from __future__ import division
import tensorflow as tf


class SSDLoss:
    """
    The SSD loss, see https://arxiv.org/abs/1512.02325.
    """

    def __init__(self,
                 neg_pos_ratio=3,
                 n_neg_min=0,
                 alpha=1.0):
        """
        Parameters
        ----------
        neg_pos_ratio : int
            The maximum ratio of negative (i.e. background) to positive 
            ground truth boxes to include in the loss computation.
            There are no actual background ground truth boxes of course, 
            but `y_true` contains anchor boxes labeled with the background 
            class. Since the number of background boxes in `y_true` will 
            usually exceed the number of positive boxes by far, it is 
            necessary to balance their influence on the loss. Defaults to 3 
            following the paper.
        n_neg_min : int
            The minimum number of negative ground truth boxes to enter the 
            loss computation *per batch*. This argument can be used to make
            sure that the model learns from a minimum number of negatives in 
            batches in which there are very few, or even none at all, 
            positive ground truth boxes. It defaults to 0 and if used, it 
            should be set to a value that stands in reasonable proportion to 
            the batch size used for training.
        alpha : float 
            A factor to weight the localization loss in the computation of 
            the total loss. Defaults to 1.0 following the paper.
        """
        self.neg_pos_ratio = neg_pos_ratio
        self.n_neg_min = n_neg_min
        self.alpha = alpha

    def smooth_L1_loss(self, y_true, y_pred):
        """
        Compute smooth L1 loss, see references.

        Parameters
        ----------
        y_true : nD tensor
            A TensorFlow tensor of any shape containing the ground truth data.
            In this context, the expected tensor has shape `(batch_size, 
            #boxes, 4)` and contains the ground truth bounding box 
            coordinates, where the last dimension contains 
            `(xmin, xmax, ymin, ymax)`.
        y_pred : nD tensor
            A TensorFlow tensor of identical structure to `y_true` containing
            the predicted data, in this context the predicted bounding box 
            coordinates.

        Returns:
            The smooth L1 loss, a nD-1 Tensorflow tensor. In this context a 
            2D tensor of shape (batch, n_boxes_total).

        References:
            https://arxiv.org/abs/1504.08083
        """
        absolute_loss = tf.abs(y_true - y_pred)
        square_loss = 0.5 * (y_true - y_pred)**2
        l1_loss = tf.where(
            tf.less(
                absolute_loss,
                1.0),
            square_loss,
            absolute_loss -
            0.5)
        return tf.reduce_sum(l1_loss, axis=-1)

    def log_loss(self, y_true, y_pred):
        """
        Compute the softmax log loss.

        Parameters
        ----------
        y_true : nD tensor 
            A TensorFlow tensor of any shape containing the ground truth data.
            In this context, the expected tensor has shape (batch_size, 
            #boxes, #classes) and contains the ground truth bounding box 
            # categories.
        y_pred : nD tensor
            A TensorFlow tensor of identical structure to `y_true` containing
            the predicted data, in this context the predicted bounding box 
            categories.

        Returns:
            The softmax log loss, a nD-1 Tensorflow tensor. In this context 
            a 2D tensor  of shape (batch, n_boxes_total).
        """
        # Make sure that `y_pred` doesn't contain any zeros (which would break
        # the log function)
        y_pred = tf.maximum(y_pred, 1e-15)
        # Compute the log loss
        log_loss = -tf.reduce_sum(y_true * tf.log(y_pred), axis=-1)
        return log_loss

    def compute_loss(self, y_true, y_pred):
        """
        Compute the loss of the SSD model prediction against the ground truth.

        Parameters
        ----------
        y_true : array
            A Numpy array of shape `(batch_size, #boxes, #classes + 12)`,
            where `#boxes` is the total number of boxes that the model 
            predicts per image. Be careful to make sure that the index 
            of each given box in `y_true` is the same as the index for the 
            corresponding box in `y_pred`. The last axis must have length 
            `#classes + 12` and contain `[classes one-hot encoded, 4 
            ground truth box coordinate offsets, 8 arbitrary entries]`
            in this order, including the background class. The last eight 
            entries of the last axis are not used by this function and 
            therefore their contents are irrelevant, they only exist so that 
            `y_true` has the same shape as `y_pred`, where the last four 
            entries of the last axis contain the anchor box coordinates, 
            which are needed during inference. Important: Boxes that
            you want the cost function to ignore need to have a one-hot
            class vector of all zeros.
        y_pred : tensor
            The model prediction. The shape is identical
            to that of `y_true`, i.e. `(batch_size, #boxes, #classes + 12)`.
            The last axis must contain entries in the format
            `[classes one-hot encoded, 4 predicted box coordinate offsets, 8 
            arbitrary entries]`.

        Returns:
            A scalar, the total multitask loss for classification and 
            localization.
        """
        self.neg_pos_ratio = tf.constant(self.neg_pos_ratio)
        self.n_neg_min = tf.constant(self.n_neg_min)
        self.alpha = tf.constant(self.alpha)

        batch_size = tf.shape(y_pred)[0]  # Output dtype: tf.int32
        # Output dtype: tf.int32, note that `n_boxes` in this context denotes
        # the total number of boxes per image, not the number of boxes per
        # cell.
        n_boxes = tf.shape(y_pred)[1]

        # 1: Compute the losses for class and box predictions for every box.

        classification_loss = tf.to_float(self.log_loss(
            y_true[:, :, :-12], y_pred[:, :, :-12]))  
            # Output shape: (batch_size, n_boxes)
        localization_loss = tf.to_float(self.smooth_L1_loss(
            y_true[:, :, -12:-8], y_pred[:, :, -12:-8]))  
            # Output shape: (batch_size, n_boxes)

        # 2: Compute the classification losses for the positive and negative
        # targets.

        # Create masks for the positive and negative ground truth classes.
        negatives = y_true[:, :, 0]  # Tensor of shape (batch_size, n_boxes)
        # Tensor of shape (batch_size, n_boxes)
        positives = tf.to_float(tf.reduce_max(y_true[:, :, 1:-12], axis=-1))

        # Count the number of positive boxes (classes 1 to n) in y_true across
        # the whole batch.
        n_positive = tf.reduce_sum(positives)

        # Now mask all negative boxes and sum up the losses for the positive 
        # boxes PER batch item
        # (Keras loss functions must output one scalar loss value PER batch 
        # item, rather than just
        # one scalar for the entire batch, that's why we're not summing across
        # all axes).
        pos_class_loss = tf.reduce_sum(
            classification_loss * positives,
            axis=-1)  # Tensor of shape (batch_size,)

        # Compute the classification loss for the negative default boxes (if
        # there are any).

        # First, compute the classification loss for all negative boxes.
        neg_class_loss_all = classification_loss * \
            negatives  # Tensor of shape (batch_size, n_boxes)
        # The number of non-zero loss entries in `neg_class_loss_all`
        n_neg_losses = tf.count_nonzero(neg_class_loss_all, dtype=tf.int32)
        # What's the point of `n_neg_losses`? For the next step, which will 
        # be to compute which negative boxes enter the classification
        # loss, we don't just want to know how many negative ground truth 
        # boxes there are, but for how many of those there actually is
        # a positive (i.e. non-zero) loss. This is necessary because 
        # `tf.nn.top-k()` in the function below will pick the top k boxes with
        # the highest losses no matter what, even if it receives a vector 
        # where all losses are zero. In the unlikely event that all negative
        # classification losses ARE actually zero though, this behavior might 
        # lead to `tf.nn.top-k()` returning the indices of positive
        # boxes, leading to an incorrect negative classification loss 
        # computation, and hence an incorrect overall loss computation.
        # We therefore need to make sure that `n_negative_keep`, which assumes
        # the role of the `k` argument in `tf.nn.top-k()`,
        # is at most the number of negative boxes for which there is a positive
        # classification loss.

        # Compute the number of negative examples we want to account for in 
        # the loss.
        # We'll keep at most `self.neg_pos_ratio` times the number of 
        # positives in `y_true`, but at least `self.n_neg_min` (unless 
        # `n_neg_loses` is smaller).
        n_negative_keep = tf.minimum(
            tf.maximum(
                self.neg_pos_ratio *
                tf.to_int32(n_positive),
                self.n_neg_min),
            n_neg_losses)

        # In the unlikely case when either (1) there are no negative ground 
        # truth boxes at all or (2) the classification loss for all 
        # negative boxes is zero, return zero as the `neg_class_loss`.
        def f1():
            return tf.zeros([batch_size])
        # Otherwise compute the negative loss.

        def f2():
            # Now we'll identify the top-k (where k == `n_negative_keep`) 
            # boxes with the highest confidence loss that
            # belong to the background class in the ground truth data. Note 
            # that this doesn't necessarily mean that the model
            # predicted the wrong class for those boxes, it just means that 
            # the loss for those boxes is the highest.

            # To do this, we reshape `neg_class_loss_all` to 1D...
            # Tensor of shape (batch_size * n_boxes,)
            neg_class_loss_all_1D = tf.reshape(neg_class_loss_all, [-1])
            # ...and then we get the indices for the `n_negative_keep` 
            # boxes with the highest loss out of those...
            values, indices = tf.nn.top_k(neg_class_loss_all_1D,
                                          k=n_negative_keep,
                                          sorted=False)
                                          # We don't need them sorted.
            # ...and with these indices we'll create a mask...
            negatives_keep = tf.scatter_nd(
                indices=tf.expand_dims(indices, axis=1),
                updates=tf.ones_like(
                    indices, dtype=tf.int32),
                shape=tf.shape(neg_class_loss_all_1D))  
                # Tensor of shape (batch_size * n_boxes,)
            # Tensor of shape (batch_size, n_boxes)
            negatives_keep = tf.to_float(
                tf.reshape(
                    negatives_keep, [
                        batch_size, n_boxes]))
            # ...and use it to keep only those boxes and 
            # mask all other classification losses
            neg_class_loss = tf.reduce_sum(
                classification_loss * negatives_keep,
                axis=-1)  # Tensor of shape (batch_size,)
            return neg_class_loss

        neg_class_loss = tf.cond(
            tf.equal(
                n_neg_losses,
                tf.constant(0)),
            f1,
            f2)

        # Tensor of shape (batch_size,)
        class_loss = pos_class_loss + neg_class_loss

        # 3: Compute the localization loss for the positive targets.
        # We don't compute a localization loss for negative predicted boxes
        # (obviously: there are no ground truth boxes they would correspond
        # to).

        loc_loss = tf.reduce_sum(
            localization_loss * positives,
            axis=-1)  # Tensor of shape (batch_size,)

        # 4: Compute the total loss.

        total_loss = (class_loss + self.alpha * loc_loss) / \
            tf.maximum(1.0, n_positive)  # In case `n_positive == 0`
        # Keras has the annoying habit of dividing the loss by the batch 
        # size, which sucks in our case because the relevant criterion to 
        # average our loss over is the number of positive boxes in the batch
        # (by which we're dividing in the line above), not the batch size. 
        # So in order to revert Keras' averaging over the batch size, we'll 
        # have to multiply by it.
        total_loss = total_loss * tf.to_float(batch_size)

        return total_loss
