Python tensorflow.keras.backend.exp() Examples

def sampling(args):
    """Reparameterization trick by sampling 
        fr an isotropic unit Gaussian.

    # Arguments:
        args (tensor): mean and log of variance of Q(z|X)

    # Returns:
        z (tensor): sampled latent vector
    """

    z_mean, z_log_var = args
    batch = K.shape(z_mean)[0]
    dim = K.int_shape(z_mean)[1]
    # by default, random_normal has mean=0 and std=1.0
    epsilon = K.random_normal(shape=(batch, dim))
    return z_mean + K.exp(0.5 * z_log_var) * epsilon 

def _softmax(x, axis=-1, alpha=1):
    """
    building on keras implementation, with additional alpha parameter

    Softmax activation function.
    # Arguments
        x : Tensor.
        axis: Integer, axis along which the softmax normalization is applied.
        alpha: a value to multiply all x
    # Returns
        Tensor, output of softmax transformation.
    # Raises
        ValueError: In case `dim(x) == 1`.
    """
    x = alpha * x
    ndim = K.ndim(x)
    if ndim == 2:
        return K.softmax(x)
    elif ndim > 2:
        e = K.exp(x - K.max(x, axis=axis, keepdims=True))
        s = K.sum(e, axis=axis, keepdims=True)
        return e / s
    else:
        raise ValueError('Cannot apply softmax to a tensor that is 1D') 

def sampling(args):
    """Reparameterization trick by sampling 
        fr an isotropic unit Gaussian.

    # Arguments:
        args (tensor): mean and log of variance of Q(z|X)

    # Returns:
        z (tensor): sampled latent vector
    """

    z_mean, z_log_var = args
    # K is the keras backend
    batch = K.shape(z_mean)[0]
    dim = K.int_shape(z_mean)[1]
    # by default, random_normal has mean=0 and std=1.0
    epsilon = K.random_normal(shape=(batch, dim))
    return z_mean + K.exp(0.5 * z_log_var) * epsilon 

def sampling(args):
    """Implements reparameterization trick by sampling
    from a gaussian with zero mean and std=1.

    Arguments:
        args (tensor): mean and log of variance of Q(z|X)

    Returns:
        sampled latent vector (tensor)
    """

    z_mean, z_log_var = args
    batch = K.shape(z_mean)[0]
    dim = K.int_shape(z_mean)[1]
    # by default, random_normal has mean=0 and std=1.0
    epsilon = K.random_normal(shape=(batch, dim))
    return z_mean + K.exp(0.5 * z_log_var) * epsilon 

def mi_loss(self, y_true, y_pred):
        """ MINE loss function

        Arguments:
            y_true (tensor): Not used since this is
                unsupervised learning
            y_pred (tensor): stack of predictions for
                joint T(x,y) and marginal T(x,y)
        """
        size = self.args.batch_size
        # lower half is pred for joint dist
        pred_xy = y_pred[0: size, :]

        # upper half is pred for marginal dist
        pred_x_y = y_pred[size : y_pred.shape[0], :]
        # implentation of MINE loss (Eq 13.7.3)
        loss = K.mean(pred_xy) \
               - K.log(K.mean(K.exp(pred_x_y)))
        return -loss 

def mi_loss(self, y_true, y_pred):
        """ MINE loss function

        Arguments:
            y_true (tensor): Not used since this is
                unsupervised learning
            y_pred (tensor): stack of predictions for
                joint T(x,y) and marginal T(x,y)
        """
        size = self.args.batch_size
        # lower half is pred for joint dist
        pred_xy = y_pred[0: size, :]

        # upper half is pred for marginal dist
        pred_x_y = y_pred[size : y_pred.shape[0], :]
        loss = K.mean(K.exp(pred_x_y))
        loss = K.clip(loss, K.epsilon(), np.finfo(float).max)
        loss = K.mean(pred_xy) - K.log(loss)
        return -loss 

def convert_exp(node, params, layers, lambda_func, node_name, keras_name):
    """
    Convert Exp layer
    :param node: current operation node
    :param params: operation attributes
    :param layers: available keras layers
    :param lambda_func: function for keras Lambda layer
    :param node_name: resulting layer name
    :return: None
    """
    if len(node.input) != 1:
        assert AttributeError('More than 1 input for log layer.')

    input_0 = ensure_tf_type(layers[node.input[0]], name="%s_const" % keras_name)

    def target_layer(x):
        import tensorflow.keras.backend as K
        return K.exp(x)

    lambda_layer = keras.layers.Lambda(target_layer, name=keras_name)
    layers[node_name] = lambda_layer(input_0)
    lambda_func[keras_name] = target_layer 

def logistic(x, x0=0., alpha=1., L=1.):
    """
    returns L/(1+exp(-alpha * (x-x0)))
    """
    assert L > 0, 'L (height of logistic) should be > 0'
    assert alpha > 0, 'alpha (slope) of logistic should be > 0'
    
    return L / (1 + tf.exp(-alpha * (x-x0))) 

def softmax(x, axis):
    """
    softmax of a numpy array along a given dimension
    """

    return np.exp(x) / np.sum(np.exp(x), axis=axis, keepdims=True) 

def call(self, tensors, mask=None):
        if self.homomorphic == True:
            tensors = K.log(tensors) 
            
        x_dct = self._dct3D(tensors)
        x_crop = self._cropping3D(x_dct)
        x_idct = self._idct3D(x_crop)
        
        if self.homomorphic == True:
            x_idct = K.exp(x_idct) 
            
        return x_idct 

def call(self, x):
        #The conditional probability of surviving each time interval (given that has survived to beginning of interval)
        #is affected by the input data according to eq. 18.13 in Harrell F.,
        #Regression Modeling Strategies 2nd ed. (available free online)
        return K.pow(K.sigmoid(self.kernel), K.exp(x)) 

def softplus2(x):
    """
    out = log(exp(x)+1) - log(2)
    softplus function that is 0 at x=0, the implementation aims at avoiding overflow

    Args:
        x: (Tensor) input tensor

    Returns:
         (Tensor) output tensor
    """
    return kb.relu(x) + kb.log(0.5*kb.exp(-kb.abs(x)) + 0.5) 

def yolo3_head(feats, anchors, num_classes, input_shape, calc_loss=False):
    """Convert final layer features to bounding box parameters."""
    num_anchors = len(anchors)
    # Reshape to batch, height, width, num_anchors, box_params.
    anchors_tensor = K.reshape(K.constant(anchors), [1, 1, 1, num_anchors, 2])

    grid_shape = K.shape(feats)[1:3] # height, width
    grid_y = K.tile(K.reshape(K.arange(0, stop=grid_shape[0]), [-1, 1, 1, 1]),
        [1, grid_shape[1], 1, 1])
    grid_x = K.tile(K.reshape(K.arange(0, stop=grid_shape[1]), [1, -1, 1, 1]),
        [grid_shape[0], 1, 1, 1])
    grid = K.concatenate([grid_x, grid_y])
    grid = K.cast(grid, K.dtype(feats))

    feats = K.reshape(
        feats, [-1, grid_shape[0], grid_shape[1], num_anchors, num_classes + 5])

    # Adjust preditions to each spatial grid point and anchor size.
    box_xy = (K.sigmoid(feats[..., :2]) + grid) / K.cast(grid_shape[..., ::-1], K.dtype(feats))
    box_wh = K.exp(feats[..., 2:4]) * anchors_tensor / K.cast(input_shape[..., ::-1], K.dtype(feats))
    box_confidence = K.sigmoid(feats[..., 4:5])
    box_class_probs = K.sigmoid(feats[..., 5:])

    if calc_loss == True:
        return grid, feats, box_xy, box_wh
    return box_xy, box_wh, box_confidence, box_class_probs 

def yolo2_head(feats, anchors, num_classes, input_shape, calc_loss=False):
    """Convert final layer features to bounding box parameters."""
    num_anchors = len(anchors)
    # Reshape to batch, height, width, num_anchors, box_params.
    anchors_tensor = K.reshape(K.constant(anchors), [1, 1, 1, num_anchors, 2])

    grid_shape = K.shape(feats)[1:3] # height, width
    grid_y = K.tile(K.reshape(K.arange(0, stop=grid_shape[0]), [-1, 1, 1, 1]),
        [1, grid_shape[1], 1, 1])
    grid_x = K.tile(K.reshape(K.arange(0, stop=grid_shape[1]), [1, -1, 1, 1]),
        [grid_shape[0], 1, 1, 1])
    grid = K.concatenate([grid_x, grid_y])
    grid = K.cast(grid, K.dtype(feats))

    feats = K.reshape(
        feats, [-1, grid_shape[0], grid_shape[1], num_anchors, num_classes + 5])

    # Adjust preditions to each spatial grid point and anchor size.
    box_xy = (K.sigmoid(feats[..., :2]) + grid) / K.cast(grid_shape[..., ::-1], K.dtype(feats))
    #box_wh = K.exp(feats[..., 2:4]) * anchors_tensor / K.cast(grid_shape[..., ::-1], K.dtype(feats))
    box_wh = K.exp(feats[..., 2:4]) * anchors_tensor / K.cast(input_shape[..., ::-1], K.dtype(feats))
    box_confidence = K.sigmoid(feats[..., 4:5])
    box_class_probs = K.softmax(feats[..., 5:])

    if calc_loss == True:
        return grid, feats, box_xy, box_wh
    return box_xy, box_wh, box_confidence, box_class_probs 

def gaussian_kernel(sigma, windowsize=None, indexing='ij'):
    """
    sigma will be a number of a list of numbers.

    # some guidance from my MATLAB file 
    https://github.com/adalca/mivt/blob/master/src/gaussFilt.m

    Parameters:
        sigma: scalar or list of scalars
        windowsize (optional): scalar or list of scalars indicating the shape of the kernel
    
    Returns:
        ND kernel the same dimensiosn as the number of sigmas.

    Todo: could use MultivariateNormalDiag
    """

    if not isinstance(sigma, (list, tuple)):
        sigma = [sigma]
    sigma = [np.maximum(f, np.finfo(float).eps) for f in sigma]

    nb_dims = len(sigma)

    # compute windowsize
    if windowsize is None:
        windowsize = [np.round(f * 3) * 2 + 1 for f in sigma]

    if len(sigma) != len(windowsize):
        raise ValueError('sigma and windowsize should have the same length.'
                         'Got vectors: ' + str(sigma) + 'and' + str(windowsize))

    # ok, let's get to work.
    mid = [(w - 1)/2 for w in windowsize]

    # list of volume ndgrid
    # N-long list, each entry of shape volshape
    mesh = volshape_to_meshgrid(windowsize, indexing=indexing)  
    mesh = [tf.cast(f, 'float32') for f in mesh]

    # compute independent gaussians
    diff = [mesh[f] - mid[f] for f in range(len(windowsize))]
    exp_term = [- K.square(diff[f])/(2 * (sigma[f]**2)) for f in range(nb_dims)]
    norms = [exp_term[f] - np.log(sigma[f] * np.sqrt(2 * np.pi)) for f in range(nb_dims)]

    # add an all-ones entry and transform into a large matrix
    norms_matrix = tf.stack(norms, axis=-1)  # *volshape x N
    g = K.sum(norms_matrix, -1)  # volshape
    g = tf.exp(g)
    g /= tf.reduce_sum(g)

    return g