Add decoding with H and HL for LibriSpeech

This commit is contained in:
Fangjun Kuang 2023-09-26 15:07:15 +08:00
parent 2d7067753e
commit 9384d63cfe
14 changed files with 674 additions and 116 deletions

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@ -44,3 +44,46 @@ log "HLG decoding"
$repo/test_wavs/1089-134686-0001.flac \
$repo/test_wavs/1221-135766-0001.flac \
$repo/test_wavs/1221-135766-0002.flac
log "CTC decoding on CPU with kaldi decoders using OpenFst"
log "Exporting model with torchscript"
pushd $repo/exp
ln -s pretrained.pt epoch-99.pt
popd
./conformer_ctc/export.py \
--epoch 99 \
--avg 1 \
--exp-dir $repo/exp \
--tokens $repo/data/lang_bpe_500/tokens.txt \
--jit 1
ls -lh $repo/exp
log "Generating H.fst, HL.fst"
./local/prepare_lang_fst.py --lang-dir $repo/data/lang_bpe_500
ls -lh $repo/data/lang_bpe_500
log "Decoding with H on CPU with OpenFst"
./conformer_ctc/jit_pretrained_decode_with_H.py \
--nn-model $repo/exp/cpu_jit.pt \
--H $repo/data/lang_bpe_500/H.fst \
--tokens $repo/data/lang_bpe_500/tokens.txt \
$repo/test_wavs/1089-134686-0001.flac \
$repo/test_wavs/1221-135766-0001.flac \
$repo/test_wavs/1221-135766-0002.flac
log "Decoding with HL on CPU with OpenFst"
./conformer_ctc/jit_pretrained_decode_with_H.py \
--nn-model $repo/exp/cpu_jit.pt \
--HL $repo/data/lang_bpe_500/HL.fst \
--words $repo/data/lang_bpe_500/words.txt \
$repo/test_wavs/1089-134686-0001.flac \
$repo/test_wavs/1221-135766-0001.flac \
$repo/test_wavs/1221-135766-0002.flac

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@ -29,7 +29,7 @@ concurrency:
jobs:
run_pre_trained_conformer_ctc:
if: github.event.label.name == 'ready' || github.event_name == 'push'
if: github.event.label.name == 'ready' || github.event_name == 'push' || github.event.label.name == 'ctc'
runs-on: ${{ matrix.os }}
strategy:
matrix:

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@ -0,0 +1,221 @@
#!/usr/bin/env python3
# Copyright 2023 Xiaomi Corp. (authors: Fangjun Kuang)
"""
This file shows how to use a torchscript model for decoding with H
on CPU using OpenFST and decoders from kaldi.
Usage:
./conformer_ctc/jit_pretrained_decode_with_H.py \
--nn-model ./cpu_jit.pt \
--H ./data/lang_bpe_500/H.fst \
--tokens ./data/lang_bpe_500/tokens.txt \
./download/LibriSpeech/test-clean/1089/134686/1089-134686-0002.flac \
./download/LibriSpeech/test-clean/1221/135766/1221-135766-0001.flac
Note that to generate ./tdnn/exp/cpu_jit.pt,
you can use ./export.py --jit 1
"""
import argparse
import logging
import math
from typing import Dict, List
import kaldi_hmm_gmm
import kaldifeat
import kaldifst
import torch
import torchaudio
from kaldi_hmm_gmm import DecodableCtc, FasterDecoder, FasterDecoderOptions
from torch.nn.utils.rnn import pad_sequence
def get_parser():
parser = argparse.ArgumentParser(
formatter_class=argparse.ArgumentDefaultsHelpFormatter
)
parser.add_argument(
"--nn-model",
type=str,
required=True,
help="""Path to the torchscript model.
You can use ./tdnn/export.py --jit 1
to obtain it
""",
)
parser.add_argument(
"--tokens",
type=str,
required=True,
help="Path to tokens.txt",
)
parser.add_argument("--H", type=str, required=True, help="Path to H.fst")
parser.add_argument(
"sound_files",
type=str,
nargs="+",
help="The input sound file(s) to transcribe. "
"Supported formats are those supported by torchaudio.load(). "
"For example, wav and flac are supported. ",
)
return parser
def read_tokens(tokens_txt: str) -> Dict[int, str]:
id2token = dict()
with open(tokens_txt, encoding="utf-8") as f:
for line in f:
token, idx = line.strip().split()
id2token[int(idx)] = token
return id2token
def read_sound_files(
filenames: List[str], expected_sample_rate: float
) -> List[torch.Tensor]:
"""Read a list of sound files into a list 1-D float32 torch tensors.
Args:
filenames:
A list of sound filenames.
expected_sample_rate:
The expected sample rate of the sound files.
Returns:
Return a list of 1-D float32 torch tensors.
"""
ans = []
for f in filenames:
wave, sample_rate = torchaudio.load(f)
if sample_rate != expected_sample_rate:
wave = torchaudio.functional.resample(
wave,
orig_freq=sample_rate,
new_freq=expected_sample_rate,
)
# We use only the first channel
ans.append(wave[0].contiguous())
return ans
def decode(
filename: str,
nnet_output: torch.Tensor,
H: kaldifst,
id2token: Dict[int, str],
) -> List[str]:
logging.info(f"{filename}, {nnet_output.shape}")
decodable = DecodableCtc(nnet_output)
decoder_opts = FasterDecoderOptions(max_active=3000)
decoder = FasterDecoder(H, decoder_opts)
decoder.decode(decodable)
if not decoder.reached_final():
print(f"failed to decode {filename}")
return ""
ok, best_path = decoder.get_best_path()
(
ok,
isymbols_out,
osymbols_out,
total_weight,
) = kaldifst.get_linear_symbol_sequence(best_path)
if not ok:
print(f"failed to get linear symbol sequence for {filename}")
return ""
# tokens are incremented during graph construction
# so they need to be decremented
hyps = [id2token[i - 1] for i in osymbols_out]
# hyps = "".join(hyps).split("▁")
hyps = "".join(hyps).split("\u2581") # unicode codepoint of ▁
return hyps
@torch.no_grad()
def main():
parser = get_parser()
args = parser.parse_args()
device = torch.device("cpu")
logging.info(f"device: {device}")
logging.info("Loading torchscript model")
model = torch.jit.load(args.nn_model)
model.eval()
model.to(device)
logging.info(f"Loading H from {args.H}")
H = kaldifst.StdVectorFst.read(args.H)
sample_rate = 16000
logging.info("Constructing Fbank computer")
opts = kaldifeat.FbankOptions()
opts.device = device
opts.frame_opts.dither = 0
opts.frame_opts.snip_edges = False
opts.frame_opts.samp_freq = sample_rate
opts.mel_opts.num_bins = 80
fbank = kaldifeat.Fbank(opts)
logging.info(f"Reading sound files: {args.sound_files}")
waves = read_sound_files(
filenames=args.sound_files, expected_sample_rate=sample_rate
)
waves = [w.to(device) for w in waves]
logging.info("Decoding started")
features = fbank(waves)
feature_lengths = [f.shape[0] for f in features]
feature_lengths = torch.tensor(feature_lengths)
supervisions = dict()
supervisions["sequence_idx"] = torch.arange(len(features))
supervisions["start_frame"] = torch.zeros(len(features))
supervisions["num_frames"] = feature_lengths
features = pad_sequence(features, batch_first=True, padding_value=math.log(1e-10))
nnet_output, _, _ = model(features, supervisions)
feature_lengths = ((feature_lengths - 1) // 2 - 1) // 2
id2token = read_tokens(args.tokens)
hyps = []
for i in range(nnet_output.shape[0]):
hyp = decode(
filename=args.sound_files[i],
nnet_output=nnet_output[i, : feature_lengths[i]],
H=H,
id2token=id2token,
)
hyps.append(hyp)
s = "\n"
for filename, hyp in zip(args.sound_files, hyps):
words = " ".join(hyp)
s += f"{filename}:\n{words}\n\n"
logging.info(s)
logging.info("Decoding Done")
if __name__ == "__main__":
formatter = "%(asctime)s %(levelname)s [%(filename)s:%(lineno)d] %(message)s"
logging.basicConfig(format=formatter, level=logging.INFO)
main()

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@ -0,0 +1,218 @@
#!/usr/bin/env python3
# Copyright 2023 Xiaomi Corp. (authors: Fangjun Kuang)
"""
This file shows how to use a torchscript model for decoding with H
on CPU using OpenFST and decoders from kaldi.
Usage:
./conformer_ctc/jit_pretrained_decode_with_H.py \
--nn-model ./cpu_jit.pt \
--HL ./data/lang_bpe_500/HL.fst \
--words ./data/lang_bpe_500/words.txt \
./download/LibriSpeech/test-clean/1089/134686/1089-134686-0002.flac \
./download/LibriSpeech/test-clean/1221/135766/1221-135766-0001.flac
Note that to generate ./tdnn/exp/cpu_jit.pt,
you can use ./export.py --jit 1
"""
import argparse
import logging
import math
from typing import Dict, List
import kaldi_hmm_gmm
import kaldifeat
import kaldifst
import torch
import torchaudio
from kaldi_hmm_gmm import DecodableCtc, FasterDecoder, FasterDecoderOptions
from torch.nn.utils.rnn import pad_sequence
def get_parser():
parser = argparse.ArgumentParser(
formatter_class=argparse.ArgumentDefaultsHelpFormatter
)
parser.add_argument(
"--nn-model",
type=str,
required=True,
help="""Path to the torchscript model.
You can use ./tdnn/export.py --jit 1
to obtain it
""",
)
parser.add_argument(
"--words",
type=str,
required=True,
help="Path to words.txt",
)
parser.add_argument("--HL", type=str, required=True, help="Path to HL.fst")
parser.add_argument(
"sound_files",
type=str,
nargs="+",
help="The input sound file(s) to transcribe. "
"Supported formats are those supported by torchaudio.load(). "
"For example, wav and flac are supported. ",
)
return parser
def read_words(words_txt: str) -> Dict[int, str]:
id2word = dict()
with open(words_txt, encoding="utf-8") as f:
for line in f:
word, idx = line.strip().split()
id2word[int(idx)] = word
return id2word
def read_sound_files(
filenames: List[str], expected_sample_rate: float
) -> List[torch.Tensor]:
"""Read a list of sound files into a list 1-D float32 torch tensors.
Args:
filenames:
A list of sound filenames.
expected_sample_rate:
The expected sample rate of the sound files.
Returns:
Return a list of 1-D float32 torch tensors.
"""
ans = []
for f in filenames:
wave, sample_rate = torchaudio.load(f)
if sample_rate != expected_sample_rate:
wave = torchaudio.functional.resample(
wave,
orig_freq=sample_rate,
new_freq=expected_sample_rate,
)
# We use only the first channel
ans.append(wave[0].contiguous())
return ans
def decode(
filename: str,
nnet_output: torch.Tensor,
HL: kaldifst,
id2word: Dict[int, str],
) -> List[str]:
logging.info(f"{filename}, {nnet_output.shape}")
decodable = DecodableCtc(nnet_output)
decoder_opts = FasterDecoderOptions(max_active=3000)
decoder = FasterDecoder(HL, decoder_opts)
decoder.decode(decodable)
if not decoder.reached_final():
print(f"failed to decode {filename}")
return ""
ok, best_path = decoder.get_best_path()
(
ok,
isymbols_out,
osymbols_out,
total_weight,
) = kaldifst.get_linear_symbol_sequence(best_path)
if not ok:
print(f"failed to get linear symbol sequence for {filename}")
return ""
# are shifted by 1 during graph construction
hyps = [id2word[i] for i in osymbols_out]
return hyps
@torch.no_grad()
def main():
parser = get_parser()
args = parser.parse_args()
device = torch.device("cpu")
logging.info(f"device: {device}")
logging.info("Loading torchscript model")
model = torch.jit.load(args.nn_model)
model.eval()
model.to(device)
logging.info(f"Loading HL from {args.HL}")
HL = kaldifst.StdVectorFst.read(args.HL)
sample_rate = 16000
logging.info("Constructing Fbank computer")
opts = kaldifeat.FbankOptions()
opts.device = device
opts.frame_opts.dither = 0
opts.frame_opts.snip_edges = False
opts.frame_opts.samp_freq = sample_rate
opts.mel_opts.num_bins = 80
fbank = kaldifeat.Fbank(opts)
logging.info(f"Reading sound files: {args.sound_files}")
waves = read_sound_files(
filenames=args.sound_files, expected_sample_rate=sample_rate
)
waves = [w.to(device) for w in waves]
logging.info("Decoding started")
features = fbank(waves)
feature_lengths = [f.shape[0] for f in features]
feature_lengths = torch.tensor(feature_lengths)
supervisions = dict()
supervisions["sequence_idx"] = torch.arange(len(features))
supervisions["start_frame"] = torch.zeros(len(features))
supervisions["num_frames"] = feature_lengths
features = pad_sequence(features, batch_first=True, padding_value=math.log(1e-10))
nnet_output, _, _ = model(features, supervisions)
feature_lengths = ((feature_lengths - 1) // 2 - 1) // 2
id2word = read_words(args.words)
hyps = []
for i in range(nnet_output.shape[0]):
hyp = decode(
filename=args.sound_files[i],
nnet_output=nnet_output[i, : feature_lengths[i]],
HL=HL,
id2word=id2word,
)
hyps.append(hyp)
s = "\n"
for filename, hyp in zip(args.sound_files, hyps):
words = " ".join(hyp)
s += f"{filename}:\n{words}\n\n"
logging.info(s)
logging.info("Decoding Done")
if __name__ == "__main__":
formatter = "%(asctime)s %(levelname)s [%(filename)s:%(lineno)d] %(message)s"
logging.basicConfig(format=formatter, level=logging.INFO)
main()

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@ -0,0 +1,127 @@
#!/usr/bin/env python3
# Copyright (c) 2023 Xiaomi Corporation (authors: Fangjun Kuang)
"""
This script takes as input lang_dir containing lexicon_disambig.txt,
tokens.txt, and words.txt and generates the following files:
- H.fst
- HL.fst
Note that saved files are in OpenFst binary format.
Usage:
./local/prepare_lang_fst.py \
--lang-dir ./data/lang_phone \
--has-silence 1
Or
./local/prepare_lang_fst.py \
--lang-dir ./data/lang_bpe_500
"""
import argparse
import logging
from pathlib import Path
import kaldifst
from icefall.ctc import (
Lexicon,
add_disambig_self_loops,
add_one,
build_standard_ctc_topo,
make_lexicon_fst_no_silence,
make_lexicon_fst_with_silence,
)
from icefall.utils import str2bool
def get_args():
parser = argparse.ArgumentParser()
parser.add_argument(
"--lang-dir",
type=str,
help="""Input and output directory.
""",
)
parser.add_argument(
"--has-silence",
type=str2bool,
default=False,
help="True if the lexicon has silence.",
)
return parser.parse_args()
def main():
args = get_args()
lang_dir = args.lang_dir
lexicon = Lexicon(lang_dir)
logging.info("Building standard CTC topology")
max_token_id = max(lexicon.tokens)
H = build_standard_ctc_topo(max_token_id=max_token_id)
# We need to add one to all tokens since we want to use ID 0
# for epsilon
add_one(H, treat_ilabel_zero_specially=False, update_olabel=True)
H.write(f"{lang_dir}/H.fst")
logging.info("Building L")
# Now for HL
if args.has_silence:
L = make_lexicon_fst_with_silence(lexicon, attach_symbol_table=False)
else:
L = make_lexicon_fst_no_silence(lexicon, attach_symbol_table=False)
if args.has_silence:
# We also need to change the input labels of L
add_one(L, treat_ilabel_zero_specially=True, update_olabel=False)
else:
add_one(L, treat_ilabel_zero_specially=False, update_olabel=False)
# Invoke add_disambig_self_loops() so that it eats the disambig symbols
# from L after composition
add_disambig_self_loops(
H,
start=lexicon.token2id["#0"] + 1,
end=lexicon.max_disambig_id + 1,
)
with open("H_1.fst.txt", "w") as f:
print(H, file=f)
kaldifst.arcsort(H, sort_type="olabel")
kaldifst.arcsort(L, sort_type="ilabel")
logging.info("Building HL")
HL = kaldifst.compose(H, L)
kaldifst.determinize_star(HL)
disambig0 = lexicon.token2id["#0"] + 1
max_disambig = lexicon.max_disambig_id + 1
for state in kaldifst.StateIterator(HL):
for arc in kaldifst.ArcIterator(HL, state):
# If treat_ilabel_zero_specially is False, we always change it
# Otherwise, we only change non-zero input labels
if disambig0 <= arc.ilabel <= max_disambig:
arc.ilabel = 0
# Note: We are not composing L with G, so there is no need to add
# self-loops to L to handle #0
HL.write(f"{lang_dir}/HL.fst")
if __name__ == "__main__":
formatter = "%(asctime)s %(levelname)s [%(filename)s:%(lineno)d] %(message)s"
logging.basicConfig(format=formatter, level=logging.INFO)
main()

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@ -242,6 +242,10 @@ if [ $stage -le 6 ] && [ $stop_stage -ge 6 ]; then
$lang_dir/L_disambig.pt \
$lang_dir/L_disambig.fst
fi
if [ ! -f $lang_dir/HL.fst ]; then
./local/prepare_lang_fst.py --lang-dir $lang_dir
fi
done
fi

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@ -1,67 +0,0 @@
#!/usr/bin/env python3
# Copyright (c) 2023 Xiaomi Corporation (authors: Fangjun Kuang)
"""
This script takes as input data/lang_phone containing lexicon_disambig.txt,
tokens.txt, and words.txt and generates the following files:
- H.fst
- HL.fst
TODO(fangjun): Generate HLG.fst
Note that saved files are in OpenFst binary format.
"""
from pathlib import Path
import kaldifst
from icefall.ctc import (
Lexicon,
add_disambig_self_loops,
add_one,
build_standard_ctc_topo,
make_lexicon_fst_with_silence,
)
def main():
lang_dir = Path("data/lang_phone")
lexicon = Lexicon(lang_dir)
max_token_id = max(lexicon.tokens)
H = build_standard_ctc_topo(max_token_id=max_token_id)
# We need to add one to all tokens since we want to use ID 0
# for epsilon
add_one(H, treat_ilabel_zero_specially=False, update_olabel=True)
H.write(f"{lang_dir}/H.fst")
# Now for HL
L = make_lexicon_fst_with_silence(lexicon, attach_symbol_table=False)
# We also need to change the input labels of L
add_one(L, treat_ilabel_zero_specially=True, update_olabel=False)
# Invoke add_disambig_self_loops() so that it eats the disambig symbols
# from L after composition
add_disambig_self_loops(
H,
start=lexicon.token2id["#0"] + 1,
end=lexicon.max_disambig_id,
)
kaldifst.arcsort(H, sort_type="olabel")
kaldifst.arcsort(L, sort_type="ilabel")
HL = kaldifst.compose(H, L)
# Note: We are not composing L with G, so there is no need to add
# self-loops to L to handle #0
HL.write(f"{lang_dir}/HL.fst")
if __name__ == "__main__":
main()

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@ -0,0 +1 @@
../../../librispeech/ASR/local/prepare_lang_fst.py

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@ -60,7 +60,7 @@ if [ $stage -le 3 ] && [ $stop_stage -ge 3 ]; then
) > $lang_dir/lexicon.txt
./local/prepare_lang.py
./local/prepare_lang_fst.py
./local/prepare_lang_fst.py --lang-dir ./data/lang_phone --has-slience 1
fi
if [ $stage -le 4 ] && [ $stop_stage -ge 4 ]; then

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@ -28,11 +28,9 @@ import kaldifeat
import kaldifst
import torch
import torchaudio
from kaldi_hmm_gmm import FasterDecoder, FasterDecoderOptions
from kaldi_hmm_gmm import DecodableCtc, FasterDecoder, FasterDecoderOptions
from torch.nn.utils.rnn import pad_sequence
from icefall.ctc import CtcDecodable
def get_parser():
parser = argparse.ArgumentParser(
@ -113,8 +111,8 @@ def decode(
H: kaldifst,
id2token: Dict[int, str],
) -> List[str]:
decodable = CtcDecodable(nnet_output)
decoder_opts = FasterDecoderOptions()
decodable = DecodableCtc(nnet_output)
decoder_opts = FasterDecoderOptions(max_active=3000)
decoder = FasterDecoder(H, decoder_opts)
decoder.decode(decodable)

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@ -28,11 +28,9 @@ import kaldifeat
import kaldifst
import torch
import torchaudio
from kaldi_hmm_gmm import FasterDecoder, FasterDecoderOptions
from kaldi_hmm_gmm import DecodableCtc, FasterDecoder, FasterDecoderOptions
from torch.nn.utils.rnn import pad_sequence
from icefall.ctc import CtcDecodable
def get_parser():
parser = argparse.ArgumentParser(
@ -113,8 +111,8 @@ def decode(
HL: kaldifst,
id2word: Dict[int, str],
) -> List[str]:
decodable = CtcDecodable(nnet_output)
decoder_opts = FasterDecoderOptions()
decodable = DecodableCtc(nnet_output)
decoder_opts = FasterDecoderOptions(max_active=3000)
decoder = FasterDecoder(HL, decoder_opts)
decoder.decode(decodable)

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@ -1,4 +1,3 @@
from .decodable import CtcDecodable
from .prepare_lang import (
Lexicon,
make_lexicon_fst_no_silence,

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@ -1,30 +0,0 @@
# Copyright 2023 Xiaomi Corp. (author: Fangjun Kuang)
import torch
from kaldi_hmm_gmm import DecodableInterface
class CtcDecodable(DecodableInterface):
"""This class implements the interface
https://github.com/kaldi-asr/kaldi/blob/master/src/itf/decodable-itf.h
"""
def __init__(self, nnet_output: torch.Tensor):
DecodableInterface.__init__(self)
assert nnet_output.ndim == 2, nnet_output.shape
self.nnet_output = nnet_output
def log_likelihood(self, frame: int, index: int) -> float:
# Note: We need to use index - 1 here since
# all the input labels of the H are incremented during graph
# construction
return self.nnet_output[frame][index - 1].item()
def is_last_frame(self, frame: int) -> bool:
return frame == self.nnet_output.shape[0] - 1
def num_frames_ready(self) -> int:
return self.nnet_output.shape[0]
def num_indices(self) -> int:
return self.nnet_output.shape[1]

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@ -5,7 +5,12 @@ from pathlib import Path
import graphviz
import kaldifst
from prepare_lang import Lexicon, make_lexicon_fst_with_silence
import sentencepiece as spm
from prepare_lang import (
Lexicon,
make_lexicon_fst_no_silence,
make_lexicon_fst_with_silence,
)
from topo import add_disambig_self_loops, add_one, build_standard_ctc_topo
@ -85,8 +90,50 @@ def test_yesno():
source.render(outfile="HL_yesno.pdf")
def test_librispeech():
lang_dir = (
"/star-fj/fangjun/open-source/icefall-2/egs/librispeech/ASR/data/lang_bpe_500"
)
if not Path(lang_dir).is_dir():
print(f"{lang_dir} does not exist! Skip testing")
return
lexicon = Lexicon(lang_dir)
HL = kaldifst.StdVectorFst.read(lang_dir + "/HL.fst")
sp = spm.SentencePieceProcessor()
sp.load(lang_dir + "/bpe.model")
i = lexicon.word2id["HELLOA"]
k = lexicon.word2id["WORLD"]
print(i, k)
s = f"""
0 1 {i} {i}
1 2 {k} {k}
2
"""
fst = kaldifst.compile(
s=s,
acceptor=False,
)
L = make_lexicon_fst_no_silence(lexicon, attach_symbol_table=False)
kaldifst.arcsort(L, sort_type="olabel")
with open("L.fst.txt", "w") as f:
print(L, file=f)
fst = kaldifst.compose(L, fst)
print(fst)
fst_dot = kaldifst.draw(fst, acceptor=False, portrait=True)
source = graphviz.Source(fst_dot)
source.render(outfile="a.pdf")
print(sp.encode(["HELLOA", "WORLD"]))
def main():
test_yesno()
test_librispeech()
if __name__ == "__main__":

View File

@ -107,9 +107,8 @@ def add_one(
def add_disambig_self_loops(fst: kaldifst.StdVectorFst, start: int, end: int):
"""Add self-loops to each state.
For each disambig symbol, we add a self-loop with input label 0 and output
label diambig_id of that disambig symbol. Note that input label 0 here
represents an epsilon.
For each disambig symbol, we add a self-loop with input label disambig_id
and output label diambig_id of that disambig symbol.
Args:
fst:
@ -119,14 +118,14 @@ def add_disambig_self_loops(fst: kaldifst.StdVectorFst, start: int, end: int):
end:
The ID of the last disambig symbol. For instance if there are 3
disambig symbols ``#0``, ``#1``, and ``#2``, then ``end`` is the ID
of ``#3``.
of ``#2``.
"""
for state in kaldifst.StateIterator(fst):
for i in range(start, end + 1):
fst.add_arc(
state=state,
arc=kaldifst.StdArc(
ilabel=0,
ilabel=i,
olabel=i,
weight=0,
nextstate=state,