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# 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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from typing import Callable
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import mcd.metrics as mt
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import numpy as np
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from mcd import dtw
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__all__ = [
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'mcd_distance',
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]
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def mcd_distance(xs: np.ndarray,
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ys: np.ndarray,
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cost_fn: Callable=mt.logSpecDbDist) -> float:
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"""Mel cepstral distortion (MCD), dtw distance.
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Dynamic Time Warping.
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Uses dynamic programming to compute:
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Examples:
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.. code-block:: python
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wps[i, j] = cost_fn(xs[i], ys[j]) + min(
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wps[i-1, j ], // vertical / insertion / expansion
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wps[i , j-1], // horizontal / deletion / compression
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wps[i-1, j-1]) // diagonal / match
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dtw = sqrt(wps[-1, -1])
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Cost Function:
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Examples:
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.. code-block:: python
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logSpecDbConst = 10.0 / math.log(10.0) * math.sqrt(2.0)
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def logSpecDbDist(x, y):
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diff = x - y
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return logSpecDbConst * math.sqrt(np.inner(diff, diff))
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Args:
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xs (np.ndarray): ref sequence, [T,D]
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ys (np.ndarray): hyp sequence, [T,D]
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cost_fn (Callable, optional): Cost function. Defaults to mt.logSpecDbDist.
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Returns:
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float: dtw distance
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"""
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min_cost, path = dtw.dtw(xs, ys, cost_fn)
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return min_cost
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