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ai-content-maker/.venv/Lib/site-packages/librosa/util/utils.py

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#!/usr/bin/env python
# -*- coding: utf-8 -*-
"""Utility functions"""
from __future__ import annotations
import scipy.ndimage
import scipy.sparse
import numpy as np
import numba
from numpy.lib.stride_tricks import as_strided
from .._cache import cache
from .exceptions import ParameterError
from .deprecation import Deprecated
from numpy.typing import ArrayLike, DTypeLike
from typing import (
Any,
Callable,
Iterable,
List,
Dict,
Optional,
Sequence,
Tuple,
TypeVar,
Union,
overload,
)
from typing_extensions import Literal
from .._typing import _SequenceLike, _FloatLike_co, _ComplexLike_co
# Constrain STFT block sizes to 256 KB
MAX_MEM_BLOCK = 2**8 * 2**10
__all__ = [
"MAX_MEM_BLOCK",
"frame",
"pad_center",
"expand_to",
"fix_length",
"valid_audio",
"valid_int",
"is_positive_int",
"valid_intervals",
"fix_frames",
"axis_sort",
"localmax",
"localmin",
"normalize",
"peak_pick",
"sparsify_rows",
"shear",
"stack",
"fill_off_diagonal",
"index_to_slice",
"sync",
"softmask",
"buf_to_float",
"tiny",
"cyclic_gradient",
"dtype_r2c",
"dtype_c2r",
"count_unique",
"is_unique",
"abs2",
"phasor",
]
def frame(
x: np.ndarray,
*,
frame_length: int,
hop_length: int,
axis: int = -1,
writeable: bool = False,
subok: bool = False,
) -> np.ndarray:
"""Slice a data array into (overlapping) frames.
This implementation uses low-level stride manipulation to avoid
making a copy of the data. The resulting frame representation
is a new view of the same input data.
For example, a one-dimensional input ``x = [0, 1, 2, 3, 4, 5, 6]``
can be framed with frame length 3 and hop length 2 in two ways.
The first (``axis=-1``), results in the array ``x_frames``::
[[0, 2, 4],
[1, 3, 5],
[2, 4, 6]]
where each column ``x_frames[:, i]`` contains a contiguous slice of
the input ``x[i * hop_length : i * hop_length + frame_length]``.
The second way (``axis=0``) results in the array ``x_frames``::
[[0, 1, 2],
[2, 3, 4],
[4, 5, 6]]
where each row ``x_frames[i]`` contains a contiguous slice of the input.
This generalizes to higher dimensional inputs, as shown in the examples below.
In general, the framing operation increments by 1 the number of dimensions,
adding a new "frame axis" either before the framing axis (if ``axis < 0``)
or after the framing axis (if ``axis >= 0``).
Parameters
----------
x : np.ndarray
Array to frame
frame_length : int > 0 [scalar]
Length of the frame
hop_length : int > 0 [scalar]
Number of steps to advance between frames
axis : int
The axis along which to frame.
writeable : bool
If ``True``, then the framed view of ``x`` is read-only.
If ``False``, then the framed view is read-write. Note that writing to the framed view
will also write to the input array ``x`` in this case.
subok : bool
If True, sub-classes will be passed-through, otherwise the returned array will be
forced to be a base-class array (default).
Returns
-------
x_frames : np.ndarray [shape=(..., frame_length, N_FRAMES, ...)]
A framed view of ``x``, for example with ``axis=-1`` (framing on the last dimension)::
x_frames[..., j] == x[..., j * hop_length : j * hop_length + frame_length]
If ``axis=0`` (framing on the first dimension), then::
x_frames[j] = x[j * hop_length : j * hop_length + frame_length]
Raises
------
ParameterError
If ``x.shape[axis] < frame_length``, there is not enough data to fill one frame.
If ``hop_length < 1``, frames cannot advance.
See Also
--------
numpy.lib.stride_tricks.as_strided
Examples
--------
Extract 2048-sample frames from monophonic signal with a hop of 64 samples per frame
>>> y, sr = librosa.load(librosa.ex('trumpet'))
>>> frames = librosa.util.frame(y, frame_length=2048, hop_length=64)
>>> frames
array([[-1.407e-03, -2.604e-02, ..., -1.795e-05, -8.108e-06],
[-4.461e-04, -3.721e-02, ..., -1.573e-05, -1.652e-05],
...,
[ 7.960e-02, -2.335e-01, ..., -6.815e-06, 1.266e-05],
[ 9.568e-02, -1.252e-01, ..., 7.397e-06, -1.921e-05]],
dtype=float32)
>>> y.shape
(117601,)
>>> frames.shape
(2048, 1806)
Or frame along the first axis instead of the last:
>>> frames = librosa.util.frame(y, frame_length=2048, hop_length=64, axis=0)
>>> frames.shape
(1806, 2048)
Frame a stereo signal:
>>> y, sr = librosa.load(librosa.ex('trumpet', hq=True), mono=False)
>>> y.shape
(2, 117601)
>>> frames = librosa.util.frame(y, frame_length=2048, hop_length=64)
(2, 2048, 1806)
Carve an STFT into fixed-length patches of 32 frames with 50% overlap
>>> y, sr = librosa.load(librosa.ex('trumpet'))
>>> S = np.abs(librosa.stft(y))
>>> S.shape
(1025, 230)
>>> S_patch = librosa.util.frame(S, frame_length=32, hop_length=16)
>>> S_patch.shape
(1025, 32, 13)
>>> # The first patch contains the first 32 frames of S
>>> np.allclose(S_patch[:, :, 0], S[:, :32])
True
>>> # The second patch contains frames 16 to 16+32=48, and so on
>>> np.allclose(S_patch[:, :, 1], S[:, 16:48])
True
"""
# This implementation is derived from numpy.lib.stride_tricks.sliding_window_view (1.20.0)
# https://numpy.org/doc/stable/reference/generated/numpy.lib.stride_tricks.sliding_window_view.html
x = np.array(x, copy=False, subok=subok)
if x.shape[axis] < frame_length:
raise ParameterError(
f"Input is too short (n={x.shape[axis]:d}) for frame_length={frame_length:d}"
)
if hop_length < 1:
raise ParameterError(f"Invalid hop_length: {hop_length:d}")
# put our new within-frame axis at the end for now
out_strides = x.strides + tuple([x.strides[axis]])
# Reduce the shape on the framing axis
x_shape_trimmed = list(x.shape)
x_shape_trimmed[axis] -= frame_length - 1
out_shape = tuple(x_shape_trimmed) + tuple([frame_length])
xw = as_strided(
x, strides=out_strides, shape=out_shape, subok=subok, writeable=writeable
)
if axis < 0:
target_axis = axis - 1
else:
target_axis = axis + 1
xw = np.moveaxis(xw, -1, target_axis)
# Downsample along the target axis
slices = [slice(None)] * xw.ndim
slices[axis] = slice(0, None, hop_length)
return xw[tuple(slices)]
@cache(level=20)
def valid_audio(y: np.ndarray, *, mono: Union[bool, Deprecated] = Deprecated()) -> bool:
"""Determine whether a variable contains valid audio data.
The following conditions must be satisfied:
- ``type(y)`` is ``np.ndarray``
- ``y.dtype`` is floating-point
- ``y.ndim != 0`` (must have at least one dimension)
- ``np.isfinite(y).all()`` samples must be all finite values
If ``mono`` is specified, then we additionally require
- ``y.ndim == 1``
Parameters
----------
y : np.ndarray
The input data to validate
mono : bool
Whether or not to require monophonic audio
.. warning:: The ``mono`` parameter is deprecated in version 0.9 and will be
removed in 0.10.
Returns
-------
valid : bool
True if all tests pass
Raises
------
ParameterError
In any of the conditions specified above fails
Notes
-----
This function caches at level 20.
Examples
--------
>>> # By default, valid_audio allows only mono signals
>>> filepath = librosa.ex('trumpet', hq=True)
>>> y_mono, sr = librosa.load(filepath, mono=True)
>>> y_stereo, _ = librosa.load(filepath, mono=False)
>>> librosa.util.valid_audio(y_mono), librosa.util.valid_audio(y_stereo)
True, False
>>> # To allow stereo signals, set mono=False
>>> librosa.util.valid_audio(y_stereo, mono=False)
True
See Also
--------
numpy.float32
"""
if not isinstance(y, np.ndarray):
raise ParameterError("Audio data must be of type numpy.ndarray")
if not np.issubdtype(y.dtype, np.floating):
raise ParameterError("Audio data must be floating-point")
if y.ndim == 0:
raise ParameterError(
f"Audio data must be at least one-dimensional, given y.shape={y.shape}"
)
if isinstance(mono, Deprecated):
mono = False
if mono and y.ndim != 1:
raise ParameterError(
f"Invalid shape for monophonic audio: ndim={y.ndim:d}, shape={y.shape}"
)
if not np.isfinite(y).all():
raise ParameterError("Audio buffer is not finite everywhere")
return True
def valid_int(x: float, *, cast: Optional[Callable[[float], float]] = None) -> int:
"""Ensure that an input value is integer-typed.
This is primarily useful for ensuring integrable-valued
array indices.
Parameters
----------
x : number
A scalar value to be cast to int
cast : function [optional]
A function to modify ``x`` before casting.
Default: `np.floor`
Returns
-------
x_int : int
``x_int = int(cast(x))``
Raises
------
ParameterError
If ``cast`` is provided and is not callable.
"""
if cast is None:
cast = np.floor
if not callable(cast):
raise ParameterError("cast parameter must be callable")
return int(cast(x))
def is_positive_int(x: float) -> bool:
"""Check that x is a positive integer, i.e. 1 or greater.
Parameters
----------
x : number
Returns
-------
positive : bool
"""
# Check type first to catch None values.
return isinstance(x, (int, np.integer)) and (x > 0)
def valid_intervals(intervals: np.ndarray) -> bool:
"""Ensure that an array is a valid representation of time intervals:
- intervals.ndim == 2
- intervals.shape[1] == 2
- intervals[i, 0] <= intervals[i, 1] for all i
Parameters
----------
intervals : np.ndarray [shape=(n, 2)]
set of time intervals
Returns
-------
valid : bool
True if ``intervals`` passes validation.
"""
if intervals.ndim != 2 or intervals.shape[-1] != 2:
raise ParameterError("intervals must have shape (n, 2)")
if np.any(intervals[:, 0] > intervals[:, 1]):
raise ParameterError(f"intervals={intervals} must have non-negative durations")
return True
def pad_center(
data: np.ndarray, *, size: int, axis: int = -1, **kwargs: Any
) -> np.ndarray:
"""Pad an array to a target length along a target axis.
This differs from `np.pad` by centering the data prior to padding,
analogous to `str.center`
Examples
--------
>>> # Generate a vector
>>> data = np.ones(5)
>>> librosa.util.pad_center(data, size=10, mode='constant')
array([ 0., 0., 1., 1., 1., 1., 1., 0., 0., 0.])
>>> # Pad a matrix along its first dimension
>>> data = np.ones((3, 5))
>>> librosa.util.pad_center(data, size=7, axis=0)
array([[ 0., 0., 0., 0., 0.],
[ 0., 0., 0., 0., 0.],
[ 1., 1., 1., 1., 1.],
[ 1., 1., 1., 1., 1.],
[ 1., 1., 1., 1., 1.],
[ 0., 0., 0., 0., 0.],
[ 0., 0., 0., 0., 0.]])
>>> # Or its second dimension
>>> librosa.util.pad_center(data, size=7, axis=1)
array([[ 0., 1., 1., 1., 1., 1., 0.],
[ 0., 1., 1., 1., 1., 1., 0.],
[ 0., 1., 1., 1., 1., 1., 0.]])
Parameters
----------
data : np.ndarray
Vector to be padded and centered
size : int >= len(data) [scalar]
Length to pad ``data``
axis : int
Axis along which to pad and center the data
**kwargs : additional keyword arguments
arguments passed to `np.pad`
Returns
-------
data_padded : np.ndarray
``data`` centered and padded to length ``size`` along the
specified axis
Raises
------
ParameterError
If ``size < data.shape[axis]``
See Also
--------
numpy.pad
"""
kwargs.setdefault("mode", "constant")
n = data.shape[axis]
lpad = int((size - n) // 2)
lengths = [(0, 0)] * data.ndim
lengths[axis] = (lpad, int(size - n - lpad))
if lpad < 0:
raise ParameterError(
f"Target size ({size:d}) must be at least input size ({n:d})"
)
return np.pad(data, lengths, **kwargs)
def expand_to(
x: np.ndarray, *, ndim: int, axes: Union[int, slice, Sequence[int], Sequence[slice]]
) -> np.ndarray:
"""Expand the dimensions of an input array with
Parameters
----------
x : np.ndarray
The input array
ndim : int
The number of dimensions to expand to. Must be at least ``x.ndim``
axes : int or slice
The target axis or axes to preserve from x.
All other axes will have length 1.
Returns
-------
x_exp : np.ndarray
The expanded version of ``x``, satisfying the following:
``x_exp[axes] == x``
``x_exp.ndim == ndim``
See Also
--------
np.expand_dims
Examples
--------
Expand a 1d array into an (n, 1) shape
>>> x = np.arange(3)
>>> librosa.util.expand_to(x, ndim=2, axes=0)
array([[0],
[1],
[2]])
Expand a 1d array into a (1, n) shape
>>> librosa.util.expand_to(x, ndim=2, axes=1)
array([[0, 1, 2]])
Expand a 2d array into (1, n, m, 1) shape
>>> x = np.vander(np.arange(3))
>>> librosa.util.expand_to(x, ndim=4, axes=[1,2]).shape
(1, 3, 3, 1)
"""
# Force axes into a tuple
axes_tup: Tuple[int]
try:
axes_tup = tuple(axes) # type: ignore
except TypeError:
axes_tup = tuple([axes]) # type: ignore
if len(axes_tup) != x.ndim:
raise ParameterError(
f"Shape mismatch between axes={axes_tup} and input x.shape={x.shape}"
)
if ndim < x.ndim:
raise ParameterError(
f"Cannot expand x.shape={x.shape} to fewer dimensions ndim={ndim}"
)
shape: List[int] = [1] * ndim
for i, axi in enumerate(axes_tup):
shape[axi] = x.shape[i]
return x.reshape(shape)
def fix_length(
data: np.ndarray, *, size: int, axis: int = -1, **kwargs: Any
) -> np.ndarray:
"""Fix the length an array ``data`` to exactly ``size`` along a target axis.
If ``data.shape[axis] < n``, pad according to the provided kwargs.
By default, ``data`` is padded with trailing zeros.
Examples
--------
>>> y = np.arange(7)
>>> # Default: pad with zeros
>>> librosa.util.fix_length(y, size=10)
array([0, 1, 2, 3, 4, 5, 6, 0, 0, 0])
>>> # Trim to a desired length
>>> librosa.util.fix_length(y, size=5)
array([0, 1, 2, 3, 4])
>>> # Use edge-padding instead of zeros
>>> librosa.util.fix_length(y, size=10, mode='edge')
array([0, 1, 2, 3, 4, 5, 6, 6, 6, 6])
Parameters
----------
data : np.ndarray
array to be length-adjusted
size : int >= 0 [scalar]
desired length of the array
axis : int, <= data.ndim
axis along which to fix length
**kwargs : additional keyword arguments
Parameters to ``np.pad``
Returns
-------
data_fixed : np.ndarray [shape=data.shape]
``data`` either trimmed or padded to length ``size``
along the specified axis.
See Also
--------
numpy.pad
"""
kwargs.setdefault("mode", "constant")
n = data.shape[axis]
if n > size:
slices = [slice(None)] * data.ndim
slices[axis] = slice(0, size)
return data[tuple(slices)]
elif n < size:
lengths = [(0, 0)] * data.ndim
lengths[axis] = (0, size - n)
return np.pad(data, lengths, **kwargs)
return data
def fix_frames(
frames: _SequenceLike[int],
*,
x_min: Optional[int] = 0,
x_max: Optional[int] = None,
pad: bool = True,
) -> np.ndarray:
"""Fix a list of frames to lie within [x_min, x_max]
Examples
--------
>>> # Generate a list of frame indices
>>> frames = np.arange(0, 1000.0, 50)
>>> frames
array([ 0., 50., 100., 150., 200., 250., 300., 350.,
400., 450., 500., 550., 600., 650., 700., 750.,
800., 850., 900., 950.])
>>> # Clip to span at most 250
>>> librosa.util.fix_frames(frames, x_max=250)
array([ 0, 50, 100, 150, 200, 250])
>>> # Or pad to span up to 2500
>>> librosa.util.fix_frames(frames, x_max=2500)
array([ 0, 50, 100, 150, 200, 250, 300, 350, 400,
450, 500, 550, 600, 650, 700, 750, 800, 850,
900, 950, 2500])
>>> librosa.util.fix_frames(frames, x_max=2500, pad=False)
array([ 0, 50, 100, 150, 200, 250, 300, 350, 400, 450, 500,
550, 600, 650, 700, 750, 800, 850, 900, 950])
>>> # Or starting away from zero
>>> frames = np.arange(200, 500, 33)
>>> frames
array([200, 233, 266, 299, 332, 365, 398, 431, 464, 497])
>>> librosa.util.fix_frames(frames)
array([ 0, 200, 233, 266, 299, 332, 365, 398, 431, 464, 497])
>>> librosa.util.fix_frames(frames, x_max=500)
array([ 0, 200, 233, 266, 299, 332, 365, 398, 431, 464, 497,
500])
Parameters
----------
frames : np.ndarray [shape=(n_frames,)]
List of non-negative frame indices
x_min : int >= 0 or None
Minimum allowed frame index
x_max : int >= 0 or None
Maximum allowed frame index
pad : boolean
If ``True``, then ``frames`` is expanded to span the full range
``[x_min, x_max]``
Returns
-------
fixed_frames : np.ndarray [shape=(n_fixed_frames,), dtype=int]
Fixed frame indices, flattened and sorted
Raises
------
ParameterError
If ``frames`` contains negative values
"""
frames = np.asarray(frames)
if np.any(frames < 0):
raise ParameterError("Negative frame index detected")
# TODO: this whole function could be made more efficient
if pad and (x_min is not None or x_max is not None):
frames = np.clip(frames, x_min, x_max)
if pad:
pad_data = []
if x_min is not None:
pad_data.append(x_min)
if x_max is not None:
pad_data.append(x_max)
frames = np.concatenate((np.asarray(pad_data), frames))
if x_min is not None:
frames = frames[frames >= x_min]
if x_max is not None:
frames = frames[frames <= x_max]
unique: np.ndarray = np.unique(frames).astype(int)
return unique
@overload
def axis_sort(
S: np.ndarray,
*,
axis: int = ...,
index: Literal[False] = ...,
value: Optional[Callable[..., Any]] = ...,
) -> np.ndarray:
...
@overload
def axis_sort(
S: np.ndarray,
*,
axis: int = ...,
index: Literal[True],
value: Optional[Callable[..., Any]] = ...,
) -> Tuple[np.ndarray, np.ndarray]:
...
def axis_sort(
S: np.ndarray,
*,
axis: int = -1,
index: bool = False,
value: Optional[Callable[..., Any]] = None,
) -> Union[np.ndarray, Tuple[np.ndarray, np.ndarray]]:
"""Sort an array along its rows or columns.
Examples
--------
Visualize NMF output for a spectrogram S
>>> # Sort the columns of W by peak frequency bin
>>> y, sr = librosa.load(librosa.ex('trumpet'))
>>> S = np.abs(librosa.stft(y))
>>> W, H = librosa.decompose.decompose(S, n_components=64)
>>> W_sort = librosa.util.axis_sort(W)
Or sort by the lowest frequency bin
>>> W_sort = librosa.util.axis_sort(W, value=np.argmin)
Or sort the rows instead of the columns
>>> W_sort_rows = librosa.util.axis_sort(W, axis=0)
Get the sorting index also, and use it to permute the rows of H
>>> W_sort, idx = librosa.util.axis_sort(W, index=True)
>>> H_sort = H[idx, :]
>>> import matplotlib.pyplot as plt
>>> fig, ax = plt.subplots(nrows=2, ncols=2)
>>> img_w = librosa.display.specshow(librosa.amplitude_to_db(W, ref=np.max),
... y_axis='log', ax=ax[0, 0])
>>> ax[0, 0].set(title='W')
>>> ax[0, 0].label_outer()
>>> img_act = librosa.display.specshow(H, x_axis='time', ax=ax[0, 1])
>>> ax[0, 1].set(title='H')
>>> ax[0, 1].label_outer()
>>> librosa.display.specshow(librosa.amplitude_to_db(W_sort,
... ref=np.max),
... y_axis='log', ax=ax[1, 0])
>>> ax[1, 0].set(title='W sorted')
>>> librosa.display.specshow(H_sort, x_axis='time', ax=ax[1, 1])
>>> ax[1, 1].set(title='H sorted')
>>> ax[1, 1].label_outer()
>>> fig.colorbar(img_w, ax=ax[:, 0], orientation='horizontal')
>>> fig.colorbar(img_act, ax=ax[:, 1], orientation='horizontal')
Parameters
----------
S : np.ndarray [shape=(d, n)]
Array to be sorted
axis : int [scalar]
The axis along which to compute the sorting values
- ``axis=0`` to sort rows by peak column index
- ``axis=1`` to sort columns by peak row index
index : boolean [scalar]
If true, returns the index array as well as the permuted data.
value : function
function to return the index corresponding to the sort order.
Default: `np.argmax`.
Returns
-------
S_sort : np.ndarray [shape=(d, n)]
``S`` with the columns or rows permuted in sorting order
idx : np.ndarray (optional) [shape=(d,) or (n,)]
If ``index == True``, the sorting index used to permute ``S``.
Length of ``idx`` corresponds to the selected ``axis``.
Raises
------
ParameterError
If ``S`` does not have exactly 2 dimensions (``S.ndim != 2``)
"""
if value is None:
value = np.argmax
if S.ndim != 2:
raise ParameterError("axis_sort is only defined for 2D arrays")
bin_idx = value(S, axis=np.mod(1 - axis, S.ndim))
idx = np.argsort(bin_idx)
sort_slice = [slice(None)] * S.ndim
sort_slice[axis] = idx # type: ignore
if index:
return S[tuple(sort_slice)], idx
else:
return S[tuple(sort_slice)]
@cache(level=40)
def normalize(
S: np.ndarray,
*,
norm: Optional[float] = np.inf,
axis: Optional[int] = 0,
threshold: Optional[_FloatLike_co] = None,
fill: Optional[bool] = None,
) -> np.ndarray:
"""Normalize an array along a chosen axis.
Given a norm (described below) and a target axis, the input
array is scaled so that::
norm(S, axis=axis) == 1
For example, ``axis=0`` normalizes each column of a 2-d array
by aggregating over the rows (0-axis).
Similarly, ``axis=1`` normalizes each row of a 2-d array.
This function also supports thresholding small-norm slices:
any slice (i.e., row or column) with norm below a specified
``threshold`` can be left un-normalized, set to all-zeros, or
filled with uniform non-zero values that normalize to 1.
Note: the semantics of this function differ from
`scipy.linalg.norm` in two ways: multi-dimensional arrays
are supported, but matrix-norms are not.
Parameters
----------
S : np.ndarray
The array to normalize
norm : {np.inf, -np.inf, 0, float > 0, None}
- `np.inf` : maximum absolute value
- `-np.inf` : minimum absolute value
- `0` : number of non-zeros (the support)
- float : corresponding l_p norm
See `scipy.linalg.norm` for details.
- None : no normalization is performed
axis : int [scalar]
Axis along which to compute the norm.
threshold : number > 0 [optional]
Only the columns (or rows) with norm at least ``threshold`` are
normalized.
By default, the threshold is determined from
the numerical precision of ``S.dtype``.
fill : None or bool
If None, then columns (or rows) with norm below ``threshold``
are left as is.
If False, then columns (rows) with norm below ``threshold``
are set to 0.
If True, then columns (rows) with norm below ``threshold``
are filled uniformly such that the corresponding norm is 1.
.. note:: ``fill=True`` is incompatible with ``norm=0`` because
no uniform vector exists with l0 "norm" equal to 1.
Returns
-------
S_norm : np.ndarray [shape=S.shape]
Normalized array
Raises
------
ParameterError
If ``norm`` is not among the valid types defined above
If ``S`` is not finite
If ``fill=True`` and ``norm=0``
See Also
--------
scipy.linalg.norm
Notes
-----
This function caches at level 40.
Examples
--------
>>> # Construct an example matrix
>>> S = np.vander(np.arange(-2.0, 2.0))
>>> S
array([[-8., 4., -2., 1.],
[-1., 1., -1., 1.],
[ 0., 0., 0., 1.],
[ 1., 1., 1., 1.]])
>>> # Max (l-infinity)-normalize the columns
>>> librosa.util.normalize(S)
array([[-1. , 1. , -1. , 1. ],
[-0.125, 0.25 , -0.5 , 1. ],
[ 0. , 0. , 0. , 1. ],
[ 0.125, 0.25 , 0.5 , 1. ]])
>>> # Max (l-infinity)-normalize the rows
>>> librosa.util.normalize(S, axis=1)
array([[-1. , 0.5 , -0.25 , 0.125],
[-1. , 1. , -1. , 1. ],
[ 0. , 0. , 0. , 1. ],
[ 1. , 1. , 1. , 1. ]])
>>> # l1-normalize the columns
>>> librosa.util.normalize(S, norm=1)
array([[-0.8 , 0.667, -0.5 , 0.25 ],
[-0.1 , 0.167, -0.25 , 0.25 ],
[ 0. , 0. , 0. , 0.25 ],
[ 0.1 , 0.167, 0.25 , 0.25 ]])
>>> # l2-normalize the columns
>>> librosa.util.normalize(S, norm=2)
array([[-0.985, 0.943, -0.816, 0.5 ],
[-0.123, 0.236, -0.408, 0.5 ],
[ 0. , 0. , 0. , 0.5 ],
[ 0.123, 0.236, 0.408, 0.5 ]])
>>> # Thresholding and filling
>>> S[:, -1] = 1e-308
>>> S
array([[ -8.000e+000, 4.000e+000, -2.000e+000,
1.000e-308],
[ -1.000e+000, 1.000e+000, -1.000e+000,
1.000e-308],
[ 0.000e+000, 0.000e+000, 0.000e+000,
1.000e-308],
[ 1.000e+000, 1.000e+000, 1.000e+000,
1.000e-308]])
>>> # By default, small-norm columns are left untouched
>>> librosa.util.normalize(S)
array([[ -1.000e+000, 1.000e+000, -1.000e+000,
1.000e-308],
[ -1.250e-001, 2.500e-001, -5.000e-001,
1.000e-308],
[ 0.000e+000, 0.000e+000, 0.000e+000,
1.000e-308],
[ 1.250e-001, 2.500e-001, 5.000e-001,
1.000e-308]])
>>> # Small-norm columns can be zeroed out
>>> librosa.util.normalize(S, fill=False)
array([[-1. , 1. , -1. , 0. ],
[-0.125, 0.25 , -0.5 , 0. ],
[ 0. , 0. , 0. , 0. ],
[ 0.125, 0.25 , 0.5 , 0. ]])
>>> # Or set to constant with unit-norm
>>> librosa.util.normalize(S, fill=True)
array([[-1. , 1. , -1. , 1. ],
[-0.125, 0.25 , -0.5 , 1. ],
[ 0. , 0. , 0. , 1. ],
[ 0.125, 0.25 , 0.5 , 1. ]])
>>> # With an l1 norm instead of max-norm
>>> librosa.util.normalize(S, norm=1, fill=True)
array([[-0.8 , 0.667, -0.5 , 0.25 ],
[-0.1 , 0.167, -0.25 , 0.25 ],
[ 0. , 0. , 0. , 0.25 ],
[ 0.1 , 0.167, 0.25 , 0.25 ]])
"""
# Avoid div-by-zero
if threshold is None:
threshold = tiny(S)
elif threshold <= 0:
raise ParameterError(f"threshold={threshold} must be strictly positive")
if fill not in [None, False, True]:
raise ParameterError(f"fill={fill} must be None or boolean")
if not np.all(np.isfinite(S)):
raise ParameterError("Input must be finite")
# All norms only depend on magnitude, let's do that first
mag = np.abs(S).astype(float)
# For max/min norms, filling with 1 works
fill_norm = 1
if norm is None:
return S
elif norm == np.inf:
length = np.max(mag, axis=axis, keepdims=True)
elif norm == -np.inf:
length = np.min(mag, axis=axis, keepdims=True)
elif norm == 0:
if fill is True:
raise ParameterError("Cannot normalize with norm=0 and fill=True")
length = np.sum(mag > 0, axis=axis, keepdims=True, dtype=mag.dtype)
elif np.issubdtype(type(norm), np.number) and norm > 0:
length = np.sum(mag**norm, axis=axis, keepdims=True) ** (1.0 / norm)
if axis is None:
fill_norm = mag.size ** (-1.0 / norm)
else:
fill_norm = mag.shape[axis] ** (-1.0 / norm)
else:
raise ParameterError(f"Unsupported norm: {repr(norm)}")
# indices where norm is below the threshold
small_idx = length < threshold
Snorm = np.empty_like(S)
if fill is None:
# Leave small indices un-normalized
length[small_idx] = 1.0
Snorm[:] = S / length
elif fill:
# If we have a non-zero fill value, we locate those entries by
# doing a nan-divide.
# If S was finite, then length is finite (except for small positions)
length[small_idx] = np.nan
Snorm[:] = S / length
Snorm[np.isnan(Snorm)] = fill_norm
else:
# Set small values to zero by doing an inf-divide.
# This is safe (by IEEE-754) as long as S is finite.
length[small_idx] = np.inf
Snorm[:] = S / length
return Snorm
@numba.stencil
def _localmax_sten(x): # pragma: no cover
"""Numba stencil for local maxima computation"""
return (x[0] > x[-1]) & (x[0] >= x[1])
@numba.stencil
def _localmin_sten(x): # pragma: no cover
"""Numba stencil for local minima computation"""
return (x[0] < x[-1]) & (x[0] <= x[1])
@numba.guvectorize(
[
"void(int16[:], bool_[:])",
"void(int32[:], bool_[:])",
"void(int64[:], bool_[:])",
"void(float32[:], bool_[:])",
"void(float64[:], bool_[:])",
],
"(n)->(n)",
cache=True,
nopython=True,
)
def _localmax(x, y): # pragma: no cover
"""Vectorized wrapper for the localmax stencil"""
y[:] = _localmax_sten(x)
@numba.guvectorize(
[
"void(int16[:], bool_[:])",
"void(int32[:], bool_[:])",
"void(int64[:], bool_[:])",
"void(float32[:], bool_[:])",
"void(float64[:], bool_[:])",
],
"(n)->(n)",
cache=True,
nopython=True,
)
def _localmin(x, y): # pragma: no cover
"""Vectorized wrapper for the localmin stencil"""
y[:] = _localmin_sten(x)
def localmax(x: np.ndarray, *, axis: int = 0) -> np.ndarray:
"""Find local maxima in an array
An element ``x[i]`` is considered a local maximum if the following
conditions are met:
- ``x[i] > x[i-1]``
- ``x[i] >= x[i+1]``
Note that the first condition is strict, and that the first element
``x[0]`` will never be considered as a local maximum.
Examples
--------
>>> x = np.array([1, 0, 1, 2, -1, 0, -2, 1])
>>> librosa.util.localmax(x)
array([False, False, False, True, False, True, False, True], dtype=bool)
>>> # Two-dimensional example
>>> x = np.array([[1,0,1], [2, -1, 0], [2, 1, 3]])
>>> librosa.util.localmax(x, axis=0)
array([[False, False, False],
[ True, False, False],
[False, True, True]], dtype=bool)
>>> librosa.util.localmax(x, axis=1)
array([[False, False, True],
[False, False, True],
[False, False, True]], dtype=bool)
Parameters
----------
x : np.ndarray [shape=(d1,d2,...)]
input vector or array
axis : int
axis along which to compute local maximality
Returns
-------
m : np.ndarray [shape=x.shape, dtype=bool]
indicator array of local maximality along ``axis``
See Also
--------
localmin
"""
# Rotate the target axis to the end
xi = x.swapaxes(-1, axis)
# Allocate the output array and rotate target axis
lmax = np.empty_like(x, dtype=bool)
lmaxi = lmax.swapaxes(-1, axis)
# Call the vectorized stencil
_localmax(xi, lmaxi)
# Handle the edge condition not covered by the stencil
lmaxi[..., -1] = xi[..., -1] > xi[..., -2]
return lmax
def localmin(x: np.ndarray, *, axis: int = 0) -> np.ndarray:
"""Find local minima in an array
An element ``x[i]`` is considered a local minimum if the following
conditions are met:
- ``x[i] < x[i-1]``
- ``x[i] <= x[i+1]``
Note that the first condition is strict, and that the first element
``x[0]`` will never be considered as a local minimum.
Examples
--------
>>> x = np.array([1, 0, 1, 2, -1, 0, -2, 1])
>>> librosa.util.localmin(x)
array([False, True, False, False, True, False, True, False])
>>> # Two-dimensional example
>>> x = np.array([[1,0,1], [2, -1, 0], [2, 1, 3]])
>>> librosa.util.localmin(x, axis=0)
array([[False, False, False],
[False, True, True],
[False, False, False]])
>>> librosa.util.localmin(x, axis=1)
array([[False, True, False],
[False, True, False],
[False, True, False]])
Parameters
----------
x : np.ndarray [shape=(d1,d2,...)]
input vector or array
axis : int
axis along which to compute local minimality
Returns
-------
m : np.ndarray [shape=x.shape, dtype=bool]
indicator array of local minimality along ``axis``
See Also
--------
localmax
"""
# Rotate the target axis to the end
xi = x.swapaxes(-1, axis)
# Allocate the output array and rotate target axis
lmin = np.empty_like(x, dtype=bool)
lmini = lmin.swapaxes(-1, axis)
# Call the vectorized stencil
_localmin(xi, lmini)
# Handle the edge condition not covered by the stencil
lmini[..., -1] = xi[..., -1] < xi[..., -2]
return lmin
def peak_pick(
x: np.ndarray,
*,
pre_max: int,
post_max: int,
pre_avg: int,
post_avg: int,
delta: float,
wait: int,
) -> np.ndarray:
"""Use a flexible heuristic to pick peaks in a signal.
A sample n is selected as an peak if the corresponding ``x[n]``
fulfills the following three conditions:
1. ``x[n] == max(x[n - pre_max:n + post_max])``
2. ``x[n] >= mean(x[n - pre_avg:n + post_avg]) + delta``
3. ``n - previous_n > wait``
where ``previous_n`` is the last sample picked as a peak (greedily).
This implementation is based on [#]_ and [#]_.
.. [#] Boeck, Sebastian, Florian Krebs, and Markus Schedl.
"Evaluating the Online Capabilities of Onset Detection Methods." ISMIR.
2012.
.. [#] https://github.com/CPJKU/onset_detection/blob/master/onset_program.py
Parameters
----------
x : np.ndarray [shape=(n,)]
input signal to peak picks from
pre_max : int >= 0 [scalar]
number of samples before ``n`` over which max is computed
post_max : int >= 1 [scalar]
number of samples after ``n`` over which max is computed
pre_avg : int >= 0 [scalar]
number of samples before ``n`` over which mean is computed
post_avg : int >= 1 [scalar]
number of samples after ``n`` over which mean is computed
delta : float >= 0 [scalar]
threshold offset for mean
wait : int >= 0 [scalar]
number of samples to wait after picking a peak
Returns
-------
peaks : np.ndarray [shape=(n_peaks,), dtype=int]
indices of peaks in ``x``
Raises
------
ParameterError
If any input lies outside its defined range
Examples
--------
>>> y, sr = librosa.load(librosa.ex('trumpet'))
>>> onset_env = librosa.onset.onset_strength(y=y, sr=sr,
... hop_length=512,
... aggregate=np.median)
>>> peaks = librosa.util.peak_pick(onset_env, pre_max=3, post_max=3, pre_avg=3, post_avg=5, delta=0.5, wait=10)
>>> peaks
array([ 3, 27, 40, 61, 72, 88, 103])
>>> import matplotlib.pyplot as plt
>>> times = librosa.times_like(onset_env, sr=sr, hop_length=512)
>>> fig, ax = plt.subplots(nrows=2, sharex=True)
>>> D = np.abs(librosa.stft(y))
>>> librosa.display.specshow(librosa.amplitude_to_db(D, ref=np.max),
... y_axis='log', x_axis='time', ax=ax[1])
>>> ax[0].plot(times, onset_env, alpha=0.8, label='Onset strength')
>>> ax[0].vlines(times[peaks], 0,
... onset_env.max(), color='r', alpha=0.8,
... label='Selected peaks')
>>> ax[0].legend(frameon=True, framealpha=0.8)
>>> ax[0].label_outer()
"""
if pre_max < 0:
raise ParameterError("pre_max must be non-negative")
if pre_avg < 0:
raise ParameterError("pre_avg must be non-negative")
if delta < 0:
raise ParameterError("delta must be non-negative")
if wait < 0:
raise ParameterError("wait must be non-negative")
if post_max <= 0:
raise ParameterError("post_max must be positive")
if post_avg <= 0:
raise ParameterError("post_avg must be positive")
if x.ndim != 1:
raise ParameterError("input array must be one-dimensional")
# Ensure valid index types
pre_max = valid_int(pre_max, cast=np.ceil)
post_max = valid_int(post_max, cast=np.ceil)
pre_avg = valid_int(pre_avg, cast=np.ceil)
post_avg = valid_int(post_avg, cast=np.ceil)
wait = valid_int(wait, cast=np.ceil)
# Get the maximum of the signal over a sliding window
max_length = pre_max + post_max
max_origin = np.ceil(0.5 * (pre_max - post_max))
# Using mode='constant' and cval=x.min() effectively truncates
# the sliding window at the boundaries
mov_max = scipy.ndimage.filters.maximum_filter1d(
x, int(max_length), mode="constant", origin=int(max_origin), cval=x.min()
)
# Get the mean of the signal over a sliding window
avg_length = pre_avg + post_avg
avg_origin = np.ceil(0.5 * (pre_avg - post_avg))
# Here, there is no mode which results in the behavior we want,
# so we'll correct below.
mov_avg = scipy.ndimage.filters.uniform_filter1d(
x, int(avg_length), mode="nearest", origin=int(avg_origin)
)
# Correct sliding average at the beginning
n = 0
# Only need to correct in the range where the window needs to be truncated
while n - pre_avg < 0 and n < x.shape[0]:
# This just explicitly does mean(x[n - pre_avg:n + post_avg])
# with truncation
start = n - pre_avg
start = start if start > 0 else 0
mov_avg[n] = np.mean(x[start : n + post_avg])
n += 1
# Correct sliding average at the end
n = x.shape[0] - post_avg
# When post_avg > x.shape[0] (weird case), reset to 0
n = n if n > 0 else 0
while n < x.shape[0]:
start = n - pre_avg
start = start if start > 0 else 0
mov_avg[n] = np.mean(x[start : n + post_avg])
n += 1
# First mask out all entries not equal to the local max
detections = x * (x == mov_max)
# Then mask out all entries less than the thresholded average
detections = detections * (detections >= (mov_avg + delta))
# Initialize peaks array, to be filled greedily
peaks = []
# Remove onsets which are close together in time
last_onset = -np.inf
for i in np.nonzero(detections)[0]:
# Only report an onset if the "wait" samples was reported
if i > last_onset + wait:
peaks.append(i)
# Save last reported onset
last_onset = i
return np.array(peaks)
@cache(level=40)
def sparsify_rows(
x: np.ndarray, *, quantile: float = 0.01, dtype: Optional[DTypeLike] = None
) -> scipy.sparse.csr_matrix:
"""Return a row-sparse matrix approximating the input
Parameters
----------
x : np.ndarray [ndim <= 2]
The input matrix to sparsify.
quantile : float in [0, 1.0)
Percentage of magnitude to discard in each row of ``x``
dtype : np.dtype, optional
The dtype of the output array.
If not provided, then ``x.dtype`` will be used.
Returns
-------
x_sparse : ``scipy.sparse.csr_matrix`` [shape=x.shape]
Row-sparsified approximation of ``x``
If ``x.ndim == 1``, then ``x`` is interpreted as a row vector,
and ``x_sparse.shape == (1, len(x))``.
Raises
------
ParameterError
If ``x.ndim > 2``
If ``quantile`` lies outside ``[0, 1.0)``
Notes
-----
This function caches at level 40.
Examples
--------
>>> # Construct a Hann window to sparsify
>>> x = scipy.signal.hann(32)
>>> x
array([ 0. , 0.01 , 0.041, 0.09 , 0.156, 0.236, 0.326,
0.424, 0.525, 0.625, 0.72 , 0.806, 0.879, 0.937,
0.977, 0.997, 0.997, 0.977, 0.937, 0.879, 0.806,
0.72 , 0.625, 0.525, 0.424, 0.326, 0.236, 0.156,
0.09 , 0.041, 0.01 , 0. ])
>>> # Discard the bottom percentile
>>> x_sparse = librosa.util.sparsify_rows(x, quantile=0.01)
>>> x_sparse
<1x32 sparse matrix of type '<type 'numpy.float64'>'
with 26 stored elements in Compressed Sparse Row format>
>>> x_sparse.todense()
matrix([[ 0. , 0. , 0. , 0.09 , 0.156, 0.236, 0.326,
0.424, 0.525, 0.625, 0.72 , 0.806, 0.879, 0.937,
0.977, 0.997, 0.997, 0.977, 0.937, 0.879, 0.806,
0.72 , 0.625, 0.525, 0.424, 0.326, 0.236, 0.156,
0.09 , 0. , 0. , 0. ]])
>>> # Discard up to the bottom 10th percentile
>>> x_sparse = librosa.util.sparsify_rows(x, quantile=0.1)
>>> x_sparse
<1x32 sparse matrix of type '<type 'numpy.float64'>'
with 20 stored elements in Compressed Sparse Row format>
>>> x_sparse.todense()
matrix([[ 0. , 0. , 0. , 0. , 0. , 0. , 0.326,
0.424, 0.525, 0.625, 0.72 , 0.806, 0.879, 0.937,
0.977, 0.997, 0.997, 0.977, 0.937, 0.879, 0.806,
0.72 , 0.625, 0.525, 0.424, 0.326, 0. , 0. ,
0. , 0. , 0. , 0. ]])
"""
if x.ndim == 1:
x = x.reshape((1, -1))
elif x.ndim > 2:
raise ParameterError(
f"Input must have 2 or fewer dimensions. Provided x.shape={x.shape}."
)
if not 0.0 <= quantile < 1:
raise ParameterError(f"Invalid quantile {quantile:.2f}")
if dtype is None:
dtype = x.dtype
x_sparse = scipy.sparse.lil_matrix(x.shape, dtype=dtype)
mags = np.abs(x)
norms = np.sum(mags, axis=1, keepdims=True)
mag_sort = np.sort(mags, axis=1)
cumulative_mag = np.cumsum(mag_sort / norms, axis=1)
threshold_idx = np.argmin(cumulative_mag < quantile, axis=1)
for i, j in enumerate(threshold_idx):
idx = np.where(mags[i] >= mag_sort[i, j])
x_sparse[i, idx] = x[i, idx]
return x_sparse.tocsr()
def buf_to_float(
x: np.ndarray, *, n_bytes: int = 2, dtype: DTypeLike = np.float32
) -> np.ndarray:
"""Convert an integer buffer to floating point values.
This is primarily useful when loading integer-valued wav data
into numpy arrays.
Parameters
----------
x : np.ndarray [dtype=int]
The integer-valued data buffer
n_bytes : int [1, 2, 4]
The number of bytes per sample in ``x``
dtype : numeric type
The target output type (default: 32-bit float)
Returns
-------
x_float : np.ndarray [dtype=float]
The input data buffer cast to floating point
"""
# Invert the scale of the data
scale = 1.0 / float(1 << ((8 * n_bytes) - 1))
# Construct the format string
fmt = f"<i{n_bytes:d}"
# Rescale and format the data buffer
return scale * np.frombuffer(x, fmt).astype(dtype)
def index_to_slice(
idx: _SequenceLike[int],
*,
idx_min: Optional[int] = None,
idx_max: Optional[int] = None,
step: Optional[int] = None,
pad: bool = True,
) -> List[slice]:
"""Generate a slice array from an index array.
Parameters
----------
idx : list-like
Array of index boundaries
idx_min, idx_max : None or int
Minimum and maximum allowed indices
step : None or int
Step size for each slice. If `None`, then the default
step of 1 is used.
pad : boolean
If `True`, pad ``idx`` to span the range ``idx_min:idx_max``.
Returns
-------
slices : list of slice
``slices[i] = slice(idx[i], idx[i+1], step)``
Additional slice objects may be added at the beginning or end,
depending on whether ``pad==True`` and the supplied values for
``idx_min`` and ``idx_max``.
See Also
--------
fix_frames
Examples
--------
>>> # Generate slices from spaced indices
>>> librosa.util.index_to_slice(np.arange(20, 100, 15))
[slice(20, 35, None), slice(35, 50, None), slice(50, 65, None), slice(65, 80, None),
slice(80, 95, None)]
>>> # Pad to span the range (0, 100)
>>> librosa.util.index_to_slice(np.arange(20, 100, 15),
... idx_min=0, idx_max=100)
[slice(0, 20, None), slice(20, 35, None), slice(35, 50, None), slice(50, 65, None),
slice(65, 80, None), slice(80, 95, None), slice(95, 100, None)]
>>> # Use a step of 5 for each slice
>>> librosa.util.index_to_slice(np.arange(20, 100, 15),
... idx_min=0, idx_max=100, step=5)
[slice(0, 20, 5), slice(20, 35, 5), slice(35, 50, 5), slice(50, 65, 5), slice(65, 80, 5),
slice(80, 95, 5), slice(95, 100, 5)]
"""
# First, normalize the index set
idx_fixed = fix_frames(idx, x_min=idx_min, x_max=idx_max, pad=pad)
# Now convert the indices to slices
return [slice(start, end, step) for (start, end) in zip(idx_fixed, idx_fixed[1:])]
@cache(level=40)
def sync(
data: np.ndarray,
idx: Union[Sequence[int], Sequence[slice]],
*,
aggregate: Optional[Callable[..., Any]] = None,
pad: bool = True,
axis: int = -1,
) -> np.ndarray:
"""Aggregate a multi-dimensional array between specified boundaries.
.. note::
In order to ensure total coverage, boundary points may be added
to ``idx``.
If synchronizing a feature matrix against beat tracker output, ensure
that frame index numbers are properly aligned and use the same hop length.
Parameters
----------
data : np.ndarray
multi-dimensional array of features
idx : sequence of ints or slices
Either an ordered array of boundary indices, or
an iterable collection of slice objects.
aggregate : function
aggregation function (default: `np.mean`)
pad : boolean
If `True`, ``idx`` is padded to span the full range ``[0, data.shape[axis]]``
axis : int
The axis along which to aggregate data
Returns
-------
data_sync : ndarray
``data_sync`` will have the same dimension as ``data``, except that the ``axis``
coordinate will be reduced according to ``idx``.
For example, a 2-dimensional ``data`` with ``axis=-1`` should satisfy::
data_sync[:, i] = aggregate(data[:, idx[i-1]:idx[i]], axis=-1)
Raises
------
ParameterError
If the index set is not of consistent type (all slices or all integers)
Notes
-----
This function caches at level 40.
Examples
--------
Beat-synchronous CQT spectra
>>> y, sr = librosa.load(librosa.ex('choice'))
>>> tempo, beats = librosa.beat.beat_track(y=y, sr=sr, trim=False)
>>> C = np.abs(librosa.cqt(y=y, sr=sr))
>>> beats = librosa.util.fix_frames(beats)
By default, use mean aggregation
>>> C_avg = librosa.util.sync(C, beats)
Use median-aggregation instead of mean
>>> C_med = librosa.util.sync(C, beats,
... aggregate=np.median)
Or sub-beat synchronization
>>> sub_beats = librosa.segment.subsegment(C, beats)
>>> sub_beats = librosa.util.fix_frames(sub_beats)
>>> C_med_sub = librosa.util.sync(C, sub_beats, aggregate=np.median)
Plot the results
>>> import matplotlib.pyplot as plt
>>> beat_t = librosa.frames_to_time(beats, sr=sr)
>>> subbeat_t = librosa.frames_to_time(sub_beats, sr=sr)
>>> fig, ax = plt.subplots(nrows=3, sharex=True, sharey=True)
>>> librosa.display.specshow(librosa.amplitude_to_db(C,
... ref=np.max),
... x_axis='time', ax=ax[0])
>>> ax[0].set(title='CQT power, shape={}'.format(C.shape))
>>> ax[0].label_outer()
>>> librosa.display.specshow(librosa.amplitude_to_db(C_med,
... ref=np.max),
... x_coords=beat_t, x_axis='time', ax=ax[1])
>>> ax[1].set(title='Beat synchronous CQT power, '
... 'shape={}'.format(C_med.shape))
>>> ax[1].label_outer()
>>> librosa.display.specshow(librosa.amplitude_to_db(C_med_sub,
... ref=np.max),
... x_coords=subbeat_t, x_axis='time', ax=ax[2])
>>> ax[2].set(title='Sub-beat synchronous CQT power, '
... 'shape={}'.format(C_med_sub.shape))
"""
if aggregate is None:
aggregate = np.mean
shape = list(data.shape)
if np.all([isinstance(_, slice) for _ in idx]):
slices = idx
elif np.all([np.issubdtype(type(_), np.integer) for _ in idx]):
slices = index_to_slice(
np.asarray(idx), idx_min=0, idx_max=shape[axis], pad=pad
)
else:
raise ParameterError(f"Invalid index set: {idx}")
agg_shape = list(shape)
agg_shape[axis] = len(slices)
data_agg = np.empty(
agg_shape, order="F" if np.isfortran(data) else "C", dtype=data.dtype
)
idx_in = [slice(None)] * data.ndim
idx_agg = [slice(None)] * data_agg.ndim
for i, segment in enumerate(slices):
idx_in[axis] = segment # type: ignore
idx_agg[axis] = i # type: ignore
data_agg[tuple(idx_agg)] = aggregate(data[tuple(idx_in)], axis=axis)
return data_agg
def softmask(
X: np.ndarray, X_ref: np.ndarray, *, power: float = 1, split_zeros: bool = False
) -> np.ndarray:
"""Robustly compute a soft-mask operation.
``M = X**power / (X**power + X_ref**power)``
Parameters
----------
X : np.ndarray
The (non-negative) input array corresponding to the positive mask elements
X_ref : np.ndarray
The (non-negative) array of reference or background elements.
Must have the same shape as ``X``.
power : number > 0 or np.inf
If finite, returns the soft mask computed in a numerically stable way
If infinite, returns a hard (binary) mask equivalent to ``X > X_ref``.
Note: for hard masks, ties are always broken in favor of ``X_ref`` (``mask=0``).
split_zeros : bool
If `True`, entries where ``X`` and ``X_ref`` are both small (close to 0)
will receive mask values of 0.5.
Otherwise, the mask is set to 0 for these entries.
Returns
-------
mask : np.ndarray, shape=X.shape
The output mask array
Raises
------
ParameterError
If ``X`` and ``X_ref`` have different shapes.
If ``X`` or ``X_ref`` are negative anywhere
If ``power <= 0``
Examples
--------
>>> X = 2 * np.ones((3, 3))
>>> X_ref = np.vander(np.arange(3.0))
>>> X
array([[ 2., 2., 2.],
[ 2., 2., 2.],
[ 2., 2., 2.]])
>>> X_ref
array([[ 0., 0., 1.],
[ 1., 1., 1.],
[ 4., 2., 1.]])
>>> librosa.util.softmask(X, X_ref, power=1)
array([[ 1. , 1. , 0.667],
[ 0.667, 0.667, 0.667],
[ 0.333, 0.5 , 0.667]])
>>> librosa.util.softmask(X_ref, X, power=1)
array([[ 0. , 0. , 0.333],
[ 0.333, 0.333, 0.333],
[ 0.667, 0.5 , 0.333]])
>>> librosa.util.softmask(X, X_ref, power=2)
array([[ 1. , 1. , 0.8],
[ 0.8, 0.8, 0.8],
[ 0.2, 0.5, 0.8]])
>>> librosa.util.softmask(X, X_ref, power=4)
array([[ 1. , 1. , 0.941],
[ 0.941, 0.941, 0.941],
[ 0.059, 0.5 , 0.941]])
>>> librosa.util.softmask(X, X_ref, power=100)
array([[ 1.000e+00, 1.000e+00, 1.000e+00],
[ 1.000e+00, 1.000e+00, 1.000e+00],
[ 7.889e-31, 5.000e-01, 1.000e+00]])
>>> librosa.util.softmask(X, X_ref, power=np.inf)
array([[ True, True, True],
[ True, True, True],
[False, False, True]], dtype=bool)
"""
if X.shape != X_ref.shape:
raise ParameterError(f"Shape mismatch: {X.shape}!={X_ref.shape}")
if np.any(X < 0) or np.any(X_ref < 0):
raise ParameterError("X and X_ref must be non-negative")
if power <= 0:
raise ParameterError("power must be strictly positive")
# We're working with ints, cast to float.
dtype = X.dtype
if not np.issubdtype(dtype, np.floating):
dtype = np.float32
# Re-scale the input arrays relative to the larger value
Z = np.maximum(X, X_ref).astype(dtype)
bad_idx = Z < np.finfo(dtype).tiny
Z[bad_idx] = 1
# For finite power, compute the softmask
mask: np.ndarray
if np.isfinite(power):
mask = (X / Z) ** power
ref_mask = (X_ref / Z) ** power
good_idx = ~bad_idx
mask[good_idx] /= mask[good_idx] + ref_mask[good_idx]
# Wherever energy is below energy in both inputs, split the mask
if split_zeros:
mask[bad_idx] = 0.5
else:
mask[bad_idx] = 0.0
else:
# Otherwise, compute the hard mask
mask = X > X_ref
return mask
def tiny(x: Union[float, np.ndarray]) -> _FloatLike_co:
"""Compute the tiny-value corresponding to an input's data type.
This is the smallest "usable" number representable in ``x.dtype``
(e.g., float32).
This is primarily useful for determining a threshold for
numerical underflow in division or multiplication operations.
Parameters
----------
x : number or np.ndarray
The array to compute the tiny-value for.
All that matters here is ``x.dtype``
Returns
-------
tiny_value : float
The smallest positive usable number for the type of ``x``.
If ``x`` is integer-typed, then the tiny value for ``np.float32``
is returned instead.
See Also
--------
numpy.finfo
Examples
--------
For a standard double-precision floating point number:
>>> librosa.util.tiny(1.0)
2.2250738585072014e-308
Or explicitly as double-precision
>>> librosa.util.tiny(np.asarray(1e-5, dtype=np.float64))
2.2250738585072014e-308
Or complex numbers
>>> librosa.util.tiny(1j)
2.2250738585072014e-308
Single-precision floating point:
>>> librosa.util.tiny(np.asarray(1e-5, dtype=np.float32))
1.1754944e-38
Integer
>>> librosa.util.tiny(5)
1.1754944e-38
"""
# Make sure we have an array view
x = np.asarray(x)
# Only floating types generate a tiny
if np.issubdtype(x.dtype, np.floating) or np.issubdtype(
x.dtype, np.complexfloating
):
dtype = x.dtype
else:
dtype = np.dtype(np.float32)
return np.finfo(dtype).tiny
def fill_off_diagonal(x: np.ndarray, *, radius: float, value: float = 0) -> None:
"""Set all cells of a matrix to a given ``value``
if they lie outside a constraint region.
In this case, the constraint region is the
Sakoe-Chiba band which runs with a fixed ``radius``
along the main diagonal.
When ``x.shape[0] != x.shape[1]``, the radius will be
expanded so that ``x[-1, -1] = 1`` always.
``x`` will be modified in place.
Parameters
----------
x : np.ndarray [shape=(N, M)]
Input matrix, will be modified in place.
radius : float
The band radius (1/2 of the width) will be
``int(radius*min(x.shape))``
value : float
``x[n, m] = value`` when ``(n, m)`` lies outside the band.
Examples
--------
>>> x = np.ones((8, 8))
>>> librosa.util.fill_off_diagonal(x, radius=0.25)
>>> x
array([[1, 1, 0, 0, 0, 0, 0, 0],
[1, 1, 1, 0, 0, 0, 0, 0],
[0, 1, 1, 1, 0, 0, 0, 0],
[0, 0, 1, 1, 1, 0, 0, 0],
[0, 0, 0, 1, 1, 1, 0, 0],
[0, 0, 0, 0, 1, 1, 1, 0],
[0, 0, 0, 0, 0, 1, 1, 1],
[0, 0, 0, 0, 0, 0, 1, 1]])
>>> x = np.ones((8, 12))
>>> librosa.util.fill_off_diagonal(x, radius=0.25)
>>> x
array([[1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0],
[1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0],
[0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0],
[0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0],
[0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0],
[0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 0],
[0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1],
[0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1]])
"""
nx, ny = x.shape
# Calculate the radius in indices, rather than proportion
radius = int(np.round(radius * np.min(x.shape)))
nx, ny = x.shape
offset = np.abs((x.shape[0] - x.shape[1]))
if nx < ny:
idx_u = np.triu_indices_from(x, k=radius + offset)
idx_l = np.tril_indices_from(x, k=-radius)
else:
idx_u = np.triu_indices_from(x, k=radius)
idx_l = np.tril_indices_from(x, k=-radius - offset)
# modify input matrix
x[idx_u] = value
x[idx_l] = value
def cyclic_gradient(
data: np.ndarray, *, edge_order: Literal[1, 2] = 1, axis: int = -1
) -> np.ndarray:
"""Estimate the gradient of a function over a uniformly sampled,
periodic domain.
This is essentially the same as `np.gradient`, except that edge effects
are handled by wrapping the observations (i.e. assuming periodicity)
rather than extrapolation.
Parameters
----------
data : np.ndarray
The function values observed at uniformly spaced positions on
a periodic domain
edge_order : {1, 2}
The order of the difference approximation used for estimating
the gradient
axis : int
The axis along which gradients are calculated.
Returns
-------
grad : np.ndarray like ``data``
The gradient of ``data`` taken along the specified axis.
See Also
--------
numpy.gradient
Examples
--------
This example estimates the gradient of cosine (-sine) from 64
samples using direct (aperiodic) and periodic gradient
calculation.
>>> import matplotlib.pyplot as plt
>>> x = 2 * np.pi * np.linspace(0, 1, num=64, endpoint=False)
>>> y = np.cos(x)
>>> grad = np.gradient(y)
>>> cyclic_grad = librosa.util.cyclic_gradient(y)
>>> true_grad = -np.sin(x) * 2 * np.pi / len(x)
>>> fig, ax = plt.subplots()
>>> ax.plot(x, true_grad, label='True gradient', linewidth=5,
... alpha=0.35)
>>> ax.plot(x, cyclic_grad, label='cyclic_gradient')
>>> ax.plot(x, grad, label='np.gradient', linestyle=':')
>>> ax.legend()
>>> # Zoom into the first part of the sequence
>>> ax.set(xlim=[0, np.pi/16], ylim=[-0.025, 0.025])
"""
# Wrap-pad the data along the target axis by `edge_order` on each side
padding = [(0, 0)] * data.ndim
padding[axis] = (edge_order, edge_order)
data_pad = np.pad(data, padding, mode="wrap")
# Compute the gradient
grad = np.gradient(data_pad, edge_order=edge_order, axis=axis)
# Remove the padding
slices = [slice(None)] * data.ndim
slices[axis] = slice(edge_order, -edge_order)
grad_slice: np.ndarray = grad[tuple(slices)]
return grad_slice
@numba.jit(nopython=True, cache=True) # type: ignore
def __shear_dense(X: np.ndarray, *, factor: int = +1, axis: int = -1) -> np.ndarray:
"""Numba-accelerated shear for dense (ndarray) arrays"""
if axis == 0:
X = X.T
X_shear = np.empty_like(X)
for i in range(X.shape[1]):
X_shear[:, i] = np.roll(X[:, i], factor * i)
if axis == 0:
X_shear = X_shear.T
return X_shear
def __shear_sparse(
X: scipy.sparse.spmatrix, *, factor: int = +1, axis: int = -1
) -> scipy.sparse.spmatrix:
"""Fast shearing for sparse matrices
Shearing is performed using CSC array indices,
and the result is converted back to whatever sparse format
the data was originally provided in.
"""
fmt = X.format
if axis == 0:
X = X.T
# Now we're definitely rolling on the correct axis
X_shear = X.tocsc(copy=True)
# The idea here is to repeat the shear amount (factor * range)
# by the number of non-zeros for each column.
# The number of non-zeros is computed by diffing the index pointer array
roll = np.repeat(factor * np.arange(X_shear.shape[1]), np.diff(X_shear.indptr))
# In-place roll
np.mod(X_shear.indices + roll, X_shear.shape[0], out=X_shear.indices)
if axis == 0:
X_shear = X_shear.T
# And convert back to the input format
return X_shear.asformat(fmt)
_ArrayOrSparseMatrix = TypeVar(
"_ArrayOrSparseMatrix", bound=Union[np.ndarray, scipy.sparse.spmatrix]
)
@overload
def shear(X: np.ndarray, *, factor: int = ..., axis: int = ...) -> np.ndarray:
...
@overload
def shear(
X: scipy.sparse.spmatrix, *, factor: int = ..., axis: int = ...
) -> scipy.sparse.spmatrix:
...
def shear(
X: _ArrayOrSparseMatrix, *, factor: int = 1, axis: int = -1
) -> _ArrayOrSparseMatrix:
"""Shear a matrix by a given factor.
The column ``X[:, n]`` will be displaced (rolled)
by ``factor * n``
This is primarily useful for converting between lag and recurrence
representations: shearing with ``factor=-1`` converts the main diagonal
to a horizontal. Shearing with ``factor=1`` converts a horizontal to
a diagonal.
Parameters
----------
X : np.ndarray [ndim=2] or scipy.sparse matrix
The array to be sheared
factor : integer
The shear factor: ``X[:, n] -> np.roll(X[:, n], factor * n)``
axis : integer
The axis along which to shear
Returns
-------
X_shear : same type as ``X``
The sheared matrix
Examples
--------
>>> E = np.eye(3)
>>> librosa.util.shear(E, factor=-1, axis=-1)
array([[1., 1., 1.],
[0., 0., 0.],
[0., 0., 0.]])
>>> librosa.util.shear(E, factor=-1, axis=0)
array([[1., 0., 0.],
[1., 0., 0.],
[1., 0., 0.]])
>>> librosa.util.shear(E, factor=1, axis=-1)
array([[1., 0., 0.],
[0., 0., 1.],
[0., 1., 0.]])
"""
if not np.issubdtype(type(factor), np.integer):
raise ParameterError(f"factor={factor} must be integer-valued")
# Suppress type checks because mypy doesn't like numba jitting
# or scipy sparse conversion
if scipy.sparse.isspmatrix(X):
return __shear_sparse(X, factor=factor, axis=axis) # type: ignore
else:
return __shear_dense(X, factor=factor, axis=axis) # type: ignore
def stack(arrays: List[np.ndarray], *, axis: int = 0) -> np.ndarray:
"""Stack one or more arrays along a target axis.
This function is similar to `np.stack`, except that memory contiguity is
retained when stacking along the first dimension.
This is useful when combining multiple monophonic audio signals into a
multi-channel signal, or when stacking multiple feature representations
to form a multi-dimensional array.
Parameters
----------
arrays : list
one or more `np.ndarray`
axis : integer
The target axis along which to stack. ``axis=0`` creates a new first axis,
and ``axis=-1`` creates a new last axis.
Returns
-------
arr_stack : np.ndarray [shape=(len(arrays), array_shape) or shape=(array_shape, len(arrays))]
The input arrays, stacked along the target dimension.
If ``axis=0``, then ``arr_stack`` will be F-contiguous.
Otherwise, ``arr_stack`` will be C-contiguous by default, as computed by
`np.stack`.
Raises
------
ParameterError
- If ``arrays`` do not all have the same shape
- If no ``arrays`` are given
See Also
--------
numpy.stack
numpy.ndarray.flags
frame
Examples
--------
Combine two buffers into a contiguous arrays
>>> y_left = np.ones(5)
>>> y_right = -np.ones(5)
>>> y_stereo = librosa.util.stack([y_left, y_right], axis=0)
>>> y_stereo
array([[ 1., 1., 1., 1., 1.],
[-1., -1., -1., -1., -1.]])
>>> y_stereo.flags
C_CONTIGUOUS : False
F_CONTIGUOUS : True
OWNDATA : True
WRITEABLE : True
ALIGNED : True
WRITEBACKIFCOPY : False
UPDATEIFCOPY : False
Or along the trailing axis
>>> y_stereo = librosa.util.stack([y_left, y_right], axis=-1)
>>> y_stereo
array([[ 1., -1.],
[ 1., -1.],
[ 1., -1.],
[ 1., -1.],
[ 1., -1.]])
>>> y_stereo.flags
C_CONTIGUOUS : True
F_CONTIGUOUS : False
OWNDATA : True
WRITEABLE : True
ALIGNED : True
WRITEBACKIFCOPY : False
UPDATEIFCOPY : False
"""
shapes = {arr.shape for arr in arrays}
if len(shapes) > 1:
raise ParameterError("all input arrays must have the same shape")
elif len(shapes) < 1:
raise ParameterError("at least one input array must be provided for stack")
shape_in = shapes.pop()
if axis != 0:
return np.stack(arrays, axis=axis)
else:
# If axis is 0, enforce F-ordering
shape = tuple([len(arrays)] + list(shape_in))
# Find the common dtype for all inputs
dtype = np.find_common_type([arr.dtype for arr in arrays], [])
# Allocate an empty array of the right shape and type
result = np.empty(shape, dtype=dtype, order="F")
# Stack into the preallocated buffer
np.stack(arrays, axis=axis, out=result)
return result
def dtype_r2c(d: DTypeLike, *, default: Optional[type] = np.complex64) -> DTypeLike:
"""Find the complex numpy dtype corresponding to a real dtype.
This is used to maintain numerical precision and memory footprint
when constructing complex arrays from real-valued data
(e.g. in a Fourier transform).
A `float32` (single-precision) type maps to `complex64`,
while a `float64` (double-precision) maps to `complex128`.
Parameters
----------
d : np.dtype
The real-valued dtype to convert to complex.
If ``d`` is a complex type already, it will be returned.
default : np.dtype, optional
The default complex target type, if ``d`` does not match a
known dtype
Returns
-------
d_c : np.dtype
The complex dtype
See Also
--------
dtype_c2r
numpy.dtype
Examples
--------
>>> librosa.util.dtype_r2c(np.float32)
dtype('complex64')
>>> librosa.util.dtype_r2c(np.int16)
dtype('complex64')
>>> librosa.util.dtype_r2c(np.complex128)
dtype('complex128')
"""
mapping: Dict[DTypeLike, type] = {
np.dtype(np.float32): np.complex64,
np.dtype(np.float64): np.complex128,
np.dtype(float): np.dtype(complex).type,
}
# If we're given a complex type already, return it
dt = np.dtype(d)
if dt.kind == "c":
return dt
# Otherwise, try to map the dtype.
# If no match is found, return the default.
return np.dtype(mapping.get(dt, default))
def dtype_c2r(d: DTypeLike, *, default: Optional[type] = np.float32) -> DTypeLike:
"""Find the real numpy dtype corresponding to a complex dtype.
This is used to maintain numerical precision and memory footprint
when constructing real arrays from complex-valued data
(e.g. in an inverse Fourier transform).
A `complex64` (single-precision) type maps to `float32`,
while a `complex128` (double-precision) maps to `float64`.
Parameters
----------
d : np.dtype
The complex-valued dtype to convert to real.
If ``d`` is a real (float) type already, it will be returned.
default : np.dtype, optional
The default real target type, if ``d`` does not match a
known dtype
Returns
-------
d_r : np.dtype
The real dtype
See Also
--------
dtype_r2c
numpy.dtype
Examples
--------
>>> librosa.util.dtype_r2c(np.complex64)
dtype('float32')
>>> librosa.util.dtype_r2c(np.float32)
dtype('float32')
>>> librosa.util.dtype_r2c(np.int16)
dtype('float32')
>>> librosa.util.dtype_r2c(np.complex128)
dtype('float64')
"""
mapping: Dict[DTypeLike, type] = {
np.dtype(np.complex64): np.float32,
np.dtype(np.complex128): np.float64,
np.dtype(complex): np.dtype(float).type,
}
# If we're given a real type already, return it
dt = np.dtype(d)
if dt.kind == "f":
return dt
# Otherwise, try to map the dtype.
# If no match is found, return the default.
return np.dtype(mapping.get(dt, default))
@numba.jit(nopython=True, cache=True)
def __count_unique(x):
"""Count the number of unique values in an array.
This function is a helper for `count_unique` and is not
to be called directly.
"""
uniques = np.unique(x)
return uniques.shape[0]
def count_unique(data: np.ndarray, *, axis: int = -1) -> np.ndarray:
"""Count the number of unique values in a multi-dimensional array
along a given axis.
Parameters
----------
data : np.ndarray
The input array
axis : int
The target axis to count
Returns
-------
n_uniques
The number of unique values.
This array will have one fewer dimension than the input.
See Also
--------
is_unique
Examples
--------
>>> x = np.vander(np.arange(5))
>>> x
array([[ 0, 0, 0, 0, 1],
[ 1, 1, 1, 1, 1],
[ 16, 8, 4, 2, 1],
[ 81, 27, 9, 3, 1],
[256, 64, 16, 4, 1]])
>>> # Count unique values along rows (within columns)
>>> librosa.util.count_unique(x, axis=0)
array([5, 5, 5, 5, 1])
>>> # Count unique values along columns (within rows)
>>> librosa.util.count_unique(x, axis=-1)
array([2, 1, 5, 5, 5])
"""
return np.apply_along_axis(__count_unique, axis, data)
@numba.jit(nopython=True, cache=True)
def __is_unique(x):
"""Determine if the input array has all unique values.
This function is a helper for `is_unique` and is not
to be called directly.
"""
uniques = np.unique(x)
return uniques.shape[0] == x.size
def is_unique(data: np.ndarray, *, axis: int = -1) -> np.ndarray:
"""Determine if the input array consists of all unique values
along a given axis.
Parameters
----------
data : np.ndarray
The input array
axis : int
The target axis
Returns
-------
is_unique
Array of booleans indicating whether the data is unique along the chosen
axis.
This array will have one fewer dimension than the input.
See Also
--------
count_unique
Examples
--------
>>> x = np.vander(np.arange(5))
>>> x
array([[ 0, 0, 0, 0, 1],
[ 1, 1, 1, 1, 1],
[ 16, 8, 4, 2, 1],
[ 81, 27, 9, 3, 1],
[256, 64, 16, 4, 1]])
>>> # Check uniqueness along rows
>>> librosa.util.is_unique(x, axis=0)
array([ True, True, True, True, False])
>>> # Check uniqueness along columns
>>> librosa.util.is_unique(x, axis=-1)
array([False, False, True, True, True])
"""
return np.apply_along_axis(__is_unique, axis, data)
@numba.vectorize(
["float32(complex64)", "float64(complex128)"], nopython=True, cache=True, identity=0
) # type: ignore
def _cabs2(x: _ComplexLike_co) -> _FloatLike_co: # pragma: no cover
"""Efficiently compute abs2 on complex inputs"""
return x.real**2 + x.imag**2
_Number = Union[complex, "np.number[Any]"]
_NumberOrArray = TypeVar("_NumberOrArray", bound=Union[_Number, np.ndarray])
def abs2(x: _NumberOrArray, dtype: Optional[DTypeLike] = None) -> _NumberOrArray:
"""Compute the squared magnitude of a real or complex array.
This function is equivalent to calling `np.abs(x)**2` but it
is slightly more efficient.
Parameters
----------
x : np.ndarray or scalar, real or complex typed
The input data, either real (float32, float64) or complex (complex64, complex128) typed
dtype : np.dtype, optional
The data type of the output array.
If not provided, it will be inferred from `x`
Returns
-------
p : np.ndarray or scale, real
squared magnitude of `x`
Examples
--------
>>> librosa.util.abs2(3 + 4j)
25.0
>>> librosa.util.abs2((0.5j)**np.arange(8))
array([1.000e+00, 2.500e-01, 6.250e-02, 1.562e-02, 3.906e-03, 9.766e-04,
2.441e-04, 6.104e-05])
"""
if np.iscomplexobj(x):
# suppress type check, mypy doesn't like vectorization
y = _cabs2(x)
if dtype is None:
return y # type: ignore
else:
return y.astype(dtype) # type: ignore
else:
# suppress type check, mypy doesn't know this is real
return np.power(x, 2, dtype=dtype) # type: ignore
@numba.vectorize(
["complex64(float32)", "complex128(float64)"], nopython=True, cache=True, identity=1
) # type: ignore
def _phasor_angles(x) -> np.complex_: # pragma: no cover
return np.cos(x) + 1j * np.sin(x) # type: ignore
_Real = Union[float, "np.integer[Any]", "np.floating[Any]"]
@overload
def phasor(angles: np.ndarray, *, mag: Optional[np.ndarray] = ...) -> np.ndarray:
...
@overload
def phasor(angles: _Real, *, mag: Optional[_Number] = ...) -> np.complex_:
...
def phasor(
angles: Union[np.ndarray, _Real],
*,
mag: Optional[Union[np.ndarray, _Number]] = None,
) -> Union[np.ndarray, np.complex_]:
"""Construct a complex phasor representation from angles.
When `mag` is not provided, this is equivalent to:
z = np.cos(angles) + 1j * np.sin(angles)
or by Euler's formula:
z = np.exp(1j * angles)
When `mag` is provided, this is equivalent to:
z = mag * np.exp(1j * angles)
This function should be more efficient (in time and memory) than the equivalent'
formulations above, but produce numerically identical results.
Parameters
----------
angles : np.ndarray or scalar, real-valued
Angle(s), measured in radians
mag : np.ndarray or scalar, optional
If provided, phasor(s) will be scaled by `mag`.
If not provided (default), phasors will have unit magnitude.
`mag` must be of compatible shape to multiply with `angles`.
Returns
-------
z : np.ndarray or scalar, complex-valued
Complex number(s) z corresponding to the given angle(s)
and optional magnitude(s).
Examples
--------
Construct unit phasors at angles 0, pi/2, and pi:
>>> librosa.util.phasor([0, np.pi/2, np.pi])
array([ 1.000e+00+0.000e+00j, 6.123e-17+1.000e+00j,
-1.000e+00+1.225e-16j])
Construct a phasor with magnitude 1/2:
>>> librosa.util.phasor(np.pi/2, mag=0.5)
(3.061616997868383e-17+0.5j)
Or arrays of angles and magnitudes:
>>> librosa.util.phasor(np.array([0, np.pi/2]), mag=np.array([0.5, 1.5]))
array([5.000e-01+0.j , 9.185e-17+1.5j])
"""
z = _phasor_angles(angles)
if mag is not None:
z *= mag
return z # type: ignore