diff --git a/python/paddle/audio/compliance/__init__.py b/python/paddle/audio/compliance/__init__.py index 0198cc71a1b21..6083e3eba77ec 100644 --- a/python/paddle/audio/compliance/__init__.py +++ b/python/paddle/audio/compliance/__init__.py @@ -12,5 +12,4 @@ # See the License for the specific language governing permissions and # limitations under the License. -from . import kaldi from . import librosa diff --git a/python/paddle/audio/compliance/kaldi.py b/python/paddle/audio/compliance/kaldi.py deleted file mode 100644 index 9f8a7f287192e..0000000000000 --- a/python/paddle/audio/compliance/kaldi.py +++ /dev/null @@ -1,615 +0,0 @@ -# Copyright (c) 2022 PaddlePaddle Authors. All Rights Reserved. -# -# Licensed under the Apache License, Version 2.0 (the "License"); -# you may not use this file except in compliance with the License. -# You may obtain a copy of the License at -# -# http://www.apache.org/licenses/LICENSE-2.0 -# -# Unless required by applicable law or agreed to in writing, software -# distributed under the License is distributed on an "AS IS" BASIS, -# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. -# See the License for the specific language governing permissions and -# limitations under the License. -# Modified from torchaudio(https://github.com/pytorch/audio) - -import math -from typing import Tuple - -import paddle -from paddle import Tensor - -from ..functional import create_dct -from ..functional.window import get_window - -__all__ = [ - 'spectrogram', - 'fbank', - 'mfcc', -] - -# window types -HANNING = 'hann' -HAMMING = 'hamming' -POVEY = 'povey' -RECTANGULAR = 'rect' -BLACKMAN = 'blackman' - - -def _get_epsilon(dtype): - return paddle.to_tensor(1e-07, dtype=dtype) - - -def _next_power_of_2(x: int) -> int: - return 1 if x == 0 else 2**(x - 1).bit_length() - - -def _get_strided(waveform: Tensor, window_size: int, window_shift: int, - snip_edges: bool) -> Tensor: - assert waveform.dim() == 1 - num_samples = waveform.shape[0] - - if snip_edges: - if num_samples < window_size: - return paddle.empty((0, 0), dtype=waveform.dtype) - else: - m = 1 + (num_samples - window_size) // window_shift - else: - reversed_waveform = paddle.flip(waveform, [0]) - m = (num_samples + (window_shift // 2)) // window_shift - pad = window_size // 2 - window_shift // 2 - pad_right = reversed_waveform - if pad > 0: - pad_left = reversed_waveform[-pad:] - waveform = paddle.concat((pad_left, waveform, pad_right), axis=0) - else: - waveform = paddle.concat((waveform[-pad:], pad_right), axis=0) - - return paddle.signal.frame(waveform, window_size, window_shift)[:, :m].T - - -def _feature_window_function( - window_type: str, - window_size: int, - blackman_coeff: float, - dtype: int, -) -> Tensor: - if window_type == HANNING: - return get_window('hann', window_size, fftbins=False, dtype=dtype) - elif window_type == HAMMING: - return get_window('hamming', window_size, fftbins=False, dtype=dtype) - elif window_type == POVEY: - return get_window('hann', window_size, fftbins=False, - dtype=dtype).pow(0.85) - elif window_type == RECTANGULAR: - return paddle.ones([window_size], dtype=dtype) - elif window_type == BLACKMAN: - a = 2 * math.pi / (window_size - 1) - window_function = paddle.arange(window_size, dtype=dtype) - return (blackman_coeff - 0.5 * paddle.cos(a * window_function) + - (0.5 - blackman_coeff) * - paddle.cos(2 * a * window_function)).astype(dtype) - else: - raise Exception('Invalid window type ' + window_type) - - -def _get_log_energy(strided_input: Tensor, epsilon: Tensor, - energy_floor: float) -> Tensor: - log_energy = paddle.maximum(strided_input.pow(2).sum(1), epsilon).log() - if energy_floor == 0.0: - return log_energy - return paddle.maximum( - log_energy, - paddle.to_tensor(math.log(energy_floor), dtype=strided_input.dtype)) - - -def _get_waveform_and_window_properties( - waveform: Tensor, channel: int, sr: int, frame_shift: float, - frame_length: float, round_to_power_of_two: bool, - preemphasis_coefficient: float) -> Tuple[Tensor, int, int, int]: - channel = max(channel, 0) - assert channel < waveform.shape[0], ( - 'Invalid channel {} for size {}'.format(channel, waveform.shape[0])) - waveform = waveform[channel, :] # size (n) - window_shift = int( - sr * frame_shift * - 0.001) # pass frame_shift and frame_length in milliseconds - window_size = int(sr * frame_length * 0.001) - padded_window_size = _next_power_of_2( - window_size) if round_to_power_of_two else window_size - - assert 2 <= window_size <= len(waveform), ( - 'choose a window size {} that is [2, {}]'.format( - window_size, len(waveform))) - assert 0 < window_shift, '`window_shift` must be greater than 0' - assert padded_window_size % 2 == 0, 'the padded `window_size` must be divisible by two.' \ - ' use `round_to_power_of_two` or change `frame_length`' - assert 0. <= preemphasis_coefficient <= 1.0, '`preemphasis_coefficient` must be between [0,1]' - assert sr > 0, '`sr` must be greater than zero' - return waveform, window_shift, window_size, padded_window_size - - -def _get_window(waveform: Tensor, padded_window_size: int, window_size: int, - window_shift: int, window_type: str, blackman_coeff: float, - snip_edges: bool, raw_energy: bool, energy_floor: float, - dither: float, remove_dc_offset: bool, - preemphasis_coefficient: float) -> Tuple[Tensor, Tensor]: - dtype = waveform.dtype - epsilon = _get_epsilon(dtype) - - # (m, window_size) - strided_input = _get_strided(waveform, window_size, window_shift, - snip_edges) - - if dither != 0.0: - x = paddle.maximum(epsilon, paddle.rand(strided_input.shape, - dtype=dtype)) - rand_gauss = paddle.sqrt(-2 * x.log()) * paddle.cos(2 * math.pi * x) - strided_input = strided_input + rand_gauss * dither - - if remove_dc_offset: - row_means = paddle.mean(strided_input, axis=1).unsqueeze(1) # (m, 1) - strided_input = strided_input - row_means - - if raw_energy: - signal_log_energy = _get_log_energy(strided_input, epsilon, - energy_floor) # (m) - - if preemphasis_coefficient != 0.0: - offset_strided_input = paddle.nn.functional.pad( - strided_input.unsqueeze(0), (1, 0), - data_format='NCL', - mode='replicate').squeeze(0) # (m, window_size + 1) - strided_input = strided_input - preemphasis_coefficient * offset_strided_input[:, : - -1] - - window_function = _feature_window_function(window_type, window_size, - blackman_coeff, dtype).unsqueeze( - 0) # (1, window_size) - strided_input = strided_input * window_function # (m, window_size) - - # (m, padded_window_size) - if padded_window_size != window_size: - padding_right = padded_window_size - window_size - strided_input = paddle.nn.functional.pad(strided_input.unsqueeze(0), - (0, padding_right), - data_format='NCL', - mode='constant', - value=0).squeeze(0) - - if not raw_energy: - signal_log_energy = _get_log_energy(strided_input, epsilon, - energy_floor) # size (m) - - return strided_input, signal_log_energy - - -def _subtract_column_mean(tensor: Tensor, subtract_mean: bool) -> Tensor: - if subtract_mean: - col_means = paddle.mean(tensor, axis=0).unsqueeze(0) - tensor = tensor - col_means - return tensor - - -def spectrogram(waveform: Tensor, - blackman_coeff: float = 0.42, - channel: int = -1, - dither: float = 0.0, - energy_floor: float = 1.0, - frame_length: float = 25.0, - frame_shift: float = 10.0, - preemphasis_coefficient: float = 0.97, - raw_energy: bool = True, - remove_dc_offset: bool = True, - round_to_power_of_two: bool = True, - sr: int = 16000, - snip_edges: bool = True, - subtract_mean: bool = False, - window_type: str = POVEY) -> Tensor: - """Compute and return a spectrogram from a waveform. The output is identical to Kaldi's. - - Args: - waveform (Tensor): A waveform tensor with shape `(C, T)`. - blackman_coeff (float, optional): Coefficient for Blackman window.. Defaults to 0.42. - channel (int, optional): Select the channel of waveform. Defaults to -1. - dither (float, optional): Dithering constant . Defaults to 0.0. - energy_floor (float, optional): Floor on energy of the output Spectrogram. Defaults to 1.0. - frame_length (float, optional): Frame length in milliseconds. Defaults to 25.0. - frame_shift (float, optional): Shift between adjacent frames in milliseconds. Defaults to 10.0. - preemphasis_coefficient (float, optional): Preemphasis coefficient for input waveform. Defaults to 0.97. - raw_energy (bool, optional): Whether to compute before preemphasis and windowing. Defaults to True. - remove_dc_offset (bool, optional): Whether to subtract mean from waveform on frames. Defaults to True. - round_to_power_of_two (bool, optional): If True, round window size to power of two by zero-padding input - to FFT. Defaults to True. - sr (int, optional): Sample rate of input waveform. Defaults to 16000. - snip_edges (bool, optional): Drop samples in the end of waveform that cann't fit a singal frame when it - is set True. Otherwise performs reflect padding to the end of waveform. Defaults to True. - subtract_mean (bool, optional): Whether to subtract mean of feature files. Defaults to False. - window_type (str, optional): Choose type of window for FFT computation. Defaults to POVEY. - - Returns: - Tensor: A spectrogram tensor with shape `(m, padded_window_size // 2 + 1)` where m is the number of frames - depends on frame_length and frame_shift. - """ - dtype = waveform.dtype - epsilon = _get_epsilon(dtype) - - waveform, window_shift, window_size, padded_window_size = _get_waveform_and_window_properties( - waveform, channel, sr, frame_shift, frame_length, round_to_power_of_two, - preemphasis_coefficient) - - strided_input, signal_log_energy = _get_window( - waveform, padded_window_size, window_size, window_shift, window_type, - blackman_coeff, snip_edges, raw_energy, energy_floor, dither, - remove_dc_offset, preemphasis_coefficient) - - # (m, padded_window_size // 2 + 1, 2) - fft = paddle.fft.rfft(strided_input) - - power_spectrum = paddle.maximum( - fft.abs().pow(2.), epsilon).log() # (m, padded_window_size // 2 + 1) - power_spectrum[:, 0] = signal_log_energy - - power_spectrum = _subtract_column_mean(power_spectrum, subtract_mean) - return power_spectrum - - -def _inverse_mel_scale_scalar(mel_freq: float) -> float: - return 700.0 * (math.exp(mel_freq / 1127.0) - 1.0) - - -def _inverse_mel_scale(mel_freq: Tensor) -> Tensor: - return 700.0 * ((mel_freq / 1127.0).exp() - 1.0) - - -def _mel_scale_scalar(freq: float) -> float: - return 1127.0 * math.log(1.0 + freq / 700.0) - - -def _mel_scale(freq: Tensor) -> Tensor: - return 1127.0 * (1.0 + freq / 700.0).log() - - -def _vtln_warp_freq(vtln_low_cutoff: float, vtln_high_cutoff: float, - low_freq: float, high_freq: float, vtln_warp_factor: float, - freq: Tensor) -> Tensor: - assert vtln_low_cutoff > low_freq, 'be sure to set the vtln_low option higher than low_freq' - assert vtln_high_cutoff < high_freq, 'be sure to set the vtln_high option lower than high_freq [or negative]' - l = vtln_low_cutoff * max(1.0, vtln_warp_factor) - h = vtln_high_cutoff * min(1.0, vtln_warp_factor) - scale = 1.0 / vtln_warp_factor - Fl = scale * l - Fh = scale * h - assert l > low_freq and h < high_freq - scale_left = (Fl - low_freq) / (l - low_freq) - scale_right = (high_freq - Fh) / (high_freq - h) - res = paddle.empty_like(freq) - - outside_low_high_freq = paddle.less_than(freq, paddle.to_tensor(low_freq)) \ - | paddle.greater_than(freq, paddle.to_tensor(high_freq)) - before_l = paddle.less_than(freq, paddle.to_tensor(l)) - before_h = paddle.less_than(freq, paddle.to_tensor(h)) - after_h = paddle.greater_equal(freq, paddle.to_tensor(h)) - - res[after_h] = high_freq + scale_right * (freq[after_h] - high_freq) - res[before_h] = scale * freq[before_h] - res[before_l] = low_freq + scale_left * (freq[before_l] - low_freq) - res[outside_low_high_freq] = freq[outside_low_high_freq] - - return res - - -def _vtln_warp_mel_freq(vtln_low_cutoff: float, vtln_high_cutoff: float, - low_freq, high_freq: float, vtln_warp_factor: float, - mel_freq: Tensor) -> Tensor: - return _mel_scale( - _vtln_warp_freq(vtln_low_cutoff, vtln_high_cutoff, low_freq, high_freq, - vtln_warp_factor, _inverse_mel_scale(mel_freq))) - - -def _get_mel_banks(num_bins: int, window_length_padded: int, sample_freq: float, - low_freq: float, high_freq: float, vtln_low: float, - vtln_high: float, - vtln_warp_factor: float) -> Tuple[Tensor, Tensor]: - assert num_bins > 3, 'Must have at least 3 mel bins' - assert window_length_padded % 2 == 0 - num_fft_bins = window_length_padded / 2 - nyquist = 0.5 * sample_freq - - if high_freq <= 0.0: - high_freq += nyquist - - assert (0.0 <= low_freq < nyquist) and (0.0 < high_freq <= nyquist) and (low_freq < high_freq), \ - ('Bad values in options: low-freq {} and high-freq {} vs. nyquist {}'.format(low_freq, high_freq, nyquist)) - - fft_bin_width = sample_freq / window_length_padded - mel_low_freq = _mel_scale_scalar(low_freq) - mel_high_freq = _mel_scale_scalar(high_freq) - - mel_freq_delta = (mel_high_freq - mel_low_freq) / (num_bins + 1) - - if vtln_high < 0.0: - vtln_high += nyquist - - assert vtln_warp_factor == 1.0 or ((low_freq < vtln_low < high_freq) and - (0.0 < vtln_high < high_freq) and (vtln_low < vtln_high)), \ - ('Bad values in options: vtln-low {} and vtln-high {}, versus ' - 'low-freq {} and high-freq {}'.format(vtln_low, vtln_high, low_freq, high_freq)) - - bin = paddle.arange(num_bins).unsqueeze(1) - left_mel = mel_low_freq + bin * mel_freq_delta # (num_bins, 1) - center_mel = mel_low_freq + (bin + 1.0) * mel_freq_delta # (num_bins, 1) - right_mel = mel_low_freq + (bin + 2.0) * mel_freq_delta # (num_bins, 1) - - if vtln_warp_factor != 1.0: - left_mel = _vtln_warp_mel_freq(vtln_low, vtln_high, low_freq, high_freq, - vtln_warp_factor, left_mel) - center_mel = _vtln_warp_mel_freq(vtln_low, vtln_high, low_freq, - high_freq, vtln_warp_factor, - center_mel) - right_mel = _vtln_warp_mel_freq(vtln_low, vtln_high, low_freq, - high_freq, vtln_warp_factor, right_mel) - - center_freqs = _inverse_mel_scale(center_mel) # (num_bins) - # (1, num_fft_bins) - mel = _mel_scale(fft_bin_width * paddle.arange(num_fft_bins)).unsqueeze(0) - - # (num_bins, num_fft_bins) - up_slope = (mel - left_mel) / (center_mel - left_mel) - down_slope = (right_mel - mel) / (right_mel - center_mel) - - if vtln_warp_factor == 1.0: - bins = paddle.maximum(paddle.zeros([1]), - paddle.minimum(up_slope, down_slope)) - else: - bins = paddle.zeros_like(up_slope) - up_idx = paddle.greater_than(mel, left_mel) & paddle.less_than( - mel, center_mel) - down_idx = paddle.greater_than(mel, center_mel) & paddle.less_than( - mel, right_mel) - bins[up_idx] = up_slope[up_idx] - bins[down_idx] = down_slope[down_idx] - - return bins, center_freqs - - -def fbank(waveform: Tensor, - blackman_coeff: float = 0.42, - channel: int = -1, - dither: float = 0.0, - energy_floor: float = 1.0, - frame_length: float = 25.0, - frame_shift: float = 10.0, - high_freq: float = 0.0, - htk_compat: bool = False, - low_freq: float = 20.0, - n_mels: int = 23, - preemphasis_coefficient: float = 0.97, - raw_energy: bool = True, - remove_dc_offset: bool = True, - round_to_power_of_two: bool = True, - sr: int = 16000, - snip_edges: bool = True, - subtract_mean: bool = False, - use_energy: bool = False, - use_log_fbank: bool = True, - use_power: bool = True, - vtln_high: float = -500.0, - vtln_low: float = 100.0, - vtln_warp: float = 1.0, - window_type: str = POVEY) -> Tensor: - """Compute and return filter banks from a waveform. The output is identical to Kaldi's. - - Args: - waveform (Tensor): A waveform tensor with shape `(C, T)`. - blackman_coeff (float, optional): Coefficient for Blackman window.. Defaults to 0.42. - channel (int, optional): Select the channel of waveform. Defaults to -1. - dither (float, optional): Dithering constant . Defaults to 0.0. - energy_floor (float, optional): Floor on energy of the output Spectrogram. Defaults to 1.0. - frame_length (float, optional): Frame length in milliseconds. Defaults to 25.0. - frame_shift (float, optional): Shift between adjacent frames in milliseconds. Defaults to 10.0. - high_freq (float, optional): The upper cut-off frequency. Defaults to 0.0. - htk_compat (bool, optional): Put energy to the last when it is set True. Defaults to False. - low_freq (float, optional): The lower cut-off frequency. Defaults to 20.0. - n_mels (int, optional): Number of output mel bins. Defaults to 23. - preemphasis_coefficient (float, optional): Preemphasis coefficient for input waveform. Defaults to 0.97. - raw_energy (bool, optional): Whether to compute before preemphasis and windowing. Defaults to True. - remove_dc_offset (bool, optional): Whether to subtract mean from waveform on frames. Defaults to True. - round_to_power_of_two (bool, optional): If True, round window size to power of two by zero-padding input - to FFT. Defaults to True. - sr (int, optional): Sample rate of input waveform. Defaults to 16000. - snip_edges (bool, optional): Drop samples in the end of waveform that cann't fit a singal frame when it - is set True. Otherwise performs reflect padding to the end of waveform. Defaults to True. - subtract_mean (bool, optional): Whether to subtract mean of feature files. Defaults to False. - use_energy (bool, optional): Add an dimension with energy of spectrogram to the output. Defaults to False. - use_log_fbank (bool, optional): Return log fbank when it is set True. Defaults to True. - use_power (bool, optional): Whether to use power instead of magnitude. Defaults to True. - vtln_high (float, optional): High inflection point in piecewise linear VTLN warping function. Defaults to -500.0. - vtln_low (float, optional): Low inflection point in piecewise linear VTLN warping function. Defaults to 100.0. - vtln_warp (float, optional): Vtln warp factor. Defaults to 1.0. - window_type (str, optional): Choose type of window for FFT computation. Defaults to POVEY. - - Returns: - Tensor: A filter banks tensor with shape `(m, n_mels)`. - """ - dtype = waveform.dtype - - waveform, window_shift, window_size, padded_window_size = _get_waveform_and_window_properties( - waveform, channel, sr, frame_shift, frame_length, round_to_power_of_two, - preemphasis_coefficient) - - strided_input, signal_log_energy = _get_window( - waveform, padded_window_size, window_size, window_shift, window_type, - blackman_coeff, snip_edges, raw_energy, energy_floor, dither, - remove_dc_offset, preemphasis_coefficient) - - # (m, padded_window_size // 2 + 1) - spectrum = paddle.fft.rfft(strided_input).abs() - if use_power: - spectrum = spectrum.pow(2.) - - # (n_mels, padded_window_size // 2) - mel_energies, _ = _get_mel_banks(n_mels, padded_window_size, sr, low_freq, - high_freq, vtln_low, vtln_high, vtln_warp) - mel_energies = mel_energies.astype(dtype) - - # (n_mels, padded_window_size // 2 + 1) - mel_energies = paddle.nn.functional.pad(mel_energies.unsqueeze(0), (0, 1), - data_format='NCL', - mode='constant', - value=0).squeeze(0) - - # (m, n_mels) - mel_energies = paddle.mm(spectrum, mel_energies.T) - if use_log_fbank: - mel_energies = paddle.maximum(mel_energies, _get_epsilon(dtype)).log() - - if use_energy: - signal_log_energy = signal_log_energy.unsqueeze(1) - if htk_compat: - mel_energies = paddle.concat((mel_energies, signal_log_energy), - axis=1) - else: - mel_energies = paddle.concat((signal_log_energy, mel_energies), - axis=1) - - # (m, n_mels + 1) - mel_energies = _subtract_column_mean(mel_energies, subtract_mean) - return mel_energies - - -def _get_dct_matrix(n_mfcc: int, n_mels: int) -> Tensor: - dct_matrix = create_dct(n_mels, n_mels, 'ortho') - dct_matrix[:, 0] = math.sqrt(1 / float(n_mels)) - dct_matrix = dct_matrix[:, :n_mfcc] # (n_mels, n_mfcc) - return dct_matrix - - -def _get_lifter_coeffs(n_mfcc: int, cepstral_lifter: float) -> Tensor: - i = paddle.arange(n_mfcc) - return 1.0 + 0.5 * cepstral_lifter * paddle.sin( - math.pi * i / cepstral_lifter) - - -def mfcc(waveform: Tensor, - blackman_coeff: float = 0.42, - cepstral_lifter: float = 22.0, - channel: int = -1, - dither: float = 0.0, - energy_floor: float = 1.0, - frame_length: float = 25.0, - frame_shift: float = 10.0, - high_freq: float = 0.0, - htk_compat: bool = False, - low_freq: float = 20.0, - n_mfcc: int = 13, - n_mels: int = 23, - preemphasis_coefficient: float = 0.97, - raw_energy: bool = True, - remove_dc_offset: bool = True, - round_to_power_of_two: bool = True, - sr: int = 16000, - snip_edges: bool = True, - subtract_mean: bool = False, - use_energy: bool = False, - vtln_high: float = -500.0, - vtln_low: float = 100.0, - vtln_warp: float = 1.0, - window_type: str = POVEY) -> Tensor: - """Compute and return mel frequency cepstral coefficients from a waveform. The output is - identical to Kaldi's. - - Args: - waveform (Tensor): A waveform tensor with shape `(C, T)`. - blackman_coeff (float, optional): Coefficient for Blackman window.. Defaults to 0.42. - cepstral_lifter (float, optional): Scaling of output mfccs. Defaults to 22.0. - channel (int, optional): Select the channel of waveform. Defaults to -1. - dither (float, optional): Dithering constant . Defaults to 0.0. - energy_floor (float, optional): Floor on energy of the output Spectrogram. Defaults to 1.0. - frame_length (float, optional): Frame length in milliseconds. Defaults to 25.0. - frame_shift (float, optional): Shift between adjacent frames in milliseconds. Defaults to 10.0. - high_freq (float, optional): The upper cut-off frequency. Defaults to 0.0. - htk_compat (bool, optional): Put energy to the last when it is set True. Defaults to False. - low_freq (float, optional): The lower cut-off frequency. Defaults to 20.0. - n_mfcc (int, optional): Number of cepstra in MFCC. Defaults to 13. - n_mels (int, optional): Number of output mel bins. Defaults to 23. - preemphasis_coefficient (float, optional): Preemphasis coefficient for input waveform. Defaults to 0.97. - raw_energy (bool, optional): Whether to compute before preemphasis and windowing. Defaults to True. - remove_dc_offset (bool, optional): Whether to subtract mean from waveform on frames. Defaults to True. - round_to_power_of_two (bool, optional): If True, round window size to power of two by zero-padding input - to FFT. Defaults to True. - sr (int, optional): Sample rate of input waveform. Defaults to 16000. - snip_edges (bool, optional): Drop samples in the end of waveform that cann't fit a singal frame when it - is set True. Otherwise performs reflect padding to the end of waveform. Defaults to True. - subtract_mean (bool, optional): Whether to subtract mean of feature files. Defaults to False. - use_energy (bool, optional): Add an dimension with energy of spectrogram to the output. Defaults to False. - vtln_high (float, optional): High inflection point in piecewise linear VTLN warping function. Defaults to -500.0. - vtln_low (float, optional): Low inflection point in piecewise linear VTLN warping function. Defaults to 100.0. - vtln_warp (float, optional): Vtln warp factor. Defaults to 1.0. - window_type (str, optional): Choose type of window for FFT computation. Defaults to POVEY. - - Returns: - Tensor: A mel frequency cepstral coefficients tensor with shape `(m, n_mfcc)`. - """ - assert n_mfcc <= n_mels, 'n_mfcc cannot be larger than n_mels: %d vs %d' % ( - n_mfcc, n_mels) - - dtype = waveform.dtype - - # (m, n_mels + use_energy) - feature = fbank(waveform=waveform, - blackman_coeff=blackman_coeff, - channel=channel, - dither=dither, - energy_floor=energy_floor, - frame_length=frame_length, - frame_shift=frame_shift, - high_freq=high_freq, - htk_compat=htk_compat, - low_freq=low_freq, - n_mels=n_mels, - preemphasis_coefficient=preemphasis_coefficient, - raw_energy=raw_energy, - remove_dc_offset=remove_dc_offset, - round_to_power_of_two=round_to_power_of_two, - sr=sr, - snip_edges=snip_edges, - subtract_mean=False, - use_energy=use_energy, - use_log_fbank=True, - use_power=True, - vtln_high=vtln_high, - vtln_low=vtln_low, - vtln_warp=vtln_warp, - window_type=window_type) - - if use_energy: - # (m) - signal_log_energy = feature[:, n_mels if htk_compat else 0] - mel_offset = int(not htk_compat) - feature = feature[:, mel_offset:(n_mels + mel_offset)] - - # (n_mels, n_mfcc) - dct_matrix = _get_dct_matrix(n_mfcc, n_mels).astype(dtype=dtype) - - # (m, n_mfcc) - feature = feature.matmul(dct_matrix) - - if cepstral_lifter != 0.0: - # (1, n_mfcc) - lifter_coeffs = _get_lifter_coeffs(n_mfcc, cepstral_lifter).unsqueeze(0) - feature *= lifter_coeffs.astype(dtype=dtype) - - if use_energy: - feature[:, 0] = signal_log_energy - - if htk_compat: - energy = feature[:, 0].unsqueeze(1) # (m, 1) - feature = feature[:, 1:] # (m, n_mfcc - 1) - if not use_energy: - energy *= math.sqrt(2) - - feature = paddle.concat((feature, energy), axis=1) - - feature = _subtract_column_mean(feature, subtract_mean) - return feature diff --git a/python/paddle/tests/audio_base.py b/python/paddle/tests/audio_base.py index ff7361ab90f2c..d38ee01f3690a 100644 --- a/python/paddle/tests/audio_base.py +++ b/python/paddle/tests/audio_base.py @@ -86,16 +86,6 @@ def get_wav_data( num_frames = 1 << 16 # paddle linspace not support uint8, int8, int16 - #if dtype == "uint8": - # base = paddle.linspace(0, 255, num_frames, dtype=dtype_) - #dtype_np = getattr(np, dtype) - #base_np = np.linspace(0, 255, num_frames, dtype_np) - #base = paddle.to_tensor(base_np, dtype=dtype_) - #elif dtype == "int8": - # base = paddle.linspace(-128, 127, num_frames, dtype=dtype_) - #dtype_np = getattr(np, dtype) - #base_np = np.linspace(-128, 127, num_frames, dtype_np) - #base = paddle.to_tensor(base_np, dtype=dtype_) if dtype == "float32": base = paddle.linspace(-1.0, 1.0, num_frames, dtype=dtype_) elif dtype == "float64": @@ -105,11 +95,6 @@ def get_wav_data( 2147483647, num_frames, dtype=dtype_) - #elif dtype == "int16": - # base = paddle.linspace(-32768, 32767, num_frames, dtype=dtype_) - #dtype_np = getattr(np, dtype) - #base_np = np.linspace(-32768, 32767, num_frames, dtype_np) - #base = paddle.to_tensor(base_np, dtype=dtype_) else: raise NotImplementedError(f"Unsupported dtype {dtype}") data = base.tile([num_channels, 1]) diff --git a/python/paddle/tests/test_audio_features.py b/python/paddle/tests/test_audio_features.py index 2474c79a82903..fcf617d4a23e2 100644 --- a/python/paddle/tests/test_audio_features.py +++ b/python/paddle/tests/test_audio_features.py @@ -13,6 +13,7 @@ # limitations under the License. import unittest +import librosa import numpy as np import paddle @@ -39,13 +40,26 @@ def initParmas(self): self.sr = 16000 self.dtype = "float32" self.window_size = 1024 - self.waveform = np.loadtxt('testdata/audio.txt') + waveform_tensor = get_wav_data(self.dtype, + self.num_channels, + normalize=False, + num_frames=self.duration * self.sr) + self.waveform = waveform_tensor.numpy() * 0.1 def test_stft(self): if len(self.waveform.shape) == 2: # (C, T) self.waveform = self.waveform.squeeze( 0) # 1D input for librosa.feature.melspectrogram - feature_librosa = np.load('testdata/librosa_stft.npy') + feature_librosa = librosa.core.stft( + y=self.waveform, + n_fft=self.n_fft, + hop_length=self.hop_length, + win_length=None, + window=self.window_str, + center=True, + dtype=None, + pad_mode=self.pad_mode, + ) x = paddle.to_tensor(self.waveform).unsqueeze(0) window = paddle.audio.functional.get_window(self.window_str, self.n_fft, @@ -71,9 +85,25 @@ def test_istft(self): self.waveform = self.waveform.squeeze( 0) # 1D input for librosa.feature.melspectrogram # librosa - stft_matrix = np.load('testdata/librosa_stft_matrix.npy') - feature_librosa = np.loadtxt('testdata/librosa_istft.txt') - + # Get stft result from librosa. + stft_matrix = librosa.core.stft( + y=self.waveform, + n_fft=self.n_fft, + hop_length=self.hop_length, + win_length=None, + window=self.window_str, + center=True, + pad_mode=self.pad_mode, + ) + feature_librosa = librosa.core.istft( + stft_matrix=stft_matrix, + hop_length=self.hop_length, + win_length=None, + window=self.window_str, + center=True, + dtype=None, + length=None, + ) x = paddle.to_tensor(stft_matrix).unsqueeze(0) window = paddle.audio.functional.get_window(self.window_str, self.n_fft, @@ -97,7 +127,16 @@ def test_istft(self): decimal=5) def test_mel(self): - feature_librosa = np.loadtxt('testdata/librosa_filters_mel.txt') + feature_librosa = librosa.filters.mel( + sr=self.sr, + n_fft=self.n_fft, + n_mels=self.n_mels, + fmin=self.fmin, + fmax=None, + htk=False, + norm='slaney', + dtype=self.waveform.dtype, + ) feature_compliance = paddle.audio.compliance.librosa.compute_fbank_matrix( sr=self.sr, n_fft=self.n_fft, @@ -131,7 +170,13 @@ def test_melspect(self): 0) # 1D input for librosa.feature.melspectrogram # librosa: - feature_librosa = np.loadtxt('testdata/librosa_melspectrogram.txt') + feature_librosa = librosa.feature.melspectrogram( + y=self.waveform, + sr=self.sr, + n_fft=self.n_fft, + hop_length=self.hop_length, + n_mels=self.n_mels, + fmin=self.fmin) # paddle.audio.compliance.librosa: feature_compliance = paddle.audio.compliance.librosa.melspectrogram( @@ -168,7 +213,14 @@ def test_log_melspect(self): 0) # 1D input for librosa.feature.melspectrogram # librosa: - feature_librosa = np.loadtxt('testdata/librosa_logmelspect.txt') + feature_librosa = librosa.feature.melspectrogram( + y=self.waveform, + sr=self.sr, + n_fft=self.n_fft, + hop_length=self.hop_length, + n_mels=self.n_mels, + fmin=self.fmin) + feature_librosa = librosa.power_to_db(feature_librosa, top_db=None) # paddle.audio.compliance.librosa: feature_compliance = paddle.audio.compliance.librosa.melspectrogram( x=self.waveform, @@ -177,20 +229,9 @@ def test_log_melspect(self): hop_length=self.hop_length, n_mels=self.n_mels, fmin=self.fmin) - - def test_spectrogram(self): - if len(self.waveform.shape) == 2: # (C, T) - self.waveform = self.waveform.squeeze( - 0) # 1D input for librosa.feature.melspectrogram - feature_librosa = np.loadtxt('testdata/librosa_spectrogram.txt') - feature_compliance = paddle.audio.compliance.librosa.spectrogram( - x=self.waveform, - sr=self.sr, - window=self.window_str, - pad_mode=self.pad_mode) np.testing.assert_array_almost_equal(feature_librosa, feature_compliance, - decimal=4) + decimal=5) def test_mfcc(self): if len(self.waveform.shape) == 2: # (C, T) @@ -198,7 +239,17 @@ def test_mfcc(self): 0) # 1D input for librosa.feature.melspectrogram # librosa: - feature_librosa = np.loadtxt('testdata/librosa_mfcc.txt') + feature_librosa = librosa.feature.mfcc(y=self.waveform, + sr=self.sr, + S=None, + n_mfcc=self.n_mfcc, + dct_type=2, + norm='ortho', + lifter=0, + n_fft=self.n_fft, + hop_length=self.hop_length, + n_mels=self.n_mels, + fmin=self.fmin) # paddle.audio.compliance.librosa: feature_compliance = paddle.audio.compliance.librosa.mfcc( x=self.waveform, @@ -233,23 +284,6 @@ def test_mfcc(self): feature_layer, decimal=4) - def test_kaldi_feature(self): - waveform = np.expand_dims(self.waveform, axis=0) - fbank = paddle.audio.compliance.kaldi.fbank(paddle.to_tensor(waveform)) - fbank_bg = np.loadtxt('testdata/kaldi_fbank.txt') - np.testing.assert_array_almost_equal(fbank, fbank_bg, decimal=4) - - mfcc = paddle.audio.compliance.kaldi.mfcc(paddle.to_tensor(waveform)) - mfcc_bg = np.loadtxt('testdata/kaldi_mfcc.txt') - np.testing.assert_array_almost_equal(mfcc, mfcc_bg, decimal=4) - - spectrogram = paddle.audio.compliance.kaldi.spectrogram( - paddle.to_tensor(waveform)) - spectrogram_bg = np.loadtxt('testdata/kaldi_spectrogram.txt') - np.testing.assert_array_almost_equal(spectrogram, - spectrogram_bg, - decimal=4) - if __name__ == '__main__': unittest.main() diff --git a/python/paddle/tests/testdata/audio.txt b/python/paddle/tests/testdata/audio.txt deleted file mode 100644 index 3f8bc33f00fa1..0000000000000 --- a/python/paddle/tests/testdata/audio.txt +++ /dev/null @@ -1 +0,0 @@ --1.000000014901161194e-01 -9.997499734163284302e-02 -9.994999319314956665e-02 -9.992499649524688721e-02 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--4.091761633753775163e-02 --4.089261218905449607e-02 --4.086760804057121971e-02 --4.084260389208793640e-02 --4.081760346889496543e-02 --4.079259932041168213e-02 --4.076759517192841270e-02 --4.074259474873542786e-02 --4.071759060025215149e-02 --4.069258645176888206e-02 --4.066758602857589722e-02 --4.064258188009262085e-02 --4.061757773160934448e-02 --4.059257730841638739e-02 --4.056757315993309715e-02 --4.054256901144982772e-02 --4.051756486296652360e-02 --4.049256071448326111e-02 --4.046755656599997780e-02 --4.044255614280701377e-02 --4.041755199432374435e-02 --4.039254784584046104e-02 --4.036754742264747620e-02 --4.034254327416420677e-02 --4.031753912568092346e-02 --4.029253870248794556e-02 --4.026753455400466919e-02 --4.024253040552139282e-02 --4.021752998232842186e-02 --4.019252583384513855e-02 --4.016752168536186218e-02 --4.014251753687859275e-02 --4.011751338839530251e-02 --4.009251296520233848e-02 --4.006750881671904824e-02 --4.004250466823577881e-02 --4.001750424504280784e-02 --3.999250009655952454e-02 --3.996749594807623429e-02 --3.994249552488327026e-02 --3.991749137639999390e-02 --3.989248722791672447e-02 --3.986748680472373962e-02 --3.984248265624046326e-02 --3.981747850775718689e-02 --3.979247435927391746e-02 --3.976747021079063416e-02 --3.974246606230736473e-02 --3.971746563911437988e-02 --3.969246149063111045e-02 --3.966745734214782021e-02 --3.964245691895484924e-02 --3.961745277047157981e-02 --3.959244862198829651e-02 --3.956744819879531860e-02 --3.954244405031204224e-02 --3.951743990182876587e-02 --3.949243947863579490e-02 --3.946743533015251160e-02 --3.944243118166922829e-02 --3.941742703318595886e-02 --3.939242288470267556e-02 --3.936741873621940613e-02 --3.934241831302643516e-02 --3.931741416454314492e-02 --3.929241374135017395e-02 --3.926740959286689758e-02 --3.924240544438362122e-02 --3.921740502119065025e-02 --3.919240087270737388e-02 --3.916739672422408364e-02 --3.914239630103110573e-02 --3.911739215254784324e-02 --3.909238800406455994e-02 --3.906738385558129051e-02 --3.904237970709800720e-02 --3.901737555861473083e-02 --3.899237513542175293e-02 --3.896737098693847656e-02 --3.894236683845520713e-02 --3.891736641526222923e-02 --3.889236226677895286e-02 --3.886735811829566956e-02 --3.884235769510269165e-02 --3.881735354661941528e-02 --3.879234939813613892e-02 --3.876734897494316101e-02 --3.874234482645989158e-02 --3.871734067797660828e-02 --3.869233652949333885e-02 --3.866733238101004166e-02 --3.864232823252677917e-02 --3.861732780933380821e-02 --3.859232366085052490e-02 --3.856731951236724854e-02 --3.854231908917427063e-02 --3.851731494069098732e-02 --3.849231451749801636e-02 --3.846731036901473999e-02 --3.844230622053147056e-02 --3.841730579733848572e-02 --3.839230164885521629e-02 --3.836729750037193992e-02 --3.834229335188865662e-02 --3.831728920340537331e-02 --3.829228505492211082e-02 --3.826728463172912598e-02 --3.824228048324584961e-02 --3.821727633476258712e-02 --3.819227591156960228e-02 --3.816727176308632591e-02 --3.814226761460304260e-02 --3.811726719141005776e-02 --3.809226304292678833e-02 --3.806725889444350502e-02 --3.804225847125054100e-02 --3.801725432276727157e-02 --3.799225017428398826e-02 --3.796724602580069802e-02 --3.794224187731743553e-02 --3.791723772883415222e-02 --3.789223730564118126e-02 --3.786723315715790489e-02 --3.784222900867461464e-02 --3.781722858548164368e-02 --3.779222443699836037e-02 --3.776722028851508400e-02 --3.774221986532211304e-02 --3.771721571683882973e-02 --3.769221156835555336e-02 --3.766721114516257546e-02 --3.764220699667929909e-02 --3.761720284819603660e-02 --3.759219869971275330e-02 --3.756719455122948387e-02 --3.754219412803650596e-02 --3.751718997955321572e-02 --3.749218583106994629e-02 --3.746718540787697532e-02 --3.744218125939368508e-02 --3.741717711091041565e-02 --3.739217668771745162e-02 --3.736717253923416138e-02 --3.734216839075089889e-02 --3.731716796755790017e-02 --3.729216381907462380e-02 --3.726715967059134743e-02 --3.724215552210808494e-02 --3.721715137362480857e-02 --3.719214722514153915e-02 --3.716714680194855430e-02 --3.714214265346529181e-02 --3.711713850498198769e-02 --3.709213808178903060e-02 --3.706713393330574036e-02 --3.704212978482247093e-02 --3.701712936162949302e-02 --3.699212521314620972e-02 --3.696712106466292641e-02 --3.694212064146996238e-02 --3.691711649298667214e-02 --3.689211234450340965e-02 --3.686710819602012634e-02 --3.684210404753685691e-02 --3.681710362434387901e-02 --3.679209947586059570e-02 --3.676709532737731240e-02 --3.674209490418434837e-02 --3.671709075570105812e-02 --3.669208660721780257e-02 --3.666708618402481079e-02 --3.664208203554154136e-02 --3.661707788705825112e-02 --3.659207746386529403e-02 --3.656707331538200378e-02 --3.654206916689873436e-02 --3.651706501841545799e-02 --3.649206086993218162e-02 --3.646705672144889138e-02 --3.644205629825592735e-02 --3.641705214977264404e-02 --3.639204800128937461e-02 --3.636704757809639671e-02 --3.634204342961312034e-02 --3.631703928112984398e-02 --3.629203885793686607e-02 --3.626703470945358970e-02 --3.624203056097031334e-02 --3.621703013777733543e-02 --3.619202598929405212e-02 --3.616702184081077576e-02 --3.614201769232750633e-02 --3.611701354384420221e-02 --3.609200939536093972e-02 --3.606700897216796181e-02 --3.604200482368469238e-02 --3.601700067520140908e-02 --3.599200025200843811e-02 --3.596699610352515480e-02 --3.594199568033219078e-02 --3.591699153184890053e-02 --3.589198738336562416e-02 --3.586698696017264626e-02 --3.584198281168938377e-02 --3.581697866320609352e-02 --3.579197451472282410e-02 --3.576697036623954773e-02 --3.574196621775627830e-02 --3.571696579456330040e-02 --3.569196164608002403e-02 --3.566695749759674072e-02 --3.564195707440376976e-02 --3.561695292592047951e-02 --3.559194877743721702e-02 --3.556694835424423218e-02 --3.554194420576095581e-02 --3.551694005727768638e-02 --3.549193963408470154e-02 --3.546693548560141823e-02 --3.544193133711815574e-02 --3.541692718863487938e-02 --3.539192304015160301e-02 --3.536691889166831970e-02 --3.534191846847534874e-02 --3.531691431999205849e-02 --3.529191017150878212e-02 --3.526690974831581116e-02 --3.524190559983252785e-02 --3.521690145134925842e-02 --3.519190102815628052e-02 --3.516689687967301109e-02 --3.514189645648001931e-02 --3.511689230799674294e-02 --3.509188815951348045e-02 --3.506688401103019714e-02 --3.504187986254691384e-02 --3.501687571406364441e-02 --3.499187529087066650e-02 --3.496687114238739014e-02 --3.494186699390412071e-02 --3.491686657071113586e-02 --3.489186242222785256e-02 --3.486685827374457619e-02 --3.484185785055161216e-02 --3.481685370206833580e-02 --3.479184955358505943e-02 --3.476684913039206765e-02 --3.474184498190880516e-02 --3.471684083342551491e-02 --3.469183668494225242e-02 --3.466683253645896912e-02 --3.464182838797568581e-02 --3.461682796478270790e-02 --3.459182381629943848e-02 --3.456681966781615517e-02 --3.454181924462319114e-02 --3.451681509613988702e-02 --3.449181094765663841e-02 --3.446681052446364663e-02 --3.444180637598037026e-02 --3.441680222749710777e-02 --3.439180180430412292e-02 --3.436679765582083962e-02 --3.434179350733757713e-02 --3.431678935885430076e-02 --3.429178521037101746e-02 --3.426678478717803261e-02 --3.424178063869474931e-02 --3.421677649021148682e-02 --3.419177606701851585e-02 --3.416677191853522561e-02 --3.414176777005197005e-02 --3.411676734685897133e-02 --3.409176319837569497e-02 --3.406675904989241860e-02 --3.404175862669944763e-02 --3.401675447821617820e-02 --3.399175032973290184e-02 --3.396674618124962547e-02 --3.394174203276634910e-02 --3.391673788428305886e-02 --3.389173746109008789e-02 --3.386673331260681152e-02 --3.384172916412353516e-02 --3.381672874093055031e-02 --3.379172459244727394e-02 --3.376672044396399758e-02 --3.374172002077103355e-02 --3.371671587228774331e-02 --3.369171172380448082e-02 --3.366671130061148903e-02 --3.364170715212820573e-02 --3.361670300364495712e-02 --3.359169885516166687e-02 --3.356669470667838356e-02 --3.354169055819511414e-02 --3.351669013500212929e-02 --3.349168598651886680e-02 --3.346668556332587502e-02 --3.344168141484259865e-02 --3.341667726635932228e-02 --3.339167684316635826e-02 --3.336667269468306107e-02 --3.334166854619981940e-02 --3.331666812300682762e-02 --3.329166397452355125e-02 --3.326665982604026101e-02 --3.324165567755698464e-02 --3.321665152907372215e-02 --3.319164738059044578e-02 --3.316664695739745400e-02 --3.314164280891419151e-02 --3.311663866043090820e-02 --3.309163823723793030e-02 --3.306663408875465393e-02 --3.304162994027137756e-02 --3.301662951707840660e-02 --3.299162536859511635e-02 --3.296662122011183998e-02 --3.294162079691888290e-02 --3.291661664843558571e-02 --3.289161249995230935e-02 --3.286660835146903298e-02 --3.284160420298575661e-02 --3.281660005450248718e-02 --3.279159963130950234e-02 --3.276659548282622597e-02 --3.274159133434295654e-02 --3.271659091114997864e-02 --3.269158676266670921e-02 --3.266658261418342590e-02 --3.264158219099043412e-02 --3.261657804250717163e-02 --3.259157761931418679e-02 --3.256657347083091042e-02 --3.254156932234764793e-02 --3.251656517386437156e-02 --3.249156102538109520e-02 --3.246655687689780495e-02 --3.244155645370483398e-02 --3.241655230522155762e-02 --3.239154815673828125e-02 --3.236654773354529641e-02 --3.234154358506202004e-02 --3.231653943657875755e-02 --3.229153901338577271e-02 --3.226653486490248940e-02 --3.224153071641921303e-02 --3.221653029322624900e-02 --3.219152614474295182e-02 --3.216652199625968239e-02 --3.214151784777641990e-02 --3.211651369929312966e-02 --3.209150955080985329e-02 --3.206650912761688926e-02 --3.204150497913359902e-02 --3.201650083065032959e-02 --3.199150040745734475e-02 --3.196649625897407532e-02 --3.194149211049079201e-02 --3.191649168729781411e-02 --3.189148753881454468e-02 --3.186648339033126831e-02 --3.184148296713828347e-02 --3.181647881865500710e-02 --3.179147467017173767e-02 --3.176647052168845436e-02 --3.174146637320519188e-02 --3.171646595001220703e-02 --3.169146180152893760e-02 --3.166645765304564736e-02 --3.164145722985267639e-02 --3.161645308136940696e-02 --3.159144893288612366e-02 --3.156644850969313881e-02 --3.154144436120986938e-02 --3.151644021272658608e-02 --3.149143978953361511e-02 --3.146643564105033181e-02 --3.144143149256705544e-02 --3.141642734408378601e-02 --3.139142319560050270e-02 --3.136641904711722634e-02 --3.134141862392426231e-02 --3.131641447544097207e-02 --3.129141032695769570e-02 --3.126640990376471779e-02 --3.124140575528143796e-02 --3.121640160679817200e-02 --3.119139932096004486e-02 --3.116639517247676502e-02 --3.114139102399349560e-02 --3.111639060080051769e-02 --3.109138645231723785e-02 --3.106638230383396149e-02 --3.104138188064096970e-02 --3.101637773215770721e-02 --3.099137358367443085e-02 --3.096637129783630024e-02 --3.094136714935303775e-02 --3.091636672616004597e-02 --3.089136257767677307e-02 --3.086635842919349323e-02 --3.084135614335536957e-02 --3.081635199487209667e-02 --3.079134784638882030e-02 --3.076634742319583546e-02 --3.074134327471256256e-02 --3.071633912622928966e-02 --3.069133870303630829e-02 --3.066633455455303192e-02 --3.064133040606974515e-02 --3.061632812023163189e-02 --3.059132397174834858e-02 --3.056631982326507915e-02 --3.054131940007209778e-02 --3.051631525158882141e-02 --3.049131110310554851e-02 --3.046630881726742138e-02 --3.044130466878413807e-02 --3.041630052030087558e-02 --3.039130009710789074e-02 --3.036629594862460743e-02 --3.034129180014132413e-02 --3.031629137694834622e-02 --3.029128722846509067e-02 --3.026628307998180736e-02 --3.024128079414366635e-02 --3.021627664566040039e-02 --3.019127249717712749e-02 --3.016627207398413571e-02 --3.014126792550087322e-02 --3.011626563966274261e-02 --3.009126149117946625e-02 --3.006625734269618988e-02 --3.004125691950320851e-02 --3.001625277101993908e-02 --2.999124862253666271e-02 --2.996624819934368480e-02 --2.994124405086040497e-02 --2.991623990237713207e-02 --2.989123761653900146e-02 --2.986623346805572510e-02 --2.984122931957244526e-02 --2.981622889637947429e-02 --2.979122474789618405e-02 --2.976622059941291809e-02 --2.974121831357479442e-02 --2.971621416509151459e-02 --2.969121001660823822e-02 --2.966620959341525685e-02 --2.964120544493198395e-02 --2.961620129644871105e-02 --2.959120087325572968e-02 --2.956619672477245331e-02 --2.954119257628917347e-02 --2.951619029045105327e-02 --2.949118614196777691e-02 --2.946618199348450054e-02 --2.944118157029151917e-02 --2.941617742180824280e-02 --2.939117327332496643e-02 --2.936617098748683582e-02 --2.934116683900356293e-02 --2.931616269052029003e-02 --2.929116226732730865e-02 --2.926615811884403576e-02 --2.924115769565105438e-02 --2.921615354716777802e-02 --2.919114939868450512e-02 --2.916614711284637451e-02 --2.914114296436309468e-02 --2.911613881587983219e-02 --2.909113839268684387e-02 --2.906613424420356750e-02 --2.904113009572029461e-02 --2.901612780988216747e-02 --2.899112366139888763e-02 --2.896611951291561127e-02 --2.894111908972263336e-02 --2.891611494123935699e-02 --2.889111079275607716e-02 --2.886611036956310619e-02 --2.884110622107982289e-02 --2.881610207259655346e-02 --2.879109978675842632e-02 --2.876609563827514995e-02 --2.874109148979187012e-02 --2.871609106659889568e-02 --2.869108691811561238e-02 --2.866608276963234295e-02 --2.864108048379420887e-02 --2.861607633531093944e-02 --2.859107218682765961e-02 --2.856607176363468517e-02 --2.854106761515140187e-02 --2.851606346666812550e-02 --2.849106304347515106e-02 --2.846605889499188510e-02 --2.844105660915374756e-02 --2.841605246067047466e-02 --2.839104831218719829e-02 --2.836604788899421345e-02 --2.834104374051094055e-02 --2.831603959202766765e-02 --2.829103730618954746e-02 --2.826603315770626415e-02 --2.824102900922298084e-02 --2.821602858603000641e-02 --2.819102443754672657e-02 --2.816602028906345020e-02 --2.814101986587047230e-02 --2.811601571738719940e-02 --2.809101156890392650e-02 --2.806600928306579937e-02 --2.804100513458251606e-02 --2.801600098609924663e-02 --2.799100056290626526e-02 --2.796599641442299236e-02 --2.794099226593971599e-02 --2.791598998010158886e-02 --2.789098583161831249e-02 --2.786598168313503612e-02 --2.784098125994204781e-02 --2.781597711145878185e-02 --2.779097296297550548e-02 --2.776597253978252758e-02 --2.774096839129924774e-02 --2.771596424281597831e-02 --2.769096195697784771e-02 --2.766595780849456440e-02 --2.764095366001129844e-02 --2.761595323681832401e-02 --2.759094908833503723e-02 --2.756594680249691356e-02 --2.754094265401363720e-02 --2.751593850553036777e-02 --2.749093808233738293e-02 --2.746593393385411003e-02 --2.744092978537082325e-02 --2.741592936217785922e-02 --2.739092521369457245e-02 --2.736592106521129608e-02 --2.734091877937316548e-02 --2.731591463088989605e-02 --2.729091048240662662e-02 --2.726591005921363831e-02 --2.724090591073036194e-02 --2.721590176224708904e-02 --2.719089947640895844e-02 --2.716589532792567860e-02 --2.714089117944239876e-02 --2.711589075624942780e-02 --2.709088660776615490e-02 --2.706588245928287506e-02 --2.704088203608989716e-02 --2.701587788760662079e-02 --2.699087373912334789e-02 --2.696587145328521035e-02 --2.694086730480194439e-02 --2.691586315631866802e-02 --2.689086273312568318e-02 --2.686585858464241028e-02 --2.684085443615913044e-02 --2.681585215032100677e-02 --2.679084800183772694e-02 --2.676584757864475250e-02 --2.674084343016147614e-02 --2.671583928167819977e-02 --2.669083885848522186e-02 --2.666583471000194897e-02 --2.664083056151866913e-02 --2.661582827568053852e-02 --2.659082412719726216e-02 --2.656581997871398579e-02 --2.654081955552101135e-02 --2.651581540703773499e-02 --2.649081125855445862e-02 --2.646580897271632454e-02 --2.644080482423305858e-02 --2.641580067574977528e-02 --2.639080025255680084e-02 --2.636579610407352101e-02 --2.634079195559024811e-02 --2.631579153239727367e-02 --2.629078738391399384e-02 --2.626578323543072094e-02 --2.624078094959259033e-02 --2.621577680110931743e-02 --2.619077265262603760e-02 --2.616577222943305622e-02 --2.614076808094978333e-02 --2.611576393246650696e-02 --2.609076164662838329e-02 --2.606575749814510692e-02 --2.604075334966183056e-02 --2.601575292646884918e-02 --2.599074877798557281e-02 --2.596574462950229645e-02 --2.594074420630931854e-02 --2.591574005782604911e-02 --2.589073777198791504e-02 --2.586573362350463173e-02 --2.584072947502136230e-02 --2.581572905182838440e-02 --2.579072490334510456e-02 --2.576572075486182473e-02 --2.574071846902370453e-02 --2.571571432054042469e-02 --2.569071017205714832e-02 --2.566570974886417736e-02 --2.564070560038089752e-02 --2.561570145189762115e-02 --2.559070102870464325e-02 --2.556569688022136688e-02 --2.554069273173808705e-02 --2.551569044589995991e-02 --2.549068629741668354e-02 --2.546568214893341064e-02 --2.544068172574042233e-02 --2.541567757725715637e-02 --2.539067342877388000e-02 --2.536567114293575287e-02 --2.534066699445247650e-02 --2.531566284596920013e-02 --2.529066242277622223e-02 --2.526565827429294239e-02 --2.524065412580966949e-02 --2.521565370261669159e-02 --2.519064955413341522e-02 --2.516564540565013539e-02 --2.514064311981201172e-02 --2.511563897132873535e-02 --2.509063854813575745e-02 --2.506563439965247761e-02 --2.504063025116920124e-02 --2.501562796533107411e-02 --2.499062381684779774e-02 --2.496561966836452137e-02 --2.494061738252639771e-02 --2.491561509668826710e-02 --2.489061281085014343e-02 --2.486560866236685666e-02 --2.484060637652873646e-02 --2.481560222804546356e-02 --2.479059807956219066e-02 --2.476559579372406353e-02 --2.474059350788593639e-02 --2.471558935940266002e-02 --2.469058707356452942e-02 --2.466558478772639881e-02 --2.464058063924312592e-02 --2.461557649075984261e-02 --2.459057420492173282e-02 --2.456557005643844604e-02 --2.454056777060032585e-02 --2.451556548476218830e-02 --2.449056133627891541e-02 --2.446555905044078480e-02 --2.444055490195751884e-02 --2.441555261611938477e-02 --2.439054846763610840e-02 --2.436554618179798820e-02 --2.434054389595985760e-02 --2.431553974747657429e-02 --2.429053746163845062e-02 --2.426553331315517772e-02 --2.424052916467189789e-02 --2.421552687883377075e-02 --2.419052459299564362e-02 --2.416552044451236725e-02 --2.414051815867424011e-02 --2.411551587283611298e-02 --2.409051172435283661e-02 --2.406550757586954983e-02 --2.404050529003143311e-02 --2.401550300419330944e-02 --2.399049885571002960e-02 --2.396549656987189900e-02 --2.394049428403377533e-02 --2.391549013555049202e-02 --2.389048598706721913e-02 --2.386548370122909199e-02 --2.384047955274581562e-02 --2.381547726690768849e-02 --2.379047498106956829e-02 --2.376547083258628151e-02 --2.374046854674816132e-02 --2.371546439826488495e-02 --2.369046024978160858e-02 --2.366545796394347104e-02 --2.364045567810535084e-02 --2.361545339226722370e-02 --2.359044924378394734e-02 --2.356544695794582714e-02 --2.354044280946254383e-02 --2.351543866097926747e-02 --2.349043637514114727e-02 --2.346543408930301319e-02 --2.344042994081974376e-02 --2.341542765498160969e-02 --2.339042536914348602e-02 --2.336542122066019925e-02 --2.334041707217693676e-02 --2.331541478633880268e-02 --2.329041063785552632e-02 --2.326540835201739571e-02 --2.324040606617928245e-02 --2.321540378034114491e-02 --2.319039963185787201e-02 --2.316539548337459217e-02 --2.314039319753646851e-02 --2.311538904905319561e-02 --2.309038676321506500e-02 --2.306538447737693787e-02 --2.304038032889365803e-02 --2.301537804305553089e-02 --2.299037389457226493e-02 --2.296536974608897469e-02 --2.294036746025085449e-02 --2.291536517441273083e-02 --2.289036102592945099e-02 --2.286535874009132385e-02 --2.284035645425320019e-02 --2.281535230576992382e-02 --2.279034815728664398e-02 --2.276534587144851685e-02 --2.274034358561037930e-02 --2.271533943712711334e-02 --2.269033715128898274e-02 --2.266533486545085213e-02 --2.264033071696758617e-02 --2.261532656848430634e-02 --2.259032428264617920e-02 --2.256532013416290283e-02 --2.254031784832477223e-02 --2.251531556248664856e-02 --2.249031141400336872e-02 --2.246530912816523812e-02 --2.244030497968196869e-02 --2.241530083119869232e-02 --2.239029854536057212e-02 --2.236529625952244152e-02 --2.234029397368431091e-02 --2.231528982520103455e-02 --2.229028753936290394e-02 --2.226528339087962757e-02 --2.224027924239635121e-02 --2.221527695655822754e-02 --2.219027467072011081e-02 --2.216527052223682057e-02 --2.214026823639869343e-02 --2.211526595056056976e-02 --2.209026180207728993e-02 --2.206525765359402050e-02 --2.204025536775589336e-02 --2.201525121927261353e-02 --2.199024893343448639e-02 --2.196524664759635925e-02 --2.194024436175823212e-02 --2.191524021327495228e-02 --2.189023606479167591e-02 --2.186523377895354878e-02 --2.184022963047027588e-02 --2.181522734463215221e-02 --2.179022505879401814e-02 --2.176522091031074177e-02 --2.174021862447261463e-02 --2.171521447598934174e-02 --2.169021032750606537e-02 --2.166520804166793476e-02 --2.164020575582981110e-02 --2.161520160734653820e-02 --2.159019932150841106e-02 --2.156519703567028046e-02 --2.154019288718700756e-02 --2.151518873870373119e-02 --2.149018645286560059e-02 --2.146518416702746651e-02 --2.144018001854418667e-02 --2.141517773270607689e-02 --2.139017544686794628e-02 --2.136517129838466297e-02 --2.134016714990139008e-02 --2.131516486406325600e-02 --2.129016071557998657e-02 --2.126515842974185597e-02 --2.124015614390373577e-02 --2.121515199542045940e-02 --2.119014970958232880e-02 --2.116514556109905243e-02 --2.114014141261577259e-02 --2.111513912677764893e-02 --2.109013684093952179e-02 --2.106513455510139812e-02 --2.104013040661811482e-02 --2.101512812077999115e-02 --2.099012397229671478e-02 --2.096511982381343842e-02 --2.094011753797530781e-02 --2.091511525213718414e-02 --2.089011110365391125e-02 --2.086510881781577717e-02 --2.084010653197765003e-02 --2.081510238349437714e-02 --2.079009823501110077e-02 --2.076509594917297363e-02 --2.074009180068969033e-02 --2.071508951485157013e-02 --2.069008722901344646e-02 --2.066508494317531586e-02 --2.064008079469203602e-02 --2.061507664620876659e-02 --2.059007436037063946e-02 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--1.963995583355427482e-02 --1.961495168507099152e-02 --1.958994939923286438e-02 --1.956494711339473377e-02 --1.953994296491145394e-02 --1.951493881642818451e-02 --1.948993653059005737e-02 --1.946493238210677407e-02 --1.943993009626865734e-02 --1.941492781043052326e-02 --1.938992552459240307e-02 --1.936492137610911976e-02 --1.933991722762583992e-02 --1.931491494178772320e-02 --1.928991079330443989e-02 --1.926490850746631622e-02 --1.923990622162818562e-02 --1.921490207314491619e-02 --1.918989978730678558e-02 --1.916489563882351616e-02 --1.913989149034022591e-02 --1.911488920450210918e-02 --1.908988691866397511e-02 --1.906488277018069874e-02 --1.903988048434257507e-02 --1.901487819850445141e-02 --1.898987405002117157e-02 --1.896486990153789867e-02 --1.893986761569976460e-02 --1.891486532986164440e-02 --1.888986118137836109e-02 --1.886485889554023743e-02 --1.883985660970211723e-02 --1.881485246121883739e-02 --1.878984831273556103e-02 --1.876484602689743042e-02 --1.873984187841414711e-02 --1.871483959257602345e-02 --1.868983730673790325e-02 --1.866483315825461994e-02 --1.863983087241649628e-02 --1.861482672393321991e-02 --1.858982443809509277e-02 --1.856482028961181294e-02 --1.853981800377367886e-02 --1.851481571793556213e-02 --1.848981156945228230e-02 --1.846480928361415516e-02 --1.843980513513087879e-02 --1.841480098664760590e-02 --1.838979870080947876e-02 --1.836479641497135509e-02 --1.833979226648807873e-02 --1.831478998064994465e-02 --1.828978769481182098e-02 --1.826478354632854115e-02 --1.823977939784526478e-02 --1.821477711200714458e-02 --1.818977482616901745e-02 --1.816477067768574108e-02 --1.813976839184761047e-02 --1.811476610600948334e-02 --1.808976195752620350e-02 --1.806475780904292713e-02 --1.803975552320481041e-02 --1.801475137472152710e-02 --1.798974908888339996e-02 --1.796474680304527630e-02 --1.793974265456198952e-02 --1.791474036872386932e-02 --1.788973622024059643e-02 --1.786473207175731659e-02 --1.783972978591918598e-02 --1.781472750008105885e-02 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