GMM-HMM_clean.ipynb

{
 "cells": [
  {
   "cell_type": "code",
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   "metadata": {
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   "source": [
    "from __future__ import division\n",
    "import numpy as np\n",
    "from numpy.random import choice, normal, multivariate_normal\n",
    "from scipy.cluster.vq import kmeans2\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "import pickle as pkl\n",
    "import glob\n",
    "%matplotlib inline\n",
    "import csv\n",
    "time_step = 0.1\n",
    "def read_data(file_path):\n",
    "    # The read-in data should be a N*W matrix,\n",
    "    # where N is the length of the time sequences,\n",
    "    # W is the number of sensors/data features\n",
    "    i = 0\n",
    "    with open(file_path, 'r') as file:\n",
    "        reader = csv.reader(file, delimiter = ',')\n",
    "        for line in reader:\n",
    "            line = np.array(line, dtype = 'float') # str2float\n",
    "            if i == 0:\n",
    "                data = line\n",
    "            else:\n",
    "                data = np.vstack((data, line))\n",
    "            i += 1\n",
    "    return data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "'''\n",
    "Load the segments where a continuous obs car exists\n",
    "'''\n",
    "data_path = \"drive_segments_9d/*.csv\"\n",
    "files = glob.glob(data_path)\n",
    "all_segs = []\n",
    "for name in files:\n",
    "    data = read_data(name)#[frame_id, x_obs,y_obs,dv,a_obs]\n",
    "    data[:,0] += 1149 # change the \n",
    "    all_segs.append(data)\n",
    "'''\n",
    "load the ego car data\n",
    "'''\n",
    "ego_data_path = \"ego_data_24d.csv\"\n",
    "ego_data = read_data(ego_data_path)\n",
    "ego_lane = ego_data[:,[18,19,15,16,20,21,22,23]]\n",
    "ego_data = ego_data[:,[0,9,17,14,18,19]] # x_dot_ego ,accel_x, psi_T_0, r_rate, left_dist, right_dist\n",
    "'''\n",
    "Load the MRM result\n",
    "'''\n",
    "data_name='MRM_result.pkl'\n",
    "MRM_results = pkl.load(open(data_name, 'rb'))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
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   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
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   "source": [
    "'''\n",
    "match obs car data segments with ego car data\n",
    "'''\n",
    "num_actions = 3\n",
    "data_segments = []\n",
    "for segment in all_segs:\n",
    "    ego_lane_list = []\n",
    "    ego_car_list = []\n",
    "    ego_prob_list = []\n",
    "    obs_prob_list = []\n",
    "    violation_prob_list = []\n",
    "    for i, MRM in enumerate(MRM_results):\n",
    "        if MRM['frame_id'] < 1150: # skip parking lot\n",
    "            continue\n",
    "        if MRM['frame_id']+1 in segment[:,0]:\n",
    "            # read ego car data\n",
    "            ego_lane_data = ego_lane[MRM['frame_id'],:]\n",
    "            ego_car_data = ego_data[MRM['frame_id'],:]\n",
    "            matched_obs_idx = np.where(MRM['obs_id'] == segment[0,1])[0]\n",
    "            ego_action_prob = np.reshape(MRM['ego_probs'], (num_actions,))\n",
    "            obs_action_prob = np.reshape(MRM['obs_probs'][:,matched_obs_idx], (num_actions,))#matched_obs_idx*3:(matched_obs_idx+1)*3\n",
    "            violation_prob = np.reshape(MRM['violation_prob'][:,matched_obs_idx,:], (num_actions, num_actions))\n",
    "\n",
    "            # save to list\n",
    "            ego_lane_list.append(ego_lane_data)\n",
    "            ego_car_list.append(ego_car_data)\n",
    "            ego_prob_list.append(ego_action_prob)\n",
    "            obs_prob_list.append(obs_action_prob)\n",
    "            violation_prob_list.append(violation_prob)\n",
    "    ego_lane_list = np.array(ego_lane_list)\n",
    "    ego_car_list = np.array(ego_car_list)\n",
    "    ego_prob_list = np.array(ego_prob_list)        \n",
    "    obs_prob_list = np.array(obs_prob_list)\n",
    "    violation_prob_list = np.array(violation_prob_list)\n",
    "    \n",
    "    '''\n",
    "    Method 1\n",
    "        Observable states are: dx, dv, obs_angle.\n",
    "        Hidden states are: daccel, angle_rate\n",
    "    '''\n",
    "    dx = np.reshape(segment[:,3], (segment.shape[0],1))\n",
    "    dv = np.reshape(segment[:,5] - ego_car_list[:,0], (segment.shape[0],1))\n",
    "    obs_angle = np.reshape(segment[:,7], (segment.shape[0],1))\n",
    "    daccel = np.reshape(segment[:,6] - ego_car_list[:,1], (segment.shape[0],1))\n",
    "    obs_angle_rate = np.reshape((segment[1:,7] - segment[0:-1,7]), (segment.shape[0]-1,1))/time_step\n",
    "    obs_angle_rate = np.vstack([obs_angle_rate, obs_angle_rate[-1]])\n",
    "    # print(dx.shape)\n",
    "    # print(dv.shape)\n",
    "    # print(obs_angle.shape)\n",
    "    # print(daccel.shape)\n",
    "    # print(obs_angle_rate.shape)\n",
    "    concat_seg = np.hstack([dx,dv,obs_angle,daccel,obs_angle_rate])\n",
    "    print(concat_seg.shape)\n",
    "    # input(\"method 1 is done...\")\n",
    "\n",
    "    \n",
    "#     concat_seg = np.hstack([segment[:,3:7],ego_car_list])\n",
    "    data_segments.append(concat_seg)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "ename": "IndentationError",
     "evalue": "unindent does not match any outer indentation level (<tokenize>, line 114)",
     "output_type": "error",
     "traceback": [
      "\u001b[0;36m  File \u001b[0;32m\"<tokenize>\"\u001b[0;36m, line \u001b[0;32m114\u001b[0m\n\u001b[0;31m    def E_step(self,alpha,beta,segment,log_like_matrix):\u001b[0m\n\u001b[0m    ^\u001b[0m\n\u001b[0;31mIndentationError\u001b[0m\u001b[0;31m:\u001b[0m unindent does not match any outer indentation level\n"
     ]
    }
   ],
   "source": [
    "\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "class GMM_HMM():\n",
    "    def __init__(self,num_seq,data,M=3,K=10,model='Gaussian',kmeans_init=False):\n",
    "        self.K = K # number of hidden states\n",
    "        self.M = M # number of modes of Gaussian mixture model for each state\n",
    "        self.data = data # all segments\n",
    "        self.num_seq = num_seq # number of sequences used to train\n",
    "        self.model = model # observation model, Gaussian or GMM\n",
    "\n",
    "        # initial prior of states\n",
    "        self.pi0 = np.ones(self.K)*1/self.K # first state prior, a (K,) array\n",
    "        #\n",
    "        if num_seq > 1:\n",
    "            self.n, self.d = data[0].shape\n",
    "            len_seq = self.data[0].shape[0] # length of each data sequence\n",
    "            self.ravel_data = self.data[0] # reshape multiple sequences in to a long sequence for GMM only\n",
    "            for i , data in enumerate(self.data):\n",
    "                if i > 0:\n",
    "                    self.ravel_data = np.vstack([self.ravel_data,data])\n",
    "                    len_seq = np.append(len_seq, data.shape[0])\n",
    "        \n",
    "        if kmeans_init:\n",
    "            self.state = kmeans2(self.ravel_data, self.K)[1]\n",
    "        else:\n",
    "            self.state = choice(self.K, self.ravel_data.shape[0])\n",
    "        if self.model == 'Gaussian' or 'GMM':\n",
    "            # compute parameter for each cluster\n",
    "            self.mu = []\n",
    "            self.sigma = []\n",
    "            for k in range(self.K):\n",
    "                idx = np.where(self.state==k)[0] # multi variable\n",
    "                nc = len(idx)\n",
    "                if nc:# multi variable\n",
    "                    cluster = np.reshape(self.ravel_data[idx,:],(nc,self.d))\n",
    "                    self.mu.append(np.mean(cluster,0)) # multi variable\n",
    "                    if nc > 1:\n",
    "                        self.sigma.append(np.cov(cluster,rowvar=False)) # multi variable\n",
    "                    else:\n",
    "                        self.sigma.append(np.eye(self.d))\n",
    "                else:\n",
    "                    cluster = []\n",
    "                    self.mu.append(multivariate_normal(np.zeros(self.d), np.eye(self.d))) # multi variable\n",
    "                    self.sigma.append(np.eye(self.d)) # multi variable\n",
    "        \n",
    "        # transition model \n",
    "        self.N = np.zeros((self.K, self.K))\n",
    "        ctr = 0\n",
    "        for i  in range(num_seq):\n",
    "            self.data[i].shape[0]\n",
    "            ctr += 1\n",
    "            for n in range(1, len_seq[i]):\n",
    "                self.N[self.state[ctr-1], self.state[ctr]] += 1\n",
    "                ctr += 1\n",
    "        self.A = (self.N.T/(np.sum(self.N, axis=1)+1e-7)).T\n",
    "                \n",
    "        if self.model == 'GMM':\n",
    "            self.omega = np.ones(self.K) * 1/self.K\n",
    "            \n",
    "        self.xi_list = []\n",
    "        self.gamma_list = []\n",
    "        self.p_list = []\n",
    "        self.log_like_matrix_list = []\n",
    "        \n",
    "    def train(self,num_iter,converge_thresh):\n",
    "        prevQ = -1e20\n",
    "        i = 0\n",
    "        while i < num_iter:\n",
    "            gamma_list = []\n",
    "            xi_list = []\n",
    "            p_list = []\n",
    "            log_like_matrix_list = [] \n",
    "            for j, segment in enumerate(self.data):\n",
    "                log_like_matrix = self.log_likelihood_matrix(segment)\n",
    "                alpha,beta = self.forward_backward_algorithm(segment,log_like_matrix)\n",
    "                gamma, xi, P = self.E_step(alpha,beta,segment,log_like_matrix)\n",
    "\n",
    "                gamma_list.append(gamma)\n",
    "                xi_list.append(xi)\n",
    "                p_list.append(P)\n",
    "                log_like_matrix_list.append(log_like_matrix)\n",
    "                \n",
    "            Q = self.check_log_likelihood(gamma_list, xi_list, log_like_matrix_list)\n",
    "\n",
    "            self.M_step(gamma_list, xi_list, p_list)\n",
    "            \n",
    "            print ('log-likelihood: ', Q)\n",
    "            if Q < prevQ:\n",
    "                print('warning: the log-likelihood is decreasing')\n",
    "            if abs(Q - prevQ) < converge_thresh:\n",
    "                print('THe log-likelihood converges')\n",
    "                return\n",
    "            prevQ = Q\n",
    "            i += 1\n",
    "            \n",
    "    def forward_backward_algorithm(self, data, log_like_matrix):\n",
    "        # forward\n",
    "        T = data.shape[0]\n",
    "        alpha = np.zeros((T, self.K))\n",
    "        alpha[0, :] = self.pi0*np.exp(log_like_matrix[0,:])#1\n",
    "        for t in range(1, T):\n",
    "            alpha[t,:] = (self.A.T.dot(alpha[t-1,:])) * np.exp(log_like_matrix[t,:])\n",
    "            alpha[t, :] /= np.max(alpha[t, :])\n",
    "        # backward\n",
    "        beta = np.zeros((T, self.K))\n",
    "        beta[-1, :] = 1\n",
    "        for t in range(T - 1, 0, -1):\n",
    "            beta[t-1, :] = self.A.dot(beta[t, :] * np.exp(log_like_matrix[t,:]))\n",
    "            beta[t-1, :] /= np.max(beta[t-1, :])\n",
    "            \n",
    "        return alpha, beta\n",
    "    \n",
    "     def E_step(self,alpha,beta,segment,log_like_matrix):\n",
    "        T = segment.shape[0]\n",
    "        pX = np.reshape(np.sum(alpha*beta,axis=1),(T,1)) \n",
    "        gamma = alpha*beta/pX # n * k matrix\n",
    "        \n",
    "        xi = np.zeros([T-1, self.K, self.K]) # n-1 * k * k matrix\n",
    "        for n in range(1,T):    \n",
    "            xi_num = (np.dot(np.reshape(alpha[n-1,:],(self.K,1)),\n",
    "                             np.reshape(np.exp(log_like_matrix[n,:]) * beta[n,:], (1,self.K))) *\\\n",
    "                                  self.A)\n",
    "            xi_den = np.sum(np.sum(xi_num,axis=1))\n",
    "            xi[n-1,:,:] = xi_num/xi_den\n",
    "        '''\n",
    "        Figure out the difference using MGD and GMM model in E-step\n",
    "        '''\n",
    "        P = self.omega * log_like_matrix / np.reshape(np.sum(self.omega * log_like_matrix, axis=1), (T,1)) # an n*K matrix\n",
    "        return gamma, xi, P"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "num_train = 250\n",
    "train_data = data_segments[0:num_train]\n",
    "test_data = data_segments[num_train:]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "'''\n",
    "Get the test data for GMM-HMM\n",
    "'''\n",
    "from hmmlearn import hmm\n",
    "length = []\n",
    "for data in test_data:\n",
    "    length.append(data.shape[0])\n",
    "X = np.concatenate(test_data)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Model name:  GMMHMM_models_9d/GMMHMM_model_15_5.pkl\n",
      "score: -19060.7117393\n",
      "Model name:  GMMHMM_models_9d/GMMHMM_model_15_2.pkl\n",
      "score: -24722.030459\n",
      "Model name:  GMMHMM_models_9d/GMMHMM_model_10_2.pkl\n",
      "score: -25722.3016441\n",
      "Model name:  GMMHMM_models_9d/GMMHMM_model_5_2.pkl\n",
      "score: -24530.7659329\n",
      "Model name:  GMMHMM_models_9d/GMMHMM_model_10_5.pkl\n",
      "score: -20108.6666323\n",
      "Model name:  GMMHMM_models_9d/GMMHMM_model_5_5.pkl\n",
      "score: -22057.7718923\n",
      "Model name:  GMMHMM_models_9d/GMMHMM_model_5_8.pkl\n",
      "score: -21773.7493232\n",
      "Model name:  GMMHMM_models_9d/GMMHMM_model_10_8.pkl\n",
      "score: -20291.501395\n",
      "Model name:  GMMHMM_models_9d/GMMHMM_model_20_5.pkl\n",
      "score: -18626.7630637\n",
      "Model name:  GMMHMM_models_9d/GMMHMM_model_20_2.pkl\n",
      "score: -23903.7888703\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<function matplotlib.pyplot.show>"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x118eb71d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "'''\n",
    "Read well-trained HMM-GMM models and find the one with best score\n",
    "'''\n",
    "from hmmlearn import hmm\n",
    "from sklearn.externals import joblib\n",
    "import glob\n",
    "import warnings\n",
    "import seaborn as sns\n",
    "\n",
    "def fxn():\n",
    "    warnings.warn(\"deprecated\", DeprecationWarning)\n",
    "    \n",
    "model_path = 'GMMHMM_models_9d/*.pkl'\n",
    "files = glob.glob(model_path)\n",
    "# best_model = []\n",
    "max_score = -1e100\n",
    "with warnings.catch_warnings():\n",
    "    warnings.simplefilter(\"ignore\")\n",
    "    fxn()\n",
    "    for name in files:\n",
    "        gmm_hmm = joblib.load(name)\n",
    "        print(\"Model name: \", name)\n",
    "        print(\"score:\", gmm_hmm.score(X, length))\n",
    "        if gmm_hmm.score(X, length) > max_score:\n",
    "            max_score = gmm_hmm.score(X, length)\n",
    "            best_model = gmm_hmm\n",
    "#     test = data_segments[251]\n",
    "#     z = best_model.predict(test)\n",
    "#     print (\"predicted state: \", z)\n",
    "#     plt.figure(2)\n",
    "#     plt.plot(test)\n",
    "#     test = data_segments[12]\n",
    "#     z = best_model.predict(test)\n",
    "#     print (\"predicted state: \", z)\n",
    "#     plt.figure(3)\n",
    "#     plt.plot(test)\n",
    "plt.figure(1)\n",
    "sns.heatmap(best_model.transmat_,vmin=0, vmax=0.05, cbar=False)\n",
    "plt.show"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def gaussian_prob(x, mu,sigma):\n",
    "    diff = np.reshape((x-mu),(1,len(x)))\n",
    "    log_prob = (-1/2) * np.dot(np.dot(diff, np.linalg.pinv(sigma)), diff.T) - np.log(np.sqrt(np.linalg.det(2*np.pi*sigma)))\n",
    "    return float(np.exp(log_prob))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "predicted state:  [ 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0\n",
      "  0  0  0  0  0  0 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11\n",
      " 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11  9  9  9  9  9  9  9\n",
      "  9  9  9  9  9  9 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16\n",
      " 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 18 18 18 18 18 18 18 18 18\n",
      " 18 18 18 18 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16\n",
      " 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18\n",
      " 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18\n",
      " 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18\n",
      " 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18\n",
      " 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18\n",
      " 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18 16 16 16 16 16 16 16 16\n",
      " 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16\n",
      " 17 17 17 17 17 17 17 17 17 17 17 17 17 17 17 17 17 17 17 17 17 17 17 17 17\n",
      " 17 17 15 15 15 15 15 15 15 15 16 16 16 16 16 16 16 16 16 16 16 16]\n",
      "beta:  [  8.03218288e-01   7.09273668e-50   4.45328285e-04   1.43047539e-08\n",
      "   1.42250699e-26   3.27423657e-05   1.10311433e-02   8.01143575e-18\n",
      "   9.74743851e-02   4.28082400e-53   3.13324078e-63   6.05332938e-14\n",
      "   1.46977339e-02   1.51343725e-20   7.10978772e-02   8.08674716e-43\n",
      "   5.86801818e-12   8.37336791e-04   1.16514150e-03   9.30422723e-09]\n"
     ]
    },
    {
     "data": {
      "image/png": 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naPGXkoT3PORyBq/84iw+b2rstkwqTM4SIzZ8FF/tXuIjJ7E6Ajg8s7ekW9dU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\nqTIQCVCZiRFLu2ioGqQ+MEh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f/OTusW87kP+AePHp/Hj2Rx7fMTZSRwgxd0smvAEcNWug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\nAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11e8560f0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "'''\n",
    "run predict using well-trained GMM-HMM model\n",
    "So far the hiddent variable is data[:,5] (accel) and data[:,7] (yaw rate)\n",
    "Method 1:\n",
    "    Observable data: {dx, dv, obs_angle}\n",
    "    Predict data: {daccel, obs_angle_rate}\n",
    "Method 2:\n",
    "    Observable data: {dx, dy, dv, v_ego, yaw_angle, velocity, d_l, d_r}\n",
    "    Predict data: {acceleration, yaw_rate}\n",
    "'''\n",
    "# method 1\n",
    "observable_col = [0,1,2]\n",
    "hidden_col = [3,4]\n",
    "# # method 2\n",
    "# observable_col = [0,1,2,3,4,6,8,9]\n",
    "# hidden_col = [5,7]\n",
    "\n",
    "test = data_segments[251]\n",
    "test_obs = test[:,observable_col] # observable variable\n",
    "test_hidden = test[:,hidden_col] # hidden variable\n",
    "with warnings.catch_warnings():\n",
    "    warnings.simplefilter(\"ignore\")\n",
    "    fxn()\n",
    "    # use build-in predictor to predict\n",
    "    z = best_model.predict(test)\n",
    "    print (\"predicted state: \", z)\n",
    "    plt.figure(1)\n",
    "    plt.plot(test)\n",
    "    \n",
    "    A = best_model.transmat_\n",
    "     \n",
    "    '''\n",
    "    init beta\n",
    "    '''\n",
    "    x0 = test_obs[0,:]\n",
    "    num = []\n",
    "    den = 0\n",
    "    for gmm in best_model.gmms_:\n",
    "        omega = gmm.weights_\n",
    "        prob = 0\n",
    "        for m in range(gmm.means_.shape[0]):\n",
    "            mu = gmm.means_[m,observable_col]\n",
    "            sigma = np.diag(gmm.covars_[m, observable_col])\n",
    "            prob += omega[m] * gaussian_prob(x0, mu, sigma)\n",
    "        num.append(prob)\n",
    "    beta = np.array(num)/np.sum(num) # beta is (k,)\n",
    "    \n",
    "    print (\"beta: \", beta)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(20, 2)\n",
      "(20, 2)\n"
     ]
    }
   ],
   "source": [
    "    # compute the mean of mu and sigma for each state\n",
    "    mu_mean_list = []\n",
    "    sigma_mean_list = []\n",
    "    for gmm in best_model.gmms_:\n",
    "        mu_mean_list.append(np.mean(gmm.means_,axis=0))\n",
    "        sigma_mean_list.append(np.mean(gmm.covars_, axis=0))\n",
    "    mu_mean_list = np.array(mu_mean_list)[:,hidden_col]\n",
    "    sigma_mean_list = np.array(sigma_mean_list)[:,hidden_col]\n",
    "    print(mu_mean_list.shape)\n",
    "    print(sigma_mean_list.shape)\n",
    "    \n",
    "    n_components = best_model.n_components"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Actual states:  [[ 31.562       -2.79544444  -1.45        -1.00244     -1.6       ]\n",
      " [ 31.062       -2.77766667  -1.61        -1.05149     -1.7       ]\n",
      " [ 30.562       -2.81288889  -1.78        -1.38468     -1.4       ]\n",
      " [ 30.125       -2.82988889  -1.92        -1.32149     -1.6       ]\n",
      " [ 29.75        -2.84711111  -2.08        -1.44149     -1.5       ]\n",
      " [ 29.062       -2.83033333  -2.23        -1.81997     -2.8       ]\n",
      " [ 27.75        -2.93433333  -2.51        -1.90563     -1.        ]\n",
      " [ 27.812       -2.86455556  -2.61        -1.18563     -1.1       ]\n",
      " [ 27.188       -2.76077778  -2.72        -0.583       -1.        ]\n",
      " [ 26.562       -2.708       -2.82        -0.38829     -0.9       ]\n",
      " [ 26.125       -2.77822222  -2.91        -0.92111     -0.9       ]\n",
      " [ 25.688       -2.76022222  -3.          -0.586425    -1.2       ]\n",
      " [ 24.625       -2.76066667  -3.12        -0.99731     -0.3       ]\n",
      " [ 23.812       -2.70788889  -3.15        -0.82563      0.        ]\n",
      " [ 23.125       -2.67388889  -3.15        -0.76563      0.1       ]\n",
      " [ 22.625       -2.62111111  -3.14        -0.4281       0.3       ]\n",
      " [ 22.125       -2.58633333  -3.11        -0.156045     0.4       ]\n",
      " [ 21.625       -2.55255556  -3.07        -0.41715      1.        ]\n",
      " [ 20.438       -2.62177778  -2.97        -0.79905      0.6       ]\n",
      " [ 19.812       -2.6215      -2.91        -1.25487      0.5       ]\n",
      " [ 19.125       -2.55204444  -2.86        -1.31487      0.5       ]\n",
      " [ 18.562       -2.49996667  -2.81        -1.23262      1.2       ]\n",
      " [ 17.438       -2.55208889  -2.69        -1.71114      0.4       ]\n",
      " [ 16.875       -2.51731111  -2.65        -1.72301      0.4       ]\n",
      " [ 16.312       -2.43053333  -2.61        -1.48301      0.3       ]\n",
      " [ 15.875       -2.37845556  -2.58        -1.61487      0.8       ]\n",
      " [ 14.875       -2.34377778  -2.5         -1.384905     0.2       ]\n",
      " [ 14.375       -2.2569      -2.48        -0.68076      0.3       ]\n",
      " [ 13.812       -2.11802222  -2.45        -0.41225      0.4       ]\n",
      " [ 13.375       -2.04856667  -2.41        -0.12719      0.5       ]\n",
      " [ 12.5         -2.04858889  -2.36        -0.8911       0.3       ]\n",
      " [ 12.062       -1.94441111  -2.33        -0.94107      0.2       ]\n",
      " [ 11.625       -1.89233333  -2.31        -0.516045     0.4       ]\n",
      " [ 10.688       -1.87495556  -2.27        -0.3114       0.3       ]\n",
      " [ 10.312       -1.78817778  -2.24        -0.27741      0.1       ]\n",
      " [  9.875       -1.68402222  -2.23        -0.84297      0.3       ]\n",
      " [  9.4375      -1.56254444  -2.2         -0.64712      0.2       ]\n",
      " [  8.6875      -1.45836667  -2.18        -0.24263      0.2       ]\n",
      " [  8.375       -1.38888889  -2.16        -0.26772     -0.3       ]\n",
      " [  8.          -1.26733333  -2.19        -0.10905     -0.5       ]\n",
      " [  7.4375      -1.18055556  -2.24        -0.19244     -0.1       ]\n",
      " [  7.1875      -1.07637778  -2.25        -0.22073     -1.3       ]\n",
      " [  6.75        -0.8854      -2.38         0.09399      0.3       ]\n",
      " [  6.4375      -0.79862222  -2.35         0.17247     -0.6       ]\n",
      " [  6.25        -0.67704444  -2.41         0.29361     -0.6       ]\n",
      " [  6.          -0.59026667  -2.47         1.26582      0.4       ]\n",
      " [  5.9375      -0.48606667  -2.43         1.57813      0.2       ]\n",
      " [  5.625       -0.36456667  -2.41         1.90174      0.8       ]\n",
      " [  5.5         -0.32986667  -2.33         1.53889      1.        ]\n",
      " [  5.4375      -0.31246667  -2.23         1.625475     2.5       ]]\n",
      "predicted states:  [[  3.15620000e+01  -2.79544444e+00  -1.45000000e+00  -1.00244000e+00\n",
      "   -1.60000000e+00]\n",
      " [  3.12774434e+01  -2.89568844e+00  -1.61000000e+00  -1.00244000e+00\n",
      "    2.79352280e+00]\n",
      " [  3.09828623e+01  -2.99593244e+00  -1.33064772e+00  -1.00244000e+00\n",
      "    2.43307746e+00]\n",
      " [  3.06782569e+01  -3.09617644e+00  -1.08733997e+00  -1.00244000e+00\n",
      "    1.41074972e+00]\n",
      " [  3.03636270e+01  -3.19642044e+00  -9.46265003e-01  -1.00244000e+00\n",
      "    6.68192187e-02]\n",
      " [  3.00389728e+01  -3.29666444e+00  -9.39583081e-01  -1.00244000e+00\n",
      "   -8.42162075e-01]\n",
      " [  2.97042941e+01  -3.39690844e+00  -1.02379929e+00  -1.00244000e+00\n",
      "   -1.27421875e+00]\n",
      " [  2.93595911e+01  -3.49715244e+00  -1.15122116e+00  -1.00244000e+00\n",
      "   -1.43137142e+00]\n",
      " [  2.90048636e+01  -3.59739644e+00  -1.29435830e+00  -1.00244000e+00\n",
      "   -1.41438191e+00]\n",
      " [  2.86401118e+01  -3.69764044e+00  -1.43579650e+00  -1.00244000e+00\n",
      "   -1.20892998e+00]\n",
      " [  2.82653356e+01  -3.79788444e+00  -1.55668949e+00  -1.00244000e+00\n",
      "   -6.75266386e-01]\n",
      " [  2.78805349e+01  -3.89812844e+00  -1.62421613e+00  -1.00244000e+00\n",
      "    4.12466376e-01]\n",
      " [  2.74857099e+01  -3.99837244e+00  -1.58296950e+00  -1.00244000e+00\n",
      "    1.82436352e+00]\n",
      " [  2.70808604e+01  -4.09861644e+00  -1.40053314e+00  -1.00244000e+00\n",
      "    2.65536702e+00]\n",
      " [  2.66659866e+01  -4.19886044e+00  -1.13499644e+00  -1.00244000e+00\n",
      "    2.86741167e+00]\n",
      " [  2.62410883e+01  -4.29910444e+00  -8.48255274e-01  -1.00244000e+00\n",
      "    2.89651674e+00]\n",
      " [  2.58061657e+01  -4.39934844e+00  -5.58603600e-01  -1.00244000e+00\n",
      "    2.89920278e+00]\n",
      " [  2.53612186e+01  -4.49959244e+00  -2.68683322e-01  -1.00244000e+00\n",
      "    2.89945578e+00]\n",
      " [  2.49062472e+01  -4.59983644e+00   2.12622557e-02  -1.00244000e+00\n",
      "    2.89941830e+00]\n",
      " [  2.44412514e+01  -4.70008044e+00   3.11204086e-01  -1.00244000e+00\n",
      "    2.89920816e+00]\n",
      " [  2.39662311e+01  -4.80032444e+00   6.01124902e-01  -1.00244000e+00\n",
      "    2.89880845e+00]\n",
      " [  2.34811865e+01  -4.90056844e+00   8.91005747e-01  -1.00244000e+00\n",
      "    2.89817335e+00]\n",
      " [  2.29861174e+01  -5.00081244e+00   1.18082308e+00  -1.00244000e+00\n",
      "    2.89722344e+00]\n",
      " [  2.24810240e+01  -5.10105644e+00   1.47054543e+00  -1.00244000e+00\n",
      "    2.89582755e+00]\n",
      " [  2.19659061e+01  -5.20130044e+00   1.76012818e+00  -1.00244000e+00\n",
      "    2.89376817e+00]\n",
      " [  2.14407639e+01  -5.30154444e+00   2.04950500e+00  -1.00244000e+00\n",
      "    2.89067574e+00]\n",
      " [  2.09055972e+01  -5.40178844e+00   2.33857257e+00  -1.00244000e+00\n",
      "    2.88590252e+00]\n",
      " [  2.03604062e+01  -5.50203244e+00   2.62716282e+00  -1.00244000e+00\n",
      "    2.87827494e+00]\n",
      " [  1.98051908e+01  -5.60227644e+00   2.91499032e+00  -1.00244000e+00\n",
      "    2.86560179e+00]\n",
      " [  1.92399509e+01  -5.70252044e+00   3.20155050e+00  -1.00244000e+00\n",
      "    2.84370217e+00]\n",
      " [  1.86646867e+01  -5.80276444e+00   3.48592072e+00  -1.00244000e+00\n",
      "    2.80456548e+00]\n",
      " [  1.80793980e+01  -5.90300844e+00   3.76637726e+00  -1.00244000e+00\n",
      "    2.73329823e+00]\n",
      " [  1.74840850e+01  -6.00325244e+00   4.03970709e+00  -1.00244000e+00\n",
      "    2.60481834e+00]\n",
      " [  1.68787475e+01  -6.10349644e+00   4.30018892e+00  -1.00244000e+00\n",
      "    2.38636038e+00]\n",
      " [  1.62633857e+01  -6.20374044e+00   4.53882496e+00  -1.00244000e+00\n",
      "    2.05922697e+00]\n",
      " [  1.56379994e+01  -6.30398444e+00   4.74474766e+00  -1.00244000e+00\n",
      "    1.65745796e+00]\n",
      " [  1.50025888e+01  -6.40422844e+00   4.91049345e+00  -1.00244000e+00\n",
      "    1.26751352e+00]\n",
      " [  1.43571538e+01  -6.50447244e+00   5.03724480e+00  -1.00244000e+00\n",
      "    9.62282160e-01]\n",
      " [  1.37016943e+01  -6.60471644e+00   5.13347302e+00  -1.00244000e+00\n",
      "    7.58903432e-01]\n",
      " [  1.30362105e+01  -6.70496044e+00   5.20936336e+00  -1.00244000e+00\n",
      "    6.39947097e-01]\n",
      " [  1.23607022e+01  -6.80520444e+00   5.27335807e+00  -1.00244000e+00\n",
      "    5.84016887e-01]\n",
      " [  1.16751696e+01  -6.90544844e+00   5.33175976e+00  -1.00244000e+00\n",
      "    5.78704085e-01]\n",
      " [  1.09796125e+01  -7.00569244e+00   5.38963017e+00  -1.00244000e+00\n",
      "    6.23202297e-01]\n",
      " [  1.02740311e+01  -7.10593644e+00   5.45195040e+00  -1.00244000e+00\n",
      "    7.28846028e-01]\n",
      " [  9.55842524e+00  -7.20618044e+00   5.52483500e+00  -1.00244000e+00\n",
      "    9.18484271e-01]\n",
      " [  8.83279500e+00  -7.30642444e+00   5.61668343e+00  -1.00244000e+00\n",
      "    1.21722618e+00]\n",
      " [  8.09714036e+00  -7.40666844e+00   5.73840605e+00  -1.00244000e+00\n",
      "    1.62147398e+00]\n",
      " [  7.35146131e+00  -7.50691244e+00   5.90055345e+00  -1.00244000e+00\n",
      "    2.06090123e+00]\n",
      " [  6.59575787e+00  -7.60715644e+00   6.10664357e+00  -1.00244000e+00\n",
      "    2.42542564e+00]\n",
      " [  5.83003002e+00  -7.70740044e+00   6.34918613e+00  -1.00244000e+00\n",
      "    2.65543298e+00]]\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<function matplotlib.pyplot.show>"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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czaLe48NtV89ly8EGNmyv4v2d1by/s5pZeQlcuCgLOcsxYt0p463eY0XUe/Bl\nBjKc5L1BluXvKYqyHTgP2DWMMgRhwtDrNCybncbSWansK23hrW1VffOH56baWbM0l5lTEkSfuDCm\nhpO8bwb+IMtyEGgAvj2yIQnC+KSRJOYWOJlb4KS0tpO3tlWx50gzv3++iLz0GC7/whSm5cRHO0xh\nkhhSn/fpam52n9ZKxG7V5DKR6l3T5GH95nL29J7UMy07jsu+MIX8jNhTLmsi1XskiXoPusyI9nkL\ngtArI8nG966YxdF6F+s3l3OgvI1DlbuYlZfABQszKcyOE90pwqgQyVsQRkBuagw/umoOR6o7WP9h\neV+feHKcmWVz0jh3ZioxYg5xYQSJ5C0II2hqpoOffH0upbWdbNpbx47DTTz/QRnrPyxn3lQny+ek\nUziCI1SEyUskb0EYYZIkUZDhoCDDwdXnFbDlYAOb9tax/VAT2w81MS07ju+smS6u5iOcFpG8BWEU\n2cx6zl+Qyer5GZTWdvL6J5XsL2/ll0/t5HtXzCQrWZygLAyPmFVQEMbAsdb49786izVLc2l1dXP/\nP3axtbgh2qEJE5RI3oIwhjSSxJqluXzviploNBJ/fbWYde+XEo5Eoh2aMMGI5C0IUTC3wMld1y0g\nOd7CW9ur+N26fbi8gWiHJUwgInkLQpSkJli565sLmJ2XQHFFO9954F3+9V4J9a3ek79YmPTEAUtB\niCKLScf3rpzFW9uqeHdnDW/vqObtHdXIvVe1ny8nodeJNpZwIpG8BSHKNJLEl87O5usXncXbn5Sz\naW8dhyrbUao7sL1bwrkzU1g+J52UeEu0QxXGEZG8BWGc0Os0LJqWzKJpyTS2dbFpXx0fFdWzYXs1\nG7ZXU5jlYPmcdOZNdYrWuCCStyCMR8nxFq5amc9lX5jCnpJmNu6p5XBVB4erOrCZ9SydmcqyOWmi\nNT6JieQtCOPYZ1vjDW1dfLi3jo/21/PW9io2bK/iihV5XLQ4S5xuPwmJ5C0IE0RKvIWrVuVz2bIp\n7DrSM2fKCxvLaGrv4htflNFpRVfKZCK2tiBMMHqdhrPPSuHOby4gK9nGh/vq+f3z++jqDkU7NGEM\nieQtCBNUnN3Iz66Zx5z8RIor2vmvZ3fR0umLdljCGBHJWxAmMJNBx62Xz2T1ggxqW7zc98wujta7\noh2WMAZE8haECU6jkfj66ql8fXUB7q4AD/7vbl7cVEZNk4exuMyhEB3igKUgnCFWL8jE6TDz19eK\neWNLJW/+svXyAAAgAElEQVRsqSQt0cqiaUksnpZMshhWeEYZUvKWZXkx8KCiKCtkWc4HngJU4ABw\ni6IoYko0QRgHZucn8vCt51JU1sr24kb2lbXy8uajvLz5KNkpdpZMT+GcGSnYzPpohyqcppMmb1mW\nfwJcCxybLedh4E5FUTbKsvwXYA2wfvRCFAThVBj1WhYWJrGwMAmfP8TuI81sP9REcUUbzzWU8MKm\nMhbISayYm0Z+eqwYIz5BDaXlXQZcDvyj9//5wKbe+28CX0Qkb0EYl8xGHefOTOXcmam4ugJ8sr+B\nTXtr2XKwgS0HG0hPtLJsThpLZqRgNYnW+EQiDeWAhizLOcC/FEU5W5blOkVR0nofXwXcoCjKNwZ7\nfSgUVnU67UjEKwjCaVJVlf1lLby1pZIt++sIhVUMOg1L56Rz4dk5FObEidb4+DHghhjOAcvP9m/b\ngY6TvaC9vWsYq/mU02mnudl9WmVMRKLek8tY1js11sT1F8pcsSyXj/fXs2lvHe/vrOb9ndWkO60s\nn93TGreMQWtcbO/BlxnIcJL3HlmWVyiKshG4CPhgGGUIgjAOxFgMXLQ4mwsWZaFUtrNxbx27jzTz\nz3dLeGFjGYvPSuaKFXnEiCvdjzvDSd7/D3hclmUDcAh4YWRDEgRhrGkkiWk58UzLicflDfDR/no2\n7a1lc1E9+0pbuO6iQuYWOKMdpvAZQ+rzPl3Nze7TWonYrZpcRL3Hh4iq8s6Oal7cVE4oHGHprFTW\nnleA2Tiyp4eMt3qPlSF2mwzY5y3OsBQEoV8aSeKCRVnc862eCbA+Kqrn7ie3c7iyPdqhCYjkLQjC\nSaQ7bdz5zQVcsiSHdref/35uD8+9WyImwYoycXq8IAgnpdNquGzZFGblJ/DEa8W8s7Oad3ZWk5Zo\nZeaUeGZOSWBqpkPMKT6GRPIWBGHI8tJi+cUNi/h4fz1FZa0crmzvu8am0aDlrOw45k11MrfAicUk\n0stoEu+uIAinxKjXsmpeBqvmZRAIhjlS3UFRWSv7y1vZU9LCnpIWdFqFWXkJLJqWxOy8RIwGcZLe\nSBPJWxCEYTPotcyYksCMKQkANLR1seNQI9sONbH7SDO7jzRj1GuZU5DIslmpFGaLszdHikjegiCM\nmJR4C5ecm8sl5+ZS0+xh+6FGthc3sa24kW3FjRRmObhs2RQKMhzRDnXCE8lbEIRRkeG0keG0cdkX\nplBe5+K1TyooKmvlv57dzYwp8Vz2hSnkpsZEO8wJSyRvQRBGlSRJ5KXH8oOvzqa0ppP1m8s5UN7G\ngfI25hYkcs1F04g1adFqxEiVUyGStyAIYyY/I5bb1s7lUGU76z8s7z3AuRmjQUteWgz56bHkZ8SS\nlxY74mdynmnEuyMIwpiblh1H4TfmceBoGwcrO9hf2kxxRTvFFT1nb0pAVrKdJTNSWDJTzDXeH5G8\nBUGICkmSmDklgVWLc2huduPxBSmt7aSstpOSmp7b597rufLPwsIkls8RV/75LJG8BUEYF2xmPXPy\nE5mTnwiAqyvQN9f4Jwca+ORAQ99c4/PlJOLsxihHHF0ieQuCMC4NNtf4P98tIcNpY1ZeAjOnxJOX\nHjvpTs0XyVsQhHHt83ONbzvUyP6yVg5XdVDT7OH/tlZiNuqYnhNHXnos6U4r6Yk2HDbDGd3FIpK3\nIAgTRozVwPkLMjl/QSb+QJjDVe0Ulbeyv6yVnUozO5XmvmWtJh3piVbSnTaykm3kZzhITbCgOUMS\nukjegiBMSEaDltn5iczOT0RVVZrafVQ1eaht9lDb7KWmxUtJbSdHajr7XmM16chLjyU/PZaCjFgy\nk+yYjdoJ2UIXyVsQhAlPkiSS4y0kx1tYWJjU93ggGKa+tYvyehelNR2U1nZSVNZKUVnrZ14LJoMO\ni1GL2ajDZNRhN+spzI5j1pQEkuMt0ajSSYnkLQjCGcug15KdYic7xc7KuekAdHj8fcMRG9q68PlD\nvX9h2lx+fAEvqgp7Slp4jhKSHGZm5iUwc0oChVkODPrxMUOiSN6CIEwqDpuR+XIS8+Wkfp9XVZV2\nt58DR9soKmuluKKN93bV8N6uGnRaDU6HifgYEwkxRuLtJuJijMTHmLCb9Vh6W+5m4+if7i+StyAI\nwmdIkkR8jIlls9NYNjuNUDhCaU0n+8tbKa5sp6XDR31r10nLMeq1mI1aFhYms3Z1wYjHOezkLcvy\nbsDV++9RRVGuH5mQBEEQxg+dVkNhdhyF2XF9j3UHQrS5/LS5u3tuXd14fSF8gdBx3TA+f4hQJDI6\ncQ3nRbIsmwBJUZQVIxuOIAjC+Gcy6EhL1JGWaI1aDMNtec8GLLIsv91bxh2KomwdubAEQRCEwUiq\nqp7yi2RZngmcDTwBFABvArKiKKH+lg+FwqpONz6O0AqCIEwgAw5AH27L+whQqiiKChyRZbkVSAWq\n+1u4vf3knfuDcTrtNDe7T6uMiUjUe3IR9Z5chlJvp9M+4HPDHctyA/AQgCzLaUAMUD/MsgRBEIRT\nNNyW95PAU7IsfwSowA0DdZkIgiAII29YyVtRlADw9RGORRAEQRiiyTUBriAIwhlCJG9BEIQJSCRv\nQRCECUgkb0EQhAlIJG9BEIQJSCRvQRCECUgkb0EQhAlIJG9BEIRRokZCqGp4VMoWyVsQBGEURMIB\nGo48SVPJM6NSvkjegiAIo6C9dgNBXyMGa/qolC+StyAIwgjzth/E27oHvTkFR+qqUVmHuIalIAjC\nSXS2d1FR2kpDjYvEZBt5hU4c8ZZ+lw35O2irfh1Joycx53IkzeikWZG8BUEQPiccjtBQ00llWSuV\npa10tPn6nitXmtn+4VESnFbyCp1MKUwiLqEnkatqhJbKl1DDfmLTv0y334akCzMaF6MRyVsQBAHw\nevxUl7dRVd5G9dE2Av6eUSI6vYbcgkSy8uNJy3TQWOui7HAT1Ufb2b65gu2bK4h3WrHaDCTEHCQ9\npYb6hiTe2NAJbCU5PYbLr5034vGK5C0IwqQUiag01nZS1ZuwWxo9fc/ZY01MnZ5Cdn4CaVmxx7Wc\nHfEW5Jkp+LuDVJS0Una4meqjbRCqZWZBKb5uM3XNs8nMtWCy6MnJTxyV+EXyFsY9NRLC1bSFcNCD\nI20lGq0p2iEJE1y3L8hbLx6gvqYTAI1WIiMnjqwp8WTlxeOItyBJA14+EgCjSY88M6UnkfvcNJc+\nTiSkIWfWWuRzMka9DiJ5C6dFVVW6XSUEuuoxxxagN6ee9EN/KvyeKlqrXifkbwHA5yohMedyjNbR\n/3IIZyZ3ZzdvrCuivbWL7LwEzpqTSnq2A73h1NKhGgkT7G4m4GvE27aHSMhDbOqqMftsiuQtDJu/\nq46O2nfweyoB6GzYhN7kxBo/C0vcTHSGmGGXHQn76ah7D0/LTgBsiQvRaA24Gj+m8chTONJWYU86\nZ8R+KFQ1QrerFElrxGTLHpEyhfGntcnDG+uK8HoCzF6YwTmr8ob8GYqE/Xhb9+LvqifoayTobwY1\n0ve8yZ5HTPK5oxX6CUTyFk5ZyN9OR937dHUcBMAUU4A1bgZdnYfxdR6ho+49Ourew2TPxRI3E70x\nAa3ehkZnRaM1nLT8juZi6g+9SDjoQmdKJCHzEoy2zJ512XNpqXiZjrp36XYfJSF7DVq9bdh1iUSC\neFv34m7aSijQ3ruOKTjSVmOwpAy7XGH8qa1s562XDhDwh1myKo/ZizKH9DpVDeNp2U1nwyYioS4A\nJI0egzkVgzkZvTkZgzkZgzVjRPc6T0ZSVXXUV9Lc7D6tlTiddpqb3SMVzoQxnuodCQcIB914Wnbh\nbtkBahiDORVH+mpM9txPlwv58HYU423bR8Bbc0I5ksaAVmdFo7ciSSe2HdRIgEBXHUgaYpKXEpu8\n9IRxsuGgl9aqV+h2laLRWYnPvBidMa6fqCW0OgsanQVJ0pxQhrtlB57mHUTCPpC0WONnEw500u0u\nA8AaP4vY1JXoDLFDfp9UVSUS6iIc8hIJegiHvISDHsIhD+Ggl0jIi0Zn+cyXPgWt3gqc2vaORIKE\nA51otObe+o1d0hhpY/E5Lylu5P3XD4MEqy4upOCsZFRVJRx0o9Xb+33/VFXF13mYjrr3CPnbkDQG\nYpKXYHFMR2eMO+EzdaqGUm+n0z7ghh1W8pZlWQP8CZgN+IH/UBSldKDlRfIenrGstxoJ9fXfBX2N\nhIKu45KPGgn0Las1xOJIXYUlbsagSSPob8PXWUI46CbSl8R6biMhL9D/x8LmyMWWcgEGc9LA8aoq\n7qatdNS9B0QGXK6HhEZnQauzodVbkTQGul2lqGoIjdaELXEhdufCvha8z1VGR927BH2NSJIOe9Ji\nbIkLUMOBviQcDnk+l5w/TdYD1WsgGp0NgzmZmLhU/EE9Wr0Nrc7au7fSE1PQ19i3bQK+RkL+1s+s\nR0LTu/yx1+lNieh7fyC0OtsJ20lVI4T8bX1lRiKBntf2rbf3VmuGfraxhAZJMzJjl0/pRyvkw928\nHUvcDPSmhBOeV1WVbl8Qj8uP1+3H4/bT1uzl4J46DEYtF14+g/TsOMJBD01l/yToa0DSGNCbkzCY\nU/pa0aoaprPuffzeakDCljif2JTlfT+0Y1XvwZL3cLtNLgVMiqKcI8vy2cBDwJphliWMAVWN9CZQ\n76cJKOgm2N3U03/X3cKJSacnKeiMcX2Jz2BJw5Ywb0hnjemN8eiTFg8Qz8AJLikp5qQfakmSiEk+\nB5M9G2/bflS1vwTe2wruTaqhQAfB7kag5wcoJukcrPFzTujKMcfkYbLn4m3bT2f9B7gaP8bV+PHg\n8Wj0aHU2DNb03vfK1ruHYet777Q6Gxqdped9/1wy7naX9bX4T0bSGDFaM9AZE4iEu/t+GEP+NoK+\nhhOW1+gs6E3JGMxJRCJBgr4Ggt3NqJHgkNY3QBSYHYXEJC3BOEpzd3xeJBKhvvQVwr4jtNd/QnPn\nEjrcTvy+IN2+EN2+IF3eAOHQiZ8Fq83AxVfNIiHJRsjfTlPps4QC7RitmUTC3QS8tf3uKZpjC3Gk\nrUJvGp3hfqdjuMl7KfAWgKIoW2VZXjByIQkjIeRvx+cuo9tVjt9b3dvS7Z+kMWCwph/Xf6czxKPR\nmU9713DAdY7Qbr7BkobBkjbk5SORIJFQV++u8sB1kyQNtoTZWOLOwtO8Hb+3tq+757hkfOx2CH35\nAF3eACZzHHpTApa4sz6NK+TDbg3S0tR43N5JOOhBJYLBlNS3bbQGx4Dv37HurZ69qIa+Hwe/5yh+\nz9HeymnQm5yfbm9TMhqduXe9XiIhz6d7EyFfv+sJB134Og7h6ziE0ZZNTNISTDH5/bTwe1rCne0+\nIhEVs1mP0azHZNah0WgIdrfgc3uA/o9bBAMhaio7qCpvw9dxgLOmHsHjMWO2dJMUu4mW+jyqq9LQ\n6bQYzTriE63Y7EZsMUasn7lNTLJhMOoI+BppKv1fIiFPT7dc6kokSerd82wi4OtpzIRDXdgS52Oy\nZQ1pu0bDcLtNngBeVBTlzd7/q4ApiqKE+ls+FAqro3F6qPCpSDiIq/VI35+/q6XvOb3JgdEUh85o\nR2+wozfa0Bvs6Ix2zNYkDOb4fhOZqqq0tXipKG3tOU24rJVQKExmbjzZUxLImhJPSnosWq2Y32wg\nXrefo6UtHC3p+eto6yLBaeWya+aRlukY8fWpqorH7cffHSIUChMKRgiFwgT9PoLdTSQmx5OYmolm\nmPNtqKpKXXUnZYcb0ai1GKT9aOltsWriwTAXty+NtuYQbS0eWpu9+LuPTwt6fZC01CYy05uJjXGh\nqhJHaxfj86ei1WrQ6jRotRq6fUGqytsIhyMYjX6Wn7sLrRZ0sV/HZo/gaVpPJOQlLnUBOdOvOGmd\nPO1HKd3zN8KhbjLkr5Cc/YVhvQf9iUQihNQwkUiYsBohrEb67seaYtANv4tpxPu8Hwa2Koqyrvf/\nGkVRBhzcKPq8PxWJqHS2+2hr9tDa5MXd2U12fgJTZCcazfHbaaj1DvnbaS7/N8HuJqCnJW2y52Ky\n52GKmYLeGD/k+Lo8firKWqmt6KCuqoMu76d93RarAa1Wwu3y9z2m02tISY8lLcsx6GQ9p2Iib+9u\nX5D66g7qqjqpqWynrfnTPR6DUUtCko366k40GokFS3OYe3ZW33Y/1XqHwxE6WrtoafLQ2uihpclD\nS6PnhGT5WRqNxLQ5qcw/Jxur3TjkdXncfo4caODIgUbaW7uOe85u9zAlp4a0lCY0vb/jXT4jbo+N\nQNABmoSePmW9C6OmFIuxHklSUVWJ9o44YmM6UIFtO2bR0Xn88NLEJBtZeXGkJX6EGqgkLvNL2BN7\ndvRDgU6ay9cR9NVjtGaSmHvVgH3Svs4jtBx9AVWNkJC9Bmv8zAHr2h3qpjPgpr27gw5/J+3dnXT4\nO2j3d9LpdxEIBwhEgoQiIYKRIMFIiEi/3XY98mJz+dH8m094PFp93h8DlwDrevu89w+znEmhvqaT\nw0X1tDZ5aGvpOqFP7sjBRhwJFuYvySZ/mhONpv+WbEdbF5VlrWi1GvIKnZgtBro9lbQcfZ5IqAtr\n/BysCbMxWjOQpKH90quqSkdrV1/LsKnu0w+TxWog/6wk0jIdpGU5cMSbkSQJj6ubuupO6ms6qa/u\noKainZqKdrZ/eBRnip2Cs5LIn5Z0SslhouryBvqSdV11x3HJWqvTkJETR3q2g/TsOJwpNjQaDTUV\nbbz/+mG2f3iUqvJWzvvyNGIc5iGtT1VVairaObSvnorS1hM+S7FxZtKyHJjMenS6T1uxWl3PZ+pw\nUT0Hd9dxuKiBGfPSmXt2JmZL/10+Xd4ANRXtKPsbqKnoGUap1UrkFTrJn5aEwagjEokQDqtEwhGC\nYRea4CH02hastlYs5lagFTi+L19vTsEaPwtr3Ayy9Tb0ajVle5/iC+cqJOR+E40+nnBYRaORMJn1\neFp201Zdick+BVvC/L5ydIZYkqd+i7bKV+jqKKbhyBPYEuby+cZqOOTD07wNJA3BpGUoIRVv7RY8\ngS7cQQ8uvwtXwE1nwI0r4CYQDjAQg9aASWtEr9Fh0lvRa3ToNHr0Gh1ajRatpEEjadFImt77GqbF\nTx3Stj1VpzvaZBY979T1iqIcHmj5ydry7mjrYuvGco4e6enC0Gol4hKtJDitJCTZiHdaMZn1HNhV\ny5GDjUQiKrFxZuadk0XB9GSSk2I4UFRLRUkLFSWtx7V4NBqJ2XNdpCbuQwLiMi/Cnjj/hBj83UFc\nHd34u0ME/CECgTDB3lufN0BVeRud7T39mpIEqZkOcgsSyZwS35esT8bXFaCqrI2SQ03UHG3j2Ecq\nLctBwfQk8gt7vuhDNRG2d7cvyCfvl6Hs//QAoVanITkthrQsB2mZsSSnxww4m1y3L8iHG45QdrgZ\nvUHL0tX5LF1VQEuLp9/lPa5uDhc1cLiovm/PxxFvJjXTQWKSjYRkGwlO60nf53A4grK/gZ0fV+J1\n+9EbtMxakEFOQQJtLV20NfV0dbQ2efB1fXpAMzk9BnlGCvnTnBhN+iG9R+Gg5zMHZZvQ6q1Y42dh\nMCcft5zTaefo4c20Vb2KVh9D8tTr+4Znhvzt1B9+DCSJ1MKbjzvxKxwJ4wl24Ql46G7Zir5j4Dak\nL6LygsdHXbj/FrKEhN1gI9Zgx260E2uIwWGMJc4Ui8PoIK73vklrGrHjNVEZKniqTid5e9x+7FYj\nbk83eoMWnV4b9T7WcKir56CXzorUz8b0dQXY+VElxXvrgBAZWUbmLEzAEQ+RsJfIZ0Z8REJeVFTC\noQhet7/nC6OCRifR1WWlvj6WljYHqmokIyeOnIJEAv4A3e0bSU2qJBDQcUCZRVJGIWmZDlwd3bS3\nddHR4qW9rQufd/ARBTq9hszceHKnJpKdl4DJPLQv5kB8XQHKDjdTUtxIQ40LAL1Bizwjmenz0olP\nPPlQq/GcvFVVpVxpZvPbJfi6gj3Tgk5LIi0zlqTUmL4W7lDLKjnYyOZ3Sgj4wziTbej02r7Pud6g\nRa/X0tnho7q8DejZXvnTkpg2O5XktJhhJ5JQKEzxnnp2b6k8LkkfY481keC04kyxk39W0oh0hw3k\n2PZ2NX5MR9176E1Okgq+hUZrorHkaQLeKlyOeRxV9dR5GmjoasQd8OL73MHUBI2E/TN7rZIkYdNb\nseqtqHoHBmMsNr0Fq96KXW/FarBi09uINdqx6a1oRung/MnqfZJlJmby9nr8PPPHLSc8rtFK6PVa\n4hKt5BQkkJOf2Def7mgLh3zUH/rTp6M3JG3f2FhJa8HVEaDL04lB58doCqLTnuzio9Lx42hVUNWe\noX3HPocqYDCnYY7Nw2TLwdX4Ed3uo0i6BGoal3DowIkHhaDnCxiXaCHWYcZo1mMwajEYdD23Rh0G\no44EpxWdfnQOJrs7u1H2N1C8rw6vu2dXNC3LwYx56eROTRiwe2i8Jm+v28+Hbx+hoqQVrU7DwqU5\nzF6UMWA9hsrd2c2mtxQa61x905B+XnJ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      "text/plain": [
       "<matplotlib.figure.Figure at 0x11ec7a240>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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tc5cbs8u16CcO42UhvdgCODVNOxh7nz/Wdf3I4jRLCBEPhmEQ8XgI9PUR7Osl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\n/wAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11f282518>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "    '''\n",
    "    predict\n",
    "    '''\n",
    "    tau = 1\n",
    "    dx = test[0,0]\n",
    "    dv = test[0,1]\n",
    "    obs_angle = test[0,2]\n",
    "    daccel = test[0,3]\n",
    "    obs_angle_rate = test[0,4]\n",
    "    \n",
    "    predict_horizon = 50 #test.shape[0]\n",
    "    predicted_states = np.zeros([predict_horizon, test.shape[1]])\n",
    "    predicted_states[0,:] = np.array([dx,dv,obs_angle,daccel,obs_angle_rate])\n",
    "    for t in range(1,predict_horizon):\n",
    "        \n",
    "        '''\n",
    "        Update observable variables using hidden variables\n",
    "        '''\n",
    "        dx = dx + dv * time_step + 1/2 * daccel * time_step**2 \n",
    "        dv = dv + daccel * time_step\n",
    "        obs_angle = obs_angle +obs_angle_rate * time_step\n",
    "        '''\n",
    "        Update beta\n",
    "        '''\n",
    "        beta_num = []\n",
    "        x = np.array([dx,dv,obs_angle])#test_obs[t,:] # daccel,obs_angle_rate\n",
    "        for k, gmm in enumerate(best_model.gmms_):\n",
    "            omega = gmm.weights_\n",
    "            prob = 0\n",
    "            for m in range(gmm.means_.shape[0]):\n",
    "                mu = gmm.means_[m,observable_col]\n",
    "                sigma = np.diag(gmm.covars_[m,observable_col])\n",
    "                prob += omega[m]*gaussian_prob(x,mu,sigma)\n",
    "            beta_num.append(np.sum(beta * A[:,k]) * prob) # should be beta k!\n",
    "        beta = beta_num/np.sum(beta_num)\n",
    "#         print (\"beta\", beta)\n",
    "        '''\n",
    "        predict hidden variable\n",
    "            Method 1: daccel and obs_angle_rate\n",
    "            Method 2: ego car accel and yaw rate.\n",
    "        '''\n",
    "        predict = np.dot(np.reshape(beta,(1,n_components)), mu_mean_list) #(1,2)\n",
    "        accel = predict[0,0]\n",
    "        obs_angle_rate = predict[0,1]\n",
    "        predicted_states[t,:] = np.array([dx,dv,obs_angle,daccel,obs_angle_rate])\n",
    "    print (\"Actual states: \", test[0:predict_horizon,:])\n",
    "    print (\"predicted states: \", predicted_states)\n",
    "    plt.figure(1)\n",
    "    plt.plot(test[0:predict_horizon,:])\n",
    "    plt.legend(['dx','dv','obs_angle','daccel','obs_angle_rate'])\n",
    "    plt.figure(2)\n",
    "    plt.plot(predicted_states)\n",
    "    \n",
    "    plt.show"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "'''\n",
    "Following are the implementation of the GMM training and HMM transition matrix estimation\n",
    "Technially this is not a GMM-HMM but a an HMM with transition matrix exmtimated from GMM\n",
    "We implement it and compare it with the GMM-HMM method\n",
    "'''\n",
    "# from sklearn.mixture import GaussianMixture\n",
    "\n",
    "# length = []\n",
    "# for data in train_data:\n",
    "#     length.append(data.shape[0])\n",
    "# X = np.concatenate(train_data)\n",
    "\n",
    "# GMM = GaussianMixture(n_components=1, \n",
    "#                       covariance_type='full', \n",
    "#                       tol=0.001,  \n",
    "#                       max_iter=1000, \n",
    "#                       init_params='kmeans',  \n",
    "#                       verbose=1)\n",
    "# GMM.fit(X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Model name:  GMM_models_method1/GMM_model_10.pkl\n",
      "score: -12.2303572346\n",
      "Model name:  GMM_models_method1/GMM_model_15.pkl\n",
      "score: -12.0417803459\n",
      "Model name:  GMM_models_method1/GMM_model_5.pkl\n",
      "score: -12.4864256004\n",
      "Model name:  GMM_models_method1/GMM_model_30.pkl\n",
      "score: -11.6621955134\n",
      "Model name:  GMM_models_method1/GMM_model_25.pkl\n",
      "score: -11.6954630992\n",
      "Model name:  GMM_models_method1/GMM_model_20.pkl\n",
      "score: -11.7014034604\n"
     ]
    }
   ],
   "source": [
    "'''\n",
    "Predict of the method 1 with GMM\n",
    "'''\n",
    "'''\n",
    "Read well-trained HMM-GMM models and find the one with best score\n",
    "'''\n",
    "from sklearn.mixture import GaussianMixture\n",
    "from sklearn.externals import joblib\n",
    "import glob\n",
    "import warnings\n",
    "\n",
    "'''\n",
    "Get the test data for GMM-HMM\n",
    "'''\n",
    "length = []\n",
    "for data in test_data:\n",
    "    length.append(data.shape[0])\n",
    "X = np.concatenate(test_data)\n",
    "\n",
    "def fxn():\n",
    "    warnings.warn(\"deprecated\", DeprecationWarning)\n",
    "    \n",
    "model_path = 'GMM_models_method1/*.pkl'\n",
    "files = glob.glob(model_path)\n",
    "# best_model = []\n",
    "max_score = -1e100\n",
    "with warnings.catch_warnings():\n",
    "    warnings.simplefilter(\"ignore\")\n",
    "    fxn()\n",
    "    for name in files:\n",
    "        GMM = joblib.load(name)\n",
    "        score = GMM.score(X)\n",
    "        print(\"Model name: \", name)\n",
    "        print(\"score:\", score)\n",
    "        if score > max_score:\n",
    "            max_score = score\n",
    "            best_GMM = GMM"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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SCwCkFYHVtgBkOZdRBD7u7pX35RQze6RKCltkx7qOlV+9Vsu7f9vjaWbTgNvM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\nxVtEpAdS8RYR6YFUvEVEeqD/D3G7qlKgOVm3AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11c9c1a58>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "with warnings.catch_warnings():\n",
    "    warnings.simplefilter(\"ignore\")\n",
    "    fxn()\n",
    "    '''\n",
    "    Find the transition matrix\n",
    "    '''\n",
    "    n_component = 30\n",
    "    PI = np.zeros([30,30])\n",
    "    for segment in train_data:\n",
    "        prev_state = int(best_GMM.predict(segment[0,:]))\n",
    "        for i in range(1,segment.shape[0]):\n",
    "            state = int(best_GMM.predict(segment[i,:]))\n",
    "            PI[prev_state,state] += 1\n",
    "            prev_state = state\n",
    "    PI = PI/np.reshape(np.sum(PI,axis=1),(n_component,1))\n",
    "    \n",
    "    plt.figure(1)\n",
    "    sns.heatmap(PI,vmin=0, vmax=0.1, cbar=False)\n",
    "    plt.show"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "beta:  [  0.00000000e+000   1.29744865e-011   6.04765411e-003   9.22104384e-203\n",
      "   0.00000000e+000   0.00000000e+000   0.00000000e+000   5.16975176e-003\n",
      "   4.21594727e-014   6.31416128e-001   0.00000000e+000   1.49663293e-005\n",
      "   2.15498494e-002   1.42439583e-001   0.00000000e+000   8.33096934e-005\n",
      "   1.09452784e-022   7.89635669e-003   8.14750158e-014   1.68013784e-007\n",
      "   1.93368681e-052   1.43367751e-002   1.66421080e-001   0.00000000e+000\n",
      "   3.63383493e-010   1.97613521e-153   4.62330605e-003   1.07055965e-006\n",
      "   0.00000000e+000   3.19521907e-024]\n"
     ]
    }
   ],
   "source": [
    "'''\n",
    "Test of method 1 with GMM\n",
    "'''\n",
    "with warnings.catch_warnings():\n",
    "    warnings.simplefilter(\"ignore\")\n",
    "    fxn()\n",
    "    '''\n",
    "    init beta\n",
    "    '''\n",
    "    x0 = test_obs[0,:]\n",
    "    num = []\n",
    "    omega = best_GMM.weights_\n",
    "    for m in range(n_component):\n",
    "        mu = best_GMM.means_[m,observable_col]\n",
    "        sigma = best_GMM.covariances_[m, 0:3, 0:3]\n",
    "        num.append(omega[m] * gaussian_prob(x0, mu, sigma))\n",
    "    \n",
    "    beta = np.array(num)/np.sum(num) # beta is (k,)\n",
    "    print (\"beta: \", beta)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "tmp:  [[-0.60666915]\n",
      " [-0.19615937]]\n",
      "tmp:  [[ 0.24811483]\n",
      " [ 0.06920915]]\n",
      "tmp:  [[ 0.45683414]\n",
      " [-0.03828502]]\n",
      "tmp:  [[-1.04542566]\n",
      " [ 0.02222004]]\n",
      "tmp:  [[ 0.1195885]\n",
      " [-3.7455306]]\n",
      "tmp:  [[-0.10899871]\n",
      " [-0.01274537]]\n",
      "tmp:  [[ 0.14060396]\n",
      " [ 0.50734203]]\n",
      "tmp:  [[ 0.71246419]\n",
      " [-0.06763313]]\n",
      "tmp:  [[ 0.2467125 ]\n",
      " [-0.00363075]]\n",
      "tmp:  [[ 1.0037088 ]\n",
      " [ 0.52195317]]\n",
      "tmp:  [[ 0.09111425]\n",
      " [ 0.00846154]]\n",
      "tmp:  [[ 0.07572748]\n",
      " [ 0.10502558]]\n",
      "tmp:  [[ 0.53578892]\n",
      " [-2.2431883 ]]\n",
      "tmp:  [[ 0.00642982]\n",
      " [-1.28654736]]\n",
      "tmp:  [[ 0.06940906]\n",
      " [ 0.01118065]]\n",
      "tmp:  [[ 0.08564849]\n",
      " [ 0.25660563]]\n",
      "tmp:  [[ 0.12276091]\n",
      " [-0.75904128]]\n",
      "tmp:  [[-0.07911902]\n",
      " [ 0.10918631]]\n",
      "tmp:  [[ 0.2081221 ]\n",
      " [ 2.29554595]]\n",
      "tmp:  [[-0.40430332]\n",
      " [-5.89738926]]\n",
      "tmp:  [[ 0.08422232]\n",
      " [-0.11780523]]\n",
      "tmp:  [[ 0.27146554]\n",
      " [-0.08872794]]\n",
      "tmp:  [[ 1.09364899]\n",
      " [-3.34854075]]\n",
      "tmp:  [[ 0.15850299]\n",
      " [-0.00494342]]\n",
      "tmp:  [[ 0.22507512]\n",
      " [-0.22438598]]\n",
      "tmp:  [[ 0.44299191]\n",
      " [ 0.48202849]]\n",
      "tmp:  [[ 0.29081781]\n",
      " [ 0.31952982]]\n",
      "tmp:  [[ 0.40991712]\n",
      " [-0.42756434]]\n",
      "tmp:  [[ 0.21808589]\n",
      " [ 0.00299656]]\n",
      "tmp:  [[ 0.24517379]\n",
      " [-2.40126606]]\n",
      "tmp:  [[-0.60666915]\n",
      " [-0.19615937]]\n",
      "tmp:  [[ 0.24811483]\n",
      " [ 0.06920915]]\n",
      "tmp:  [[ 0.45683414]\n",
      " [-0.03828502]]\n",
      "tmp:  [[-1.04542566]\n",
      " [ 0.02222004]]\n",
      "tmp:  [[ 0.1195885]\n",
      " [-3.7455306]]\n",
      "tmp:  [[-0.10899871]\n",
      " [-0.01274537]]\n",
      "tmp:  [[ 0.14060396]\n",
      " [ 0.50734203]]\n",
      "tmp:  [[ 0.71246419]\n",
      " [-0.06763313]]\n",
      "tmp:  [[ 0.2467125 ]\n",
      " [-0.00363075]]\n",
      "tmp:  [[ 1.0037088 ]\n",
      " [ 0.52195317]]\n",
      "tmp:  [[ 0.09111425]\n",
      " [ 0.00846154]]\n",
      "tmp:  [[ 0.07572748]\n",
      " [ 0.10502558]]\n",
      "tmp:  [[ 0.53578892]\n",
      " [-2.2431883 ]]\n",
      "tmp:  [[ 0.00642982]\n",
      " [-1.28654736]]\n",
      "tmp:  [[ 0.06940906]\n",
      " [ 0.01118065]]\n",
      "tmp:  [[ 0.08564849]\n",
      " [ 0.25660563]]\n",
      "tmp:  [[ 0.12276091]\n",
      " [-0.75904128]]\n",
      "tmp:  [[-0.07911902]\n",
      " [ 0.10918631]]\n",
      "tmp:  [[ 0.2081221 ]\n",
      " [ 2.29554595]]\n",
      "tmp:  [[-0.40430332]\n",
      " [-5.89738926]]\n",
      "tmp:  [[ 0.08422232]\n",
      " [-0.11780523]]\n",
      "tmp:  [[ 0.27146554]\n",
      " [-0.08872794]]\n",
      "tmp:  [[ 1.09364899]\n",
      " [-3.34854075]]\n",
      "tmp:  [[ 0.15850299]\n",
      " [-0.00494342]]\n",
      "tmp:  [[ 0.22507512]\n",
      " [-0.22438598]]\n",
      "tmp:  [[ 0.44299191]\n",
      " [ 0.48202849]]\n",
      "tmp:  [[ 0.29081781]\n",
      " [ 0.31952982]]\n",
      "tmp:  [[ 0.40991712]\n",
      " [-0.42756434]]\n",
      "tmp:  [[ 0.21808589]\n",
      " [ 0.00299656]]\n",
      "tmp:  [[ 0.24517379]\n",
      " [-2.40126606]]\n",
      "tmp:  [[-0.60666915]\n",
      " [-0.19615937]]\n",
      "tmp:  [[ 0.24811483]\n",
      " [ 0.06920915]]\n",
      "tmp:  [[ 0.45683414]\n",
      " [-0.03828502]]\n",
      "tmp:  [[-1.04542566]\n",
      " [ 0.02222004]]\n",
      "tmp:  [[ 0.1195885]\n",
      " [-3.7455306]]\n",
      "tmp:  [[-0.10899871]\n",
      " [-0.01274537]]\n",
      "tmp:  [[ 0.14060396]\n",
      " [ 0.50734203]]\n",
      "tmp:  [[ 0.71246419]\n",
      " [-0.06763313]]\n",
      "tmp:  [[ 0.2467125 ]\n",
      " [-0.00363075]]\n",
      "tmp:  [[ 1.0037088 ]\n",
      " [ 0.52195317]]\n",
      "tmp:  [[ 0.09111425]\n",
      " [ 0.00846154]]\n",
      "tmp:  [[ 0.07572748]\n",
      " [ 0.10502558]]\n",
      "tmp:  [[ 0.53578892]\n",
      " [-2.2431883 ]]\n",
      "tmp:  [[ 0.00642982]\n",
      " [-1.28654736]]\n",
      "tmp:  [[ 0.06940906]\n",
      " [ 0.01118065]]\n",
      "tmp:  [[ 0.08564849]\n",
      " [ 0.25660563]]\n",
      "tmp:  [[ 0.12276091]\n",
      " [-0.75904128]]\n",
      "tmp:  [[-0.07911902]\n",
      " [ 0.10918631]]\n",
      "tmp:  [[ 0.2081221 ]\n",
      " [ 2.29554595]]\n",
      "tmp:  [[-0.40430332]\n",
      " [-5.89738926]]\n",
      "tmp:  [[ 0.08422232]\n",
      " [-0.11780523]]\n",
      "tmp:  [[ 0.27146554]\n",
      " [-0.08872794]]\n",
      "tmp:  [[ 1.09364899]\n",
      " [-3.34854075]]\n",
      "tmp:  [[ 0.15850299]\n",
      " [-0.00494342]]\n",
      "tmp:  [[ 0.22507512]\n",
      " [-0.22438598]]\n",
      "tmp:  [[ 0.44299191]\n",
      " [ 0.48202849]]\n",
      "tmp:  [[ 0.29081781]\n",
      " [ 0.31952982]]\n",
      "tmp:  [[ 0.40991712]\n",
      " [-0.42756434]]\n",
      "tmp:  [[ 0.21808589]\n",
      " [ 0.00299656]]\n",
      "tmp:  [[ 0.24517379]\n",
      " [-2.40126606]]\n",
      "tmp:  [[-0.60666915]\n",
      " [-0.19615937]]\n",
      "tmp:  [[ 0.24811483]\n",
      " [ 0.06920915]]\n",
      "tmp:  [[ 0.45683414]\n",
      " [-0.03828502]]\n",
      "tmp:  [[-1.04542566]\n",
      " [ 0.02222004]]\n",
      "tmp:  [[ 0.1195885]\n",
      " [-3.7455306]]\n",
      "tmp:  [[-0.10899871]\n",
      " [-0.01274537]]\n",
      "tmp:  [[ 0.14060396]\n",
      " [ 0.50734203]]\n",
      "tmp:  [[ 0.71246419]\n",
      " [-0.06763313]]\n",
      "tmp:  [[ 0.2467125 ]\n",
      " [-0.00363075]]\n",
      "tmp:  [[ 1.0037088 ]\n",
      " [ 0.52195317]]\n",
      "tmp:  [[ 0.09111425]\n",
      " [ 0.00846154]]\n",
      "tmp:  [[ 0.07572748]\n",
      " [ 0.10502558]]\n",
      "tmp:  [[ 0.53578892]\n",
      " [-2.2431883 ]]\n",
      "tmp:  [[ 0.00642982]\n",
      " [-1.28654736]]\n",
      "tmp:  [[ 0.06940906]\n",
      " [ 0.01118065]]\n",
      "tmp:  [[ 0.08564849]\n",
      " [ 0.25660563]]\n",
      "tmp:  [[ 0.12276091]\n",
      " [-0.75904128]]\n",
      "tmp:  [[-0.07911902]\n",
      " [ 0.10918631]]\n",
      "tmp:  [[ 0.2081221 ]\n",
      " [ 2.29554595]]\n",
      "tmp:  [[-0.40430332]\n",
      " [-5.89738926]]\n",
      "tmp:  [[ 0.08422232]\n",
      " [-0.11780523]]\n",
      "tmp:  [[ 0.27146554]\n",
      " [-0.08872794]]\n",
      "tmp:  [[ 1.09364899]\n",
      " [-3.34854075]]\n",
      "tmp:  [[ 0.15850299]\n",
      " [-0.00494342]]\n",
      "tmp:  [[ 0.22507512]\n",
      " [-0.22438598]]\n",
      "tmp:  [[ 0.44299191]\n",
      " [ 0.48202849]]\n",
      "tmp:  [[ 0.29081781]\n",
      " [ 0.31952982]]\n",
      "tmp:  [[ 0.40991712]\n",
      " [-0.42756434]]\n",
      "tmp:  [[ 0.21808589]\n",
      " [ 0.00299656]]\n",
      "tmp:  [[ 0.24517379]\n",
      " [-2.40126606]]\n",
      "tmp:  [[-0.60666915]\n",
      " [-0.19615937]]\n",
      "tmp:  [[ 0.24811483]\n",
      " [ 0.06920915]]\n",
      "tmp:  [[ 0.45683414]\n",
      " [-0.03828502]]\n",
      "tmp:  [[-1.04542566]\n",
      " [ 0.02222004]]\n",
      "tmp:  [[ 0.1195885]\n",
      " [-3.7455306]]\n",
      "tmp:  [[-0.10899871]\n",
      " [-0.01274537]]\n",
      "tmp:  [[ 0.14060396]\n",
      " [ 0.50734203]]\n",
      "tmp:  [[ 0.71246419]\n",
      " [-0.06763313]]\n",
      "tmp:  [[ 0.2467125 ]\n",
      " [-0.00363075]]\n",
      "tmp:  [[ 1.0037088 ]\n",
      " [ 0.52195317]]\n",
      "tmp:  [[ 0.09111425]\n",
      " [ 0.00846154]]\n",
      "tmp:  [[ 0.07572748]\n",
      " [ 0.10502558]]\n",
      "tmp:  [[ 0.53578892]\n",
      " [-2.2431883 ]]\n",
      "tmp:  [[ 0.00642982]\n",
      " [-1.28654736]]\n",
      "tmp:  [[ 0.06940906]\n",
      " [ 0.01118065]]\n",
      "tmp:  [[ 0.08564849]\n",
      " [ 0.25660563]]\n",
      "tmp:  [[ 0.12276091]\n",
      " [-0.75904128]]\n",
      "tmp:  [[-0.07911902]\n",
      " [ 0.10918631]]\n",
      "tmp:  [[ 0.2081221 ]\n",
      " [ 2.29554595]]\n",
      "tmp:  [[-0.40430332]\n",
      " [-5.89738926]]\n",
      "tmp:  [[ 0.08422232]\n",
      " [-0.11780523]]\n",
      "tmp:  [[ 0.27146554]\n",
      " [-0.08872794]]\n",
      "tmp:  [[ 1.09364899]\n",
      " [-3.34854075]]\n",
      "tmp:  [[ 0.15850299]\n",
      " [-0.00494342]]\n",
      "tmp:  [[ 0.22507512]\n",
      " [-0.22438598]]\n",
      "tmp:  [[ 0.44299191]\n",
      " [ 0.48202849]]\n",
      "tmp:  [[ 0.29081781]\n",
      " [ 0.31952982]]\n",
      "tmp:  [[ 0.40991712]\n",
      " [-0.42756434]]\n",
      "tmp:  [[ 0.21808589]\n",
      " [ 0.00299656]]\n",
      "tmp:  [[ 0.24517379]\n",
      " [-2.40126606]]\n",
      "tmp:  [[-0.60666915]\n",
      " [-0.19615937]]\n",
      "tmp:  [[ 0.24811483]\n",
      " [ 0.06920915]]\n",
      "tmp:  [[ 0.45683414]\n",
      " [-0.03828502]]\n",
      "tmp:  [[-1.04542566]\n",
      " [ 0.02222004]]\n",
      "tmp:  [[ 0.1195885]\n",
      " [-3.7455306]]\n",
      "tmp:  [[-0.10899871]\n",
      " [-0.01274537]]\n",
      "tmp:  [[ 0.14060396]\n",
      " [ 0.50734203]]\n",
      "tmp:  [[ 0.71246419]\n",
      " [-0.06763313]]\n",
      "tmp:  [[ 0.2467125 ]\n",
      " [-0.00363075]]\n",
      "tmp:  [[ 1.0037088 ]\n",
      " [ 0.52195317]]\n",
      "tmp:  [[ 0.09111425]\n",
      " [ 0.00846154]]\n",
      "tmp:  [[ 0.07572748]\n",
      " [ 0.10502558]]\n",
      "tmp:  [[ 0.53578892]\n",
      " [-2.2431883 ]]\n",
      "tmp:  [[ 0.00642982]\n",
      " [-1.28654736]]\n",
      "tmp:  [[ 0.06940906]\n",
      " [ 0.01118065]]\n",
      "tmp:  [[ 0.08564849]\n",
      " [ 0.25660563]]\n",
      "tmp:  [[ 0.12276091]\n",
      " [-0.75904128]]\n",
      "tmp:  [[-0.07911902]\n",
      " [ 0.10918631]]\n",
      "tmp:  [[ 0.2081221 ]\n",
      " [ 2.29554595]]\n",
      "tmp:  [[-0.40430332]\n",
      " [-5.89738926]]\n",
      "tmp:  [[ 0.08422232]\n",
      " [-0.11780523]]\n",
      "tmp:  [[ 0.27146554]\n",
      " [-0.08872794]]\n",
      "tmp:  [[ 1.09364899]\n",
      " [-3.34854075]]\n",
      "tmp:  [[ 0.15850299]\n",
      " [-0.00494342]]\n",
      "tmp:  [[ 0.22507512]\n",
      " [-0.22438598]]\n",
      "tmp:  [[ 0.44299191]\n",
      " [ 0.48202849]]\n",
      "tmp:  [[ 0.29081781]\n",
      " [ 0.31952982]]\n",
      "tmp:  [[ 0.40991712]\n",
      " [-0.42756434]]\n",
      "tmp:  [[ 0.21808589]\n",
      " [ 0.00299656]]\n",
      "tmp:  [[ 0.24517379]\n",
      " [-2.40126606]]\n",
      "tmp:  [[-0.60666915]\n",
      " [-0.19615937]]\n",
      "tmp:  [[ 0.24811483]\n",
      " [ 0.06920915]]\n",
      "tmp:  [[ 0.45683414]\n",
      " [-0.03828502]]\n",
      "tmp:  [[-1.04542566]\n",
      " [ 0.02222004]]\n",
      "tmp:  [[ 0.1195885]\n",
      " [-3.7455306]]\n",
      "tmp:  [[-0.10899871]\n",
      " [-0.01274537]]\n",
      "tmp:  [[ 0.14060396]\n",
      " [ 0.50734203]]\n",
      "tmp:  [[ 0.71246419]\n",
      " [-0.06763313]]\n",
      "tmp:  [[ 0.2467125 ]\n",
      " [-0.00363075]]\n",
      "tmp:  [[ 1.0037088 ]\n",
      " [ 0.52195317]]\n",
      "tmp:  [[ 0.09111425]\n",
      " [ 0.00846154]]\n",
      "tmp:  [[ 0.07572748]\n",
      " [ 0.10502558]]\n",
      "tmp:  [[ 0.53578892]\n",
      " [-2.2431883 ]]\n",
      "tmp:  [[ 0.00642982]\n",
      " [-1.28654736]]\n",
      "tmp:  [[ 0.06940906]\n",
      " [ 0.01118065]]\n",
      "tmp:  [[ 0.08564849]\n",
      " [ 0.25660563]]\n",
      "tmp:  [[ 0.12276091]\n",
      " [-0.75904128]]\n",
      "tmp:  [[-0.07911902]\n",
      " [ 0.10918631]]\n",
      "tmp:  [[ 0.2081221 ]\n",
      " [ 2.29554595]]\n",
      "tmp:  [[-0.40430332]\n",
      " [-5.89738926]]\n",
      "tmp:  [[ 0.08422232]\n",
      " [-0.11780523]]\n",
      "tmp:  [[ 0.27146554]\n",
      " [-0.08872794]]\n",
      "tmp:  [[ 1.09364899]\n",
      " [-3.34854075]]\n",
      "tmp:  [[ 0.15850299]\n",
      " [-0.00494342]]\n",
      "tmp:  [[ 0.22507512]\n",
      " [-0.22438598]]\n",
      "tmp:  [[ 0.44299191]\n",
      " [ 0.48202849]]\n",
      "tmp:  [[ 0.29081781]\n",
      " [ 0.31952982]]\n",
      "tmp:  [[ 0.40991712]\n",
      " [-0.42756434]]\n",
      "tmp:  [[ 0.21808589]\n",
      " [ 0.00299656]]\n",
      "tmp:  [[ 0.24517379]\n",
      " [-2.40126606]]\n",
      "tmp:  [[-0.60666915]\n",
      " [-0.19615937]]\n",
      "tmp:  [[ 0.24811483]\n",
      " [ 0.06920915]]\n",
      "tmp:  [[ 0.45683414]\n",
      " [-0.03828502]]\n",
      "tmp:  [[-1.04542566]\n",
      " [ 0.02222004]]\n",
      "tmp:  [[ 0.1195885]\n",
      " [-3.7455306]]\n",
      "tmp:  [[-0.10899871]\n",
      " [-0.01274537]]\n",
      "tmp:  [[ 0.14060396]\n",
      " [ 0.50734203]]\n",
      "tmp:  [[ 0.71246419]\n",
      " [-0.06763313]]\n",
      "tmp:  [[ 0.2467125 ]\n",
      " [-0.00363075]]\n",
      "tmp:  [[ 1.0037088 ]\n",
      " [ 0.52195317]]\n",
      "tmp:  [[ 0.09111425]\n",
      " [ 0.00846154]]\n",
      "tmp:  [[ 0.07572748]\n",
      " [ 0.10502558]]\n",
      "tmp:  [[ 0.53578892]\n",
      " [-2.2431883 ]]\n",
      "tmp:  [[ 0.00642982]\n",
      " [-1.28654736]]\n",
      "tmp:  [[ 0.06940906]\n",
      " [ 0.01118065]]\n",
      "tmp:  [[ 0.08564849]\n",
      " [ 0.25660563]]\n",
      "tmp:  [[ 0.12276091]\n",
      " [-0.75904128]]\n",
      "tmp:  [[-0.07911902]\n",
      " [ 0.10918631]]\n",
      "tmp:  [[ 0.2081221 ]\n",
      " [ 2.29554595]]\n",
      "tmp:  [[-0.40430332]\n",
      " [-5.89738926]]\n",
      "tmp:  [[ 0.08422232]\n",
      " [-0.11780523]]\n",
      "tmp:  [[ 0.27146554]\n",
      " [-0.08872794]]\n",
      "tmp:  [[ 1.09364899]\n",
      " [-3.34854075]]\n",
      "tmp:  [[ 0.15850299]\n",
      " [-0.00494342]]\n",
      "tmp:  [[ 0.22507512]\n",
      " [-0.22438598]]\n",
      "tmp:  [[ 0.44299191]\n",
      " [ 0.48202849]]\n",
      "tmp:  [[ 0.29081781]\n",
      " [ 0.31952982]]\n",
      "tmp:  [[ 0.40991712]\n",
      " [-0.42756434]]\n",
      "tmp:  [[ 0.21808589]\n",
      " [ 0.00299656]]\n",
      "tmp:  [[ 0.24517379]\n",
      " [-2.40126606]]\n",
      "tmp:  [[-0.60666915]\n",
      " [-0.19615937]]\n",
      "tmp:  [[ 0.24811483]\n",
      " [ 0.06920915]]\n",
      "tmp:  [[ 0.45683414]\n",
      " [-0.03828502]]\n",
      "tmp:  [[-1.04542566]\n",
      " [ 0.02222004]]\n",
      "tmp:  [[ 0.1195885]\n",
      " [-3.7455306]]\n",
      "tmp:  [[-0.10899871]\n",
      " [-0.01274537]]\n",
      "tmp:  [[ 0.14060396]\n",
      " [ 0.50734203]]\n",
      "tmp:  [[ 0.71246419]\n",
      " [-0.06763313]]\n",
      "tmp:  [[ 0.2467125 ]\n",
      " [-0.00363075]]\n",
      "tmp:  [[ 1.0037088 ]\n",
      " [ 0.52195317]]\n",
      "tmp:  [[ 0.09111425]\n",
      " [ 0.00846154]]\n",
      "tmp:  [[ 0.07572748]\n",
      " [ 0.10502558]]\n",
      "tmp:  [[ 0.53578892]\n",
      " [-2.2431883 ]]\n",
      "tmp:  [[ 0.00642982]\n",
      " [-1.28654736]]\n",
      "tmp:  [[ 0.06940906]\n",
      " [ 0.01118065]]\n",
      "tmp:  [[ 0.08564849]\n",
      " [ 0.25660563]]\n",
      "tmp:  [[ 0.12276091]\n",
      " [-0.75904128]]\n",
      "tmp:  [[-0.07911902]\n",
      " [ 0.10918631]]\n",
      "tmp:  [[ 0.2081221 ]\n",
      " [ 2.29554595]]\n",
      "tmp:  [[-0.40430332]\n",
      " [-5.89738926]]\n",
      "tmp:  [[ 0.08422232]\n",
      " [-0.11780523]]\n",
      "tmp:  [[ 0.27146554]\n",
      " [-0.08872794]]\n",
      "tmp:  [[ 1.09364899]\n",
      " [-3.34854075]]\n",
      "tmp:  [[ 0.15850299]\n",
      " [-0.00494342]]\n",
      "tmp:  [[ 0.22507512]\n",
      " [-0.22438598]]\n",
      "tmp:  [[ 0.44299191]\n",
      " [ 0.48202849]]\n",
      "tmp:  [[ 0.29081781]\n",
      " [ 0.31952982]]\n",
      "tmp:  [[ 0.40991712]\n",
      " [-0.42756434]]\n",
      "tmp:  [[ 0.21808589]\n",
      " [ 0.00299656]]\n",
      "tmp:  [[ 0.24517379]\n",
      " [-2.40126606]]\n",
      "Actual states:  [[ 31.562       -2.79544444  -1.45        -1.00244     -1.6       ]\n",
      " [ 31.062       -2.77766667  -1.61        -1.05149     -1.7       ]\n",
      " [ 30.562       -2.81288889  -1.78        -1.38468     -1.4       ]\n",
      " [ 30.125       -2.82988889  -1.92        -1.32149     -1.6       ]\n",
      " [ 29.75        -2.84711111  -2.08        -1.44149     -1.5       ]\n",
      " [ 29.062       -2.83033333  -2.23        -1.81997     -2.8       ]\n",
      " [ 27.75        -2.93433333  -2.51        -1.90563     -1.        ]\n",
      " [ 27.812       -2.86455556  -2.61        -1.18563     -1.1       ]\n",
      " [ 27.188       -2.76077778  -2.72        -0.583       -1.        ]\n",
      " [ 26.562       -2.708       -2.82        -0.38829     -0.9       ]]\n",
      "predicted states:  [[ 31.562       -2.79544444  -1.45        -1.00244     -1.6       ]\n",
      " [ 31.27744336  -2.89568844  -1.61        -1.00244     -2.17828617]\n",
      " [ 30.98286231  -2.99593244  -1.82782862  -1.00244     -2.01852418]\n",
      " [ 30.67825687  -3.09617644  -2.02968104  -1.00244     -1.84836737]\n",
      " [ 30.36362702  -3.19642044  -2.21451777  -1.00244     -1.74226686]\n",
      " [ 30.03897278  -3.29666444  -2.38874446  -1.00244     -1.68394506]\n",
      " [ 29.70429413  -3.39690844  -2.55713896  -1.00244     -1.62948297]\n",
      " [ 29.35959109  -3.49715244  -2.72008726  -1.00244     -1.56657269]\n",
      " [ 29.00486364  -3.59739644  -2.87674453  -1.00244     -1.50914251]\n",
      " [ 28.6401118   -3.69764044  -3.02765878  -1.00244     -1.46682315]]\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<function matplotlib.pyplot.show>"
      ]
     },
     "execution_count": 74,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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w/Obg9byAwA/3uG5b9uufdXhPZbbh/QDwbsdxfgUYwDlzVyURkbpKJQ7loSiU\ni3E4j3/uVYJZbd80DSzbxLJNbNsknbGx89XnVjS1TKzUJNOG9arbaJx29+TnuEUiswpv13UD4II5\nrsuEgiDE9wKCIMAwDAzD2BtvK5I4YeAT+BXCMAAW/t+K7wdNQdzYa67PL1Eu+VNuJ5dP07UkR749\nQ76QIteeJp+3Wba8neLoGJYFtg2mCZYFlhViWmCZYFohhgFh6EMYRG0XBoQEzc9Db5L5/iTz46kf\n4BVXkckePuftN9ue914xWizz3W88QmmseTjdMIh+MeOpMcGUieYDhmlM/Nrasgm2jYFhGqTSFpmM\nTSpjkc7YpNPxNGOTzlik0/E0npdKW1iWPgcl86cytoPRAZfRgWcpjWxmM42H+SaGYYJRnVrRdLL5\nholB4/yG5ZPON+LnVm1+GBpUypXoUapQqURlr+LheR5+xcPzfULfi/6+zBDTCDCMkJQRsqQtpCcX\nYu4HtlUN3ChozXh9wwgxCMGIQrIWpA0/f/G1aOrHj1bxxl4nv2QfC+902uagQ3rwyj6lkkcYRmNb\nYQjE07BpWi+zy7JoGvhh/A+9e6+drephWGqCcK+Hf3PgV3cQmYxNKn7NXPSiaj9nUC8HAUBIEMQ/\nb9DcFrX5YRgvi9uI6HDTtAwsy4zKpoFZLVsGphmVZe6EYUB55GWKA88yOvAsXun12rJ0bgXZtnZK\npfIUvUGfkKgnGQa7ziec3dDDZAwgDaTTcWF3Xtm4s6jtPKzpdzZEyzOZNOVKUH9dvNOqrltdv3nb\nk73nRPPHLZ9kvp3qmNM2rVrQ4W1aBm9ZspMsZYpjPoadwrDt6JGyG56n4ucTlG0bI5XCMPesBxwE\nIZWyR7nkUy55lMvxtORRiXculVJ9Xn15fd7wYAnfC4AQ2/KxbB/b9rEtH9v24mk8Py5Hyz1S6YBU\nKsC2Q3zfJAjM+rRa9utlzzMIAhPPN/E9E9838H2rtn513cbtRH9qcy8K8oaQbwh20zKwTLO2Tm15\ntcdlgmmDbUaHuqYJlhlGvTDLoL3QjeenSWdtMtVHxq4939NLVBeCwC8zNvRC1MMefI7Ai67eMswU\nbZ1O9Og4FCuVn5MrLEpjZYYGi4wMjEXToVGGB8cojoxSHCoxNlau9ZQNI8Q069O2nE0ub5Npy5DN\npsnkMmTbMrTlMrTlo2kqk55BD3/PfxcX+5U3Czq8K307eX39vdBmQRBCAIRhrRwGUS+5tiwIm9YL\ng4ZlUN/VXrS+AAAMd0lEQVRrmyaYFoZhY5hW7YFlY5jxw4p3AFYKw0phWjZG2oK0CSkDO2Vg25Cz\niFrRDiETgBkSGn7tAR4hHkFYIQwqhEGZMKy0pkGnEYQmYWjVHkFoAfHzhimhTYgB1McHjVqvLST+\nx6iVDSMqG4T1shGVjcZyLQx2o9IhjIxmef3VDvr7O+jrLzA0nCcMo41YlkEmm4rCPBMFeroh5GvP\nMzaZbKq2A6geCbXqyMGrDDE68CyjAy5jQxshjA78Tbud9p6jaOs8jExhFaaZ2q3thmFIacxjaGCs\n/hgcY3igxNBg9Hz8MGWVaRq0d+TpWtpDR2eW9s4shY4Mhc4shc4s+UJGw4R70YIOb6uQwX5LD7X0\nnVchUCGkwqxHSUImHFwLKwFUAsJyCJUAygGhF4IHhm+Ab0BgQmBgBBYGFoQWBnb8SGGaKQwzRa49\nz5gXYKRMQtvEsE2wDQzLjHciBtGRowHRkWK8QwnjaQBGNFYYEgDxYTR+dOgcevEhdXU6Shh4MKtW\n2XU8tNqzqs4fPwZL/Dw6CojKYVyOAtmIdgOhAaGJyRA5tpDPb+OAFdsACEKLsVI3w8UuBgY72dlX\nYHgoZLBvlCDYvZ+jOqTV3KNP7RL8lh0dSRhGdPRgmAamybjn45fX52FA6G2nMvI8peHn8MZerdUh\nlV1GW+dhtHU6pHMrpuyVhkHIyHCpFszDg6WmkB4aGJv0qgzbNmnvzLJsRUctlNs7srWgzuXTGgZb\nQIxwTwZ0Z2j79qFZv4nvFenqMNixY3CSs8HVs8Rh07jdRON8k50lrs0L/Ci0fA8CP37uR+sGfhyo\nFgQmRmCAHwUuHvVHJQ7oSkBQCgjLHlQ8Qi9+VCrRo1r2PEKvQjBuHn4LT7FYVnzUYWPYVn2oKmNj\nZCyMVApSVnT0YkbLTDM+SqkerdgpTDsVDVlVX2+PH9pqHAZLjRvqit+/cb0JuuS9vQW2bRvEK+2g\nNPIy5ZGXKY1soTK2jcYdjpXuJJM7ADu7AqzlePRQLoWUxzxKJY/SmBeVa88rzcviIbC5ZBgBS7oH\nWL5sB8uX7SDXVgIgCAx29nXy2rYeXtu+hNHRtvjEnoFpTL4jIAwpjlTw/YnDOZ2xol5yR7YWzFGv\nOQrqbFtqwV+hsjsWw7BJb29h0n+QBd3zBrDsHNl8gXSxrdVV2avCIGgK92q5qz3NztcH6zsD36+X\na/M88DxCLzqjX50Xen69XJlkvfHbjOcH5TIUR5vW26MzubNhWbvsADZn0viYUfhbVm1qZgvQEUJH\nSFjw8PNDFMtPAU/FDWxgVnJk/AL5oAubTiyrgNHZuJPJYNjt8Q4sRWiaVEKTsm9Q8aDsQdkLKVei\nE+FBfFI3CKong+Nyw/MwLJG1X6EtvYVceiumGQ2h+UGKgZE3MjTyBoZGluH5KUIrZMmyeJvV18fD\nhY3vFTScZF6+ooNsLhUFci2co6DOZBf8n7vsBv1rLlCGaWJkMpDJNM3P9xYotre+NxGGIeyy46ge\nPTSUPa9+VOFV4mXVHUh9naZybb0Ku+yYxq3nDY/gN8yLL5+ZkNFpYyzPYi7PYL4hS7g0IEiPUCEa\nogiHPYKXxwheKxG8Oka4vQwz+ISdDRjpNGYmg5nJYmQymNls9MhkMAo2wVKPsLNEkC3WzgubYZYU\nbySTfiOZ3AFY2TaMTBYzG2/H2v2TrYuhtykzo/CWWTEMA+IeaiuND6swCBp2JP64afOOIKiMUfF3\n4gc78OjDyw1gHGJjHdIebwzMchZjNIs5ksYYtgmLE+y0KhWCcpmwVCIojeH39RF2Bli9WcyVecye\n+jVywWtj+BuLBBtHCHdWgKcn/dmMVCoK8TjMazuHbLxzqM6r7iQyGYKudoaLFbDM6ER8fMlOvRyd\nsN+lbFrReRPLnni5NTeXq8rcUXjLomKYJkY6HV9YvHvCMMSvDFAa2RKPnb9M2dwKmTH8rmgd086T\nye9POncAmfwBpHMrMK00QVCJL+eLrr8OvJG4QhaZzAGkUweQYjlGxiBcPkZwZBT0QalEMDYWBf/Y\n2K7zSmMEYyW8vj6C0ti050K27fZPvRsMY1yo2xPuJGrLbSteZ9xOwLJ2LZv18vhl9fdsKNtW/b0m\ned3wUIHSYCneKcXrmwZYJqFhEpoGoWUSGgahaUB86j4MQ0JCgvhcWlSuzo/mTbkeQcP6IW/IL6Mj\nPfd3N1zQJywrfoW7fv8PjAYjVCp+fPqp8UMzIWHt/0QfrmmeE10y2DyHxp85rC4Jm9aI5ob1Z0D8\naTIwMKNPZBpG9OnLuEdiRh/LpPZf9ZOb0Uc+43mMW15/vdH02vh9qtuIt53NpCiX6pdy1V5bu0a7\n/h7U59QO1Y3akup7Nr+6Wv+GNah3uBrqEq8w0fsYDe/SWMem9zfGvce4edV3mqiOje+Tz2cYHhlr\n+req/p5AdVh+3Nxd/q1rK+7yu0LgkwuK5P1hcv4IeX+YTMOlniEwambJBCWs+HWeYTOc6mEk3cNY\nZimGmcIyLCzDxDIsTMPEMuOpYWLWlkXza+uMn5omph9ilitQrmCUKlAqQ0Ovvz2XYqi/GH1UPj5/\nEfjxNKie84jL8fzaI/CbnhME0XkRP4g+0OP7tWm0LJriB/HUjy/N9TGq8/1gnj49MPf86AImAsOo\nXvxFYBrxFELDwI+nTcvjcm15w2sCw2Dk4OWc+ZFrZ1WnxJ6wLAVlNvRvZKg8XJs3Pqyqf/TjIqRp\nXi1yZhBC4+c1bre6Z67uJMLa3re6Q6guD2txUd37hrVw2Msn+WTOtRsGK2yTFbbFCsviDfYo/UHI\ncxWP58ser/gBIf3Ahr1Wp+qOIByDIAwIwqB6pSXs3qXgu8GKH1MzghAzBLM2bSyH0fOGshWEGCFY\nE6xnhQZ2aGCFYIcmVhjNswKwMLADMOPnNgbUth/W3teoba9ejuoYYgTUy36IFYbYQYgRBBg+GJUA\nIwgxwug1xgx2TmE4P1eOLeied9ViOwnTGOiNIU982MUEO4bqfz1L8ry+I9qZ1XqT448kxh2ZNPZC\nq8chtbkT9UIbtjn+iGW6o5OZvX/je0yzTsPOsmGtWv06O3MMDBQbjm4i4482mqbjjzYajn6qS6rr\nNP7fGLe9xnJIiB/6+EGAH/oEYeM0IAh8/Li8y/LAb1rXD32CYPJ1q8+r2wvi9w3CgHTKwvdDDExM\nw8A0TMz4E4smZvzcwDBMTJqXW/G1+GbDayd+3bjlDfOMeL3oSKN+lDH+CMM0rOhIIj6yaFpu7nrk\nYTXUc6b2Vm6EQVA7Emk8Ygn9AAIfq7MLMzW7PWhie96LVXV4ZDbHk11tBSoZfYqtqre3wPbU4tmx\n76nF1tFJgugT2+ZeP3mvFBARSSCFt4hIAim8RUQSSOEtIpJACm8RkQRSeIuIJJDCW0QkgRTeIiIJ\ntFc+YSkiInNLPW8RkQRSeIuIJJDCW0QkgRTeIiIJpPAWEUkghbeISAIpvEVEEmjBfhmD4zgm8FXg\nD4ES8Beu6z7f2lq1juM4KeCbwEogA1znuu4PW1qpFnMcZxnwKPBu13WfaXV9WslxnMuA9wFp4Kuu\n697R4iq1TPy3chfR34oPnL8Yfz8Wcs/7NCDruu7bgUuBm1pcn1b7KLDDdd0/Bv4U+EqL69NS8R/o\nrcBoq+vSao7jnAQcBxwPnAi8saUVar33ArbruscBnwE+1+L6zIuFHN7vAP4XgOu6DwPHtLY6Lfc9\n4Kq4bADeFOvuC74AfB14pdUVWQDeAzwJPAD8CPhxa6vTcs8Cdnz03gFUWlyfebGQw7sDGGh47juO\ns2CHeeab67rDrusOOY5TAO4Frmx1nVrFcZz/D9juuu5Dra7LArGUqHPzIeAC4P93HGcW35C6aAwT\nDZk8A9wGfKmltZknCzm8B4FCw3PTdd19urfpOM4bgZ8Df+e67ndaXZ8WOhd4t+M4vwCOBL7tOM4b\nWlulltoBPOS6btl1XRcYA3pbXKdW+gRRexxGdM7sLsdxsi2u05xbyD3ZfwNOAe5xHOdYosPCfZbj\nOMuBfwQucl33Z62uTyu5rntCtRwH+AWu677auhq13L8CFzuOczOwH5AnCvR9VR/1oZKdQAqwWled\n+bGQw/sBot7Vr4jGeM9pcX1a7XKgG7jKcZzq2Pefua67z5+w29e5rvtjx3FOAB4hOppe57qu3+Jq\ntdIXgW86jvNLoqtvLnddd6TFdZpzuiWsiEgCLeQxbxERmYTCW0QkgRTeIiIJpPAWEUkghbeISAIp\nvEVEEkjhLSKSQP8Xh2q6R0lkcJQAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1202d3048>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x11cb45828>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "    '''\n",
    "    predict\n",
    "    '''\n",
    "    tau = 1\n",
    "    dx = test[0,0]\n",
    "    dv = test[0,1]\n",
    "    obs_angle = test[0,2]\n",
    "    daccel = test[0,3]\n",
    "    obs_angle_rate = test[0,4]\n",
    "    \n",
    "    predict_horizon = 10 #test.shape[0]\n",
    "    predicted_states = np.zeros([predict_horizon, test.shape[1]])\n",
    "    predicted_states[0,:] = np.array([dx,dv,obs_angle,daccel,obs_angle_rate])\n",
    "    for t in range(1,predict_horizon):\n",
    "        '''\n",
    "        Update observable variables using hidden variables\n",
    "        '''\n",
    "        dx = dx + dv * time_step + 1/2 * daccel * time_step**2 \n",
    "        dv = dv + daccel * time_step\n",
    "        obs_angle = obs_angle +obs_angle_rate * time_step\n",
    "        '''\n",
    "        Update beta\n",
    "        '''\n",
    "        beta_num = []\n",
    "        x = np.array([dx,dv,obs_angle])#test_obs[t,:] # daccel,obs_angle_rate\n",
    "        for m in range(n_component):\n",
    "            mu = best_GMM.means_[m,observable_col]\n",
    "            sigma = best_GMM.covariances_[m,0:len(observable_col), 0:len(observable_col)]\n",
    "            prob = gaussian_prob(x,mu,sigma)\n",
    "            beta_num.append(np.sum(beta * PI[:,m]) * prob)\n",
    "        beta = beta_num/np.sum(beta_num)\n",
    "#         print (\"beta\", beta)\n",
    "        '''\n",
    "        predict hidden variable\n",
    "            Method 1: daccel and obs_angle_rate\n",
    "            Method 2: ego car accel and yaw rate.\n",
    "        '''\n",
    "        predict = 0\n",
    "        for m in range(n_component):\n",
    "            sigma_inv = np.linalg.pinv(best_GMM.covariances_[m,0:len(observable_col),0:len(observable_col)]) # (3,3) \n",
    "            observable_diff = np.reshape((x-best_GMM.means_[m,observable_col]),(len(observable_col),1)) # (3,1)\n",
    "            hidden_observable_cov = best_GMM.covariances_[m,len(observable_col):,0:len(observable_col)] # (2,3)\n",
    "            tmp = np.reshape(best_GMM.means_[m,hidden_col],(len(hidden_col),1)) #+ \\\n",
    "                    #np.dot(np.dot(hidden_observable_cov, sigma_inv),observable_diff) #(2,1)\n",
    "            predict += beta[m] * tmp #(2,1)\n",
    "            print (\"tmp: \", tmp)\n",
    "        accel = predict[0,0]\n",
    "        obs_angle_rate = predict[1,0]\n",
    "        predicted_states[t,:] = np.array([dx,dv,obs_angle,daccel,obs_angle_rate])\n",
    "    print (\"Actual states: \", test[0:predict_horizon,:])\n",
    "    print (\"predicted states: \", predicted_states)\n",
    "    plt.figure(1)\n",
    "    plt.plot(test[0:predict_horizon,:])\n",
    "    plt.legend(['dx','dv','obs_angle','daccel','obs_angle_rate'])\n",
    "    plt.figure(2)\n",
    "    plt.plot(predicted_states)\n",
    "    \n",
    "    plt.show"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ -6.06669153e-01,  -1.96159365e-01],\n",
       "       [  2.48114834e-01,   6.92091504e-02],\n",
       "       [  4.56834145e-01,  -3.82850228e-02],\n",
       "       [ -1.04542566e+00,   2.22200435e-02],\n",
       "       [  1.19588500e-01,  -3.74553060e+00],\n",
       "       [ -1.08998710e-01,  -1.27453696e-02],\n",
       "       [  1.40603963e-01,   5.07342034e-01],\n",
       "       [  7.12464193e-01,  -6.76331316e-02],\n",
       "       [  2.46712502e-01,  -3.63074810e-03],\n",
       "       [  1.00370880e+00,   5.21953172e-01],\n",
       "       [  9.11142522e-02,   8.46153968e-03],\n",
       "       [  7.57274786e-02,   1.05025579e-01],\n",
       "       [  5.35788916e-01,  -2.24318830e+00],\n",
       "       [  6.42981987e-03,  -1.28654736e+00],\n",
       "       [  6.94090578e-02,   1.11806495e-02],\n",
       "       [  8.56484852e-02,   2.56605628e-01],\n",
       "       [  1.22760914e-01,  -7.59041281e-01],\n",
       "       [ -7.91190167e-02,   1.09186312e-01],\n",
       "       [  2.08122101e-01,   2.29554595e+00],\n",
       "       [ -4.04303315e-01,  -5.89738926e+00],\n",
       "       [  8.42223210e-02,  -1.17805231e-01],\n",
       "       [  2.71465537e-01,  -8.87279418e-02],\n",
       "       [  1.09364899e+00,  -3.34854075e+00],\n",
       "       [  1.58502986e-01,  -4.94341960e-03],\n",
       "       [  2.25075122e-01,  -2.24385983e-01],\n",
       "       [  4.42991907e-01,   4.82028492e-01],\n",
       "       [  2.90817815e-01,   3.19529819e-01],\n",
       "       [  4.09917119e-01,  -4.27564336e-01],\n",
       "       [  2.18085886e-01,   2.99655673e-03],\n",
       "       [  2.45173794e-01,  -2.40126606e+00]])"
      ]
     },
     "execution_count": 71,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "best_GMM.means_[:,[3,4]]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
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