Paper_Prinz_clean_code_eigfunc.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Find good u and fix it to see if S converges to good result..."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-01-15T14:26:13.939213Z",
     "start_time": "2020-01-15T14:26:12.013650Z"
    }
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import tensorflow as tf\n",
    "import vampnet\n",
    "from tensorflow import keras\n",
    "from tensorflow.keras.callbacks import EarlyStopping\n",
    "from vampnet import data_generator\n",
    "import os\n",
    "from tensorflow.keras.backend import get_session\n",
    "from tensorflow.keras.layers import Layer\n",
    "import datetime"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Specify hyperparameters"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-01-15T14:26:14.017978Z",
     "start_time": "2020-01-15T14:26:13.941306Z"
    }
   },
   "outputs": [],
   "source": [
    "kT_prinz = 1.\n",
    "prinz = data_generator.PrinzModel(dt = 0.001, kT = kT_prinz)\n",
    "\n",
    "# we skip frames to make events rarer so it's harder for the model to identify them\n",
    "# the trajectory length has > 11 since we want to calculate timescales for up to 10 timesteps\n",
    "skip = 5\n",
    "traj_len = 11 * skip\n",
    "traj_num = 1000\n",
    "\n",
    "\n",
    "# should be scaled according to trajectory length and number\n",
    "# the full model and chi requires more training steps\n",
    "epoch_chi = 300\n",
    "epoch_S = 10000\n",
    "epoch_all = epoch_chi * 10\n",
    "\n",
    "\n",
    "# define starting distribution\n",
    "starting_dist = np.array([15, 70, 9, 6])\n",
    "norm_traj_num = np.ceil(starting_dist/starting_dist.sum()*traj_num).astype('int')\n",
    "\n",
    "\n",
    "# number of output nodes/states of the MSM or Koopman model, therefore also nodes of chi\n",
    "output_size = 4\n",
    "# tau list for timescales estimation\n",
    "tau_list = [1,2,3,4,6,8,10]\n",
    "number_taus = len(tau_list)\n",
    "\n",
    "# Tau, how much is the timeshift of the two datasets in the default training\n",
    "tau = 1\n",
    "\n",
    "# Batch size for Stochastic Gradient descent\n",
    "batch_size = 5000\n",
    "\n",
    "# Which trajectory points percentage is used as training\n",
    "train_ratio = 0.5\n",
    "\n",
    "# How many hidden layers the network chi has\n",
    "network_depth = 6\n",
    "\n",
    "# Width of every layer of chi\n",
    "layer_width = 100\n",
    "\n",
    "# Learning rate used for the ADAM optimizer\n",
    "learning_rate = 5e-4\n",
    "\n",
    "# create a list with the number of nodes for each layer\n",
    "nodes = [layer_width]*network_depth\n",
    "\n",
    "# epsilon for numerical inversion of correlation matrices\n",
    "epsilon = 1e-6\n",
    "# use vampnet functionality for pretraining\n",
    "vamp = vampnet.VampnetTools(epsilon = epsilon)\n",
    "# input size of the data\n",
    "input_size = 1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Data generation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-01-15T14:26:16.121766Z",
     "start_time": "2020-01-15T14:26:14.020044Z"
    }
   },
   "outputs": [],
   "source": [
    "# function for data generation\n",
    "\n",
    "def get_short_trajs():\n",
    "    '''\n",
    "    Generate a number of short trajectories starting from the state centers for the prinz potential\n",
    "    Trajectories per state are defined above in norm_traj_num\n",
    "    Adds noise to starting point of trajectory to avoid a delta-like distribution in the state centers\n",
    "    '''\n",
    "    short_trajs = []\n",
    "    state_centers = (-0.75, -0.25, 0.25, 0.75)\n",
    "    \n",
    "    for traj_per_state, state_center in zip(norm_traj_num, state_centers):\n",
    "        short_trajs += [prinz.sample(state_center + 0.15 * np.random.rand(1), traj_len) for i in range(traj_per_state)]\n",
    "        \n",
    "    short_trajs = np.array(short_trajs)\n",
    "    short_trajs_skip = short_trajs[:,::skip]\n",
    "    \n",
    "    \n",
    "    return short_trajs_skip\n",
    "\n",
    "def split_lag(data, lag):\n",
    "    '''\n",
    "    Splits data from a list of short trajectories into a trajectories and a lagged trajectories lists\n",
    "    [:, None] adds a dimension to our trajectories which corresponds to input_size = 1\n",
    "    '''\n",
    "    traj = np.concatenate([traj[:-lag] for traj in data])[:,None]\n",
    "    traj_lag = np.concatenate([traj[lag:] for traj in data])[:,None]\n",
    "    \n",
    "    return traj, traj_lag\n",
    "\n",
    "\n",
    "training_trajs = get_short_trajs()\n",
    "validation_trajs = get_short_trajs()\n",
    "\n",
    "traj_data_train, traj_data_train_lag = split_lag(training_trajs, tau)\n",
    "traj_data_valid, traj_data_valid_lag = split_lag(validation_trajs, tau)\n",
    "\n",
    "\n",
    "\n",
    "# function here too for astype? is astype necessary?\n",
    "\n",
    "# Input of the first network\n",
    "X1_train = traj_data_train.astype('float32')\n",
    "X2_train  = traj_data_train_lag.astype('float32')\n",
    "\n",
    "# Input for validation\n",
    "X1_vali = traj_data_valid.astype('float32')\n",
    "X2_vali = traj_data_valid_lag.astype('float32')\n",
    "\n",
    "# Needs a Y-train set which we dont have.\n",
    "Y_train = np.zeros((X1_train.shape[0],2*output_size)).astype('float32')\n",
    "Y_vali = np.zeros((X1_vali.shape[0],2*output_size)).astype('float32')\n",
    "\n",
    "# store this so that all the data are transformed into a whitened dataset w.r.t. the same mean and std\n",
    "# we assume a gaussian distribution of our data\n",
    "train_mean = X1_train.mean(0)\n",
    "train_std = X1_train.std(0)\n",
    "\n",
    "# function for whitening data\n",
    "whiten = lambda x, m = train_mean, s = train_std : (x-m)/s"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Define helper layers for keras"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-01-15T14:26:16.335320Z",
     "start_time": "2020-01-15T14:26:16.123618Z"
    }
   },
   "outputs": [],
   "source": [
    "# keras layer that implements the u vector, its constraints, and mu and sigma, along with the three correlation matrices\n",
    "# the reason for this structure is mostly to comply with keras standards for shape (eg. stacking)\n",
    "# the structure revolves around a 1xn vector of trainable weights called the \"kernel\"\n",
    "\n",
    "class Vamp_matrix_u(Layer):\n",
    "\n",
    "    def __init__(self, output_dim, transform_kernel, **kwargs):\n",
    "\n",
    "        self.M = output_dim\n",
    "        self.acti = transform_kernel\n",
    "\n",
    "        super(Vamp_matrix_u, self).__init__(**kwargs)\n",
    "\n",
    "    def build(self, input_shape):\n",
    "        \n",
    "        # u has to act as a reweighting factor for the stationary distribution,\n",
    "        # so we initialize it equally for all states\n",
    "\n",
    "        self.u_kernel = self.add_weight(name='u_var', \n",
    "                                shape=(self.M,),\n",
    "                                 initializer=tf.constant_initializer(1/output_size),\n",
    "                                 trainable=True)\n",
    "\n",
    "        super(Vamp_matrix_u, self).build(input_shape)\n",
    "\n",
    "    # function required by keras, has to return the shape of the outputs\n",
    "    def compute_output_shape(self, input_shape):\n",
    "        return [(self.M), (self.M), (self.M, self.M), (self.M, self.M), (self.M, self.M), (self.M, self.M), (self.M)]\n",
    "\n",
    "    # the call function accepts as input the transformed chi_t and chi_tau trajectories,\n",
    "    # normalizes u accordingly and calculates mu, sigma and the other elements necessary\n",
    "    # for the futher computation blocks\n",
    "    \n",
    "    def call(self, x):\n",
    "\n",
    "        chi_t, chi_tau = x\n",
    "        \n",
    "        # we need batchsize to stack the outputs later so that it fullfills keras' requirements\n",
    "        batchsize_int = tf.shape(chi_t)[0]\n",
    "        batchsize = tf.to_float(batchsize_int)\n",
    "\n",
    "        # note: corr_tau is the correlation matrix of the time-shifted data\n",
    "        # presented in the paper at page 6, \"Normalization of transition density\"\n",
    "        corr_tau = 1./batchsize * tf.matmul(chi_tau, chi_tau, transpose_a=True)\n",
    "        chi_mean = tf.reduce_mean(chi_tau, axis=0, keepdims=True)\n",
    "\n",
    "        kernel_u = tf.expand_dims(self.acti(self.u_kernel), axis=0)\n",
    "\n",
    "        # u is the normalized and transformed kernel of this layer\n",
    "        u = kernel_u / tf.reduce_sum(chi_mean * kernel_u, keepdims=True)\n",
    "\n",
    "        v = tf.matmul(corr_tau, u, transpose_b=True)\n",
    "\n",
    "        mu = 1./batchsize * tf.matmul(chi_tau, u, transpose_b=True)\n",
    "        Sigma =  tf.matmul(chi_tau * mu, chi_tau, transpose_a=True)\n",
    "\n",
    "        gamma = chi_tau * (tf.matmul(chi_tau, u, transpose_b=True))\n",
    "\n",
    "        C_00 = 1./batchsize * tf.matmul(chi_t, chi_t, transpose_a=True)\n",
    "        C_11 = 1./batchsize * tf.matmul(gamma, gamma, transpose_a=True)\n",
    "        C_01 = 1./batchsize * tf.matmul(chi_t, gamma, transpose_a=True)\n",
    "\n",
    "        \n",
    "        # stack outputs so that the first dimension is = batchsize, keras requirement\n",
    "        def tile_for_keras(x):\n",
    "            x_exp = tf.expand_dims(x, axis=0)\n",
    "            x_shape = x.get_shape().as_list()\n",
    "            ones = [1] * len(x_shape)\n",
    "            stack_x = tf.tile(x_exp, [batchsize_int, *ones])\n",
    "            \n",
    "            return stack_x\n",
    "\n",
    "        ret = [\n",
    "            tile_for_keras(u),\n",
    "            tile_for_keras(v),\n",
    "            tile_for_keras(C_00),\n",
    "            tile_for_keras(C_11),\n",
    "            tile_for_keras(C_01),\n",
    "            tile_for_keras(Sigma),\n",
    "            mu\n",
    "        ]\n",
    "\n",
    "        return ret"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-01-15T14:26:16.626285Z",
     "start_time": "2020-01-15T14:26:16.337509Z"
    }
   },
   "outputs": [],
   "source": [
    "# keras layer that implements the S matrix and its constraints, and calculates the K matrix\n",
    "\n",
    "class Vamp_matrix_S(Layer):\n",
    "\n",
    "    def __init__(self, output_dim, transform_kernel, renorm = False, **kwargs):\n",
    "        # renorm forces the S values to be positive\n",
    "        self.M = output_dim\n",
    "        self.acti = transform_kernel\n",
    "        self.renorm = renorm\n",
    "\n",
    "        super(Vamp_matrix_S, self).__init__(**kwargs)\n",
    "\n",
    "    def build(self, input_shape):\n",
    "\n",
    "        self.S_kernel = self.add_weight(name='S_var', \n",
    "                                shape=(self.M,self.M),\n",
    "                                 initializer=tf.constant_initializer(.1),\n",
    "                                 trainable=True)\n",
    "\n",
    "        super(Vamp_matrix_S, self).build(input_shape)\n",
    "\n",
    "    # function required by keras, has to return the shape of the outputs\n",
    "    def compute_output_shape(self, input_shape):\n",
    "        return [(self.M, self.M), (self.M, self.M), (self.M), (self.M, self.M)]\n",
    "\n",
    "    # this function has two different behaviours distinguished through how many parameters are passed in the input list\n",
    "    # for len(x) == 8 it is used to train the full network, with the data being transformed through chi first\n",
    "    # for len(x) == 5 it is used to train only S with a full batch of data, thus the two chis aren't necessary anymore\n",
    "    # training is faster for len(x) == 5 since it requires less calculations\n",
    "    def call(self, x):\n",
    "\n",
    "        # unpack input list for the 2 cases\n",
    "        # selects the first elements of the inputs due to keras batchsize input requirement\n",
    "        \n",
    "        if len(x) == 5:\n",
    "            v, C_00, C_11, C_01, Sigma = x\n",
    "        else:\n",
    "            chi_t, chi_tau, u, v, C_00, C_11, C_01, Sigma = x\n",
    "            u = u[0]\n",
    "            \n",
    "        batchsize_int = tf.shape(v)[0]\n",
    "        batchsize = tf.to_float(batchsize_int)\n",
    "        C_00 = C_00[0]\n",
    "        C_11 = C_11[0]\n",
    "        C_01 = C_01[0]\n",
    "        Sigma = Sigma[0]\n",
    "        v = v[0]\n",
    "\n",
    "        # transform the kernel weights\n",
    "        kernel_w = self.acti(self.S_kernel)\n",
    "\n",
    "        # enforce symmetry\n",
    "        W1 = kernel_w + tf.transpose(kernel_w)\n",
    "\n",
    "        # normalize the weights\n",
    "        norm = W1 @ v\n",
    "        \n",
    "        if self.renorm:\n",
    "            # make sure that the largest value of norm is < 1\n",
    "            quasi_inf_norm = lambda x: tf.reduce_sum((x**20))**(1./20)\n",
    "            W1 = W1 / quasi_inf_norm(norm)\n",
    "            norm = W1 @ v\n",
    "\n",
    "        \n",
    "        w2 = (1 - tf.squeeze(norm)) / tf.squeeze(v)\n",
    "        S = W1 + tf.diag(w2)\n",
    "\n",
    "        # calculate the probabilities to observe the data pair\n",
    "        if len(x) == 8:\n",
    "            q =  tf.transpose(tf.matmul(S, chi_tau, transpose_b=True)) * tf.matmul(chi_tau, u, transpose_b=True) / batchsize\n",
    "            probs = tf.reduce_sum(chi_t * q, axis=1) \n",
    "\n",
    "        # calculate K\n",
    "        K = S @ Sigma\n",
    "\n",
    "        # VAMP-E matrix for the computation of the loss\n",
    "        VampE_matrix = tf.transpose(S) @ C_00 @ S @ C_11 - 2*tf.transpose(S) @ C_01\n",
    "\n",
    "        # stack outputs so that the first dimension is = batchsize, keras requirement\n",
    "        VampE_matrix_tile = tf.tile(tf.expand_dims(VampE_matrix, axis=0), [batchsize_int,1,1])\n",
    "        K_mult = tf.tile(tf.expand_dims(K, axis=0), [batchsize_int,1,1])\n",
    "        S_mult = tf.tile(tf.expand_dims(S, axis=0), [batchsize_int,1,1])\n",
    "\n",
    "        if len(x) == 5:\n",
    "            ret = [VampE_matrix_tile, K_mult, tf.zeros((batchsize_int, self.M)), S_mult]\n",
    "        else:\n",
    "            ret = [VampE_matrix_tile, K_mult, probs, S_mult] \n",
    "\n",
    "        return ret"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-01-15T14:26:16.653708Z",
     "start_time": "2020-01-15T14:26:16.628296Z"
    }
   },
   "outputs": [],
   "source": [
    "# we transform the kernels using a linear transformation with very small slope for learning stability\n",
    "# only for reversible VAMPnets\n",
    "factor_S = 0.001\n",
    "factor_u = .000001\n",
    "\n",
    "linear_S = lambda x: factor_S * x\n",
    "linear_u = lambda x: factor_u * x\n",
    "\n",
    "# activations for reversible VAMPnets\n",
    "acti_S = linear_S\n",
    "acti_u = linear_u\n",
    "\n",
    "#activations for revDMSM\n",
    "acti_S2 = tf.exp\n",
    "acti_u2 = tf.exp\n",
    "\n",
    "# define loss functions\n",
    "maximum_likelihood = lambda x: - tf.reduce_sum( tf.log(y_pred), axis=0)\n",
    "loss_vampe = lambda y_true, y_pred: tf.trace(y_pred[0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-01-15T14:26:16.848212Z",
     "start_time": "2020-01-15T14:26:16.660400Z"
    }
   },
   "outputs": [],
   "source": [
    "def estimate_koopman_op(trajs, tau, force_symmetric = False):\n",
    "    '''Estimates the koopman operator for a given trajectory at the lag time\n",
    "        specified. The formula for the estimation is:\n",
    "            K = C00 ^ -1 @ C01\n",
    "\n",
    "    Parameters\n",
    "    ----------\n",
    "    traj: numpy array with size [traj_timesteps, traj_dimensions]\n",
    "        Trajectory described by the returned koopman operator\n",
    "\n",
    "    tau: int\n",
    "        Time shift at which the koopman operator is estimated\n",
    "        \n",
    "    force_symmetric: boolean, default = False\n",
    "        if true, calculates the symmetrized version of K instead\n",
    "\n",
    "    Returns\n",
    "    -------\n",
    "    koopman_op: numpy array with shape [traj_dimensions, traj_dimensions]\n",
    "        Koopman operator estimated at timeshift tau\n",
    "\n",
    "    '''\n",
    "    # if tau larger 0, interpret trajs as either a list of trajectories\n",
    "    # or a single trajectory\n",
    "    # otherwise interpret trajs as a list of the data and time-lagged data\n",
    "    # possibly in random order\n",
    "    if tau > 0:\n",
    "        if type(trajs) == list:\n",
    "            traj = np.concatenate([t[:-tau] for t in trajs], axis = 0)\n",
    "            traj_lag = np.concatenate([t[tau:] for t in trajs], axis = 0)\n",
    "        else:\n",
    "            traj = trajs[:-tau]\n",
    "            traj_lag = trajs[tau:]\n",
    "    else:\n",
    "        traj = traj[0]\n",
    "        traj_lag = traj[1]\n",
    "        \n",
    "        \n",
    "    koopman_op = np.eye(traj.shape[1])\n",
    "\n",
    "    c_0 = traj.T @ traj\n",
    "    c_tau = traj.T @ traj_lag\n",
    "    \n",
    "    # if you want to symmetrize the correlation matrices\n",
    "    if force_symmetric:\n",
    "        c_0 = c_0 + traj_lag.T @ traj_lag\n",
    "        c_tau = c_tau + traj_lag.T @ traj\n",
    "\n",
    "    eigv_all, eigvec_all = np.linalg.eig(c_0)\n",
    "    include = eigv_all > epsilon\n",
    "    eigv = eigv_all[include]\n",
    "    eigvec = eigvec_all[:,include]\n",
    "    c0_inv = eigvec @ np.diag(1/eigv) @ np.transpose(eigvec)\n",
    "\n",
    "    koopman_op = c0_inv @ c_tau\n",
    "\n",
    "    return koopman_op\n",
    "\n",
    "\n",
    "\n",
    "# utility function for plotting implied timescales\n",
    "# the hyperparameters allow for it to calculate errorbars and work from different input data types\n",
    "def get_its(data, lags, calculate_K = True, multiple_runs = False):\n",
    "    \n",
    "    def get_single_its(data):\n",
    "\n",
    "        if type(data) == list:\n",
    "            outputsize = data[0].shape[1]\n",
    "        else:\n",
    "            outputsize = data.shape[1]\n",
    "\n",
    "        single_its = np.zeros((outputsize-1, len(lags)))\n",
    "\n",
    "        for t, tau_lag in enumerate(lags):\n",
    "            if calculate_K:\n",
    "                koopman_op = self.estimate_koopman_op(data, tau_lag)\n",
    "            else:\n",
    "                koopman_op = data[t]\n",
    "            k_eigvals, k_eigvec = np.linalg.eig(np.real(koopman_op))\n",
    "            k_eigvals = np.sort(np.absolute(k_eigvals))\n",
    "            k_eigvals = k_eigvals[:-1]\n",
    "            single_its[:,t] = (-tau_lag / np.log(k_eigvals))\n",
    "\n",
    "        return np.array(single_its)\n",
    "\n",
    "\n",
    "    if not multiple_runs:\n",
    "\n",
    "        its = get_single_its(data)\n",
    "\n",
    "    else:\n",
    "\n",
    "        its = []\n",
    "        for data_run in data:\n",
    "            its.append(get_single_its(data_run))\n",
    "\n",
    "    return its\n",
    "\n",
    "# utility function, resets all the weights in the graph    \n",
    "def reset_weights(var):\n",
    "    session = get_session()\n",
    "    var.initializer.run(session=session)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Define ordinary VAMPnet"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-01-15T14:26:17.239185Z",
     "start_time": "2020-01-15T14:26:16.850018Z"
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "WARNING: Logging before flag parsing goes to stderr.\n",
      "W0115 15:26:16.961718 140414737237760 deprecation.py:506] From /home/andreasmardt/anaconda2/envs/tf15/lib/python3.6/site-packages/tensorflow/python/ops/init_ops.py:1251: calling VarianceScaling.__init__ (from tensorflow.python.ops.init_ops) with dtype is deprecated and will be removed in a future version.\n",
      "Instructions for updating:\n",
      "Call initializer instance with the dtype argument instead of passing it to the constructor\n"
     ]
    }
   ],
   "source": [
    "# Input layers, through which our trajectory and lagged trajectory will be passed\n",
    "Data_X_keras = keras.layers.Input(shape = (input_size,))\n",
    "Data_Y_keras = keras.layers.Input(shape = (input_size,))\n",
    "\n",
    "# Dense layers that compose the network \n",
    "dense_layers = [tf.keras.layers.Dense(node, activation = tf.nn.elu)\n",
    "                for index_layer,node in enumerate(nodes)]\n",
    "\n",
    "# Add a softmax output layer.\n",
    "softmax = tf.keras.layers.Dense(output_size, activation='softmax')\n",
    "\n",
    "# The layers for trainable vector u and matrix S for the revVAMPnet\n",
    "vamp_layer_u = Vamp_matrix_u(output_size, acti_u)\n",
    "vamp_layer_S = Vamp_matrix_S(output_size, acti_S, renorm=False)\n",
    "\n",
    "# The layers for trainable vector u and matrix S for the revMSM\n",
    "vamp_layer_u_msm = Vamp_matrix_u(output_size, acti_u2)\n",
    "vamp_layer_S_msm = Vamp_matrix_S(output_size, acti_S2, renorm=True)\n",
    "\n",
    "# Assign instance layers to the two lobes of the network\n",
    "lx_branch_keras = Data_X_keras\n",
    "rx_branch_keras = Data_Y_keras\n",
    "\n",
    "# Connect the layers into a network\n",
    "for i, layer in enumerate(dense_layers):\n",
    "\n",
    "    lx_branch_keras = dense_layers[i](lx_branch_keras)\n",
    "    rx_branch_keras = dense_layers[i](rx_branch_keras)\n",
    "\n",
    "\n",
    "# Connect a softmax output layer.\n",
    "lx_branch_keras = softmax(lx_branch_keras)\n",
    "rx_branch_keras = softmax(rx_branch_keras)\n",
    "\n",
    "# Merge them to use the VAMP loss functions\n",
    "merged_chi = keras.layers.concatenate([lx_branch_keras, rx_branch_keras]) "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Define the network for the revVAMPnet"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-01-15T14:26:18.674460Z",
     "start_time": "2020-01-15T14:26:17.240696Z"
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "W0115 15:26:17.675978 140414737237760 deprecation.py:323] From /home/andreasmardt/anaconda2/envs/tf15/lib/python3.6/site-packages/tensorflow/python/autograph/impl/api.py:255: to_float (from tensorflow.python.ops.math_ops) is deprecated and will be removed in a future version.\n",
      "Instructions for updating:\n",
      "Use `tf.cast` instead.\n",
      "W0115 15:26:17.894759 140414737237760 deprecation_wrapper.py:119] From /home/andreasmardt/anaconda2/envs/tf15/lib/python3.6/site-packages/tensorflow/python/autograph/converters/directives.py:117: The name tf.diag is deprecated. Please use tf.linalg.tensor_diag instead.\n",
      "\n"
     ]
    }
   ],
   "source": [
    "# Use auxiliary u layer with the output of the network as input\n",
    "# to build a model wich depends on all variables\n",
    "tf_u_all, tf_v_all, tf_C_00_all, tf_C_11_all , tf_C_01_all, Sigma_all, mu_all = vamp_layer_u([lx_branch_keras, rx_branch_keras])\n",
    "\n",
    "# Pass it to the auxiliary S layer which provides all outputs\n",
    "# for the different losses and to predict the transition matrix\n",
    "VampE_matrix_all, K_all, probs_all, S_all = vamp_layer_S([lx_branch_keras, rx_branch_keras, tf_u_all, tf_v_all, tf_C_00_all, tf_C_11_all , tf_C_01_all, Sigma_all])\n",
    "\n",
    "# Define inputs, where the output of the chi network can be fed in \n",
    "# in order to train just for u and S without computational overhead\n",
    "Data_chi_t_keras = keras.layers.Input(shape = (output_size,))\n",
    "Data_chi_tau_keras = keras.layers.Input(shape = (output_size,))\n",
    "\n",
    "# Pass it again through the u and S layer starting from the new inputs\n",
    "tf_u_both, tf_v_both, tf_C_00_both, tf_C_11_both , tf_C_01_both, Sigma_both, _ = vamp_layer_u([Data_chi_t_keras, Data_chi_tau_keras])\n",
    "VampE_matrix_both, K_both, probs_both, S_both = vamp_layer_S([Data_chi_t_keras, Data_chi_tau_keras, tf_u_both, tf_v_both, tf_C_00_both, tf_C_11_both , tf_C_01_both, Sigma_both])\n",
    "\n",
    "# Auxiliary inputs to just train for S, where a lot of computational overhead \n",
    "# can be reduced\n",
    "Data_v_keras = keras.layers.Input(shape = (output_size, 1))\n",
    "Data_C_00_keras = keras.layers.Input(shape = (output_size,output_size))\n",
    "Data_C_01_keras = keras.layers.Input(shape = (output_size,output_size))\n",
    "Data_C_11_keras = keras.layers.Input(shape = (output_size,output_size))\n",
    "Data_Sigma_keras = keras.layers.Input(shape = (output_size,output_size))\n",
    "\n",
    "# Pass these new inputs just through the S layer\n",
    "VampE_matrix_S, K_S, _ , S_S= vamp_layer_S([Data_v_keras, Data_C_00_keras, Data_C_11_keras, Data_C_01_keras, Data_Sigma_keras])\n",
    "\n",
    "# Get access through the shared weights of u and S\n",
    "var_u = vamp_layer_u.weights\n",
    "var_S = vamp_layer_S.weights"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Define revDMSM"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-01-15T14:26:19.066290Z",
     "start_time": "2020-01-15T14:26:18.675979Z"
    }
   },
   "outputs": [],
   "source": [
    "# Use auxiliary u layer with the output of the network as input\n",
    "# to build a model wich depends on all variables\n",
    "tf_u_all_msm, tf_v_all_msm, tf_C_00_all_msm, tf_C_11_all_msm , tf_C_01_all_msm, Sigma_all_msm, mu_all_msm = vamp_layer_u_msm([lx_branch_keras, rx_branch_keras])\n",
    "\n",
    "# Pass it to the auxiliary S layer which provides all outputs\n",
    "# for the different losses and to predict the transition matrix\n",
    "VampE_matrix_all_msm, K_all_msm, probs_all_msm, S_all_msm = vamp_layer_S_msm([lx_branch_keras, rx_branch_keras, tf_u_all_msm, tf_v_all_msm, tf_C_00_all_msm, tf_C_11_all_msm , tf_C_01_all_msm, Sigma_all_msm])\n",
    "\n",
    "# Pass it again through the u and S layer starting from the auxiliary inputs replacing chi from before\n",
    "tf_u_both_msm, tf_v_both_msm, tf_C_00_both_msm, tf_C_11_both_msm , tf_C_01_both_msm, Sigma_both_msm, _ = vamp_layer_u_msm([Data_chi_t_keras, Data_chi_tau_keras])\n",
    "VampE_matrix_both_msm, K_both_msm, probs_both_msm, S_both_msm = vamp_layer_S_msm([Data_chi_t_keras, Data_chi_tau_keras, tf_u_both_msm, tf_v_both_msm, tf_C_00_both_msm, tf_C_11_both_msm , tf_C_01_both_msm, Sigma_both_msm])\n",
    "\n",
    "# Pass it just through the S layer starting from the auxiliary inputs replacing chi and u from before\n",
    "VampE_matrix_S_msm, K_S_msm, _ , S_S_msm= vamp_layer_S_msm([Data_v_keras, Data_C_00_keras, Data_C_11_keras, Data_C_01_keras, Data_Sigma_keras])\n",
    "\n",
    "# Get access through the shared weights of u and S\n",
    "var_u_msm = vamp_layer_u_msm.weights\n",
    "var_S_msm = vamp_layer_S_msm.weights"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Define actual models"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-01-15T14:26:19.452454Z",
     "start_time": "2020-01-15T14:26:19.068215Z"
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "W0115 15:26:19.145850 140414737237760 deprecation_wrapper.py:119] From /home/andreasmardt/gitreps/deeptime/vampnet/vampnet/vampnet.py:608: The name tf.self_adjoint_eig is deprecated. Please use tf.linalg.eigh instead.\n",
      "\n",
      "W0115 15:26:19.150459 140414737237760 deprecation.py:323] From /home/andreasmardt/gitreps/deeptime/vampnet/vampnet/vampnet.py:612: to_int32 (from tensorflow.python.ops.math_ops) is deprecated and will be removed in a future version.\n",
      "Instructions for updating:\n",
      "Use `tf.cast` instead.\n",
      "W0115 15:26:19.191824 140414737237760 deprecation_wrapper.py:119] From /home/andreasmardt/gitreps/deeptime/vampnet/vampnet/vampnet.py:268: The name tf.svd is deprecated. Please use tf.linalg.svd instead.\n",
      "\n"
     ]
    }
   ],
   "source": [
    "# Define a normal VAMPnet model, which will be used for pretraining\n",
    "model_chi = keras.models.Model(inputs = [Data_X_keras, Data_Y_keras], outputs = merged_chi)\n",
    "model_chi.compile(keras.optimizers.Adam(learning_rate=learning_rate*.5),\n",
    "                 vamp._loss_VAMP_sym,\n",
    "                 metrics = [\n",
    "                      vamp.metric_VAMP,\n",
    "                      vamp.metric_VAMP2,])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Define models for the revVAMPnet case"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-01-15T14:26:19.459675Z",
     "start_time": "2020-01-15T14:26:19.454256Z"
    }
   },
   "outputs": [],
   "source": [
    "# Define a model to predict the stationary distribution mu\n",
    "model_mu = keras.models.Model(inputs= [Data_X_keras, Data_Y_keras], outputs=mu_all)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-01-15T14:26:19.515999Z",
     "start_time": "2020-01-15T14:26:19.462443Z"
    }
   },
   "outputs": [],
   "source": [
    "# Define a model to train for all parameters with VAMP-E\n",
    "model_all_vampE = keras.models.Model(inputs = [Data_X_keras, Data_Y_keras], outputs = VampE_matrix_all)\n",
    "model_all_vampE.compile(keras.optimizers.Adam(learning_rate=learning_rate, clipnorm=1.),\n",
    "                 loss_vampe,\n",
    "             )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-01-15T14:26:19.525890Z",
     "start_time": "2020-01-15T14:26:19.517885Z"
    }
   },
   "outputs": [],
   "source": [
    "# Define a model to predict the transition matrix from a model using the whole pipeline\n",
    "model_K_all = keras.models.Model(inputs = [Data_X_keras, Data_Y_keras], outputs = K_all)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-01-15T14:26:19.588642Z",
     "start_time": "2020-01-15T14:26:19.527760Z"
    }
   },
   "outputs": [],
   "source": [
    "# Define a model to train only u and S with VAMP-E\n",
    "model_both_vampE = keras.models.Model(inputs = [Data_chi_t_keras, Data_chi_tau_keras], outputs = VampE_matrix_both)\n",
    "model_both_vampE.compile(keras.optimizers.Adam(learning_rate=learning_rate*1000),\n",
    "                 loss_vampe,\n",
    "                 )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-01-15T14:26:19.601968Z",
     "start_time": "2020-01-15T14:26:19.590566Z"
    }
   },
   "outputs": [],
   "source": [
    "# Define a model to predict the transition matrix omitting the chi network\n",
    "model_K_both = keras.models.Model(inputs = [Data_chi_t_keras, Data_chi_tau_keras], outputs = K_both)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-01-15T14:26:19.636418Z",
     "start_time": "2020-01-15T14:26:19.603936Z"
    }
   },
   "outputs": [],
   "source": [
    "# Define a model to predict to get access to the matrix S omitting the chi network\n",
    "model_S_both = keras.models.Model(inputs =  [Data_chi_t_keras, Data_chi_tau_keras], outputs = S_both)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-01-15T14:26:19.660518Z",
     "start_time": "2020-01-15T14:26:19.639041Z"
    }
   },
   "outputs": [],
   "source": [
    "# Define a helper model to get access to intermediate results\n",
    "model_input_S = keras.models.Model(inputs = [Data_chi_t_keras, Data_chi_tau_keras], outputs = [tf_v_both, tf_C_00_both, tf_C_11_both , tf_C_01_both, Sigma_both])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-01-15T14:26:19.723535Z",
     "start_time": "2020-01-15T14:26:19.666820Z"
    }
   },
   "outputs": [],
   "source": [
    "# Define a model to train only for S with VAMP-E\n",
    "model_S_vampE = keras.models.Model(inputs = [Data_v_keras, Data_C_00_keras, Data_C_11_keras, Data_C_01_keras, Data_Sigma_keras], outputs = VampE_matrix_S)\n",
    "model_S_vampE.compile(keras.optimizers.Adam(learning_rate=learning_rate*1000, ),\n",
    "                 loss_vampe,\n",
    "             )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-01-15T14:26:19.735520Z",
     "start_time": "2020-01-15T14:26:19.725141Z"
    }
   },
   "outputs": [],
   "source": [
    "# Define models to predict the transition matrix and the S matrix omitting the chi network and u layer\n",
    "model_K_S = keras.models.Model(inputs = [Data_v_keras, Data_C_00_keras, Data_C_11_keras, Data_C_01_keras, Data_Sigma_keras], outputs = K_S)\n",
    "model_S_S = keras.models.Model(inputs = [Data_v_keras, Data_C_00_keras, Data_C_11_keras, Data_C_01_keras, Data_Sigma_keras], outputs = S_S)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Define models for the revMSM case"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-01-15T14:26:19.772343Z",
     "start_time": "2020-01-15T14:26:19.737313Z"
    }
   },
   "outputs": [],
   "source": [
    "# Define a model to predict the stationary distribution mu\n",
    "model_mu_msm = keras.models.Model(inputs= [Data_X_keras, Data_Y_keras], outputs=mu_all_msm)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-01-15T14:26:19.827344Z",
     "start_time": "2020-01-15T14:26:19.774183Z"
    }
   },
   "outputs": [],
   "source": [
    "# Define a model to train for all parameters with VAMP-E\n",
    "model_all_vampE_msm = keras.models.Model(inputs = [Data_X_keras, Data_Y_keras], outputs = VampE_matrix_all_msm)\n",
    "model_all_vampE_msm.compile(keras.optimizers.Adam(learning_rate=learning_rate, clipnorm=1.),\n",
    "                 loss_vampe,\n",
    "             )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-01-15T14:26:19.839497Z",
     "start_time": "2020-01-15T14:26:19.829015Z"
    }
   },
   "outputs": [],
   "source": [
    "# Define a model to predict the transition matrix from a model using the whole pipeline\n",
    "model_K_all_msm = keras.models.Model(inputs = [Data_X_keras, Data_Y_keras], outputs = K_all_msm)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-01-15T14:26:19.899578Z",
     "start_time": "2020-01-15T14:26:19.843791Z"
    }
   },
   "outputs": [],
   "source": [
    "# Define a model to train only u and S with VAMP-E\n",
    "model_both_vampE_msm = keras.models.Model(inputs = [Data_chi_t_keras, Data_chi_tau_keras], outputs = VampE_matrix_both_msm)\n",
    "model_both_vampE_msm.compile(keras.optimizers.Adam(learning_rate=learning_rate*1000),\n",
    "                 loss_vampe,\n",
    "                 )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-01-15T14:26:19.907430Z",
     "start_time": "2020-01-15T14:26:19.901293Z"
    }
   },
   "outputs": [],
   "source": [
    "# Define a model to predict the transition matrix omitting the chi network\n",
    "model_K_both_msm = keras.models.Model(inputs = [Data_chi_t_keras, Data_chi_tau_keras], outputs = K_both_msm)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-01-15T14:26:19.932777Z",
     "start_time": "2020-01-15T14:26:19.909090Z"
    }
   },
   "outputs": [],
   "source": [
    "# Define a model to predict to get access to the matrix S omitting the chi network\n",
    "model_S_both_msm = keras.models.Model(inputs =  [Data_chi_t_keras, Data_chi_tau_keras], outputs = S_both_msm)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-01-15T14:26:19.962357Z",
     "start_time": "2020-01-15T14:26:19.935347Z"
    }
   },
   "outputs": [],
   "source": [
    "# Define a helper model to get access to intermediate results\n",
    "model_input_S_msm = keras.models.Model(inputs = [Data_chi_t_keras, Data_chi_tau_keras], outputs = [tf_v_both_msm, tf_C_00_both_msm, tf_C_11_both_msm , tf_C_01_both_msm, Sigma_both_msm])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-01-15T14:26:20.018674Z",
     "start_time": "2020-01-15T14:26:19.967982Z"
    }
   },
   "outputs": [],
   "source": [
    "# Define a model to train only for S with VAMP-E\n",
    "model_S_vampE_msm = keras.models.Model(inputs = [Data_v_keras, Data_C_00_keras, Data_C_11_keras, Data_C_01_keras, Data_Sigma_keras], outputs = VampE_matrix_S_msm)\n",
    "model_S_vampE_msm.compile(keras.optimizers.Adam(learning_rate=learning_rate*1000, ),\n",
    "                 loss_vampe,\n",
    "             )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-01-15T14:26:20.031522Z",
     "start_time": "2020-01-15T14:26:20.020318Z"
    }
   },
   "outputs": [],
   "source": [
    "# Define models to predict the transition matrix and the S matrix omitting the chi network and u layer\n",
    "model_K_S_msm = keras.models.Model(inputs = [Data_v_keras, Data_C_00_keras, Data_C_11_keras, Data_C_01_keras, Data_Sigma_keras], outputs = K_S_msm)\n",
    "model_S_S_msm = keras.models.Model(inputs = [Data_v_keras, Data_C_00_keras, Data_C_11_keras, Data_C_01_keras, Data_Sigma_keras], outputs = S_S_msm)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Train chi"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-01-15T14:26:20.068133Z",
     "start_time": "2020-01-15T14:26:20.033011Z"
    }
   },
   "outputs": [],
   "source": [
    "# define helper function to re-initilize the layers of the chi network\n",
    "def get_initializers_list(model):\n",
    "    list_initializers = []\n",
    "    for layer in model_chi.layers:\n",
    "        if layer:\n",
    "            [list_initializers.append(t) for t in layer.variables]\n",
    "    return list_initializers"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-01-15T14:26:20.096135Z",
     "start_time": "2020-01-15T14:26:20.070162Z"
    }
   },
   "outputs": [],
   "source": [
    "# define a function to predict the chi for all short trajectories with just one call \n",
    "# to the graphics cards to increase performance\n",
    "# therefore appropriate reshaping is necessary\n",
    "\n",
    "def predict(model, trajs):\n",
    "    resh_traj = trajs.reshape(-1)\n",
    "    batch_size_traj = resh_traj.shape[0]\n",
    "    pred = model.predict([whiten(resh_traj), whiten(resh_traj)],batch_size = batch_size_traj)\n",
    "    pred_arr = pred.reshape(*trajs.shape, 2*output_size)[:,:,:output_size]\n",
    "    pred_list = [t for t in pred_arr]\n",
    "    return pred_list"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Define helper functions for building symmetrized VAMP2 model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-01-15T14:26:20.278496Z",
     "start_time": "2020-01-15T14:26:20.100864Z"
    }
   },
   "outputs": [],
   "source": [
    "def loss_VAMP2_autograd_sym(y_true, y_pred):\n",
    "    '''Calculates the VAMP-2 score with respect to the network lobes while \n",
    "    symmetrizing the correlation matrices. Can be used as a loss function\n",
    "    for keras models.\n",
    "    Parameters\n",
    "    ----------\n",
    "    y_true: tensorflow tensor.\n",
    "        parameter not needed for the calculation, added to comply with Keras\n",
    "        rules for loss fuctions format.\n",
    "\n",
    "    y_pred: tensorflow tensor with shape [batch_size, 2 * output_size]\n",
    "        output of the two lobes of the network\n",
    "\n",
    "    Returns\n",
    "    -------\n",
    "    loss_score: tensorflow tensor with shape [1].\n",
    "    '''\n",
    "\n",
    "    # Remove the mean from the data\n",
    "    x, y, batch_size, output_size = _prep_data(y_pred) \n",
    "\n",
    "    # Calculate the covariance matrices\n",
    "    cov_01 = 1/(batch_size - 1) * tf.matmul(x, y, transpose_b=True)\n",
    "    cov_00 = 1/(batch_size - 1) * tf.matmul(x, x, transpose_b=True) \n",
    "    cov_11 = 1/(batch_size - 1) * tf.matmul(y, y, transpose_b=True)\n",
    "    \n",
    "    cov_00 = 1/2*(cov_00 + cov_11)\n",
    "    cov_01 = 1/2*(cov_01 + tf.transpose(cov_01))\n",
    "    \n",
    "    # Calculate the inverse of the self-covariance matrices\n",
    "    cov_00_inv = _inv(cov_00, ret_sqrt = True)\n",
    "    cov_11_inv = cov_00_inv\n",
    "\n",
    "    vamp_matrix = tf.matmul(tf.matmul(cov_00_inv, cov_01), cov_11_inv)\n",
    "\n",
    "\n",
    "    vamp_score = tf.norm(vamp_matrix)\n",
    "\n",
    "    return - tf.square(vamp_score)\n",
    "\n",
    "def _inv(x, ret_sqrt=False):\n",
    "    '''Utility function that returns the inverse of a matrix, with the\n",
    "    option to return the square root of the inverse matrix.\n",
    "    Parameters\n",
    "    ----------\n",
    "    x: numpy array with shape [m,m]\n",
    "        matrix to be inverted\n",
    "\n",
    "    ret_sqrt: bool, optional, default = False\n",
    "        if True, the square root of the inverse matrix is returned instead\n",
    "    Returns\n",
    "    -------\n",
    "    x_inv: numpy array with shape [m,m]\n",
    "        inverse of the original matrix\n",
    "    '''\n",
    "\n",
    "    # Calculate eigvalues and eigvectors\n",
    "    eigval_all, eigvec_all = tf.self_adjoint_eig(x)\n",
    "\n",
    "    # Filter out eigvalues below threshold and corresponding eigvectors\n",
    "    eig_th = tf.constant(epsilon, dtype=tf.float32)\n",
    "    index_eig = tf.to_int32(eigval_all > eig_th)\n",
    "    _, eigval = tf.dynamic_partition(eigval_all, index_eig, 2)\n",
    "    _, eigvec = tf.dynamic_partition(tf.transpose(eigvec_all), index_eig, 2)\n",
    "\n",
    "    # Build the diagonal matrix with the filtered eigenvalues or square\n",
    "    # root of the filtered eigenvalues according to the parameter\n",
    "    eigval_inv = tf.diag(1/eigval)\n",
    "    eigval_inv_sqrt = tf.diag(tf.sqrt(1/eigval))\n",
    "\n",
    "    cond_sqrt = tf.convert_to_tensor(ret_sqrt)\n",
    "\n",
    "    diag = tf.cond(cond_sqrt, lambda: eigval_inv_sqrt, lambda: eigval_inv)\n",
    "\n",
    "    # Rebuild the square root of the inverse matrix\n",
    "    x_inv = tf.matmul(tf.transpose(eigvec), tf.matmul(diag, eigvec))\n",
    "\n",
    "    return x_inv\n",
    "\n",
    "\n",
    "def _prep_data(data):\n",
    "    '''Utility function that transorms the input data from a tensorflow - \n",
    "    viable format to a structure used by the following functions in the\n",
    "    pipeline.\n",
    "    Parameters\n",
    "    ----------\n",
    "    data: tensorflow tensor with shape [b, 2*o]\n",
    "        original format of the data\n",
    "    Returns\n",
    "    -------\n",
    "    x: tensorflow tensor with shape [o, b]\n",
    "        transposed, mean-free data corresponding to the left, lag-free lobe\n",
    "        of the network\n",
    "\n",
    "    y: tensorflow tensor with shape [o, b]\n",
    "        transposed, mean-free data corresponding to the right, lagged lobe\n",
    "        of the network\n",
    "\n",
    "    b: tensorflow float32\n",
    "        batch size of the data\n",
    "\n",
    "    o: int\n",
    "        output size of each lobe of the network\n",
    "\n",
    "    '''\n",
    "\n",
    "    shape = tf.shape(data)\n",
    "    b = tf.to_float(shape[0])\n",
    "    o = shape[1]//2\n",
    "\n",
    "    # Split the data of the two networks and transpose it\n",
    "    x_biased = tf.transpose(data[:,:o])\n",
    "    y_biased = tf.transpose(data[:,o:])\n",
    "\n",
    "    # Subtract the mean\n",
    "    x = x_biased - tf.reduce_mean(x_biased, axis=1, keepdims=True)\n",
    "    y = y_biased - tf.reduce_mean(y_biased, axis=1, keepdims=True)\n",
    "\n",
    "    return x, y, b, o"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Train Vampnets"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-01-15T14:28:56.694755Z",
     "start_time": "2020-01-15T14:26:20.688798Z"
    }
   },
   "outputs": [],
   "source": [
    "# train a chi model, uses loss_VAMP_sym pretraining for a faster convergence \n",
    "# to a probabilistic encoding\n",
    "\n",
    "model_chi.compile(\n",
    "    keras.optimizers.Adam(learning_rate=learning_rate*0.1),\n",
    "    vamp._loss_VAMP_sym,\n",
    "    metrics = [\n",
    "              vamp.metric_VAMP,\n",
    "              vamp.metric_VAMP2,]\n",
    ")\n",
    "\n",
    "[reset_weights(v) for v in get_initializers_list(model_chi)]\n",
    "\n",
    "hist = model_chi.fit([whiten(X1_train), whiten(X2_train)], Y_train ,\n",
    "                 batch_size = batch_size,\n",
    "                 epochs = epoch_chi,\n",
    "                 validation_data=([whiten(X1_vali), whiten(X2_vali)], Y_vali ),\n",
    "                 verbose=0,\n",
    "                 shuffle=True)\n",
    "\n",
    "model_chi.compile(\n",
    "    keras.optimizers.Adam(learning_rate=learning_rate*0.1),\n",
    "    vamp.loss_VAMP2_autograd,\n",
    "    metrics = [\n",
    "              vamp.metric_VAMP,\n",
    "              vamp.metric_VAMP2,]\n",
    ")\n",
    "\n",
    "hist = model_chi.fit([whiten(X1_train), whiten(X2_train)], Y_train ,\n",
    "                 batch_size = batch_size,\n",
    "                 epochs = epoch_chi,\n",
    "                 validation_data=([whiten(X1_vali), whiten(X2_vali)], Y_vali ),\n",
    "                 verbose=0,\n",
    "                 shuffle=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Plot $\\chi$ output"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-01-15T14:28:57.309396Z",
     "start_time": "2020-01-15T14:28:56.696286Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fb483f102b0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plot the chi function\n",
    "\n",
    "pred_ord_chi = predict(model_chi, training_trajs)\n",
    "\n",
    "xax = np.linspace(-1, 1, 10000)\n",
    "pred_xax = model_chi.predict([whiten(xax), whiten(xax)], batch_size=xax.shape[0])[:,:output_size]\n",
    "for i in range(output_size):\n",
    "    plt.plot(xax, pred_xax[:,i])\n",
    "pot = data_generator.prinz_energy(xax)\n",
    "plt.plot(xax, pot / pot.max())\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-01-15T14:32:26.030322Z",
     "start_time": "2020-01-15T14:32:26.022955Z"
    }
   },
   "outputs": [],
   "source": [
    "np.save('../vampnet_wip/prinz_traj_test', pred_ord_chi)\n",
    "np.save('../vampnet_wip/prinz_pred_xax_test', pred_xax)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "ExecuteTime": {
     "start_time": "2020-01-10T14:19:54.928Z"
    }
   },
   "outputs": [],
   "source": [
    "# Save weights to reuse as initialization of training other models\n",
    "weights_chi = model_chi.get_weights()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Train symVAMPnet"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "ExecuteTime": {
     "start_time": "2020-01-10T14:20:00.613Z"
    },
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "model_chi.compile(\n",
    "    keras.optimizers.Adam(learning_rate=learning_rate*1),\n",
    "    loss_VAMP2_autograd_sym,\n",
    "    metrics = [\n",
    "              loss_VAMP2_autograd_sym,\n",
    "              vamp.metric_VAMP,\n",
    "    ]\n",
    ")\n",
    "\n",
    "[reset_weights(v) for v in get_initializers_list(model_chi)]\n",
    "\n",
    "model_chi.set_weights(weights_chi)\n",
    "\n",
    "hist = model_chi.fit([whiten(X1_train), whiten(X2_train)], Y_train ,\n",
    "                 batch_size = batch_size,\n",
    "                 epochs = epoch_chi,\n",
    "                 validation_data=([whiten(X1_vali), whiten(X2_vali)], Y_vali ),\n",
    "                 verbose=0,\n",
    "                 shuffle=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Plot $\\chi$ output"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-01-10T14:56:11.969734Z",
     "start_time": "2020-01-10T14:56:10.294066Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "pred_ord_chi = predict(model_chi, training_trajs)\n",
    "\n",
    "xax = np.linspace(-1, 1, 10000)\n",
    "pred_xax = model_chi.predict([whiten(xax), whiten(xax)], batch_size=xax.shape[0])[:,:output_size]\n",
    "for i in range(output_size):\n",
    "    plt.plot(pred_xax[:,i])\n",
    "pot = data_generator.prinz_energy(xax)\n",
    "plt.plot(pot / pot.max())\n",
    "plt.show()\n",
    "\n",
    "score_vamp_sym = model_chi.evaluate([whiten(X1_vali), whiten(X2_vali)],  batch_size=batch_size, verbose = 0)[-1]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Save weights for later analysis"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-01-10T14:56:13.634357Z",
     "start_time": "2020-01-10T14:56:13.630545Z"
    }
   },
   "outputs": [],
   "source": [
    "# weights_chi_sym = model_chi.get_weights()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Get mu and implied timescales for symVAMPnet\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-01-10T14:56:14.415773Z",
     "start_time": "2020-01-10T14:56:14.381450Z"
    }
   },
   "outputs": [],
   "source": [
    "# estimate the transition matrix while enforcing the symmetric counts for the correlation matrices\n",
    "K_mat_sym = estimate_koopman_op(pred_ord_chi, tau, force_symmetric = True)\n",
    "# estimate the covariance matrix non symmetric\n",
    "C00 = np.concatenate(pred_ord_chi, axis=0).T @ np.concatenate(pred_ord_chi, axis=0)\n",
    "# estimate the helper matrix according to the following paper:\n",
    "# https://arxiv.org/pdf/1610.06773, eq. 32\n",
    "shifted_K_sym = np.linalg.inv(C00) @ K_mat_sym.T @ C00"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-01-10T14:56:15.017861Z",
     "start_time": "2020-01-10T14:56:15.003706Z"
    }
   },
   "outputs": [],
   "source": [
    "# estimate the eigenvector of that matrix with eigenvalue 1\n",
    "ev, ew = np.linalg.eig(shifted_K_sym)\n",
    "u_vec = ew[:,np.argmin((ev-1)**2)]\n",
    "# estimate the stationary distribution\n",
    "mu_result_sym = np.concatenate(pred_ord_chi, axis=0) @ u_vec\n",
    "# normalize the stationary distribution\n",
    "mu_result_sym = mu_result_sym / mu_result_sym.sum()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-01-10T14:56:15.501655Z",
     "start_time": "2020-01-10T14:56:15.492710Z"
    }
   },
   "outputs": [],
   "source": [
    "# estimate the stationary distribution according to the model via the energy\n",
    "xax = np.linspace(-1,1,10000)\n",
    "prinz_en = data_generator.prinz_energy(xax)\n",
    "prinz_stat = np.exp(-prinz_en/kT_prinz)\n",
    "scaled_prinz_stat = prinz_stat / (prinz_stat.sum() * (xax[1]-xax[0]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-01-10T14:56:16.746103Z",
     "start_time": "2020-01-10T14:56:16.724526Z"
    }
   },
   "outputs": [],
   "source": [
    "# calculate a density out of the predicted stationary distribution of the symVAMPnet\n",
    "hist_sym, bin = np.histogram(training_trajs.reshape(-1), bins=200, range=(-1,1), density=True, weights=mu_result_sym)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-01-10T14:56:16.982062Z",
     "start_time": "2020-01-10T14:56:16.923356Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1\n",
      "2\n",
      "3\n",
      "4\n",
      "6\n",
      "8\n",
      "10\n"
     ]
    }
   ],
   "source": [
    "# estimate the transition matrixes for different taus for the symVAMPnet\n",
    "K_results = np.ones((len(tau_list) ,output_size, output_size))\n",
    "for i, tau_i in enumerate(tau_list):\n",
    "    print(tau_i)\n",
    "#     K_results_rev[i]= training_for_tau_both(tau_i)\n",
    "    K_results[i]  = estimate_koopman_op(pred_ord_chi, tau_i, force_symmetric = True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-01-10T14:56:17.620442Z",
     "start_time": "2020-01-10T14:56:17.099302Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plot the implied timescales against the true values\n",
    "timescale_real_values = np.array([ 11.53593249,  24.48666445, 163.41165771])\n",
    "for tsrv in timescale_real_values:\n",
    "    plt.hlines(tsrv, tau_list[0], tau_list[-1])\n",
    "vamp.plot_its(get_its(K_results, tau_list, False), tau_list)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-01-10T14:56:17.633174Z",
     "start_time": "2020-01-10T14:56:17.627196Z"
    }
   },
   "outputs": [],
   "source": [
    "# estimate the eigenvectors of the transition matrix of the symVAMPnet\n",
    "eigvals_sym, eigvec_sym = np.linalg.eig(K_mat_sym)\n",
    "sort_ind = np.argsort(eigvals_sym)[::-1]\n",
    "eigvals_sym = eigvals_sym[sort_ind]\n",
    "eigvec_sym = eigvec_sym[:,sort_ind]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-01-10T14:56:17.685651Z",
     "start_time": "2020-01-10T14:56:17.673573Z"
    }
   },
   "outputs": [],
   "source": [
    "# load the true eigenfunctions computed with a \n",
    "# high resolution MSM and euqilibrium trajectory\n",
    "data_true = np.load('./True_eigfunc_Prinz.npz')\n",
    "true_eigfunc = data_true['true_eigfunc']\n",
    "true_eigvals = data_true['true_eigvals']"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Plot eigenfunctions for symVAMPnet"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-01-10T14:56:20.413736Z",
     "start_time": "2020-01-10T14:56:19.641185Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# estimate the eigenfunctions\n",
    "eigfunc_sym = pred_xax @ eigvec_sym\n",
    "\n",
    "# plot them against the real once\n",
    "for i in range(1,output_size):\n",
    "    plt.title('Eigfunc with $\\lambda={:.3}$'.format(true_eigvals[i]), fontsize=18)\n",
    "    fac = true_eigfunc[0,i] / eigfunc_sym[0,i]\n",
    "    fac1 = true_eigfunc[0,i] / eigfunc_sym[0,i]\n",
    "    fac2 = true_eigfunc[-1,i] / eigfunc_sym[-1,i]\n",
    "    fac = (fac1 + fac2)/2\n",
    "    plt.plot(xax, fac*eigfunc_sym[:,i], label='Sym')\n",
    "    plt.plot(xax[::10], true_eigfunc[:,i], 'k', label='True')\n",
    "    plt.legend(fontsize=14)\n",
    "    plt.xlabel('x [a.u.]', fontsize=16)\n",
    "    plt.xticks([-1,-.5,0.,.5,1.],fontsize=14)\n",
    "    plt.yticks(fontsize=14)\n",
    "    plt.ylabel('$\\psi$ [a.u.]', fontsize=16)\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Training for revVAMPnet"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Initialization of u and S"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-01-10T14:56:23.877733Z",
     "start_time": "2020-01-10T14:56:23.702840Z"
    }
   },
   "outputs": [],
   "source": [
    "def optimize_u(factor_u, reset_chi=True):\n",
    "    ''' \n",
    "    Calculate the optimal u for a given chi via a non-reversible Koopman model, \n",
    "    and set the kernel of the corresponding layer to the optimal value. \n",
    "    This is necessary to stabilize the training.\n",
    "    Needs to be rewritten if the activation functions for the weights are changed!\n",
    "    '''\n",
    "    if reset_chi:\n",
    "        model_chi.set_weights(weights_chi)\n",
    "    fullbatch = X1_train.shape[0]\n",
    "        \n",
    "    Data_chi = model_chi.predict([whiten(X1_train), whiten(X2_train)], batch_size=fullbatch)\n",
    "    Data_chi_X = Data_chi[:,:output_size]\n",
    "    Data_chi_Y = Data_chi[:,output_size:]\n",
    "    fullbatch = Data_chi_X.shape[0]\n",
    "    \n",
    "    \n",
    "    c_0 = 1/fullbatch * Data_chi_X.T @ Data_chi_X\n",
    "    c_tau = 1/fullbatch * Data_chi_X.T @ Data_chi_Y\n",
    "    c_1 = 1/fullbatch * Data_chi_Y.T @ Data_chi_Y\n",
    "    \n",
    "    eigv_all, eigvec_all = np.linalg.eigh(c_0)\n",
    "    include = eigv_all > epsilon\n",
    "    eigv = eigv_all[include]\n",
    "    eigvec = eigvec_all[:,include]\n",
    "    c0_inv = eigvec @ np.diag(1/eigv) @ np.transpose(eigvec)\n",
    "        \n",
    "    K_vamp = c0_inv @ c_tau\n",
    "    \n",
    "    # estimate pi, the stationary distribution vector\n",
    "    eigv, eigvec = np.linalg.eig(K_vamp.T)\n",
    "    ind_pi = np.argmin((eigv-1)**2)\n",
    "    \n",
    "    pi_vec = eigvec[:,ind_pi]\n",
    "    pi = pi_vec / np.sum(pi_vec, keepdims=True)\n",
    "        \n",
    "    # reverse the consruction of u \n",
    "    u_optimal = c0_inv @ pi\n",
    "    u_kernel = u_optimal / factor_u\n",
    "    vamp_layer_u.set_weights([u_kernel])\n",
    "    \n",
    "    return None\n",
    "\n",
    "def optimize_S(factor_S, reset_chi=True):\n",
    "    ''' \n",
    "    Calculate the optimal S for a given chi, and set the kernel of the corresponding layer\n",
    "    to the optimal value. This is necessary to stabilize the training.\n",
    "    Needs to be rewritten if the activation functions for the weights are changed!\n",
    "    '''\n",
    "    if reset_chi:\n",
    "        model_chi.set_weights(weights_chi)\n",
    "    fullbatch = X1_train.shape[0]\n",
    "        \n",
    "    Data_chi = model_chi.predict([whiten(X1_train), whiten(X2_train)], batch_size=fullbatch)\n",
    "    Data_chi_X = Data_chi[:,:output_size]\n",
    "    Data_chi_Y = Data_chi[:,output_size:]\n",
    "    fullbatch = Data_chi_X.shape[0]\n",
    "    \n",
    "    \n",
    "    c_0 = 1/fullbatch * Data_chi_X.T @ Data_chi_X\n",
    "    c_tau = 1/fullbatch * Data_chi_X.T @ Data_chi_Y\n",
    "    c_1 = 1/fullbatch * Data_chi_Y.T @ Data_chi_Y\n",
    "    \n",
    "    eigv_all, eigvec_all = np.linalg.eigh(c_0)\n",
    "    include = eigv_all > epsilon\n",
    "    eigv = eigv_all[include]\n",
    "    eigvec = eigvec_all[:,include]\n",
    "    c0_inv = eigvec @ np.diag(1/eigv) @ np.transpose(eigvec)\n",
    "        \n",
    "    K_vamp = c0_inv @ c_tau\n",
    "    \n",
    "    # get Sigma, invert it to get proxy S, meaning the closest symmetric S you can obtain to the optimal S\n",
    "    \n",
    "    v_input, C_00_input, C_11_input, C_01_input, Sigma_input = model_input_S.predict([Data_chi_X, Data_chi_Y], batch_size=Data_chi_X.shape[0])\n",
    "    \n",
    "    eigv_all, eigvec_all = np.linalg.eigh(Sigma_input[0])\n",
    "    include = eigv_all > epsilon\n",
    "    eigv = eigv_all[include]\n",
    "    eigvec = eigvec_all[:,include]\n",
    "    sigma_inv = eigvec @ np.diag(1/eigv) @ np.transpose(eigvec)\n",
    "    \n",
    "    # reverse the construction of S\n",
    "    S_nonrev = K_vamp @ sigma_inv\n",
    "    S_rev_add = 1/2 * (S_nonrev + S_nonrev.T)\n",
    "    kernel_S = S_rev_add / 2. / factor_S\n",
    "    \n",
    "    vamp_layer_S.set_weights([kernel_S])\n",
    "        \n",
    "    return None"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-01-10T14:56:26.534531Z",
     "start_time": "2020-01-10T14:56:24.455170Z"
    }
   },
   "outputs": [],
   "source": [
    "optimize_u(factor_u)\n",
    "optimize_S(factor_S)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Train $\\mathbf{u}$, and $\\mathbf{S}$ with full batch"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-01-10T14:57:55.977452Z",
     "start_time": "2020-01-10T14:57:36.599050Z"
    },
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "W0113 17:05:08.468381 140620064429888 deprecation.py:323] From /storage/mi/andreasmardt/anaconda3/envs/tf14/lib/python3.7/site-packages/tensorflow/python/ops/clip_ops.py:157: add_dispatch_support.<locals>.wrapper (from tensorflow.python.ops.array_ops) is deprecated and will be removed in a future version.\n",
      "Instructions for updating:\n",
      "Use tf.where in 2.0, which has the same broadcast rule as np.where\n"
     ]
    }
   ],
   "source": [
    "vamp_layer_u.trainable = True\n",
    "vamp_layer_S.trainable = True\n",
    "\n",
    "Data_chi = model_chi.predict([whiten(X1_train), whiten(X2_train)], batch_size=X1_train.shape[0])\n",
    "\n",
    "Data_chi_X = Data_chi[:,:output_size]\n",
    "Data_chi_Y = Data_chi[:,output_size:]\n",
    "\n",
    "Data_chi_vali = model_chi.predict([whiten(X1_vali), whiten(X2_vali)], batch_size=X1_vali.shape[0])\n",
    "\n",
    "Data_chi_X_vali = Data_chi_vali[:,:output_size]\n",
    "Data_chi_Y_vali = Data_chi_vali[:,output_size:]\n",
    "\n",
    "\n",
    "model_both_vampE.compile(\n",
    "    keras.optimizers.Adam(learning_rate=learning_rate*10000, clipnorm=1.),\n",
    "    loss_vampe,\n",
    ")\n",
    "\n",
    "hist = model_both_vampE.fit([Data_chi_X, Data_chi_Y], Y_train ,\n",
    "                 batch_size=Data_chi_X.shape[0],\n",
    "                 epochs = epoch_S,\n",
    "                 validation_data=([Data_chi_X_vali, Data_chi_Y_vali], Y_vali ),\n",
    "                 verbose=0,\n",
    "                 callbacks=[EarlyStopping('val_loss', patience=100, mode='min', restore_best_weights=True)],\n",
    "                 shuffle=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Train $\\boldsymbol{\\chi}$, $\\mathbf{u}$, and $\\mathbf{S}$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {
    "ExecuteTime": {
     "start_time": "2020-01-10T14:57:39.730Z"
    },
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "vamp_layer_u.trainable = True\n",
    "vamp_layer_S.trainable = True\n",
    "\n",
    "model_all_vampE.compile(\n",
    "    keras.optimizers.Adam(learning_rate=learning_rate*0.04,  clipnorm=1.),\n",
    "    loss_vampe,\n",
    ")\n",
    "\n",
    "hist = model_all_vampE.fit(\n",
    "    [whiten(X1_train), whiten(X2_train)],\n",
    "    Y_train,\n",
    "    batch_size = X1_train.shape[0],\n",
    "    epochs = epoch_all,\n",
    "    validation_data = ([whiten(X1_vali), whiten(X2_vali)], Y_vali ),\n",
    "    verbose = 0,\n",
    "    callbacks = [EarlyStopping('val_loss', patience=100, mode='min', restore_best_weights=True)],\n",
    "    shuffle = True\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {
    "ExecuteTime": {
     "start_time": "2020-01-10T14:57:40.771Z"
    }
   },
   "outputs": [],
   "source": [
    "K_result = model_K_all.predict([whiten(X1_train), whiten(X2_train)], batch_size=X1_train.shape[0])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Estimate $\\mu$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {
    "ExecuteTime": {
     "start_time": "2020-01-10T14:57:42.070Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Error of rev: 0.9238958094052178, of sym: 5.0150186078936985\n"
     ]
    }
   ],
   "source": [
    "# plot the stationary distribution and compare them to the result of the symVAMPnet\n",
    "\n",
    "mu_result_rev = model_mu.predict([whiten(X1_train), whiten(X2_train)], batch_size=X1_train.shape[0])\n",
    "\n",
    "hist_rev, bin = np.histogram(X1_train.reshape(-1), bins=200, range=(-1,1), density=True, weights=mu_result_rev.reshape(-1))\n",
    "prinz_en = data_generator.prinz_energy(bin[:-1])\n",
    "prinz_stat = np.exp(-prinz_en/kT_prinz)\n",
    "scaled_prinz_stat = prinz_stat / (prinz_stat.sum() * (bin[1]-bin[0]))       \n",
    "plt.plot(bin[:-1], scaled_prinz_stat, label = 'True', c='k')\n",
    "plt.plot(bin[:-1], hist_rev, label = 'Rev')\n",
    "plt.plot(bin[:-1], hist_sym, label = 'Sym')\n",
    "plt.legend()\n",
    "plt.show()\n",
    "\n",
    "rev_states_prob = np.sum(np.split(hist_rev, 4), 1)\n",
    "sym_states_prob = np.sum(np.split(hist_sym, 4), 1)\n",
    "tru_states_prob = np.sum(np.split(scaled_prinz_stat, 4), 1)\n",
    "plt.plot(np.abs(rev_states_prob), '.', ms=12, label = \"Rev\")\n",
    "plt.plot(np.abs(sym_states_prob), '.', ms=12, label = \"Sym\")\n",
    "for j in range(4):\n",
    "    legend=None\n",
    "    if j>2:\n",
    "        legend='True'\n",
    "    plt.hlines(tru_states_prob[j], j-0.3, j+0.3, colors='k', linestyles='--', label=legend, lw=2)\n",
    "plt.legend()\n",
    "plt.show()\n",
    "\n",
    "print('Error of rev: {}, of sym: {}'.format(np.linalg.norm(hist_rev - prinz_stat), np.linalg.norm(hist_sym - prinz_stat)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Estimate eigenfunctions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Estimate the eigenfunctions for the revVAMPnet\n",
    "K_rev = model_K_all.predict([whiten(X1_train), whiten(X2_train)], batch_size=X1_train.shape[0])[0]\n",
    "eigvals_rev, eigvec_rev = np.linalg.eig(K_rev)\n",
    "\n",
    "sort_ind = np.argsort(eigvals_rev)[::-1]\n",
    "eigvals_rev = eigvals_rev[sort_ind]\n",
    "eigvec_rev = eigvec_rev[:,sort_ind]\n",
    "\n",
    "pred_xax = model_chi.predict([whiten(xax), whiten(xax)], batch_size=xax.shape[0])[:,:output_size]\n",
    "eigfunc_rev1 = pred_xax @ eigvec_rev\n",
    "\n",
    "for i in range(1,output_size):\n",
    "    plt.title('Eigfunc with $\\lambda={:.3}$'.format(true_eigvals[i]), fontsize=18)\n",
    "    fac = true_eigfunc[0,i] / eigfunc_rev1[0,i]\n",
    "    fac = true_eigfunc[-1,i] / eigfunc_rev1[-1,i]\n",
    "    fac1 = true_eigfunc[0,i] / eigfunc_rev1[0,i]\n",
    "    fac2 = true_eigfunc[-1,i] / eigfunc_rev1[-1,i]\n",
    "    fac = (fac1 + fac2)/2\n",
    "    plt.plot(xax, fac*eigfunc_rev1[:,i], label='Rev')\n",
    "    plt.plot(xax[::10], true_eigfunc[:,i], 'k', label='True')\n",
    "    plt.legend(fontsize=16)\n",
    "    plt.xlabel('x [a.u.]', fontsize=16)\n",
    "    plt.xticks([-1.,-.5,0,0.5,1.],fontsize=14)\n",
    "    plt.yticks(fontsize=14)\n",
    "    plt.ylabel('$\\psi$ [a.u.]', fontsize=16)\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Training loop with reseting u, stopping criteria via validation set score"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Old score 0.0, new score 3.7550110816955566\n",
      "Score is better and weights are saved\n",
      "Old score 3.7550110816955566, new score 3.754998207092285\n"
     ]
    }
   ],
   "source": [
    "# train for an optimal model while resetting u to an optimal solution for the given chi. \n",
    "# This should stabilize the training\n",
    "\n",
    "# starting conditions\n",
    "score = 0.\n",
    "weights_all = model_all_vampE.get_weights()\n",
    "score_old = score\n",
    "\n",
    "\n",
    "model_both_vampE.compile(\n",
    "    keras.optimizers.Adam(learning_rate=learning_rate*10000, clipnorm=1.),\n",
    "    loss_vampe,\n",
    ")\n",
    "\n",
    "callbacks = [EarlyStopping('val_loss', patience=100, mode='min', restore_best_weights=True)]\n",
    "\n",
    "# while the score is not improving of the validation/test set do the following\n",
    "while (score >= score_old):\n",
    "    \n",
    "    # set u to the optimal value\n",
    "    optimize_u(factor_u, reset_chi=False)\n",
    "\n",
    "    vamp_layer_u.trainable = True\n",
    "    vamp_layer_S.trainable = True\n",
    "    \n",
    "    Data_chi = model_chi.predict([whiten(X1_train), whiten(X2_train)], batch_size=X1_train.shape[0])\n",
    "    Data_chi_X = Data_chi[:,:output_size]\n",
    "    Data_chi_Y = Data_chi[:,output_size:]\n",
    "    \n",
    "    Data_chi_vali = model_chi.predict([whiten(X1_vali), whiten(X2_vali)], batch_size=X1_vali.shape[0])\n",
    "    Data_chi_X_vali = Data_chi_vali[:,:output_size]\n",
    "    Data_chi_Y_vali = Data_chi_vali[:,output_size:]\n",
    "    \n",
    "    # train u and S\n",
    "    hist = model_both_vampE.fit([Data_chi_X, Data_chi_Y], Y_train ,\n",
    "                     batch_size = Data_chi_X.shape[0],\n",
    "                     epochs = epoch_S,\n",
    "                     validation_data = ([Data_chi_X_vali, Data_chi_Y_vali], Y_vali ),\n",
    "                     verbose = 0,\n",
    "                     callbacks = callbacks,\n",
    "                     shuffle = True)\n",
    "\n",
    "    # train for all, chi, u, and S\n",
    "    hist = model_all_vampE.fit(\n",
    "        [whiten(X1_train), whiten(X2_train)],\n",
    "        Y_train,\n",
    "        batch_size = X1_train.shape[0],\n",
    "        epochs = epoch_all,\n",
    "        validation_data = ([whiten(X1_vali), whiten(X2_vali)], Y_vali ),\n",
    "        verbose = 0,\n",
    "        shuffle = True\n",
    "    )\n",
    "\n",
    "    # check if validation score is better than before\n",
    "    score = - model_all_vampE.evaluate([whiten(X1_vali), whiten(X2_vali)], batch_size=X1_vali.shape[0], verbose = 0)\n",
    "    print('Old score {}, new score {}'.format(score_old, score))\n",
    "    if (score>score_old):\n",
    "        print('Score is better and weights are saved')\n",
    "        score_old = score\n",
    "        weights_all = model_all_vampE.get_weights()\n",
    "        \n",
    "# reset to the best model        \n",
    "model_all_vampE.set_weights(weights_all)\n",
    "# optimize once more\n",
    "optimize_u(factor_u, reset_chi=False)\n",
    "\n",
    "Data_chi = model_chi.predict([whiten(X1_train), whiten(X2_train)], batch_size=X1_train.shape[0])\n",
    "Data_chi_X = Data_chi[:,:output_size]\n",
    "Data_chi_Y = Data_chi[:,output_size:]\n",
    "\n",
    "Data_chi_vali = model_chi.predict([whiten(X1_vali), whiten(X2_vali)], batch_size=X1_vali.shape[0])\n",
    "Data_chi_X_vali = Data_chi_vali[:,:output_size]\n",
    "Data_chi_Y_vali = Data_chi_vali[:,output_size:]\n",
    "\n",
    "hist = model_both_vampE.fit([Data_chi_X, Data_chi_Y], Y_train ,\n",
    "                 batch_size=Data_chi_X.shape[0],\n",
    "                 epochs = epoch_S,\n",
    "                 validation_data=([Data_chi_X_vali, Data_chi_Y_vali], Y_vali ),\n",
    "                 verbose=0,\n",
    "                 callbacks=callbacks,\n",
    "                 shuffle=True)\n",
    "weights_chi_rev = model_all_vampE.get_weights()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXAAAAD4CAYAAAD1jb0+AAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADh0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uMy4xLjAsIGh0dHA6Ly9tYXRwbG90bGliLm9yZy+17YcXAAAXL0lEQVR4nO3dcXCU9Z3H8fc3cTUZsQQh9oBoQWsZEWJiIqPjzJkRWqgnFR2ldDqcduhEr7XYuYpKp6PUaefsoPWGGdrretqjZ680Y5Fazw5SWnXqWbmsxIBNc3g3KAkIkRoUu9QYv/fHbmKIG7Kb7GafX/J5zezsPr/n9+zz5ad+fPg9zz6PuTsiIhKekmIXICIiI6MAFxEJlAJcRCRQCnARkUApwEVEAnXKWO5s2rRpPmvWrLHcpYhI8BKJxJvuXjm4fUwDfNasWTQ3N4/lLkVEgmdmr2Vq1xSKiEigFOAiIoFSgIuIBGpM58BFREaip6eHjo4Ojh8/XuxSCqqsrIyqqipisVhW/RXgIhJ5HR0dnHHGGcyaNQszK3Y5BeHuHDlyhI6ODmbPnp3VNppCkcJobYIH58G6itR7a1OxK5KAHT9+nKlTp47b8AYwM6ZOnZrT3zJ0BC7519oEv1oNPcnU8tH9qWWA6uXFq0uCNp7Du0+uf0YdgUv+7bj3w/Du05NMtYtI3ijAJf+OduTWLhKA0tJSampqmDdvHkuXLqW7u7vYJSnApQAmV+XWLpJnW3d1cvl9v2X2Xf/J5ff9lq27Okf9neXl5bS0tLBnzx7OPPNMNm7cmIdKR0cBLvm38G6IlZ/YFitPtYsU2NZdnazdspvO7iQOdHYnWbtld15CvM9ll11GZ+eH37d+/XouueQSqqurueeeewC48847+cEPftDfZ926dTzwwAN5qwEU4FII1cth6QaYfDZgqfelG3QCU8bE+m3tJHt6T2hL9vSyflt7Xr6/t7eXHTt28LnPfQ6Ap59+mr1797Jz505aWlpIJBI899xzrFixgp///Of92zU1NXHDDTfkpYY+ugpFCqN6uQJbiuJAdzKn9mwlk0lqamrYt28fdXV1fPrTnwZSAf70009TW1sLwLFjx9i7dy+rVq3i8OHDHDhwgK6uLqZMmcI555wzqhoGU4CLyLgyo6KczgxhPaOiPEPv7PXNgR89epSrr76ajRs3snr1atydtWvXcvPNN39km+uvv57HHnuMN954gxUrVoxq/5loCkVExpU1i+dQHis9oa08VsqaxXPy8v2TJ09mw4YN3H///fT09LB48WIeeeQRjh07BkBnZyeHDx8GYMWKFWzevJnHHnuM66+/Pi/7H0hH4CIyriyrnQmk5sIPdCeZUVHOmsVz+tvzoba2losuuojNmzezcuVK2trauOyyywCYNGkSjz76KGeddRYXXngh77zzDjNnzmT69Ol5238fc/e8f+lQ6uvrXQ90EJFctbW1ccEFFxS7jDGR6c9qZgl3rx/cV1MoIiKBUoCLiARKAS4iEigFuIhIoBTgIiKBUoCLiARKAS4ikqXvfve7XHjhhVRXV1NTU8OLL75Y1Hr0Qx4RGX9am1IPEDnakbqN8cK7R31vnhdeeIEnn3ySl156idNOO40333yT9957L08Fj0zWR+BmVmpmu8zsyfTymWa23cz2pt+nFK5MEZEs9T3S7+h+wD98pN8on8t68OBBpk2bxmmnnQbAtGnTaGtr49prr+3vs337dq677jog9YvMO++8k7q6OhYtWsTOnTtpaGjg3HPP5YknnhhVLX1ymUK5DWgbsHwXsMPdzwd2pJdFRIqrQI/0+8xnPsP+/fv51Kc+xVe+8hWeffZZrrzyStra2ujq6gLgxz/+MV/60pcAePfdd2loaCCRSHDGGWfwrW99i+3bt/P4449z9935uTd+VgFuZlXA3wH/OqD5GmBT+vMmYFleKhIRGY0CPdJv0qRJJBIJ4vE4lZWVfP7zn2fTpk2sXLmSRx99lO7ubl544QU++9nPAnDqqaeyZMkSAObPn88VV1xBLBZj/vz57Nu3b1S19Ml2DvyfgTuAMwa0fdzdDwK4+0EzOyvThmbWCDQCeb8XrojIR0yuSk+fZGgfpdLSUhoaGmhoaGD+/Pls2rSJH/3oRyxdupSysjJuuOEGTjklFauxWKz/KfMlJSX9Uy8lJSW8//77o64FsjgCN7OrgcPunhjJDtw97u717l5fWVk5kq8QEclegR7p197ezt69e/uXW1pa+MQnPsGMGTOYMWMG3/nOd7jppptGtY9cZXMEfjnwOTO7CigDPmZmjwKHzGx6+uh7OnC4kIWKiGSl72qTPF+FcuzYMb72ta/R3d3NKaecwic/+Uni8TgAX/ziF+nq6mLu3LmjrT4nOd1O1swagNvd/WozWw8ccff7zOwu4Ex3v+Nk2+t2siIyElG/neytt95KbW0tq1atGvV35XI72dFcB34f0GRmq4DXgfw+rVNEJAB1dXWcfvrpeX/ifDZyCnB3fwZ4Jv35CLAw/yWJiIQjkRjR6cG80E/pRUQCpQAXEQmUAlxEJFAKcBGRQOluhCIiwzhy5AgLF6au2XjjjTcoLS2l74eJO3fu5NRTTy1KXQpwEZFhTJ06lZaWFgDWrVvHpEmTuP3220/o4+64OyUlYzexoSkUEZERevXVV5k3bx633HILF198Mfv376eioqJ//ebNm/nyl78MwKFDh7juuuuor69nwYIF/OEPfxj1/hXgIhIcMxvy1ffzdoB4PH7Svvnwxz/+kVWrVrFr1y5mzpw5ZL/Vq1dzxx130NzcTFNTU3+wj4amUERERuG8887jkksuGbbfb37zG9rb2/uX33rrLZLJJOXl5SfZ6uQU4CISnGzv4dTY2EhjY2NBazn99NP7P5eUlJxQ2/Hjx/s/u3veT3hqCkVEJE9KSkqYMmUKe/fu5YMPPuDxxx/vX7do0SI2btzYv9x3UnRU+xv1N4iISL/vfe97LFmyhIULF1JV9eFDJDZu3Mjzzz9PdXU1c+fO5aGHHhr1vnK6nexo6XayIjISUb+dbD7lcjtZHYGLiARKAS4iEigFuIgEYSyne4sl1z+jAlxEIq+srIwjR46M6xB3d44cOUJZWVnW2+g6cBGJvKqqKjo6Oujq6ip2KQVVVlZ2wpUrw1GAi0jkxWIxZs+eXewyIkdTKCIigVKAi4gESgEuIhIoBbiISKCGDXAzKzOznWb2spm9YmbfTrevM7NOM2tJv64qfLkiItInm6tQ/gpc6e7HzCwG/N7Mfp1e96C731+48kREZCjDBrinrpw/ll6MpV/j92p6EZFAZDUHbmalZtYCHAa2u/uL6VW3mlmrmT1iZlOG2LbRzJrNrHm8X4QvIjKWsgpwd+919xqgClhgZvOAHwLnATXAQeCBIbaNu3u9u9dXVlbmqWwREcnpKhR37waeAZa4+6F0sH8APAQsKEB9IiIyhGyuQqk0s4r053JgEfAnM5s+oNu1wJ7ClCgiIplkcxXKdGCTmZWSCvwmd3/SzP7dzGpIndDcB9xcuDJFRGSwbK5CaQVqM7SvLEhFIpLR1l2drN/WzoHuJDMqylmzeA7LamcWuywpIt2NUCQAW3d1snbLbpI9vQB0didZu2U3gEJ8AtNP6UUCsH5be39490n29LJ+W3uRKpIoUICL5ImZDfmKx+P9/eLx+En7DlRXV4eZ0fHWuxn3eaA7CUAikTjpdyYSif5tGhsbh+xXV1dXgJGRQlGAiwSg9+03M7bPqCgf40okSmwsnzFXX1/vzc3NY7Y/kfFi8Bw4QHmslH+6br7mwCcAM0u4e/3gdp3EFAlAX0jrKhQZSAEuEohltTMV2HICzYGLiARKAS4iEigFuIhIoBTgIiKBUoCLiARKAS4iEigFuIhIoBTgIiKBUoCLiARKAS4iEigFuIhIoBTgIiKBUoCLiARKAS4iEigFuIhIoIYNcDMrM7OdZvaymb1iZt9Ot59pZtvNbG/6fUrhyxURkT7ZHIH/FbjS3S8CaoAlZnYpcBeww93PB3akl0VEZIwMG+Ceciy9GEu/HLgG2JRu3wQsK0iFIiKSUVZz4GZWamYtwGFgu7u/CHzc3Q8CpN/PGmLbRjNrNrPmrq6ufNUtIjLhZRXg7t7r7jVAFbDAzOZluwN3j7t7vbvXV1ZWjrROEREZJKerUNy9G3gGWAIcMrPpAOn3w3mvTkREhpTNVSiVZlaR/lwOLAL+BDwB3JjudiPwy0IVKSIiH3VKFn2mA5vMrJRU4De5+5Nm9gLQZGargNeBGwpYp4iIDDJsgLt7K1Cbof0IsLAQRYmIyPD0S0wRkUApwEVEAqUAFxEJlAJcRCRQCnARkUApwEVEAqUAFxEJlAJcRCRQCnARkUApwEVEAqUAFxEJlAK8T2sTPDgP1lWk3lubil2RiMhJZXM3wvGvtQl+tRp6kqnlo/tTywDVy4tXl4jISegIHGDHvR+Gd5+eZKpdRCSiFOAARztyaxcRiQAFOMDkqtzaRUQiQAEOsPBuiJWf2BYrT7WLSNGY2ZCveDze3y8ej5+070B1dXVD9mtsbOzvl0gkTvqdiUSiv29jY+OQ/erq6go2PgpwSJ2oXLoBJp8NWOp96QadwBSRSDN3H7Od1dfXe3Nz85jtT0RkKFt3dbJ+WzsHupPMqChnzeI5LKudWeyyMjKzhLvXD27XZYQiMuFs3dXJ2i27Sfb0AtDZnWTtlt0AkQ3xTDSFIiITzvpt7f3h3SfZ08v6be1FqmhkFOAiMuEc6E7m1B5Vwwa4mZ1tZr8zszYze8XMbku3rzOzTjNrSb+uKny5IiKjN6OiPKf2qMrmCPx94BvufgFwKfBVM5ubXvegu9ekX08VrEoRkTxas3gO5bHSE9rKY6WsWTynSBWNzLAnMd39IHAw/fkdM2sDwpnlFxEZpO9EZShXoQwlp8sIzWwW8BwwD/hH4CbgbaCZ1FH6Wxm2aQQaAc4555y61157bbQ1i4hMKENdRpj1SUwzmwT8Avi6u78N/BA4D6ghdYT+QKbt3D3u7vXuXl9ZWTmi4kVE5KOyCnAzi5EK75+6+xYAdz/k7r3u/gHwELCgcGWKiMhg2VyFYsDDQJu7f39A+/QB3a4F9uS/PBERGUo2v8S8HFgJ7DazlnTbN4EvmFkN4MA+4OaCVCgiIhllcxXK7wHLsEqXDYqIFJF+iSkiEigFuIhIoHQ3QimIkG7VKRIqBbjk3Xi5VadI1GkKZQIr1OOqbo0/nfFWnXf9x3/1L4fwuCqRqFOAS96VfmxaxvbjJWHd6U0k6vRINcm7y+/7LZ0Z7qs8s6Kc5++6sggViYRt1PdCEcnWeLlVp0jU6SSm5N14uVWnSNQpwKUgltXOVGCLFJimUEREAqUAFxEJlAJcRCRQCnARkUApwEVEAqUAFxEJlAJcRCRQCnARkUApwEVEAqUAFxEJlAJcRCRQCnARkUANG+BmdraZ/c7M2szsFTO7Ld1+ppltN7O96fcphS9XRET6ZHME/j7wDXe/ALgU+KqZzQXuAna4+/nAjvSyiIiMkWED3N0PuvtL6c/vAG3ATOAaYFO62yZgWaGKFBGRj8ppDtzMZgG1wIvAx939IKRCHjgr38WJiMjQsg5wM5sE/AL4uru/ncN2jWbWbGbNXV1dI6lRREQyyCrAzSxGKrx/6u5b0s2HzGx6ev104HCmbd097u717l5fWVmZj5pFRITsrkIx4GGgzd2/P2DVE8CN6c83Ar/Mf3kiIjKUbJ6JeTmwEthtZi3ptm8C9wFNZrYKeB24oTAliohIJsMGuLv/HrAhVi/MbzkiIpIt/RJTRCRQCnARkUApwEVC0doED86DdRWp99amYlckRZbNSUwRKbbWJvjVauhJppaP7k8tA1QvL15dUlQ6AhcJwY57PwzvPj3JVLtMWApwkRAc7citXSYEBbhICCZX5dYuE4ICXCQEC++GWPmJbbHyVLtMWDqJmbZ1Vyfrt7VzoDvJjIpy1iyew7LamcUuSySl70TljntT0yaTq1LhrROYE5oCnFR4r92ym2RPLwCd3UnWbtkNoBCX6KhersCWE2gKBVi/rb0/vPske3pZv629SBWJiAxPAQ4c6E7m1C4iEgUKcGBGRXlO7SIiURBMgJvZkK94PN7fLx6Pn7TvQHV1dZgZLT+5lw96jp+wrsTfZ83iOQAkEomTfmcikejfrrGxcch+dXV1BRwhEZlodBIT+EvbswBMueJGSj82jd6336Sm9HWW1V5T5MpERIZm7j5mO6uvr/fm5uYx25+IyHhgZgl3rx/cHswUioiInEgBLiISKAW4iEigFOAiIoFSgIuIBEoBLiISKAW4iEighg1wM3vEzA6b2Z4BbevMrNPMWtKvqwpbpoiIDJbNEfi/AUsytD/o7jXp11P5LUtERIYzbIC7+3PAn8egFhERycFo5sBvNbPW9BTLlKE6mVmjmTWbWXNXV9codiciIgONNMB/CJwH1AAHgQeG6ujucXevd/f6ysrKEe5OREQGG1GAu/shd+919w+Ah4AF+S1LRESGM6IAN7PpAxavBfYM1VdERApj2PuBm9nPgAZgmpl1APcADWZWAziwD7i5gDWKiEgGwwa4u38hQ/PDBahFRERyoF9iiogESgEuIhIoBbiISKAU4CIigVKAi4gESgEuIhIoBbiISKAU4CIigVKAi4gESgEuIhIoBbiISKAU4CIigVKAi8jE1NoED86DdRWp99amYleUs2HvRigiMu60NsGvVkNPMrV8dH9qGaB6efHqypGOwEVk4tlx74fh3acnmWoPiAJcRCaeox25tUeUAlxEJp7JVbm1R5QCXEQmnoV3Q6z8xLZYeao9IApwEZl4qpfD0g0w+WzAUu9LNwR1AhN0FYqITFTVy4ML7MF0BC4iEigFuIhIoBTgIiKBUoCLiARKAS4iEihz97HbmVkX8NqY7XBkpgFvFruILKjO/AqlTginVtWZP59w98rBjWMa4CEws2Z3ry92HcNRnfkVSp0QTq2qs/A0hSIiEigFuIhIoBTgHxUvdgFZUp35FUqdEE6tqrPANAcuIhIoHYGLiARKAS4iEqgJGeBmtsTM2s3sVTO7K8N6M7MN6fWtZnZxROtsMLOjZtaSfhXlZsZm9oiZHTazPUOsj8p4DldnVMbzbDP7nZm1mdkrZnZbhj5RGdNsai36uJpZmZntNLOX03V+O0OfSIxpTtx9Qr2AUuB/gXOBU4GXgbmD+lwF/Bow4FLgxYjW2QA8GYEx/VvgYmDPEOuLPp5Z1hmV8ZwOXJz+fAbwP1H8dzSHWos+rulxmpT+HANeBC6N4pjm8pqIR+ALgFfd/f/c/T1gM3DNoD7XAD/xlD8AFWY2PYJ1RoK7Pwf8+SRdojCe2dQZCe5+0N1fSn9+B2gDZg7qFpUxzabWokuP07H0Yiz9GnwFRyTGNBcTMcBnAvsHLHfw0X/hsulTaNnWcFn6r4W/NrMLx6a0nEVhPLMVqfE0s1lALakjxoEiN6YnqRUiMK5mVmpmLcBhYLu7R35MhzMRn8hjGdoG/584mz6Flk0NL5G6R8IxM7sK2AqcX/DKcheF8cxGpMbTzCYBvwC+7u5vD16dYZOijekwtUZiXN29F6gxswrgcTOb5+4Dz4dEakyzMRGPwDuAswcsVwEHRtCn0Iatwd3f7vtrobs/BcTMbNrYlZi1KIznsKI0nmYWIxWIP3X3LRm6RGZMh6s1SuOarqEbeAZYMmhVZMY0WxMxwP8bON/MZpvZqcAK4IlBfZ4A/j59VvpS4Ki7H4xanWb2N2Zm6c8LSP3zPDLGdWYjCuM5rKiMZ7qGh4E2d//+EN0iMabZ1BqFcTWzyvSRN2ZWDiwC/jSoWyTGNBcTbgrF3d83s1uBbaSu9HjE3V8xs1vS6/8FeIrUGelXgb8AX4pondcD/2Bm7wNJYIWnT6ePJTP7GakrDaaZWQdwD6mTRJEZzyzrjMR4ApcDK4Hd6TlbgG8C5wyoNRJjSna1RmFcpwObzKyU1P9Amtz9yaj9d58r/ZReRCRQE3EKRURkXFCAi4gESgEuIhIoBbiISKAU4CIigVKAi4gESgEuIhKo/wcc/WL2ToLxYAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Error of rev: 0.8811040154420743, of sym: 5.0150186078936985\n"
     ]
    }
   ],
   "source": [
    "# check for the stationary distribution again\n",
    "mu_result_rev = model_mu.predict([whiten(X1_train), whiten(X2_train)], batch_size=X1_train.shape[0])\n",
    "hist_rev, bin = np.histogram(X1_train.reshape(-1), bins=200, range=(-1,1), density=True, weights=mu_result_rev.reshape(-1))\n",
    "prinz_en = data_generator.prinz_energy(bin[:-1])\n",
    "prinz_stat = np.exp(-prinz_en/kT_prinz)\n",
    "scaled_prinz_stat = prinz_stat / (prinz_stat.sum() * (bin[1]-bin[0]))       \n",
    "plt.plot(bin[:-1], scaled_prinz_stat, label = 'True', c='k')\n",
    "plt.plot(bin[:-1], hist_rev, label = 'Rev')\n",
    "plt.plot(bin[:-1], hist_sym, label = 'Sym')\n",
    "plt.legend()\n",
    "plt.show()\n",
    "\n",
    "rev_states_prob = np.sum(np.split(hist_rev, 4), 1)\n",
    "sym_states_prob = np.sum(np.split(hist_sym, 4), 1)\n",
    "tru_states_prob = np.sum(np.split(scaled_prinz_stat, 4), 1)\n",
    "plt.plot(np.abs(rev_states_prob), '.', ms=12, label = \"Rev\")\n",
    "plt.plot(np.abs(sym_states_prob), '.', ms=12, label = \"Sym\")\n",
    "for j in range(4):\n",
    "    legend=None\n",
    "    if j>2:\n",
    "        legend='True'\n",
    "    plt.hlines(tru_states_prob[j], j-0.3, j+0.3, colors='k', linestyles='--', label=legend, lw=2)\n",
    "plt.legend()\n",
    "plt.show()\n",
    "print('Error of rev: {}, of sym: {}'.format(np.linalg.norm(hist_rev - prinz_stat), np.linalg.norm(hist_sym - prinz_stat)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Plotting eigenfunctions for revVAMPnet"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAZ0AAAElCAYAAAA/Rj+6AAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADh0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uMy4xLjAsIGh0dHA6Ly9tYXRwbG90bGliLm9yZy+17YcXAAAgAElEQVR4nOzdd3yV1f3A8c83e5EEEsKGMERFtmEIigMQR7GluFdVrKPF1Wqt1iquqpU6Wmsd9SfWUa0DFy6UocgMe28CIYQMQsie398fz00MIZskT27yfb9ez+vee571vZdwv/c85zzniKpijDHGNAcftwMwxhjTdljSMcYY02ws6RhjjGk2lnSMMcY0G0s6xhhjmo0lHWOMMc3Gko4xxphmY0nHGGNMs7GkY5qMiJwlIioi1x3HMXqLyMcikuo51qzGi7Blqe/nJSLXebY/qxHOvVhECkRkqYjEHu/xjKmOJR1TLxW+GKtbihv5lLOAM4GngGuAlxv5+C2aiAwVkRnNkAj+BvwHGAXc3cTnOoaI+IjIXSKyRUTyRWSfiPxNRELrcYxOIvKSZ99CEdkrIs+LSGQ123cQkZkissNzzlQRmS8iZ1Tarr+IPOJJyKkikiUia0TkT/WJzzj83A7AeK3/Al9UUV5a4fn3QDBQ1JATiEggcAbwgqrObMgxvExVn9dQ4CFgAbCnqU6sqh+KyCfA5cCpTXWeGjwL3A7MxkmAJ3teDxORCapaWtPOIhIDLAO64vww2QAMBG4FxonIWFXNrbB9L5zPNAx4DdgGRACDgW6VDn8D8FvgU+BtnH+fs4HHgEtFZLSq5jX4nbcxlnRMQ61S1bdq2sDzRZF/HOfoBAhw6DiO4TUa4fM63vMXi8gGYKCIiDbTwIwicgpwG/CRqk6tUL4b+DtOInynlsPcD/QCrlTV/1Y4xmLPvr/DSRJl3sL5/husqgdqOfYHwBOqmlmh7CUR2Q78CZgGvFDLMYyHXV4zTaa6NgoRiRWRD0XkiIhkisgnnrabPSKywLPNLCDBs8tDFS7fneVZP8PzOraK85Yfx/O6rO3jHBG5W0R2etovtonIr6rYP0BE/uC5hJLriTFeRKbX8n57ec4zo1L5N57yOyuVLxORTdV9Xp7jvO5ZPb/CZzCr0ql96vK+aiMiAgTg/PqPre/+x+EKnB8Xz1UqfxXIBa6uwzHOBvKAdyuVv4eTyK8vKxCRccDpwF9V9YCI+ItISHUHVtX4Sgmn4rHBqVGZOrKajmmoEBGJrqK8UFWPVLeTiEQBP+DUYl4CNuNcQpsPVLw+/jKwBueyy2zgI0/55uOI+S84l69eBgpwLr3MEpEdqvqjJ74A4GvgLOAbnF/E+cAg4JfU8ItWVRM8v87HAzMqHG8szmXH8Xi+WEUkHOcy1ks1xPsR0AW4yRN72XvfWd/3VUe3AsM9zwcBu6vbUER8gA71OPahGi6RjcD5fJZXLFTVfBFZ41lfm0Agv3LtTFVLRSQP6CMi0aqaBlzgWb1XRD4Dzgd8PTWXR2qrwVfQ3fN4sI7bGwBVtcWWOi84X8Zaw/J5FdteV6Hsr56yqyodt6x8QYWyWE/ZjCrimOFZF1vFuj2VjnOdZ9vVQECF8m44X9L/rVD2B8+2f6niuD51+Hz+DRQCoZ7X4zzHexM4Avh5yid7yn9Zy+dVFvtZVZyrzu+rDnF3BTKBA55j/qmW7cv+beq6HPPvVOFY64GD1az7n2f/gFri+dCz3dBK5UMrxDDcUzbb8zoF+BG4CqfdZoOn/Po6fF6+wBKc9p0T3f5/6U2L1XRMQ70CvF9FeWot+03G+WL7b6XymcA9jRBXTV5U1cKyF6q6X0S2ASdU2OYqIAN4pPLOWktjtsc8nGv8p+PUmM7B+XJ7Hucy0QicL6uzcX7dL2jIG6mkLu+rNi8A/sBUnC/iQbVsnwxMrMfxk2tYF4KTJKuSX2Gbwmq2AacG+Qvgf57LmBuAUzzlRTjvrewSWjvPYxZwdtlnJyKzgV3AX0TkjVr+vZ8DRgP3q+rWGrYzlVjSMQ21XVW/bcB+vYHllf9Dq2qKiBxunNCqtauKsnScBugyJwBrVLWhDfrzPI/n8FPSmQ+swklm5+AknXOAtaraGJ0k6vK+qiUivwCmAH9Q1cUikkIt7RSez6ch//5VyQViqlkXVGGbmuL5QUQux+l4MMdTXIJT89yI8/7KLvuW9TT7b6VknSEinwLXAidSzaVcEXkUmA68oqpP1BSXOZYlHeOtaupZVd3fdUk15VKPY9dIVZNFZDNwjqdxehRwmzptCwuB8SLyEk7X3Gcaep5K6vq+jt3AaVt6AVhZIZ51wFkiElDxS7nSfr5Ax3rEmKqq1cWZBAwQkUBVrVzj6QakVRdHRar6voh8hFNLawds9fyYWQ4UAzs8myZ6HquqfZX1ZGtf1Tk8nTsewOngcUttMZljWe8109z2AP08DdHlPPdZVHkTXzXKaghHNWaLSBBO43tDbQNO9twj1FDzcBrkJ+P0BvvOU/4dMAan4Vr4qVZUk6butvwETqeOGyskhXU4ifukGvbrgfMFXdelRw3HWoHzXTSyYqHn33IoEF/XN6OqJaq6RlV/8CSczsAwYKH+dJ9OWYeF7lUcoqwspfIKEXkI556p/+B8Xs3Spby1saRjmttnOEnhikrl9b0LfpvncUKl8rs4vr/rt3F+5T5QeYWnS3FdzPPE8BCwV1V3VigPBO7D+eX9Qx2Ole15rE9PsToRkdE4v9ZnquqaCqvWeR5ratcpa9Op61JTm857OMn1zkrlv8Zph3m7Qsz+InKSiPSs8c1R3sPu7ziN/o9XWPUxTnvO1SISVmH7LjjtQttVdUelYz2I03nlTZyOBnVp3zNVsMtrpqGGi0h19098rKrZ1ax7CrgSeF1ERgJbcBrdxwJp1P2X/beefR/xdMPe7TnOaM9xGup5nBrKAyIyAqfbdD5Oo/SJHJvkqjIfp5PAyTjD+ACgqptEJBkYACxR1aw6HGuF51h/EpH2QA6wW1WX1fkdVUFE/HHug9kJPFxpda1JpzHbdFR1vYj8E5juuTz2BT+NSLCQo28M7YbT1rIQp7cfAJ7ksRynZ9punNEFrsDplv4nVZ1f4XwZInI3ThfzpSLyfzg10ls9j0fdjyUiv8X5jPZ63vOVlX5/HFTVucf3KbQdlnRMQ13BsbWVMifw0/Xzo6hqmoicjjPUyQ04SWY+Tm+uFfzUyFsjVS0RkZ/j/JK9Dadn0zc447TV596UysctFJFzgd/jJMe/4CSd7fx0o2Ztx8jw3F8ynGMvoc3zHLcul9ZQ1b0icgNwL/AvnF5Yb+AM+XI8/oCTSM+uotPEJpyaWG092BrTnTiXXm8CLsT54fAP4ME61ioKcZLllTg16Vycv6fzVPXryhur6isikobzOTyKk9iX4IxoUPnvp+w+oZ44n31lCwFLOnUkdlnStASe2koa8LKqWgOtMa2UtemYZiciwVUU3+t5tF+MxrRiVtMxzc4zLloCTq8kX5zhYX4GLAbG1dC11hjj5SzpmGYnIr/HuQEvFmfMsEScccYermPjujHGS1nSMcYY02ys91oNoqOjNTY21u0wjDHGq6xcuTJNVascscKSTg1iY2OJj6/zzdDGGGMAEUmobp31XjPGGNNsLOkYY4xpNpZ0jDHGNBtLOsYYY5qNJR1jjDHNxpKOMcaYZmNdpo0xXi0zM5O0tDQKC2udXNQcp4CAAKKjo4mIiGjwMSzpGNNAh3ML2ZOey8Ej+WTmFnE4r5C8wlL8fAVfHyE8yJ+O7QLp2C6Q3lGhRIT4ux1yq5Ofn8/Bgwfp3r07wcHB1H2ePVNfqkpeXh6JiYkEBgYSFBTUoONY0jGmFqWlypbkLNYlHmbd/kw27s9kd1oOR/KL63WczuFBDOgazpi+UZxxQkf6dwqzL8njlJqaSseOHQkJCXE7lFZPRAgJCSE6OprU1FR69KhpBvLqWdIxpgq5hcXM3XSQ+VtS+GF7Guk5zqWbdkF+DOwawUVDuxIbFUqvqFC6RAQRGeJPZEgAwf6+lJQqxaWlZOYVkZZVyMEj+exMzWZrchZrEw8zb0sKsJmTOrfjylE9uTSuB0H+vu6+YS+Vn59P586d3Q6jTWnXrh3p6ekN3t+SjjEVrN13mDeXJvDl+gPkFJbQITSAcSdEc8YJHRneqz29OoTg41Nz7cTXRwjAh5AAP7pEBDOICCbQqXx90uE8vtuSwvvx+3jwk428tGAnD04ewHkDuzT122t1iouL8fOzr7Hm5OfnR3Fx/Wr5R+3fiLEY47WW7Urn7/O28+OOdMIC/bhwcBemDu/OiNgOtSaZ+uoaGcw1o3txzeheLN6ZxmOfb+aWt1Yx7fTe/OmCkxv9fK2dXaJsXsf7eVvSMW3a/sN5/GXOZuasP0DHdoHcd/5JXDmqJ+2CmqfRf0zfaD7+7Vgen7OJ1xbtpqRUmXHRKc1ybmPcYEnHtEmqygcrE5nx6UZKVLlrQn9uPrOPK20rAX4+zLjoFPx8fXht0W4GdYtg6qndmz0OY5qD3Rxq2pz8ohLufG8N93ywjoHdIvj2d2dyx4QTXG3MFxHuv+BkRvXuwIxPN5KWXeBaLMZds2bNQkTKl4CAAPr27cv9999Pfn6+2+EdN0s6pk1Jyy7gileX8unaJO4+tz/v/Ho03du3jO62vj7C41MGkVdUwrNzt7kdjnHZ+++/z5IlS5gzZw6TJk3iiSee4J577nE7rONml9dMm5FyJJ/LX1lKUmYe/7rqVM4b2DhdbVWVlJQUtm7dyuHDh2nfvj27du3ihBNOICMjgzFjxtC+ffs6HatfTBiXjujB+/GJ3DWxP9FhgY0So/E+Q4cOpV+/fgBMnDiR7du389prr/H888/j4+O99QXvjdyYekjLLuDKfy8j+Ug+b04bVe+Ek5yczOrVq/n000+57rrrGDJkCEOGDKFLly74+PjQuXNnzjzzTH7+858zbtw4rrvuOsaOHcvPfvYzOnToQPv27RERhgwZwiuvvEJWVla155p2em8KS0p5e+ne433bphUZPnw4eXl5pKWllZft3r2bq666io4dOxIYGMjQoUOZPXt2+fr//e9/iAjr1q075njnn38+Q4cObZbYK7Kajmn18otKmDZrBYkZucy6fiQjYjvUbb/8fN58801mz57Nl19+WV4eFhbG2LFjCQoKIi4ujvDwcAICAsjPz6dv375ERkaSm5tLcnIyqsqhQ4fYu3cvX3/9NevWrePmm2/m5ptvBuC5555jypQp9OzZs/z4fTuGcXq/aD5ancjt4/tZl+B6evizjWxKOuJqDAO6hvPQ5Mbthbhnzx4iIiKIiooCYN++fYwaNYqYmBieffZZOnbsyHvvvcfUqVP5+OOPueiii7jooouIiIjgrbfe4q9//Wv5sQ4ePMi3337Lk08+2agx1oUlHdOqqSp/+GAd6/Zn8vLVpzK6T1St269evZq///3vvPHGG0etGzVqFI899hjjxo0jICCgQbGkpaXx2WefMW3aNADuvPNO7rzzTpYsWcLo0aPLt/3Z4C788aP1bEw6wsBuDR9c0XivkpISiouLycrKYvbs2Xz44Yc899xz+Po6HV5mzJiBqrJw4cLyRDRp0iT27dvHgw8+yEUXXURQUBCXXHIJ77zzDk8++WT5Zbn//ve/qCpXXnll878xVbWlmuXUU09V493+/cMu7XXv5/rCvO21brt27VodOHCgAioievLJJ+vUqVM1Ozu70eNKSkrShx9+WIHyZe/eveXrD2UXaJ/75ujTX21p9HO3Jps2bXI7hEb3+uuvH/V3Ubb85je/OWq7rl276rXXXqtFRUVHLU8//bQCmpmZqaqqCxcuVEDnzp1bvu/w4cN10qRJDY6xts8diNdqvldd/2Kv7wKMAz4F9nv+Ma6rZfvYqv4BgfNqO5clHe+2+UCmnnD/Fzpt1gotLS2tcpvS0lJdvHixXnPNNQpodHS0PvTQQ5qamtpscb744osKaGRkpKalpZWX/+Kfi/QX/1zUbHF4o9acdGbPnq0rVqzQL774QidMmKCAvvHGG+Xb+fn5VZmcypZdu3apqvM3Hhsbq9dee62qOp8ZoG+99VaDYzyepOONHQnCgA3AHUBePfY7D+hSYZnX+KGZlqKguIQ7311DeLAfT04dVGW7SGlpKTNmzGDMmDG8+eabXHPNNaxevZoZM2YQHR3dbLHeeuutREZGcvjwYaKjo9m9ezcAY/tGsy4xk6z8omaLxbQcAwcOJC4ujvPPP5/PP/+c/v37c88995CTkwNAVFQUF198MStWrKhy6dq1K+DcA3b11Vfz0UcfkZuby5tvvklYWBhTpkxx5X15XdJR1S9U9X5V/QAorceu6aqaXGGxGZ9asX//sJstyVk8+cvBVXY7/vbbbzn55JN55JFHAPjqq6/4z3/+Q/fu7owEMHfuXOLi4gC45ZZbKCoqYkzfKEpKlfg9Ga7EZFqOwMBAnn76aVJSUnjxxRcBOO+881i3bh2nnHIKcXFxxyyBgT/93V9zzTVkZ2fz0Ucf8fbbbzN16lTXpoPwuqRzHD4SkRQR+VFELq5uIxG5SUTiRSQ+NTW1OeMzjWT/4Tz+MW87k07pxIQBnY5aV1BQwCOPPMLEiRPJyMjg9ddfp7S0lEmTJrkUrSMuLo4VK1bw0EMP8c033/Dss88ypEckIrAuMdPV2EzLcNFFFzFixAhmzpxJXl4ejzzyCJmZmYwbN4433niDhQsX8vHHH/PYY49xww03HLVv//79GTVqFH/84x/Zu3cv11xzjUvvAu9r06m4ANnU3qYTDfweGA3EAY8AJcDVtR3f2nS8061vxeuJD3yh+w7lHLPOx8dHAR06dKju3r27+YOrRWlpqYaHhyugJSUles7M+Tpt1gq3w2qxWnObzvbtx3Z++frrrxXQZ555RlVV9+3bp9OmTdOuXbuqv7+/du7cWSdMmKBvvvnmMfu+8MILCmi3bt20pKTkuGI8njYdcdZ7JxHJBqar6qx67vcicLqqDq5pu7i4OI2Pjz+OCE1zW7vvMD//54/cMf4E7prYv7w8JSWFkSNHkpCQADj3OLh1Ka02Ze1Pn332GXOzurJsdwZL7x/vclQt0+bNmzn55JPdDqPNqe1zF5GVqhpX1bq2dHmtomXACW4HYRrfM3O3ERniz41n9C4vKyws5NZbbyUhIYFx48axdOnSFptwABYtWgTA5MmTyVr/HclH8m0AUNNqtNWkMxQ44HYQpnGtTDjEwm2p3Dyub/l8OKrK6NGj+eijj7j55ptZsGABo0aNcjnSmo0dO7b8+bvPzwBgR0q2S9EY07i8bkQCEQkD+nle+gA9RWQocEhV94rIE8BIVR3v2f5XQBGwGqe322Tgt8C9zR68aVIvzNtBVGgAvxrTC4D169ezatUqVq9eTVRUFM8++6zXDSmTl5tLaX42u1Jzah1NwRhv4HVJB6czwPwKrx/2LG8A1+Hcg9O30j4PAL1wOhBsA25Q1beaPFLTbHakZDF/ayp3TehPSIAf+fn5DB7sNNl17dqV3bt3N2joGrf4+vpSUlICgKbsYGfqIJcjMqZxeF3SUdUFQLU/V1X1ukqv38BJSKYVe/3HPQT4+XDVaGfgzB9++KF83WOPPeZVCQfgwIEDpKenc/LJJ5Oz/H12TpzodkjGNAqvSzrGVJaRU8iHqxKZMrQb0WGBFBUVMXPmTAAeeOABrr76apcjrL+OHTvSsWNHADJ2rmVnqrXpmNahrXYkMK3Ih6sSyS8q5frTY8vur+Kbb77h3HPP5dFHH8Xf39/tEBvs4YcfBmB/WhbFJfUZgMOYlsmSjvFqqsr/4vcxtEckJ3UOZ/Hixaxfvx6Al19+2eXojl9Z1+6kd+7nQGa+y9EYc/ws6Rivti4xk20Hs7k0rgfg3FAJsH//fmJjY12MrHGMGTMGgIL9m/hm4Y8uR2PM8bOkY7za+yv3EeTvw8+GdGH16tU89dRTTJw4sXyEXW930kknMWCg03Pt0XvvdDkaY46fJR3jtQqKS/hkTRLnndKZvTu2Mnz4cIDyqaBbi8jwcACKvXfEKlMHIlLr0hpq79Z7zXitRdvTyMov5ufDurFt46Ly8l/84hcuRtX4goKcIer379jkciSmKS1ZsuSo11OmTGHIkCHMmDGjvKzidAXeypKO8Vpz1h8gPMiPsX2jGfzz+wFIT08vn0O+tXjttdfo3dsZS66wsNDr7jkydTN69OijXgcGBhIdHX1MeXUKCgq8IinZ5TXjlQqLS5m76SATB3QmPzebrVu30rt3b9q3b+92aI0uNjaW4RdcBcDhw4ddjsa0BJdffjn9+vXj+++/Z/To0QQHB/Pggw+Sn5+PiPDkk08etf2WLVsQEd59992jyr/99lvOOusswsLCCAsL48ILL2Tz5s1NGrvVdIxX+nGnc2ntwsGd2b59OwDPPPOM142tVlcDBg9l1RdvczA1jZiYGLfDadHuvPNO1qxZ42oMQ4cO5bnnnmvSc6SlpXHNNddw7733MmDAAEJDQ+u1/0cffcQll1zClClTeOeddygpKeGJJ55g3LhxrFu3ji5dujRJ3JZ0jFf6cv0B2gX6EdejHRFhzrQdraGRtTrdOzujE0z+2WT27N7pcjSmJcjMzOS99947atbb/Py63ctVWlrKHXfcwaRJk/jggw/Ky88880z69OnD888/f0xtqbFY0jFep7RU+W5zCmefFMP/vfpKeXm/fv1q2Mu7xbQLAiBhzy5n9sVWWqNrDE1dw2gpQkJCGjzN+saNG0lMTOSpp56iuLi4vDw8PJwRI0bw/fffN1aYx7A2HeN1NiRlkp5TyNje7bjrrrvw9fVl0aJFhIWFuR1akxl32k+TMG7bts3FSExL0blz5wbvm5KSAsBVV12Fv7//Ucu3335Lenp6Y4V5DKvpGK8zf0sqIrD2C2d2ittvv/2oic9ao6En9qH7dc+SOOsutm3bxoknnuh2SMZlVdV2/f398fX1pbCw8KjyykkkKsqZm+lvf/sb48aNO+Y4QUFBjRjp0SzpGK+zYFsKg7tH8sR0ZzDMivcxtFa+PkKP7t1IBJKSktwOx7RQvr6+dOvWjQ0bNhxVPmfOnKNeDxo0iK5du7J582Z+97vfNWeI3pd0RGQccDdwKtAVuF5VZ9WyzyDgBWAkcAh4GXhUVe0eby9zKKeQNfsOc+OIjnwKhIWFEe65Y7+169OzG0tELOmYGl1++eU888wzPPXUU8TFxTF//nzef//9o7bx9fXlhRde4JJLLiE3N5epU6cSFRVFcnIyP/74I/3792f69OlNEp83tumEARuAO4C82jYWkXBgLnAQGAHcDtwDNG96N43ih+2pqEJM0UGAo3retHa9O4bjFxLBd99953YopgV76KGH+PWvf82zzz7LlClT2L17N7NmzTpmuylTpjB//nwOHTrEtGnTmDRpEn/84x9JS0tj5MiRTRafePOPfRHJBqbXVNMRkVuBp4BOqprnKXsAuBXoXlNtJy4uTuPj4xs3aHNcfv+/tXy3OZnY1S/xyScfk5ycTKdOndwOq1m8+v0ubjrTmYl93bp1DBpkU1hv3ryZk08+2e0w2pzaPncRWamqcVWt88aaTn2dBvxQlnA8vsa5NBfrSkSmwZbuSic6JZ5PPvmYnj17tpmEA9CjQ0j587I5g4zxNm0h6XTGubRW0cEK644iIjeJSLyIxKempjZ5cKbu9h3KZf/hPLK2OAMjRkZGuhxR8+rZIYSYyx4DnGFNjPFGbSHpAFS+hCbVlKOqr6hqnKrGlc1Rb1qGpbucbp9RYc6ghpXHkWrtekaFEBw7lA6dupVPVmeMt2kLSSeZY2s0ZYNXVa4BmRZsya50gjL38OWnH3Haaae1uWv5YYF+RIUG4BsYwpo1a2zwT+OV2kLSWQKcISIV73aaCCQBe1yJyNSbqrJs1yG2vuR047z00ktdjsgdPTqE0Occ570fOHDA5WhaBm/uDOWNjvfz9rqkIyJhIjJURIbixN/T87qnZ/0TIlKxT+k7QC4wS0QGisgvgT8Cz9h9Ot4jMSOPxIyc8tetZTrq+urZIYQcf6ct6+BBq6j7+/uTl1frnROmEeXl5eHv79/g/b0u6QBxwGrPEgw87Hn+iGd9F6Bv2caqmolTs+kKxAP/BP4GPNN8IZvjtWRXOqV5WeWvu3Xr5mI07ukVFcJhdXqxWdKBmJgY9u/fT25urtV4mpiqkpuby/79+49reg2vG5FAVRfwU0eAqtZfV0XZeuDYAYaM11i6K52grMTy16NGjXIxGvf06BACwVbTKVM2GkVSUhJFRUUuR9P6+fv706lTp+MaBcTrko5pm5Zs2MmOWfcCzgi5fn5t80+3Z4cQfILb4evrWz5ScFsXHh7eZoZCag288fKaaWPSsgvYvWtX+eu23JU9NioUER+Cw8J5/PHHKSgocDskY+rFko5p8VYlZFCSfcjtMFqETuGBhAX6kZ2ZAcArr7xSyx7GtCyWdEyLt3JvBuSkAXDfffe5HI27RIS+HUM5645nARuZwHgfSzqmxVuVkEFESRYhISE8/vjjbofjun4x7ciNGchJJ51k7TrG61jSMS1aYXEpa/cd5vC2ZfTs2bPK2RLbmn4xYRw8UkCHqGhsfEDjbdpmFyDjNTYdOEJ6/BwO7d9DThNOoetN+sWEARAYFsn8rz+nuLi4zfbmM97HajqmRVuZkEFRWgIA+fn5LkfTMpQlnQJ1/vuuWbPGzXCMqRdLOqZFW7U3g4iI9gBMnTrV5Whahh7tgwnw9eHks34BQE5OTi17GNNyWNIxLdqqhAyigpzhTd566y2Xo2kZ/Hx96NMxlAM5zueybds2lyMypu4s6ZgW60BmHnt3bWftl2/Tp08fgqxNp9wpXSNIOFICwE033eRyNMbUnSUd02Jt2H+E1NlPADBy5EiXo2lZTukaTkbhT/99bbBL4y0s6ZgWa8P+THxCnDG1nnzySZejaVkGdovAxz+w/HVCQoKL0RhTd5Z0TIu1MekIwf4+nHHGGfTq1cvtcFqUAV3DEf+fLjc+8cQTLkZjTN1Z0jEt1vp96RSm72+zE7bVJCzQj76dO5S/XrVqlaKYuYIAACAASURBVIvRGFN3Xpl0ROQ3IrJbRPJFZKWInFHDtrEiolUs5zVnzKZ+0rML2L7gQ3Iz09vs1NS1GdijPSP+/DG/+tWv2L9/v9vhGFMnXpd0ROQy4HngL8AwYDHwZdl01TU4D2dW0bJlXlPGaY7PxqQj5Gz+HoAJEya4HE3LNLRHJCmFfkR17kZycrJNYma8gtclHeB3wCxVfVVVN6vqbcAB4NZa9ktX1eQKS2HTh2oaakNSJqW5R7jgZ5Ntgq5qjIh1bpotDGyPqrJ3716XIzKmdl6VdEQkADgV+KbSqm+AMbXs/pGIpIjIjyJycZMEaBrNF198QfHhA/SJtQ4E1Tm5SzjB/r5kSDsA+vXrR0lJictRGVMzr0o6QDTgC1SeHP4g0LmafbKBu4FLgQuA74D3ROTqqjYWkZtEJF5E4m0EX/fMefoOAKKjo12OpOXy9/VhWM9I9mv78rLVq1e7GJExtfO2pFOm8p1wUkWZs6Fqmqr+TVWXqmq8qj4IvAz8oZrtX1HVOFWNa8vTIrvpSP5PbROdOnVyMZKWLy62AwmFoXz17XzA7tcxLZ+3JZ00oIRjazUxHFv7qcky4ITGCso0rs1JR8qfjxo1ysVIWr4Rse0pVcgPdZJzUlKSyxEZU7Nak46I7G3AkiAiAxs7WE/j/0pgYqVVE3F6sdXVUJzOB6YF2pB0BPEP5KxzJjBs2DC3w2nRTu3VngBfH9amlBASEsL//vc/t0MypkZ1mfmpO/AFUNcGDh/gaiCgoUHV4hngTRFZDvwI3AJ0BV4CEJEngJGqOt7z+ldAEbAaKAUmA78F7m2i+MxxWrs7BS0qYMI5Z7kdSosXEuDHyN4dWLQznbvvvptHHnmEzz77jMmTJ7sdmjFVqut0g4+o6vK6bCgifsA1DQ+pZqr6nohEAQ/g3G+zAbhAVcsuZncB+lba7QGgF86luW3ADapq4+S3UGt37APA2tTqZlz/aP7yxRZe+d1dPPLII3z33XeWdEyLVZc2nT8D++p6QFUt9uzTZLdIq+qLqhqrqoGqeqqqfl9h3XWqGlvh9RuqOkBVQ1U13NNJwBJOC3UwLYNFM28ELOnU1bj+zue0PCGLwYMH8/zzz7NgwQJ3gzKmGrUmHVV9XFXr1f7h2ac+DfvGAPDSG+9QmpsJWM+1ujqxUzs6hQcyb0sKf/7znwEbANS0XN7We820csnZxeXPreda3YgIk07pzIJtKZw/+Rfcf//9zJ0716axNi2SJR3Tohw4UlD+3NfX18VIvMuFg7qQX1TKvC0pjBo1ClVl/fr1bodlzDEaLemIyNUicm1jHc+0TXsOHnY7BK8UF9uBju0C+WL9AYYMGQLAXXfdRWlpqcuRGXO0xqzpvO5ZjGmQopJSklIyALjhhhtcjsa7+PoIFwzszLwtKUR07ALA0qVLmT59usuRGXO0xkw644FzGvF4po3ZfjCbonynHeLFF190ORrvc0lcDwqKS/l49X6+++47AP71r3+xadMmlyMz5ieNlnRU9XtVXdhYxzNtz4akTEpyDtEuPILAwEC3w/E6A7tFMKRHJG8v28vZZ5/Nm2++CcBvf/tblyMz5ifWkcC0GBv3Z5K1ag5RHdrXvrGp0lUje7I9JZtluw9x9dVX89BDD7FgwQJuuukmt0MzBqhn0hGRebUs3zVVoKb1W7RkGQDdu3d3ORLvNXlIV6LDAvjn/B0ATJ06FYBXX32VdevWuRmaMUD9azo+ONMIVFyigbFAf89rY+qtpFTZuM6ZC6bsspCpv+AAX359Rh9+2J7GyoQMBg0axPvvvw/AkCFDEBH27avzACPGNLp6JR1VPUtVz660DAYGABnAX5okStPq7UnPIT/zECJiNZ3jdM1pvYgKDeDJLzejqlx88cUsWrSofH3Pnj1ZunSpixGatqxR2nRUdSfwJPB0YxzPtD0b9mdSkpdJRGR7/PzqOg6tqUpIgB9/OO9EVuzJ4MNVzhCIY8eOpaioiJ49ewJw2mmnISLMmDHD7uUxzaoxOxKk4lxiM6beNiYdgdxMOnWKcTuUVuGSU3twaq/2PDZnE/sP5wHg5+dHQkLCUXPuPPzww/j6+vL888+TkJCAapUT8BrTaBol6YhIB+B3wM7GOJ5pe9YlpFJ8cBsnnXii26G0Cj4+wsxLhlBcotz2zioKi3+qzVxyySVkZWWxYsWK8ptH77zzTmJjY/Hx8WHy5MksXLiQgoKC6g5vTINJfX7ZiMhuoPIOAUDZcMBTVfXTRorNdXFxcRofH+92GK2eqhJ76Z/Y+8ETfPrppzYXTCOas+4Av31nFecP7Mw/rhiGn++xvzMLCgqYPXs2V1xxxTHrxowZw5lnnknXrl0ZMWIEI0aMwMfH7rQwNRORlaoaV+W6eiadWRybdPKBBOB9T9tOq2FJp3nsO5TLwPOvIXf15+TmZOPv7+92SK3Ka4t28+jnmzh/YGeeuXQowQE1D6S6a9cuXnzxRdasWUNaWhpr164tXxcQEECPHj04/fTTOf/88xkxYkR5DcmYMo2WdFoKEfkNcA/OLKEbgTtV9Ycath8EvACMBA4BLwOPai1v3pJO8/hqQzJTL76EmOKD7N6xze1wWqV//7CLx7/YzIAu4Txz6VBO7NyuzvseOnSIZcuWkZSUxPbt25k7dy6rVq0qXx8YGMjIkSM544wzGDJkCMOGDaNv376WiNqwVpV0ROQy4C3gN8Aiz+P1wABV3VvF9uE4U1R/DzwCnAjMAmao6t9qOpclnebxt2+28uebL2NIlxCWLF7sdjit1nebD3LPB+vIyi/i2tNiufnMPsS0C2rQsbKzs9myZQvx8fFs27aNuXPnsmXLFoqLnfmQ2rVrV56Ahg8fzrBhwxgwYIDVYtuIZkk6InI14KOq/2mUA1Z/nmXAOlX9dYWy7cAHqnpfFdvfCjwFdFLVPE/ZA8CtQPeaajuWdJrHlMfe5eM/X0GPHj3Yu/eY3w2mER3KKeSJLzbz0er9+PoI5w7oxJRh3RjTN7rWy261KSgoYNOmTaxevZpVq1axevVq1q5dWz6ZXEBAAAMHDixPQnFxcQwfPty6yLdCzZV0inCSTpPNvCUiAUAucIWqvl+h/J/AQFU9s4p9/gNEqeqFFcpGAMuBPqq6u9L2NwE3AfTs2fPUhISEJnkv5iddzriM5EVON15vq3l7qz1pObz+424+XZtERm4R/r7CsB7tGdw9gv6d23FCTBjdIoOJCgvE16fhA42UlJSwY8cOVq9efVQySk9PByA4OJjhw4czcuTI8qV3796I2OAm3qy5ks44z/GabKRpEekK7AfOVNXvK5Q/CFylqsf0txWRb4BEVb2hQllPnM4PY1R1SXXns5pO00vJyqfvGVPIXvsVM2fO5Pe//73bIbUphcWlLNmVzuKdaSzdmc6W5CwKKnSv9vURYtoF0rFdIBHB/oQH+xMR7E+k57FsiQwJICosgA6hAbQPCagxUakqiYmJLF26lCVLlrB8+XJWrlxJfn4+AFFRUYwcOZLTTjuNcePGMWbMGLss52VqSjqNVq+tmASaQeVMKVWU1bZ9VeWmmW1MOkJJdjr9BwyyhOOCAD8fzuzfkTP7dwScMfD2HsplR0o2yZl5JB/JJzmzgLTsAjLzitifkUdmXhGZeUUUl1b930cEIoP96RAaQFRooPMYFkCn8CC6RATRNTKYLhHtmfyLX3LJJZcAUFRUxMaNG1m+fDnLly9n2bJlfPXVV6gqQUFBDBw4kLPOOotzzz2X8ePHWycFL+ZtF1PTgBKgc6XyGOBgNfskV7M9NexjmsmGxMMUpScSO3qo26EYnJpN7+hQekeH1ridqpJTWOIkoNwiDucWkp5TyKGcsscC53l2ITtTs1m+x1lXWYfQALpEBBEb5ZyzT9wFTD//Up7pGEppfg4LFizgq6++4vvvv2fmzJnMnDmTrl278stf/pJevXpxwQUXMGDAgKb6OEwTaFDSEZEhOL3Ajun60pQdCVS1UERWAhOB9yusmgh8WM1uS4CnRCRIVfMrbJ8E7GmqWE3dvPbMYxQfPsD4s+90OxRTDyJCWKAfYYF+dIsMrtM++UUlHDyST9LhfJIO53EgM4+kTOf5xqRMvtqYTEmF2lNMu0BO6dqVQb+8iym3zaB7SAkrFs5l9uzZvPjii5SWlnLPPfcQFxfH1KlTue222wgNrTlZGvfV9+bQSGAOMLqsyPNYfpCm7EjgieEy4E2crtI/ArcA04BTVDVBRJ4ARqrqeM/2EcBWYAHwGM74cLOAh63LtPvKGowXLVrE2LFjXY7GuKmwuJS9h3LYmZrDrtQctqdksXH/EbanZFGWi6LDAhndpwNxPdrR3T+bpd/O4eWXXyYxMZHw8HDGjRvH9OnTOffcc60zgosas03nL0AUMA74AZgCZAI3AKcBlx9HnHWiqu+JSBTwAM7NoRuAC1S1rJtZF6Bvhe0zRWQi8E8gHmcKhr8BzzR1rKZmmblF5c+7dOniYiSmJQjw86FfTDv6xRx942peYQmbk4+wYX8mqxIyWLIrnc/XHQCgS8RpXP/CL+iQsZUNP37Fl198wXnnnUeXLl24/fbbmT59OmFhYW68HVON+tZ0dgIPA28DRcAIVV3pWfcvIFRVr22KQN1gNZ2mtXhHGmNPcBqw8/PzCQwMdDki4w1UlT3puSzdlc6CrSks3JZKflEpEcH+TDopitDEpXz/xUfMmzcPEWH8+PHMnDmTIUOGuB16m9GYNZ0uwC5VLRGRfKDiT5KPgHcbGKNpg9bvywDgnvv+ZAnH1JnIT50drhjZk7zCEr7fnspXG5L5bEMyeUWx9Lngz9w99RZWffwa3879mqFDhzJw4ECmT5/ODTfcYF2wXVTffofJQKTneQLOJbUy/RolItNmxG9zRh/o0aVTLVsaU73gAF8mndKZZy8byooHJvDXqYOJDg3k/b0h7Im7ncv+9hmXTZtOQUEBt9xyC927d2fatGkcOHDA7dDbpPrWdBbhJJrPcRrzHxKRWKAY+BXQaqY1ME1vzZYdAOWzWRpzvMIC/bh0RA8uHdGD3Wk5vB+/j/dXJpIafR4dLjmbS/O3krl1Cf/3f//H66+/zvjx47nxxhuZMmUKAQEBboffJtQ36TwMdPU8fxqnU8FlQAhOwrmt8UIzrVluYTEJCU5Nx5KOaQq9o0P5w3kncdfE/izYmsq7y/cyf2sgpQMHc97wiyle/yXLvpvDt99+S2hoKBdeeCGTJk3izDPPpE+fPtb7rYl43SjTzck6EjSdlQmHmHDNnRz+4U0yMzMJDw93OyTTBiRn5vPByn28F7+PfYfyCA/0ZaDuomDHUpYs+Lb8ktvgwYO54IILGDhwIJMmTSI6OtrlyL1Lq5raoDlZ0mk6byzew29u/BVROQnsTdjjdjimjSktVZbsSufdFfv4ekMyhSWl9O4QzMk+Sfge3MKqxfNZsmQJqoqIMGDAAE466SSGDx/OqaeeyoknnkjPnj1tOJ5qHFfvNRGZB/xGVbfU8WQ+wLfAzaq6vV6RmjZjY1ImvvlH6NG9m9uhmDbIx0cY2y+asf2iycgp5IsNB/hi/QG+2tmeUt/T6D1lAn+YHkhXPUTK1hWsW72KNWvW8OGHPw18EhYWxpAhQxg6dCg9evTglFNOoVu3bvTt29dq7jWoS5vOWRzdNbo20oB9TBuzYf8R/IpziYrq4XYopo1rHxrAVaN6cdWoXqRnF/D1xoN8ueEAszceoqAYfH1GMvDcCVxxQyR9I0AOJZCbuo/NnrmD/vOf/5CVlXXUMTt06EBsbGz50rNnT7p37063bt0ICwujT58+BAcHt8l2o7p2JPhYRArqcVy7ZmeqVVBcwraDWZTmZ9GhQwe3wzGmXFRYIFeO6smVo3qSX1TC6r2HWbwzjeW7DzF79X6yC5yZUYP8e9Gn7ykMO+16Lo4OoVNgEXo4idLsdBL37WXPnj0kJCSwefNmvvzyS/Ly8o45V3BwMN26daNLly7ExMQQExNDp06d6N69OzExMURGRpYv7du3JzQ0tFUkqboknTcaeOy0Bu5nWrntB7MpKiokN/MQUVFRbodjTJWC/H05rW8Up/V1/kZLS5VdaTms33+YDfuPsCMlm5UJGXy6Nql8Hx8Jp0vECHoMG8cp54RwfocQurcPJlzykJxDZGekknEonQMHDpCamkpiYiLJycls3LiR+fPnc+jQoWrj8fX1PSoJRUREEBYWRnh4OBEREYSHhxMWFkZoaOgxS3BwMMHBwQQFBREUFERwcDD+/v4EBgYSFBSEr2+TDpl5lFqTjqpe3xyBmLZjw/5M8nasoKiwgHPOOcftcIypEx8foV9MGP1iwpgy7Kfy3MJidqbksCM1i12pOew7lMu+jDwWbkslJevoC0S+Pj50DOtOTHhfYroE0e/0QMaGB9EpPJCYdkGE+UNBZirFuVkU5WWRmZlJRkYGhw8fLl/KXmdkZJCamkpmZiZHjhzhyJEjlJSUNOi9+fn5ERISctTy6quvMnr06Np3ru+5Gv2IxtRi1c4DHFn0Ju3atePcc891OxxjjktIgB+DukcwqHvEMevyi0pIzMhl36E8EjNySckq4OCRfA4eKSAxI5dVezOqnGcInLmNIoMjaB/akfbt/InsFEBksD8dPVNKhAb6ERboS6jneWiAL34U41tSQElhAcUFeRTl51GYn0txUSFFhQXk5eWRn59PXl4eRUVFFBQUUFDglOfl5ZGbm1u+NNVAqZZ0TLNbvGw5BWn7uPtPf7IxsEyrFuTvW+XI2RUVFJeQmlXAwSMFHM4tJCO3iIycQjI8z52yQvYdymV9bhE5BcVkFxZT37td/HwCCPALIsDPh0A/HwL8fAjw9cG/nQ++EYKfrw9+PoKvjxDoI2zIDWfgcb7/KuNogmMaU63iklJ27toNwPXX25VbYwL9fOnePoTu7UPqvI+qkldUQnZBMTkFJU4iKigufywoLqWwuLT80Xle4jwvKaWgyHksLC6lqKSUklKluFQ9j05ZUTXTkR8vSzqmWe1IzSbvUDIiQo8e1l3amIYQEUIC/AgJ8PO6m1PqdTutiHwuIg+LyC9EpNkHzBKRQBH5h4ikiUiOiHwqIt1r2ec6EdEqlmOm2jZNb11iJsWZqcR06mwDLBrTBtV3DIdgYDrO3Dm7RSRVRD4RkZ83fmhVeg6YClwBnAGEA5+LSG39/XJx5gIqX1Q1vykDNVXbsD8TzU6lb5/ebodijHFBvS6vqep4ABHpDQwHhgITgY9E5F+qOr3xQ3SISAQwDbheVed6yq7BmddnAvB1zaFrclPFZupuXWImkp1Kr14D3A7FGOOC+l5eCwFQ1d2q+qGq/llVRwOTgRtFZGRTBOlxKuAPfFNWoKr7gM3AmFr2DRaRBBFJ9FwiHFbdhiJyk4jEi0h8ampqowRuHMUlpWzan0HuoWR69erldjjGGBfU9/JalohsFpG3ReT3InK2iISr6hfAf3BqIk2lM1DCsSMdHPSsq85W4Abg5ziX5fKBH0XkhKo2VtVXVDVOVeM6dux4/FGbcttTstnz79vQ0lL69OnjdjjGGBfUt/fajcAwnEtrFwGhgIrIHiAPCBWRicBqVa3TMDgi8hjwp1o2O7umQ1DDWG+qugRYUuF8i4E1OBPO3V6XGE3jWJ+YSVHqHgAmT57sbjDGGFfUt03ndeB1AHFGnjsJJwENB84FeuG0raiIJKpqXa6hPAe8Vcs2e4HRgC8QDVS87hUDfF+P91AiIvFAlTUd03S++X4xAKeddhqdO9dUOTXGtFb1SjoiciOwCtigqoU47SmbgbdF5FUgG7gKp/2l2naTijw1olprRSKyEijC6bjwjqesO3AysLge70GAwcDauu5jGsfSJU6F8+yza6q4GmNas/peXnvZ81gsIptwEtAeoCtwHfBHVd0F7ALeb6QYAVDVTBF5DXhaRFKAdOAZYB3OpHEAiMh3wHJVvc/z+iFgKbAdp4v17ThJ59bGjM/ULLewmOQsZ4ypO+64w+VojDFuqW/SieSnNp3hwCjgGs+6D4C/N15oVboLKAbew7ln6DvgWlWtOLRqX2BfpZhfwelskAmsBsap6vImjtVUsHZfJtmbFgLYrIrGtGH1bdPJwmk/KW9D8VyuElUtbeTYqjp/Pk4HgNtq2Ca20uu7cJKVcdGqvRkUJG4CIDAw0OVojDFuOe6x11RVsZlCTS3i9/w0OVVrmP3QGNMw9b1Px5h6Ky1VVu5OcTsMY0wLYEnHNLldaTkkb3Ka0B577DGXozHGuMmSjmlyKxMOkfrhowBERUW5HI0xxk2WdEyTW7Izvfx5fr4N7m1MW2ZJxzQpVWXe8vXlr3NyclyMxhjjNks6pkntSsthy1sPlb+OiYlxMRpjjNss6ZgmtXhnevkgnwDTpjXlQOTGmJbOko5pUgvW7yl//vvf/x4fH/uTM6YtE+feTlOVuLg4jY+PdzsMr1VaqkT2jyNr5yrA6URgoxEY0/qJyEpVjatqnf3sNE1mQ1JmecJZuHChJRxjjCUd03TmbflpFILBgwe7GIkxpqWwpGOazLfrnMG+L7/8ciIjI12OxhjTEljSMU0iNauAZd870xxt3brV5WiMMS2FJR3TJBZsTUEL8wB49tlnXY7GGNNSeFXSEZGbRGS+iBwWERWR2DruN1VENolIgedxStNGar5Zm0D6l88DMGxYnWYuN8a0AV6VdIAQ4BtgRl13EJHTcGYafRsY6nl8X0RGNUWABvIKS/hq7rzy1+3atXMxGmNMS3Lck7g1J1V9DkBEquz/XY07gfmq+rjn9eMicran/IpGDtHgXFrLSU8qf22TthljynhbTachTsOpHVX0NTDGhVjahM/XH8Av6wChoaE2wKcx5ihtIel0Bg5WKjvoKT+Gp90oXkTiU1NTmzy41ia3sJh5m1MIzU1mwIABhISEuB2SMaYFcT3piMhjnk4BNS1nHedpKo/1I1WUORuqvqKqcaoa17Fjx+M8bdszb0sK2YfT2bN+OePGjXM7HGNMC9MS2nSeA96qZZu9x3H8ZI6t1cRwbO3HNIIPVyaS9PKNAFx44YUuR2OMaWlcTzqqmgakNeEplgATgacrlE0EFjfhOduk5Mx8Fm5LpbTImR10yJAhLkdkjGlpXE869SEinXFqLf09RQNEJBLYq6qHPNt8ByxX1fs82zwPfC8i9wGzgSnA2cDpzRp8G/DhqkSKCwsQEe6++246dOjgdkjGmBbG9TaderoFWI1zrw3AHM/riyps0xfoUvZCVRcDlwO/AtYB1wKXqeqy5gi4rVBV3o/fR9fD61FVRowY4XZIxpgWyKtqOqo6g1puDFXV2CrKPgA+aJKgDODMELorOQNd8A4AcXH1uZXKGNNWeFXSMS3Xa4t2s++ZqQDcdddd9O7d2+WIjDEtkbddXjMt0K7U7KPmzrn22mtdjMYY05JZ0jHHbdbiPfhX+EuyXmvGmOpY0jHHJSUrn//F72PSCc6gns8++6yNtWaMqZYlHXNcXlqwi8LiUhI+/TsAUVFRLkdkjGnJLOmYBks5ks/byxI4p6vy+ccfAjBw4ECXozLGtGSWdEyD/WPeDopLlVGRP40kPWjQIBcjMsa0dJZ0TINsTc7ineV7uWJkD+Z+5tRyXnrpJfz8rBe+MaZ69g1h6k1VeeTzjYQF+nH7WX048fq5TJ06lZtvvtnt0IwxLZzVdEy9fbUhmR93pHPn+H7ccPVlHD58mPHjx7sdljHGC1jSMfWSkVPInz/ZwIAu4URlbGLOnDmMHz+eG2+80e3QjDFewC6vmXqZ8dlGDucW8cb1I7ls0ljat2/PJ598gr+/v9uhGWO8gCUdU2efrU3ikzVJ3DnhBLYu+46NGzfyj3/8g9DQULdDM8Z4CUs6pk52pGTzxw/XcWqv9tw4pgexPccQFxfHTTfd5HZoxhgvYknH1CqnoJjfvL2SQH9fHji7EzP/+hTp6em8+uqrBAQEuB2eMcaLeFXSEZGbgCuAYUAE0FtV99Syz3XA61WsClbV/MaOsbUpLinlt++sYkdKNm/cMJLh/WPK15111lnuBWaM8UpelXSAEOAb4BPg2Xrsl4szo2g5Szi1U1Ue+HgDC7am8pcpgxjU8afOAm+//Tbt27d3MTpjjDfyqqSjqs8BiEh9p6VUVU1ugpBaLVXl8TmbeXfFPm47px9XjurJz372MwDeffddLrvsMpcjNMZ4o7Zyn06wiCSISKKIfC4iw9wOqCVzRhzYxL8X7ea6MbHcdlZvHn30UebMmcOFF17IxRdf7HaIxhgv1RaSzlbgBuDnOO1B+cCPInJCVRuLyE0iEi8i8ampqc0YZstQXFLK/bM38PqPe5h2em8emjyATz75hAcffBCAp556Cl9fX5ejNMZ4K9eTjog8JiJay3JWQ4+vqktU9Q1VXaOqPwCXATuB26rZ/hVVjVPVuI4dOzb0tF4pK7+IaW/E89/le5l+dj8euPBk5s6dy6WXXgrAp59+yimnnOJylMYYb9YS2nSeA96qZZu9jXUyVS0RkXigyppOW7U7LYdb31rJ9pRsnvzlIC4f2ROASZMmAfDWW28xefJkN0M0xrQCricdVU0D0prrfOLMpTwYWNtc52zpPl2bxH0frsPfz4fXrxvBuP4dUVXuvfdeAIYPH85VV13lcpTGmNbA9aRTHyLSGegM9PcUDRCRSGCvqh7ybPMdsFxV7/O8fghYCmwHwoHbcZLOrc0cfotzOLeQRz/fzIerEjm1V3v+ccUwukYGU1hYyHnnncf8+fPp2LEjH3/8sduhGmNaCa9KOsAtwEMVXs/xPF4PzPI87wvsq7BNJPAKTrLKBFYD41R1eZNG2oKpKnPWH2DGpxvJyC1i+tn9uGPCCfj7+nDw4EE6d+5cvu26deuOem2MMcdDVNXtGFqsuLg4jY+PdzuMRrVqbwZPfLGZFXsyGNQtgqemonJBxAAADfJJREFUDmZA13AAvv76a8477zwAfv3rX/Pyyy/jXI00xpi6E5GVqlrl/ZTeVtMxDbRqbwYvLdjJN5sOEh0WyONTBnJZXA/8fJ0OjE8++ST33Xcf4Ew7bbOAGmOagiWdVqyguITvNqfw+o+7WbEng4hgf+6a0J8bz+hNaKDzT5+RkcHtt9/Oe++9R//+/fn888854QTr2GeMaRqWdFqZ0lJlTeJhPl69n0/XJnE4t4hukcE8+LMBXDaiR3myAVi1ahWnnnpq+ev/b+/eg7Oq7zyOv7+EBJJAuCyDiFHYba3QXVodLsIiitIAwziy4K1YRimzu7PbTrduuyBOa7puLU512JWt3Q44rbZbFcWluLBltA1eUAQXQddqpeIEL7RiuJbcCEm++8fvBB9yIXmS5znPxc9r5gzJ7/n9Tr7nx0m+zznn9/x+L7zwAp+0zyaJSLyUdPLAkbomXq4+zNa3PmLrWzUcqj3JgP79mP3no7huYjmXfXoEBf0+fjazceNGbrrpJhoaGk6X7d69WwlHRNJOSSfH1Dc18/bBWvZ+eILd7x3lf/cf4Z2aOgAGD+zPzItGMmvcSK4cN5IhxWcuIe3ubN26lQULFgAwa9Ys1q1bx4gRI2I/DhH5ZFLSyTKtrc7R+iZ+f6yRA8fq+eBoAweONfD+kXp+d7CW94/W0zbgcEhxIRPHDOPaieVMGjOcSy4YSmFBx5mNWltbWblyJXfccQcA48eP5/7772fGjBkUFhZ2qC8iki5KOmlwvP4U1YfrqG9qpqGphfqmlujfZupPtZwuq21s5mh9E0frmzhS18TR+lMcq2+itd0o9pKiAsqHFTOhfAjXTSznolGD+cw5gxkzvIR+/boe0tzY2MiKFStYvXr16bKrr76adevWUVpamq7DFxHpkpJOGjz/dg1fe3RPl6+bQUlhAaUD+jO8tIhhJUWMG1XGsNJChpcUMay0iNFDizlvaDHlw4oZUlyY1OdlmpqaWLNmDXfeeSeHDx8GoLCwkP379zN69Og+H5+ISG8p6aTBlD8dzoNLJlNcVEBJtBUX9aeksIDiogIG9O+X8g9dtrS0UF1dzT333MMjjzxCXV0dgwYNYtOmTcyePZuioqKU/jwRkd5Q0kmDc8oGck7ZwFh+1r59+9i5cyerVq1iz549DBgwgGuuuYY5c+Zw/fXXU1ZWFkscIiI9oaSTg9544w22bdvG2rVr2bMn3MYrKyvj1ltvZdmyZbqFJiJZS0knBzQ0NHDbbbdRUFBAVVUVr7/+OgAFBQVMmTKF5cuXM3/+fPr313+niGQ3/ZXKMm0TsJ44cYKHH36YjRs3sn37dmprawEoLy+nsrKSmTNnMmXKFI1CE5GcoqSTQc3NzdTU1ODuVFVV8eSTT7Jjxw4OHDhwRr0JEyYwa9YsKisrGTJkCP36ZXyVcRGRXlHSicnevXs5dOgQ1dXVHD9+nAceeIDXXut88dJzzz2XpUuXMnXqVObNm6ckIyJ5I2eSjpkNB+4EKoAxhCWuNwPfdvfD3bS9FvguYYG3d4Bvufsv0hVra2srixYtYsOGDVxxxRVUVVWdtf4NN9zA4sWLGTZsGNOnT9caNiKSt3Im6QCjgfOA5cCb0df/ATwKzO6qkZlNAx4jrDi6AVgIrDez6e6+Mx2Bbt++nccffxzgdMK56qqr2L17N5MnT2bhwoVUVFRQUlLC0KFDKS4uTkcYIiJZJ2eSjrv/hpAw2uwzs2XAZjMrc/c/dtH0VuAZd/9e9P33zOzKqHxROmI1M+bOncv69espLS3VlYuISCTXHxaUASeB+rPUmQY83a7sKeAv0xXU9OnT2bJlC4MGDVLCERFJkLNJx8yGEp7TPODuzWepOgo42K7sYFTe2X7/1sx2mdmumpqa1AQrIiJAFiQdM7vLzLybbWa7NqXAJuAA4RlPd9rN24x1UhYquq9190nuPkmLmomIpFY2PNO5D/h5N3Xea/vCzAYBv4y+vdrdG7tp+yEdr2pG0vHqR0RE0izjScfdDxGGP3fLzAYDWwhXKnPdvbYHzV4iDLO+N6GsAtieZKgiItJHGU86PRUlnKcJgwf+CiiNbrMBHHH3pqheFfCyu98evbYaeN7Mbgd+ASwArgQuizN+ERHJgmc6SZgITAU+C/wO+EPCljgS7VPAuW3fuPt24IvALcD/ATcDN6brMzoiItK1nLnScfdnCbfVuqs3tpOyJ4AnUh+ViIgkI5eudEREJMdZ21T60pGZ1QDv9rL5CHo4QEJOU58lR/2VHPVXcvrSX2PcvdPPnCjppImZ7XL3SZmOI5eoz5Kj/kqO+is56eov3V4TEZHYKOmIiEhslHTSZ22mA8hB6rPkqL+So/5KTlr6S890REQkNrrSERGR2CjpiIhIbJR0REQkNko6KRIt/vaMmR2L1gAa28N215rZm2Z2Mvp3QXojzQ5mNsDMfmBmh8yszsz+28zKu2mzpIv1lgbGFXdczOwrZlZtZo1m9oqZzeim/gQze87MGszsgJlV2ido2dpk+svMxnZxHs2NM+ZMMbPLo9+3A9FxL+lBm5SdX0o6qVNCmAX7n3vawMymAY8BDwMXR/+uN7NL0xFglrkPuBZYBMwgzB6+2cwKumlXT5jQ9fTWgzWVcoqZ3UiYHX0lcAlhGY4tZnZBF/XLgF8R1oiaDPwDsAz4RiwBZ1iy/ZVgLmeeS1vTGWcWGQT8Bvg60NBd5ZSfX+6uLYUbMImwKunYHtR9DPhVu7JfA49m+jjS3EdDgCbgSwll5wOtwJyztFsC1GY6/hj6ZydhGfbEsreBu7uo//fAH4HihLJvE1bWtUwfTxb219jod3RSpmPP9AbUAku6qZPS80tXOpk1jXB1lOgpzlyqIR9NBApJOHZ3fx/4Ld0fe7GZvWtmH5jZZjO7JI1xxs7Migj90/68eJqu+2YasM3dE9+1PgWMJvyBzVu97K82G8zsIzN70cyuS0uA+SGl55eSTmaNouOy2QfpuLx2vhkFtNBxMsHujn0vsBSYT7gt1wi8aGYXpiPIDBkBFJDcedHVedT2Wj7rTX/VAv8E3ADMA6qAx8xscbqCzHEpPb+UdM7CzO7q4oFj4jazjz+m/adzrZOynJCC/jrrsbv7S+7+U3d/1d23ATcC7wBfS+2RZIVkz4vO6ndWnq963F/ufsjdV7n7Dnff5e6VwBpgebqDzGEpO79yZhG3DLkP+Hk3dd7rw/4/pOM7hZF0fFeRK3raX1MJ705HADUJr40Enu/pD3P3FjPbBeTTlc4hwlVgMudFV+cRZ2mTL3rTX53ZCXw5VUHlmZSeX0o6Z+Huh0jv+hsvARXAvQllFYTRNzmnp/1lZq8ApwjH+khUVg6MJ4ljj4Zsfg54rTfxZiN3b4r6pwJYn/BSBfBfXTR7Cfi+mQ30j0fyVQC/B/anK9Zs0Mv+6szFwB9SGVseSe35lenRE/myEd4JXAzcRLjknBd9PzyhThUJI2oIDzqbgduBcdG/p4BLM308MfTXjwijX75AGOb6DPAqUHCW/voOMAf4s6hvfxL115RMH0+K++ZGwui+vyYk4tWE5xBjotfvBqoS6g8hvBtdB/wFsJAw2uibmT6WLO2vW6Lf0/HARYTnO03AP2b6WGLqr0HR78/FhI8gVEZfXxDH+ZXxDsiXjfD5HO9kW5JQZz/wULt21wFvRSf9b4GFmT6WmPprIPAD4HB04m8Czm9X54z+Av6NsJLrSeAjwgiaaZk+ljT1z1ei4z8JvAJcnvDaQ8D+dvUnEG5NNhLesX+HT8Bw6d70V5R03gTqoj+eu4DFmT6GGPtqZhd/qx6K4/zSLNMiIhIbjV4TEZHYKOmIiEhslHRERCQ2SjoiIhIbJR0REYmNko6IiMRGSUckC7Sbn25JFsRzWbuYPp3pmCQ/KOmIZI8fE6aR/59MB0KYWmgacFemA5H8ornXRLLHB+6+I9NBALj7CWCHmY3LdCySX3SlI5ICZlZqZm+Z2ctmVphQPtvMWs3sq73c72QzeyJatK7BzPaa2UozK+5B22fN7NlOyveb2UO9iUekr5R0RFLA3esIC8t9HvgugJmNBH4GbHb3H/Zy1xcQJkL9O2AuYTLLpcCDfY1ZJBN0e00kRdx9j5mtAFaZ2a8Jsxe3EJJEb/d5enr+aCmHFwmTVP7MzL7q7of7GLZIrJR0RFLrPsJaI5uBIqDCwzpDvWJmZcC3CLORnw8UJrx8IWGWbpGcodtrIinkYdr2/wQGAK+5e1Ufd/kg4dbavxOS2WSg7fnQwD7uWyR2SjoiKWRmowhXO7uBz5vZ1/uwr4HAfOBed1/t7s+5+y6goYe7aCRcbbU3vLcxifSVko5IikTPXH5KWJCvgpB8vm9mn+vlLgcABYTVURMt6WH7d4HPmNnpxGNmlwODexmPSJ8p6YikzjcIy28vdvcjwArCCpWP9mSIc3vufhzYAXzTzG42s3lm9gRwXvu6ZlZpZs1mNiaheB3wJ8BPzOwLZvY3wBrgeLu2Y6K2lcnGKJIsJR2RFDCzS4CVwN3u/hyAuzcRhlGPBf61l7teRFh++YeEZYQ/BDq7ZdePcFVkbQXu/gzhedClhOXAvwwsBo61Dz9qq78HknZarlokC5iZEz7f8y9Ai2fBL6aZ9QduJkzPc6G778twSJIH9M5GJHvcQXh+c0umAzGzy6JYfpzpWCS/6HM6ItlhcsLX1RmL4mOvcmZM72cqEMkvur0mIiKx0e01ERGJjZKOiIjERklHRERio6QjIiKxUdIREZHY/D/ZTrXylk5qaQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "K_rev = model_K_all.predict([whiten(X1_train), whiten(X2_train)], batch_size=X1_train.shape[0])[0]\n",
    "eigvals_rev, eigvec_rev = np.linalg.eig(K_rev)\n",
    "sort_ind = np.argsort(eigvals_rev)[::-1]\n",
    "eigvals_rev = eigvals_rev[sort_ind]\n",
    "eigvec_rev = eigvec_rev[:,sort_ind]\n",
    "\n",
    "pred_xax = model_chi.predict([whiten(xax), whiten(xax)], batch_size=xax.shape[0])[:,:output_size]\n",
    "eigfunc_rev = pred_xax @ eigvec_rev\n",
    "for i in range(1,output_size):\n",
    "    plt.title('Eigfunc with $\\lambda={:.3}$'.format(true_eigvals[i]),fontsize=18)\n",
    "\n",
    "    fac1 = true_eigfunc[0,i] / eigfunc_rev[0,i]\n",
    "    fac2 = true_eigfunc[-1,i] / eigfunc_rev[-1,i]\n",
    "    fac = (fac1 + fac2)/2\n",
    "    plt.plot(xax, fac*eigfunc_rev[:,i], label='Rev')\n",
    "    plt.plot(xax[::10], true_eigfunc[:,i], 'k', label='True')\n",
    "    plt.legend(fontsize=16)\n",
    "    plt.xlabel('x [a.u.]', fontsize=16)\n",
    "    plt.xticks([-1.,-.5,0,0.5,1.],fontsize=14)\n",
    "    plt.yticks(fontsize=14)\n",
    "    plt.ylabel('$\\psi$ [a.u.]', fontsize=16)\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Training for revDMSM"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Initialization method"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [],
   "source": [
    "def optimize_u_dmsm(reset_chi=True):\n",
    "    ''' \n",
    "    Calculate the optimal u for a given chi, and set the kernel of the corresponding layer\n",
    "    to the optimal value. This is necessary to stabilize the training.\n",
    "    Needs to be rewritten if the activation functions for the weights are changed!\n",
    "    Uses another activation than revVAMPnet.\n",
    "    '''\n",
    "    if reset_chi:\n",
    "        model_chi.set_weights(weights_chi)\n",
    "    fullbatch = X1_train.shape[0]\n",
    "        \n",
    "    Data_chi = model_chi.predict([whiten(X1_train), whiten(X2_train)], batch_size=fullbatch)\n",
    "    Data_chi_X = Data_chi[:,:output_size]\n",
    "    Data_chi_Y = Data_chi[:,output_size:]\n",
    "    fullbatch = Data_chi_X.shape[0]\n",
    "    \n",
    "    \n",
    "    c_0 = 1/fullbatch * Data_chi_X.T @ Data_chi_X\n",
    "    c_tau = 1/fullbatch * Data_chi_X.T @ Data_chi_Y\n",
    "    c_1 = 1/fullbatch * Data_chi_Y.T @ Data_chi_Y\n",
    "    \n",
    "    eigv_all, eigvec_all = np.linalg.eigh(c_0)\n",
    "    include = eigv_all > epsilon\n",
    "    eigv = eigv_all[include]\n",
    "    eigvec = eigvec_all[:,include]\n",
    "    c0_inv = eigvec @ np.diag(1/eigv) @ np.transpose(eigvec)\n",
    "        \n",
    "    K_vamp = c0_inv @ c_tau\n",
    "    \n",
    "    # estimate pi, the stationary distribution vector\n",
    "    eigv, eigvec = np.linalg.eig(K_vamp.T)\n",
    "    ind_pi = np.argmin((eigv-1)**2)\n",
    "    \n",
    "    pi_vec = eigvec[:,ind_pi]\n",
    "    pi = pi_vec / np.sum(pi_vec, keepdims=True)\n",
    "        \n",
    "    \n",
    "    u_optimal = c0_inv @ pi\n",
    "    u_kernel = np.log(np.abs(u_optimal))\n",
    "    vamp_layer_u_msm.set_weights([u_kernel])\n",
    "    \n",
    "    return None\n",
    "\n",
    "def optimize_S_dmsm(reset_chi=True):\n",
    "    ''' \n",
    "    Calculate the optimal S for a given chi, and set the kernel of the corresponding layer\n",
    "    to the optimal value. This is necessary to stabilize the training.\n",
    "    Needs to be rewritten if the activation functions for the weights are changed!\n",
    "    '''\n",
    "    if reset_chi:\n",
    "        model_chi.set_weights(weights_chi)\n",
    "    fullbatch = X1_train.shape[0]\n",
    "        \n",
    "    Data_chi = model_chi.predict([whiten(X1_train), whiten(X2_train)], batch_size=fullbatch)\n",
    "    Data_chi_X = Data_chi[:,:output_size]\n",
    "    Data_chi_Y = Data_chi[:,output_size:]\n",
    "    fullbatch = Data_chi_X.shape[0]\n",
    "    \n",
    "    \n",
    "    c_0 = 1/fullbatch * Data_chi_X.T @ Data_chi_X\n",
    "    c_tau = 1/fullbatch * Data_chi_X.T @ Data_chi_Y\n",
    "    c_1 = 1/fullbatch * Data_chi_Y.T @ Data_chi_Y\n",
    "    \n",
    "    eigv_all, eigvec_all = np.linalg.eigh(c_0)\n",
    "    include = eigv_all > epsilon\n",
    "    eigv = eigv_all[include]\n",
    "    eigvec = eigvec_all[:,include]\n",
    "    c0_inv = eigvec @ np.diag(1/eigv) @ np.transpose(eigvec)\n",
    "        \n",
    "    K_vamp = c0_inv @ c_tau\n",
    "    \n",
    "    # get Sigma, invert it to get proxy S, meaning the closest symmetric S you can obtain to the optimal S\n",
    "    \n",
    "    v_input, C_00_input, C_11_input, C_01_input, Sigma_input = model_input_S_msm.predict([Data_chi_X, Data_chi_Y], batch_size=Data_chi_X.shape[0])\n",
    "    \n",
    "    eigv_all, eigvec_all = np.linalg.eigh(Sigma_input[0])\n",
    "    include = eigv_all > epsilon\n",
    "    eigv = eigv_all[include]\n",
    "    eigvec = eigvec_all[:,include]\n",
    "    sigma_inv = eigvec @ np.diag(1/eigv) @ np.transpose(eigvec)\n",
    "    \n",
    "    S_nonrev = K_vamp @ sigma_inv\n",
    "    \n",
    "    S_rev_add = 1/2 * (S_nonrev + S_nonrev.T)\n",
    "    \n",
    "    kernel_S = S_rev_add / 2.\n",
    "    kernel_S = np.log(np.abs(kernel_S))\n",
    "    \n",
    "    vamp_layer_S_msm.set_weights([kernel_S])\n",
    "            \n",
    "    return None"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [],
   "source": [
    "optimize_u_dmsm()\n",
    "optimize_S_dmsm()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "Data_chi = model_chi.predict([whiten(X1_train), whiten(X2_train)], batch_size=X1_train.shape[0])\n",
    "Data_chi_X = Data_chi[:,:output_size]\n",
    "Data_chi_Y = Data_chi[:,output_size:]\n",
    "\n",
    "Data_chi_vali = model_chi.predict([whiten(X1_vali), whiten(X2_vali)], batch_size=X1_vali.shape[0])\n",
    "Data_chi_X_vali = Data_chi_vali[:,:output_size]\n",
    "Data_chi_Y_vali = Data_chi_vali[:,output_size:]\n",
    "\n",
    "\n",
    "model_both_vampE_msm.compile(keras.optimizers.Adam(learning_rate=learning_rate*10, clipnorm=1.),\n",
    "             loss_vampe,\n",
    "         )\n",
    "\n",
    "hist = model_both_vampE_msm.fit([Data_chi_X, Data_chi_Y], Y_train ,\n",
    "                 batch_size = Data_chi_X.shape[0],\n",
    "                 epochs = epoch_S,\n",
    "                 validation_data = ([Data_chi_X_vali, Data_chi_Y_vali], Y_vali ),\n",
    "                 verbose = 0,\n",
    "                 callbacks = callbacks,\n",
    "                 shuffle = True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "model_all_vampE_msm.compile(keras.optimizers.Adam(learning_rate=learning_rate*0.04, clipnorm=1.),\n",
    "                 loss_vampe,\n",
    "             )\n",
    "\n",
    "hist = model_all_vampE_msm.fit(\n",
    "    [whiten(X1_train), whiten(X2_train)],\n",
    "    Y_train,\n",
    "    batch_size = X1_train.shape[0],\n",
    "    epochs = epoch_all,\n",
    "    validation_data = ([whiten(X1_vali), whiten(X2_vali)], Y_vali ),\n",
    "    verbose = 0,\n",
    "    callbacks = [EarlyStopping('val_loss', patience=50, mode='min', restore_best_weights=True)],\n",
    "    shuffle = True\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Error of rev: 2.838046737599744, of sym: 5.0150186078936985\n"
     ]
    }
   ],
   "source": [
    "K_result = model_K_all_msm.predict([whiten(X1_train), whiten(X2_train)], batch_size=X1_train.shape[0])\n",
    "\n",
    "mu_result_rev = model_mu_msm.predict([whiten(X1_train), whiten(X2_train)], batch_size=X1_train.shape[0])\n",
    "hist_rev, bin = np.histogram(X1_train.reshape(-1), bins=200, range=(-1,1), density=True, weights=mu_result_rev.reshape(-1))\n",
    "prinz_en = data_generator.prinz_energy(bin[:-1])\n",
    "prinz_stat = np.exp(-prinz_en/kT_prinz)\n",
    "scaled_prinz_stat = prinz_stat / (prinz_stat.sum() * (bin[1]-bin[0]))       \n",
    "plt.plot(bin[:-1], scaled_prinz_stat, label = 'True', c='k')\n",
    "plt.plot(bin[:-1], hist_rev, label = 'Rev')\n",
    "plt.plot(bin[:-1], hist_sym, label = 'Sym')\n",
    "plt.legend()\n",
    "plt.show()\n",
    "\n",
    "rev_states_prob = np.sum(np.split(hist_rev, 4), 1)\n",
    "sym_states_prob = np.sum(np.split(hist_sym, 4), 1)\n",
    "tru_states_prob = np.sum(np.split(scaled_prinz_stat, 4), 1)\n",
    "plt.plot(np.abs(rev_states_prob), '.', ms=12, label = \"Rev\")\n",
    "plt.plot(np.abs(sym_states_prob), '.', ms=12, label = \"Sym\")\n",
    "for j in range(4):\n",
    "    legend=None\n",
    "    if j>2:\n",
    "        legend='True'\n",
    "    plt.hlines(tru_states_prob[j], j-0.3, j+0.3, colors='k', linestyles='--', label=legend, lw=2)\n",
    "plt.legend()\n",
    "plt.show()\n",
    "\n",
    "print('Error of rev: {}, of sym: {}'.format(np.linalg.norm(hist_rev - prinz_stat), np.linalg.norm(hist_sym - prinz_stat)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "K_rev_msm = model_K_all_msm.predict([whiten(X1_train), whiten(X2_train)], batch_size=X1_train.shape[0])[0]\n",
    "eigvals_rev, eigvec_rev = np.linalg.eig(K_rev_msm)\n",
    "sort_ind = np.argsort(eigvals_rev)[::-1]\n",
    "eigvals_rev = eigvals_rev[sort_ind]\n",
    "eigvec_rev = eigvec_rev[:,sort_ind]\n",
    "\n",
    "pred_xax = model_chi.predict([whiten(xax), whiten(xax)], batch_size=xax.shape[0])[:,:output_size]\n",
    "eigfunc_rev_msm1 = pred_xax @ eigvec_rev\n",
    "for i in range(1,output_size):\n",
    "    plt.title('Eigfunc with $\\lambda={}$'.format(true_eigvals[i]))\n",
    "    fac = true_eigfunc[0,i] / eigfunc_rev_msm1[0,i]\n",
    "    plt.plot(xax, fac*eigfunc_rev_msm1[:,i], label='Rev')\n",
    "    plt.plot(xax[::10], true_eigfunc[:,i], 'k', label='True')\n",
    "    plt.legend()\n",
    "    plt.xlabel('x [a.u.]', fontsize=14)\n",
    "    plt.xticks(fontsize=12)\n",
    "    plt.yticks(fontsize=12)\n",
    "    plt.ylabel('$\\psi$ [a.u.]', fontsize=14)\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Old score 0.0, new score 3.7249302864074707\n",
      "Score is better and weights are saved\n",
      "Old score 3.7249302864074707, new score 3.7248692512512207\n"
     ]
    }
   ],
   "source": [
    "score = 0.\n",
    "weights_all = model_all_vampE.get_weights()\n",
    "score_old = score\n",
    "\n",
    "model_both_vampE_msm.compile(\n",
    "    keras.optimizers.Adam(learning_rate=learning_rate*100, clipnorm=1.),\n",
    "    loss_vampe,\n",
    ")\n",
    "\n",
    "model_all_vampE_msm.compile(\n",
    "    keras.optimizers.Adam(learning_rate=learning_rate*0.04, clipnorm=1.),\n",
    "    loss_vampe,\n",
    ")\n",
    "\n",
    "while (score >= score_old):\n",
    "    \n",
    "    optimize_u_dmsm(reset_chi=False)\n",
    "\n",
    "    Data_chi = model_chi.predict([whiten(X1_train), whiten(X2_train)], batch_size=X1_train.shape[0])\n",
    "    Data_chi_X = Data_chi[:,:output_size]\n",
    "    Data_chi_Y = Data_chi[:,output_size:]\n",
    "    \n",
    "    Data_chi_vali = model_chi.predict([whiten(X1_vali), whiten(X2_vali)], batch_size=X1_vali.shape[0])\n",
    "    Data_chi_X_vali = Data_chi_vali[:,:output_size]\n",
    "    Data_chi_Y_vali = Data_chi_vali[:,output_size:]\n",
    "\n",
    "    hist = model_both_vampE_msm.fit([Data_chi_X, Data_chi_Y], Y_train ,\n",
    "                     batch_size = Data_chi_X.shape[0],\n",
    "                     epochs = epoch_S,\n",
    "                     validation_data = ([Data_chi_X_vali, Data_chi_Y_vali], Y_vali ),\n",
    "                     verbose = 0,\n",
    "                     callbacks = [EarlyStopping('val_loss', patience=50, mode='min', restore_best_weights=True)],\n",
    "                     shuffle = True)\n",
    "    \n",
    "    hist = model_all_vampE_msm.fit(\n",
    "        [whiten(X1_train), whiten(X2_train)],\n",
    "        Y_train,\n",
    "        batch_size = X1_train.shape[0],\n",
    "        epochs = epoch_all,\n",
    "        validation_data = ([whiten(X1_vali), whiten(X2_vali)], Y_vali ),\n",
    "        verbose = 0,\n",
    "        callbacks = callbacks,\n",
    "        shuffle = True\n",
    "    )\n",
    "\n",
    "    score = - model_all_vampE_msm.evaluate([whiten(X1_vali), whiten(X2_vali)], batch_size = X1_vali.shape[0], verbose = 0)\n",
    "\n",
    "    print('Old score {}, new score {}'.format(score_old, score))\n",
    "    if (score>score_old):\n",
    "        print('Score is better and weights are saved')\n",
    "        score_old = score\n",
    "        weights_all = model_all_vampE_msm.get_weights()\n",
    "        \n",
    "        \n",
    "model_all_vampE_msm.set_weights(weights_all)\n",
    "optimize_u_dmsm(reset_chi=False)\n",
    "\n",
    "Data_chi = model_chi.predict([whiten(X1_train), whiten(X2_train)], batch_size=X1_train.shape[0])\n",
    "Data_chi_X = Data_chi[:,:output_size]\n",
    "Data_chi_Y = Data_chi[:,output_size:]\n",
    "\n",
    "Data_chi_vali = model_chi.predict([whiten(X1_vali), whiten(X2_vali)], batch_size=X1_vali.shape[0])\n",
    "Data_chi_X_vali = Data_chi_vali[:,:output_size]\n",
    "Data_chi_Y_vali = Data_chi_vali[:,output_size:]\n",
    "\n",
    "hist = model_both_vampE_msm.fit([Data_chi_X, Data_chi_Y], Y_train ,\n",
    "                 batch_size=Data_chi_X.shape[0],\n",
    "                 epochs = epoch_S,\n",
    "                 validation_data=([Data_chi_X_vali, Data_chi_Y_vali], Y_vali ),\n",
    "                 verbose=0,\n",
    "                 callbacks=callbacks,\n",
    "                 shuffle=True)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Error of rev: 2.49789350834939, of sym: 5.0150186078936985\n"
     ]
    }
   ],
   "source": [
    "mu_result_rev = model_mu_msm.predict([whiten(X1_train), whiten(X2_train)], batch_size=X1_train.shape[0])\n",
    "hist_rev, bin = np.histogram(X1_train.reshape(-1), bins=200, range=(-1,1), density=True, weights=mu_result_rev.reshape(-1))\n",
    "prinz_en = data_generator.prinz_energy(bin[:-1])\n",
    "prinz_stat = np.exp(-prinz_en/kT_prinz)\n",
    "scaled_prinz_stat = prinz_stat / (prinz_stat.sum() * (bin[1]-bin[0]))       \n",
    "plt.plot(bin[:-1], scaled_prinz_stat, label = 'True', c='k')\n",
    "plt.plot(bin[:-1], hist_rev, label = 'Rev')\n",
    "plt.plot(bin[:-1], hist_sym, label = 'Sym')\n",
    "plt.legend()\n",
    "plt.show()\n",
    "\n",
    "rev_states_prob = np.sum(np.split(hist_rev, 4), 1)\n",
    "sym_states_prob = np.sum(np.split(hist_sym, 4), 1)\n",
    "tru_states_prob = np.sum(np.split(scaled_prinz_stat, 4), 1)\n",
    "plt.plot(np.abs(rev_states_prob), '.', ms=12, label = \"Rev\")\n",
    "plt.plot(np.abs(sym_states_prob), '.', ms=12, label = \"Sym\")\n",
    "for j in range(4):\n",
    "    legend=None\n",
    "    if j>2:\n",
    "        legend='True'\n",
    "    plt.hlines(tru_states_prob[j], j-0.3, j+0.3, colors='k', linestyles='--', label=legend, lw=2)\n",
    "plt.legend()\n",
    "plt.show()\n",
    "print('Error of rev: {}, of sym: {}'.format(np.linalg.norm(hist_rev - prinz_stat), np.linalg.norm(hist_sym - prinz_stat)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "K_rev_msm = model_K_all_msm.predict([whiten(X1_train), whiten(X2_train)], batch_size=X1_train.shape[0])[0]\n",
    "eigvals_rev, eigvec_rev = np.linalg.eig(K_rev_msm)\n",
    "sort_ind = np.argsort(eigvals_rev)[::-1]\n",
    "# sort_ind = [2,1,3,0]\n",
    "eigvals_rev = eigvals_rev[sort_ind]\n",
    "eigvec_rev = eigvec_rev[:,sort_ind]\n",
    "\n",
    "pred_xax = model_chi.predict([whiten(xax), whiten(xax)], batch_size=xax.shape[0])[:,:output_size]\n",
    "eigfunc_rev_msm = pred_xax @ eigvec_rev\n",
    "for i in range(1,output_size):\n",
    "    plt.title('Eigfunc with $\\lambda={}$'.format(true_eigvals[i]))\n",
    "    fac = true_eigfunc[0,i] / eigfunc_rev_msm[0,i]\n",
    "    plt.plot(xax, fac*eigfunc_rev_msm[:,i], label='Rev')\n",
    "    plt.plot(xax[::10], true_eigfunc[:,i], 'k', label='True')\n",
    "    plt.legend()\n",
    "    plt.xlabel('x [a.u.]', fontsize=14)\n",
    "    plt.xticks(fontsize=12)\n",
    "    plt.yticks(fontsize=12)\n",
    "    plt.ylabel('$\\psi$ [a.u.]', fontsize=14)\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# compare all three methods for the eigenfunctions\n",
    "x_pos = [0.25,0.25,-0.5]\n",
    "y=[-1.,1.5,1.7]\n",
    "fontsize2 = 14\n",
    "fontsize1 = 12\n",
    "for i in range(1,output_size):\n",
    "    index_al = np.argmax(np.abs(true_eigfunc[:,i]))\n",
    "    plt.text(x_pos[i-1],y[i-1],'$\\lambda_{}={:.3}$'.format(i,true_eigvals[i]), fontsize=fontsize2+2)\n",
    "    plt.plot(xax[::10], true_eigfunc[:,i], 'k', lw=3, label='True')\n",
    "    fac = true_eigfunc[index_al,i] / eigfunc_rev[index_al,i]\n",
    "    fac1 = true_eigfunc[0,i] / eigfunc_rev[0,i]\n",
    "    fac2 = true_eigfunc[-1,i] / eigfunc_rev[-1,i]\n",
    "    fac = (fac1 + fac2)/2\n",
    "    plt.plot(xax, fac*eigfunc_rev[:,i], lw=3, label='Rev VAMPnet')\n",
    "    \n",
    "    \n",
    "    index_al = np.argmax(np.abs(true_eigfunc[:,i]))\n",
    "    fac = true_eigfunc[index_al,i] / eigfunc_rev_msm[index_al,i]\n",
    "    fac1 = true_eigfunc[0,i] / eigfunc_rev_msm[0,i]\n",
    "    fac2 = true_eigfunc[-1,i] / eigfunc_rev_msm[-1,i]\n",
    "    fac = (fac1 + fac2)/2\n",
    "    plt.plot(xax, fac*eigfunc_rev_msm[:,i], lw=3, label='Rev MSMVAMPnet')\n",
    "    \n",
    "    index_al = np.argmax(np.abs(true_eigfunc[:,i]))\n",
    "    fac = true_eigfunc[index_al,i] / eigfunc_sym[index_al,i]\n",
    "    fac1 = true_eigfunc[0,i] / eigfunc_sym[0,i]\n",
    "    fac2 = true_eigfunc[-1,i] / eigfunc_sym[-1,i]\n",
    "    fac = (fac1 + fac2)/2\n",
    "    plt.plot(xax, fac*eigfunc_sym[:,i], lw=3, label='Sym VAMPnet')\n",
    "    if i==1:\n",
    "        plt.legend(fontsize=fontsize2)\n",
    "    plt.xlabel('x [a.u.]', fontsize=fontsize1)\n",
    "    plt.xticks([-1,-.5,0,.5,1], fontsize=fontsize2)\n",
    "    plt.yticks(fontsize=fontsize2)\n",
    "    plt.ylabel('$\\psi_{}$ [a.u.]'.format(i), fontsize=fontsize1)\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-11-06T22:59:14.811029Z",
     "start_time": "2019-11-06T22:48:58.197Z"
    }
   },
   "outputs": [],
   "source": [
    "# code to estimate the implied timescales for the revVAMPnet\n",
    "\n",
    "def optimize_S_new_tau(factor_S, X1_train, X2_train):\n",
    "    ''' \n",
    "    Calculate the optimal S for a given chi, and set the kernel of the corresponding layer\n",
    "    to the optimal value. This is necessary to stabilize the training.\n",
    "    Needs to be rewritten if the activation functions for the weights are changed!\n",
    "    '''\n",
    "    fullbatch = X1_train.shape[0]\n",
    "        \n",
    "    Data_chi = model_chi.predict([whiten(X1_train), whiten(X2_train)], batch_size=fullbatch)\n",
    "    Data_chi_X = Data_chi[:,:output_size]\n",
    "    Data_chi_Y = Data_chi[:,output_size:]\n",
    "    fullbatch = Data_chi_X.shape[0]\n",
    "    \n",
    "    \n",
    "    c_0 = 1/fullbatch * Data_chi_X.T @ Data_chi_X\n",
    "    c_tau = 1/fullbatch * Data_chi_X.T @ Data_chi_Y\n",
    "    c_1 = 1/fullbatch * Data_chi_Y.T @ Data_chi_Y\n",
    "    \n",
    "    eigv_all, eigvec_all = np.linalg.eigh(c_0)\n",
    "    include = eigv_all > epsilon\n",
    "    eigv = eigv_all[include]\n",
    "    eigvec = eigvec_all[:,include]\n",
    "    c0_inv = eigvec @ np.diag(1/eigv) @ np.transpose(eigvec)\n",
    "        \n",
    "    K_vamp = c0_inv @ c_tau\n",
    "    \n",
    "    # get Sigma, invert it to get proxy S, meaning the closest symmetric S you can obtain to the optimal S\n",
    "    \n",
    "    v_input, C_00_input, C_11_input, C_01_input, Sigma_input = model_input_S.predict([Data_chi_X, Data_chi_Y], batch_size=Data_chi_X.shape[0])\n",
    "    \n",
    "    eigv_all, eigvec_all = np.linalg.eigh(Sigma_input[0])\n",
    "    include = eigv_all > epsilon\n",
    "    eigv = eigv_all[include]\n",
    "    eigvec = eigvec_all[:,include]\n",
    "    sigma_inv = eigvec @ np.diag(1/eigv) @ np.transpose(eigvec)\n",
    "    \n",
    "    # reverse the construction of S\n",
    "    S_nonrev = K_vamp @ sigma_inv\n",
    "    S_rev_add = 1/2 * (S_nonrev + S_nonrev.T)\n",
    "    kernel_S = S_nonrev / 2. / factor_S\n",
    "    \n",
    "    vamp_layer_S.set_weights([kernel_S])\n",
    "        \n",
    "    return None\n",
    "\n",
    "def training_for_tau_both(new_tau):\n",
    "    '''Estimate the Koopman matrix for a specific tau in order to estimate the\n",
    "    implied timescales. Therefore, u and S have to be retrained for the new tau,\n",
    "    while we keep chi fixed.'''\n",
    "    \n",
    "    # reestimate the training and validation data for the new tau\n",
    "    traj_data_train = np.concatenate([traj[:-new_tau] for traj in training_trajs])\n",
    "    traj_data_train_lag = np.concatenate([traj[new_tau:] for traj in training_trajs])\n",
    "\n",
    "    traj_data_valid = np.concatenate([traj[:-new_tau] for traj in validation_trajs])\n",
    "    traj_data_valid_lag = np.concatenate([traj[new_tau:] for traj in validation_trajs])\n",
    "\n",
    "    # Input of the first network\n",
    "    X1_train = traj_data_train.astype('float32')\n",
    "    X2_train  = traj_data_train_lag.astype('float32')\n",
    "\n",
    "    X1_vali = traj_data_valid.astype('float32')\n",
    "    X2_vali  = traj_data_valid_lag.astype('float32')\n",
    "\n",
    "    Y_train = np.zeros((X1_train.shape[0], output_size))\n",
    "    Y_vali = np.zeros((X1_vali.shape[0], output_size))\n",
    "    \n",
    "    # reset S, u should not change to much\n",
    "    reset_weights(vamp_layer_S.variables[0])\n",
    "    # estimate a new guess\n",
    "    optimize_S_new_tau(factor_S, X1_train, X2_train)\n",
    "    \n",
    "    model_S_vampE = keras.models.Model(inputs = [Data_v_keras, Data_C_00_keras, Data_C_11_keras, Data_C_01_keras, Data_Sigma_keras], outputs = VampE_matrix_S)\n",
    "    adam = keras.optimizers.Adam(learning_rate=learning_rate*1000, )\n",
    "    model_S_vampE.compile(adam, loss_vampe)\n",
    "\n",
    "    model_K_S = keras.models.Model(inputs = [Data_v_keras, Data_C_00_keras, Data_C_11_keras, Data_C_01_keras, Data_Sigma_keras], outputs = K_S)\n",
    "\n",
    "    Data_chi = model_chi.predict([whiten(X1_train), whiten(X2_train)], batch_size=X1_train.shape[0])\n",
    "    Data_chi_X = Data_chi[:,:output_size]\n",
    "    Data_chi_Y = Data_chi[:,output_size:]\n",
    "    Data_chi_vali = model_chi.predict([whiten(X1_vali), whiten(X2_vali)], batch_size=X1_vali.shape[0])\n",
    "    Data_chi_X_vali = Data_chi_vali[:,:output_size]\n",
    "    Data_chi_Y_vali = Data_chi_vali[:,output_size:]\n",
    "\n",
    "    v_input, C_00_input, C_11_input, C_01_input, Sigma_input = model_input_S.predict([Data_chi_X, Data_chi_Y], batch_size=Data_chi_X.shape[0])\n",
    "    v_input_vali, C_00_input_vali, C_11_input_vali, C_01_input_vali, Sigma_input_vali = model_input_S.predict([Data_chi_X_vali, Data_chi_Y_vali], batch_size=Data_chi_X_vali.shape[0])\n",
    "\n",
    "    hist = model_S_vampE.fit([v_input[0][None], C_00_input[0][None], C_11_input[0][None], C_01_input[0][None], Sigma_input[0][None]], np.zeros_like(v_input[0][None]) ,\n",
    "                 batch_size=v_input[0][None].shape[0],\n",
    "                 epochs = epoch_S,\n",
    "                 validation_data=([v_input_vali[0][None], C_00_input_vali[0][None], C_11_input_vali[0][None], C_01_input_vali[0][None], Sigma_input_vali[0][None]], np.zeros_like(v_input_vali[0][None])),\n",
    "                 verbose=0,\n",
    "                 callbacks=callbacks,\n",
    "                 shuffle=True)\n",
    "\n",
    "    adam = keras.optimizers.Adam(learning_rate=learning_rate*2, clipnorm=1.)\n",
    "    model_both_vampE.compile(adam,\n",
    "                     loss_vampe,\n",
    "                     )\n",
    "    model_K_both = keras.models.Model(inputs = [Data_chi_t_keras, Data_chi_tau_keras], outputs = K_both)\n",
    "    hist = model_both_vampE.fit([Data_chi_X, Data_chi_Y], Y_train,\n",
    "                 batch_size=Data_chi_X.shape[0],\n",
    "                 epochs=epoch_all,\n",
    "                 validation_data=([Data_chi_X_vali, Data_chi_Y_vali], Y_vali ),\n",
    "                 verbose=0,\n",
    "                 callbacks = [EarlyStopping('val_loss', patience=500, mode='min', restore_best_weights=True)],\n",
    "                 shuffle=True)\n",
    "\n",
    "\n",
    "    K_result = model_K_all.predict([whiten(X1_train), whiten(X2_train)], batch_size=X1_train.shape[0])\n",
    "\n",
    "    return K_result[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-11-06T22:59:14.812777Z",
     "start_time": "2019-11-06T22:48:58.455Z"
    },
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1\n",
      "2\n",
      "3\n",
      "4\n",
      "6\n",
      "8\n",
      "10\n"
     ]
    }
   ],
   "source": [
    "model_all_vampE.set_weights(weights_chi_rev)\n",
    "K_results_rev = np.ones((number_taus, output_size, output_size))\n",
    "K_results = np.ones_like(K_results_rev)\n",
    "for i, tau_i in enumerate(tau_list):\n",
    "    print(tau_i)\n",
    "    K_results_rev[i]= training_for_tau_both(tau_i)\n",
    "    K_results[i]  = estimate_koopman_op(pred_ord_chi, tau_i, force_symmetric = True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-11-06T22:59:14.814297Z",
     "start_time": "2019-11-06T22:48:58.814Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXcAAAD4CAYAAAAXUaZHAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADh0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uMy4xLjAsIGh0dHA6Ly9tYXRwbG90bGliLm9yZy+17YcXAAAelklEQVR4nO3df3BU9b3/8ed7s/lJCFRIQsgPggiGgLVC1EI6CForjiCIVNBpRYtinWuL337H2vbbzv3OdO617Yh+tdrO4PVHv61T61iqeLU/rvpl7BRwBLUjBWzBGoiIcFFQfiTZH5/vH7s52d1sQiAbTnLyejg7e87nfM7nfPZIXjn57GfPmnMOEREJlpDfHRARkdxTuIuIBJDCXUQkgBTuIiIBpHAXEQmgsN8dABg7dqyrr6/3uxsiIkPK1q1b/9s5V55t26AI9/r6erZs2eJ3N0REhhQza+lpm4ZlREQCSOEuIhJACncRkQBSuIuIBJDCXUQkgBTuIiIB5Gu4m9lCM1t75MgRP7shIhI4vs5zd849Dzzf1NR0q5/9EBkOnHM4B65zGZLryfLUZSCerE8P5S6xIaOs6zhkK8/oh7fdJZaha7mzbtwByePHXVc7cZf9+J3lmWUu2U485bV2tkeWviSrp/Qltdxl9CX1daX01Tu32c5fonz+9HFMGz8q5/+/B8WHmCQ4YnHH0fYo0VicmHPE4ySfHbG461p2iXXnSC/3lrPvF3c9t9dVRrJuajk91D1Zu2Q/Vk/l3msjpW62EEoJ1GxBS/Ywjse7QietPKVuZxjHM9qWwccMzi4foXCXgdMRjXO0PcrRtiiftkc42hZNrLdH+bRzuS11PZJSv2vb8Y6Y3y+lVyGDvJARMiMvZOSZEQpZt3Jve5ZteSHDzMhLKS8Ih7Lsj1fXgJAZZmDglVlaGRjJ9SzloWQ5GXU7yw0grW5Ke8mdQhll6cfqKu/sK2l9TX8NZH1diXborOsdI+O1ZTsfGcdOrWuZfU97/d3bCWX0mW797zpHpJzbzNceCmW89uQ5DmXrV4i+9TXlvA8khfsQFIs72iIx2qNx2iKxtOXjHbGUME4GcHssEcZtGWGdEs4d0fhJjxsyKC0MM7Ion9LCMKVFYUaXFFBzVgkjC8NeWWlhmPy8EKFkeOaFyAjLrmcvOL26qSFKRt3s5ZntJgK7e53QGfiBEhksFO795FxiGOJYe4z2aIy2SDwtbLMFcHs0TnskRlvncyROWzRGe8ZzWyROe3I9te1o/NT+xi4IhxLhmwze0sIwVaOKUsI4n5Ep20YUhrvWi8LevsX5eQpHkSFiyIf73Llz+92GA1won3i4iHi4iFi4iHhekbceDxd66zFvvTjxHC4CO71JRxaPYPFo8hFLWY91lbuotxyKRxkRj6bs01mnq34o1oHFOgjF2gnFOhLrrmuo5Fjy8WG/z5qI5MKGDRsGpN0hH+6deg7oRAB3hXUhsXBxWmDH8wohlNdL43FC0TZC0XZCsTZC0TbCbUfIi7Yl1xNBmgjYSI/h3C2Qz9jZEZHhZkiH+//d9B6hBf+bIyciHDkR6XW4ImRQVpzPmOJ8RhXnU5Z87vFR0rVcWhjWcISIDClDOtw/U1LA1PFlXgiPzgjospSgLi0IEwopoEVkeBjS4b7w/PEsPH+8390QERl0dG8ZEZEAUriLiASQwl1EJIAU7iIiAaRwFxEJIIW7iEgAKdxFRAJI4S4iEkAKdxGRAFK4i4gEkMJdRCSAFO4iIgE0IOFuZovN7BEze87MvjQQxxARkZ71OdzN7DEzO2Bm2zLK55vZO2a2y8y+A+Cce9Y5dytwE7Aspz0WEZGTOpUr9yeA+akFZpYHPAxcCTQC15tZY0qV7ye3i4jIGdTncHfOvQp8lFF8EbDLOfeuc64DeApYZAk/Bn7vnHsjW3tmtsrMtpjZloMHD55u/0VEJIv+jrlXA3tT1luTZd8AvggsNbOvZ9vRObfWOdfknGsqLy/vZzdERCRVf7+JKdv31jnn3IPAg/1sW0RETlN/r9xbgdqU9RpgXz/bFBGRfupvuL8OTDaziWZWACwH1vd1ZzNbaGZrjxw50s9uiIhIqlOZCvlrYBNwrpm1mtlK51wUuAP4I7ADeNo597e+tumce945t2rUqFGn2m8REelFn8fcnXPX91D+IvBiznokIiL9ptsPiIgEkK/hrjF3EZGB4Wu4a8xdRGRgaFhGRCSAFO4iIgGkcBcRCSC9oSoiEkB6Q1VEJIA0LCMiEkAKdxGRAFK4i4gEkMJdRCSANFtGRCSANFtGRCSANCwjIhJACncRkQBSuIuIBJDCXUQkgBTuIiIBpKmQIiIBpKmQIiIBpGEZEZEAUriLiASQwl1EJIAU7iIiAaRwFxEJIIW7iEgAKdxFRAJIH2ISEQkgfYhJRCSANCwjIhJACncRkQBSuIuIBJDCXUQkgBTuIiIBpHAXEQkghbuISAAp3EVEAkifUBURCSB9QlVEJIA0LCMiEkAKdxGRAFK4i4gEkMJdRCSAwn53YFCLxyDaDrH2xHO0HWId2ctiEXBxcLHEczyesR5LWXcZ66nb41nWT7FNXMq+Gcs9bfPKXQ/lp9gWAAZm6c/Qvcx77mGfrM+91e3tGH1t61Tb6GkfwELJ5VCi3EI9lFlKWUp5t7K+1stss7djJ6/zeqyXeRw7+bHTjpHRpneuUs99X5f7s28fl9OOkfL/dSCWzdKPlSNDO9z3b+PfVt9AQShOQciRb3HyQ478kEspc+SH4smyRHl6Wc/18nJ/vk9JzEHcGQ6IOUvkN0Y8WR4H4g4cRsyBS5Z1PkPX/ol9e9uWaD8R2ZZsN3v9zmN2tkla/cS2RKnrykm6nhNliVpd68n6aevd2/DaMZdWdqptdO7fvY1s/eq9jfR+dW8jtU+p+4aybA8lj2NAKNm+3/8OZYBdsxbOX5bzZod2uO9Yz/+a2pJ1U0fcko8QkbgRiYeIuERZJB6iI260RUJEXH6yrKs84kInLetsq7P9qLM+BHHn9q7QjLtkHS8gE0HdFRci0PkLI5T8Z5Htl0Dil0VqvdRfIH2t53o4RuYvKZcs6/rF13mM1F9gXfumt535S7qzLPOXZPbyzvquh/Lcte9tz2jfO37W8u7Hzd5Oos7XKqcxEIZ2uF90G5y/HPIKIZx85BVCXj4FZhT43T8REZ8M7XAfMSbxEBGRNJotIyISQAp3EZEAUriLiASQwl1EJIAU7iIiAaT7uYuIBJDu5y4iEkAalhERCSCFu4hIACncRUQCSOEuIhJACncRkQBSuIuIBJDCXUQkgBTuIiIBpHAXEQkghbuISAAp3EVEAkjhLiISQAp3EZEAGtpfkC0545wj7uLEieOcI+ZiXpm3TDxRJ/lIq0c8bR+HwzmXaBvnHaPzv+SGbvVS172y1O1Z2sy2r0s03lUvuc07dkp/ui2fZN9u2zNeV2YfOxmWvm7mlXnPKWUYvW63RIX07Rhm3ZdT+5C2PeVY2bZnaye1Lz3t0217tteX3rHez1WWfbK9tt5k1u/Lcfp0jH72fUzRGEoLSrP2uT+GZbg754jEI7TH2umIdaQtd8Q7Es+pj2RZe6ydSDziLafuG41HvVBLDb9sgZgaop3L8XhGWUpbnSHa5/ZT2ssaxiltpB5LRM68f//Cv7Nw0sKctzukw/3lPS/zyp5XuoVwb8udAZ0LIQtRmFdIfiifcChMyEJdD0KYmbduWPr2jDIzI8/yvLJwKJzYn4ztGWXZjpWtH3mW12M7mX3o7JtX71TaC3W9Lki5aku9Muzl6rJzPfPqtKcr1173zbhK7Fzvtj2jb/3Zt9vVamcT3h8rvfwVkvyLoLftmX/VQPe/XjqP19v2ntrp7a+Pbn+9ZJRl/rXTbXvGcTOP31OdbBce3cq6rfahjZMc52THyLrPafT9c+Wf695wDgzpcG/9tJXX97+eCNi8fApCBRTmFVIYLmRkaKRXXphXSEGogIK8lEeo52WvvbwCb99s7YRDQ/r0iUiADel0WjFtBY//y+N00OF3V0RETsuGDRsGpF3NlhERCaAhfeUOA/dbT0RkKMv5lbuZnW1mj5rZM7luW0RE+qZP4W5mj5nZATPbllE+38zeMbNdZvYdAOfcu865lQPRWRER6Zu+Xrk/AcxPLTCzPOBh4EqgEbjezBpz2jsRkQCLRqNEIrmZmp2pT2PuzrlXzaw+o/giYJdz7l0AM3sKWARsz2UHRUSGqmg0SmtrKy0tLbz33nvdHq2trfziF7/ghhtuyPmx+/OGajWwN2W9FbjYzMYA/wZcYGbfdc7dk21nM1sFrAKoq6vrRzdERPwRiURobW31wjozxFtbW4nFYl59M2Ps2LFUVlZSX1/PhRdeSFlZ2YD0rT/hnu1GDs45dwj4+sl2ds6tBdYCNDU16bPvIjLodHR0pIV3Zoi3trYSj8e9+mZGeXk5FRUVnH322cyePZuKigoqKysZN24c48ePp7S0lHA4TDgc5vDhwwN2cdufcG8FalPWa4B9/euOiMiZ097ezt69e3scNtm3b19aeIdCISoqKigvL2fy5Mk0NzdTWVnphXd1dTUlJSVeePupP0d/HZhsZhOB94HlQO4HjkRETlN7ezt79uzJetXdGd6p94PpDO+KigoaGhqYM2eOF95VVVWMHz+e4uJi8vPzycvL8/GVnVyfwt3Mfg3MBcaaWSvwr865R83sDuCPQB7wmHPub6dycDNbCCw855xzTq3XIiJAW1tbt/BODfB9+9IHE/Ly8rzwbmxsZN68ed6wSVVVFVVVVUMmvE/Gst2l7UxrampyW7Zs8bsbIjLInDhxgpaWlh6HTfbv359WPxwOe+FdXl7uXXVXVlYyfvx4xo0bR1FR0aAJ784x98mTJ5/W/ma21TnXlG3bkL/9gIgMXcePH08L7swQ//DDD9Pqh8NhKisrqaio4Pzzz+fyyy9PGzapqqqisLBw0IS3nxTuIjKgPv30U3bu3MmOHTvYsWMHu3fv9kL8wIEDaXXz8/OprKykvLycCy64wBsy6bzyrqysVHj3ka/hrjF3keA4ePCgF+Dbt2/3lltbW7064XCYqqoqKioqmDFjRrdhk9TwDoV009r+8DXcnXPPA883NTXd6mc/RKRv4vE4e/fu9YI79XHo0CGvXnFxMbW1tUyZMoXLLruM2tpaJkyYwIQJEygpKaGgoEDhPcA0LCMi3UQiEXbt2tUtwHfu3Mnx48e9eqNHj6a2tpaLLrqI2tpa6urqmDBhAtXV1d6sE/GHwl1kGDt27FjaeHjnY9euXUSjUa9eZWUlNTU1XH755dTV1VFbW8vEiROpqKigsLDQ9w/sSHf6PyIyDBw6dCjrUEpLS4tXJy8vj+rqampqaliyZIkX4meffTajR4+moKBAb2IOIXpDVSQgnHO0trZmDfGDBw969YqKirwr7zlz5lBXV0ddXR319fWMGDGCwsJCzLLdOkqGEr2hKjLERKNRdu/enXU8/OjRo169srIyamtrmTlzJjU1Nd54eG1trfdBHoV4cGlYRmSQOnHiBO+8805agG/fvp1//OMfaV/wUF5eTm1tLZdeeqn3pmbneHhRUZHGw4cp/V8X8dnHH3+cdSjlvffe825qFQqFqK6uprq6msWLF6eF+FlnnaXxcOlG4S5yBjjn2LdvX9YQT/2IfUFBgTcG3tzc7M0Pr6+vp7S0VPPDpc8U7iI55pyjpaWFjRs3smnTJl5//XV27NjBJ5984tUpLS2lrq6Oz372s96slM4x8c754RoPl/7QbBmRfmpvb+fNN99k48aN3uODDz4AEp/UnDJlCpdccgm1tbXU1tZSX19PVVWVxsNlQGm2jMgp2r9/P5s2bfKCfOvWrbS3twNQXV1NQ0MDS5YsYerUqTQ0NHhfqyZyJulfnEgvotEo27Zt84J806ZNvPvuu0DiDobnnnsuCxYsYOrUqUybNo2amhqKioo0pCK+U7iLpPj444/ZvHmzd2X+2muveXPHx4wZw9SpU7nssstoaGigsbGR0aNH6/4pMigp3GXYcs7x97//PW2sfPv27UDio/iTJk1i7ty5NDY20tjYSH19PSUlJZqtIkOCwl2GjWPHjvH666+nDbF89NFHQOLTnA0NDdx44400NjYybdo0zjrrLAoLC33utcjpUbhLIDnn2LNnT1qQv/XWW8RiMQDq6+u58MILvbHySZMmUVJSojc+JTA0FVICoaOjo9t0xH37Et98X1xcTENDA0uXLqWxsZHp06d73/ijNz4lqDQVUoakDz/8MG064pYtW7zpiFVVVTQ0NLBo0SIaGxtpaGhg5MiRuiqXYUX/2mXQi8Vi3aYj7t69G0hMR5wyZQpXXXVVt+mIeuNThjOFuww6hw8fZvPmzV6Qb968OW06YkNDA/PmzaOhoYFp06YxatQoCgoKfO61yOCicBdfdU5HTB1i2b59O845QqEQkyZN4pJLLvFmsNTX11NcXKw7IIqchMJdzqjjx493m4546NAhAEaOHMnUqVP5yle+wtSpU5k+fTpjxozRdESR06BwlwHjnGPv3r3dpiN2fvHyhAkTmDlzpvem55QpUzQdUSRH9FMkOdXS0sL69ev585//zMaNG3n//feBxPd2NjQ0cO2113pDLOPGjdN0RJEBonnu0m87d+5k3bp1rFu3jq1btwKJ6YjnnnsuV199taYjivhA89zllDnnePPNN71A37FjBwDTpk3ja1/7Gl/4whc455xzNB1RxEe6jJI+icfjbNy40Qv0lpYWQqEQn/vc57j99ttpbm6mvr6eoqIiv7sqIijcpReRSIQNGzawbt06nn32Wfbv309+fj4zZ87kmmuuYfbs2dTU1GiOucggpHCXNCdOnOBPf/oT69atY/369Rw+fJji4mIuvPBCVqxYwec//3nGjRune5iLDHIKd+GTTz7hhRdeYN26dbz44oscP36csrIyLr74YmbNmsXFF1/MmDFj9GaoyBCin9Zh6uDBg6xfv55169bx0ksv0dHRwdixY7n00kuZNWsWTU1NjB49Wp8EFRmiFO7DSGtrK88++yy//e1vefXVV4nH44wfP54FCxYwa9YsZsyYwciRIzXDRSQAFO4Bt2vXLm+Gy2uvvQbAxIkTue6662hubmb69OmUlpbqg0QiAaNwDxjnHG+//bYX6G+//TYADQ0NrFixgubmZhoaGiguLlagiwSYwj0gPvjgAx5++GGeeuopdu/ejZlx3nnnsWrVKpqbm5k0aZLmoIsMI7r9wBC3bds21qxZw5NPPkk0GmXmzJl84xvfoLm5mdraWt1RUWSY0u0HhiDnHC+//DJr1qzhD3/4A8XFxcyfP5/FixczdepUfahIRDQsM5REIhF+85vfcO+99/LXv/6VMWPGcOONN7JgwQLq6uo0D11EPEqDIeDIkSOsXbuWBx54gPfff5+JEyeyevVqrrjiCsaOHaupiyLSjcJ9ENuzZw8PPPAAjzzyCJ9++ikzZszg1ltvZc6cOZSVlfndPREZxBTug9DWrVtZs2YNTz/9NABz585l0aJFzJgxQzNeRKRPFO6DRDwe5/e//z333nsvGzZsYMSIESxevJhFixYxefJk3ahLRE6Jwt1nbW1t/OpXv+K+++5jx44dVFZWcsstt3DVVVcxfvx43dtFRE6Lwt0nhw4d4uc//zk//elPOXDgAJMnT+auu+7ii1/8ImeddZY+PSoi/aJwP8N27drF/fffz+OPP86JEye4+OKLufPOO5k9ezalpaV+d09EAkLhfoZs3LiRNWvW8Lvf/Y78/HzmzZvHNddcw/Tp0/UmqYjknMJ9AMViMZ577jnuvfdeNm3aRFlZGcuWLWPRokVMnDhRHzoSkQGjdBkAx48f54knnuC+++5j9+7dVFdXc/vttzN//nyqqqr0oSMRGXAK9xz68MMPeeihh/jZz37GRx99xLRp0/je977HvHnzGD16tN4kFZEzRuGeA7t37+aee+7hl7/8JZFIhObmZhYvXsxFF11ESUmJ390TkWFIt/ztp2eeeYabb76ZaDTKFVdcwaJFi2hsbNSdGUXEV7rl72mKRCLcfffd3H///Zx33nncddddTJkyRW+SisigoCQ6Dfv27eO6667jL3/5C4sXL+a2226jvLzc726JiHgU7qdow4YNLFu2jKNHj/Ltb3+bq6++WvPURWTQ0Zy8PnLO8eMf/5jLLruMkpIS1qxZw7XXXqtgF5FBSVfufXD48GFuuukmnnvuOebNm8fq1aupqanxu1siIj1SuJ/EW2+9xdKlS2lpaeHrX/86y5cv1z1gRGTQ07BML5544glmzZrF0aNHueeee7jpppsU7CIyJOjKPYu2tja++c1v8sgjjzBz5kzuuusuJk2apE+YisiQoXDP8M9//pOlS5fyxhtvsHz5clauXMlnPvMZv7slInJKFO4pXnjhBb761a8Si8X4wQ9+wPz58yksLPS7WyIip0xj7uCF+YIFC6ioqOC+++5j4cKFCnYRGbKG/ZX7wYMHueGGG3jppZe48sorueOOO6isrPS7WyIi/TKsw33z5s18+ctf5uDBg6xevZqlS5dSXFzsd7dERPptWA7LOOd46KGHmDNnDgA/+clPuP766xXsIhIYw+7K/ejRo9x666089dRTzJ49m29961tMmDBB0xxFJFCGVbjv3LmTJUuW8M4773DTTTdx4403UlZW5ne3RERybtiE+9NPP83KlSspKCjghz/8IZdeein5+fl+d0tEZEAEfsy9o6ODO++8k2XLllFfX88DDzzAl770JQW7iARaoK/c33//fa677jo2btzINddcw6pVq/SlGiIyLAQ23F955RWWL1/OsWPHuPvuu1m4cKHuvS4iw0bghmXi8Tg/+tGPuPzyyyktLWXNmjUsWbJEwS4iw0qgrtw//vhjVqxYwfPPP8+8efO48847qa6u9rtbIiJnXM7D3cxGAD8DOoANzrknc32MbN566y2uvfZa9uzZw2233cYNN9zAiBEjzsShRUQGnT4Ny5jZY2Z2wMy2ZZTPN7N3zGyXmX0nWbwEeMY5dytwdY77m9Vjjz2W9qUaN998s4JdRIa1vo65PwHMTy0wszzgYeBKoBG43swagRpgb7JaLDfdzO7EiRPccsstrFy5kmnTpvHggw8yd+5cwuFAjTaJiJyyPqWgc+5VM6vPKL4I2OWcexfAzJ4CFgGtJAL+LQb4Ddvvfve7PProoyxbtoybb76Z0aNHE4sN6O8TEZGcicfjA9Z2fy5xq+m6QodEqF8MPAg8ZGZXAc/3tLOZrQJWAdTV1Z1WB77//e8zffp06uvrycvL4/jx46fVjoiIH8Lh8IDdsLA/4Z7tTlvOOXcMuPlkOzvn1gJrAZqamtzpdGDs2LHccsstp7OriEig9WfYpBWoTVmvAfb1rzsiIpIL/Qn314HJZjbRzAqA5cD63HRLRET6o69TIX8NbALONbNWM1vpnIsCdwB/BHYATzvn/nYqBzezhWa29siRI6fabxER6YU5d1rD3TnV1NTktmzZ4nc3RESGFDPb6pxryrYtcPeWERERhbuISCD5Gu4acxcRGRi+hrtz7nnn3KpRo0b52Q0RkcAZFG+omtlBoMXvfvTTWOC//e7EIKLz0UXnIp3OR7r+nI8JzrmsXy83KMI9CMxsS0/vWg9HOh9ddC7S6XykG6jzoTdURUQCSOEuIhJACvfcWet3BwYZnY8uOhfpdD7SDcj50Ji7iEgA6cpdRCSAFO4iIgGkcO8nM6s1s/9nZjvM7G9mttrvPvnNzPLM7E0z+0+/++I3MxttZs+Y2c7kv5FZfvfJL2b2P5I/I9vM7NdmVuR3n84kM3vMzA6Y2baUsrPM7L/M7B/J58/k6ngK9/6LAv/TOTcV+DzwL8kvCh/OVpO4DbTAA8AfnHMNwPkM0/NiZtXAN4Em59x0II/Ed0AMJ08A8zPKvgO87JybDLycXM8JhXs/Oec+cM69kVz+lMQPb7W/vfKPmdUAVwH/4Xdf/GZmZcAc4FEA51yHc+6wv73yVRgoNrMwUMIw++Y259yrwEcZxYuAXySXfwEsztXxFO45ZGb1wAXAa/72xFf/B/g2MHBf6z50nA0cBB5PDlP9h5mN8LtTfnDOvQ/cC+wBPgCOOOf+5G+vBoVK59wHkLhQBCpy1bDCPUfMrBT4LXCnc+4Tv/vjBzNbABxwzm31uy+DRBiYAfzcOXcBcIwc/tk9lCTHkhcBE4HxwAgz+4q/vQo2hXsOmFk+iWB/0jm3zu/++KgZuNrM3gOeAi41s1/52yVftQKtzrnOv+SeIRH2w9EXgX865w465yLAOmC2z30aDD40syqA5POBXDWscO8nMzMSY6o7nHP3+d0fPznnvuucq3HO1ZN4s+wV59ywvTpzzu0H9prZucmiy4DtPnbJT3uAz5tZSfJn5jKG6ZvLGdYDK5LLK4DnctVwOFcNDWPNwFeBt83srWTZ95xzL/rYJxk8vgE8aWYFwLvAzT73xxfOudfM7BngDRIzzN5kmN2GwMx+DcwFxppZK/CvwI+Ap81sJYlfgF/O2fF0+wERkeDRsIyISAAp3EVEAkjhLiISQAp3EZEAUriLiASQwl1EJIAU7iIiAfT/AcFjjfGOuZw9AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "timescale_real_values = np.array([ 11.53593249,  24.48666445, 163.41165771])\n",
    "for tsrv in timescale_real_values:\n",
    "    plt.hlines(tsrv, tau_list[0], tau_list[-1])\n",
    "vamp.plot_its(get_its(K_results_rev, tau_list, False), tau_list)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-11-06T22:59:14.815964Z",
     "start_time": "2019-11-06T22:48:59.309Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "for tsrv in timescale_real_values:\n",
    "    plt.hlines(tsrv, tau_list[0], tau_list[-1])\n",
    "vamp.plot_its(get_its(K_results, tau_list, False), tau_list)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}