777021\n",
      "[1.2495963272106403, 0.6976527248730114, 0.44568268549391327, 1.7268953989899878, 1.4895313566908464, 1.0577086725806983, 1.223452973774487, 2.3539843856709224, 2.2875170526368174]\n",
      "9\n",
      "-0.151818212768\n",
      "[1.28732077343224, 0.9691296828165238, 0.7467919159584979, 1.49228843742796, 1.1551293227732484, 0.9874795866834801, 0.7659342724205592, 1.1954542217971622, 1.366275394783508]\n",
      "9\n",
      "-0.0806924484961\n",
      "[1.2525021888552301, 0.6732671106970202, 0.4262859846868486, 1.749140731459809, 1.5119436826319879, 1.0573081724641749, 1.257759240917263, 2.4295121004339624, 2.3674159086725717]\n",
      "9\n",
      "-0.154961785974\n",
      "[1.290669706103121, 0.9784017500151857, 0.762668773293344, 1.4713314465012683, 1.1309244579587172, 0.9897619018114215, 0.7337129624514201, 1.1278969334778888, 1.3248072427353461]\n",
      "9\n",
      "-0.0752129636019\n",
      "[1.2546369078287747, 0.6564711435009627, 0.4102932816063045, 1.7717673466093682, 1.5345161337560416, 1.0485078324396568, 1.2926835258549465, 2.5061394766622724, 2.4437908282078786]\n",
      "9\n",
      "-0.157826680941\n",
      "[1.2938388422863687, 0.9869797812177187, 0.7781042331380487, 1.4482137211032367, 1.1065249165508233, 0.9924975870648887, 0.7005888937943796, 1.0614126619660158, 1.288087909463356]\n",
      "9\n",
      "-0.069430428433\n",
      "[1.2578294445017097, 0.6402161528704465, 0.3946849629751327, 1.7973052896466326, 1.5580323543592023, 1.0361681080168017, 1.3297653173335602, 2.585809261974343, 2.5239332666622425]\n",
      "9\n",
      "-0.160552541268\n",
      "[1.297462567396082, 0.9951567142780946, 0.7924485883395008, 1.4227582755978951, 1.0820497614157163, 0.9955680303149126, 0.6675819868250047, 1.004369001491214, 1.2536848813105426]\n",
      "9\n",
      "-0.0633031551791\n",
      "[1.2621797325534054, 0.6245082640797556, 0.37946226689841145, 1.8254924822722012, 1.5822489166781752, 1.0202349711311574, 1.36890701291585, 2.6683912461212373, 2.6085584572720064]\n",
      "9\n",
      "-0.163237295969\n",
      "[1.3025070092786732, 1.0036031356283641, 0.8060083310350631, 1.3959951460604239, 1.0563712811430364, 0.9988029048075918, 0.6344166033671674, 0.9523507480057669, 1.2198941244092483]\n",
      "9\n",
      "-0.0567771296295\n",
      "[1.2677973282302442, 0.6093202130321429, 0.36459392282767045, 1.856673990189606, 1.607066525810377, 1.0004786122729463, 1.4103522058166835, 2.7541195719218643, 2.698459934336174]\n",
      "9\n",
      "-0.165796916888\n",
      "[1.3099733135249747, 1.0128253576234445, 0.8170077466429861, 1.3711599136932902, 1.034936990600787, 1.0012276741452821, 0.602372860348532, 0.9060710893918277, 1.1858058044618376]\n",
      "9\n",
      "-0.0514192602545\n",
      "[1.2592109666960714, 0.5898832665041781, 0.3493717906602718, 1.8801689531565784, 1.6352622880082495, 0.9935175344974007, 1.4499664575637674, 2.8442888617852486, 2.775186558554351]\n",
      "9\n",
      "-0.168373213501\n",
      "[1.3181700924759485, 1.0220733956638988, 0.8274714124888162, 1.34444540981004, 1.0139867887991891, 1.0039829615140545, 0.5699983663247933, 0.8620391941242667, 1.1512837683370332]\n",
      "9\n",
      "-0.0468638073083\n",
      "[1.2441954148539043, 0.5690009538717664, 0.33457009402114685, 1.9006325176604282, 1.661784683961064, 0.9935250548345661, 1.4885802643412724, 2.9334580017165393, 2.8424714805799525]\n",
      "9\n",
      "-0.171169906564\n",
      "[1.3281339517169708, 1.0333267867810076, 0.8391125843974034, 1.3140072158841287, 0.9900741508965827, 1.0056183102899487, 0.535117382974393, 0.8171931512734948, 1.1139110945181219]\n",
      "9\n",
      "-0.0422279239987\n",
      "[1.2273827762871217, 0.5480676507593827, 0.3200692086035134, 1.9240973298385649, 1.6899187780680998, 0.991868566915302, 1.5303701417071947, 3.0283482309812304, 2.910874641053048]\n",
      "9\n",
      "-0.174145503659\n",
      "[1.3411352368080542, 1.0461330844125245, 0.8514340464015657, 1.279977481379427, 0.9632578551461349, 1.0059807044745666, 0.501803659078562, 0.7728393714053354, 1.0738461667827794]\n",
      "9\n",
      "-0.0375011505464\n",
      "[1.2093857622623343, 0.5272684126245746, 0.30587624998914165, 1.9517344350827868, 1.7198844176093966, 0.9877025920706608, 1.5762082609224448, 3.1301316552941376, 2.980138339103194]\n",
      "9\n",
      "-0.176634625705\n",
      "[1.340966528933809, 1.0492594380835762, 0.8584447661084165, 1.2377260032564472, 0.9364930664155376, 1.023939786722369, 0.4744897475174773, 0.7322208485180847, 1.0471609071324501]\n",
      "9\n",
      "-0.0326607078986\n",
      "[1.19071409098212, 0.506723268556265, 0.29196364151316867, 1.9850946163990524, 1.7520275361022344, 0.980118622239169, 1.6272269872387788, 3.240354561460342, 3.0501559773179485]\n",
      "9\n",
      "-0.179097339535\n",
      "[1.3380223416830754, 1.0500219400943138, 0.8634272701754523, 1.203551850157576, 0.9102075644710268, 1.0453331365533496, 0.4510913519659061, 0.6947915955092165, 1.0208025094780098]\n",
      "9\n",
      "-0.0276560975394\n",
      "[1.1709666511229484, 0.48627483404325506, 0.2782361361300122, 2.0251244973210483, 1.7868260011554926, 0.9688063326019624, 1.6843699097916105, 3.3607138809012898, 3.1216227200616498]\n",
      "9\n",
      "-0.181789967393\n",
      "[1.3322002576521612, 1.048688763049612, 0.8691185012452355, 1.1655012031882177, 0.8799299234484678, 1.0710418040156344, 0.4272753126122718, 0.6563757643914094, 0.9934272948358436]\n",
      "9\n",
      "-0.0224403291748\n",
      "[1.1501677860445843, 0.4658884554919986, 0.26461997625713096, 2.073273113625265, 1.8247908569037827, 0.9530410115788703, 1.7488943806841377, 3.49323611940236, 3.1949553139383564]\n",
      "9\n",
      "-0.184673468005\n",
      "[1.3213927174653182, 1.0436849328583526, 0.874574607195685, 1.1229398020294863, 0.8467166105384609, 1.1037796837759581, 0.40293050976250944, 0.6175892707289338, 0.9662015347158512]\n",
      "9\n",
      "-0.0169540265079\n",
      "[1.1283385167433846, 0.44551643044348704, 0.2510223564204844, 2.1314662110320794, 1.8665933759634774, 0.931886893132195, 1.8224222403327792, 3.640503090155991, 3.2706656442414697]\n",
      "9\n",
      "-0.187831746729\n",
      "[1.3050814341889603, 1.0345662208474207, 0.8797073564624383, 1.0753579487305809, 0.808840483998182, 1.1452102549196082, 0.3778658021622647, 0.5773994615424382, 0.9385264182137094]\n",
      "9\n",
      "-0.011289631477\n",
      "[1.1113418565340807, 0.4265818727857089, 0.23769066916619092, 2.203949848783246, 1.911801656636632, 0.9011497313089596, 1.9072028559800875, 3.8040178321425344, 3.344786079955733]\n",
      "9\n",
      "-0.19026517391\n",
      "[1.2965554273424884, 1.030699831762891, 0.8864329648784989, 1.0322049480603714, 0.7717187490137469, 1.1741020086448812, 0.35525147389298456, 0.5398867889812425, 0.9186664761354304]\n",
      "9\n",
      "-0.00419585621398\n",
      "[1.0993817428485604, 0.40886226552425603, 0.22433221583224677, 2.2897870733196983, 1.9582466213285086, 0.8582268472548626, 2.002251893989156, 3.9809833234351815, 3.4375772158522016]\n",
      "9\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-0.191700999349\n",
      "[1.2966062876070117, 1.0330009142005026, 0.8929021671956, 1.0057003994144529, 0.7549254606641439, 1.1814442633893327, 0.33962443816936944, 0.5169896849761489, 0.9038417952562875]\n",
      "9\n",
      "0.00476367669929\n",
      "[1.0940614746862005, 0.39333308039197157, 0.21144181661682648, 2.375244474447777, 2.001410431711335, 0.8047207933419674, 2.099571229132448, 4.161126712077814, 3.558170686383519]\n",
      "9\n",
      "-0.193050406907\n",
      "[1.2966488581586015, 1.0351068706827335, 0.8992603618336898, 0.9793616765501174, 0.738669458740289, 1.1882093508531837, 0.3248615037922213, 0.4967917954627566, 0.8902104576662566]\n",
      "9\n",
      "0.0137365314951\n",
      "[1.0879067916594345, 0.377963399055164, 0.19928875258378909, 2.4349118645915064, 2.0423221881583475, 0.7552619847821851, 2.1890399074657543, 4.34137541624878, 3.6829667313628103]\n",
      "9\n",
      "-0.195074058187\n",
      "[0.5256514628030868, 0.737014999583053, 0.9515004313256848, 0.5563920844164101, 0.7853250114880481, 1.6938299984502025, 0.19765378976236336, 0.47145879365207727, 1.1760500282139057]\n",
      "9\n",
      "None\n",
      "None\n",
      "9\n",
      "None\n",
      "None\n",
      "9\n",
      "None\n",
      "None\n",
      "9\n",
      "None\n",
      "None\n",
      "9\n",
      "None\n",
      "None\n",
      "9\n",
      "None\n",
      "None\n",
      "9\n",
      "-0.0804786733725\n",
      "[1.2975256273052471, 0.7274074417322128, 0.41524268143595877, 1.8563385537405814, 1.517771738579948, 1.0239163524447006, 1.021930388598646, 2.3558284774108023, 2.3400517327559887]\n",
      "9\n",
      "-0.116239891039\n",
      "[1.3435137507206292, 0.8927205261809139, 0.5855922612267388, 1.7552107271245632, 1.3234645864842531, 0.9602207154866668, 0.8237105432605211, 1.6627313871945506, 1.8270561565694892]\n",
      "9\n",
      "-0.0741592573884\n",
      "[1.295927238141438, 0.7014688233616355, 0.3946613903744157, 1.8734213993446187, 1.5382988193088614, 1.0247580454556215, 1.0512543704960196, 2.4561397299057104, 2.4321776930935974]\n",
      "9\n",
      "-0.122504533136\n",
      "[1.3564624668461347, 0.9131475351170171, 0.6078105968492602, 1.747571520194591, 1.300129475731264, 0.9541505911860501, 0.7980586797028283, 1.5674450123334098, 1.7313058565985748]\n",
      "9\n",
      "-0.0675841187578\n",
      "[1.2957247827827394, 0.6763372149367344, 0.3748427825208135, 1.8923732089740626, 1.5596650749972896, 1.0212680778788419, 1.082303640544579, 2.5623959735655824, 2.527358727801711]\n",
      "9\n",
      "-0.128425681502\n",
      "[1.366112303366908, 0.9304545344846875, 0.6289748447059618, 1.7341343042417516, 1.2737666549394733, 0.9535295122483392, 0.7697430145619933, 1.473096196298073, 1.6436564649857626]\n",
      "9\n",
      "-0.0605701992868\n",
      "[1.297442442434717, 0.6504285882716124, 0.3550918339529976, 1.914665056967066, 1.5821698551718693, 1.0139576699679655, 1.1159662282346006, 2.6762937380652683, 2.628020090204598]\n",
      "9\n",
      "-0.134166807213\n",
      "[1.3757345229964977, 0.9465651752096819, 0.6498451039684151, 1.717543390491399, 1.2448458406839027, 0.9546224603904527, 0.7397255259753119, 1.3803881232152708, 1.5599127529410932]\n",
      "9\n",
      "-0.0531169559506\n",
      "[1.3010001384172394, 0.6233083497564113, 0.3353029364131071, 1.9404725882435772, 1.6059615336475646, 1.0038024815422446, 1.1517380907627397, 2.792796526282767, 2.7341381084366656]\n",
      "9\n",
      "-0.139761404684\n",
      "[1.3853353255971377, 0.9619726009245881, 0.6706570297367502, 1.697141611314838, 1.2126812199800947, 0.9573035105410119, 0.7078792200471286, 1.2887840091060754, 1.479811542134129]\n",
      "9\n",
      "-0.0455591572531\n",
      "[1.3043546334699, 0.5953577625811403, 0.31594014563584644, 1.9670425218258598, 1.6298117704943405, 0.9954166896196347, 1.1856263847555772, 2.8906870949435084, 2.8418635021122793]\n",
      "9\n",
      "-0.143864548889\n",
      "[1.392996385239949, 0.9753264995073665, 0.6897905217856064, 1.6718986624601382, 1.1792230055790225, 0.9601101626111107, 0.6748196079975053, 1.2002948790530104, 1.424745714837164]\n",
      "9\n",
      "-0.0383688298342\n",
      "[1.3067514891932175, 0.5780170910133481, 0.30114428388550774, 1.994284040731932, 1.6536328969567433, 0.9756800834790559, 1.2202077319660087, 2.990248104206504, 2.9440980989318977]\n",
      "9\n",
      "-0.14751922544\n",
      "[1.3977926348062935, 0.9864807555487504, 0.7090380792551092, 1.6408105731413258, 1.1449516503142225, 0.9647351562695826, 0.6397353404862811, 1.1142818349659236, 1.3786749286055942]\n",
      "9\n",
      "-0.0307783390549\n",
      "[1.3108820117161812, 0.5617154290971068, 0.287043872283231, 2.0246020056638154, 1.6776665586568182, 0.9512898755819299, 1.2566262906477934, 3.092791250439308, 3.0515575607079883]\n",
      "9\n",
      "-0.150983503032\n",
      "[1.4036426313254926, 0.9974118706329572, 0.7267206883154701, 1.6075568373704094, 1.1107989091557573, 0.9693830588661222, 0.6047165011545305, 1.040616876337988, 1.3354357332651963]\n",
      "9\n",
      "-0.0227186570861\n",
      "[1.316861064320659, 0.5464100289669658, 0.27358651888781826, 2.0586604708219194, 1.7017096336171469, 0.9219656932805518, 1.2953467356758135, 3.198647907940729, 3.165259169034638]\n",
      "9\n",
      "-0.154356351595\n",
      "[1.4092603844679317, 1.0076291116706177, 0.7437984787771037, 1.570951609822084, 1.0764376240626015, 0.97477623497159, 0.5689264083207308, 0.9747406375665552, 1.294172211328152]\n",
      "9\n",
      "-0.0141311312026\n",
      "[1.3249001565255798, 0.532093421756826, 0.2607542846414897, 2.09597724912087, 1.7252316245205053, 0.8877805664438432, 1.336006405284648, 3.3071721936851697, 3.2862480748349223]\n",
      "9\n",
      "-0.157554986516\n",
      "[1.4186759022682447, 1.0191847938527319, 0.7572889563450367, 1.537863305576078, 1.047921482881112, 0.9786125043544307, 0.5344463983244255, 0.9171570514668363, 1.252257685791726]\n",
      "9\n",
      "-0.00742615599148\n",
      "[1.3222137511574041, 0.5149870523250691, 0.24788395354778694, 2.128134027994284, 1.7524767897207016, 0.8650921910723269, 1.376148464297791, 3.4232775502948543, 3.381195103658287]\n",
      "9\n",
      "-0.16077162477\n",
      "[1.4290339083328671, 1.0310383963781595, 0.7701797045885977, 1.5005973221182547, 1.0200063226693732, 0.9828861597749521, 0.49831761836535615, 0.8626258611321245, 1.2100543962042227]\n",
      "9\n",
      "-0.00186678308385\n",
      "[1.3135589367282545, 0.49673292469657465, 0.23541144572912126, 2.1575938023224155, 1.7785297130280058, 0.8497201137717995, 1.4158301079622502, 3.5404575581382707, 3.460977789411511]\n",
      "9\n",
      "-0.164044638328\n",
      "[1.4395258494722847, 1.0429375562693426, 0.782875924747119, 1.4594719045390387, 0.9912679442766945, 0.9880172039580286, 0.4627005703761257, 0.8107434460210572, 1.1676022226891143]\n",
      "9\n",
      "0.003756836203\n",
      "[1.3048215136339758, 0.47904160015142566, 0.2234454434504229, 2.1913083426964346, 1.805847065585349, 0.8310425402610743, 1.4589018936732525, 3.665278055493592, 3.5409472702085902]\n",
      "9\n",
      "-0.167616496851\n",
      "[1.4554133782523953, 1.0574410968411119, 0.7969109662402752, 1.4139784038413248, 0.9581803591099521, 0.9906512263338856, 0.4256840467036102, 0.7577530302687001, 1.120205272010514]\n",
      "9\n",
      "0.0095629227134\n",
      "[1.2935855722417995, 0.46117679357535474, 0.21175297319864878, 2.228165006484621, 1.8349529516219156, 0.8102974108299912, 1.5052780874980052, 3.799184758626854, 3.6238257351581664]\n",
      "9\n",
      "-0.170973648029\n",
      "[1.4628690383377665, 1.067448598704476, 0.8082766791169779, 1.3604908644988787, 0.9239754874493189, 1.0029373868372906, 0.39904412677287937, 0.7097961903672625, 1.0804945625326732]\n",
      "9\n",
      "0.0156622095812\n",
      "[1.2780956491847981, 0.4426621460961672, 0.20016650890145846, 2.2685077901983277, 1.8665826219660433, 0.7877800146162103, 1.555642056313318, 3.9446224561279943, 3.711746998872522]\n",
      "9\n",
      "-0.173958827712\n",
      "[1.4609003892493446, 1.0697814053796733, 0.8146591165909428, 1.3173845532099646, 0.8915205076024469, 1.026738556657894, 0.37631073219974304, 0.6664072051696327, 1.048325431829895]\n",
      "9\n",
      "0.0219928408893\n",
      "[1.2622837342047284, 0.4245913386219595, 0.18890944185014147, 2.316548073915581, 1.9008541838708675, 0.7599538128184241, 1.6122334999823065, 4.1042687373895035, 3.801778859034504]\n",
      "9\n",
      "-0.177057812572\n",
      "[1.4568241663687396, 1.070270208362518, 0.8195460451601662, 1.2718521542586925, 0.8570562852756604, 1.0558503409686935, 0.35422509736736757, 0.6240785514506239, 1.0159703998151146]\n",
      "9\n",
      "0.0286257700939\n",
      "[1.246307053242342, 0.4069440267685468, 0.17791649607353954, 2.373933423385106, 1.9383014069840458, 0.7257839848164623, 1.6763834350182212, 4.28111278592195, 3.894635977548898]\n",
      "9\n",
      "-0.180342548838\n",
      "[1.4466679583146922, 1.066412458760985, 0.8235750042211804, 1.220788417595901, 0.8180136163408016, 1.0941236918724688, 0.33529142485444685, 0.5819023729552548, 0.9848101148093025]\n",
      "9\n",
      "0.035650576198\n",
      "[1.2302725824288638, 0.38967406926235154, 0.16710394049605837, 2.4425496760269083, 1.979612727239366, 0.684059272325157, 1.7496743220185837, 4.47881702581274, 3.991273067554259]\n",
      "9\n",
      "-0.183934640538\n",
      "[1.4290763053235094, 1.0573509753729557, 0.8271700557494642, 1.1635111288816504, 0.7750279035914137, 1.1433073920273662, 0.3086657284399183, 0.537210732639486, 0.9533372943483501]\n",
      "9\n",
      "0.0430136207991\n",
      "[1.219062328254958, 0.3738914738726099, 0.15666731200378323, 2.5266599530955096, 2.0246964834073724, 0.6308149382287327, 1.8345432800867016, 4.700634873254145, 4.0885929218644055]\n",
      "9\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-0.186679697808\n",
      "[1.4213729811662748, 1.0548264125680014, 0.8332535332097915, 1.1120037678707246, 0.732203370091036, 1.1762925337352848, 0.2881086788384986, 0.4962529595449095, 0.9308346296553278]\n",
      "9\n",
      "0.0535749962798\n",
      "[1.2200167981637469, 0.36099082897243057, 0.14668676686363466, 2.6227177244011677, 2.0649004582426485, 0.557556296027249, 1.926805441951907, 4.930526397055522, 4.231581804995253]\n",
      "9\n",
      "-0.188272201818\n",
      "[1.4229370108406991, 1.0585396313114694, 0.8398253662707167, 1.0809876006599444, 0.714276900432882, 1.1834116504006942, 0.2741859615611953, 0.47351913980650917, 0.9138487739050885]\n",
      "9\n",
      "0.0656009016159\n",
      "[1.2255051996473543, 0.34968946948373136, 0.13716199269280943, 2.7174113937620916, 2.1036973495508113, 0.47464716110189176, 2.02273320583329, 5.1738360780865635, 4.396450304677551]\n",
      "9\n",
      "-0.189796705834\n",
      "[1.42468334767272, 1.062284597827722, 0.8463261236263282, 1.0503428453840649, 0.6970458966839835, 1.1898669828624344, 0.2608526289850849, 0.451824883543335, 0.8976306243601496]\n",
      "9\n",
      "0.0780303534909\n",
      "[1.2315997791058595, 0.33869128948507515, 0.12813066880098667, 2.784203754533956, 2.1401714799272997, 0.39350400387170276, 2.1117601758537448, 5.42459823751269, 4.5713929656483385]\n",
      "9\n",
      "-0.191235193182\n",
      "[1.4264581715891127, 1.0658663225983775, 0.8526578492362852, 1.0200489544801616, 0.6805245886628717, 1.195761072166844, 0.2483484761878332, 0.4323896389958223, 0.8825172838430898]\n",
      "9\n",
      "None\n",
      "None\n",
      "9\n",
      "None\n",
      "None\n",
      "9\n",
      "None\n",
      "None\n",
      "9\n",
      "None\n",
      "None\n",
      "9\n",
      "None\n",
      "None\n",
      "9\n",
      "None\n",
      "None\n",
      "9\n",
      "-0.0553772042965\n",
      "[1.3372335443009824, 0.6731822038804495, 0.32976067907789003, 2.034616123395657, 1.612196311316303, 0.985691173280222, 0.9075921879265213, 2.6687104239687995, 2.6725918593599025]\n",
      "9\n",
      "-0.0992715025185\n",
      "[1.4115103858261435, 0.8690730888747865, 0.5085645612215361, 1.9540587571387211, 1.402440621827453, 0.9236460959006446, 0.7439790909906423, 1.8345975970898012, 2.023453153764693]\n",
      "9\n",
      "-0.0477362194137\n",
      "[1.33306095352369, 0.6451757882906146, 0.3099760710308446, 2.050529523598901, 1.6326661266456555, 0.9820800738711667, 0.9299615260552213, 2.7847052169179034, 2.7865437408703904]\n",
      "9\n",
      "-0.107185830705\n",
      "[1.4306817742029847, 0.8937727969001033, 0.5330564934560807, 1.9512981224061086, 1.3761936105384405, 0.9169224327529714, 0.7232625628819844, 1.7205142124590682, 1.8997677079435003]\n",
      "9\n",
      "-0.0397204581464\n",
      "[1.330873782172283, 0.6173928914668284, 0.29089073971083435, 2.06922515941357, 1.6537993726616471, 0.9736806758214713, 0.9548960695052605, 2.9076521395425514, 2.9051435298986403]\n",
      "9\n",
      "-0.114632158175\n",
      "[1.4457028534738159, 0.9151112607184173, 0.5565373292790561, 1.9402469362565993, 1.3452654936285426, 0.9166988936101896, 0.6990941323558423, 1.6066477950793692, 1.7871921752600037]\n",
      "9\n",
      "-0.0311830124474\n",
      "[1.3311545398264821, 0.588825595085395, 0.27208509855510743, 2.092012588603824, 1.6757434356492793, 0.9607194096172397, 0.9814161514399038, 3.0381707296288476, 3.0303249049983547]\n",
      "9\n",
      "-0.121894755915\n",
      "[1.461419841329743, 0.935888579054934, 0.5803019877961254, 1.924448853416469, 1.308002885653819, 0.9184490288247972, 0.672555546004075, 1.4920372460805766, 1.6795333179954746]\n",
      "9\n",
      "-0.0221076137886\n",
      "[1.3337287396136106, 0.5589933376740328, 0.25341077237054105, 2.1188363694631565, 1.698640377761332, 0.9442488059446367, 1.0097298232264058, 3.171154400520697, 3.1623745045406495]\n",
      "9\n",
      "-0.128895829336\n",
      "[1.4765446239136493, 0.9556808660563343, 0.6040610529731418, 1.90298718024387, 1.266783245580806, 0.9221867183305393, 0.6436130549454431, 1.3792495014842328, 1.5779432981644654]\n",
      "9\n",
      "-0.0128629089864\n",
      "[1.3366821625198044, 0.5286084473373657, 0.23529371968347104, 2.1474081711521857, 1.7216525179664854, 0.9285598890057016, 1.037397080480322, 3.284982926082363, 3.296703090092873]\n",
      "9\n",
      "-0.13386383495\n",
      "[1.4869263388300022, 0.9719062434060959, 0.6261369780134322, 1.8731409002422366, 1.224913111374558, 0.926501703825598, 0.6122556050942125, 1.271375347253308, 1.5111528308258018]\n",
      "9\n",
      "-0.00411662739455\n",
      "[1.3384321422468666, 0.5115044287874181, 0.22264678082606454, 2.176239680175421, 1.7445612986658598, 0.8992626284304914, 1.065381615466324, 3.400960880165005, 3.4236446391911057]\n",
      "9\n",
      "-0.138181550586\n",
      "[1.4955595510473327, 0.9864197529040711, 0.6475590331237099, 1.8373208121299904, 1.182009107825358, 0.932098461525742, 0.5786988664806862, 1.1679058630192634, 1.4561944268815747]\n",
      "9\n",
      "0.00512396445872\n",
      "[1.3424788238913445, 0.49583616560165295, 0.21089199510088055, 2.208957354525806, 1.7670113160444962, 0.8643440997816577, 1.0951143152351914, 3.519915980736297, 3.5571695527373155]\n",
      "9\n",
      "-0.142295643773\n",
      "[1.5033026705422476, 0.9997002391613783, 0.6681186585772286, 1.7962935841932681, 1.1387331322533392, 0.938599521878852, 0.5439167450400639, 1.0787943638529505, 1.4054767538759332]\n",
      "9\n",
      "0.0149306943692\n",
      "[1.349035596840525, 0.4815703123831822, 0.1999780200857073, 2.245354701729231, 1.7884071762832032, 0.8238489821275983, 1.1265077608244645, 3.641292554217355, 3.6985137258032554]\n",
      "9\n",
      "-0.146272366995\n",
      "[1.5108339944801612, 1.012200883547818, 0.6879549884254179, 1.7506433695840107, 1.095131843278319, 0.9459178189077195, 0.5078012365474504, 0.9993500493846476, 1.3576317128929645]\n",
      "9\n",
      "0.0253785082516\n",
      "[1.3582551107520162, 0.46865037997269077, 0.18984881833794282, 2.2852516406856482, 1.8080882723887197, 0.7778929980231349, 1.1594658225563386, 3.7643871653933494, 3.848998567139801]\n",
      "9\n",
      "-0.150027602993\n",
      "[1.5226530655411497, 1.026119794329524, 0.7035036490755484, 1.7081369201739307, 1.0595669535083705, 0.9512464903171759, 0.47242410362045417, 0.9312079785767312, 1.309149396584241]\n",
      "9\n",
      "0.0333838318755\n",
      "[1.3554888240745893, 0.4528012068184737, 0.1794581112794018, 2.3186418318859814, 1.8322634149583992, 0.745939292027934, 1.1910964255222254, 3.897915071372922, 3.965064386225422]\n",
      "9\n",
      "-0.153777445424\n",
      "[1.5359198004417363, 1.0404706361277931, 0.7180865540040334, 1.6620065301545865, 1.0249170527458114, 0.9567786035970024, 0.4356041709132446, 0.867539999716226, 1.2604107801764812]\n",
      "9\n",
      "0.0399561320023\n",
      "[1.3464211707811724, 0.43589924665378627, 0.16932511516916082, 2.349362940689827, 1.8561935532766776, 0.721880556112437, 1.2223607787894895, 4.035677723416231, 4.061316296724551]\n",
      "9\n",
      "-0.15759996449\n",
      "[1.5498381972900168, 1.0550763711846125, 0.7325829384925886, 1.6099387133058127, 0.989205557202333, 0.9632033352578755, 0.3973612723433939, 0.8065499914467644, 1.211292471675585]\n",
      "9\n",
      "0.0466055171584\n",
      "[1.3378834402368422, 0.4199039932129594, 0.15980730313808109, 2.3849735509846526, 1.8811791655085666, 0.6936204087316077, 1.2565719084369704, 4.183090741161735, 4.157715128930306]\n",
      "9\n",
      "-0.161583705654\n",
      "[1.565921992514428, 1.0707030892757219, 0.7474523312010384, 1.5513714739717297, 0.9511605861514616, 0.9694544938876365, 0.36042245724083105, 0.7478547214619403, 1.160268208835219]\n",
      "9\n",
      "0.0533863200217\n",
      "[1.3299831757019938, 0.4047731337704346, 0.15084753115811045, 2.4261133330018114, 1.907454212143541, 0.6606175262401336, 1.294226773841197, 4.342054374838294, 4.254934506058368]\n",
      "9\n",
      "-0.165636227544\n",
      "[1.5790326418932648, 1.0841689293771621, 0.7606012438059814, 1.4879124097019276, 0.9093617560466216, 0.9723149470917906, 0.44563729432091637, 0.7206984920608039, 1.1108465836038948]\n",
      "9\n",
      "0.0603606497992\n",
      "[1.3228409426786933, 0.3904676554920542, 0.14238885741675236, 2.4737436262584542, 1.935320240432893, 0.6221655636740349, 1.3359972531410766, 4.5149293695378425, 4.353708592330668]\n",
      "9\n",
      "-0.169148777023\n",
      "[1.577893993923899, 1.0876203386735475, 0.766999748855928, 1.4404760698227956, 0.8694258186156517, 0.9820578420477747, 0.6426319248254005, 0.7249270162415745, 1.0726490580852626]\n",
      "9\n",
      "0.06761454754\n",
      "[1.3166277632211894, 0.3769570768003355, 0.13437254302369425, 2.529208909265827, 1.9653009738850444, 0.5772282753874018, 1.3827244160370988, 4.704837721878384, 4.455022700058384]\n",
      "9\n",
      "-0.172640737645\n",
      "[1.5754841330337834, 1.089948876812012, 0.7728131442203762, 1.3962119072537966, 0.8312624071212937, 1.010608891776083, 0.624716748893146, 0.6789013288747813, 1.0343759228484968]\n",
      "9\n",
      "0.0752492973739\n",
      "[1.3115498927274258, 0.36421442920806135, 0.12674305736824423, 2.593563981207692, 1.9977088316645535, 0.5247144474870438, 1.4354958776485338, 4.915572742949698, 4.560180483304397]\n",
      "9\n",
      "-0.176193324702\n",
      "[1.5670088926803873, 1.087810518382695, 0.7757143890352814, 1.3294685486210753, 0.7881457132149137, 1.0543862550096694, 0.5970045069466958, 0.6300743739098713, 1.0013809803199605]\n",
      "9\n",
      "0.0833619911659\n",
      "[1.3077690743799573, 0.35222380299897177, 0.11945286012782806, 2.6683755901880186, 2.033194513223661, 0.4633445834972025, 1.4952575480624402, 5.151183807806562, 4.670283011815389]\n",
      "9\n",
      "-0.180006216827\n",
      "[1.550074165036596, 1.0799917708256304, 0.7778946384225309, 1.2566736417788664, 0.7414233606184693, 1.1355897707482674, 0.2545569241440695, 0.505632054546966, 0.9690724104466857]\n",
      "9\n",
      "0.0920082669494\n",
      "[1.3084178756429599, 0.34158969698994357, 0.11258077214272413, 2.7569471158034715, 2.071944311533688, 0.38987579413782447, 1.5639778747770055, 5.416698556108364, 4.784621655215912]\n",
      "9\n",
      "-0.182979640878\n",
      "[1.543651688842836, 1.078866717137217, 0.7829161142812916, 1.1968769879238128, 0.6938797854351672, 1.1723745363360631, 0.23548570831067608, 0.46171653149538805, 0.9447924553420698]\n",
      "9\n",
      "0.100083866797\n",
      "[1.3101976207338577, 0.33190829894928, 0.10697386196456081, 2.724916534327394, 2.0890456059623803, 0.349491694617238, 1.5839455455949574, 5.621544306415055, 4.909872437214128]\n",
      "9\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-0.184725850518\n",
      "[1.5468520473042964, 1.0840191841093831, 0.7896103014023633, 1.161934528674337, 0.6755463276039188, 1.178952006628795, 0.22322512261254657, 0.4382316153176209, 0.9253803712494927]\n",
      "9\n",
      "0.108049463986\n",
      "[1.3145265845343919, 0.3237608158557528, 0.10263100249741104, 2.5791231767852794, 2.086120619714646, 0.33740742309365834, 1.5583349467979695, 5.770665750179807, 5.05149215641038]\n",
      "9\n",
      "-0.186384440725\n",
      "[1.5504119892169659, 1.0892238914449754, 0.7961950418588313, 1.1275067731654327, 0.657767105045874, 1.1846422273529347, 0.21170376788316675, 0.41697665161854447, 0.907000744547815]\n",
      "9\n",
      "0.116743332308\n",
      "[1.3174362734160252, 0.31557212424431985, 0.09845696201501306, 2.4024473679835703, 2.0833135560384957, 0.3260005997317862, 1.525157088825749, 5.937548020688212, 5.2087096548659035]\n",
      "9\n",
      "-0.187948479803\n",
      "[1.553920910163576, 1.094216339160804, 0.8025091448494812, 1.0936647808599258, 0.6409825010775257, 1.1898255470763308, 0.2016273009178212, 0.3976290483976708, 0.8897833002977842]\n",
      "9\n",
      "None\n",
      "None\n",
      "9\n",
      "None\n",
      "None\n",
      "9\n",
      "None\n",
      "None\n",
      "9\n",
      "None\n",
      "None\n",
      "9\n",
      "None\n",
      "None\n",
      "9\n",
      "None\n",
      "None\n",
      "9\n",
      "-0.0318097767695\n",
      "[1.3652505769840457, 0.6236599406120982, 0.26189835388164945, 2.184021610049324, 1.691553839979495, 0.945988638944814, 0.7558477065509046, 2.945635328160938, 2.9928407407395134]\n",
      "9\n",
      "-0.0833888548436\n",
      "[1.4687102924816586, 0.8455961586415567, 0.4425661316830439, 2.141575160471035, 1.477986886868101, 0.8848199791269911, 0.6483762487113829, 1.9979833432759053, 2.209015412973645]\n",
      "9\n",
      "-0.0229449740324\n",
      "[1.3577460568270672, 0.5941879634568746, 0.24351654193949177, 2.2022204584714213, 1.7122219515384745, 0.9371044984811078, 0.7707316750819646, 3.0750468418511185, 3.1268777676787574]\n",
      "9\n",
      "-0.0929219515408\n",
      "[1.4946544846296577, 0.8741042961760997, 0.4681638617649772, 2.147411171519804, 1.4503651608474504, 0.8773939054958804, 0.6354197487266682, 1.8685856928354116, 2.0568191135668266]\n",
      "9\n",
      "-0.0136076897864\n",
      "[1.3529500018161853, 0.5643717285503254, 0.22577564566767033, 2.2185277782729482, 1.7316355732861617, 0.9252524577001066, 0.7846029879199599, 3.206607033796703, 3.267912123624477]\n",
      "9\n",
      "-0.101998110838\n",
      "[1.516707687846336, 0.8999081670189775, 0.4938491093341008, 2.1408331766712445, 1.4124266849801186, 0.877597780252854, 0.6178271436010425, 1.7339484055347383, 1.9174871816283716]\n",
      "9\n",
      "-0.0036794271375\n",
      "[1.3509873170173108, 0.5337262336550602, 0.20846362202254737, 2.239539831152347, 1.7515383071056658, 0.9082878160890835, 0.8003020025540349, 3.3455827066228894, 3.41649689472087]\n",
      "9\n",
      "-0.110720401835\n",
      "[1.5385077551479354, 0.9248038542041461, 0.5195039315368671, 2.1278451912053113, 1.3688353772091697, 0.8800645197752349, 0.5974374715538151, 1.6005157788744628, 1.7860994686601077]\n",
      "9\n",
      "0.00685758956377\n",
      "[1.3517107031512214, 0.5018102279579839, 0.19142307445586434, 2.265016469187531, 1.7718834654276738, 0.8874580895080554, 0.8171656098579835, 3.486112240495137, 3.57300579313106]\n",
      "9\n",
      "-0.119066602528\n",
      "[1.559250324440784, 0.9486252536942702, 0.5452903542906716, 2.107162562149909, 1.3201833767980786, 0.8848509809525782, 0.5741159069264025, 1.4691008815935034, 1.6632891780139212]\n",
      "9\n",
      "0.0176481487511\n",
      "[1.3534084587141593, 0.4696306547635481, 0.17504376593290727, 2.29321855162382, 1.7927571603864463, 0.8659714205261616, 0.8345091486325713, 3.6095628607269137, 3.7326705730129213]\n",
      "9\n",
      "-0.124832845348\n",
      "[1.5737544770252798, 0.9681533180067085, 0.5692915778050552, 2.0749862907701546, 1.2702999850267873, 0.8902106733408972, 0.5471075911025713, 1.3432301638041857, 1.5849311753888897]\n",
      "9\n",
      "0.027807331858\n",
      "[1.3536452970521988, 0.45306262840374606, 0.1648123460022374, 2.3214696969476676, 1.8135323857387637, 0.8290893594864576, 0.8517703760492394, 3.7356764290037137, 3.882979404227983]\n",
      "9\n",
      "-0.129777429465\n",
      "[1.5861271727572857, 0.9857141415344859, 0.5926685669210879, 2.0349328187089157, 1.2187416156415978, 0.8970128377287461, 0.5165658149059134, 1.22254723940279, 1.521634433421382]\n",
      "9\n",
      "0.0385326339716\n",
      "[1.356659318385604, 0.43825551146304914, 0.15559963573731256, 2.3536013435643826, 1.8330272841384854, 0.7861581142163834, 0.8702588543754656, 3.8639024439401446, 4.041047696382494]\n",
      "9\n",
      "-0.134439674339\n",
      "[1.59665657424948, 1.0016136689370365, 0.6153808253855301, 1.9873935198986747, 1.1664193501823532, 0.9050764582334702, 0.4839468889331838, 1.1186278073855145, 1.464537903655334]\n",
      "9\n",
      "0.0499093517562\n",
      "[1.362665665526831, 0.42514939061106527, 0.14732802084357016, 2.389960276709114, 1.8505165798022958, 0.7371634124417416, 0.8901151456525166, 3.993813968346475, 4.208291239765618]\n",
      "9\n",
      "-0.138943745116\n",
      "[1.6060947951308375, 1.0162757205038464, 0.6376931471070466, 1.9327326318492966, 1.113439536986069, 0.9144537718519138, 0.44901673640811557, 1.0258302214546666, 1.4113480537361958]\n",
      "9\n",
      "0.0620126014679\n",
      "[1.371906693850354, 0.41369329914115466, 0.13992942804787734, 2.4295285882072757, 1.8652426240986473, 0.6824298093624542, 0.9109937620025772, 4.124097639862954, 4.386127949390112]\n",
      "9\n",
      "-0.143187221423\n",
      "[1.6210216761969531, 1.0327424623699133, 0.6548263886528147, 1.8818631756830961, 1.0704692144635994, 0.9210527838703665, 0.4151132067601539, 0.9475908613680075, 1.357085889580144]\n",
      "9\n",
      "0.0711520253157\n",
      "[1.3683225556210583, 0.3992442710866342, 0.13197977932377125, 2.4614693266100707, 1.8851724165995167, 0.6439404045312169, 0.929456280160497, 4.267645830747354, 4.5216111188946675]\n",
      "9\n",
      "-0.147387520149\n",
      "[1.6366477998125182, 1.0490069220283063, 0.6702335757828165, 1.8258382869146748, 1.0286061457776685, 0.9270920495743573, 0.40822652064870957, 0.8820103523430609, 1.3035625325727893]\n",
      "9\n",
      "0.0785878731487\n",
      "[1.3585068893522392, 0.38393539311272845, 0.12414946834383474, 2.4909560944243414, 1.9057596735188866, 0.6136294027309552, 0.9471762101395093, 4.41872457252624, 4.6327391487669525]\n",
      "9\n",
      "-0.15168687122\n",
      "[1.6557264224451684, 1.0671342511355522, 0.6865474515705401, 1.763582797852619, 0.9864066693402023, 0.9352716196317825, 0.3394604061541815, 0.8060513677602156, 1.2480675105710057]\n",
      "9\n",
      "0.0861172078191\n",
      "[1.3498545694147626, 0.3697887119318487, 0.11699129896364292, 2.525782927442882, 1.9271148939539866, 0.5784473537764835, 0.9669360178770892, 4.581071534155121, 4.744065870447561]\n",
      "9\n",
      "-0.156087684796\n",
      "[1.6748944855062855, 1.0849887301776637, 0.702415282450191, 1.692160569043612, 0.9422538225458336, 0.9436194818343983, 0.3005219333757195, 0.7403443761019258, 1.1925727842742497]\n",
      "9\n",
      "0.0937911939204\n",
      "[1.3426878934613131, 0.3568547046973122, 0.11047900773839094, 2.5666259942356966, 1.949400221023453, 0.5376639691316927, 0.9890601125335021, 4.756898429171855, 4.856152410843616]\n",
      "9\n",
      "-0.160591228884\n",
      "[1.6888456165054893, 1.0991007938246113, 0.7154229212619255, 1.6132074509217504, 0.8942544032837033, 0.9482898940055091, 0.4403558975478644, 0.7159033755123907, 1.1393024214505632]\n",
      "9\n",
      "0.101717133636\n",
      "[1.3366800343450367, 0.3449317796796346, 0.1045143586350721, 2.6138827879298727, 1.9729191332682832, 0.49082513161857944, 1.013775655790153, 4.948981642038522, 4.970671192065729]\n",
      "9\n",
      "-0.164607104563\n",
      "[1.687775304057247, 1.10319423946649, 0.7221146882291304, 1.6512512561752934, 0.8601824955993442, 0.9484018014957167, 0.6016519058145268, 0.7065500806383993, 1.0813838641206734]\n",
      "9\n",
      "0.10996816159\n",
      "[1.3326342896823227, 0.3341622414423239, 0.09910175143340146, 2.6687997703875252, 1.9978216718407087, 0.43661008990632644, 1.0416888941756244, 5.160541981569412, 5.088288732900568]\n",
      "9\n",
      "-0.168555093751\n",
      "[1.6867975099616999, 1.1069580523114053, 0.7281157435806346, 1.7439985973618624, 0.8322606582320327, 0.9491009039736502, 0.6370108301678962, 0.6761236499547156, 1.0162956300221533]\n",
      "9\n",
      "0.118680394567\n",
      "[1.3305580322283561, 0.32445626374662095, 0.09417955571191701, 2.732197226206036, 2.0246683057033383, 0.3738685421914361, 1.0730578699448692, 5.396005754223156, 5.210888079108398]\n",
      "9\n",
      "-0.172480591487\n",
      "[1.6819039467550272, 1.107813789160819, 0.7319601207000146, 1.8768226749873134, 0.8068078796263181, 0.9480815280503605, 0.6871385043002985, 0.6518966472015996, 0.9475255302355423]\n",
      "9\n",
      "0.12696630928\n",
      "[1.329497017547048, 0.3155751850101431, 0.0898022080209916, 2.7098710155715713, 2.0359223484783233, 0.33450418590190184, 1.074107073715494, 5.591279259647285, 5.340898126533803]\n",
      "9\n",
      "-0.176446651065\n",
      "[1.6744474555518023, 1.10664078647586, 0.7341387213510232, 2.0396526532833748, 0.7823270353960653, 0.9461592949003225, 0.748477641531325, 0.6315063351026076, 0.8752022273579421]\n",
      "9\n",
      "0.134687288956\n",
      "[1.3299895118403122, 0.30759590700012457, 0.08597775541080128, 2.587898335273168, 2.0302649497972287, 0.32231741490916377, 1.039318354129482, 5.738580934469193, 5.477968990917816]\n",
      "9\n",
      "-0.179497780499\n",
      "[1.6609004667202771, 1.101166165960311, 0.7348184316674486, 1.3096940597761055, 0.6570502486559749, 1.140785099639038, 0.48223371435622614, 0.4903596607278556, 0.9534094483502472]\n",
      "9\n",
      "0.142763711598\n",
      "[1.3328301193836898, 0.3005956055225935, 0.08257925738780462, 2.4381575773150233, 2.0222386218838087, 0.3109434767768976, 0.9948216371428139, 5.895060940096357, 5.623723796459671]\n",
      "9\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-0.18148823526\n",
      "[1.6924473036207957, 1.1252140240923822, 0.7516190736774826, 2.0833559167782676, 0.7273340287719882, 0.9376143493627768, 0.7680398848601382, 0.5722048573714507, 0.7992729990716816]\n",
      "9\n",
      "0.151334505007\n",
      "[1.3384021563876323, 0.2946654167606918, 0.07960855495658965, 2.2544312106290345, 2.0116060172991634, 0.300353687440377, 0.9394063322303611, 6.063878336540817, 5.7810102050117225]\n",
      "9\n",
      "-0.183413594643\n",
      "[1.7065684019520835, 1.1376074869530577, 0.7621010074975992, 2.0844894950701756, 0.7110590873694905, 0.9236724327473852, 0.7700976500303707, 0.5503581768731123, 0.7682208991160812]\n",
      "9\n",
      "0.160590904328\n",
      "[1.3473002652493018, 0.28975800110445243, 0.07703119735490278, 2.028799187100251, 1.9986458173476425, 0.2904566937851251, 0.8696900008612015, 6.249273365405441, 5.953483168134046]\n",
      "9\n",
      "-0.185253123867\n",
      "[1.720514880516723, 1.1497205619962017, 0.7723595451139255, 2.058519392168279, 0.6930911210624323, 0.9151972582296519, 0.7620433133287728, 0.5265745351859892, 0.7422748083589723]\n"
     ]
    },
    {
     "data": {
      "application/javascript": [
       "$(document).ready(\n",
       "    function() {\n",
       "        function appendUniqueDiv(){\n",
       "            // append a div with our uuid so we can check that it's already\n",
       "            // been sent and avoid duplicates on page reload\n",
       "            var notifiedDiv = document.createElement(\"div\")\n",
       "            notifiedDiv.id = \"93d178f5-57ab-4915-b291-8f8e01dcf4ae\"\n",
       "            element.append(notifiedDiv)\n",
       "        }\n",
       "\n",
       "        // only send notifications if the pageload is complete; this will\n",
       "        // help stop extra notifications when a saved notebook is loaded,\n",
       "        // which during testing gives us state \"interactive\", not \"complete\"\n",
       "        if (document.readyState === 'complete') {\n",
       "            // check for the div that signifies that the notification\n",
       "            // was already sent\n",
       "            if (document.getElementById(\"93d178f5-57ab-4915-b291-8f8e01dcf4ae\") === null) {\n",
       "                var notificationPayload = {\"body\": \"Cell execution has finished!\", \"requireInteraction\": false, \"icon\": \"/static/base/images/favicon.ico\"};\n",
       "                if (Notification.permission !== 'denied') {\n",
       "                    if (Notification.permission !== 'granted') { \n",
       "                        Notification.requestPermission(function (permission) {\n",
       "                            if(!('permission' in Notification)) {\n",
       "                                Notification.permission = permission\n",
       "                            }\n",
       "                        })\n",
       "                    }\n",
       "                    if (Notification.permission === 'granted') {\n",
       "                    var notification = new Notification(\"Jupyter Notebook\", notificationPayload)\n",
       "                    appendUniqueDiv()\n",
       "                    notification.onclick = function () {\n",
       "                        window.focus();\n",
       "                        this.close();\n",
       "                        };\n",
       "                    } \n",
       "                }     \n",
       "            }\n",
       "        }\n",
       "    }\n",
       ")\n"
      ],
      "text/plain": [
       "<IPython.core.display.Javascript object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%%notify\n",
    "tight = True; quiet = True; sense_min = False\n",
    "# fix parameters\n",
    "ngams = 25\n",
    "logGams_full = np.linspace(0.1, 1.7, ngams)\n",
    "phi = R_u0_vec\n",
    "nmus = 5\n",
    "# set evaluation policy\n",
    "PI_E = pi_opt_s_\n",
    "\n",
    "\n",
    "\n",
    "min_bnds = [[None] * ngams for m_ in range(nmus)];\n",
    "max_bnds = [[None] * ngams for m_ in range(nmus)];\n",
    "gamma = 1\n",
    "mus = np.linspace(0.3,0.95,nmus)\n",
    "\n",
    "print nA, nS\n",
    "for m_ in range(nmus): \n",
    "    p_e_su = PI_E*mus[m_] + uniform_pi*(1-mus[m_])\n",
    "    p_e_s = reshape_byxrow(p_e_su.T,nU).T / nU \n",
    "    for ind,logGam in enumerate(logGams_full): \n",
    "        sense_min = False\n",
    "        [a_bnd, b_bnd] = get_bnds_as( p_a1_s, logGam )\n",
    "        [objVal, w_, m] = primal_opt_outer_L1_test_function_joint_distn(gamma, phi, a_bnd,b_bnd, joint_s_a_sprime_agg, p_infty_b_s, p_e_s, nSmarg, nA, tight, sense_min, quiet)\n",
    "        print objVal\n",
    "        print w_\n",
    "        min_bnds[m_][ind] = objVal#; w_min_bnds[ind] = w_; \n",
    "        sense_min = True\n",
    "        [objVal, w_, m] = primal_opt_outer_L1_test_function_joint_distn(gamma, phi, a_bnd,b_bnd, joint_s_a_sprime_agg, p_infty_b_s, p_e_s, nSmarg, nA, tight, sense_min, quiet)\n",
    "        print objVal\n",
    "        max_bnds[m_][ind] = objVal#; w_max_bnds[ind] = w_; \n",
    "        print w_  \n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Get true evaluation policy values (by simulation) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0.05555556 0.05555556 0.05555556 0.05555556 0.05555556 0.05555556\n",
      " 0.05555556 0.05555556 0.05555556 0.05555556 0.05555556 0.05555556\n",
      " 0.05555556 0.05555556 0.05555556 0.05555556 0.05555556 0.05555556]\n",
      "[0.05555556 0.05555556 0.05555556 0.05555556 0.05555556 0.05555556\n",
      " 0.05555556 0.05555556 0.05555556 0.05555556 0.05555556 0.05555556\n",
      " 0.05555556 0.05555556 0.05555556 0.05555556 0.05555556 0.05555556]\n",
      "[0.05555556 0.05555556 0.05555556 0.05555556 0.05555556 0.05555556\n",
      " 0.05555556 0.05555556 0.05555556 0.05555556 0.05555556 0.05555556\n",
      " 0.05555556 0.05555556 0.05555556 0.05555556 0.05555556 0.05555556]\n",
      "[0.05555556 0.05555556 0.05555556 0.05555556 0.05555556 0.05555556\n",
      " 0.05555556 0.05555556 0.05555556 0.05555556 0.05555556 0.05555556\n",
      " 0.05555556 0.05555556 0.05555556 0.05555556 0.05555556 0.05555556]\n",
      "[0.05555556 0.05555556 0.05555556 0.05555556 0.05555556 0.05555556\n",
      " 0.05555556 0.05555556 0.05555556 0.05555556 0.05555556 0.05555556\n",
      " 0.05555556 0.05555556 0.05555556 0.05555556 0.05555556 0.05555556]\n",
      "[-0.1735063246837658, -0.15669216539173042, -0.13408829558522073, -0.1120293985300735, -0.09350532473376329]\n"
     ]
    }
   ],
   "source": [
    "w_s_normalized_ = [None]* nmus\n",
    "vals = [None] * nmus\n",
    "\n",
    "for m_ in range(nmus): \n",
    "\n",
    "    p_e_su = PI_E*mus[m_] + uniform_pi*(1-mus[m_])\n",
    "    [ stateChangeHist_e, stateHist_e, a_s, s_a_sprime_e, p_infty_e_long, distr_hist_e ] =  simulate_rollouts( \n",
    "        nS, nA, P, p_e_su, state_dist, 20000 )\n",
    "\n",
    "    w_su_oracle_norm = p_infty_b_su/p_infty_e_long\n",
    "\n",
    "    w_s_oracle_norm = reshape_byxrow(w_su_oracle_norm.T,nU).T.flatten()\n",
    "    w_s_oracle_normalized = w_s_oracle_norm / np.dot(w_s_oracle_norm, p_infty_b_s)\n",
    "    w_s_normalized_[m_] = w_s_oracle_normalized\n",
    "    # stationary evaluation occupancy\n",
    "    vals[m_] = np.dot(np.ones(len(phi)), phi*reshape_byxrow(p_infty_e_long.T,nU).T.flatten())\n",
    "\n",
    "\n",
    "print vals\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 288x216 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import pickle\n",
    "plt.figure(figsize=(4.,3))\n",
    "gams___ = np.exp(logGams_full)\n",
    "scenario_title = 'mixture-pi-opt-s-ka-ctrl-var'\n",
    "# load from output\n",
    "# vals_ = pickle.load( open('policy_smarg_-vals.p', 'r') )\n",
    "# vals = vals_['vals']\n",
    "\n",
    "for m_ in range(nmus-1): \n",
    "    plt.plot(np.exp(logGams_full),min_bnds[m_],color=((m_+1)*1.0/(nmus-1), 0.3,0),label=np.round(mus[m_],2)) #if m_%2 ==0 else None ) \n",
    "    plt.plot(np.exp(logGams_full),max_bnds[m_],color=((m_+1)*1.0/(nmus-1), 0.3,0))\n",
    "\n",
    "    plt.axhline(vals[m_], linestyle='--',color=((m_+1)*1.0/(nmus-1), 0.3,0 ))\n",
    "plt.xlabel(r'$\\Gamma$ parameter')\n",
    "plt.legend(framealpha=1)\n",
    "plt.savefig(\"3-3gridworld-\"+scenario_title+\".pdf\",bbox_inches = 'tight')\n",
    "# optional output storage \n",
    "# pickle.dump({'min_bnds':min_bnds, 'max_bnds':max_bnds}, open('bnds-'+scenario_title+'.p','w'))\n",
    "# pickle.dump( {'pib':p_a1_su, 'pie-mix-comp':p_e_su}, open(scenario_title+'-params.p', 'w') )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Figure 6 is generated by changing PI_E to pi_opt_smarg_"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 2",
   "language": "python",
   "name": "python2"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.17"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}