Python tensorflow.keras.backend.square() Examples

def huber_loss(y_true, y_pred, clip_value):
    # Huber loss, see https://en.wikipedia.org/wiki/Huber_loss and
    # https://medium.com/@karpathy/yes-you-should-understand-backprop-e2f06eab496b
    # for details.
    assert clip_value > 0.

    x = y_true - y_pred
    if np.isinf(clip_value):
        # Spacial case for infinity since Tensorflow does have problems
        # if we compare `K.abs(x) < np.inf`.
        return .5 * K.square(x)

    condition = K.abs(x) < clip_value
    squared_loss = .5 * K.square(x)
    linear_loss = clip_value * (K.abs(x) - .5 * clip_value)
    import tensorflow as tf
    if hasattr(tf, 'select'):
        return tf.select(condition, squared_loss, linear_loss)  # condition, true, false
    else:
        return tf.where(condition, squared_loss, linear_loss)  # condition, true, false 

def loss(self, y_true, y_pred):

        if self.crop_indices is not None:
            y_true = utils.batch_gather(y_true, self.crop_indices)
            y_pred = utils.batch_gather(y_pred, self.crop_indices)

        ksq = K.square(y_pred - y_true)

        if self.vox_weights is not None:
            if self.vox_weights == 'y_true':
                ksq *= y_true
            elif self.vox_weights == 'expy_true':
                ksq *= tf.exp(y_true)
            else:
                ksq *= self.vox_weights

        if self.weights is not None:
            ksq *= self.weights

        return K.mean(ksq) 

def loss(self, y_true, y_pred):

        # get the value for the true and fake images
        disc_true = self.disc(y_true)
        disc_pred = self.disc(y_pred)

        # sample a x_hat by sampling along the line between true and pred
        # z = tf.placeholder(tf.float32, shape=[None, 1])
        # shp = y_true.get_shape()[0]
        # WARNING: SHOULD REALLY BE shape=[batch_size, 1] !!!
        # self.batch_size does not work, since it's not None!!!
        alpha = K.random_uniform(shape=[K.shape(y_pred)[0], 1, 1, 1])
        diff = y_pred - y_true
        interp = y_true + alpha * diff

        # take gradient of D(x_hat)
        gradients = K.gradients(self.disc(interp), [interp])[0]
        grad_pen = K.mean(K.square(K.sqrt(K.sum(K.square(gradients), axis=1))-1))

        # compute loss
        return (K.mean(disc_pred) - K.mean(disc_true)) + self.lambda_gp * grad_pen 

def call(self, inputs):

        #To channels last
        x = tf.transpose(inputs[0], [0, 3, 1, 2])

        #Get weight and bias modulations
        #Make sure w's shape is compatible with self.kernel
        w = K.expand_dims(K.expand_dims(K.expand_dims(inputs[1], axis = 1), axis = 1), axis = -1)

        #Add minibatch layer to weights
        wo = K.expand_dims(self.kernel, axis = 0)

        #Modulate
        weights = wo * (w+1)

        #Demodulate
        if self.demod:
            d = K.sqrt(K.sum(K.square(weights), axis=[1,2,3], keepdims = True) + 1e-8)
            weights = weights / d

        #Reshape/scale input
        x = tf.reshape(x, [1, -1, x.shape[2], x.shape[3]]) # Fused => reshape minibatch to convolution groups.
        w = tf.reshape(tf.transpose(weights, [1, 2, 3, 0, 4]), [weights.shape[1], weights.shape[2], weights.shape[3], -1])

        x = tf.nn.conv2d(x, w,
                strides=self.strides,
                padding="SAME",
                data_format="NCHW")

        # Reshape/scale output.
        x = tf.reshape(x, [-1, self.filters, x.shape[2], x.shape[3]]) # Fused => reshape convolution groups back to minibatch.
        x = tf.transpose(x, [0, 2, 3, 1])

        return x 

def gradient_penalty(samples, output, weight):
    gradients = K.gradients(output, samples)[0]
    gradients_sqr = K.square(gradients)
    gradient_penalty = K.sum(gradients_sqr,
                              axis=np.arange(1, len(gradients_sqr.shape)))

    # (weight / 2) * ||grad||^2
    # Penalize the gradient norm
    return K.mean(gradient_penalty) * weight 

def update(self, x):
        if x.ndim == len(self.shape):
            x = x.reshape(-1, *self.shape)
        assert x.shape[1:] == self.shape

        self._count += x.shape[0]
        self._sum += np.sum(x, axis=0)
        self._sumsq += np.sum(np.square(x), axis=0)

        self.mean = self._sum / float(self._count)
        self.std = np.sqrt(np.maximum(np.square(self.eps), self._sumsq / float(self._count) - np.square(self.mean))) 

def call(self, x):
        return K.mean(K.batch_flatten(K.square(x[0] - x[1])), -1) 

def earth_movers_distance(y_true, y_pred):
    cdf_true = K.cumsum(y_true, axis=-1)
    cdf_pred = K.cumsum(y_pred, axis=-1)
    emd = K.sqrt(K.mean(K.square(cdf_true - cdf_pred), axis=-1))
    return K.mean(emd) 

def correlation_coefficient_loss(y_true, y_pred):
    x = y_true                      
    y = y_pred                                  
    mx = K.mean(x)  

    my = K.mean(y)                                     
    xm, ym = x-mx, y-my                                                
    r_num = K.sum(tf.multiply(xm,ym))                                     
    r_den = K.sqrt(tf.multiply(K.sum(K.square(xm)), K.sum(K.square(ym))))
    r = r_num / r_den
    r = K.maximum(K.minimum(r, 1.0), -1.0)

    return 1 - K.square(r) 

def angle_zyz_difference(ang1=np.zeros(3), ang2=np.zeros(3)):
    loc1_r = np.zeros(ang1.shape)
    loc2_r = np.zeros(ang2.shape)

    rm1 = rotation_matrix_zyz(ang1)
    rm2 = rotation_matrix_zyz(ang2)
    loc1_r_t = np.array([loc1_r, loc1_r, loc1_r])
    loc2_r_t = np.array([loc2_r, loc2_r, loc2_r])

    dif_m = (rm1.dot(np.eye(3) - loc1_r_t)).transpose() - (rm2.dot(np.eye(3) - loc2_r_t)).transpose()
    dif_d = math.sqrt(np.square(dif_m).sum())


    return dif_d 

def _euclidian_dist(self, x_pair: List[Tensor]) -> Tensor:
        x1_norm = K.l2_normalize(x_pair[0], axis=1)
        x2_norm = K.l2_normalize(x_pair[1], axis=1)
        diff = x1_norm - x2_norm
        square = K.square(diff)
        _sum = K.sum(square, axis=1)
        _sum = K.clip(_sum, min_value=1e-12, max_value=None)
        dist = K.sqrt(_sum) / 2.
        return dist 

def train_step(self, images, style, noise, perform_gp = True, perform_pl = False):

        with tf.GradientTape() as gen_tape, tf.GradientTape() as disc_tape:
            #Get style information
            w_space = []
            pl_lengths = self.pl_mean
            for i in range(len(style)):
                w_space.append(self.GAN.S(style[i]))

            #Generate images
            generated_images = self.GAN.G(w_space + [noise])

            #Discriminate
            real_output = self.GAN.D(images, training=True)
            fake_output = self.GAN.D(generated_images, training=True)

            #Hinge loss function
            gen_loss = K.mean(fake_output)
            divergence = K.mean(K.relu(1 + real_output) + K.relu(1 - fake_output))
            disc_loss = divergence

            if perform_gp:
                #R1 gradient penalty
                disc_loss += gradient_penalty(images, real_output, 10)

            if perform_pl:
                #Slightly adjust W space
                w_space_2 = []
                for i in range(len(style)):
                    std = 0.1 / (K.std(w_space[i], axis = 0, keepdims = True) + 1e-8)
                    w_space_2.append(w_space[i] + K.random_normal(tf.shape(w_space[i])) / (std + 1e-8))

                #Generate from slightly adjusted W space
                pl_images = self.GAN.G(w_space_2 + [noise])

                #Get distance after adjustment (path length)
                delta_g = K.mean(K.square(pl_images - generated_images), axis = [1, 2, 3])
                pl_lengths = delta_g

                if self.pl_mean > 0:
                    gen_loss += K.mean(K.square(pl_lengths - self.pl_mean))

        #Get gradients for respective areas
        gradients_of_generator = gen_tape.gradient(gen_loss, self.GAN.GM.trainable_variables)
        gradients_of_discriminator = disc_tape.gradient(disc_loss, self.GAN.D.trainable_variables)

        #Apply gradients
        self.GAN.GMO.apply_gradients(zip(gradients_of_generator, self.GAN.GM.trainable_variables))
        self.GAN.DMO.apply_gradients(zip(gradients_of_discriminator, self.GAN.D.trainable_variables))

        return disc_loss, gen_loss, divergence, pl_lengths 

def dice(self, y_true, y_pred):
        """
        compute dice for given Tensors

        """
        if self.crop_indices is not None:
            y_true = utils.batch_gather(y_true, self.crop_indices)
            y_pred = utils.batch_gather(y_pred, self.crop_indices)

        if self.input_type == 'prob':
            # We assume that y_true is probabilistic, but just in case:
            if self.re_norm:
                y_true = tf.div_no_nan(y_true, K.sum(y_true, axis=-1, keepdims=True))
            y_true = K.clip(y_true, K.epsilon(), 1)

            # make sure pred is a probability
            if self.re_norm:
                y_pred = tf.div_no_nan(y_pred, K.sum(y_pred, axis=-1, keepdims=True))
            y_pred = K.clip(y_pred, K.epsilon(), 1)

        # Prepare the volumes to operate on
        # If we're doing 'hard' Dice, then we will prepare one-hot-based matrices of size
        # [batch_size, nb_voxels, nb_labels], where for each voxel in each batch entry,
        # the entries are either 0 or 1
        if self.dice_type == 'hard':

            # if given predicted probability, transform to "hard max""
            if self.input_type == 'prob':
                if self.approx_hard_max:
                    y_pred_op = _hard_max(y_pred, axis=-1)
                    y_true_op = _hard_max(y_true, axis=-1)
                else:
                    y_pred_op = _label_to_one_hot(K.argmax(y_pred, axis=-1), self.nb_labels)
                    y_true_op = _label_to_one_hot(K.argmax(y_true, axis=-1), self.nb_labels)

            # if given predicted label, transform to one hot notation
            else:
                assert self.input_type == 'max_label'
                y_pred_op = _label_to_one_hot(y_pred, self.nb_labels)
                y_true_op = _label_to_one_hot(y_true, self.nb_labels)

        # If we're doing soft Dice, require prob output, and the data already is as we need it
        # [batch_size, nb_voxels, nb_labels]
        else:
            assert self.input_type == 'prob', "cannot do soft dice with max_label input"
            y_pred_op = y_pred
            y_true_op = y_true

        # reshape to [batch_size, nb_voxels, nb_labels]
        batch_size = K.shape(y_true)[0]
        y_pred_op = K.reshape(y_pred_op, [batch_size, -1, K.shape(y_true)[-1]])
        y_true_op = K.reshape(y_true_op, [batch_size, -1, K.shape(y_true)[-1]])

        # compute dice for each entry in batch.
        # dice will now be [batch_size, nb_labels]
        top = 2 * K.sum(y_true_op * y_pred_op, 1)
        bottom = K.sum(K.square(y_true_op), 1) + K.sum(K.square(y_pred_op), 1)
        # make sure we have no 0s on the bottom. K.epsilon()
        bottom = K.maximum(bottom, self.area_reg)
        return top / bottom 

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