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251 lines
9.3 KiB
251 lines
9.3 KiB
# Copyright (c) 2022 PaddlePaddle Authors. All Rights Reserved.
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#
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# Licensed under the Apache License, Version 2.0 (the "License");
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# you may not use this file except in compliance with the License.
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# You may obtain a copy of the License at
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#
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# http://www.apache.org/licenses/LICENSE-2.0
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#
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# Unless required by applicable law or agreed to in writing, software
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# distributed under the License is distributed on an "AS IS" BASIS,
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# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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# See the License for the specific language governing permissions and
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# limitations under the License.
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"""Flow-related transformation.
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This code is based on https://github.com/bayesiains/nflows.
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"""
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import numpy as np
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import paddle
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from paddle import nn
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from paddle.nn import functional as F
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from paddlespeech.t2s.modules.nets_utils import paddle_gather
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DEFAULT_MIN_BIN_WIDTH = 1e-3
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DEFAULT_MIN_BIN_HEIGHT = 1e-3
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DEFAULT_MIN_DERIVATIVE = 1e-3
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def piecewise_rational_quadratic_transform(
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inputs,
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unnormalized_widths,
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unnormalized_heights,
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unnormalized_derivatives,
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inverse=False,
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tails=None,
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tail_bound=1.0,
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# for dygraph-to-static
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min_bin_width=1e-3,
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min_bin_height=1e-3,
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min_derivative=1e-3, ):
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if tails is None:
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spline_fn = rational_quadratic_spline
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spline_kwargs = {}
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else:
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spline_fn = unconstrained_rational_quadratic_spline
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spline_kwargs = {"tails": tails, "tail_bound": tail_bound}
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outputs, logabsdet = spline_fn(
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inputs=inputs,
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unnormalized_widths=unnormalized_widths,
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unnormalized_heights=unnormalized_heights,
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unnormalized_derivatives=unnormalized_derivatives,
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inverse=inverse,
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min_bin_width=min_bin_width,
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min_bin_height=min_bin_height,
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min_derivative=min_derivative,
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**spline_kwargs)
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return outputs, logabsdet
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def mask_preprocess(x, mask):
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# bins.dtype = int32
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B, C, T, bins = paddle.shape(x)
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mask_int = paddle.cast(mask, dtype='int64')
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# paddle.sum 输入是 int32 或 bool 的时候，输出是 int64
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# paddle.zeros (fill_constant) 的 shape 会被强制转成 int32 类型
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new_x = paddle.zeros([paddle.sum(mask_int), bins])
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for i in range(bins):
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new_x[:, i] = x[:, :, :, i][mask]
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return new_x
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def unconstrained_rational_quadratic_spline(
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inputs,
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unnormalized_widths,
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unnormalized_heights,
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unnormalized_derivatives,
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inverse=False,
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tails="linear",
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tail_bound=1.0,
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# for dygraph-to-static
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min_bin_width=1e-3,
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min_bin_height=1e-3,
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min_derivative=1e-3, ):
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inside_interval_mask = (inputs >= -tail_bound) & (inputs <= tail_bound)
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outside_interval_mask = ~inside_interval_mask
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# for dygraph to static
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# 这里用 paddle.shape(x) 然后调用 zeros 会得到一个全 -1 shape 的 var
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# 如果用 x.shape 的话可以保留确定的维度
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outputs = paddle.zeros(inputs.shape)
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logabsdet = paddle.zeros(inputs.shape)
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if tails == "linear":
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# 注意 padding 的参数顺序
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pad2d = nn.Pad2D(padding=[1, 1, 0, 0], mode='constant')
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unnormalized_derivatives = pad2d(unnormalized_derivatives)
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constant = np.log(np.exp(1 - min_derivative) - 1)
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unnormalized_derivatives[..., 0] = constant
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unnormalized_derivatives[..., -1] = constant
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# for dygraph to static
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tmp = inputs[outside_interval_mask]
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outputs[outside_interval_mask] = tmp
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logabsdet[outside_interval_mask] = 0
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else:
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raise RuntimeError("{} tails are not implemented.".format(tails))
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unnormalized_widths = mask_preprocess(unnormalized_widths,
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inside_interval_mask)
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unnormalized_heights = mask_preprocess(unnormalized_heights,
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inside_interval_mask)
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unnormalized_derivatives = mask_preprocess(unnormalized_derivatives,
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inside_interval_mask)
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(outputs[inside_interval_mask],
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logabsdet[inside_interval_mask], ) = rational_quadratic_spline(
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inputs=inputs[inside_interval_mask],
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unnormalized_widths=unnormalized_widths,
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unnormalized_heights=unnormalized_heights,
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unnormalized_derivatives=unnormalized_derivatives,
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inverse=inverse,
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left=-tail_bound,
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right=tail_bound,
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bottom=-tail_bound,
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top=tail_bound,
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min_bin_width=min_bin_width,
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min_bin_height=min_bin_height,
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min_derivative=min_derivative, )
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return outputs, logabsdet
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def rational_quadratic_spline(
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inputs,
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unnormalized_widths,
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unnormalized_heights,
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unnormalized_derivatives,
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inverse=False,
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left=0.0,
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right=1.0,
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bottom=0.0,
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top=1.0,
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# for dygraph-to-static
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min_bin_width=1e-3,
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min_bin_height=1e-3,
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min_derivative=1e-3, ):
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# for dygraph to static
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# if paddle.min(inputs) < left or paddle.max(inputs) > right:
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# raise ValueError("Input to a transform is not within its domain")
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pad1d = nn.Pad1D(
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padding=[1, 0],
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mode='constant',
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data_format='NCL', )
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num_bins = unnormalized_widths.shape[-1]
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# for dygraph to static
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# if min_bin_width * num_bins > 1.0:
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# raise ValueError("Minimal bin width too large for the number of bins")
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# if min_bin_height * num_bins > 1.0:
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# raise ValueError("Minimal bin height too large for the number of bins")
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widths = F.softmax(unnormalized_widths, axis=-1)
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widths = min_bin_width + (1 - min_bin_width * num_bins) * widths
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cumwidths = paddle.cumsum(widths, axis=-1)
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cumwidths = pad1d(cumwidths.unsqueeze(0)).squeeze()
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cumwidths = (right - left) * cumwidths + left
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cumwidths[..., 0] = left
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cumwidths[..., -1] = right
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widths = cumwidths[..., 1:] - cumwidths[..., :-1]
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derivatives = min_derivative + F.softplus(unnormalized_derivatives)
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heights = F.softmax(unnormalized_heights, axis=-1)
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heights = min_bin_height + (1 - min_bin_height * num_bins) * heights
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cumheights = paddle.cumsum(heights, axis=-1)
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cumheights = pad1d(cumheights.unsqueeze(0)).squeeze()
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cumheights = (top - bottom) * cumheights + bottom
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cumheights[..., 0] = bottom
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cumheights[..., -1] = top
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heights = cumheights[..., 1:] - cumheights[..., :-1]
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if inverse:
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bin_idx = _searchsorted(cumheights, inputs)[..., None]
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else:
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bin_idx = _searchsorted(cumwidths, inputs)[..., None]
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input_cumwidths = paddle_gather(cumwidths, -1, bin_idx)[..., 0]
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input_bin_widths = paddle_gather(widths, -1, bin_idx)[..., 0]
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input_cumheights = paddle_gather(cumheights, -1, bin_idx)[..., 0]
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delta = heights / widths
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input_delta = paddle_gather(delta, -1, bin_idx)[..., 0]
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input_derivatives = paddle_gather(derivatives, -1, bin_idx)[..., 0]
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input_derivatives_plus_one = paddle_gather(derivatives[..., 1:], -1,
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bin_idx)[..., 0]
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input_heights = paddle_gather(heights, -1, bin_idx)[..., 0]
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if inverse:
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a = (inputs - input_cumheights) * (
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input_derivatives + input_derivatives_plus_one - 2 * input_delta
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) + input_heights * (input_delta - input_derivatives)
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b = input_heights * input_derivatives - (inputs - input_cumheights) * (
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input_derivatives + input_derivatives_plus_one - 2 * input_delta)
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c = -input_delta * (inputs - input_cumheights)
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discriminant = b.pow(2) - 4 * a * c
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assert (discriminant >= 0).all()
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root = (2 * c) / (-b - paddle.sqrt(discriminant))
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outputs = root * input_bin_widths + input_cumwidths
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theta_one_minus_theta = root * (1 - root)
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denominator = input_delta + (
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(input_derivatives + input_derivatives_plus_one - 2 * input_delta
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) * theta_one_minus_theta)
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derivative_numerator = input_delta.pow(2) * (
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input_derivatives_plus_one * root.pow(2) + 2 * input_delta *
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theta_one_minus_theta + input_derivatives * (1 - root).pow(2))
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logabsdet = paddle.log(derivative_numerator) - 2 * paddle.log(
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denominator)
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return outputs, -logabsdet
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else:
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theta = (inputs - input_cumwidths) / input_bin_widths
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theta_one_minus_theta = theta * (1 - theta)
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numerator = input_heights * (input_delta * theta.pow(2) +
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input_derivatives * theta_one_minus_theta)
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denominator = input_delta + (
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(input_derivatives + input_derivatives_plus_one - 2 * input_delta
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) * theta_one_minus_theta)
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outputs = input_cumheights + numerator / denominator
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derivative_numerator = input_delta.pow(2) * (
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input_derivatives_plus_one * theta.pow(2) + 2 * input_delta *
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theta_one_minus_theta + input_derivatives * (1 - theta).pow(2))
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logabsdet = paddle.log(derivative_numerator) - 2 * paddle.log(
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denominator)
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return outputs, logabsdet
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def _searchsorted(bin_locations, inputs, eps=1e-6):
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bin_locations[..., -1] += eps
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mask = inputs[..., None] >= bin_locations
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mask_int = paddle.cast(mask, dtype='int64')
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out = paddle.sum(mask_int, axis=-1) - 1
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return out
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