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- import torch
- from torch.nn import functional as F
-
- import numpy as np
-
-
- DEFAULT_MIN_BIN_WIDTH = 1e-3
- DEFAULT_MIN_BIN_HEIGHT = 1e-3
- DEFAULT_MIN_DERIVATIVE = 1e-3
-
-
- def piecewise_rational_quadratic_transform(
- inputs,
- unnormalized_widths,
- unnormalized_heights,
- unnormalized_derivatives,
- inverse=False,
- tails=None,
- tail_bound=1.0,
- min_bin_width=DEFAULT_MIN_BIN_WIDTH,
- min_bin_height=DEFAULT_MIN_BIN_HEIGHT,
- min_derivative=DEFAULT_MIN_DERIVATIVE,
- ):
- if tails is None:
- spline_fn = rational_quadratic_spline
- spline_kwargs = {}
- else:
- spline_fn = unconstrained_rational_quadratic_spline
- spline_kwargs = {"tails": tails, "tail_bound": tail_bound}
-
- outputs, logabsdet = spline_fn(
- inputs=inputs,
- unnormalized_widths=unnormalized_widths,
- unnormalized_heights=unnormalized_heights,
- unnormalized_derivatives=unnormalized_derivatives,
- inverse=inverse,
- min_bin_width=min_bin_width,
- min_bin_height=min_bin_height,
- min_derivative=min_derivative,
- **spline_kwargs
- )
- return outputs, logabsdet
-
-
- def searchsorted(bin_locations, inputs, eps=1e-6):
- bin_locations[..., -1] += eps
- return torch.sum(inputs[..., None] >= bin_locations, dim=-1) - 1
-
-
- 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,
- ):
- 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))
-
- (
- 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,
- ):
- if torch.min(inputs) < left or torch.max(inputs) > right:
- raise ValueError("Input to a transform is not within its domain")
-
- 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 = searchsorted(cumheights, inputs)[..., None]
- else:
- bin_idx = 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()
-
- 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
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