import torch


def convert_locations_to_boxes(locations, priors, center_variance, size_variance):
    """Convert regressional location results of SSD into boxes in the form of (center_x, center_y, h, w).

    The conversion:
        $$predicted\_center * center_variance = \frac {real\_center - prior\_center} {prior\_hw}$$
        $$exp(predicted\_hw * size_variance) = \frac {real\_hw} {prior\_hw}$$
    We do it in the inverse direction here.
    Args:
        locations (batch_size, num_priors, 4): the regression output of SSD. It will contain the outputs as well.
        priors (num_priors, 4) or (batch_size/1, num_priors, 4): prior boxes.
        center_variance: a float used to change the scale of center.
        size_variance: a float used to change of scale of size.
    Returns:
        boxes:  priors: [[center_x, center_y, h, w]]. All the values
            are relative to the image size.
    """
    # priors can have one dimension less.
    if priors.dim() + 1 == locations.dim():
        priors = priors.unsqueeze(0)
    return torch.cat([locations[..., :2] * center_variance * priors[..., 2:] + priors[..., :2],
                      torch.exp(locations[..., 2:] * size_variance) * priors[..., 2:]], dim=locations.dim() - 1)