forked from YYuX-1145/Bert-VITS2-Integration-package
-
Notifications
You must be signed in to change notification settings - Fork 0
/
transforms.py
193 lines (158 loc) · 8.29 KB
/
transforms.py
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
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.,
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.,
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., right=1., bottom=0., top=1.,
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