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Source code for librosa.feature.utils
#!/usr/bin/env python
# -*- coding: utf-8 -*-
"""Feature manipulation utilities"""
import numpy as np
import scipy.signal
from numba import jit
from .._cache import cache
from ..util.exceptions import ParameterError
from typing import Any
__all__ = ["delta", "stack_memory"]
[docs]@cache(level=40)
def delta(
data: np.ndarray,
*,
width: int = 9,
order: int = 1,
axis: int = -1,
mode: str = "interp",
**kwargs: Any,
) -> np.ndarray:
r"""Compute delta features: local estimate of the derivative
of the input data along the selected axis.
Delta features are computed Savitsky-Golay filtering.
Parameters
----------
data : np.ndarray
the input data matrix (eg, spectrogram)
width : int, positive, odd [scalar]
Number of frames over which to compute the delta features.
Cannot exceed the length of ``data`` along the specified axis.
If ``mode='interp'``, then ``width`` must be at least ``data.shape[axis]``.
order : int > 0 [scalar]
the order of the difference operator.
1 for first derivative, 2 for second, etc.
axis : int [scalar]
the axis along which to compute deltas.
Default is -1 (columns).
mode : str, {'interp', 'nearest', 'mirror', 'constant', 'wrap'}
Padding mode for estimating differences at the boundaries.
**kwargs : additional keyword arguments
See `scipy.signal.savgol_filter`
Returns
-------
delta_data : np.ndarray [shape=(..., t)]
delta matrix of ``data`` at specified order
Notes
-----
This function caches at level 40.
See Also
--------
scipy.signal.savgol_filter
Examples
--------
Compute MFCC deltas, delta-deltas
>>> y, sr = librosa.load(librosa.ex('libri1'), duration=5)
>>> mfcc = librosa.feature.mfcc(y=y, sr=sr)
>>> mfcc_delta = librosa.feature.delta(mfcc)
>>> mfcc_delta
array([[-5.713e+02, -5.697e+02, ..., -1.522e+02, -1.224e+02],
[ 1.104e+01, 1.330e+01, ..., 2.089e+02, 1.698e+02],
...,
[ 2.829e+00, 1.933e+00, ..., -3.149e+00, 2.294e-01],
[ 2.890e+00, 2.187e+00, ..., 6.959e+00, -1.039e+00]],
dtype=float32)
>>> mfcc_delta2 = librosa.feature.delta(mfcc, order=2)
>>> mfcc_delta2
array([[-1.195, -1.195, ..., -4.328, -4.328],
[-1.566, -1.566, ..., -9.949, -9.949],
...,
[ 0.707, 0.707, ..., 2.287, 2.287],
[ 0.655, 0.655, ..., -1.719, -1.719]], dtype=float32)
>>> import matplotlib.pyplot as plt
>>> fig, ax = plt.subplots(nrows=3, sharex=True, sharey=True)
>>> img1 = librosa.display.specshow(mfcc, ax=ax[0], x_axis='time')
>>> ax[0].set(title='MFCC')
>>> ax[0].label_outer()
>>> img2 = librosa.display.specshow(mfcc_delta, ax=ax[1], x_axis='time')
>>> ax[1].set(title=r'MFCC-$\Delta$')
>>> ax[1].label_outer()
>>> img3 = librosa.display.specshow(mfcc_delta2, ax=ax[2], x_axis='time')
>>> ax[2].set(title=r'MFCC-$\Delta^2$')
>>> fig.colorbar(img1, ax=[ax[0]])
>>> fig.colorbar(img2, ax=[ax[1]])
>>> fig.colorbar(img3, ax=[ax[2]])
"""
data = np.atleast_1d(data)
if mode == "interp" and width > data.shape[axis]:
raise ParameterError(
f"when mode='interp', width={width} "
f"cannot exceed data.shape[axis]={data.shape[axis]}"
)
if width < 3 or np.mod(width, 2) != 1:
raise ParameterError("width must be an odd integer >= 3")
if order <= 0 or not isinstance(order, (int, np.integer)):
raise ParameterError("order must be a positive integer")
kwargs.pop("deriv", None)
kwargs.setdefault("polyorder", order)
result: np.ndarray = scipy.signal.savgol_filter(
data, width, deriv=order, axis=axis, mode=mode, **kwargs
)
return result
[docs]@cache(level=40)
def stack_memory(
data: np.ndarray, *, n_steps: int = 2, delay: int = 1, **kwargs: Any
) -> np.ndarray:
"""Short-term history embedding: vertically concatenate a data
vector or matrix with delayed copies of itself.
Each column ``data[:, i]`` is mapped to::
data[..., i] -> [data[..., i],
data[..., i - delay],
...
data[..., i - (n_steps-1)*delay]]
For columns ``i < (n_steps - 1) * delay``, the data will be padded.
By default, the data is padded with zeros, but this behavior can be
overridden by supplying additional keyword arguments which are passed
to `np.pad()`.
Parameters
----------
data : np.ndarray [shape=(..., d, t)]
Input data matrix. If ``data`` is a vector (``data.ndim == 1``),
it will be interpreted as a row matrix and reshaped to ``(1, t)``.
n_steps : int > 0 [scalar]
embedding dimension, the number of steps back in time to stack
delay : int != 0 [scalar]
the number of columns to step.
Positive values embed from the past (previous columns).
Negative values embed from the future (subsequent columns).
**kwargs : additional keyword arguments
Additional arguments to pass to `numpy.pad`
Returns
-------
data_history : np.ndarray [shape=(..., m * d, t)]
data augmented with lagged copies of itself,
where ``m == n_steps - 1``.
Notes
-----
This function caches at level 40.
Examples
--------
Keep two steps (current and previous)
>>> data = np.arange(-3, 3)
>>> librosa.feature.stack_memory(data)
array([[-3, -2, -1, 0, 1, 2],
[ 0, -3, -2, -1, 0, 1]])
Or three steps
>>> librosa.feature.stack_memory(data, n_steps=3)
array([[-3, -2, -1, 0, 1, 2],
[ 0, -3, -2, -1, 0, 1],
[ 0, 0, -3, -2, -1, 0]])
Use reflection padding instead of zero-padding
>>> librosa.feature.stack_memory(data, n_steps=3, mode='reflect')
array([[-3, -2, -1, 0, 1, 2],
[-2, -3, -2, -1, 0, 1],
[-1, -2, -3, -2, -1, 0]])
Or pad with edge-values, and delay by 2
>>> librosa.feature.stack_memory(data, n_steps=3, delay=2, mode='edge')
array([[-3, -2, -1, 0, 1, 2],
[-3, -3, -3, -2, -1, 0],
[-3, -3, -3, -3, -3, -2]])
Stack time-lagged beat-synchronous chroma edge padding
>>> y, sr = librosa.load(librosa.ex('sweetwaltz'), duration=10)
>>> chroma = librosa.feature.chroma_cqt(y=y, sr=sr)
>>> tempo, beats = librosa.beat.beat_track(y=y, sr=sr, hop_length=512)
>>> beats = librosa.util.fix_frames(beats, x_min=0)
>>> chroma_sync = librosa.util.sync(chroma, beats)
>>> chroma_lag = librosa.feature.stack_memory(chroma_sync, n_steps=3,
... mode='edge')
Plot the result
>>> import matplotlib.pyplot as plt
>>> fig, ax = plt.subplots()
>>> beat_times = librosa.frames_to_time(beats, sr=sr, hop_length=512)
>>> librosa.display.specshow(chroma_lag, y_axis='chroma', x_axis='time',
... x_coords=beat_times, ax=ax)
>>> ax.text(1.0, 1/6, "Lag=0", transform=ax.transAxes, rotation=-90, ha="left", va="center")
>>> ax.text(1.0, 3/6, "Lag=1", transform=ax.transAxes, rotation=-90, ha="left", va="center")
>>> ax.text(1.0, 5/6, "Lag=2", transform=ax.transAxes, rotation=-90, ha="left", va="center")
>>> ax.set(title='Time-lagged chroma', ylabel="")
"""
if n_steps < 1:
raise ParameterError("n_steps must be a positive integer")
if delay == 0:
raise ParameterError("delay must be a non-zero integer")
data = np.atleast_2d(data)
t = data.shape[-1]
if t < 1:
raise ParameterError(
"Cannot stack memory when input data has "
f"no columns. Given data.shape={data.shape}"
)
kwargs.setdefault("mode", "constant")
if kwargs["mode"] == "constant":
kwargs.setdefault("constant_values", [0])
padding = [(0, 0) for _ in range(data.ndim)]
# Pad the end with zeros, which will roll to the front below
if delay > 0:
padding[-1] = (int((n_steps - 1) * delay), 0)
else:
padding[-1] = (0, int((n_steps - 1) * -delay))
data = np.pad(data, padding, **kwargs)
# Construct the shape of the target array
shape = list(data.shape)
shape[-2] = shape[-2] * n_steps
shape[-1] = t
shape = tuple(shape)
# Construct the output array to match layout and dtype of input
history = np.empty_like(data, shape=shape)
# Populate the output array
__stack(history, data, n_steps, delay)
return history
@jit(nopython=True, cache=True)
def __stack(history, data, n_steps, delay):
"""Memory-stacking helper function.
Parameters
----------
history : output array (2-dimensional)
data : pre-padded input array (2-dimensional)
n_steps : int > 0, the number of steps to stack
delay : int != 0, the amount of delay between steps
Returns
-------
None
Output is stored directly in the history array
"""
# Dimension of each copy of the data
d = data.shape[-2]
# Total number of time-steps to output
t = history.shape[-1]
if delay > 0:
for step in range(n_steps):
q = n_steps - 1 - step
# nth block is original shifted left by n*delay steps
history[..., step * d : (step + 1) * d, :] = data[
..., q * delay : q * delay + t
]
else:
# Handle the last block separately to avoid -t:0 empty slices
history[..., -d:, :] = data[..., -t:]
for step in range(n_steps - 1):
# nth block is original shifted right by n*delay steps
q = n_steps - 1 - step
history[..., step * d : (step + 1) * d, :] = data[
..., -t + q * delay : q * delay
]