import torch
from torch.nn import functional as F
import logging
import numpy as np

from manifold_flow import transforms
from manifold_flow.utils import various

logger = logging.getLogger(__name__)

DEFAULT_MIN_BIN_WIDTH = 1e-3
DEFAULT_MIN_BIN_HEIGHT = 1e-3
DEFAULT_MIN_DERIVATIVE = 1e-3


def unconstrained_rational_quadratic_spline(
    inputs,
    unnormalized_widths,
    unnormalized_heights,
    unnormalized_derivatives,
    inverse=False,
    tails="linear",
    tail_bound=1.0,
    min_bin_width=DEFAULT_MIN_BIN_WIDTH,
    min_bin_height=DEFAULT_MIN_BIN_HEIGHT,
    min_derivative=DEFAULT_MIN_DERIVATIVE,
    full_jacobian=False,
):
    assert not full_jacobian

    inside_interval_mask = (inputs >= -tail_bound) & (inputs <= tail_bound)
    outside_interval_mask = ~inside_interval_mask

    outputs = torch.zeros_like(inputs)
    logabsdet = torch.zeros_like(inputs)

    if tails == "linear":
        unnormalized_derivatives = F.pad(unnormalized_derivatives, pad=(1, 1))
        constant = np.log(np.exp(1 - min_derivative) - 1)
        unnormalized_derivatives[..., 0] = constant
        unnormalized_derivatives[..., -1] = constant

        outputs[outside_interval_mask] = inputs[outside_interval_mask]
        logabsdet[outside_interval_mask] = 0
    else:
        raise RuntimeError("{} tails are not implemented.".format(tails))

    if torch.sum(inside_interval_mask).item() > 0:
        outputs[inside_interval_mask], logabsdet[inside_interval_mask] = rational_quadratic_spline(
            inputs=inputs[inside_interval_mask],
            unnormalized_widths=unnormalized_widths[inside_interval_mask, :],
            unnormalized_heights=unnormalized_heights[inside_interval_mask, :],
            unnormalized_derivatives=unnormalized_derivatives[inside_interval_mask, :],
            inverse=inverse,
            left=-tail_bound,
            right=tail_bound,
            bottom=-tail_bound,
            top=tail_bound,
            min_bin_width=min_bin_width,
            min_bin_height=min_bin_height,
            min_derivative=min_derivative,
        )

    return outputs, logabsdet


def rational_quadratic_spline(
    inputs,
    unnormalized_widths,
    unnormalized_heights,
    unnormalized_derivatives,
    inverse=False,
    left=0.0,
    right=1.0,
    bottom=0.0,
    top=1.0,
    min_bin_width=DEFAULT_MIN_BIN_WIDTH,
    min_bin_height=DEFAULT_MIN_BIN_HEIGHT,
    min_derivative=DEFAULT_MIN_DERIVATIVE,
    full_jacobian=False,
):
    assert not full_jacobian

    try:
        if torch.min(inputs) < left or torch.max(inputs) > right:
            raise transforms.InputOutsideDomain()
    except RuntimeError:
        logger.error("Error in rational_quadratic_spline!")
        logger.error("  Left: %s", left)
        logger.error("  Right: %s", left)
        logger.error("  Input shape: %s", inputs.size())
        logger.error("  Input: %s", inputs)
        raise

    num_bins = unnormalized_widths.shape[-1]

    if min_bin_width * num_bins > 1.0:
        raise ValueError("Minimal bin width too large for the number of bins")
    if min_bin_height * num_bins > 1.0:
        raise ValueError("Minimal bin height too large for the number of bins")

    widths = F.softmax(unnormalized_widths, dim=-1)
    widths = min_bin_width + (1 - min_bin_width * num_bins) * widths
    cumwidths = torch.cumsum(widths, dim=-1)
    cumwidths = F.pad(cumwidths, pad=(1, 0), mode="constant", value=0.0)
    cumwidths = (right - left) * cumwidths + left
    cumwidths[..., 0] = left
    cumwidths[..., -1] = right
    widths = cumwidths[..., 1:] - cumwidths[..., :-1]

    derivatives = min_derivative + F.softplus(unnormalized_derivatives)

    heights = F.softmax(unnormalized_heights, dim=-1)
    heights = min_bin_height + (1 - min_bin_height * num_bins) * heights
    cumheights = torch.cumsum(heights, dim=-1)
    cumheights = F.pad(cumheights, pad=(1, 0), mode="constant", value=0.0)
    cumheights = (top - bottom) * cumheights + bottom
    cumheights[..., 0] = bottom
    cumheights[..., -1] = top
    heights = cumheights[..., 1:] - cumheights[..., :-1]

    if inverse:
        bin_idx = various.searchsorted(cumheights, inputs)[..., None]
    else:
        bin_idx = various.searchsorted(cumwidths, inputs)[..., None]

    input_cumwidths = cumwidths.gather(-1, bin_idx)[..., 0]
    input_bin_widths = widths.gather(-1, bin_idx)[..., 0]

    input_cumheights = cumheights.gather(-1, bin_idx)[..., 0]
    delta = heights / widths
    input_delta = delta.gather(-1, bin_idx)[..., 0]

    input_derivatives = derivatives.gather(-1, bin_idx)[..., 0]
    input_derivatives_plus_one = derivatives[..., 1:].gather(-1, bin_idx)[..., 0]

    input_heights = heights.gather(-1, bin_idx)[..., 0]

    if inverse:
        a = (inputs - input_cumheights) * (input_derivatives + input_derivatives_plus_one - 2 * input_delta) + input_heights * (input_delta - input_derivatives)
        b = input_heights * input_derivatives - (inputs - input_cumheights) * (input_derivatives + input_derivatives_plus_one - 2 * input_delta)
        c = -input_delta * (inputs - input_cumheights)

        discriminant = b.pow(2) - 4 * a * c
        # assert (discriminant >= 0).all()
        discriminant = torch.clamp(discriminant, min=0.0)

        root = (2 * c) / (-b - torch.sqrt(discriminant))
        outputs = root * input_bin_widths + input_cumwidths

        theta_one_minus_theta = root * (1 - root)
        denominator = input_delta + ((input_derivatives + input_derivatives_plus_one - 2 * input_delta) * theta_one_minus_theta)
        derivative_numerator = input_delta.pow(2) * (input_derivatives_plus_one * root.pow(2) + 2 * input_delta * theta_one_minus_theta + input_derivatives * (1 - root).pow(2))
        logabsdet = torch.log(derivative_numerator) - 2 * torch.log(denominator)

        return outputs, -logabsdet
    else:
        theta = (inputs - input_cumwidths) / input_bin_widths
        theta_one_minus_theta = theta * (1 - theta)

        numerator = input_heights * (input_delta * theta.pow(2) + input_derivatives * theta_one_minus_theta)
        denominator = input_delta + ((input_derivatives + input_derivatives_plus_one - 2 * input_delta) * theta_one_minus_theta)
        outputs = input_cumheights + numerator / denominator

        derivative_numerator = input_delta.pow(2) * (input_derivatives_plus_one * theta.pow(2) + 2 * input_delta * theta_one_minus_theta + input_derivatives * (1 - theta).pow(2))
        logabsdet = torch.log(derivative_numerator) - 2 * torch.log(denominator)

        return outputs, logabsdet
