test_features.py

#!/usr/bin/env python
# -*- encoding: utf-8 -*-

from __future__ import print_function
import warnings
import numpy as np

import pytest

import librosa

from test_core import load, srand

# Disable cache
import os

try:
    os.environ.pop("LIBROSA_CACHE_DIR")
except KeyError:
    pass

__EXAMPLE_FILE = os.path.join("tests", "data", "test1_22050.wav")
warnings.resetwarnings()
warnings.simplefilter("always")
warnings.filterwarnings("module", ".*", FutureWarning, "scipy.*")


# utils submodule
@pytest.mark.parametrize("slope", np.linspace(-2, 2, num=6))
@pytest.mark.parametrize("xin", [np.vstack([np.arange(100.0)] * 3)])
@pytest.mark.parametrize("order", [1])
@pytest.mark.parametrize("width, axis", [(3, 0), (3, 1), (5, 1), (7, 1)])
@pytest.mark.parametrize("bias", [-10, 0, 10])
def test_delta(xin, width, slope, order, axis, bias):

    x = slope * xin + bias

    # Note: this test currently only checks first-order differences
    #    if width < 3 or np.mod(width, 2) != 1 or width > x.shape[axis]:
    #        pytest.raises(librosa.ParameterError)

    delta = librosa.feature.delta(x, width=width, order=order, axis=axis)

    # Check that trimming matches the expected shape
    assert x.shape == delta.shape

    # Once we're sufficiently far into the signal (ie beyond half_len)
    # (x + delta)[t] should approximate x[t+1] if x is actually linear
    slice_orig = [slice(None)] * x.ndim
    slice_out = [slice(None)] * delta.ndim
    slice_orig[axis] = slice(width // 2 + 1, -width // 2 + 1)
    slice_out[axis] = slice(width // 2, -width // 2)
    assert np.allclose((x + delta)[tuple(slice_out)], x[tuple(slice_orig)])


@pytest.mark.xfail(raises=librosa.ParameterError)
def test_delta_badorder():
    x = np.ones((10, 10))
    librosa.feature.delta(x, order=0)


@pytest.mark.xfail(raises=librosa.ParameterError)
@pytest.mark.parametrize("x", [np.ones((3, 100))])
@pytest.mark.parametrize(
    "width, axis",
    [(-1, 0), (-1, 1), (0, 0), (0, 1), (1, 0), (1, 1), (2, 0), (2, 1), (4, 0), (4, 1), (5, 0), (6, 0), (6, 1), (7, 0)],
)
def test_delta_badwidthaxis(x, width, axis):
    librosa.feature.delta(x, width=width, axis=axis)


@pytest.mark.parametrize("data", [np.arange(5.), np.remainder(np.arange(10000), 24)])
@pytest.mark.parametrize("delay", [-4, -2, -1, 1, 2, 4])
@pytest.mark.parametrize("n_steps", [1, 2, 3, 300])
def test_stack_memory(data, n_steps, delay):

    data_stack = librosa.feature.stack_memory(data, n_steps=n_steps, delay=delay)

    # If we're one-dimensional, reshape for testing
    if data.ndim == 1:
        data = data.reshape((1, -1))

    d, t = data.shape

    assert data_stack.shape[0] == n_steps * d
    assert data_stack.shape[1] == t

    assert np.allclose(data_stack[0], data[0])

    for i in range(d):
        for step in range(1, n_steps):
            if delay > 0:
                assert np.allclose(data[i, : -step * delay], data_stack[step * d + i, step * delay:])
            else:
                assert np.allclose(data[i, -step * delay:], data_stack[step * d + i, : step * delay])
    assert np.max(data) + 1e-7 >= np.max(data_stack)
    assert np.min(data) - 1e-7 <= np.min(data_stack)


@pytest.mark.parametrize("n_steps,delay", [(0, 1), (-1, 1), (1, 0)])
@pytest.mark.parametrize("data", [np.zeros((2, 2))])
@pytest.mark.xfail(raises=librosa.ParameterError)
def test_stack_memory_fail(data, n_steps, delay):
    librosa.feature.stack_memory(data, n_steps=n_steps, delay=delay)


@pytest.mark.xfail(raises=librosa.ParameterError)
def test_stack_memory_ndim_toobig():
    librosa.feature.stack_memory(np.zeros((2,2,2)), n_steps=3, delay=1)

@pytest.mark.parametrize('data', [np.zeros((2, 0))])
@pytest.mark.xfail(raises=librosa.ParameterError)
@pytest.mark.parametrize('delay', [-2, -1, 1, 2])
@pytest.mark.parametrize('n_steps', [1, 2])
def test_stack_memory_ndim_badshape(data, delay, n_steps):
    librosa.feature.stack_memory(data, n_steps=n_steps, delay=delay)


@pytest.fixture(scope="module")
def S_ideal():
    # An idealized spectrum with all zero energy except at one DFT band
    S = np.zeros((513, 3))
    S[5, :] = 1.0
    return S


# spectral submodule
@pytest.mark.parametrize(
    "freq",
    [
        None,
        librosa.fft_frequencies(sr=22050, n_fft=1024),
        3 * librosa.fft_frequencies(sr=22050, n_fft=1024),
        np.random.randn(513, 3),
    ],
)
def test_spectral_centroid_synthetic(S_ideal, freq):
    n_fft = 2 * (S_ideal.shape[0] - 1)
    cent = librosa.feature.spectral_centroid(S=S_ideal, freq=freq)

    if freq is None:
        freq = librosa.fft_frequencies(sr=22050, n_fft=n_fft)

    assert np.allclose(cent, freq[5])


@pytest.mark.parametrize("S", [-np.ones((9, 3)), -np.ones((9, 3)) * 1.0j])
@pytest.mark.xfail(raises=librosa.ParameterError)
def test_spectral_centroid_errors(S):
    librosa.feature.spectral_centroid(S=S)


@pytest.mark.parametrize("sr", [22050])
@pytest.mark.parametrize("y,S", [(np.zeros(3 * 22050), None), (None, np.zeros((1025, 10)))])
def test_spectral_centroid_empty(y, sr, S):
    cent = librosa.feature.spectral_centroid(y=y, sr=sr, S=S)
    assert not np.any(cent)


@pytest.mark.parametrize(
    "freq",
    [
        None,
        librosa.fft_frequencies(sr=22050, n_fft=1024),
        3 * librosa.fft_frequencies(sr=22050, n_fft=1024),
        np.random.randn(513, 3),
    ],
)
@pytest.mark.parametrize("norm", [False, True])
@pytest.mark.parametrize("p", [1, 2])
def test_spectral_bandwidth_synthetic(S_ideal, freq, norm, p):
    # This test ensures that a signal confined to a single frequency bin
    # always achieves 0 bandwidth

    bw = librosa.feature.spectral_bandwidth(S=S_ideal, freq=freq, norm=norm, p=p)

    assert not np.any(bw)


@pytest.mark.parametrize(
    "freq",
    [
        None,
        librosa.fft_frequencies(sr=22050, n_fft=1024),
        3 * librosa.fft_frequencies(sr=22050, n_fft=1024),
        np.random.randn(513, 1),
    ],
)
def test_spectral_bandwidth_onecol(S_ideal, freq):
    # This test checks for issue https://github.com/librosa/librosa/issues/552
    # failure when the spectrogram has a single column

    bw = librosa.feature.spectral_bandwidth(S=S_ideal[:, :1], freq=freq)
    assert bw.shape == (1, 1)


@pytest.mark.xfail(raises=librosa.ParameterError)
@pytest.mark.parametrize("S", [-np.ones((17, 2)), -np.ones((17, 2)) * 1.0j])
def test_spectral_bandwidth_errors(S):
    librosa.feature.spectral_bandwidth(S=S)


@pytest.mark.parametrize("S", [np.ones((1025, 3))])
@pytest.mark.parametrize(
    "freq", [None, librosa.fft_frequencies(sr=22050, n_fft=2048), np.cumsum(np.abs(np.random.randn(1025, 3)), axis=0)]
)
@pytest.mark.parametrize("pct", [0.25, 0.5, 0.95])
def test_spectral_rolloff_synthetic(S, freq, pct):

    sr = 22050
    rolloff = librosa.feature.spectral_rolloff(S=S, sr=sr, freq=freq, roll_percent=pct)

    n_fft = 2 * (S.shape[0] - 1)
    if freq is None:
        freq = librosa.fft_frequencies(sr=sr, n_fft=n_fft)

    idx = np.floor(pct * freq.shape[0]).astype(int)
    assert np.allclose(rolloff, freq[idx])


@pytest.mark.xfail(raises=librosa.ParameterError)
@pytest.mark.parametrize(
    "S,pct",
    [(-np.ones((513, 3)), 0.95), (-np.ones((513, 3)) * 1.0j, 0.95), (np.ones((513, 3)), -1), (np.ones((513, 3)), 2)],
)
def test_spectral_rolloff_errors(S, pct):
    librosa.feature.spectral_rolloff(S=S, roll_percent=pct)


@pytest.fixture(scope="module")
def y_ex():
    return librosa.load(os.path.join("tests", "data", "test1_22050.wav"))


def test_spectral_contrast_log(y_ex):
    # We already have a regression test for linear energy difference
    # This test just does a sanity-check on the log-scaled version

    y, sr = y_ex

    contrast = librosa.feature.spectral_contrast(y=y, sr=sr, linear=False)

    assert not np.any(contrast < 0)


@pytest.mark.parametrize("S", [np.ones((1025, 10))])
@pytest.mark.parametrize(
    "freq,fmin,n_bands,quantile",
    [
        (0, 200, 6, 0.02),
        (np.zeros(1 + 1025), 200, 6, 0.02),
        (np.zeros((1025, 10)), 200, 6, 0.02),
        (None, -1, 6, 0.02),
        (None, 0, 6, 0.02),
        (None, 200, -1, 0.02),
        (None, 200, 6, -1),
        (None, 200, 6, 2),
        (None, 200, 7, 0.02),
    ],
)
@pytest.mark.xfail(raises=librosa.ParameterError)
def test_spectral_contrast_errors(S, freq, fmin, n_bands, quantile):

    librosa.feature.spectral_contrast(S=S, freq=freq, fmin=fmin, n_bands=n_bands, quantile=quantile)


@pytest.mark.parametrize(
    "S,flatness_ref",
    [
        (np.array([[1, 3], [2, 1], [1, 2]]), np.array([[0.7937005259, 0.7075558390]])),
        (np.ones((1025, 2)), np.ones((1, 2))),
        (np.zeros((1025, 2)), np.ones((1, 2))),
    ],
)
def test_spectral_flatness_synthetic(S, flatness_ref):
    flatness = librosa.feature.spectral_flatness(S=S)
    assert np.allclose(flatness, flatness_ref)


@pytest.mark.parametrize("S", [np.ones((1025, 2))])
@pytest.mark.parametrize("amin", [0, -1])
@pytest.mark.xfail(raises=librosa.ParameterError)
def test_spectral_flatness_errors(S, amin):
    librosa.feature.spectral_flatness(S=S, amin=amin)


@pytest.mark.parametrize("S", [-np.ones((1025, 2)), -np.ones((1025, 2)) * 1.0j])
@pytest.mark.xfail(raises=librosa.ParameterError)
def test_spectral_flatness_badtype(S):
    librosa.feature.spectral_flatness(S=S)


@pytest.mark.parametrize("n", range(10, 100, 10))
def test_rms_const(n):
    S = np.ones((n, 5))

    # RMSE of an all-ones band is 1
    frame_length = 2 * (n - 1)
    rms = librosa.feature.rms(S=S, frame_length=frame_length)
    assert np.allclose(rms, np.ones_like(rms) / np.sqrt(frame_length), atol=1e-2)


@pytest.mark.parametrize("frame_length", [2048, 2049, 4096, 4097])
@pytest.mark.parametrize("hop_length", [128, 512, 1024])
@pytest.mark.parametrize("center", [False, True])
@pytest.mark.parametrize("y2", [np.random.randn(100000)])
def test_rms(y_ex, y2, frame_length, hop_length, center):
    y1, sr = y_ex
    # Ensure audio is divisible into frame size.
    y1 = librosa.util.fix_length(y1, y1.size - y1.size % frame_length)
    y2 = librosa.util.fix_length(y2, y2.size - y2.size % frame_length)
    assert y1.size % frame_length == 0
    assert y2.size % frame_length == 0

    # STFT magnitudes with a constant windowing function and no centering.
    S1 = librosa.magphase(librosa.stft(y1, n_fft=frame_length,
                                       hop_length=hop_length, window=np.ones, center=center))[0]
    S2 = librosa.magphase(librosa.stft(y2, n_fft=frame_length,
                                       hop_length=hop_length, window=np.ones, center=center))[0]

    # Try both RMS methods.
    rms1 = librosa.feature.rms(S=S1, frame_length=frame_length, hop_length=hop_length)
    rms2 = librosa.feature.rms(y=y1, frame_length=frame_length, hop_length=hop_length, center=center)
    rms3 = librosa.feature.rms(S=S2, frame_length=frame_length, hop_length=hop_length)
    rms4 = librosa.feature.rms(y=y2, frame_length=frame_length, hop_length=hop_length, center=center)

    assert rms1.shape == rms2.shape
    assert rms3.shape == rms4.shape

    # Ensure results are similar.
    np.testing.assert_allclose(rms1, rms2, atol=5e-4)
    np.testing.assert_allclose(rms3, rms4, atol=5e-4)


@pytest.mark.xfail(raises=librosa.ParameterError)
def test_rms_noinput():
    librosa.feature.rms(y=None, S=None)


@pytest.mark.xfail(raises=librosa.ParameterError)
def test_rms_badshape():
    S = np.empty((100, 3))
    librosa.feature.rms(S=S, frame_length=100)


@pytest.fixture(params=[32, 16, 8, 4, 2], scope="module")
def y_zcr(request):
    sr = 16384
    period = request.param
    y = np.ones(sr)
    y[::period] = -1
    rate = 2.0 / period
    return y, sr, rate


@pytest.mark.parametrize("frame_length", [513, 2049])
@pytest.mark.parametrize("hop_length", [128, 256])
@pytest.mark.parametrize("center", [False, True])
def test_zcr_synthetic(y_zcr, frame_length, hop_length, center):

    y, sr, rate = y_zcr
    zcr = librosa.feature.zero_crossing_rate(y, frame_length=frame_length, hop_length=hop_length, center=center)

    # We don't care too much about the edges if there's padding
    if center:
        zcr = zcr[:, frame_length // 2: -frame_length // 2]

    # We'll allow 1% relative error
    assert np.allclose(zcr, rate, rtol=1e-2)


@pytest.fixture(scope="module", params=[1, 2])
def poly_order(request):
    return request.param


@pytest.fixture(scope="module")
def poly_coeffs(poly_order):
    return np.atleast_1d(np.arange(1, 1 + poly_order))


@pytest.fixture(scope="module", params=[None, 1, 2, -1, "varying"])
def poly_freq(request):
    srand()
    freq = librosa.fft_frequencies()

    if request.param in (1, 2):
        return freq ** request.param

    elif request.param == -1:
        return np.cumsum(np.abs(np.random.randn(1 + 2048 // 2)), axis=0)
    elif request.param == "varying":
        return np.cumsum(np.abs(np.random.randn(1 + 2048 // 2, 5)), axis=0)
    else:
        return None


@pytest.fixture(scope="module")
def poly_S(poly_coeffs, poly_freq):
    if poly_freq is None:
        poly_freq = librosa.fft_frequencies()

    S = np.zeros_like(poly_freq)
    for i, c in enumerate(poly_coeffs):
        S += c * poly_freq ** i

    return S.reshape((poly_freq.shape[0], -1))


def test_poly_features_synthetic(poly_S, poly_coeffs, poly_freq):
    sr = 22050
    n_fft = 2048
    order = poly_coeffs.shape[0] - 1
    p = librosa.feature.poly_features(S=poly_S, sr=sr, n_fft=n_fft, order=order, freq=poly_freq)

    for i in range(poly_S.shape[-1]):
        assert np.allclose(poly_coeffs, p[::-1, i].squeeze())


@pytest.mark.xfail(raises=librosa.ParameterError)
def test_tonnetz_fail_empty():
    librosa.feature.tonnetz(y=None, chroma=None)


def test_tonnetz_audio(y_ex):
    y, sr = y_ex
    tonnetz = librosa.feature.tonnetz(y=y, sr=sr)
    assert tonnetz.shape[0] == 6


def test_tonnetz_cqt(y_ex):
    y, sr = y_ex
    chroma_cqt = librosa.feature.chroma_cqt(y=y, sr=sr, n_chroma=24)
    tonnetz = librosa.feature.tonnetz(chroma=chroma_cqt, sr=sr)
    assert tonnetz.shape[1] == chroma_cqt.shape[1]
    assert tonnetz.shape[0] == 6


def test_tonnetz_msaf():
    # Use pre-computed chroma
    tonnetz_chroma = np.load(os.path.join("tests", "data", "feature-tonnetz-chroma.npy"))
    tonnetz_msaf = np.load(os.path.join("tests", "data", "feature-tonnetz-msaf.npy"))

    tonnetz = librosa.feature.tonnetz(chroma=tonnetz_chroma)
    assert tonnetz.shape[1] == tonnetz_chroma.shape[1]
    assert tonnetz.shape[0] == 6
    assert np.allclose(tonnetz_msaf, tonnetz)


@pytest.mark.xfail(raises=librosa.ParameterError)
def test_tempogram_fail_noinput():
    librosa.feature.tempogram(y=None, onset_envelope=None)


@pytest.mark.parametrize("y", [np.zeros(10 * 1000)])
@pytest.mark.parametrize("sr", [1000])
@pytest.mark.parametrize("win_length,window", [(-384, "hann"), (0, "hann"), (384, np.ones(3))])
@pytest.mark.xfail(raises=librosa.ParameterError)
def test_tempogram_fail_badwin(y, sr, win_length, window):
    librosa.feature.tempogram(y=y, sr=sr, win_length=win_length, window=window)


@pytest.mark.parametrize("hop_length", [512, 1024])
def test_tempogram_audio(y_ex, hop_length):
    y, sr = y_ex

    oenv = librosa.onset.onset_strength(y=y, sr=sr, hop_length=hop_length)

    # Get the tempogram from audio
    t1 = librosa.feature.tempogram(y=y, sr=sr, onset_envelope=None, hop_length=hop_length)

    # Get the tempogram from oenv
    t2 = librosa.feature.tempogram(y=None, sr=sr, onset_envelope=oenv, hop_length=hop_length)

    # Make sure it works when both are provided
    t3 = librosa.feature.tempogram(y=y, sr=sr, onset_envelope=oenv, hop_length=hop_length)

    # And that oenv overrides y
    t4 = librosa.feature.tempogram(y=0 * y, sr=sr, onset_envelope=oenv, hop_length=hop_length)

    assert np.allclose(t1, t2)
    assert np.allclose(t1, t3)
    assert np.allclose(t1, t4)


@pytest.mark.parametrize("tempo", [60, 120, 200])
@pytest.mark.parametrize("center", [False, True])
def test_tempogram_odf_equiv(tempo, center):
    sr = 22050
    hop_length = 512
    duration = 8

    odf = np.zeros(duration * sr // hop_length)
    spacing = sr * 60.0 // (hop_length * tempo)
    odf[:: int(spacing)] = 1

    odf_ac = librosa.autocorrelate(odf)

    tempogram = librosa.feature.tempogram(
        onset_envelope=odf, sr=sr, hop_length=hop_length, win_length=len(odf), window=np.ones, center=center, norm=None
    )

    idx = 0
    if center:
        idx = len(odf) // 2

    assert np.allclose(odf_ac, tempogram[:, idx])


@pytest.mark.parametrize("tempo", [60, 90, 200])
@pytest.mark.parametrize("win_length", [192, 384])
@pytest.mark.parametrize("window", ["hann", np.ones])
@pytest.mark.parametrize("norm", [None, 1, 2, np.inf])
def test_tempogram_odf_peak(tempo, win_length, window, norm):
    sr = 22050
    hop_length = 512
    duration = 8

    # Generate an evenly-spaced pulse train
    odf = np.zeros(duration * sr // hop_length)
    spacing = sr * 60.0 // (hop_length * tempo)
    odf[:: int(spacing)] = 1

    tempogram = librosa.feature.tempogram(
        onset_envelope=odf, sr=sr, hop_length=hop_length, win_length=win_length, window=window, norm=norm
    )

    # Check the shape of the output
    assert tempogram.shape[0] == win_length

    assert tempogram.shape[1] == len(odf)

    # Mean over time to wash over the boundary padding effects
    idx = np.where(librosa.util.localmax(tempogram.max(axis=1)))[0]

    # Indices should all be non-zero integer multiples of spacing
    assert np.allclose(idx, spacing * np.arange(1, 1 + len(idx)))


@pytest.mark.parametrize("center", [False, True])
@pytest.mark.parametrize("win_length", [192, 384])
@pytest.mark.parametrize("window", ["hann", np.ones])
@pytest.mark.parametrize("norm", [None, 1, 2, np.inf])
def test_tempogram_odf_multi(center, win_length, window, norm):

    sr = 22050
    hop_length = 512
    duration = 8

    # Generate an evenly-spaced pulse train
    odf = np.zeros((10, duration * sr // hop_length))
    for i in range(10):
        spacing = sr * 60.0 // (hop_length * (60 + 12 * i))
        odf[i, :: int(spacing)] = 1

    tempogram = librosa.feature.tempogram(
        onset_envelope=odf, sr=sr, hop_length=hop_length, win_length=win_length, window=window, norm=norm
    )

    for i in range(10):
        tg_local = librosa.feature.tempogram(
            onset_envelope=odf[i], sr=sr, hop_length=hop_length, win_length=win_length, window=window, norm=norm
        )

        assert np.allclose(tempogram[i], tg_local)


@pytest.mark.parametrize("y", [np.zeros(10 * 1000)])
@pytest.mark.parametrize("sr", [1000])
@pytest.mark.parametrize("win_length,window", [(-384, "hann"), (0, "hann"), (384, np.ones(3))])
@pytest.mark.xfail(raises=librosa.ParameterError)
def test_fourier_tempogram_fail_badwin(y, sr, win_length, window):
    librosa.feature.fourier_tempogram(y=y, sr=sr, win_length=win_length, window=window)


@pytest.mark.xfail(raises=librosa.ParameterError)
def test_fourier_tempogram_fail_noinput():
    librosa.feature.fourier_tempogram(y=None, onset_envelope=None)


@pytest.mark.parametrize("hop_length", [512, 1024])
def test_fourier_tempogram_audio(y_ex, hop_length):
    y, sr = y_ex
    oenv = librosa.onset.onset_strength(y=y, sr=sr, hop_length=hop_length)
    # Get the tempogram from audio
    t1 = librosa.feature.fourier_tempogram(y=y, sr=sr, onset_envelope=None, hop_length=hop_length)

    # Get the tempogram from oenv
    t2 = librosa.feature.fourier_tempogram(y=None, sr=sr, onset_envelope=oenv, hop_length=hop_length)

    # Make sure it works when both are provided
    t3 = librosa.feature.fourier_tempogram(y=y, sr=sr, onset_envelope=oenv, hop_length=hop_length)

    # And that oenv overrides y
    t4 = librosa.feature.fourier_tempogram(y=0 * y, sr=sr, onset_envelope=oenv, hop_length=hop_length)

    assert np.iscomplexobj(t1)
    assert np.allclose(t1, t2)
    assert np.allclose(t1, t3)
    assert np.allclose(t1, t4)


@pytest.mark.parametrize("sr", [22050])
@pytest.mark.parametrize("hop_length", [512])
@pytest.mark.parametrize("win_length", [192, 384])
@pytest.mark.parametrize("center", [False, True])
@pytest.mark.parametrize("window", ["hann", np.ones])
def test_fourier_tempogram_invert(sr, hop_length, win_length, center, window):
    duration = 16
    tempo = 100

    odf = np.zeros(duration * sr // hop_length, dtype=np.float32)
    spacing = sr * 60.0 // (hop_length * tempo)
    odf[:: int(spacing)] = 1

    tempogram = librosa.feature.fourier_tempogram(
        onset_envelope=odf, sr=sr, hop_length=hop_length, win_length=win_length, window=window, center=center
    )

    if center:
        sl = slice(None)
    else:
        sl = slice(win_length // 2, -win_length // 2)

    odf_inv = librosa.istft(tempogram, hop_length=1, center=center, window=window, length=len(odf))
    assert np.allclose(odf_inv[sl], odf[sl], atol=1e-6)


def test_cens():
    # load CQT data from Chroma Toolbox
    ct_cqt = load(os.path.join("tests", "data", "features-CT-cqt.mat"))

    fn_ct_chroma_cens = ["features-CT-CENS_9-2.mat", "features-CT-CENS_21-5.mat", "features-CT-CENS_41-1.mat"]

    cens_params = [(9, 2), (21, 5), (41, 1)]

    for cur_test_case, cur_fn_ct_chroma_cens in enumerate(fn_ct_chroma_cens):
        win_len_smooth = cens_params[cur_test_case][0]
        downsample_smooth = cens_params[cur_test_case][1]

        # plug into librosa cens computation
        lr_chroma_cens = librosa.feature.chroma_cens(
            C=ct_cqt["f_cqt"],
            win_len_smooth=win_len_smooth,
            fmin=librosa.core.midi_to_hz(1),
            bins_per_octave=12,
            n_octaves=10,
        )

        # leaving out frames to match chroma toolbox behaviour
        # lr_chroma_cens = librosa.resample(lr_chroma_cens, orig_sr=1, target_sr=1/downsample_smooth)
        lr_chroma_cens = lr_chroma_cens[:, ::downsample_smooth]

        # load CENS-41-1 features
        ct_chroma_cens = load(os.path.join("tests", "data", cur_fn_ct_chroma_cens))

        maxdev = np.abs(ct_chroma_cens["f_CENS"] - lr_chroma_cens)
        assert np.allclose(ct_chroma_cens["f_CENS"], lr_chroma_cens, rtol=1e-15, atol=1e-15), maxdev


@pytest.mark.xfail(raises=librosa.ParameterError)
@pytest.mark.parametrize("win_len_smooth", [-1, 0, 1.5, "foo"])
def test_cens_fail(y_ex, win_len_smooth):
    y, sr = y_ex
    librosa.feature.chroma_cens(y=y, sr=sr, win_len_smooth=win_len_smooth)


@pytest.mark.parametrize("S", [librosa.power_to_db(np.random.randn(128, 1) ** 2, ref=np.max)])
@pytest.mark.parametrize("dct_type", [1, 2, 3])
@pytest.mark.parametrize("norm", [None, "ortho"])
@pytest.mark.parametrize("n_mfcc", [13, 20])
@pytest.mark.parametrize("lifter", [0, 13])
def test_mfcc(S, dct_type, norm, n_mfcc, lifter):

    E_total = np.sum(S, axis=0)

    mfcc = librosa.feature.mfcc(S=S, dct_type=dct_type, norm=norm, n_mfcc=n_mfcc, lifter=lifter)

    assert mfcc.shape[0] == n_mfcc
    assert mfcc.shape[1] == S.shape[1]

    # In type-2 mode, DC component should be constant over all frames
    if dct_type == 2:
        assert np.var(mfcc[0] / E_total) <= 1e-29


# This test is no longer relevant since scipy 1.2.0
# @pytest.mark.xfail(raises=NotImplementedError)
# def test_mfcc_dct1_ortho():
#    S = np.ones((65, 3))
#    librosa.feature.mfcc(S=S, dct_type=1, norm='ortho')


@pytest.mark.xfail(raises=librosa.ParameterError)
@pytest.mark.parametrize("lifter", [-1, np.nan])
def test_mfcc_badlifter(lifter):
    S = np.random.randn(128, 100) ** 2
    librosa.feature.mfcc(S=S, lifter=lifter)


# -- feature inversion tests
@pytest.mark.parametrize("power", [1, 2])
@pytest.mark.parametrize("dtype", [np.float32, np.float64])
@pytest.mark.parametrize("n_fft", [1024, 2048])
def test_mel_to_stft(power, dtype, n_fft):
    srand()

    # Make a random mel spectrum, 4 frames
    mel_basis = librosa.filters.mel(22050, n_fft, n_mels=128, dtype=dtype)

    stft_orig = np.random.randn(n_fft // 2 + 1, 4) ** power
    mels = mel_basis.dot(stft_orig.astype(dtype))

    stft = librosa.feature.inverse.mel_to_stft(mels, power=power, n_fft=n_fft)

    # Check precision
    assert stft.dtype == dtype

    # Check for non-negative spectrum
    assert np.all(stft >= 0)

    # Check that the shape is good
    assert stft.shape[0] == 1 + n_fft // 2

    # Check that the approximation is good in RMSE terms
    assert np.sqrt(np.mean((mel_basis.dot(stft ** power) - mels) ** 2)) <= 5e-2


def test_mel_to_audio():
    y = librosa.tone(440.0, sr=22050, duration=1)

    M = librosa.feature.melspectrogram(y=y, sr=22050)

    y_inv = librosa.feature.inverse.mel_to_audio(M, sr=22050, length=len(y))

    # Sanity check the length
    assert len(y) == len(y_inv)

    # And that it's valid audio
    assert librosa.util.valid_audio(y_inv)


@pytest.mark.parametrize("n_mfcc", [13, 20])
@pytest.mark.parametrize("n_mels", [64, 128])
@pytest.mark.parametrize("dct_type", [2, 3])
@pytest.mark.parametrize("lifter", [-1, 0, 1, 2, 3])
@pytest.mark.parametrize("y", [librosa.tone(440.0, sr=22050, duration=1)])
def test_mfcc_to_mel(y, n_mfcc, n_mels, dct_type, lifter):
    mfcc = librosa.feature.mfcc(y=y, sr=22050, n_mels=n_mels, n_mfcc=n_mfcc, dct_type=dct_type)

    # check lifter parameter error
    if lifter < 0:
        with pytest.raises(librosa.ParameterError):
            librosa.feature.inverse.mfcc_to_mel(mfcc * 10 ** 3, n_mels=n_mels, dct_type=dct_type, lifter=lifter)

    # check no lifter computations
    elif lifter == 0:
        melspec = librosa.feature.melspectrogram(y=y, sr=22050, n_mels=n_mels)

        mel_recover = librosa.feature.inverse.mfcc_to_mel(mfcc, n_mels=n_mels, dct_type=dct_type)
        # Quick shape check
        assert melspec.shape == mel_recover.shape

        # Check non-negativity
        assert np.all(mel_recover >= 0)

    # check that runtime warnings are triggered when appropriate
    elif lifter == 2:
        with pytest.warns(UserWarning):
            librosa.feature.inverse.mfcc_to_mel(mfcc * 10 ** 3, n_mels=n_mels, dct_type=dct_type, lifter=lifter)

    # check if mfcc_to_mel works correctly with lifter
    else:
        ones = np.ones(mfcc.shape, dtype=mfcc.dtype)
        n_mfcc = mfcc.shape[0]
        idx = np.arange(1, 1 + n_mfcc, dtype=mfcc.dtype)
        lifter_sine = 1 + lifter * 0.5 * np.sin(np.pi * idx / lifter)[:, np.newaxis]

        # compute the recovered mel
        mel_recover = librosa.feature.inverse.mfcc_to_mel(
            ones * lifter_sine, n_mels=n_mels, dct_type=dct_type, lifter=lifter
        )

        # compute the expected mel
        mel_expected = librosa.feature.inverse.mfcc_to_mel(ones, n_mels=n_mels, dct_type=dct_type, lifter=0)

        # assert equality of expected and recovered mels
        np.testing.assert_almost_equal(mel_recover, mel_expected, 3)


@pytest.mark.parametrize("n_mfcc", [13, 20])
@pytest.mark.parametrize("n_mels", [64, 128])
@pytest.mark.parametrize("dct_type", [2, 3])
@pytest.mark.parametrize("lifter", [0, 3])
@pytest.mark.parametrize("y", [librosa.tone(440.0, sr=22050, duration=1)])
def test_mfcc_to_audio(y, n_mfcc, n_mels, dct_type, lifter):

    mfcc = librosa.feature.mfcc(y=y, sr=22050, n_mels=n_mels, n_mfcc=n_mfcc, dct_type=dct_type)

    y_inv = librosa.feature.inverse.mfcc_to_audio(mfcc, n_mels=n_mels, dct_type=dct_type, lifter=lifter, length=len(y))

    # Sanity check the length
    assert len(y) == len(y_inv)

    # And that it's valid audio
    assert librosa.util.valid_audio(y_inv)