mirror of
https://github.com/ROCm/jax.git
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319ab98980
Notable changes: * use PEP 585 type names * use PEP 604 type union syntax where `from __future__ import annotations` is present. * use f-strings in more places. * remove redundant arguments to open().
701 lines
27 KiB
Python
701 lines
27 KiB
Python
# Copyright 2020 The JAX Authors.
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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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# https://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 collections.abc import Sequence
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from functools import partial
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import math
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import operator
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from typing import Callable, Optional, Union
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import warnings
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import numpy as np
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import scipy.signal as osp_signal
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from scipy.fft import next_fast_len as osp_fft_next_fast_len
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import jax
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import jax.numpy.fft
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import jax.numpy as jnp
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from jax import lax
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from jax._src.api_util import _ensure_index_tuple
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from jax._src import dtypes
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from jax._src.lax.lax import PrecisionLike
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from jax._src.numpy import linalg
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from jax._src.numpy.util import (
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check_arraylike, _wraps, promote_dtypes_inexact, promote_dtypes_complex)
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from jax._src.third_party.scipy import signal_helper
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from jax._src.typing import Array, ArrayLike
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from jax._src.util import canonicalize_axis, tuple_delete, tuple_insert
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@_wraps(osp_signal.fftconvolve)
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def fftconvolve(in1: ArrayLike, in2: ArrayLike, mode: str = "full",
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axes: Optional[Sequence[int]] = None) -> Array:
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check_arraylike('fftconvolve', in1, in2)
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in1, in2 = promote_dtypes_inexact(in1, in2)
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if in1.ndim != in2.ndim:
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raise ValueError("in1 and in2 should have the same dimensionality")
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if mode not in ["same", "full", "valid"]:
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raise ValueError("mode must be one of ['same', 'full', 'valid']")
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_fftconvolve = partial(_fftconvolve_unbatched, mode=mode)
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if axes is None:
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return _fftconvolve(in1, in2)
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axes = _ensure_index_tuple(axes)
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axes = tuple(canonicalize_axis(ax, in1.ndim) for ax in axes)
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mapped_axes = set(range(in1.ndim)) - set(axes)
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if any(in1.shape[i] != in2.shape[i] for i in mapped_axes):
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raise ValueError(f"mapped axes must have same shape; got {in1.shape=} {in2.shape=} {axes=}")
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for ax in sorted(mapped_axes):
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_fftconvolve = jax.vmap(_fftconvolve, in_axes=ax, out_axes=ax)
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return _fftconvolve(in1, in2)
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def _fftconvolve_unbatched(in1: Array, in2: Array, mode: str) -> Array:
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full_shape = tuple(s1 + s2 - 1 for s1, s2 in zip(in1.shape, in2.shape))
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fft_shape = tuple(osp_fft_next_fast_len(s) for s in full_shape)
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if mode == 'valid':
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no_swap = all(s1 >= s2 for s1, s2 in zip(in1.shape, in2.shape))
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swap = all(s1 <= s2 for s1, s2 in zip(in1.shape, in2.shape))
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if not (no_swap or swap):
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raise ValueError("For 'valid' mode, One input must be at least as "
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"large as the other in every dimension.")
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if swap:
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in1, in2 = in2, in1
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if jnp.iscomplexobj(in1):
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fft, ifft = jnp.fft.fftn, jnp.fft.ifftn
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else:
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fft, ifft = jnp.fft.rfftn, jnp.fft.irfftn
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sp1 = fft(in1, fft_shape)
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sp2 = fft(in2, fft_shape)
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conv = ifft(sp1 * sp2, fft_shape)
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if mode == "full":
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out_shape = full_shape
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elif mode == "same":
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out_shape = in1.shape
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elif mode == "valid":
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out_shape = tuple(s1 - s2 + 1 for s1, s2 in zip(in1.shape, in2.shape))
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else:
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raise ValueError(f"Unrecognized {mode=}")
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start_indices = tuple((full_size - out_size) // 2
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for full_size, out_size in zip(full_shape, out_shape))
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return lax.dynamic_slice(conv, start_indices, out_shape)
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# Note: we do not re-use the code from jax.numpy.convolve here, because the handling
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# of padding differs slightly between the two implementations (particularly for
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# mode='same').
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def _convolve_nd(in1: Array, in2: Array, mode: str, *, precision: PrecisionLike) -> Array:
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if mode not in ["full", "same", "valid"]:
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raise ValueError("mode must be one of ['full', 'same', 'valid']")
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if in1.ndim != in2.ndim:
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raise ValueError("in1 and in2 must have the same number of dimensions")
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if in1.size == 0 or in2.size == 0:
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raise ValueError(f"zero-size arrays not supported in convolutions, got shapes {in1.shape} and {in2.shape}.")
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in1, in2 = promote_dtypes_inexact(in1, in2)
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no_swap = all(s1 >= s2 for s1, s2 in zip(in1.shape, in2.shape))
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swap = all(s1 <= s2 for s1, s2 in zip(in1.shape, in2.shape))
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if not (no_swap or swap):
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raise ValueError("One input must be smaller than the other in every dimension.")
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shape_o = in2.shape
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if swap:
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in1, in2 = in2, in1
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shape = in2.shape
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in2 = jnp.flip(in2)
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if mode == 'valid':
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padding = [(0, 0) for s in shape]
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elif mode == 'same':
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padding = [(s - 1 - (s_o - 1) // 2, s - s_o + (s_o - 1) // 2)
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for (s, s_o) in zip(shape, shape_o)]
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elif mode == 'full':
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padding = [(s - 1, s - 1) for s in shape]
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strides = tuple(1 for s in shape)
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result = lax.conv_general_dilated(in1[None, None], in2[None, None], strides,
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padding, precision=precision)
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return result[0, 0]
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@_wraps(osp_signal.convolve)
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def convolve(in1: Array, in2: Array, mode: str = 'full', method: str = 'auto',
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precision: PrecisionLike = None) -> Array:
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if method == 'fft':
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return fftconvolve(in1, in2, mode=mode)
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elif method in ['direct', 'auto']:
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return _convolve_nd(in1, in2, mode, precision=precision)
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else:
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raise ValueError(f"Got {method=}; expected 'auto', 'fft', or 'direct'.")
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@_wraps(osp_signal.convolve2d)
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def convolve2d(in1: Array, in2: Array, mode: str = 'full', boundary: str = 'fill',
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fillvalue: float = 0, precision: PrecisionLike = None) -> Array:
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if boundary != 'fill' or fillvalue != 0:
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raise NotImplementedError("convolve2d() only supports boundary='fill', fillvalue=0")
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if jnp.ndim(in1) != 2 or jnp.ndim(in2) != 2:
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raise ValueError("convolve2d() only supports 2-dimensional inputs.")
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return _convolve_nd(in1, in2, mode, precision=precision)
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@_wraps(osp_signal.correlate)
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def correlate(in1: Array, in2: Array, mode: str = 'full', method: str = 'auto',
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precision: PrecisionLike = None) -> Array:
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return convolve(in1, jnp.flip(in2.conj()), mode, precision=precision, method=method)
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@_wraps(osp_signal.correlate2d)
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def correlate2d(in1: Array, in2: Array, mode: str = 'full', boundary: str = 'fill',
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fillvalue: float = 0, precision: PrecisionLike = None) -> Array:
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if boundary != 'fill' or fillvalue != 0:
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raise NotImplementedError("correlate2d() only supports boundary='fill', fillvalue=0")
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if jnp.ndim(in1) != 2 or jnp.ndim(in2) != 2:
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raise ValueError("correlate2d() only supports 2-dimensional inputs.")
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swap = all(s1 <= s2 for s1, s2 in zip(in1.shape, in2.shape))
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same_shape = all(s1 == s2 for s1, s2 in zip(in1.shape, in2.shape))
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if mode == "same":
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in1, in2 = jnp.flip(in1), in2.conj()
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result = jnp.flip(_convolve_nd(in1, in2, mode, precision=precision))
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elif mode == "valid":
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if swap and not same_shape:
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in1, in2 = jnp.flip(in2), in1.conj()
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result = _convolve_nd(in1, in2, mode, precision=precision)
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else:
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in1, in2 = jnp.flip(in1), in2.conj()
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result = jnp.flip(_convolve_nd(in1, in2, mode, precision=precision))
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else:
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if swap:
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in1, in2 = jnp.flip(in2), in1.conj()
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result = _convolve_nd(in1, in2, mode, precision=precision).conj()
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else:
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in1, in2 = jnp.flip(in1), in2.conj()
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result = jnp.flip(_convolve_nd(in1, in2, mode, precision=precision))
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return result
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@_wraps(osp_signal.detrend)
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def detrend(data: ArrayLike, axis: int = -1, type: str = 'linear', bp: int = 0,
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overwrite_data: None = None) -> Array:
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if overwrite_data is not None:
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raise NotImplementedError("overwrite_data argument not implemented.")
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if type not in ['constant', 'linear']:
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raise ValueError("Trend type must be 'linear' or 'constant'.")
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data_arr, = promote_dtypes_inexact(jnp.asarray(data))
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if type == 'constant':
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return data_arr - data_arr.mean(axis, keepdims=True)
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else:
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N = data_arr.shape[axis]
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# bp is static, so we use np operations to avoid pushing to device.
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bp_arr = np.sort(np.unique(np.r_[0, bp, N]))
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if bp_arr[0] < 0 or bp_arr[-1] > N:
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raise ValueError("Breakpoints must be non-negative and less than length of data along given axis.")
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data_arr = jnp.moveaxis(data_arr, axis, 0)
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shape = data_arr.shape
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data_arr = data_arr.reshape(N, -1)
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for m in range(len(bp_arr) - 1):
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Npts = bp_arr[m + 1] - bp_arr[m]
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A = jnp.vstack([
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jnp.ones(Npts, dtype=data_arr.dtype),
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jnp.arange(1, Npts + 1, dtype=data_arr.dtype) / Npts.astype(data_arr.dtype)
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]).T
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sl = slice(bp_arr[m], bp_arr[m + 1])
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coef, *_ = linalg.lstsq(A, data_arr[sl])
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data_arr = data_arr.at[sl].add(-jnp.matmul(A, coef, precision=lax.Precision.HIGHEST))
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return jnp.moveaxis(data_arr.reshape(shape), 0, axis)
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def _fft_helper(x: Array, win: Array, detrend_func: Callable[[Array], Array],
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nperseg: int, noverlap: int, nfft: Optional[int], sides: str) -> Array:
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"""Calculate windowed FFT in the same way the original SciPy does.
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"""
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if x.dtype.kind == 'i':
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x = x.astype(win.dtype)
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*batch_shape, signal_length = x.shape
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# Created strided array of data segments
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if nperseg == 1 and noverlap == 0:
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result = x[..., np.newaxis]
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else:
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step = nperseg - noverlap
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batch_shape = list(batch_shape)
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x = x.reshape((math.prod(batch_shape), signal_length, 1))
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result = jax.lax.conv_general_dilated_patches(
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x, (nperseg,), (step,),
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'VALID',
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dimension_numbers=('NTC', 'OIT', 'NTC'))
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result = result.reshape(*batch_shape, *result.shape[-2:])
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# Detrend each data segment individually
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result = detrend_func(result)
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# Apply window by multiplication
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if jnp.iscomplexobj(win):
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result, = promote_dtypes_complex(result)
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result = win.reshape((1,) * len(batch_shape) + (1, nperseg)) * result
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# Perform the fft on last axis. Zero-pads automatically
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if sides == 'twosided':
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return jax.numpy.fft.fft(result, n=nfft)
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else:
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return jax.numpy.fft.rfft(result.real, n=nfft)
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def odd_ext(x: Array, n: int, axis: int = -1) -> Array:
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"""Extends `x` along with `axis` by odd-extension.
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This function was previously a part of "scipy.signal.signaltools" but is no
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longer exposed.
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Args:
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x : input array
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n : the number of points to be added to the both end
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axis: the axis to be extended
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"""
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if n < 1:
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return x
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if n > x.shape[axis] - 1:
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raise ValueError(
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f"The extension length n ({n}) is too big. "
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f"It must not exceed x.shape[axis]-1, which is {x.shape[axis] - 1}.")
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left_end = lax.slice_in_dim(x, 0, 1, axis=axis)
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left_ext = jnp.flip(lax.slice_in_dim(x, 1, n + 1, axis=axis), axis=axis)
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right_end = lax.slice_in_dim(x, -1, None, axis=axis)
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right_ext = jnp.flip(lax.slice_in_dim(x, -(n + 1), -1, axis=axis), axis=axis)
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ext = jnp.concatenate((2 * left_end - left_ext,
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x,
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2 * right_end - right_ext),
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axis=axis)
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return ext
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def _spectral_helper(x: Array, y: Optional[ArrayLike], fs: ArrayLike = 1.0,
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window: str = 'hann', nperseg: Optional[int] = None,
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noverlap: Optional[int] = None, nfft: Optional[int] = None,
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detrend_type: Union[bool, str, Callable[[Array], Array]] = 'constant',
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return_onesided: bool = True, scaling: str = 'density',
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axis: int = -1, mode: str = 'psd', boundary: Optional[str] = None,
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padded: bool = False) -> tuple[Array, Array, Array]:
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"""LAX-backend implementation of `scipy.signal._spectral_helper`.
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Unlike the original helper function, `y` can be None for explicitly
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indicating auto-spectral (non cross-spectral) computation. In addition to
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this, `detrend` argument is renamed to `detrend_type` for avoiding internal
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name overlap.
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"""
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if mode not in ('psd', 'stft'):
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raise ValueError(f"Unknown value for mode {mode}, "
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"must be one of: ('psd', 'stft')")
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def make_pad(mode, **kwargs):
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def pad(x, n, axis=-1):
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pad_width = [(0, 0) for unused_n in range(x.ndim)]
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pad_width[axis] = (n, n)
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return jnp.pad(x, pad_width, mode, **kwargs)
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return pad
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boundary_funcs = {
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'even': make_pad('reflect'),
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'odd': odd_ext,
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'constant': make_pad('edge'),
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'zeros': make_pad('constant', constant_values=0.0),
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None: lambda x, *args, **kwargs: x
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}
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# Check/ normalize inputs
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if boundary not in boundary_funcs:
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raise ValueError(
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f"Unknown boundary option '{boundary}', "
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f"must be one of: {list(boundary_funcs.keys())}")
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axis = jax.core.concrete_or_error(operator.index, axis,
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"axis of windowed-FFT")
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axis = canonicalize_axis(axis, x.ndim)
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if y is None:
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check_arraylike('spectral_helper', x)
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x, = promote_dtypes_inexact(x)
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y_arr = x # place-holder for type checking
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outershape = tuple_delete(x.shape, axis)
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else:
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if mode != 'psd':
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raise ValueError("two-argument mode is available only when mode=='psd'")
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check_arraylike('spectral_helper', x, y)
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x, y_arr = promote_dtypes_inexact(x, y)
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if x.ndim != y_arr.ndim:
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raise ValueError("two-arguments must have the same rank ({x.ndim} vs {y.ndim}).")
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# Check if we can broadcast the outer axes together
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try:
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outershape = jnp.broadcast_shapes(tuple_delete(x.shape, axis),
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tuple_delete(y_arr.shape, axis))
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except ValueError as err:
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raise ValueError('x and y cannot be broadcast together.') from err
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result_dtype = dtypes.to_complex_dtype(x.dtype)
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freq_dtype = np.finfo(result_dtype).dtype
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nperseg_int: int = 0
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nfft_int: int = 0
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noverlap_int: int = 0
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if nperseg is not None: # if specified by user
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nperseg_int = jax.core.concrete_or_error(int, nperseg,
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"nperseg of windowed-FFT")
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if nperseg_int < 1: # type: ignore[operator]
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raise ValueError('nperseg must be a positive integer')
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# parse window; if array like, then set nperseg = win.shape
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win, nperseg_int = signal_helper._triage_segments(
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window, nperseg if nperseg is None else nperseg_int,
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input_length=x.shape[axis], dtype=x.dtype)
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if noverlap is None:
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noverlap_int = nperseg_int // 2 # type: ignore[operator]
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else:
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noverlap_int = jax.core.concrete_or_error(int, noverlap,
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"noverlap of windowed-FFT")
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if nfft is None:
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nfft_int = nperseg_int
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else:
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nfft_int = jax.core.concrete_or_error(int, nfft,
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"nfft of windowed-FFT")
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# Special cases for size == 0
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if y is None:
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if x.size == 0:
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return jnp.zeros(x.shape, freq_dtype), jnp.zeros(x.shape, freq_dtype), jnp.zeros(x.shape, result_dtype)
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else:
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if x.size == 0 or y_arr.size == 0:
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shape = tuple_insert(outershape, min([x.shape[axis], y_arr.shape[axis]]), axis)
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return jnp.zeros(shape, freq_dtype), jnp.zeros(shape, freq_dtype), jnp.zeros(shape, result_dtype)
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# Move time-axis to the end
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x = jnp.moveaxis(x, axis, -1)
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if y is not None and y_arr.ndim > 1:
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y_arr = jnp.moveaxis(y_arr, axis, -1)
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# Check if x and y are the same length, zero-pad if necessary
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if y is not None and x.shape[-1] != y_arr.shape[-1]:
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if x.shape[-1] < y_arr.shape[-1]:
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pad_shape = list(x.shape)
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pad_shape[-1] = y_arr.shape[-1] - x.shape[-1]
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x = jnp.concatenate((x, jnp.zeros_like(x, shape=pad_shape)), -1)
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else:
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pad_shape = list(y_arr.shape)
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pad_shape[-1] = x.shape[-1] - y_arr.shape[-1]
|
|
y_arr = jnp.concatenate((y_arr, jnp.zeros_like(x, shape=pad_shape)), -1)
|
|
|
|
if nfft_int < nperseg_int:
|
|
raise ValueError('nfft must be greater than or equal to nperseg.')
|
|
if noverlap_int >= nperseg_int:
|
|
raise ValueError('noverlap must be less than nperseg.')
|
|
nstep = nperseg_int - noverlap_int
|
|
|
|
# Apply paddings
|
|
if boundary is not None:
|
|
ext_func = boundary_funcs[boundary]
|
|
x = ext_func(x, nperseg_int // 2, axis=-1)
|
|
if y is not None:
|
|
y_arr = ext_func(y_arr, nperseg_int // 2, axis=-1)
|
|
|
|
if padded:
|
|
# Pad to integer number of windowed segments
|
|
# I.e make x.shape[-1] = nperseg + (nseg-1)*nstep, with integer nseg
|
|
nadd = (-(x.shape[-1]-nperseg_int) % nstep) % nperseg_int
|
|
x = jnp.concatenate((x, jnp.zeros_like(x, shape=(*x.shape[:-1], nadd))), axis=-1)
|
|
if y is not None:
|
|
y_arr = jnp.concatenate((y_arr, jnp.zeros_like(x, shape=(*y_arr.shape[:-1], nadd))), axis=-1)
|
|
|
|
# Handle detrending and window functions
|
|
if not detrend_type:
|
|
detrend_func = lambda d: d
|
|
elif not callable(detrend_type):
|
|
detrend_func = partial(detrend, type=detrend_type, axis=-1)
|
|
elif axis != -1:
|
|
# Wrap this function so that it receives a shape that it could
|
|
# reasonably expect to receive.
|
|
def detrend_func(d):
|
|
d = jnp.moveaxis(d, axis, -1)
|
|
d = detrend_type(d)
|
|
return jnp.moveaxis(d, -1, axis)
|
|
else:
|
|
detrend_func = detrend_type
|
|
|
|
# Determine scale
|
|
if scaling == 'density':
|
|
scale = 1.0 / (fs * (win * win).sum())
|
|
elif scaling == 'spectrum':
|
|
scale = 1.0 / win.sum()**2
|
|
else:
|
|
raise ValueError(f'Unknown scaling: {scaling}')
|
|
if mode == 'stft':
|
|
scale = jnp.sqrt(scale)
|
|
scale, = promote_dtypes_complex(scale)
|
|
|
|
# Determine onesided/ two-sided
|
|
if return_onesided:
|
|
sides = 'onesided'
|
|
if jnp.iscomplexobj(x) or jnp.iscomplexobj(y):
|
|
sides = 'twosided'
|
|
warnings.warn('Input data is complex, switching to '
|
|
'return_onesided=False')
|
|
else:
|
|
sides = 'twosided'
|
|
|
|
if sides == 'twosided':
|
|
freqs = jax.numpy.fft.fftfreq(nfft_int, 1/fs, dtype=freq_dtype)
|
|
elif sides == 'onesided':
|
|
freqs = jax.numpy.fft.rfftfreq(nfft_int, 1/fs, dtype=freq_dtype)
|
|
|
|
# Perform the windowed FFTs
|
|
result = _fft_helper(x, win, detrend_func,
|
|
nperseg_int, noverlap_int, nfft_int, sides)
|
|
|
|
if y is not None:
|
|
# All the same operations on the y data
|
|
result_y = _fft_helper(y_arr, win, detrend_func,
|
|
nperseg_int, noverlap_int, nfft_int, sides)
|
|
result = jnp.conjugate(result) * result_y
|
|
elif mode == 'psd':
|
|
result = jnp.conjugate(result) * result
|
|
|
|
result *= scale
|
|
|
|
if sides == 'onesided' and mode == 'psd':
|
|
end = None if nfft_int % 2 else -1
|
|
result = result.at[..., 1:end].mul(2)
|
|
|
|
time = jnp.arange(nperseg_int / 2, x.shape[-1] - nperseg_int / 2 + 1,
|
|
nperseg_int - noverlap_int, dtype=freq_dtype) / fs
|
|
if boundary is not None:
|
|
time -= (nperseg_int / 2) / fs
|
|
|
|
result = result.astype(result_dtype)
|
|
|
|
# All imaginary parts are zero anyways
|
|
if y is None and mode != 'stft':
|
|
result = result.real
|
|
|
|
# Move frequency axis back to axis where the data came from
|
|
result = jnp.moveaxis(result, -1, axis)
|
|
|
|
return freqs, time, result
|
|
|
|
|
|
@_wraps(osp_signal.stft)
|
|
def stft(x: Array, fs: ArrayLike = 1.0, window: str = 'hann', nperseg: int = 256,
|
|
noverlap: Optional[int] = None, nfft: Optional[int] = None,
|
|
detrend: bool = False, return_onesided: bool = True, boundary: Optional[str] = 'zeros',
|
|
padded: bool = True, axis: int = -1) -> tuple[Array, Array, Array]:
|
|
return _spectral_helper(x, None, fs, window, nperseg, noverlap,
|
|
nfft, detrend, return_onesided,
|
|
scaling='spectrum', axis=axis,
|
|
mode='stft', boundary=boundary,
|
|
padded=padded)
|
|
|
|
|
|
_csd_description = """
|
|
The original SciPy function exhibits slightly different behavior between
|
|
``csd(x, x)``` and ```csd(x, x.copy())```. The LAX-backend version is designed
|
|
to follow the latter behavior. For using the former behavior, call this
|
|
function as `csd(x, None)`."""
|
|
|
|
|
|
@_wraps(osp_signal.csd, lax_description=_csd_description)
|
|
def csd(x: Array, y: Optional[ArrayLike], fs: ArrayLike = 1.0, window: str = 'hann',
|
|
nperseg: Optional[int] = None, noverlap: Optional[int] = None,
|
|
nfft: Optional[int] = None, detrend: str = 'constant',
|
|
return_onesided: bool = True, scaling: str = 'density',
|
|
axis: int = -1, average: str = 'mean') -> tuple[Array, Array]:
|
|
freqs, _, Pxy = _spectral_helper(x, y, fs, window, nperseg, noverlap, nfft,
|
|
detrend, return_onesided, scaling, axis,
|
|
mode='psd')
|
|
if y is not None:
|
|
Pxy = Pxy + 0j # Ensure complex output when x is not y
|
|
|
|
# Average over windows.
|
|
if Pxy.ndim >= 2 and Pxy.size > 0:
|
|
if Pxy.shape[-1] > 1:
|
|
if average == 'median':
|
|
bias = signal_helper._median_bias(Pxy.shape[-1]).astype(Pxy.dtype)
|
|
if jnp.iscomplexobj(Pxy):
|
|
Pxy = (jnp.median(jnp.real(Pxy), axis=-1)
|
|
+ 1j * jnp.median(jnp.imag(Pxy), axis=-1))
|
|
else:
|
|
Pxy = jnp.median(Pxy, axis=-1)
|
|
Pxy /= bias
|
|
elif average == 'mean':
|
|
Pxy = Pxy.mean(axis=-1)
|
|
else:
|
|
raise ValueError(f'average must be "median" or "mean", got {average}')
|
|
else:
|
|
Pxy = jnp.reshape(Pxy, Pxy.shape[:-1])
|
|
|
|
return freqs, Pxy
|
|
|
|
|
|
@_wraps(osp_signal.welch)
|
|
def welch(x: Array, fs: ArrayLike = 1.0, window: str = 'hann',
|
|
nperseg: Optional[int] = None, noverlap: Optional[int] = None,
|
|
nfft: Optional[int] = None, detrend: str = 'constant',
|
|
return_onesided: bool = True, scaling: str = 'density',
|
|
axis: int = -1, average: str = 'mean') -> tuple[Array, Array]:
|
|
freqs, Pxx = csd(x, None, fs=fs, window=window, nperseg=nperseg,
|
|
noverlap=noverlap, nfft=nfft, detrend=detrend,
|
|
return_onesided=return_onesided, scaling=scaling,
|
|
axis=axis, average=average)
|
|
|
|
return freqs, Pxx.real
|
|
|
|
|
|
def _overlap_and_add(x: Array, step_size: int) -> Array:
|
|
"""Utility function compatible with tf.signal.overlap_and_add.
|
|
|
|
Args:
|
|
x: An array with `(..., frames, frame_length)`-shape.
|
|
step_size: An integer denoting overlap offsets. Must be less than
|
|
`frame_length`.
|
|
|
|
Returns:
|
|
An array with `(..., output_size)`-shape containing overlapped signal.
|
|
"""
|
|
check_arraylike("_overlap_and_add", x)
|
|
step_size = jax.core.concrete_or_error(int, step_size,
|
|
"step_size for overlap_and_add")
|
|
if x.ndim < 2:
|
|
raise ValueError('Input must have (..., frames, frame_length) shape.')
|
|
|
|
*batch_shape, nframes, segment_len = x.shape
|
|
flat_batchsize = math.prod(batch_shape)
|
|
x = x.reshape((flat_batchsize, nframes, segment_len))
|
|
output_size = step_size * (nframes - 1) + segment_len
|
|
nstep_per_segment = 1 + (segment_len - 1) // step_size
|
|
|
|
# Here, we use shorter notation for axes.
|
|
# B: batch_size, N: nframes, S: nstep_per_segment,
|
|
# T: segment_len divided by S
|
|
|
|
padded_segment_len = nstep_per_segment * step_size
|
|
x = jnp.pad(x, ((0, 0), (0, 0), (0, padded_segment_len - segment_len)))
|
|
x = x.reshape((flat_batchsize, nframes, nstep_per_segment, step_size))
|
|
|
|
# For obtaining shifted signals, this routine reinterprets flattened array
|
|
# with a shrinked axis. With appropriate truncation/ padding, this operation
|
|
# pushes the last padded elements of the previous row to the head of the
|
|
# current row.
|
|
# See implementation of `overlap_and_add` in Tensorflow for details.
|
|
x = x.transpose((0, 2, 1, 3)) # x: (B, S, N, T)
|
|
x = jnp.pad(x, ((0, 0), (0, 0), (0, nframes), (0, 0))) # x: (B, S, N*2, T)
|
|
shrinked = x.shape[2] - 1
|
|
x = x.reshape((flat_batchsize, -1))
|
|
x = x[:, :(nstep_per_segment * shrinked * step_size)]
|
|
x = x.reshape((flat_batchsize, nstep_per_segment, shrinked * step_size))
|
|
|
|
# Finally, sum shifted segments, and truncate results to the output_size.
|
|
x = x.sum(axis=1)[:, :output_size]
|
|
return x.reshape(tuple(batch_shape) + (-1,))
|
|
|
|
|
|
@_wraps(osp_signal.istft)
|
|
def istft(Zxx: Array, fs: ArrayLike = 1.0, window: str = 'hann',
|
|
nperseg: Optional[int] = None, noverlap: Optional[int] = None,
|
|
nfft: Optional[int] = None, input_onesided: bool = True,
|
|
boundary: bool = True, time_axis: int = -1,
|
|
freq_axis: int = -2) -> tuple[Array, Array]:
|
|
# Input validation
|
|
check_arraylike("istft", Zxx)
|
|
if Zxx.ndim < 2:
|
|
raise ValueError('Input stft must be at least 2d!')
|
|
freq_axis = canonicalize_axis(freq_axis, Zxx.ndim)
|
|
time_axis = canonicalize_axis(time_axis, Zxx.ndim)
|
|
if freq_axis == time_axis:
|
|
raise ValueError('Must specify differing time and frequency axes!')
|
|
|
|
Zxx = jnp.asarray(Zxx, dtype=jax.dtypes.canonicalize_dtype(
|
|
np.result_type(Zxx, np.complex64)))
|
|
|
|
n_default = (2 * (Zxx.shape[freq_axis] - 1) if input_onesided
|
|
else Zxx.shape[freq_axis])
|
|
|
|
nperseg_int = jax.core.concrete_or_error(int, nperseg or n_default,
|
|
"nperseg: segment length of STFT")
|
|
if nperseg_int < 1:
|
|
raise ValueError('nperseg must be a positive integer')
|
|
|
|
nfft_int: int = 0
|
|
if nfft is None:
|
|
nfft_int = n_default
|
|
if input_onesided and nperseg_int == n_default + 1:
|
|
nfft_int += 1 # Odd nperseg, no FFT padding
|
|
else:
|
|
nfft_int = jax.core.concrete_or_error(int, nfft, "nfft of STFT")
|
|
if nfft_int < nperseg_int:
|
|
raise ValueError(
|
|
f'FFT length ({nfft_int}) must be longer than nperseg ({nperseg_int}).')
|
|
|
|
noverlap_int = jax.core.concrete_or_error(int, noverlap or nperseg_int // 2,
|
|
"noverlap of STFT")
|
|
if noverlap_int >= nperseg_int:
|
|
raise ValueError('noverlap must be less than nperseg.')
|
|
nstep = nperseg_int - noverlap_int
|
|
|
|
# Rearrange axes if necessary
|
|
if time_axis != Zxx.ndim - 1 or freq_axis != Zxx.ndim - 2:
|
|
outer_idxs = tuple(
|
|
idx for idx in range(Zxx.ndim) if idx not in {time_axis, freq_axis})
|
|
Zxx = jnp.transpose(Zxx, outer_idxs + (freq_axis, time_axis))
|
|
|
|
# Perform IFFT
|
|
ifunc = jax.numpy.fft.irfft if input_onesided else jax.numpy.fft.ifft
|
|
# xsubs: [..., T, N], N is the number of frames, T is the frame length.
|
|
xsubs = ifunc(Zxx, axis=-2, n=nfft)[..., :nperseg_int, :]
|
|
|
|
# Get window as array
|
|
if isinstance(window, (str, tuple)):
|
|
win = osp_signal.get_window(window, nperseg_int)
|
|
win = jnp.asarray(win, dtype=xsubs.dtype)
|
|
else:
|
|
win = jnp.asarray(window)
|
|
if len(win.shape) != 1:
|
|
raise ValueError('window must be 1-D')
|
|
if win.shape[0] != nperseg_int:
|
|
raise ValueError(f'window must have length of {nperseg_int}')
|
|
xsubs *= win.sum() # This takes care of the 'spectrum' scaling
|
|
|
|
# make win broadcastable over xsubs
|
|
win = win.reshape((1, ) * (xsubs.ndim - 2) + win.shape + (1,))
|
|
x = _overlap_and_add((xsubs * win).swapaxes(-2, -1), nstep)
|
|
win_squared = jnp.repeat((win * win), xsubs.shape[-1], axis=-1)
|
|
norm = _overlap_and_add(win_squared.swapaxes(-2, -1), nstep)
|
|
|
|
# Remove extension points
|
|
if boundary:
|
|
x = x[..., nperseg_int//2:-(nperseg_int//2)]
|
|
norm = norm[..., nperseg_int//2:-(nperseg_int//2)]
|
|
x /= jnp.where(norm > 1e-10, norm, 1.0)
|
|
|
|
# Put axes back
|
|
if x.ndim > 1:
|
|
if time_axis != Zxx.ndim - 1:
|
|
if freq_axis < time_axis:
|
|
time_axis -= 1
|
|
x = jnp.moveaxis(x, -1, time_axis)
|
|
|
|
time = jnp.arange(x.shape[0], dtype=np.finfo(x.dtype).dtype) / fs
|
|
return time, x
|