surfmore/SimpleRVC

1import torch2from torch.nn import functional as F3 4import numpy as np5 6DEFAULT_MIN_BIN_WIDTH = 1e-37DEFAULT_MIN_BIN_HEIGHT = 1e-38DEFAULT_MIN_DERIVATIVE = 1e-39 10 11def piecewise_rational_quadratic_transform(12    inputs,13    unnormalized_widths,14    unnormalized_heights,15    unnormalized_derivatives,16    inverse=False,17    tails=None,18    tail_bound=1.0,19    min_bin_width=DEFAULT_MIN_BIN_WIDTH,20    min_bin_height=DEFAULT_MIN_BIN_HEIGHT,21    min_derivative=DEFAULT_MIN_DERIVATIVE,22):23    if tails is None:24        spline_fn = rational_quadratic_spline25        spline_kwargs = {}26    else:27        spline_fn = unconstrained_rational_quadratic_spline28        spline_kwargs = {"tails": tails, "tail_bound": tail_bound}29 30    outputs, logabsdet = spline_fn(31        inputs=inputs,32        unnormalized_widths=unnormalized_widths,33        unnormalized_heights=unnormalized_heights,34        unnormalized_derivatives=unnormalized_derivatives,35        inverse=inverse,36        min_bin_width=min_bin_width,37        min_bin_height=min_bin_height,38        min_derivative=min_derivative,39        **spline_kwargs40    )41    return outputs, logabsdet42 43 44def searchsorted(bin_locations, inputs, eps=1e-6):45    bin_locations[..., -1] += eps46    return torch.sum(inputs[..., None] >= bin_locations, dim=-1) - 147 48 49def unconstrained_rational_quadratic_spline(50    inputs,51    unnormalized_widths,52    unnormalized_heights,53    unnormalized_derivatives,54    inverse=False,55    tails="linear",56    tail_bound=1.0,57    min_bin_width=DEFAULT_MIN_BIN_WIDTH,58    min_bin_height=DEFAULT_MIN_BIN_HEIGHT,59    min_derivative=DEFAULT_MIN_DERIVATIVE,60):61    inside_interval_mask = (inputs >= -tail_bound) & (inputs <= tail_bound)62    outside_interval_mask = ~inside_interval_mask63 64    outputs = torch.zeros_like(inputs)65    logabsdet = torch.zeros_like(inputs)66 67    if tails == "linear":68        unnormalized_derivatives = F.pad(unnormalized_derivatives, pad=(1, 1))69        constant = np.log(np.exp(1 - min_derivative) - 1)70        unnormalized_derivatives[..., 0] = constant71        unnormalized_derivatives[..., -1] = constant72 73        outputs[outside_interval_mask] = inputs[outside_interval_mask]74        logabsdet[outside_interval_mask] = 075    else:76        raise RuntimeError("{} tails are not implemented.".format(tails))77 78    (79        outputs[inside_interval_mask],80        logabsdet[inside_interval_mask],81    ) = rational_quadratic_spline(82        inputs=inputs[inside_interval_mask],83        unnormalized_widths=unnormalized_widths[inside_interval_mask, :],84        unnormalized_heights=unnormalized_heights[inside_interval_mask, :],85        unnormalized_derivatives=unnormalized_derivatives[inside_interval_mask, :],86        inverse=inverse,87        left=-tail_bound,88        right=tail_bound,89        bottom=-tail_bound,90        top=tail_bound,91        min_bin_width=min_bin_width,92        min_bin_height=min_bin_height,93        min_derivative=min_derivative,94    )95 96    return outputs, logabsdet97 98 99def rational_quadratic_spline(100    inputs,101    unnormalized_widths,102    unnormalized_heights,103    unnormalized_derivatives,104    inverse=False,105    left=0.0,106    right=1.0,107    bottom=0.0,108    top=1.0,109    min_bin_width=DEFAULT_MIN_BIN_WIDTH,110    min_bin_height=DEFAULT_MIN_BIN_HEIGHT,111    min_derivative=DEFAULT_MIN_DERIVATIVE,112):113    if torch.min(inputs) < left or torch.max(inputs) > right:114        raise ValueError("Input to a transform is not within its domain")115 116    num_bins = unnormalized_widths.shape[-1]117 118    if min_bin_width * num_bins > 1.0:119        raise ValueError("Minimal bin width too large for the number of bins")120    if min_bin_height * num_bins > 1.0:121        raise ValueError("Minimal bin height too large for the number of bins")122 123    widths = F.softmax(unnormalized_widths, dim=-1)124    widths = min_bin_width + (1 - min_bin_width * num_bins) * widths125    cumwidths = torch.cumsum(widths, dim=-1)126    cumwidths = F.pad(cumwidths, pad=(1, 0), mode="constant", value=0.0)127    cumwidths = (right - left) * cumwidths + left128    cumwidths[..., 0] = left129    cumwidths[..., -1] = right130    widths = cumwidths[..., 1:] - cumwidths[..., :-1]131 132    derivatives = min_derivative + F.softplus(unnormalized_derivatives)133 134    heights = F.softmax(unnormalized_heights, dim=-1)135    heights = min_bin_height + (1 - min_bin_height * num_bins) * heights136    cumheights = torch.cumsum(heights, dim=-1)137    cumheights = F.pad(cumheights, pad=(1, 0), mode="constant", value=0.0)138    cumheights = (top - bottom) * cumheights + bottom139    cumheights[..., 0] = bottom140    cumheights[..., -1] = top141    heights = cumheights[..., 1:] - cumheights[..., :-1]142 143    if inverse:144        bin_idx = searchsorted(cumheights, inputs)[..., None]145    else:146        bin_idx = searchsorted(cumwidths, inputs)[..., None]147 148    input_cumwidths = cumwidths.gather(-1, bin_idx)[..., 0]149    input_bin_widths = widths.gather(-1, bin_idx)[..., 0]150 151    input_cumheights = cumheights.gather(-1, bin_idx)[..., 0]152    delta = heights / widths153    input_delta = delta.gather(-1, bin_idx)[..., 0]154 155    input_derivatives = derivatives.gather(-1, bin_idx)[..., 0]156    input_derivatives_plus_one = derivatives[..., 1:].gather(-1, bin_idx)[..., 0]157 158    input_heights = heights.gather(-1, bin_idx)[..., 0]159 160    if inverse:161        a = (inputs - input_cumheights) * (162            input_derivatives + input_derivatives_plus_one - 2 * input_delta163        ) + input_heights * (input_delta - input_derivatives)164        b = input_heights * input_derivatives - (inputs - input_cumheights) * (165            input_derivatives + input_derivatives_plus_one - 2 * input_delta166        )167        c = -input_delta * (inputs - input_cumheights)168 169        discriminant = b.pow(2) - 4 * a * c170        assert (discriminant >= 0).all()171 172        root = (2 * c) / (-b - torch.sqrt(discriminant))173        outputs = root * input_bin_widths + input_cumwidths174 175        theta_one_minus_theta = root * (1 - root)176        denominator = input_delta + (177            (input_derivatives + input_derivatives_plus_one - 2 * input_delta)178            * theta_one_minus_theta179        )180        derivative_numerator = input_delta.pow(2) * (181            input_derivatives_plus_one * root.pow(2)182            + 2 * input_delta * theta_one_minus_theta183            + input_derivatives * (1 - root).pow(2)184        )185        logabsdet = torch.log(derivative_numerator) - 2 * torch.log(denominator)186 187        return outputs, -logabsdet188    else:189        theta = (inputs - input_cumwidths) / input_bin_widths190        theta_one_minus_theta = theta * (1 - theta)191 192        numerator = input_heights * (193            input_delta * theta.pow(2) + input_derivatives * theta_one_minus_theta194        )195        denominator = input_delta + (196            (input_derivatives + input_derivatives_plus_one - 2 * input_delta)197            * theta_one_minus_theta198        )199        outputs = input_cumheights + numerator / denominator200 201        derivative_numerator = input_delta.pow(2) * (202            input_derivatives_plus_one * theta.pow(2)203            + 2 * input_delta * theta_one_minus_theta204            + input_derivatives * (1 - theta).pow(2)205        )206        logabsdet = torch.log(derivative_numerator) - 2 * torch.log(denominator)207 208        return outputs, logabsdet209