# Copyright Contributors to the Pyro project.
# SPDX-License-Identifier: Apache-2.0

import torch
from pyro.distributions.transforms import Transform
from pyro.distributions import constraints


class OrderedTransform(Transform):
    """
    Transforms a real vector into an ordered vector.

    Specifically, enforces monotonically increasing order on the last dimension
    of a given tensor via the transformation :math:`y_0 = x_0`,
    :math:`y_i = \\sum_{1 \\le j \\le i} \\exp(x_i)`
    """
    domain = constraints.real_vector
    codomain = constraints.ordered_vector
    bijective = True
    sign = +1
    event_dim = 1

    def _call(self, x):
        z = torch.cat([x[..., :1], x[..., 1:].exp()], dim=-1)
        return torch.cumsum(z, dim=-1)

    def _inverse(self, y):
        x = (y[..., 1:] - y[..., :-1]).log()
        return torch.cat([y[..., :1], x], dim=-1)

    def log_abs_det_jacobian(self, x, y):
        return torch.sum(x[..., 1:], dim=-1)

torch.sum torch.cat torch.cumsum