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"""Utility functions""" |
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import scipy.ndimage |
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import scipy.sparse |
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import numpy as np |
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import numba |
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from numpy.lib.stride_tricks import as_strided |
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from .._cache import cache |
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from .exceptions import ParameterError |
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from .deprecation import Deprecated |
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from .decorators import deprecate_positional_args |
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MAX_MEM_BLOCK = 2 ** 8 * 2 ** 10 |
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__all__ = [ |
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"MAX_MEM_BLOCK", |
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"frame", |
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"pad_center", |
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"expand_to", |
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"fix_length", |
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"valid_audio", |
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"valid_int", |
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"valid_intervals", |
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"fix_frames", |
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"axis_sort", |
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"localmax", |
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"localmin", |
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"normalize", |
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"peak_pick", |
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"sparsify_rows", |
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"shear", |
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"stack", |
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"fill_off_diagonal", |
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"index_to_slice", |
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"sync", |
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"softmask", |
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"buf_to_float", |
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"tiny", |
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"cyclic_gradient", |
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"dtype_r2c", |
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"dtype_c2r", |
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"count_unique", |
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"is_unique", |
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] |
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@deprecate_positional_args |
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def frame(x, *, frame_length, hop_length, axis=-1, writeable=False, subok=False): |
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"""Slice a data array into (overlapping) frames. |
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This implementation uses low-level stride manipulation to avoid |
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making a copy of the data. The resulting frame representation |
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is a new view of the same input data. |
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For example, a one-dimensional input ``x = [0, 1, 2, 3, 4, 5, 6]`` |
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can be framed with frame length 3 and hop length 2 in two ways. |
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The first (``axis=-1``), results in the array ``x_frames``:: |
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[[0, 2, 4], |
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[1, 3, 5], |
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[2, 4, 6]] |
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where each column ``x_frames[:, i]`` contains a contiguous slice of |
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the input ``x[i * hop_length : i * hop_length + frame_length]``. |
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The second way (``axis=0``) results in the array ``x_frames``:: |
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[[0, 1, 2], |
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[2, 3, 4], |
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[4, 5, 6]] |
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where each row ``x_frames[i]`` contains a contiguous slice of the input. |
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This generalizes to higher dimensional inputs, as shown in the examples below. |
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In general, the framing operation increments by 1 the number of dimensions, |
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adding a new "frame axis" either before the framing axis (if ``axis < 0``) |
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or after the framing axis (if ``axis >= 0``). |
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Parameters |
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---------- |
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x : np.ndarray |
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Array to frame |
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frame_length : int > 0 [scalar] |
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Length of the frame |
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hop_length : int > 0 [scalar] |
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Number of steps to advance between frames |
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axis : int |
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The axis along which to frame. |
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writeable : bool |
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If ``True``, then the framed view of ``x`` is read-only. |
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If ``False``, then the framed view is read-write. Note that writing to the framed view |
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will also write to the input array ``x`` in this case. |
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subok : bool |
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If True, sub-classes will be passed-through, otherwise the returned array will be |
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forced to be a base-class array (default). |
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Returns |
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------- |
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x_frames : np.ndarray [shape=(..., frame_length, N_FRAMES, ...)] |
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A framed view of ``x``, for example with ``axis=-1`` (framing on the last dimension):: |
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x_frames[..., j] == x[..., j * hop_length : j * hop_length + frame_length] |
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If ``axis=0`` (framing on the first dimension), then:: |
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x_frames[j] = x[j * hop_length : j * hop_length + frame_length] |
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Raises |
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------ |
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ParameterError |
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If ``x.shape[axis] < frame_length``, there is not enough data to fill one frame. |
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If ``hop_length < 1``, frames cannot advance. |
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See Also |
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-------- |
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numpy.lib.stride_tricks.as_strided |
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Examples |
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-------- |
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Extract 2048-sample frames from monophonic signal with a hop of 64 samples per frame |
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>>> y, sr = librosa.load(librosa.ex('trumpet')) |
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>>> frames = librosa.util.frame(y, frame_length=2048, hop_length=64) |
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>>> frames |
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array([[-1.407e-03, -2.604e-02, ..., -1.795e-05, -8.108e-06], |
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[-4.461e-04, -3.721e-02, ..., -1.573e-05, -1.652e-05], |
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..., |
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[ 7.960e-02, -2.335e-01, ..., -6.815e-06, 1.266e-05], |
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[ 9.568e-02, -1.252e-01, ..., 7.397e-06, -1.921e-05]], |
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dtype=float32) |
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>>> y.shape |
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(117601,) |
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>>> frames.shape |
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(2048, 1806) |
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Or frame along the first axis instead of the last: |
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>>> frames = librosa.util.frame(y, frame_length=2048, hop_length=64, axis=0) |
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>>> frames.shape |
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(1806, 2048) |
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Frame a stereo signal: |
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>>> y, sr = librosa.load(librosa.ex('trumpet', hq=True), mono=False) |
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>>> y.shape |
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(2, 117601) |
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>>> frames = librosa.util.frame(y, frame_length=2048, hop_length=64) |
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(2, 2048, 1806) |
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Carve an STFT into fixed-length patches of 32 frames with 50% overlap |
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>>> y, sr = librosa.load(librosa.ex('trumpet')) |
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>>> S = np.abs(librosa.stft(y)) |
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>>> S.shape |
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(1025, 230) |
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>>> S_patch = librosa.util.frame(S, frame_length=32, hop_length=16) |
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>>> S_patch.shape |
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(1025, 32, 13) |
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>>> # The first patch contains the first 32 frames of S |
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>>> np.allclose(S_patch[:, :, 0], S[:, :32]) |
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True |
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>>> # The second patch contains frames 16 to 16+32=48, and so on |
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>>> np.allclose(S_patch[:, :, 1], S[:, 16:48]) |
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True |
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""" |
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x = np.array(x, copy=False, subok=subok) |
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if x.shape[axis] < frame_length: |
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raise ParameterError( |
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"Input is too short (n={:d})" |
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" for frame_length={:d}".format(x.shape[axis], frame_length) |
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) |
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if hop_length < 1: |
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raise ParameterError("Invalid hop_length: {:d}".format(hop_length)) |
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out_strides = x.strides + tuple([x.strides[axis]]) |
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x_shape_trimmed = list(x.shape) |
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x_shape_trimmed[axis] -= frame_length - 1 |
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out_shape = tuple(x_shape_trimmed) + tuple([frame_length]) |
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xw = as_strided( |
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x, strides=out_strides, shape=out_shape, subok=subok, writeable=writeable |
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) |
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if axis < 0: |
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target_axis = axis - 1 |
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else: |
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target_axis = axis + 1 |
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xw = np.moveaxis(xw, -1, target_axis) |
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slices = [slice(None)] * xw.ndim |
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slices[axis] = slice(0, None, hop_length) |
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return xw[tuple(slices)] |
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@deprecate_positional_args |
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@cache(level=20) |
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def valid_audio(y, *, mono=Deprecated()): |
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"""Determine whether a variable contains valid audio data. |
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The following conditions must be satisfied: |
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- ``type(y)`` is ``np.ndarray`` |
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- ``y.dtype`` is floating-point |
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- ``y.ndim != 0`` (must have at least one dimension) |
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- ``np.isfinite(y).all()`` samples must be all finite values |
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If ``mono`` is specified, then we additionally require |
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- ``y.ndim == 1`` |
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Parameters |
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---------- |
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y : np.ndarray |
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The input data to validate |
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mono : bool |
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Whether or not to require monophonic audio |
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.. warning:: The ``mono`` parameter is deprecated in version 0.9 and will be |
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removed in 0.10. |
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Returns |
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------- |
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valid : bool |
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True if all tests pass |
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Raises |
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------ |
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ParameterError |
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In any of the conditions specified above fails |
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Notes |
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----- |
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This function caches at level 20. |
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Examples |
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-------- |
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>>> # By default, valid_audio allows only mono signals |
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>>> filepath = librosa.ex('trumpet', hq=True) |
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>>> y_mono, sr = librosa.load(filepath, mono=True) |
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>>> y_stereo, _ = librosa.load(filepath, mono=False) |
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>>> librosa.util.valid_audio(y_mono), librosa.util.valid_audio(y_stereo) |
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True, False |
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>>> # To allow stereo signals, set mono=False |
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>>> librosa.util.valid_audio(y_stereo, mono=False) |
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True |
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See Also |
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-------- |
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numpy.float32 |
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""" |
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if not isinstance(y, np.ndarray): |
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raise ParameterError("Audio data must be of type numpy.ndarray") |
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if not np.issubdtype(y.dtype, np.floating): |
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raise ParameterError("Audio data must be floating-point") |
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if y.ndim == 0: |
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raise ParameterError( |
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"Audio data must be at least one-dimensional, given y.shape={}".format( |
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y.shape |
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) |
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) |
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if isinstance(mono, Deprecated): |
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mono = False |
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if mono and y.ndim != 1: |
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raise ParameterError( |
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"Invalid shape for monophonic audio: " |
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"ndim={:d}, shape={}".format(y.ndim, y.shape) |
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) |
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if not np.isfinite(y).all(): |
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raise ParameterError("Audio buffer is not finite everywhere") |
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return True |
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@deprecate_positional_args |
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def valid_int(x, *, cast=None): |
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"""Ensure that an input value is integer-typed. |
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This is primarily useful for ensuring integrable-valued |
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array indices. |
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Parameters |
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---------- |
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x : number |
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A scalar value to be cast to int |
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cast : function [optional] |
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A function to modify ``x`` before casting. |
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Default: `np.floor` |
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Returns |
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------- |
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x_int : int |
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``x_int = int(cast(x))`` |
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Raises |
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------ |
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ParameterError |
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If ``cast`` is provided and is not callable. |
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""" |
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if cast is None: |
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cast = np.floor |
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if not callable(cast): |
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raise ParameterError("cast parameter must be callable") |
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return int(cast(x)) |
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def valid_intervals(intervals): |
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"""Ensure that an array is a valid representation of time intervals: |
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- intervals.ndim == 2 |
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- intervals.shape[1] == 2 |
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- intervals[i, 0] <= intervals[i, 1] for all i |
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Parameters |
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---------- |
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intervals : np.ndarray [shape=(n, 2)] |
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set of time intervals |
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Returns |
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------- |
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valid : bool |
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True if ``intervals`` passes validation. |
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""" |
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if intervals.ndim != 2 or intervals.shape[-1] != 2: |
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raise ParameterError("intervals must have shape (n, 2)") |
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if np.any(intervals[:, 0] > intervals[:, 1]): |
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raise ParameterError( |
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"intervals={} must have non-negative durations".format(intervals) |
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) |
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return True |
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@deprecate_positional_args |
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def pad_center(data, *, size, axis=-1, **kwargs): |
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"""Pad an array to a target length along a target axis. |
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This differs from `np.pad` by centering the data prior to padding, |
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analogous to `str.center` |
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Examples |
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-------- |
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>>> # Generate a vector |
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>>> data = np.ones(5) |
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>>> librosa.util.pad_center(data, size=10, mode='constant') |
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array([ 0., 0., 1., 1., 1., 1., 1., 0., 0., 0.]) |
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>>> # Pad a matrix along its first dimension |
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>>> data = np.ones((3, 5)) |
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>>> librosa.util.pad_center(data, size=7, axis=0) |
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array([[ 0., 0., 0., 0., 0.], |
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[ 0., 0., 0., 0., 0.], |
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[ 1., 1., 1., 1., 1.], |
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[ 1., 1., 1., 1., 1.], |
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[ 1., 1., 1., 1., 1.], |
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[ 0., 0., 0., 0., 0.], |
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[ 0., 0., 0., 0., 0.]]) |
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>>> # Or its second dimension |
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>>> librosa.util.pad_center(data, size=7, axis=1) |
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array([[ 0., 1., 1., 1., 1., 1., 0.], |
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[ 0., 1., 1., 1., 1., 1., 0.], |
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[ 0., 1., 1., 1., 1., 1., 0.]]) |
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Parameters |
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---------- |
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data : np.ndarray |
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Vector to be padded and centered |
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size : int >= len(data) [scalar] |
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Length to pad ``data`` |
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axis : int |
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Axis along which to pad and center the data |
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**kwargs : additional keyword arguments |
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arguments passed to `np.pad` |
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Returns |
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------- |
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data_padded : np.ndarray |
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``data`` centered and padded to length ``size`` along the |
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specified axis |
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Raises |
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------ |
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ParameterError |
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If ``size < data.shape[axis]`` |
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See Also |
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-------- |
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numpy.pad |
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""" |
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kwargs.setdefault("mode", "constant") |
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n = data.shape[axis] |
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lpad = int((size - n) // 2) |
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lengths = [(0, 0)] * data.ndim |
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lengths[axis] = (lpad, int(size - n - lpad)) |
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if lpad < 0: |
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raise ParameterError( |
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("Target size ({:d}) must be " "at least input size ({:d})").format(size, n) |
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) |
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return np.pad(data, lengths, **kwargs) |
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@deprecate_positional_args |
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def expand_to(x, *, ndim, axes): |
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"""Expand the dimensions of an input array with |
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Parameters |
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---------- |
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x : np.ndarray |
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The input array |
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ndim : int |
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The number of dimensions to expand to. Must be at least ``x.ndim`` |
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axes : int or slice |
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The target axis or axes to preserve from x. |
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All other axes will have length 1. |
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Returns |
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------- |
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x_exp : np.ndarray |
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The expanded version of ``x``, satisfying the following: |
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``x_exp[axes] == x`` |
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``x_exp.ndim == ndim`` |
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See Also |
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-------- |
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np.expand_dims |
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Examples |
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-------- |
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Expand a 1d array into an (n, 1) shape |
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>>> x = np.arange(3) |
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>>> librosa.util.expand_to(x, ndim=2, axes=0) |
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array([[0], |
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[1], |
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[2]]) |
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Expand a 1d array into a (1, n) shape |
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>>> librosa.util.expand_to(x, ndim=2, axes=1) |
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array([[0, 1, 2]]) |
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Expand a 2d array into (1, n, m, 1) shape |
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>>> x = np.vander(np.arange(3)) |
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>>> librosa.util.expand_to(x, ndim=4, axes=[1,2]).shape |
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(1, 3, 3, 1) |
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""" |
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try: |
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axes = tuple(axes) |
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except TypeError: |
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axes = tuple([axes]) |
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if len(axes) != x.ndim: |
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raise ParameterError( |
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"Shape mismatch between axes={} and input x.shape={}".format(axes, x.shape) |
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) |
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if ndim < x.ndim: |
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raise ParameterError( |
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"Cannot expand x.shape={} to fewer dimensions ndim={}".format(x.shape, ndim) |
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) |
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shape = [1] * ndim |
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for i, axi in enumerate(axes): |
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shape[axi] = x.shape[i] |
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return x.reshape(shape) |
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@deprecate_positional_args |
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def fix_length(data, *, size, axis=-1, **kwargs): |
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"""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 |
|
|
|
|
|
|
|
|
@deprecate_positional_args |
|
|
def fix_frames(frames, *, x_min=0, x_max=None, pad=True): |
|
|
"""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") |
|
|
|
|
|
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((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] |
|
|
|
|
|
return np.unique(frames).astype(int) |
|
|
|
|
|
|
|
|
@deprecate_positional_args |
|
|
def axis_sort(S, *, axis=-1, index=False, value=None): |
|
|
"""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 |
|
|
|
|
|
if index: |
|
|
return S[tuple(sort_slice)], idx |
|
|
else: |
|
|
return S[tuple(sort_slice)] |
|
|
|
|
|
|
|
|
@deprecate_positional_args |
|
|
@cache(level=40) |
|
|
def normalize(S, *, norm=np.inf, axis=0, threshold=None, fill=None): |
|
|
"""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 ]]) |
|
|
""" |
|
|
|
|
|
|
|
|
if threshold is None: |
|
|
threshold = tiny(S) |
|
|
|
|
|
elif threshold <= 0: |
|
|
raise ParameterError( |
|
|
"threshold={} must be strictly " "positive".format(threshold) |
|
|
) |
|
|
|
|
|
if fill not in [None, False, True]: |
|
|
raise ParameterError("fill={} must be None or boolean".format(fill)) |
|
|
|
|
|
if not np.all(np.isfinite(S)): |
|
|
raise ParameterError("Input must be finite") |
|
|
|
|
|
|
|
|
mag = np.abs(S).astype(float) |
|
|
|
|
|
|
|
|
fill_norm = 1 |
|
|
|
|
|
if 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) |
|
|
|
|
|
elif norm is None: |
|
|
return S |
|
|
|
|
|
else: |
|
|
raise ParameterError("Unsupported norm: {}".format(repr(norm))) |
|
|
|
|
|
|
|
|
small_idx = length < threshold |
|
|
|
|
|
Snorm = np.empty_like(S) |
|
|
if fill is None: |
|
|
|
|
|
length[small_idx] = 1.0 |
|
|
Snorm[:] = S / length |
|
|
|
|
|
elif fill: |
|
|
|
|
|
|
|
|
|
|
|
length[small_idx] = np.nan |
|
|
Snorm[:] = S / length |
|
|
Snorm[np.isnan(Snorm)] = fill_norm |
|
|
else: |
|
|
|
|
|
|
|
|
length[small_idx] = np.inf |
|
|
Snorm[:] = S / length |
|
|
|
|
|
return Snorm |
|
|
|
|
|
|
|
|
@deprecate_positional_args |
|
|
def localmax(x, *, axis=0): |
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"""Find local maxima in an array |
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|
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|
An element ``x[i]`` is considered a local maximum if the following |
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|
conditions are met: |
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|
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- ``x[i] > x[i-1]`` |
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- ``x[i] >= x[i+1]`` |
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|
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Note that the first condition is strict, and that the first element |
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``x[0]`` will never be considered as a local maximum. |
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|
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Examples |
|
|
-------- |
|
|
>>> x = np.array([1, 0, 1, 2, -1, 0, -2, 1]) |
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>>> librosa.util.localmax(x) |
|
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array([False, False, False, True, False, True, False, True], dtype=bool) |
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|
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>>> # Two-dimensional example |
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>>> x = np.array([[1,0,1], [2, -1, 0], [2, 1, 3]]) |
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>>> librosa.util.localmax(x, axis=0) |
|
|
array([[False, False, False], |
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[ True, False, False], |
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[False, True, True]], dtype=bool) |
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>>> librosa.util.localmax(x, axis=1) |
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|
array([[False, False, True], |
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[False, False, True], |
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[False, False, True]], dtype=bool) |
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|
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Parameters |
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|
---------- |
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|
x : np.ndarray [shape=(d1,d2,...)] |
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|
input vector or array |
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axis : int |
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|
axis along which to compute local maximality |
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|
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|
Returns |
|
|
------- |
|
|
m : np.ndarray [shape=x.shape, dtype=bool] |
|
|
indicator array of local maximality along ``axis`` |
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|
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|
See Also |
|
|
-------- |
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|
localmin |
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|
""" |
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|
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paddings = [(0, 0)] * x.ndim |
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paddings[axis] = (1, 1) |
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|
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x_pad = np.pad(x, paddings, mode="edge") |
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inds1 = [slice(None)] * x.ndim |
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inds1[axis] = slice(0, -2) |
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inds2 = [slice(None)] * x.ndim |
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inds2[axis] = slice(2, x_pad.shape[axis]) |
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return (x > x_pad[tuple(inds1)]) & (x >= x_pad[tuple(inds2)]) |
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@deprecate_positional_args |
|
|
def localmin(x, *, axis=0): |
|
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"""Find local minima in an array |
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|
|
|
An element ``x[i]`` is considered a local minimum if the following |
|
|
conditions are met: |
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|
|
|
- ``x[i] < x[i-1]`` |
|
|
- ``x[i] <= x[i+1]`` |
|
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|
|
|
Note that the first condition is strict, and that the first element |
|
|
``x[0]`` will never be considered as a local minimum. |
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|
|
|
Examples |
|
|
-------- |
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|
>>> x = np.array([1, 0, 1, 2, -1, 0, -2, 1]) |
|
|
>>> librosa.util.localmin(x) |
|
|
array([False, True, False, False, True, False, True, False]) |
|
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|
|
|
>>> # 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]]) |
|
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|
|
|
>>> librosa.util.localmin(x, axis=1) |
|
|
array([[False, True, False], |
|
|
[False, True, False], |
|
|
[False, True, False]]) |
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|
|
|
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 |
|
|
""" |
|
|
|
|
|
paddings = [(0, 0)] * x.ndim |
|
|
paddings[axis] = (1, 1) |
|
|
|
|
|
x_pad = np.pad(x, paddings, mode="edge") |
|
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|
|
inds1 = [slice(None)] * x.ndim |
|
|
inds1[axis] = slice(0, -2) |
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|
|
inds2 = [slice(None)] * x.ndim |
|
|
inds2[axis] = slice(2, x_pad.shape[axis]) |
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|
|
return (x < x_pad[tuple(inds1)]) & (x <= x_pad[tuple(inds2)]) |
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|
@deprecate_positional_args |
|
|
def peak_pick(x, *, pre_max, post_max, pre_avg, post_avg, delta, wait): |
|
|
"""Uses a flexible heuristic to pick peaks in a signal. |
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|
|
A sample n is selected as an peak if the corresponding ``x[n]`` |
|
|
fulfills the following three conditions: |
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|
|
|
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). |
|
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|
|
|
This implementation is based on [#]_ and [#]_. |
|
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|
|
|
.. [#] Boeck, Sebastian, Florian Krebs, and Markus Schedl. |
|
|
"Evaluating the Online Capabilities of Onset Detection Methods." ISMIR. |
|
|
2012. |
|
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|
|
|
.. [#] 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") |
|
|
|
|
|
|
|
|
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) |
|
|
|
|
|
|
|
|
max_length = pre_max + post_max |
|
|
max_origin = np.ceil(0.5 * (pre_max - post_max)) |
|
|
|
|
|
|
|
|
mov_max = scipy.ndimage.filters.maximum_filter1d( |
|
|
x, int(max_length), mode="constant", origin=int(max_origin), cval=x.min() |
|
|
) |
|
|
|
|
|
|
|
|
avg_length = pre_avg + post_avg |
|
|
avg_origin = np.ceil(0.5 * (pre_avg - post_avg)) |
|
|
|
|
|
|
|
|
mov_avg = scipy.ndimage.filters.uniform_filter1d( |
|
|
x, int(avg_length), mode="nearest", origin=int(avg_origin) |
|
|
) |
|
|
|
|
|
|
|
|
n = 0 |
|
|
|
|
|
while n - pre_avg < 0 and 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 |
|
|
|
|
|
n = x.shape[0] - post_avg |
|
|
|
|
|
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 |
|
|
|
|
|
|
|
|
detections = x * (x == mov_max) |
|
|
|
|
|
|
|
|
detections = detections * (detections >= (mov_avg + delta)) |
|
|
|
|
|
|
|
|
peaks = [] |
|
|
|
|
|
|
|
|
last_onset = -np.inf |
|
|
|
|
|
for i in np.nonzero(detections)[0]: |
|
|
|
|
|
if i > last_onset + wait: |
|
|
peaks.append(i) |
|
|
|
|
|
last_onset = i |
|
|
|
|
|
return np.array(peaks) |
|
|
|
|
|
|
|
|
@deprecate_positional_args |
|
|
@cache(level=40) |
|
|
def sparsify_rows(x, *, quantile=0.01, dtype=None): |
|
|
"""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( |
|
|
"Input must have 2 or fewer dimensions. " |
|
|
"Provided x.shape={}.".format(x.shape) |
|
|
) |
|
|
|
|
|
if not 0.0 <= quantile < 1: |
|
|
raise ParameterError("Invalid quantile {:.2f}".format(quantile)) |
|
|
|
|
|
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() |
|
|
|
|
|
|
|
|
@deprecate_positional_args |
|
|
def buf_to_float(x, *, n_bytes=2, dtype=np.float32): |
|
|
"""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 |
|
|
""" |
|
|
|
|
|
|
|
|
scale = 1.0 / float(1 << ((8 * n_bytes) - 1)) |
|
|
|
|
|
|
|
|
fmt = "<i{:d}".format(n_bytes) |
|
|
|
|
|
|
|
|
return scale * np.frombuffer(x, fmt).astype(dtype) |
|
|
|
|
|
|
|
|
@deprecate_positional_args |
|
|
def index_to_slice(idx, *, idx_min=None, idx_max=None, step=None, pad=True): |
|
|
"""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)] |
|
|
""" |
|
|
|
|
|
|
|
|
idx_fixed = fix_frames(idx, x_min=idx_min, x_max=idx_max, pad=pad) |
|
|
|
|
|
|
|
|
return [slice(start, end, step) for (start, end) in zip(idx_fixed, idx_fixed[1:])] |
|
|
|
|
|
|
|
|
@deprecate_positional_args |
|
|
@cache(level=40) |
|
|
def sync(data, idx, *, aggregate=None, pad=True, axis=-1): |
|
|
"""Synchronous aggregation of a multi-dimensional array between 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 : iterable 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("Invalid index set: {}".format(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 |
|
|
idx_agg[axis] = i |
|
|
data_agg[tuple(idx_agg)] = aggregate(data[tuple(idx_in)], axis=axis) |
|
|
|
|
|
return data_agg |
|
|
|
|
|
|
|
|
@deprecate_positional_args |
|
|
def softmask(X, X_ref, *, power=1, split_zeros=False): |
|
|
"""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("Shape mismatch: {}!={}".format(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") |
|
|
|
|
|
|
|
|
dtype = X.dtype |
|
|
if not np.issubdtype(dtype, np.floating): |
|
|
dtype = np.float32 |
|
|
|
|
|
|
|
|
Z = np.maximum(X, X_ref).astype(dtype) |
|
|
bad_idx = Z < np.finfo(dtype).tiny |
|
|
Z[bad_idx] = 1 |
|
|
|
|
|
|
|
|
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] |
|
|
|
|
|
if split_zeros: |
|
|
mask[bad_idx] = 0.5 |
|
|
else: |
|
|
mask[bad_idx] = 0.0 |
|
|
else: |
|
|
|
|
|
mask = X > X_ref |
|
|
|
|
|
return mask |
|
|
|
|
|
|
|
|
def tiny(x): |
|
|
"""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 |
|
|
""" |
|
|
|
|
|
|
|
|
x = np.asarray(x) |
|
|
|
|
|
|
|
|
if np.issubdtype(x.dtype, np.floating) or np.issubdtype( |
|
|
x.dtype, np.complexfloating |
|
|
): |
|
|
dtype = x.dtype |
|
|
else: |
|
|
dtype = np.float32 |
|
|
|
|
|
return np.finfo(dtype).tiny |
|
|
|
|
|
|
|
|
@deprecate_positional_args |
|
|
def fill_off_diagonal(x, *, radius, value=0): |
|
|
"""Sets 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 : int |
|
|
``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 |
|
|
|
|
|
|
|
|
radius = 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) |
|
|
|
|
|
|
|
|
x[idx_u] = value |
|
|
x[idx_l] = value |
|
|
|
|
|
|
|
|
@deprecate_positional_args |
|
|
def cyclic_gradient(data, *, edge_order=1, axis=-1): |
|
|
"""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]) |
|
|
""" |
|
|
|
|
|
padding = [(0, 0)] * data.ndim |
|
|
padding[axis] = (edge_order, edge_order) |
|
|
data_pad = np.pad(data, padding, mode="wrap") |
|
|
|
|
|
|
|
|
grad = np.gradient(data_pad, edge_order=edge_order, axis=axis) |
|
|
|
|
|
|
|
|
slices = [slice(None)] * data.ndim |
|
|
slices[axis] = slice(edge_order, -edge_order) |
|
|
return grad[tuple(slices)] |
|
|
|
|
|
|
|
|
@numba.jit(nopython=True, cache=True) |
|
|
def __shear_dense(X, *, factor=+1, axis=-1): |
|
|
"""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 |
|
|
|
|
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|
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|
def __shear_sparse(X, *, factor=+1, axis=-1): |
|
|
"""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 |
|
|
|
|
|
|
|
|
X_shear = X.tocsc(copy=True) |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
roll = np.repeat(factor * np.arange(X_shear.shape[1]), np.diff(X_shear.indptr)) |
|
|
|
|
|
|
|
|
np.mod(X_shear.indices + roll, X_shear.shape[0], out=X_shear.indices) |
|
|
|
|
|
if axis == 0: |
|
|
X_shear = X_shear.T |
|
|
|
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|
|
|
|
return X_shear.asformat(fmt) |
|
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|
|
|
@deprecate_positional_args |
|
|
def shear(X, *, factor=1, axis=-1): |
|
|
"""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("factor={} must be integer-valued".format(factor)) |
|
|
|
|
|
if scipy.sparse.isspmatrix(X): |
|
|
return __shear_sparse(X, factor=factor, axis=axis) |
|
|
else: |
|
|
return __shear_dense(X, factor=factor, axis=axis) |
|
|
|
|
|
|
|
|
@deprecate_positional_args |
|
|
def stack(arrays, *, axis=0): |
|
|
"""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: |
|
|
|
|
|
shape = tuple([len(arrays)] + list(shape_in)) |
|
|
|
|
|
|
|
|
dtype = np.find_common_type([arr.dtype for arr in arrays], []) |
|
|
|
|
|
|
|
|
result = np.empty(shape, dtype=dtype, order="F") |
|
|
|
|
|
|
|
|
np.stack(arrays, axis=axis, out=result) |
|
|
|
|
|
return result |
|
|
|
|
|
|
|
|
@deprecate_positional_args |
|
|
def dtype_r2c(d, *, default=np.complex64): |
|
|
"""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 = { |
|
|
np.dtype(np.float32): np.complex64, |
|
|
np.dtype(np.float64): np.complex128, |
|
|
np.dtype(float): np.dtype(complex).type, |
|
|
} |
|
|
|
|
|
|
|
|
dt = np.dtype(d) |
|
|
if dt.kind == "c": |
|
|
return dt |
|
|
|
|
|
|
|
|
|
|
|
return np.dtype(mapping.get(dt, default)) |
|
|
|
|
|
|
|
|
@deprecate_positional_args |
|
|
def dtype_c2r(d, *, default=np.float32): |
|
|
"""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 = { |
|
|
np.dtype(np.complex64): np.float32, |
|
|
np.dtype(np.complex128): np.float64, |
|
|
np.dtype(complex): np.dtype(np.float).type, |
|
|
} |
|
|
|
|
|
|
|
|
dt = np.dtype(d) |
|
|
if dt.kind == "f": |
|
|
return dt |
|
|
|
|
|
|
|
|
|
|
|
return np.dtype(mapping.get(np.dtype(d), default)) |
|
|
|
|
|
|
|
|
@numba.jit(nopython=True, cache=True) |
|
|
def __count_unique(x): |
|
|
"""Counts 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] |
|
|
|
|
|
|
|
|
@deprecate_positional_args |
|
|
def count_unique(data, *, axis=-1): |
|
|
"""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): |
|
|
"""Determines 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 |
|
|
|
|
|
|
|
|
@deprecate_positional_args |
|
|
def is_unique(data, *, axis=-1): |
|
|
"""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) |
|
|
|
