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

__all__ = ["delta", "stack_memory"]


[docs]@cache(level=40) def delta(data, *, width=9, order=1, axis=-1, mode="interp", **kwargs): 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( "when mode='interp', width={} " "cannot exceed data.shape[axis]={}".format(width, 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) return scipy.signal.savgol_filter( data, width, deriv=order, axis=axis, mode=mode, **kwargs )
[docs]@cache(level=40) def stack_memory(data, *, n_steps=2, delay=1, **kwargs): """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 " "no columns. Given data.shape={}".format(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 ]