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