Python keras.backend.shape() Examples

def get_output(self, train=False):
        def format_shape(shape):
            if K._BACKEND == 'tensorflow':
                def trf(x):
                    try:
                        return int(x)
                    except TypeError:
                        return x

                return map(trf, shape)
            return shape

        X = self.get_input(train)

        in_shape = format_shape(K.shape(X))
        batch_flatten_len = K.prod(in_shape[:2])
        cast_in_shape = (batch_flatten_len, ) + tuple(in_shape[i] for i in range(2, K.ndim(X)))
        
        pre_outs = self.layer(K.reshape(X, cast_in_shape))
        
        out_shape = format_shape(K.shape(pre_outs))
        cast_out_shape = (in_shape[0], in_shape[1]) + tuple(out_shape[i] for i in range(1, K.ndim(pre_outs)))
        
        outputs = K.reshape(pre_outs, cast_out_shape)
        return outputs 

def get_anchors(self, image_shape):
        """Returns anchor pyramid for the given image size."""
        backbone_shapes = compute_backbone_shapes(self.config, image_shape)
        # Cache anchors and reuse if image shape is the same
        if not hasattr(self, "_anchor_cache"):
            self._anchor_cache = {}
        if not tuple(image_shape) in self._anchor_cache:
            # Generate Anchors
            a = utils.generate_pyramid_anchors(
                self.config.RPN_ANCHOR_SCALES,
                self.config.RPN_ANCHOR_RATIOS,
                backbone_shapes,
                self.config.BACKBONE_STRIDES,
                self.config.RPN_ANCHOR_STRIDE)
            # Keep a copy of the latest anchors in pixel coordinates because
            # it's used in inspect_model notebooks.
            # TODO: Remove this after the notebook are refactored to not use it
            self.anchors = a
            # Normalize coordinates
            self._anchor_cache[tuple(image_shape)] = utils.norm_boxes(a, image_shape[:2])
        return self._anchor_cache[tuple(image_shape)] 

def step(self, x, states):   
        h = states[0]
        # states[1] necessary?

        # equals K.dot(X, self._W1) + self._b2 with X.shape=[bs, T, input_dim]
        total_x_prod = states[-1]
        # comes from the constants (equals the input sequence)
        X = states[-2]
        
        # expand dims to add the vector which is only valid for this time step
        # to total_x_prod which is valid for all time steps
        hw = K.expand_dims(K.dot(h, self._W2), 1)
        additive_atn = total_x_prod + hw
        attention = K.softmax(K.dot(additive_atn, self._V), axis=1)
        x_weighted = K.sum(attention * X, [1])

        x = K.dot(K.concatenate([x, x_weighted], 1), self._W3) + self._b3
        
        h, new_states = self.layer.cell.call(x, states[:-2])
        
        return h, new_states 

def build(self, input_shape):
        self._validate_input_shape(input_shape)

        self.input_spec = InputSpec(shape=input_shape)
        
        if not self.layer.built:
            self.layer.build(input_shape)
            self.layer.built = True
            
        input_dim = input_shape[-1]

        if self.layer.return_sequences:
            output_dim = self.layer.compute_output_shape(input_shape)[0][-1]
        else:
            output_dim = self.layer.compute_output_shape(input_shape)[-1]
      
        self._W1 = self.add_weight(shape=(input_dim, input_dim), name="{}_W1".format(self.name), initializer=self.weight_initializer)
        self._W2 = self.add_weight(shape=(output_dim, input_dim), name="{}_W2".format(self.name), initializer=self.weight_initializer)
        self._W3 = self.add_weight(shape=(2*input_dim, input_dim), name="{}_W3".format(self.name), initializer=self.weight_initializer)
        self._b2 = self.add_weight(shape=(input_dim,), name="{}_b2".format(self.name), initializer=self.weight_initializer)
        self._b3 = self.add_weight(shape=(input_dim,), name="{}_b3".format(self.name), initializer=self.weight_initializer)
        self._V = self.add_weight(shape=(input_dim,1), name="{}_V".format(self.name), initializer=self.weight_initializer)
        
        super(AttentionRNNWrapper, self).build() 

def predict_on_batch(self, inputs):
            if inputs.shape == (2,):
                inputs = inputs[np.newaxis, :]
            # Encode
            max_len = len(max(inputs, key=len))
            one_hot_ref =  self.encode(inputs[:,0])
            one_hot_alt = self.encode(inputs[:,1])
            # Construct dummy library indicator
            indicator = np.zeros((inputs.shape[0],2))
            indicator[:,1] = 1
            # Compute fold change for all three frames
            fc_changes = []
            for shift in range(3):
                if shift > 0:
                    shifter = np.zeros((one_hot_ref.shape[0],1,4))
                    one_hot_ref = np.concatenate([one_hot_ref, shifter], axis=1)
                    one_hot_alt = np.concatenate([one_hot_alt, shifter], axis=1)
                pred_ref = self.model.predict_on_batch([one_hot_ref, indicator]).reshape(-1)
                pred_variant = self.model.predict_on_batch([one_hot_alt, indicator]).reshape(-1)
                fc_changes.append(np.log2(pred_variant/pred_ref))
            # Return
            return {"mrl_fold_change":fc_changes[0], 
                    "shift_1":fc_changes[1],
                    "shift_2":fc_changes[2]} 

def step(self, x, states):  
        h = states[0]
        # states[1] necessary?
        
        # comes from the constants
        X_static = states[-2]
        # equals K.dot(static_x, self._W1) + self._b2 with X.shape=[bs, L, static_input_dim]
        total_x_static_prod = states[-1]

        # expand dims to add the vector which is only valid for this time step
        # to total_x_prod which is valid for all time steps
        hw = K.expand_dims(K.dot(h, self._W2), 1)
        additive_atn = total_x_static_prod + hw
        attention = K.softmax(K.dot(additive_atn, self._V), axis=1)
        static_x_weighted = K.sum(attention * X_static, [1])
        
        x = K.dot(K.concatenate([x, static_x_weighted], 1), self._W3) + self._b3

        h, new_states = self.layer.cell.call(x, states[:-2])
        
        # append attention to the states to "smuggle" it out of the RNN wrapper
        attention = K.squeeze(attention, -1)
        h = K.concatenate([h, attention])

        return h, new_states 

def call(self, x, mask=None):
        # computes a probability distribution over the timesteps
        # uses 'max trick' for numerical stability
        # reshape is done to avoid issue with Tensorflow
        # and 1-dimensional weights
        logits = K.dot(x, self.W)
        x_shape = K.shape(x)
        logits = K.reshape(logits, (x_shape[0], x_shape[1]))
        ai = K.exp(logits - K.max(logits, axis=-1, keepdims=True))

        # masked timesteps have zero weight
        if mask is not None:
            mask = K.cast(mask, K.floatx())
            ai = ai * mask
        att_weights = ai / (K.sum(ai, axis=1, keepdims=True) + K.epsilon())
        weighted_input = x * K.expand_dims(att_weights)
        result = K.sum(weighted_input, axis=1)
        if self.return_attention:
            return [result, att_weights]
        return result 

def call(self, inputs, **kwargs):
        # (batch_size, 1, input_num_capsule, input_dim_capsule)
        expand_inputs = K.expand_dims(inputs, axis=1)
        # (batch_size, num_capsule, input_num_capsule, input_dim_capsule)
        expand_inputs = K.tile(expand_inputs, (1, self.num_capsule, 1, 1))
        # (batch_size, num_capsule, input_num_capsule, dim_capsule)
        u_hat = K.map_fn(lambda x: K.batch_dot(x, self.W, axes=[2, 3]), expand_inputs)

        if self.num_routing <= 0:
            self.num_routing = 3
        # (batch_size, num_capsule, input_num_capsule)
        b = K.zeros((K.shape(u_hat)[0], self.num_capsule, self.input_num_capsule))
        for i in xrange(self.num_routing):
            # (batch_size, num_capsule, input_num_capsule)
            c = softmax(b, axis=1)
            # (batch_size, num_capsule, dim_capsule)
            s = K.batch_dot(c, u_hat, axes=[2, 2])
            squashed_s = squash(s)
            if i < self.num_routing - 1:
                # (batch_size, num_capsule, input_num_capsule)
                b += K.batch_dot(squashed_s, u_hat, axes=[2, 3])
        return squashed_s 

def call(self,x,mask=None):
        conv_input,theta = x
        s = theta.shape
        theta = T.reshape(theta,[-1,s[2]])
        m = K.not_equal(conv_input,0.)

        #### For translation
        trans = _trans(theta)
        output = _transform_trans(trans, conv_input)
        output = output * K.cast(m,K.floatx())

        ### For rotation
        M = _fusion(theta)
        output = _transform_rot(M,output)

        return output 

def call(self,x,training=None):
        deta1 = 0.3
        deta2 = 0.3
        deta3 = 0.3
        seed = np.random.randint(1, 10e6)
        rng = RandomStreams(seed=seed)
        theta1 = rng.uniform(size=(x.shape[0],1),low=-deta1,high=deta1,dtype='float32')
        theta2 = rng.uniform(size=(x.shape[0],1),low=-deta2,high=deta2,dtype='float32')
        theta3 = rng.uniform(size=(x.shape[0],1),low=-deta3,high=deta3,dtype='float32')
        theta = K.concatenate([theta1,theta2,theta3],axis=-1)
        theta = K.tile(theta,x.shape[1])
        theta = theta.reshape((x.shape[0], x.shape[1], 3))

        theta = theta.reshape((theta.shape[0]*theta.shape[1], theta.shape[2]))
        M = _fusion(theta)
        output = _transform_rot(M, x)

        return K.in_train_phase(output,x,training = training) 

def clip_boxes_graph(boxes, window):
    """
    boxes: [N, (y1, x1, y2, x2)]
    window: [4] in the form y1, x1, y2, x2
    """
    # Split
    wy1, wx1, wy2, wx2 = tf.split(window, 4)
    y1, x1, y2, x2 = tf.split(boxes, 4, axis=1)
    # Clip
    y1 = tf.maximum(tf.minimum(y1, wy2), wy1)
    x1 = tf.maximum(tf.minimum(x1, wx2), wx1)
    y2 = tf.maximum(tf.minimum(y2, wy2), wy1)
    x2 = tf.maximum(tf.minimum(x2, wx2), wx1)
    clipped = tf.concat([y1, x1, y2, x2], axis=1, name="clipped_boxes")
    clipped.set_shape((clipped.shape[0], 4))
    return clipped 

def yolo_correct_boxes(box_xy, box_wh, input_shape, image_shape):
    '''Get corrected boxes'''
    box_yx = box_xy[..., ::-1]
    box_hw = box_wh[..., ::-1]
    input_shape = K.cast(input_shape, K.dtype(box_yx))
    image_shape = K.cast(image_shape, K.dtype(box_yx))
    new_shape = K.round(image_shape * K.min(input_shape/image_shape))
    offset = (input_shape-new_shape)/2./input_shape
    scale = input_shape/new_shape
    box_yx = (box_yx - offset) * scale
    box_hw *= scale

    box_mins = box_yx - (box_hw / 2.)
    box_maxes = box_yx + (box_hw / 2.)
    boxes =  K.concatenate([
        box_mins[..., 0:1],  # y_min
        box_mins[..., 1:2],  # x_min
        box_maxes[..., 0:1],  # y_max
        box_maxes[..., 1:2]  # x_max
    ])

    # Scale boxes back to original image shape.
    boxes *= K.concatenate([image_shape, image_shape])
    return boxes 

def get_anchors(self, image_shape):
        """Returns anchor pyramid for the given image size."""
        backbone_shapes = compute_backbone_shapes(self.config, image_shape)
        # Cache anchors and reuse if image shape is the same
        if not hasattr(self, "_anchor_cache"):
            self._anchor_cache = {}
        if not tuple(image_shape) in self._anchor_cache:
            # Generate Anchors
            a = utils.generate_pyramid_anchors(
                self.config.RPN_ANCHOR_SCALES,
                self.config.RPN_ANCHOR_RATIOS,
                backbone_shapes,
                self.config.BACKBONE_STRIDES,
                self.config.RPN_ANCHOR_STRIDE)
            # Keep a copy of the latest anchors in pixel coordinates because
            # it's used in inspect_model notebooks.
            # TODO: Remove this after the notebook are refactored to not use it
            self.anchors = a
            # Normalize coordinates
            self._anchor_cache[tuple(image_shape)] = utils.norm_boxes(a, image_shape[:2])
        return self._anchor_cache[tuple(image_shape)] 

def build_rpn_model(anchor_stride, anchors_per_location, depth):
    """Builds a Keras model of the Region Proposal Network.
    It wraps the RPN graph so it can be used multiple times with shared
    weights.

    anchors_per_location: number of anchors per pixel in the feature map
    anchor_stride: Controls the density of anchors. Typically 1 (anchors for
                   every pixel in the feature map), or 2 (every other pixel).
    depth: Depth of the backbone feature map.

    Returns a Keras Model object. The model outputs, when called, are:
    rpn_class_logits: [batch, H * W * anchors_per_location, 2] Anchor classifier logits (before softmax)
    rpn_probs: [batch, H * W * anchors_per_location, 2] Anchor classifier probabilities.
    rpn_bbox: [batch, H * W * anchors_per_location, (dy, dx, log(dh), log(dw))] Deltas to be
                applied to anchors.
    """
    input_feature_map = KL.Input(shape=[None, None, depth],
                                 name="input_rpn_feature_map")
    outputs = rpn_graph(input_feature_map, anchors_per_location, anchor_stride)
    return KM.Model([input_feature_map], outputs, name="rpn_model")


############################################################
#  Feature Pyramid Network Heads
############################################################ 

def clip_boxes_graph(boxes, window):
    """
    boxes: [N, (y1, x1, y2, x2)]
    window: [4] in the form y1, x1, y2, x2
    """
    # Split
    wy1, wx1, wy2, wx2 = tf.split(window, 4)
    y1, x1, y2, x2 = tf.split(boxes, 4, axis=1)
    # Clip
    y1 = tf.maximum(tf.minimum(y1, wy2), wy1)
    x1 = tf.maximum(tf.minimum(x1, wx2), wx1)
    y2 = tf.maximum(tf.minimum(y2, wy2), wy1)
    x2 = tf.maximum(tf.minimum(x2, wx2), wx1)
    clipped = tf.concat([y1, x1, y2, x2], axis=1, name="clipped_boxes")
    clipped.set_shape((clipped.shape[0], 4))
    return clipped 

def call(self , x, mask=None):
        
        e1=x[0].T
        e2=x[1].T
        
        batch_size = K.shape(x[0])[0]
        sim = []
        V_out = K.dot(self.V, K.concatenate([e1,e2],axis=0))     

        for i in range(self.k): 
            temp = K.batch_dot(K.dot(e1.T,self.W[i,:,:]),e2.T,axes=1)
            sim.append(temp)
        sim=K.reshape(sim,(self.k,batch_size))

        tensor_bi_product = self.activation(V_out+sim)
        tensor_bi_product = K.dot(self.U.T, tensor_bi_product).T

        return tensor_bi_product 

def build(self,input_shape):
        
        self.W = self.add_weight(name='w',shape=(self.k, self.d, self.d),
                                      initializer='glorot_uniform',trainable=True)
                                      #initializer='ones',trainable=False)
        
        self.V = self.add_weight(name='v',shape=(self.k, self.d*2),
                                      initializer='glorot_uniform',trainable=True)
                                    #initializer='ones',trainable=False)
                                  
        #self.b = self.add_weight(name='b',shape=(self.k,1),
        #                              initializer='glorot_uniform',trainable=True)
#                                    initializer='ones',trainable=False)
        
        self.U = self.add_weight(name='u',shape=(self.k,1),
#                                      initializer='ones',trainable=False)
                initializer='glorot_uniform',trainable=True)
                                  
        super(ntn, self).build(input_shape) 

def yolo_correct_boxes(box_xy, box_wh, input_shape, image_shape):
    '''Get corrected boxes'''
    box_yx = box_xy[..., ::-1]
    box_hw = box_wh[..., ::-1]
    input_shape = K.cast(input_shape, K.dtype(box_yx))
    image_shape = K.cast(image_shape, K.dtype(box_yx))
    new_shape = K.round(image_shape * K.min(input_shape/image_shape))
    offset = (input_shape-new_shape)/2./input_shape
    scale = input_shape/new_shape
    box_yx = (box_yx - offset) * scale
    box_hw *= scale

    box_mins = box_yx - (box_hw / 2.)
    box_maxes = box_yx + (box_hw / 2.)
    boxes =  K.concatenate([
        box_mins[..., 0:1],  # y_min
        box_mins[..., 1:2],  # x_min
        box_maxes[..., 0:1],  # y_max
        box_maxes[..., 1:2]  # x_max
    ])

    # Scale boxes back to original image shape.
    boxes *= K.concatenate([image_shape, image_shape])
    return boxes 

def yolo_correct_boxes(box_xy, box_wh, input_shape, image_shape):
    '''Get corrected boxes'''
    box_yx = box_xy[..., ::-1]
    box_hw = box_wh[..., ::-1]
    input_shape = K.cast(input_shape, K.dtype(box_yx))
    image_shape = K.cast(image_shape, K.dtype(box_yx))
    new_shape = K.round(image_shape * K.min(input_shape/image_shape))
    offset = (input_shape-new_shape)/2./input_shape
    scale = input_shape/new_shape
    box_yx = (box_yx - offset) * scale
    box_hw *= scale

    box_mins = box_yx - (box_hw / 2.)
    box_maxes = box_yx + (box_hw / 2.)
    boxes =  K.concatenate([
        box_mins[..., 0:1],  # y_min
        box_mins[..., 1:2],  # x_min
        box_maxes[..., 0:1],  # y_max
        box_maxes[..., 1:2]  # x_max
    ])

    # Scale boxes back to original image shape.
    boxes *= K.concatenate([image_shape, image_shape])
    return boxes 

def sampling(args: tuple):
    """
    Reparameterization trick by sampling z from unit Gaussian
    :param args: (tensor, tensor) mean and log of variance of q(z|x)
    :returns tensor: sampled latent vector z
    """

    # unpack the input tuple
    z_mean, z_log_var = args

    # mini-batch size
    mb_size = K.shape(z_mean)[0]

    # latent space size
    dim = K.int_shape(z_mean)[1]

    # random normal vector with mean=0 and std=1.0
    epsilon = K.random_normal(shape=(mb_size, dim))

    return z_mean + K.exp(0.5 * z_log_var) * epsilon 

def build_rpn_model(anchor_stride, anchors_per_location, depth):
    """Builds a Keras model of the Region Proposal Network.
    It wraps the RPN graph so it can be used multiple times with shared
    weights.
    anchors_per_location: number of anchors per pixel in the feature map
    anchor_stride: Controls the density of anchors. Typically 1 (anchors for
                   every pixel in the feature map), or 2 (every other pixel).
    depth: Depth of the backbone feature map.
    Returns a Keras Model object. The model outputs, when called, are:
    rpn_class_logits: [batch, H * W * anchors_per_location, 2] Anchor classifier logits (before softmax)
    rpn_probs: [batch, H * W * anchors_per_location, 2] Anchor classifier probabilities.
    rpn_bbox: [batch, H * W * anchors_per_location, (dy, dx, log(dh), log(dw))] Deltas to be
                applied to anchors.
    """
    input_feature_map = KL.Input(shape=[None, None, depth],
                                 name="input_rpn_feature_map")
    outputs = rpn_graph(input_feature_map, anchors_per_location, anchor_stride)
    return KM.Model([input_feature_map], outputs, name="rpn_model")


############################################################
#  Feature Pyramid Network Heads
############################################################ 

def build(self, input_shape):
        super(SequenceAttention, self).build(input_shape)
        self._validate_input_shape(input_shape)
        
        self._weights = {}
        if self._similarity == self._additive_similarity:
            self._weights["w_a"] = self.add_weight(
                name='w_a', 
                shape=(input_shape[0][-1] + input_shape[1][-1], input_shape[0][-1]),
                initializer=self._kernel_initializer,
                trainable=True
            )
            
            self._weights["v_a"] = self.add_weight(
                name='v_a', 
                shape=(1, input_shape[0][-1]),
                initializer=self._kernel_initializer,
                trainable=True
            )
            
        elif self._similarity == self._multiplicative_similarity:
            self._weights["w_a"] = self.add_weight(
                name='w_a', 
                shape=(input_shape[1][-1], input_shape[0][-1]),
                initializer=self._kernel_initializer,
                trainable=True
            )

        self.built = True 

def box_iou(b1, b2):
    '''Return iou tensor

    Parameters
    ----------
    b1: tensor, shape=(i1,...,iN, 4), xywh
    b2: tensor, shape=(j, 4), xywh

    Returns
    -------
    iou: tensor, shape=(i1,...,iN, j)

    '''

    # Expand dim to apply broadcasting.
    b1 = K.expand_dims(b1, -2)
    b1_xy = b1[..., :2]
    b1_wh = b1[..., 2:4]
    b1_wh_half = b1_wh/2.
    b1_mins = b1_xy - b1_wh_half
    b1_maxes = b1_xy + b1_wh_half

    # Expand dim to apply broadcasting.
    b2 = K.expand_dims(b2, 0)
    b2_xy = b2[..., :2]
    b2_wh = b2[..., 2:4]
    b2_wh_half = b2_wh/2.
    b2_mins = b2_xy - b2_wh_half
    b2_maxes = b2_xy + b2_wh_half

    intersect_mins = K.maximum(b1_mins, b2_mins)
    intersect_maxes = K.minimum(b1_maxes, b2_maxes)
    intersect_wh = K.maximum(intersect_maxes - intersect_mins, 0.)
    intersect_area = intersect_wh[..., 0] * intersect_wh[..., 1]
    b1_area = b1_wh[..., 0] * b1_wh[..., 1]
    b2_area = b2_wh[..., 0] * b2_wh[..., 1]
    iou = intersect_area / (b1_area + b2_area - intersect_area)

    return iou 

def call(self, x, mask=None):
        q, k, v = x
        d_k = q.shape.as_list()[2]

        # in pure tensorflow:
        # weights = tf.matmul(x_batch, tf.transpose(y_batch, perm=[0, 2, 1]))
        # normalized_weights = tf.nn.softmax(weights/scaling)
        # output = tf.matmul(normalized_weights, x_batch)
        
        weights = K.batch_dot(q,  k, axes=[2, 2])

        if mask is not None:
            # add mask weights
            if isinstance(mask, (list, tuple)):
                if len(mask) > 0:
                    raise ValueError("mask can only be a Tensor or a list of length 1 containing a tensor.")

                mask = mask[0]

            weights += -1e10*(1-mask)

        normalized_weights = K.softmax(weights / np.sqrt(d_k))
        output = K.batch_dot(normalized_weights, v)
        
        if self._return_attention:
            return [output, normalized_weights]
        else:
            return output 

def yolo_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 box_iou(b1, b2):
    '''Return iou tensor

    Parameters
    ----------
    b1: tensor, shape=(i1,...,iN, 4), xywh
    b2: tensor, shape=(j, 4), xywh

    Returns
    -------
    iou: tensor, shape=(i1,...,iN, j)

    '''

    # Expand dim to apply broadcasting.
    b1 = K.expand_dims(b1, -2)
    b1_xy = b1[..., :2]
    b1_wh = b1[..., 2:4]
    b1_wh_half = b1_wh/2.
    b1_mins = b1_xy - b1_wh_half
    b1_maxes = b1_xy + b1_wh_half

    # Expand dim to apply broadcasting.
    b2 = K.expand_dims(b2, 0)
    b2_xy = b2[..., :2]
    b2_wh = b2[..., 2:4]
    b2_wh_half = b2_wh/2.
    b2_mins = b2_xy - b2_wh_half
    b2_maxes = b2_xy + b2_wh_half

    intersect_mins = K.maximum(b1_mins, b2_mins)
    intersect_maxes = K.minimum(b1_maxes, b2_maxes)
    intersect_wh = K.maximum(intersect_maxes - intersect_mins, 0.)
    intersect_area = intersect_wh[..., 0] * intersect_wh[..., 1]
    b1_area = b1_wh[..., 0] * b1_wh[..., 1]
    b2_area = b2_wh[..., 0] * b2_wh[..., 1]
    iou = intersect_area / (b1_area + b2_area - intersect_area)

    return iou 

def __call__(self, x, mask=None):
        if isinstance(x, (list, tuple)):
            self.build([it.shape for it in x])
        else:
            self.build(x.shape)

        q, k, v = x
        
        outputs = []
        attentions = []
        for i in range(self._h):
            qi = self._q_layers[i](q)
            ki = self._k_layers[i](k)
            vi = self._v_layers[i](v)
            
            if self._return_attention:
                output, attention = self._sdp_layer([qi, ki, vi], mask=mask)
                outputs.append(output)
                attentions.append(attention)
            else:
                output = self._sdp_layer([qi, ki, vi], mask=mask)
                outputs.append(output)
            
        concatenated_outputs = Concatenate()(outputs)
        output = self._output(concatenated_outputs)
        
        if self._return_attention:
            attention = Concatenate()(attentions)
            # print("attention", attention, attention.shape)
       
        if self._return_attention:
            return [output, attention]
        else:
            return output        

# https://wanasit.github.io/attention-based-sequence-to-sequence-in-keras.html
# https://arxiv.org/pdf/1508.04025.pdf 

def yolo_head(feats, anchors, num_classes, input_shape):
    """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])

    box_xy = K.sigmoid(feats[..., :2])
    box_wh = K.exp(feats[..., 2:4])
    box_confidence = K.sigmoid(feats[..., 4:5])
    box_class_probs = K.sigmoid(feats[..., 5:])

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

    return box_xy, box_wh, box_confidence, box_class_probs 

def build(self, input_shape):
        self._validate_input_shape(input_shape)

        for i, x in enumerate(input_shape):
            self.input_spec[i] = InputSpec(shape=x)
        
        if not self.layer.built:
            self.layer.build(input_shape)
            self.layer.built = True
            
        temporal_input_dim = input_shape[0][-1]
        static_input_dim = input_shape[1][-1]

        if self.layer.return_sequences:
            output_dim = self.layer.compute_output_shape(input_shape[0])[0][-1]
        else:
            output_dim = self.layer.compute_output_shape(input_shape[0])[-1]
      
        self._W1 = self.add_weight(shape=(static_input_dim, temporal_input_dim), name="{}_W1".format(self.name), initializer=self.weight_initializer)
        self._W2 = self.add_weight(shape=(output_dim, temporal_input_dim), name="{}_W2".format(self.name), initializer=self.weight_initializer)
        self._W3 = self.add_weight(shape=(temporal_input_dim + static_input_dim, temporal_input_dim), name="{}_W3".format(self.name), initializer=self.weight_initializer)
        self._b2 = self.add_weight(shape=(temporal_input_dim,), name="{}_b2".format(self.name), initializer=self.weight_initializer)
        self._b3 = self.add_weight(shape=(temporal_input_dim,), name="{}_b3".format(self.name), initializer=self.weight_initializer)
        self._V = self.add_weight(shape=(temporal_input_dim, 1), name="{}_V".format(self.name), initializer=self.weight_initializer)
        
        super(ExternalAttentionRNNWrapper, self).build() 

def box_iou(b1, b2):
    '''Return iou tensor

    Parameters
    ----------
    b1: tensor, shape=(i1,...,iN, 4), xywh
    b2: tensor, shape=(j, 4), xywh

    Returns
    -------
    iou: tensor, shape=(i1,...,iN, j)

    '''

    # Expand dim to apply broadcasting.
    b1 = K.expand_dims(b1, -2)
    b1_xy = b1[..., :2]
    b1_wh = b1[..., 2:4]
    b1_wh_half = b1_wh/2.
    b1_mins = b1_xy - b1_wh_half
    b1_maxes = b1_xy + b1_wh_half

    # Expand dim to apply broadcasting.
    b2 = K.expand_dims(b2, 0)
    b2_xy = b2[..., :2]
    b2_wh = b2[..., 2:4]
    b2_wh_half = b2_wh/2.
    b2_mins = b2_xy - b2_wh_half
    b2_maxes = b2_xy + b2_wh_half

    intersect_mins = K.maximum(b1_mins, b2_mins)
    intersect_maxes = K.minimum(b1_maxes, b2_maxes)
    intersect_wh = K.maximum(intersect_maxes - intersect_mins, 0.)
    intersect_area = intersect_wh[..., 0] * intersect_wh[..., 1]
    b1_area = b1_wh[..., 0] * b1_wh[..., 1]
    b2_area = b2_wh[..., 0] * b2_wh[..., 1]
    iou = intersect_area / (b1_area + b2_area - intersect_area)

    return iou