Python tensorflow.subtract函数代码示例

def killRegions(anchors, image_attr, axis=-1):
    """ Prune the anchors so that only those entirely within the image remain

    This function is the RPN-training analog of clipRegions, just more murderous

    Output:
        The anchors that survive the slaughter, along with their indices
    """

    with tf.device("/cpu:0"):
        # Assumes input of shape (numBaseAnchors, feature_h, feature_w, 4)
        # Or, was previously as above but then got flattened to (-1,4)

        anchors = tf.reshape(anchors, [-1, 4], name="flattened_anchors")
        x1, y1, x2, y2 = tf.unstack(anchors, num=4, axis=axis)

        zero = tf.constant([0.])

        max_x = [tf.subtract(image_attr[1] * image_attr[2], tf.constant([1.]),
            name="murder_img_w")]
        max_y = [tf.subtract(image_attr[0] * image_attr[2], tf.constant([1.]),
            name="murder_img_h")]

        x1_valid = x1 >= zero
        x2_valid = x2 <= max_x
        y1_valid = y1 >= zero
        y2_valid = y2 <= max_y

        anchor_valid = x1_valid and x2_valid and y1_valid and y2_valid
        valid_indices = tf.where(anchor_valid, name="surviving_indices")
    return tf.gather_nd(anchors, valid_indices, name="surviving_anchors"), valid_indices

def logits_to_log_prob(logits):
  """Computes log probabilities using numerically stable trick.

  This uses two numerical stability tricks:
  1) softmax(x) = softmax(x - c) where c is a constant applied to all
  arguments. If we set c = max(x) then the softmax is more numerically
  stable.
  2) log softmax(x) is not numerically stable, but we can stabilize it
  by using the identity log softmax(x) = x - log sum exp(x)

  Args:
    logits: Tensor of arbitrary shape whose last dimension contains logits.

  Returns:
    A tensor of the same shape as the input, but with corresponding log
    probabilities.
  """

  with tf.variable_scope('log_probabilities'):
    reduction_indices = len(logits.shape.as_list()) - 1
    max_logits = tf.reduce_max(
        logits, reduction_indices=reduction_indices, keep_dims=True)
    safe_logits = tf.subtract(logits, max_logits)
    sum_exp = tf.reduce_sum(
        tf.exp(safe_logits),
        reduction_indices=reduction_indices,
        keep_dims=True)
    log_probs = tf.subtract(safe_logits, tf.log(sum_exp))
  return log_probs

    def attention_mechanism_parallel(self,c_full,m,q,i):
        """ parallel implemtation of gate function given a list of candidate sentence, a query, and previous memory.
        Input:
           c_full: candidate fact. shape:[batch_size,story_length,hidden_size]
           m: previous memory. shape:[batch_size,hidden_size]
           q: question. shape:[batch_size,hidden_size]
        Output: a scalar score (in batch). shape:[batch_size,story_length]
        """
        q=tf.expand_dims(q,axis=1) #[batch_size,1,hidden_size]
        m=tf.expand_dims(m,axis=1) #[batch_size,1,hidden_size]

        # 1.define a large feature vector that captures a variety of similarities between input,memory and question vector: z(c,m,q)
        c_q_elementwise=tf.multiply(c_full,q)          #[batch_size,story_length,hidden_size]
        c_m_elementwise=tf.multiply(c_full,m)          #[batch_size,story_length,hidden_size]
        c_q_minus=tf.abs(tf.subtract(c_full,q))        #[batch_size,story_length,hidden_size]
        c_m_minus=tf.abs(tf.subtract(c_full,m))        #[batch_size,story_length,hidden_size]
        # c_transpose Wq
        c_w_q=self.x1Wx2_parallel(c_full,q,"c_w_q"+str(i))   #[batch_size,story_length,hidden_size]
        c_w_m=self.x1Wx2_parallel(c_full,m,"c_w_m"+str(i))   #[batch_size,story_length,hidden_size]
        # c_transposeWm
        q_tile=tf.tile(q,[1,self.story_length,1])     #[batch_size,story_length,hidden_size]
        m_tile=tf.tile(m,[1,self.story_length,1])     #[batch_size,story_length,hidden_size]
        z=tf.concat([c_full,m_tile,q_tile,c_q_elementwise,c_m_elementwise,c_q_minus,c_m_minus,c_w_q,c_w_m],2) #[batch_size,story_length,hidden_size*9]
        # 2. two layer feed foward
        g=tf.layers.dense(z,self.hidden_size*3,activation=tf.nn.tanh)  #[batch_size,story_length,hidden_size*3]
        g=tf.layers.dense(g,1,activation=tf.nn.sigmoid)                #[batch_size,story_length,1]
        g=tf.squeeze(g,axis=2)                                         #[batch_size,story_length]
        return g

    def __build(self):
        self.__init_global_epoch()
        self.__init_global_step()
        self.__init_input()

        with tf.name_scope('Preprocessing'):
            red, green, blue = tf.split(self.X, num_or_size_splits=3, axis=3)
            preprocessed_input = tf.concat([
                tf.subtract(blue, ShuffleNet.MEAN[0]) * ShuffleNet.NORMALIZER,
                tf.subtract(green, ShuffleNet.MEAN[1]) * ShuffleNet.NORMALIZER,
                tf.subtract(red, ShuffleNet.MEAN[2]) * ShuffleNet.NORMALIZER,
            ], 3)
        x_padded = tf.pad(preprocessed_input, [[0, 0], [1, 1], [1, 1], [0, 0]], "CONSTANT")
        conv1 = conv2d('conv1', x=x_padded, w=None, num_filters=self.output_channels['conv1'], kernel_size=(3, 3),
                       stride=(2, 2), l2_strength=self.args.l2_strength, bias=self.args.bias,
                       batchnorm_enabled=self.args.batchnorm_enabled, is_training=self.is_training,
                       activation=tf.nn.relu, padding='VALID')
        padded = tf.pad(conv1, [[0, 0], [0, 1], [0, 1], [0, 0]], "CONSTANT")
        max_pool = max_pool_2d(padded, size=(3, 3), stride=(2, 2), name='max_pool')
        stage2 = self.__stage(max_pool, stage=2, repeat=3)
        stage3 = self.__stage(stage2, stage=3, repeat=7)
        stage4 = self.__stage(stage3, stage=4, repeat=3)
        global_pool = avg_pool_2d(stage4, size=(7, 7), stride=(1, 1), name='global_pool', padding='VALID')

        logits_unflattened = conv2d('fc', global_pool, w=None, num_filters=self.args.num_classes,
                                    kernel_size=(1, 1),
                                    l2_strength=self.args.l2_strength,
                                    bias=self.args.bias,
                                    is_training=self.is_training)
        self.logits = flatten(logits_unflattened)

        self.__init_output()

 def getLoss(trueCosSim, falseCosSim, margin):
     zero = tf.fill(tf.shape(trueCosSim), 0.0)
     tfMargin = tf.fill(tf.shape(trueCosSim), margin)
     with tf.name_scope("loss"):
         losses = tf.maximum(zero, tf.subtract(tfMargin, tf.subtract(trueCosSim, falseCosSim)))
         loss = tf.reduce_sum(losses)
     return loss

def r2_op(predictions, targets):
    """ r2_op.

    An op that calculates the standard error.

    Examples:
        ```python
        input_data = placeholder(shape=[None, 784])
        y_pred = my_network(input_data) # Apply some ops
        y_true = placeholder(shape=[None, 10]) # Labels
        stderr_op = r2_op(y_pred, y_true)

        # Calculate standard error by feeding data X and labels Y
        std_error = sess.run(stderr_op, feed_dict={input_data: X, y_true: Y})
        ```

    Arguments:
        predictions: `Tensor`.
        targets: `Tensor`.

    Returns:
        `Float`. The standard error.

    """
    with tf.name_scope('StandardError'):
        a = tf.reduce_sum(tf.square(tf.subtract(targets, predictions)))
        b = tf.reduce_sum(tf.square(tf.subtract(targets, tf.reduce_mean(targets))))
        return tf.subtract(1.0, tf.divide(a, b))

def tf_image_processing(tf_images, basenet, crop_size, distort=False, hp_filter=False):
    if len(tf_images.shape) == 3:
        tf_images = tf.expand_dims(tf_images, -1)
    if basenet == 'sketchanet':
        mean_value = 250.42
        tf_images = tf.subtract(tf_images, mean_value)
        if distort:
            print("Distorting photos")
            FLAGS.crop_size = crop_size
            FLAGS.dist_chn_size = 1
            tf_images = data_augmentation(tf_images)
        else:
            tf_images = tf.image.resize_images(tf_images, (crop_size, crop_size))
    elif basenet in ['inceptionv1', 'inceptionv3', 'gen_cnn']:
        tf_images = tf.divide(tf_images, 255.0)
        tf_images = tf.subtract(tf_images, 0.5)
        tf_images = tf.multiply(tf_images, 2.0)
        if int(tf_images.shape[-1]) != 3:
            tf_images = tf.concat([tf_images, tf_images, tf_images], axis=-1)
        if distort:
            print("Distorting photos")
            FLAGS.crop_size = crop_size
            FLAGS.dist_chn_size = 3
            tf_images = data_augmentation(tf_images)
            # Display the training images in the visualizer.
            # tf.image_summary('input_images', input_images)
        else:
            tf_images = tf.image.resize_images(tf_images, (crop_size, crop_size))

    if hp_filter:
        tf_images = tf_high_pass_filter(tf_images)

    return tf_images

def triplet_loss(y_true, y_pred, alpha = 0.2):
    """
    Implementation of the triplet loss as defined by formula

    Arguments:
    y_true -- true labels, required when you define a loss in Keras, you don't need it in this function.
    y_pred -- python list containing three objects:
            anchor -- the encodings for the anchor images, of shape (None, 128)
            positive -- the encodings for the positive images, of shape (None, 128)
            negative -- the encodings for the negative images, of shape (None, 128)

    Returns:
    loss -- real number, value of the loss
    """

    anchor, positive, negative = y_pred[0], y_pred[1], y_pred[2]

    ### START CODE HERE ### (≈ 4 lines)
    # Step 1: Compute the (encoding) distance between the anchor and the positive, you will need to sum over axis=-1
    pos_dist = tf.reduce_sum(tf.square(tf.subtract(anchor, positive)))
    # Step 2: Compute the (encoding) distance between the anchor and the negative, you will need to sum over axis=-1
    neg_dist = tf.reduce_sum(tf.square(tf.subtract(anchor, negative)))
    # Step 3: subtract the two previous distances and add alpha.
    basic_loss = tf.add(tf.subtract(pos_dist,neg_dist), alpha)
    # Step 4: Take the maximum of basic_loss and 0.0. Sum over the training examples.
    loss = tf.reduce_sum(tf.maximum(basic_loss, 0.))
    ### END CODE HERE ###

    return loss

 def addLayer(self, n, activation_function = 'tanh', include_bias = False, sd = 0.35, dropout = 0, normalization = None, weights = None):
     """
     
     :Description:
         Adds a layer to the network, including a weight tensor and an activation tensor.
         
     :Input parameters:
         activation_function:    type of activation function to be applied to each unit (string)
         include_bias:           if true, a column of ones will be added to the weights (boolean)
         sd:                     standard deviation of the zero-mean gaussian from which the weights will be drawn (float)
         dropout:                the chance with which each weight will be set to zero for a given training step (float)
         normalization:          the type of normalization imposed on the layer activations. Can be
                                     a) 'softmax' for softmax normalization
                                     b) 'Shift' for de-meaning
                                     c) 'ShiftScale' for de-meaning and standard deviation normalization
         weights:                if provided, will be used as weights of layer instead of drawing from gaussian (tensor)
         
     """
     
     """ initialize weights and use them to calculate layer activations """
     
     if weights: # if weights are provided, use those
         
         weights = tf.mul(tf.ones(weights.shape),weights)
         activations = tf.matmul(self.data, weights) if not self.weights else tf.matmul(self.Activations[-1], weights)
     
     elif not self.Weights: # else if first layer 
         
         weights = tf.Variable(tf.random_normal([self.data.get_shape()[1].value, n], stddev = sd))      
         weights = tf.concat(1,[weights,tf.ones([weights.get_shape()[0],1])]) if include_bias else weights
         activations = tf.matmul(self.data, weights)
         
     else: # for every other layer
         
         weights = tf.Variable(tf.random_normal([self.Activations[-1].get_shape()[-1].value, n], stddev = sd))
         weights = tf.concat(1,[weights,tf.ones([weights.get_shape()[0],1])]) if include_bias else weights
         activations = tf.matmul(self.Activations[-1], weights)
     
     self.Weights.append(weights)
     self.Activations.append(self.applyActivation(activations, activation_function)) # apply activation function on raw activations
     
     """ add dropout and/or normalization """
     
     if dropout:
         
         self.Activations.append(tf.nn.dropout(self.Activations[-1], dropout))
         
     if normalization == 'softmax': # for softmax normalization
         
         self.Activations.append(tf.nn.softmax(self.Activations[-1]))
         
     elif normalization == 'Shift': # for de-meaning
         
         self.Activations[-1] = tf.subtract(self.Activations[-1],tf.reduce_mean(self.Activations[-1]))
         
     elif normalization == 'ShiftScale': # for de-meaning & and rescaling by variance
         
         mu = tf.reduce_mean(self.Activations[-1])
         diff = tf.subtract(self.Activations[-1],mu)
         self.Activations[-1] = tf.div(diff,tf.reduce_sum(tf.mul(diff,diff)))            

    def __init__(
        self, sequence_length, vocab_size, embedding_size, hidden_units, l2_reg_lambda, batch_size, trainableEmbeddings):

        # Placeholders for input, output and dropout
        self.input_x1 = tf.placeholder(tf.int32, [None, sequence_length], name="input_x1")
        self.input_x2 = tf.placeholder(tf.int32, [None, sequence_length], name="input_x2")
        self.input_y = tf.placeholder(tf.float32, [None], name="input_y")
        self.dropout_keep_prob = tf.placeholder(tf.float32, name="dropout_keep_prob")

        # Keeping track of l2 regularization loss (optional)
        l2_loss = tf.constant(0.0, name="l2_loss")
          
        # Embedding layer
        with tf.name_scope("embedding"):
            self.W = tf.Variable(
                tf.constant(0.0, shape=[vocab_size, embedding_size]),
                trainable=trainableEmbeddings,name="W")
            self.embedded_words1 = tf.nn.embedding_lookup(self.W, self.input_x1)
            self.embedded_words2 = tf.nn.embedding_lookup(self.W, self.input_x2)
        print self.embedded_words1
        # Create a convolution + maxpool layer for each filter size
        with tf.name_scope("output"):
            self.out1=self.stackedRNN(self.embedded_words1, self.dropout_keep_prob, "side1", embedding_size, sequence_length, hidden_units)
            self.out2=self.stackedRNN(self.embedded_words2, self.dropout_keep_prob, "side2", embedding_size, sequence_length, hidden_units)
            self.distance = tf.sqrt(tf.reduce_sum(tf.square(tf.subtract(self.out1,self.out2)),1,keep_dims=True))
            self.distance = tf.div(self.distance, tf.add(tf.sqrt(tf.reduce_sum(tf.square(self.out1),1,keep_dims=True)),tf.sqrt(tf.reduce_sum(tf.square(self.out2),1,keep_dims=True))))
            self.distance = tf.reshape(self.distance, [-1], name="distance")
        with tf.name_scope("loss"):
            self.loss = self.contrastive_loss(self.input_y,self.distance, batch_size)
        #### Accuracy computation is outside of this class.
        with tf.name_scope("accuracy"):
            self.temp_sim = tf.subtract(tf.ones_like(self.distance),tf.rint(self.distance), name="temp_sim") #auto threshold 0.5
            correct_predictions = tf.equal(self.temp_sim, self.input_y)
            self.accuracy=tf.reduce_mean(tf.cast(correct_predictions, "float"), name="accuracy")

def cosineface_losses(embedding, labels, out_num, w_init=None, s=30., m=0.4):
    '''
    :param embedding: the input embedding vectors
    :param labels:  the input labels, the shape should be eg: (batch_size, 1)
    :param s: scalar value, default is 30
    :param out_num: output class num
    :param m: the margin value, default is 0.4
    :return: the final cacualted output, this output is send into the tf.nn.softmax directly
    '''
    with tf.variable_scope('cosineface_loss'):
        # inputs and weights norm
        embedding_norm = tf.norm(embedding, axis=1, keep_dims=True)
        embedding = tf.div(embedding, embedding_norm, name='norm_embedding')
        weights = tf.get_variable(name='embedding_weights', shape=(embedding.get_shape().as_list()[-1], out_num),
                                  initializer=w_init, dtype=tf.float32)
        weights_norm = tf.norm(weights, axis=0, keep_dims=True)
        weights = tf.div(weights, weights_norm, name='norm_weights')
        # cos_theta - m
        cos_t = tf.matmul(embedding, weights, name='cos_t')
        cos_t_m = tf.subtract(cos_t, m, name='cos_t_m')

        mask = tf.one_hot(labels, depth=out_num, name='one_hot_mask')
        inv_mask = tf.subtract(1., mask, name='inverse_mask')

        output = tf.add(s * tf.multiply(cos_t, inv_mask), s * tf.multiply(cos_t_m, mask), name='cosineface_loss_output')
    return output

def auto_encoder(x_1, x_2, x_mask_1, x_mask_2, y, dropout, opt):
    x_1_emb, W_emb = embedding(x_1, opt)  # batch L emb
    x_2_emb = tf.nn.embedding_lookup(W_emb, x_2)

    x_1_emb = tf.nn.dropout(x_1_emb, dropout)  # batch L emb
    x_2_emb = tf.nn.dropout(x_2_emb, dropout)  # batch L emb

    biasInit = tf.constant_initializer(0.001, dtype=tf.float32)
    x_1_emb = layers.fully_connected(tf.squeeze(x_1_emb), num_outputs=opt.embed_size, biases_initializer=biasInit, activation_fn=tf.nn.relu, scope='trans', reuse=None)  # batch L emb
    x_2_emb = layers.fully_connected(tf.squeeze(x_2_emb), num_outputs=opt.embed_size, biases_initializer=biasInit, activation_fn=tf.nn.relu, scope='trans', reuse=True)

    x_1_emb = tf.expand_dims(x_1_emb, 3)  # batch L emb 1
    x_2_emb = tf.expand_dims(x_2_emb, 3)

    if opt.encoder == 'aver':
        H_enc_1 = aver_emb_encoder(x_1_emb, x_mask_1)
        H_enc_2 = aver_emb_encoder(x_2_emb, x_mask_2)

    elif opt.encoder == 'max':
        H_enc_1 = max_emb_encoder(x_1_emb, x_mask_1, opt)
        H_enc_2 = max_emb_encoder(x_2_emb, x_mask_2, opt)

    elif opt.encoder == 'concat':
        H_enc_1 = concat_emb_encoder(x_1_emb, x_mask_1, opt)
        H_enc_2 = concat_emb_encoder(x_2_emb, x_mask_2, opt)

    # discriminative loss term
    if opt.combine_enc == 'mult':
        H_enc = tf.multiply(H_enc_1, H_enc_2)  # batch * n_gan

    if opt.combine_enc == 'concat':
        H_enc = tf.concat([H_enc_1, H_enc_2], 1)

    if opt.combine_enc == 'sub':
        H_enc = tf.subtract(H_enc_1, H_enc_2)

    if opt.combine_enc == 'mix':
        H_1 = tf.multiply(H_enc_1, H_enc_2)
        H_2 = tf.concat([H_enc_1, H_enc_2], 1)
        H_3 = tf.subtract(H_enc_1, H_enc_2)
        H_enc = tf.concat([H_1, H_2, H_3], 1)

    # calculate the accuracy
    logits = discriminator_2layer(H_enc, opt, dropout, prefix='classify_', num_outputs=opt.category, is_reuse=None)
    prob = tf.nn.softmax(logits)

    correct_prediction = tf.equal(tf.argmax(prob, 1), tf.argmax(y, 1))
    accuracy = tf.reduce_mean(tf.cast(correct_prediction, tf.float32))
    loss = tf.reduce_mean(tf.nn.softmax_cross_entropy_with_logits(labels=y, logits=logits))

    train_op = layers.optimize_loss(
        loss,
        framework.get_global_step(),
        optimizer='Adam',
        # variables=d_vars,
        learning_rate=opt.lr)

    return accuracy, loss, train_op, W_emb

    def single_image_TV(patch, patch_size):
        result = tf.Variable(tf.zeros([1, patch_size - 1, 3]))
        slice_result = tf.assign(result, patch[0: 1, 1:, 0: 3])
        for iter in range(1, patch_size - 1):
            temp = tf.assign(result,tf.add(tf.subtract(patch[iter:iter + 1, 1:, 0: 3], patch[iter:iter + 1, 0:-1, 0: 3]),
                                           tf.subtract(patch[iter:iter + 1, 0:-1, 0: 3],patch[iter + 1:iter + 2, 0:-1, 0: 3])))
            slice_result = tf.concat([slice_result, temp], 0)

            return slice_result

    def __init__(self, config, is_training=True):
        self.batch_size = tf.Variable(0, dtype=tf.int32, trainable=False)

        num_step = config.num_step
        embed_dim = config.embed_dim
        self.input_data_s1 = tf.placeholder(tf.float64, [None, num_step, embed_dim])
        self.input_data_s2 = tf.placeholder(tf.float64, [None, num_step, embed_dim])
        self.target = tf.placeholder(tf.float64, [None])
        self.mask_s1 = tf.placeholder(tf.float64, [None, num_step])
        self.mask_s2 = tf.placeholder(tf.float64, [None, num_step])

        self.hidden_neural_size = config.hidden_neural_size
        self.new_batch_size = tf.placeholder(tf.int32, shape=[], name="new_batch_size")
        self._batch_size_update = tf.assign(self.batch_size, self.new_batch_size)

        with tf.name_scope('lstm_output_layer'):
            self.cell_outputs1 = self.singleRNN(x=self.input_data_s1, scope='side1', cell='lstm', reuse=None)
            self.cell_outputs2 = self.singleRNN(x=self.input_data_s2, scope='side1', cell='lstm', reuse=True)

        with tf.name_scope('Sentence_Layer'):
            # self.sent1 = tf.reduce_sum(self.cell_outputs1 * self.mask_s1[:, :, None], axis=1)
            # self.sent2 = tf.reduce_sum(self.cell_outputs2 * self.mask_s2[:, :, None], axis=1)
            # self.mask_s1_sum=tf.reduce_sum(self.mask_s1,axis=0)
            # self.mask_s2_sum=tf.reduce_sum(self.mask_s2,axis=0)
            # self.mask_s1_sum1 = tf.reduce_sum(self.mask_s1, axis=1)
            # self.mask_s2_sum1 = tf.reduce_sum(self.mask_s2, axis=1)
            self.sent1 = tf.reduce_sum(self.cell_outputs1 * self.mask_s1[:, :, None], axis=1)
            self.sent2 = tf.reduce_sum(self.cell_outputs2 * self.mask_s2[:, :, None], axis=1)

        with tf.name_scope('loss'):
            diff = tf.abs(tf.subtract(self.sent1, self.sent2), name='err_l1')
            diff = tf.reduce_sum(diff, axis=1)
            self.sim = tf.clip_by_value(tf.exp(-1.0 * diff), 1e-7, 1.0 - 1e-7)
            self.loss = tf.square(tf.subtract(self.sim, tf.clip_by_value((self.target - 1.0) / 4.0, 1e-7, 1.0 - 1e-7)))

        with tf.name_scope('cost'):
            self.cost = tf.reduce_mean(self.loss)
            self.truecost = tf.reduce_mean(tf.square(tf.subtract(self.sim * 4.0 + 1.0, self.target)))

        if not is_training:
            return

        self.globle_step = tf.Variable(0, name="globle_step", trainable=False, dtype=tf.float64)
        self.lr = tf.Variable(0.0, trainable=False, dtype=tf.float64)

        tvars = tf.trainable_variables()
        grads = tf.gradients(self.cost, tvars)
        optimizer = tf.train.AdadeltaOptimizer(learning_rate=self.lr, epsilon=1e-6)

        with tf.name_scope('train'):
            self.train_op = optimizer.apply_gradients(zip(grads, tvars))

        self.new_lr = tf.placeholder(tf.float64, shape=[], name="new_learning_rate")
        self._lr_update = tf.assign(self.lr, self.new_lr)

 def tf_2d_normal(x1, x2, mu1, mu2, s1, s2, rho):
   """Returns result of eq # 24 and 25 of http://arxiv.org/abs/1308.0850."""
   norm1 = tf.subtract(x1, mu1)
   norm2 = tf.subtract(x2, mu2)
   s1s2 = tf.multiply(s1, s2)
   z = (tf.square(tf.div(norm1, s1)) + tf.square(tf.div(norm2, s2)) -
        2 * tf.div(tf.multiply(rho, tf.multiply(norm1, norm2)), s1s2))
   neg_rho = 1 - tf.square(rho)
   result = tf.exp(tf.div(-z, 2 * neg_rho))
   denom = 2 * np.pi * tf.multiply(s1s2, tf.sqrt(neg_rho))
   result = tf.div(result, denom)
   return result