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#   Licensed under the Apache License, Version 2.0 (the "License");
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from functools import singledispatch

import numpy as np
import pytensor.tensor as pt

from numpy.lib.array_utils import normalize_axis_tuple
from pytensor.graph import Op
from pytensor.tensor import TensorVariable

from pymc.logprob.transforms import (
    ChainedTransform,
    CircularTransform,
    IntervalTransform,
    LogOddsTransform,
    LogTransform,
    SimplexTransform,
    Transform,
)

__all__ = [
    "Chain",
    "CholeskyCovPacked",
    "Interval",
    "Transform",
    "ZeroSumTransform",
    "circular",
    "log",
    "log_exp_m1",
    "logodds",
    "ordered",
    "simplex",
    "sum_to_1",
]


@singledispatch
def _default_transform(op: Op, rv: TensorVariable):
    """Return default transform for a given Distribution `Op`."""
    return None


class LogExpM1(Transform):
    name = "log_exp_m1"

    def backward(self, value, *inputs):
        return pt.softplus(value)

    def forward(self, value, *inputs):
        """Inverse operation of softplus.

        y = Log(Exp(x) - 1)
          = Log(1 - Exp(-x)) + x
        """
        return pt.log(1.0 - pt.exp(-value)) + value

    def log_jac_det(self, value, *inputs):
        return -pt.softplus(-value)


class Ordered(Transform):
    """
    Transforms a vector of values into a vector of ordered values.

    Parameters
    ----------
    positive: If True, all values are positive. This has better geometry than just chaining with a log transform.
    ascending: If True, the values are in ascending order (default). If False, the values are in descending order.
    """

    name = "ordered"

    def __init__(self, positive=False, ascending=True):
        self.positive = positive
        self.ascending = ascending

    def backward(self, value, *inputs):
        if self.positive:  # Transform both initial value and deltas to be positive
            x = pt.exp(value)
        else:  # Transform only deltas to be positive
            x = pt.empty(value.shape)
            x = pt.set_subtensor(x[..., 0], value[..., 0])
            x = pt.set_subtensor(x[..., 1:], pt.exp(value[..., 1:]))
        x = pt.cumsum(x, axis=-1)  # Add deltas cumulatively to initial value
        if not self.ascending:
            x = x[..., ::-1]
        return x

    def forward(self, value, *inputs):
        if not self.ascending:
            value = value[..., ::-1]
        y = pt.empty(value.shape)
        y = pt.set_subtensor(y[..., 0], pt.log(value[..., 0]) if self.positive else value[..., 0])
        y = pt.set_subtensor(y[..., 1:], pt.log(value[..., 1:] - value[..., :-1]))
        return y

    def log_jac_det(self, value, *inputs):
        if self.positive:
            return pt.sum(value, axis=-1)
        else:
            return pt.sum(value[..., 1:], axis=-1)


class SumTo1(Transform):
    """
    Transforms K - 1 dimensional simplex space (K values in [0, 1] that sum to 1) to a K - 1 vector of values in [0, 1].

    This transformation operates on the last dimension of the input tensor.
    """

    name = "sumto1"

    def backward(self, value, *inputs):
        remaining = 1 - pt.sum(value[..., :], axis=-1, keepdims=True)
        return pt.concatenate([value[..., :], remaining], axis=-1)

    def forward(self, value, *inputs):
        return value[..., :-1]

    def log_jac_det(self, value, *inputs):
        y = pt.zeros(value.shape)
        return pt.sum(y, axis=-1)


class CholeskyCovPacked(Transform):
    """Transforms the diagonal elements of the LKJCholeskyCov distribution to be on the log scale."""

    name = "cholesky-cov-packed"

    def __init__(self, n):
        """Create a CholeskyCovPack object.

        Parameters
        ----------
        n: int
            Number of diagonal entries in the LKJCholeskyCov distribution
        """
        self.diag_idxs = pt.arange(1, n + 1).cumsum() - 1

    def backward(self, value, *inputs):
        return pt.set_subtensor(value[..., self.diag_idxs], pt.exp(value[..., self.diag_idxs]))

    def forward(self, value, *inputs):
        return pt.set_subtensor(value[..., self.diag_idxs], pt.log(value[..., self.diag_idxs]))

    def log_jac_det(self, value, *inputs):
        return pt.sum(value[..., self.diag_idxs], axis=-1)


Chain = ChainedTransform

simplex = SimplexTransform()
simplex.__doc__ = """
Instantiation of :class:`pymc.logprob.transforms.SimplexTransform`
for use in the ``transform`` argument of a random variable."""

logodds = LogOddsTransform()
logodds.__doc__ = """
Instantiation of :class:`pymc.logprob.transforms.LogOddsTransform`
for use in the ``transform`` argument of a random variable."""


class Interval(IntervalTransform):
    """Wrapper around  :class:`pymc.logprob.transforms.IntervalTransform` for use in the ``transform`` argument of a random variable.

    Parameters
    ----------
    lower : int or float, optional
        Lower bound of the interval transform. Must be a constant finite value.
        By default (``lower=None``), the interval is not bounded below.
    upper : int or float, optional
        Upper bound of the interval transform. Must be a constant finite value.
        By default (``upper=None``), the interval is not bounded above.
    bounds_fn : callable, optional
        Alternative to lower and upper. Must return a tuple of lower and upper bounds
        as a symbolic function of the respective distribution inputs. If one of lower or
        upper is ``None``, the interval is unbounded on that edge.

        .. warning:: Expressions returned by `bounds_fn` should depend only on the
            distribution inputs or other constants. Expressions that depend on nonlocal
            variables, such as other distributions defined in the model context will
            likely break sampling.


    Examples
    --------
    Create an interval transform between -1 and +1

    .. code-block:: python

        with pm.Model():
            interval = pm.distributions.transforms.Interval(lower=-1, upper=1)
            x = pm.Normal("x", transform=interval)

    Create a lower-bounded interval transform at 0, using a callable

    .. code-block:: python

        def get_bounds(rng, size, mu, sigma):
            return 0, None


        with pm.Model():
            interval = pm.distributions.transforms.Interval(bounds_fn=get_bounds)
            x = pm.Normal("x", transform=interval)

    Create a lower-bounded interval transform that depends on a distribution parameter

    .. code-block:: python

        def get_bounds(rng, size, mu, sigma):
            return mu - 1, None


        interval = pm.distributions.transforms.Interval(bounds_fn=get_bounds)

        with pm.Model():
            mu = pm.Normal("mu")
            x = pm.Normal("x", mu=mu, sigma=2, transform=interval)
    """

    def __init__(self, lower=None, upper=None, *, bounds_fn=None):
        if bounds_fn is None:
            try:
                bounds = tuple(
                    None if bound is None else pt.constant(bound, ndim=0).data
                    for bound in (lower, upper)
                )
            except (ValueError, TypeError):
                raise ValueError(
                    "Interval bounds must be constant values. If you need expressions that "
                    "depend on symbolic variables use `args_fn`"
                )

            lower, upper = (
                None if (bound is None or np.isinf(bound)) else bound for bound in bounds
            )

            if lower is None and upper is None:
                raise ValueError("Lower and upper interval bounds cannot both be None")

            def bounds_fn(*rv_inputs):
                return lower, upper

        super().__init__(args_fn=bounds_fn)


class ZeroSumTransform(Transform):
    """
    Constrains any random samples to sum to zero along the user-provided ``zerosum_axes``.

    Parameters
    ----------
    zerosum_axes : list of ints
        Must be a list of integers (positive or negative).
    """

    name = "zerosum"

    __props__ = ("zerosum_axes",)

    def __init__(self, zerosum_axes):
        self.zerosum_axes = tuple(int(axis) for axis in zerosum_axes)

    @staticmethod
    def extend_axis(array, axis):
        n = (array.shape[axis] + 1).astype("floatX")
        sum_vals = array.sum(axis, keepdims=True)
        norm = sum_vals / (pt.sqrt(n) + n)
        fill_val = norm - sum_vals / pt.sqrt(n)

        out = pt.concatenate([array, fill_val], axis=axis)
        return out - norm

    @staticmethod
    def extend_axis_rev(array, axis):
        normalized_axis = normalize_axis_tuple(axis, array.ndim)[0]

        n = array.shape[normalized_axis].astype("floatX")
        last = pt.take(array, [-1], axis=normalized_axis)

        sum_vals = -last * pt.sqrt(n)
        norm = sum_vals / (pt.sqrt(n) + n)
        slice_before = (slice(None, None),) * normalized_axis

        return array[(*slice_before, slice(None, -1))] + norm

    def forward(self, value, *rv_inputs):
        for axis in self.zerosum_axes:
            value = self.extend_axis_rev(value, axis=axis)
        return value

    def backward(self, value, *rv_inputs):
        for axis in self.zerosum_axes:
            value = self.extend_axis(value, axis=axis)
        return value

    def log_jac_det(self, value, *rv_inputs):
        return pt.constant(0.0)


log_exp_m1 = LogExpM1()
log_exp_m1.__doc__ = """
Instantiation of :class:`pymc.distributions.transforms.LogExpM1`
for use in the ``transform`` argument of a random variable."""

ordered = Ordered()
ordered.__doc__ = """
Instantiation of :class:`pymc.distributions.transforms.Ordered`
for use in the ``transform`` argument of a random variable."""

log = LogTransform()
log.__doc__ = """
Instantiation of :class:`pymc.logprob.transforms.LogTransform`
for use in the ``transform`` argument of a random variable."""

sum_to_1 = SumTo1()
sum_to_1.__doc__ = """
Instantiation of :class:`pymc.distributions.transforms.SumTo1`
for use in the ``transform`` argument of a random variable."""

circular = CircularTransform()
circular.__doc__ = """
Instantiation of :class:`pymc.logprob.transforms.CircularTransform`
for use in the ``transform`` argument of a random variable."""
