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# Source code for librosa.core.harmonic

```#!/usr/bin/env python
# -*- coding: utf-8 -*-
"""Harmonic calculations for frequency representations"""

import numpy as np
import scipy.interpolate
import scipy.signal
from ..util.exceptions import ParameterError

__all__ = ["salience", "interp_harmonics"]

[docs]def salience(
S,
freqs,
h_range,
weights=None,
aggregate=None,
filter_peaks=True,
fill_value=np.nan,
kind="linear",
axis=0,
):
"""Harmonic salience function.

Parameters
----------
S : np.ndarray [shape=(d, n)]
input time frequency magnitude representation (e.g. STFT or CQT magnitudes).
Must be real-valued and non-negative.

freqs : np.ndarray, shape=(S.shape[axis])
The frequency values corresponding to S's elements along the
chosen axis.

h_range : list-like, non-negative
Harmonics to include in salience computation.  The first harmonic (1)
corresponds to ``S`` itself. Values less than one (e.g., 1/2) correspond
to sub-harmonics.

weights : list-like
The weight to apply to each harmonic in the summation. (default:
uniform weights). Must be the same length as ``harmonics``.

aggregate : function
aggregation function (default: `np.average`)

If ``aggregate=np.average``, then a weighted average is
computed per-harmonic according to the specified weights.
For all other aggregation functions, all harmonics
are treated equally.

filter_peaks : bool
If true, returns harmonic summation only on frequencies of peak
magnitude. Otherwise returns harmonic summation over the full spectrum.
Defaults to True.

fill_value : float
The value to fill non-peaks in the output representation. (default:
`np.nan`) Only used if ``filter_peaks == True``.

kind : str
Interpolation type for harmonic estimation.
See `scipy.interpolate.interp1d`.

axis : int
The axis along which to compute harmonics

Returns
-------
S_sal : np.ndarray, shape=(len(h_range), [x.shape])
``S_sal`` will have the same shape as ``S``, and measure
the overal harmonic energy at each frequency.

--------
interp_harmonics

Examples
--------
>>> y, sr = librosa.load(librosa.ex('trumpet'), duration=3)
>>> S = np.abs(librosa.stft(y))
>>> freqs = librosa.fft_frequencies(sr)
>>> harms = [1, 2, 3, 4]
>>> weights = [1.0, 0.5, 0.33, 0.25]
>>> S_sal = librosa.salience(S, freqs, harms, weights, fill_value=0)
>>> print(S_sal.shape)
(1025, 115)
>>> import matplotlib.pyplot as plt
>>> fig, ax = plt.subplots(nrows=2, sharex=True, sharey=True)
>>> librosa.display.specshow(librosa.amplitude_to_db(S, ref=np.max),
...                          sr=sr, y_axis='log', x_axis='time', ax=ax[0])
>>> ax[0].set(title='Magnitude spectrogram')
>>> ax[0].label_outer()
>>> img = librosa.display.specshow(librosa.amplitude_to_db(S_sal,
...                                                        ref=np.max),
...                                sr=sr, y_axis='log', x_axis='time', ax=ax[1])
>>> ax[1].set(title='Salience spectrogram')
>>> fig.colorbar(img, ax=ax, format="%+2.0f dB")
"""
if aggregate is None:
aggregate = np.average

if weights is None:
weights = np.ones((len(h_range),))
else:
weights = np.array(weights, dtype=float)

S_harm = interp_harmonics(S, freqs, h_range, kind=kind, axis=axis)

if aggregate is np.average:
S_sal = aggregate(S_harm, axis=0, weights=weights)
else:
S_sal = aggregate(S_harm, axis=0)

if filter_peaks:
S_peaks = scipy.signal.argrelmax(S, axis=0)
S_out = np.empty(S.shape)
S_out.fill(fill_value)
S_out[S_peaks[0], S_peaks[1]] = S_sal[S_peaks[0], S_peaks[1]]

S_sal = S_out

return S_sal

[docs]def interp_harmonics(x, freqs, h_range, kind="linear", fill_value=0, axis=0):
"""Compute the energy at harmonics of time-frequency representation.

Given a frequency-based energy representation such as a spectrogram
or tempogram, this function computes the energy at the chosen harmonics
of the frequency axis.  (See examples below.)
The resulting harmonic array can then be used as input to a salience
computation.

Parameters
----------
x : np.ndarray
The input energy

freqs : np.ndarray, shape=(X.shape[axis])
The frequency values corresponding to X's elements along the
chosen axis.

h_range : list-like, non-negative
Harmonics to compute.  The first harmonic (1) corresponds to ``x``
itself.
Values less than one (e.g., 1/2) correspond to sub-harmonics.

kind : str
Interpolation type.  See `scipy.interpolate.interp1d`.

fill_value : float
The value to fill when extrapolating beyond the observed
frequency range.

axis : int
The axis along which to compute harmonics

Returns
-------
x_harm : np.ndarray, shape=(len(h_range), [x.shape])
``x_harm[i]`` will have the same shape as ``x``, and measure
the energy at the ``h_range[i]`` harmonic of each frequency.

--------
scipy.interpolate.interp1d

Examples
--------
Estimate the harmonics of a time-averaged tempogram

>>> # Compute the time-varying tempogram and average over time
>>> tempi = np.mean(librosa.feature.tempogram(y=y, sr=sr), axis=1)
>>> # We'll measure the first five harmonics
>>> h_range = [1, 2, 3, 4, 5]
>>> f_tempo = librosa.tempo_frequencies(len(tempi), sr=sr)
>>> # Build the harmonic tensor
>>> t_harmonics = librosa.interp_harmonics(tempi, f_tempo, h_range)
>>> print(t_harmonics.shape)
(5, 384)

>>> # And plot the results
>>> import matplotlib.pyplot as plt
>>> fig, ax = plt.subplots()
>>> librosa.display.specshow(t_harmonics, x_axis='tempo', sr=sr, ax=ax)
>>> ax.set(yticks=0.5 + np.arange(len(h_range)),
...        yticklabels=['{:.3g}'.format(_) for _ in h_range],
...        ylabel='Harmonic', xlabel='Tempo (BPM)')

We can also compute frequency harmonics for spectrograms.
To calculate sub-harmonic energy, use values < 1.

>>> y, sr = librosa.load(librosa.ex('trumpet'), duration=3)
>>> h_range = [1./3, 1./2, 1, 2, 3, 4]
>>> S = np.abs(librosa.stft(y))
>>> fft_freqs = librosa.fft_frequencies(sr=sr)
>>> S_harm = librosa.interp_harmonics(S, fft_freqs, h_range, axis=0)
>>> print(S_harm.shape)
(6, 1025, 646)

>>> fig, ax = plt.subplots(nrows=3, ncols=2, sharex=True, sharey=True)
>>> for i, _sh in enumerate(S_harm):
...     img = librosa.display.specshow(librosa.amplitude_to_db(_sh,
...                                                      ref=S.max()),
...                              sr=sr, y_axis='log', x_axis='time',
...                              ax=ax.flat[i])
...     ax.flat[i].set(title='h={:.3g}'.format(h_range[i]))
...     ax.flat[i].label_outer()
>>> fig.colorbar(img, ax=ax, format="%+2.f dB")
"""

# X_out will be the same shape as X, plus a leading
# axis that has length = len(h_range)
out_shape = [len(h_range)]
out_shape.extend(x.shape)

x_out = np.zeros(out_shape, dtype=x.dtype)

if freqs.ndim == 1 and len(freqs) == x.shape[axis]:
harmonics_1d(
x_out, x, freqs, h_range, kind=kind, fill_value=fill_value, axis=axis
)

elif freqs.ndim == 2 and freqs.shape == x.shape:
harmonics_2d(
x_out, x, freqs, h_range, kind=kind, fill_value=fill_value, axis=axis
)
else:
raise ParameterError(
"freqs.shape={} does not match "
"input shape={}".format(freqs.shape, x.shape)
)

return x_out

def harmonics_1d(harmonic_out, x, freqs, h_range, kind="linear", fill_value=0, axis=0):
"""Populate a harmonic tensor from a time-frequency representation.

Parameters
----------
harmonic_out : np.ndarray, shape=(len(h_range), X.shape)
The output array to store harmonics

X : np.ndarray
The input energy

freqs : np.ndarray, shape=(x.shape[axis])
The frequency values corresponding to x's elements along the
chosen axis.

h_range : list-like, non-negative
Harmonics to compute.  The first harmonic (1) corresponds to ``x``
itself.
Values less than one (e.g., 1/2) correspond to sub-harmonics.

kind : str
Interpolation type.  See `scipy.interpolate.interp1d`.

fill_value : float
The value to fill when extrapolating beyond the observed
frequency range.

axis : int
The axis along which to compute harmonics

--------
harmonics
scipy.interpolate.interp1d

Examples
--------
Estimate the harmonics of a time-averaged tempogram

>>> # Compute the time-varying tempogram and average over time
>>> tempi = np.mean(librosa.feature.tempogram(y=y, sr=sr), axis=1)
>>> # We'll measure the first five harmonics
>>> h_range = [1, 2, 3, 4, 5]
>>> f_tempo = librosa.tempo_frequencies(len(tempi), sr=sr)
>>> # Build the harmonic tensor
>>> t_harmonics = librosa.interp_harmonics(tempi, f_tempo, h_range)
>>> print(t_harmonics.shape)
(5, 384)

>>> # And plot the results
>>> import matplotlib.pyplot as plt
>>> fig, ax = plt.subplots()
>>> librosa.display.specshow(t_harmonics, x_axis='tempo', sr=sr, ax=ax)
>>> ax.set(yticks=0.5 + np.arange(len(h_range)),
...        yticklabels=['{:.3g}'.format(_) for _ in h_range],
...        ylabel='Harmonic')
...        xlabel='Tempo (BPM)')

We can also compute frequency harmonics for spectrograms.
To calculate subharmonic energy, use values < 1.

>>> h_range = [1./3, 1./2, 1, 2, 3, 4]
>>> S = np.abs(librosa.stft(y))
>>> fft_freqs = librosa.fft_frequencies(sr=sr)
>>> S_harm = librosa.interp_harmonics(S, fft_freqs, h_range, axis=0)
>>> print(S_harm.shape)
(6, 1025, 646)

>>> fig, ax = plt.subplots(nrows=3, ncols=2, sharex=True, sharey=True)
>>> for i, _sh in enumerate(S_harm):
...     librosa.display.specshow(librosa.amplitude_to_db(_sh,
...                                                      ref=S.max()),
...                              sr=sr, y_axis='log', x_axis='time', ax=ax.flat[i])
...     ax.flat[i].set(title='h={:.3g}'.format(h_range[i]))
...     ax.flat[i].label_outer()
"""

# Note: this only works for fixed-grid, 1d interpolation
f_interp = scipy.interpolate.interp1d(
freqs,
x,
kind=kind,
axis=axis,
copy=False,
bounds_error=False,
fill_value=fill_value,
)

idx_out = [slice(None)] * harmonic_out.ndim

# Compute the output index of the interpolated values
interp_axis = 1 + (axis % x.ndim)

# Iterate over the harmonics range
for h_index, harmonic in enumerate(h_range):
idx_out[0] = h_index

# Iterate over frequencies
for f_index, frequency in enumerate(freqs):
# Offset the output axis by 1 to account for the harmonic index
idx_out[interp_axis] = f_index

# Estimate the harmonic energy at this frequency across time
harmonic_out[tuple(idx_out)] = f_interp(harmonic * frequency)

def harmonics_2d(harmonic_out, x, freqs, h_range, kind="linear", fill_value=0, axis=0):
"""Populate a harmonic tensor from a time-frequency representation with
time-varying frequencies.

Parameters
----------
harmonic_out : np.ndarray
The output array to store harmonics

x : np.ndarray
The input energy

freqs : np.ndarray, shape=x.shape
The frequency values corresponding to each element of ``x``

h_range : list-like, non-negative
Harmonics to compute.  The first harmonic (1) corresponds to ``x``
itself.  Values less than one (e.g., 1/2) correspond to
sub-harmonics.

kind : str
Interpolation type.  See `scipy.interpolate.interp1d`.

fill_value : float
The value to fill when extrapolating beyond the observed
frequency range.

axis : int
The axis along which to compute harmonics

--------
harmonics
harmonics_1d
"""
idx_in = [slice(None)] * x.ndim
idx_freq = [slice(None)] * x.ndim
idx_out = [slice(None)] * harmonic_out.ndim

# This is the non-interpolation axis
ni_axis = (1 + axis) % x.ndim

# For each value in the non-interpolated axis, compute its harmonics
for i in range(x.shape[ni_axis]):
idx_in[ni_axis] = slice(i, i + 1)
idx_freq[ni_axis] = i
idx_out[1 + ni_axis] = idx_in[ni_axis]

harmonics_1d(
harmonic_out[tuple(idx_out)],
x[tuple(idx_in)],
freqs[tuple(idx_freq)],
h_range,
kind=kind,
fill_value=fill_value,
axis=axis,
)
```