1023 lines
41 KiB
Python
1023 lines
41 KiB
Python
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from numpy.testing import (assert_allclose, assert_almost_equal,
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assert_array_equal, assert_array_almost_equal_nulp)
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import numpy as np
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import pytest
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from matplotlib import mlab
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def test_window():
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np.random.seed(0)
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n = 1000
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rand = np.random.standard_normal(n) + 100
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ones = np.ones(n)
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assert_array_equal(mlab.window_none(ones), ones)
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assert_array_equal(mlab.window_none(rand), rand)
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assert_array_equal(np.hanning(len(rand)) * rand, mlab.window_hanning(rand))
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assert_array_equal(np.hanning(len(ones)), mlab.window_hanning(ones))
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class TestDetrend:
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def setup_method(self):
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np.random.seed(0)
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n = 1000
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x = np.linspace(0., 100, n)
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self.sig_zeros = np.zeros(n)
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self.sig_off = self.sig_zeros + 100.
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self.sig_slope = np.linspace(-10., 90., n)
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self.sig_slope_mean = x - x.mean()
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self.sig_base = (
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np.random.standard_normal(n) + np.sin(x*2*np.pi/(n/100)))
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self.sig_base -= self.sig_base.mean()
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def allclose(self, *args):
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assert_allclose(*args, atol=1e-8)
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def test_detrend_none(self):
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assert mlab.detrend_none(0.) == 0.
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assert mlab.detrend_none(0., axis=1) == 0.
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assert mlab.detrend(0., key="none") == 0.
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assert mlab.detrend(0., key=mlab.detrend_none) == 0.
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for sig in [
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5.5, self.sig_off, self.sig_slope, self.sig_base,
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(self.sig_base + self.sig_slope + self.sig_off).tolist(),
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np.vstack([self.sig_base, # 2D case.
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self.sig_base + self.sig_off,
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self.sig_base + self.sig_slope,
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self.sig_base + self.sig_off + self.sig_slope]),
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np.vstack([self.sig_base, # 2D transposed case.
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self.sig_base + self.sig_off,
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self.sig_base + self.sig_slope,
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self.sig_base + self.sig_off + self.sig_slope]).T,
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]:
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if isinstance(sig, np.ndarray):
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assert_array_equal(mlab.detrend_none(sig), sig)
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else:
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assert mlab.detrend_none(sig) == sig
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def test_detrend_mean(self):
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for sig in [0., 5.5]: # 0D.
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assert mlab.detrend_mean(sig) == 0.
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assert mlab.detrend(sig, key="mean") == 0.
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assert mlab.detrend(sig, key=mlab.detrend_mean) == 0.
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# 1D.
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self.allclose(mlab.detrend_mean(self.sig_zeros), self.sig_zeros)
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self.allclose(mlab.detrend_mean(self.sig_base), self.sig_base)
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self.allclose(mlab.detrend_mean(self.sig_base + self.sig_off),
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self.sig_base)
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self.allclose(mlab.detrend_mean(self.sig_base + self.sig_slope),
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self.sig_base + self.sig_slope_mean)
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self.allclose(
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mlab.detrend_mean(self.sig_base + self.sig_slope + self.sig_off),
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self.sig_base + self.sig_slope_mean)
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def test_detrend_mean_1d_base_slope_off_list_andor_axis0(self):
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input = self.sig_base + self.sig_slope + self.sig_off
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target = self.sig_base + self.sig_slope_mean
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self.allclose(mlab.detrend_mean(input, axis=0), target)
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self.allclose(mlab.detrend_mean(input.tolist()), target)
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self.allclose(mlab.detrend_mean(input.tolist(), axis=0), target)
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def test_detrend_mean_2d(self):
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input = np.vstack([self.sig_off,
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self.sig_base + self.sig_off])
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target = np.vstack([self.sig_zeros,
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self.sig_base])
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self.allclose(mlab.detrend_mean(input), target)
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self.allclose(mlab.detrend_mean(input, axis=None), target)
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self.allclose(mlab.detrend_mean(input.T, axis=None).T, target)
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self.allclose(mlab.detrend(input), target)
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self.allclose(mlab.detrend(input, axis=None), target)
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self.allclose(
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mlab.detrend(input.T, key="constant", axis=None), target.T)
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input = np.vstack([self.sig_base,
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self.sig_base + self.sig_off,
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self.sig_base + self.sig_slope,
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self.sig_base + self.sig_off + self.sig_slope])
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target = np.vstack([self.sig_base,
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self.sig_base,
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self.sig_base + self.sig_slope_mean,
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self.sig_base + self.sig_slope_mean])
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self.allclose(mlab.detrend_mean(input.T, axis=0), target.T)
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self.allclose(mlab.detrend_mean(input, axis=1), target)
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self.allclose(mlab.detrend_mean(input, axis=-1), target)
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self.allclose(mlab.detrend(input, key="default", axis=1), target)
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self.allclose(mlab.detrend(input.T, key="mean", axis=0), target.T)
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self.allclose(
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mlab.detrend(input.T, key=mlab.detrend_mean, axis=0), target.T)
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def test_detrend_ValueError(self):
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for signal, kwargs in [
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(self.sig_slope[np.newaxis], {"key": "spam"}),
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(self.sig_slope[np.newaxis], {"key": 5}),
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(5.5, {"axis": 0}),
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(self.sig_slope, {"axis": 1}),
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(self.sig_slope[np.newaxis], {"axis": 2}),
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]:
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with pytest.raises(ValueError):
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mlab.detrend(signal, **kwargs)
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def test_detrend_mean_ValueError(self):
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for signal, kwargs in [
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(5.5, {"axis": 0}),
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(self.sig_slope, {"axis": 1}),
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(self.sig_slope[np.newaxis], {"axis": 2}),
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]:
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with pytest.raises(ValueError):
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mlab.detrend_mean(signal, **kwargs)
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def test_detrend_linear(self):
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# 0D.
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assert mlab.detrend_linear(0.) == 0.
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assert mlab.detrend_linear(5.5) == 0.
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assert mlab.detrend(5.5, key="linear") == 0.
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assert mlab.detrend(5.5, key=mlab.detrend_linear) == 0.
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for sig in [ # 1D.
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self.sig_off,
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self.sig_slope,
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self.sig_slope + self.sig_off,
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]:
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self.allclose(mlab.detrend_linear(sig), self.sig_zeros)
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def test_detrend_str_linear_1d(self):
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input = self.sig_slope + self.sig_off
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target = self.sig_zeros
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self.allclose(mlab.detrend(input, key="linear"), target)
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self.allclose(mlab.detrend(input, key=mlab.detrend_linear), target)
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self.allclose(mlab.detrend_linear(input.tolist()), target)
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def test_detrend_linear_2d(self):
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input = np.vstack([self.sig_off,
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self.sig_slope,
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self.sig_slope + self.sig_off])
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target = np.vstack([self.sig_zeros,
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self.sig_zeros,
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self.sig_zeros])
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self.allclose(
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mlab.detrend(input.T, key="linear", axis=0), target.T)
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self.allclose(
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mlab.detrend(input.T, key=mlab.detrend_linear, axis=0), target.T)
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self.allclose(
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mlab.detrend(input, key="linear", axis=1), target)
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self.allclose(
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mlab.detrend(input, key=mlab.detrend_linear, axis=1), target)
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with pytest.raises(ValueError):
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mlab.detrend_linear(self.sig_slope[np.newaxis])
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@pytest.mark.parametrize('iscomplex', [False, True],
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ids=['real', 'complex'], scope='class')
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@pytest.mark.parametrize('sides', ['onesided', 'twosided', 'default'],
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scope='class')
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@pytest.mark.parametrize(
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'fstims,len_x,NFFT_density,nover_density,pad_to_density,pad_to_spectrum',
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[
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([], None, -1, -1, -1, -1),
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([4], None, -1, -1, -1, -1),
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([4, 5, 10], None, -1, -1, -1, -1),
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([], None, None, -1, -1, None),
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([], None, -1, -1, None, None),
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([], None, None, -1, None, None),
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([], 1024, 512, -1, -1, 128),
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([], 256, -1, -1, 33, 257),
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([], 255, 33, -1, -1, None),
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([], 256, 128, -1, 256, 256),
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([], None, -1, 32, -1, -1),
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],
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ids=[
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'nosig',
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'Fs4',
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'FsAll',
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'nosig_noNFFT',
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'nosig_nopad_to',
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'nosig_noNFFT_no_pad_to',
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'nosig_trim',
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'nosig_odd',
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'nosig_oddlen',
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'nosig_stretch',
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'nosig_overlap',
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],
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scope='class')
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class TestSpectral:
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@pytest.fixture(scope='class', autouse=True)
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def stim(self, request, fstims, iscomplex, sides, len_x, NFFT_density,
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nover_density, pad_to_density, pad_to_spectrum):
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Fs = 100.
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x = np.arange(0, 10, 1 / Fs)
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if len_x is not None:
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x = x[:len_x]
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# get the stimulus frequencies, defaulting to None
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fstims = [Fs / fstim for fstim in fstims]
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# get the constants, default to calculated values
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if NFFT_density is None:
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NFFT_density_real = 256
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elif NFFT_density < 0:
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NFFT_density_real = NFFT_density = 100
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else:
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NFFT_density_real = NFFT_density
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if nover_density is None:
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nover_density_real = 0
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elif nover_density < 0:
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nover_density_real = nover_density = NFFT_density_real // 2
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else:
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nover_density_real = nover_density
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if pad_to_density is None:
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pad_to_density_real = NFFT_density_real
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elif pad_to_density < 0:
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pad_to_density = int(2**np.ceil(np.log2(NFFT_density_real)))
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pad_to_density_real = pad_to_density
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else:
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pad_to_density_real = pad_to_density
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if pad_to_spectrum is None:
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pad_to_spectrum_real = len(x)
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elif pad_to_spectrum < 0:
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pad_to_spectrum_real = pad_to_spectrum = len(x)
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else:
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pad_to_spectrum_real = pad_to_spectrum
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if pad_to_spectrum is None:
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NFFT_spectrum_real = NFFT_spectrum = pad_to_spectrum_real
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else:
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NFFT_spectrum_real = NFFT_spectrum = len(x)
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nover_spectrum = 0
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NFFT_specgram = NFFT_density
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nover_specgram = nover_density
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pad_to_specgram = pad_to_density
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NFFT_specgram_real = NFFT_density_real
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nover_specgram_real = nover_density_real
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if sides == 'onesided' or (sides == 'default' and not iscomplex):
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# frequencies for specgram, psd, and csd
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# need to handle even and odd differently
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if pad_to_density_real % 2:
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freqs_density = np.linspace(0, Fs / 2,
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num=pad_to_density_real,
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endpoint=False)[::2]
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else:
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freqs_density = np.linspace(0, Fs / 2,
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num=pad_to_density_real // 2 + 1)
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# frequencies for complex, magnitude, angle, and phase spectrums
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# need to handle even and odd differently
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if pad_to_spectrum_real % 2:
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freqs_spectrum = np.linspace(0, Fs / 2,
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num=pad_to_spectrum_real,
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endpoint=False)[::2]
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else:
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freqs_spectrum = np.linspace(0, Fs / 2,
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num=pad_to_spectrum_real // 2 + 1)
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else:
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# frequencies for specgram, psd, and csd
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# need to handle even and odd differently
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if pad_to_density_real % 2:
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freqs_density = np.linspace(-Fs / 2, Fs / 2,
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num=2 * pad_to_density_real,
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endpoint=False)[1::2]
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else:
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freqs_density = np.linspace(-Fs / 2, Fs / 2,
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num=pad_to_density_real,
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endpoint=False)
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# frequencies for complex, magnitude, angle, and phase spectrums
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# need to handle even and odd differently
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if pad_to_spectrum_real % 2:
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freqs_spectrum = np.linspace(-Fs / 2, Fs / 2,
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num=2 * pad_to_spectrum_real,
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endpoint=False)[1::2]
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else:
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freqs_spectrum = np.linspace(-Fs / 2, Fs / 2,
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num=pad_to_spectrum_real,
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endpoint=False)
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freqs_specgram = freqs_density
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# time points for specgram
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t_start = NFFT_specgram_real // 2
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t_stop = len(x) - NFFT_specgram_real // 2 + 1
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t_step = NFFT_specgram_real - nover_specgram_real
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t_specgram = x[t_start:t_stop:t_step]
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if NFFT_specgram_real % 2:
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t_specgram += 1 / Fs / 2
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if len(t_specgram) == 0:
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t_specgram = np.array([NFFT_specgram_real / (2 * Fs)])
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t_spectrum = np.array([NFFT_spectrum_real / (2 * Fs)])
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t_density = t_specgram
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y = np.zeros_like(x)
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for i, fstim in enumerate(fstims):
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y += np.sin(fstim * x * np.pi * 2) * 10**i
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if iscomplex:
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y = y.astype('complex')
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# Interestingly, the instance on which this fixture is called is not
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|
|
# the same as the one on which a test is run. So we need to modify the
|
||
|
|
# class itself when using a class-scoped fixture.
|
||
|
|
cls = request.cls
|
||
|
|
|
||
|
|
cls.Fs = Fs
|
||
|
|
cls.sides = sides
|
||
|
|
cls.fstims = fstims
|
||
|
|
|
||
|
|
cls.NFFT_density = NFFT_density
|
||
|
|
cls.nover_density = nover_density
|
||
|
|
cls.pad_to_density = pad_to_density
|
||
|
|
|
||
|
|
cls.NFFT_spectrum = NFFT_spectrum
|
||
|
|
cls.nover_spectrum = nover_spectrum
|
||
|
|
cls.pad_to_spectrum = pad_to_spectrum
|
||
|
|
|
||
|
|
cls.NFFT_specgram = NFFT_specgram
|
||
|
|
cls.nover_specgram = nover_specgram
|
||
|
|
cls.pad_to_specgram = pad_to_specgram
|
||
|
|
|
||
|
|
cls.t_specgram = t_specgram
|
||
|
|
cls.t_density = t_density
|
||
|
|
cls.t_spectrum = t_spectrum
|
||
|
|
cls.y = y
|
||
|
|
|
||
|
|
cls.freqs_density = freqs_density
|
||
|
|
cls.freqs_spectrum = freqs_spectrum
|
||
|
|
cls.freqs_specgram = freqs_specgram
|
||
|
|
|
||
|
|
cls.NFFT_density_real = NFFT_density_real
|
||
|
|
|
||
|
|
def check_freqs(self, vals, targfreqs, resfreqs, fstims):
|
||
|
|
assert resfreqs.argmin() == 0
|
||
|
|
assert resfreqs.argmax() == len(resfreqs)-1
|
||
|
|
assert_allclose(resfreqs, targfreqs, atol=1e-06)
|
||
|
|
for fstim in fstims:
|
||
|
|
i = np.abs(resfreqs - fstim).argmin()
|
||
|
|
assert vals[i] > vals[i+2]
|
||
|
|
assert vals[i] > vals[i-2]
|
||
|
|
|
||
|
|
def check_maxfreq(self, spec, fsp, fstims):
|
||
|
|
# skip the test if there are no frequencies
|
||
|
|
if len(fstims) == 0:
|
||
|
|
return
|
||
|
|
|
||
|
|
# if twosided, do the test for each side
|
||
|
|
if fsp.min() < 0:
|
||
|
|
fspa = np.abs(fsp)
|
||
|
|
zeroind = fspa.argmin()
|
||
|
|
self.check_maxfreq(spec[:zeroind], fspa[:zeroind], fstims)
|
||
|
|
self.check_maxfreq(spec[zeroind:], fspa[zeroind:], fstims)
|
||
|
|
return
|
||
|
|
|
||
|
|
fstimst = fstims[:]
|
||
|
|
spect = spec.copy()
|
||
|
|
|
||
|
|
# go through each peak and make sure it is correctly the maximum peak
|
||
|
|
while fstimst:
|
||
|
|
maxind = spect.argmax()
|
||
|
|
maxfreq = fsp[maxind]
|
||
|
|
assert_almost_equal(maxfreq, fstimst[-1])
|
||
|
|
del fstimst[-1]
|
||
|
|
spect[maxind-5:maxind+5] = 0
|
||
|
|
|
||
|
|
def test_spectral_helper_raises(self):
|
||
|
|
# We don't use parametrize here to handle ``y = self.y``.
|
||
|
|
for kwargs in [ # Various error conditions:
|
||
|
|
{"y": self.y+1, "mode": "complex"}, # Modes requiring ``x is y``.
|
||
|
|
{"y": self.y+1, "mode": "magnitude"},
|
||
|
|
{"y": self.y+1, "mode": "angle"},
|
||
|
|
{"y": self.y+1, "mode": "phase"},
|
||
|
|
{"mode": "spam"}, # Bad mode.
|
||
|
|
{"y": self.y, "sides": "eggs"}, # Bad sides.
|
||
|
|
{"y": self.y, "NFFT": 10, "noverlap": 20}, # noverlap > NFFT.
|
||
|
|
{"NFFT": 10, "noverlap": 10}, # noverlap == NFFT.
|
||
|
|
{"y": self.y, "NFFT": 10,
|
||
|
|
"window": np.ones(9)}, # len(win) != NFFT.
|
||
|
|
]:
|
||
|
|
with pytest.raises(ValueError):
|
||
|
|
mlab._spectral_helper(x=self.y, **kwargs)
|
||
|
|
|
||
|
|
@pytest.mark.parametrize('mode', ['default', 'psd'])
|
||
|
|
def test_single_spectrum_helper_unsupported_modes(self, mode):
|
||
|
|
with pytest.raises(ValueError):
|
||
|
|
mlab._single_spectrum_helper(x=self.y, mode=mode)
|
||
|
|
|
||
|
|
@pytest.mark.parametrize("mode, case", [
|
||
|
|
("psd", "density"),
|
||
|
|
("magnitude", "specgram"),
|
||
|
|
("magnitude", "spectrum"),
|
||
|
|
])
|
||
|
|
def test_spectral_helper_psd(self, mode, case):
|
||
|
|
freqs = getattr(self, f"freqs_{case}")
|
||
|
|
spec, fsp, t = mlab._spectral_helper(
|
||
|
|
x=self.y, y=self.y,
|
||
|
|
NFFT=getattr(self, f"NFFT_{case}"),
|
||
|
|
Fs=self.Fs,
|
||
|
|
noverlap=getattr(self, f"nover_{case}"),
|
||
|
|
pad_to=getattr(self, f"pad_to_{case}"),
|
||
|
|
sides=self.sides,
|
||
|
|
mode=mode)
|
||
|
|
|
||
|
|
assert_allclose(fsp, freqs, atol=1e-06)
|
||
|
|
assert_allclose(t, getattr(self, f"t_{case}"), atol=1e-06)
|
||
|
|
assert spec.shape[0] == freqs.shape[0]
|
||
|
|
assert spec.shape[1] == getattr(self, f"t_{case}").shape[0]
|
||
|
|
|
||
|
|
def test_csd(self):
|
||
|
|
freqs = self.freqs_density
|
||
|
|
spec, fsp = mlab.csd(x=self.y, y=self.y+1,
|
||
|
|
NFFT=self.NFFT_density,
|
||
|
|
Fs=self.Fs,
|
||
|
|
noverlap=self.nover_density,
|
||
|
|
pad_to=self.pad_to_density,
|
||
|
|
sides=self.sides)
|
||
|
|
assert_allclose(fsp, freqs, atol=1e-06)
|
||
|
|
assert spec.shape == freqs.shape
|
||
|
|
|
||
|
|
def test_csd_padding(self):
|
||
|
|
"""Test zero padding of csd()."""
|
||
|
|
if self.NFFT_density is None: # for derived classes
|
||
|
|
return
|
||
|
|
sargs = dict(x=self.y, y=self.y+1, Fs=self.Fs, window=mlab.window_none,
|
||
|
|
sides=self.sides)
|
||
|
|
|
||
|
|
spec0, _ = mlab.csd(NFFT=self.NFFT_density, **sargs)
|
||
|
|
spec1, _ = mlab.csd(NFFT=self.NFFT_density*2, **sargs)
|
||
|
|
assert_almost_equal(np.sum(np.conjugate(spec0)*spec0).real,
|
||
|
|
np.sum(np.conjugate(spec1/2)*spec1/2).real)
|
||
|
|
|
||
|
|
def test_psd(self):
|
||
|
|
freqs = self.freqs_density
|
||
|
|
spec, fsp = mlab.psd(x=self.y,
|
||
|
|
NFFT=self.NFFT_density,
|
||
|
|
Fs=self.Fs,
|
||
|
|
noverlap=self.nover_density,
|
||
|
|
pad_to=self.pad_to_density,
|
||
|
|
sides=self.sides)
|
||
|
|
assert spec.shape == freqs.shape
|
||
|
|
self.check_freqs(spec, freqs, fsp, self.fstims)
|
||
|
|
|
||
|
|
@pytest.mark.parametrize(
|
||
|
|
'make_data, detrend',
|
||
|
|
[(np.zeros, mlab.detrend_mean), (np.zeros, 'mean'),
|
||
|
|
(np.arange, mlab.detrend_linear), (np.arange, 'linear')])
|
||
|
|
def test_psd_detrend(self, make_data, detrend):
|
||
|
|
if self.NFFT_density is None:
|
||
|
|
return
|
||
|
|
ydata = make_data(self.NFFT_density)
|
||
|
|
ydata1 = ydata+5
|
||
|
|
ydata2 = ydata+3.3
|
||
|
|
ydata = np.vstack([ydata1, ydata2])
|
||
|
|
ydata = np.tile(ydata, (20, 1))
|
||
|
|
ydatab = ydata.T.flatten()
|
||
|
|
ydata = ydata.flatten()
|
||
|
|
ycontrol = np.zeros_like(ydata)
|
||
|
|
spec_g, fsp_g = mlab.psd(x=ydata,
|
||
|
|
NFFT=self.NFFT_density,
|
||
|
|
Fs=self.Fs,
|
||
|
|
noverlap=0,
|
||
|
|
sides=self.sides,
|
||
|
|
detrend=detrend)
|
||
|
|
spec_b, fsp_b = mlab.psd(x=ydatab,
|
||
|
|
NFFT=self.NFFT_density,
|
||
|
|
Fs=self.Fs,
|
||
|
|
noverlap=0,
|
||
|
|
sides=self.sides,
|
||
|
|
detrend=detrend)
|
||
|
|
spec_c, fsp_c = mlab.psd(x=ycontrol,
|
||
|
|
NFFT=self.NFFT_density,
|
||
|
|
Fs=self.Fs,
|
||
|
|
noverlap=0,
|
||
|
|
sides=self.sides)
|
||
|
|
assert_array_equal(fsp_g, fsp_c)
|
||
|
|
assert_array_equal(fsp_b, fsp_c)
|
||
|
|
assert_allclose(spec_g, spec_c, atol=1e-08)
|
||
|
|
# these should not be almost equal
|
||
|
|
with pytest.raises(AssertionError):
|
||
|
|
assert_allclose(spec_b, spec_c, atol=1e-08)
|
||
|
|
|
||
|
|
def test_psd_window_hanning(self):
|
||
|
|
if self.NFFT_density is None:
|
||
|
|
return
|
||
|
|
ydata = np.arange(self.NFFT_density)
|
||
|
|
ydata1 = ydata+5
|
||
|
|
ydata2 = ydata+3.3
|
||
|
|
windowVals = mlab.window_hanning(np.ones_like(ydata1))
|
||
|
|
ycontrol1 = ydata1 * windowVals
|
||
|
|
ycontrol2 = mlab.window_hanning(ydata2)
|
||
|
|
ydata = np.vstack([ydata1, ydata2])
|
||
|
|
ycontrol = np.vstack([ycontrol1, ycontrol2])
|
||
|
|
ydata = np.tile(ydata, (20, 1))
|
||
|
|
ycontrol = np.tile(ycontrol, (20, 1))
|
||
|
|
ydatab = ydata.T.flatten()
|
||
|
|
ydataf = ydata.flatten()
|
||
|
|
ycontrol = ycontrol.flatten()
|
||
|
|
spec_g, fsp_g = mlab.psd(x=ydataf,
|
||
|
|
NFFT=self.NFFT_density,
|
||
|
|
Fs=self.Fs,
|
||
|
|
noverlap=0,
|
||
|
|
sides=self.sides,
|
||
|
|
window=mlab.window_hanning)
|
||
|
|
spec_b, fsp_b = mlab.psd(x=ydatab,
|
||
|
|
NFFT=self.NFFT_density,
|
||
|
|
Fs=self.Fs,
|
||
|
|
noverlap=0,
|
||
|
|
sides=self.sides,
|
||
|
|
window=mlab.window_hanning)
|
||
|
|
spec_c, fsp_c = mlab.psd(x=ycontrol,
|
||
|
|
NFFT=self.NFFT_density,
|
||
|
|
Fs=self.Fs,
|
||
|
|
noverlap=0,
|
||
|
|
sides=self.sides,
|
||
|
|
window=mlab.window_none)
|
||
|
|
spec_c *= len(ycontrol1)/(windowVals**2).sum()
|
||
|
|
assert_array_equal(fsp_g, fsp_c)
|
||
|
|
assert_array_equal(fsp_b, fsp_c)
|
||
|
|
assert_allclose(spec_g, spec_c, atol=1e-08)
|
||
|
|
# these should not be almost equal
|
||
|
|
with pytest.raises(AssertionError):
|
||
|
|
assert_allclose(spec_b, spec_c, atol=1e-08)
|
||
|
|
|
||
|
|
def test_psd_window_hanning_detrend_linear(self):
|
||
|
|
if self.NFFT_density is None:
|
||
|
|
return
|
||
|
|
ydata = np.arange(self.NFFT_density)
|
||
|
|
ycontrol = np.zeros(self.NFFT_density)
|
||
|
|
ydata1 = ydata+5
|
||
|
|
ydata2 = ydata+3.3
|
||
|
|
ycontrol1 = ycontrol
|
||
|
|
ycontrol2 = ycontrol
|
||
|
|
windowVals = mlab.window_hanning(np.ones_like(ycontrol1))
|
||
|
|
ycontrol1 = ycontrol1 * windowVals
|
||
|
|
ycontrol2 = mlab.window_hanning(ycontrol2)
|
||
|
|
ydata = np.vstack([ydata1, ydata2])
|
||
|
|
ycontrol = np.vstack([ycontrol1, ycontrol2])
|
||
|
|
ydata = np.tile(ydata, (20, 1))
|
||
|
|
ycontrol = np.tile(ycontrol, (20, 1))
|
||
|
|
ydatab = ydata.T.flatten()
|
||
|
|
ydataf = ydata.flatten()
|
||
|
|
ycontrol = ycontrol.flatten()
|
||
|
|
spec_g, fsp_g = mlab.psd(x=ydataf,
|
||
|
|
NFFT=self.NFFT_density,
|
||
|
|
Fs=self.Fs,
|
||
|
|
noverlap=0,
|
||
|
|
sides=self.sides,
|
||
|
|
detrend=mlab.detrend_linear,
|
||
|
|
window=mlab.window_hanning)
|
||
|
|
spec_b, fsp_b = mlab.psd(x=ydatab,
|
||
|
|
NFFT=self.NFFT_density,
|
||
|
|
Fs=self.Fs,
|
||
|
|
noverlap=0,
|
||
|
|
sides=self.sides,
|
||
|
|
detrend=mlab.detrend_linear,
|
||
|
|
window=mlab.window_hanning)
|
||
|
|
spec_c, fsp_c = mlab.psd(x=ycontrol,
|
||
|
|
NFFT=self.NFFT_density,
|
||
|
|
Fs=self.Fs,
|
||
|
|
noverlap=0,
|
||
|
|
sides=self.sides,
|
||
|
|
window=mlab.window_none)
|
||
|
|
spec_c *= len(ycontrol1)/(windowVals**2).sum()
|
||
|
|
assert_array_equal(fsp_g, fsp_c)
|
||
|
|
assert_array_equal(fsp_b, fsp_c)
|
||
|
|
assert_allclose(spec_g, spec_c, atol=1e-08)
|
||
|
|
# these should not be almost equal
|
||
|
|
with pytest.raises(AssertionError):
|
||
|
|
assert_allclose(spec_b, spec_c, atol=1e-08)
|
||
|
|
|
||
|
|
def test_psd_window_flattop(self):
|
||
|
|
# flattop window
|
||
|
|
# adaption from https://github.com/scipy/scipy/blob\
|
||
|
|
# /v1.10.0/scipy/signal/windows/_windows.py#L562-L622
|
||
|
|
a = [0.21557895, 0.41663158, 0.277263158, 0.083578947, 0.006947368]
|
||
|
|
fac = np.linspace(-np.pi, np.pi, self.NFFT_density_real)
|
||
|
|
win = np.zeros(self.NFFT_density_real)
|
||
|
|
for k in range(len(a)):
|
||
|
|
win += a[k] * np.cos(k * fac)
|
||
|
|
|
||
|
|
spec, fsp = mlab.psd(x=self.y,
|
||
|
|
NFFT=self.NFFT_density,
|
||
|
|
Fs=self.Fs,
|
||
|
|
noverlap=0,
|
||
|
|
sides=self.sides,
|
||
|
|
window=win,
|
||
|
|
scale_by_freq=False)
|
||
|
|
spec_a, fsp_a = mlab.psd(x=self.y,
|
||
|
|
NFFT=self.NFFT_density,
|
||
|
|
Fs=self.Fs,
|
||
|
|
noverlap=0,
|
||
|
|
sides=self.sides,
|
||
|
|
window=win)
|
||
|
|
assert_allclose(spec*win.sum()**2,
|
||
|
|
spec_a*self.Fs*(win**2).sum(),
|
||
|
|
atol=1e-08)
|
||
|
|
|
||
|
|
def test_psd_windowarray(self):
|
||
|
|
freqs = self.freqs_density
|
||
|
|
spec, fsp = mlab.psd(x=self.y,
|
||
|
|
NFFT=self.NFFT_density,
|
||
|
|
Fs=self.Fs,
|
||
|
|
noverlap=self.nover_density,
|
||
|
|
pad_to=self.pad_to_density,
|
||
|
|
sides=self.sides,
|
||
|
|
window=np.ones(self.NFFT_density_real))
|
||
|
|
assert_allclose(fsp, freqs, atol=1e-06)
|
||
|
|
assert spec.shape == freqs.shape
|
||
|
|
|
||
|
|
def test_psd_windowarray_scale_by_freq(self):
|
||
|
|
win = mlab.window_hanning(np.ones(self.NFFT_density_real))
|
||
|
|
|
||
|
|
spec, fsp = mlab.psd(x=self.y,
|
||
|
|
NFFT=self.NFFT_density,
|
||
|
|
Fs=self.Fs,
|
||
|
|
noverlap=self.nover_density,
|
||
|
|
pad_to=self.pad_to_density,
|
||
|
|
sides=self.sides,
|
||
|
|
window=mlab.window_hanning)
|
||
|
|
spec_s, fsp_s = mlab.psd(x=self.y,
|
||
|
|
NFFT=self.NFFT_density,
|
||
|
|
Fs=self.Fs,
|
||
|
|
noverlap=self.nover_density,
|
||
|
|
pad_to=self.pad_to_density,
|
||
|
|
sides=self.sides,
|
||
|
|
window=mlab.window_hanning,
|
||
|
|
scale_by_freq=True)
|
||
|
|
spec_n, fsp_n = mlab.psd(x=self.y,
|
||
|
|
NFFT=self.NFFT_density,
|
||
|
|
Fs=self.Fs,
|
||
|
|
noverlap=self.nover_density,
|
||
|
|
pad_to=self.pad_to_density,
|
||
|
|
sides=self.sides,
|
||
|
|
window=mlab.window_hanning,
|
||
|
|
scale_by_freq=False)
|
||
|
|
assert_array_equal(fsp, fsp_s)
|
||
|
|
assert_array_equal(fsp, fsp_n)
|
||
|
|
assert_array_equal(spec, spec_s)
|
||
|
|
assert_allclose(spec_s*(win**2).sum(),
|
||
|
|
spec_n/self.Fs*win.sum()**2,
|
||
|
|
atol=1e-08)
|
||
|
|
|
||
|
|
@pytest.mark.parametrize(
|
||
|
|
"kind", ["complex", "magnitude", "angle", "phase"])
|
||
|
|
def test_spectrum(self, kind):
|
||
|
|
freqs = self.freqs_spectrum
|
||
|
|
spec, fsp = getattr(mlab, f"{kind}_spectrum")(
|
||
|
|
x=self.y,
|
||
|
|
Fs=self.Fs, sides=self.sides, pad_to=self.pad_to_spectrum)
|
||
|
|
assert_allclose(fsp, freqs, atol=1e-06)
|
||
|
|
assert spec.shape == freqs.shape
|
||
|
|
if kind == "magnitude":
|
||
|
|
self.check_maxfreq(spec, fsp, self.fstims)
|
||
|
|
self.check_freqs(spec, freqs, fsp, self.fstims)
|
||
|
|
|
||
|
|
@pytest.mark.parametrize(
|
||
|
|
'kwargs',
|
||
|
|
[{}, {'mode': 'default'}, {'mode': 'psd'}, {'mode': 'magnitude'},
|
||
|
|
{'mode': 'complex'}, {'mode': 'angle'}, {'mode': 'phase'}])
|
||
|
|
def test_specgram(self, kwargs):
|
||
|
|
freqs = self.freqs_specgram
|
||
|
|
spec, fsp, t = mlab.specgram(x=self.y,
|
||
|
|
NFFT=self.NFFT_specgram,
|
||
|
|
Fs=self.Fs,
|
||
|
|
noverlap=self.nover_specgram,
|
||
|
|
pad_to=self.pad_to_specgram,
|
||
|
|
sides=self.sides,
|
||
|
|
**kwargs)
|
||
|
|
if kwargs.get('mode') == 'complex':
|
||
|
|
spec = np.abs(spec)
|
||
|
|
specm = np.mean(spec, axis=1)
|
||
|
|
|
||
|
|
assert_allclose(fsp, freqs, atol=1e-06)
|
||
|
|
assert_allclose(t, self.t_specgram, atol=1e-06)
|
||
|
|
|
||
|
|
assert spec.shape[0] == freqs.shape[0]
|
||
|
|
assert spec.shape[1] == self.t_specgram.shape[0]
|
||
|
|
|
||
|
|
if kwargs.get('mode') not in ['complex', 'angle', 'phase']:
|
||
|
|
# using a single freq, so all time slices should be about the same
|
||
|
|
if np.abs(spec.max()) != 0:
|
||
|
|
assert_allclose(
|
||
|
|
np.diff(spec, axis=1).max() / np.abs(spec.max()), 0,
|
||
|
|
atol=1e-02)
|
||
|
|
if kwargs.get('mode') not in ['angle', 'phase']:
|
||
|
|
self.check_freqs(specm, freqs, fsp, self.fstims)
|
||
|
|
|
||
|
|
def test_specgram_warn_only1seg(self):
|
||
|
|
"""Warning should be raised if len(x) <= NFFT."""
|
||
|
|
with pytest.warns(UserWarning, match="Only one segment is calculated"):
|
||
|
|
mlab.specgram(x=self.y, NFFT=len(self.y), Fs=self.Fs)
|
||
|
|
|
||
|
|
def test_psd_csd_equal(self):
|
||
|
|
Pxx, freqsxx = mlab.psd(x=self.y,
|
||
|
|
NFFT=self.NFFT_density,
|
||
|
|
Fs=self.Fs,
|
||
|
|
noverlap=self.nover_density,
|
||
|
|
pad_to=self.pad_to_density,
|
||
|
|
sides=self.sides)
|
||
|
|
Pxy, freqsxy = mlab.csd(x=self.y, y=self.y,
|
||
|
|
NFFT=self.NFFT_density,
|
||
|
|
Fs=self.Fs,
|
||
|
|
noverlap=self.nover_density,
|
||
|
|
pad_to=self.pad_to_density,
|
||
|
|
sides=self.sides)
|
||
|
|
assert_array_almost_equal_nulp(Pxx, Pxy)
|
||
|
|
assert_array_equal(freqsxx, freqsxy)
|
||
|
|
|
||
|
|
@pytest.mark.parametrize("mode", ["default", "psd"])
|
||
|
|
def test_specgram_auto_default_psd_equal(self, mode):
|
||
|
|
"""
|
||
|
|
Test that mlab.specgram without mode and with mode 'default' and 'psd'
|
||
|
|
are all the same.
|
||
|
|
"""
|
||
|
|
speca, freqspeca, ta = mlab.specgram(x=self.y,
|
||
|
|
NFFT=self.NFFT_specgram,
|
||
|
|
Fs=self.Fs,
|
||
|
|
noverlap=self.nover_specgram,
|
||
|
|
pad_to=self.pad_to_specgram,
|
||
|
|
sides=self.sides)
|
||
|
|
specb, freqspecb, tb = mlab.specgram(x=self.y,
|
||
|
|
NFFT=self.NFFT_specgram,
|
||
|
|
Fs=self.Fs,
|
||
|
|
noverlap=self.nover_specgram,
|
||
|
|
pad_to=self.pad_to_specgram,
|
||
|
|
sides=self.sides,
|
||
|
|
mode=mode)
|
||
|
|
assert_array_equal(speca, specb)
|
||
|
|
assert_array_equal(freqspeca, freqspecb)
|
||
|
|
assert_array_equal(ta, tb)
|
||
|
|
|
||
|
|
@pytest.mark.parametrize(
|
||
|
|
"mode, conv", [
|
||
|
|
("magnitude", np.abs),
|
||
|
|
("angle", np.angle),
|
||
|
|
("phase", lambda x: np.unwrap(np.angle(x), axis=0))
|
||
|
|
])
|
||
|
|
def test_specgram_complex_equivalent(self, mode, conv):
|
||
|
|
specc, freqspecc, tc = mlab.specgram(x=self.y,
|
||
|
|
NFFT=self.NFFT_specgram,
|
||
|
|
Fs=self.Fs,
|
||
|
|
noverlap=self.nover_specgram,
|
||
|
|
pad_to=self.pad_to_specgram,
|
||
|
|
sides=self.sides,
|
||
|
|
mode='complex')
|
||
|
|
specm, freqspecm, tm = mlab.specgram(x=self.y,
|
||
|
|
NFFT=self.NFFT_specgram,
|
||
|
|
Fs=self.Fs,
|
||
|
|
noverlap=self.nover_specgram,
|
||
|
|
pad_to=self.pad_to_specgram,
|
||
|
|
sides=self.sides,
|
||
|
|
mode=mode)
|
||
|
|
|
||
|
|
assert_array_equal(freqspecc, freqspecm)
|
||
|
|
assert_array_equal(tc, tm)
|
||
|
|
assert_allclose(conv(specc), specm, atol=1e-06)
|
||
|
|
|
||
|
|
def test_psd_windowarray_equal(self):
|
||
|
|
win = mlab.window_hanning(np.ones(self.NFFT_density_real))
|
||
|
|
speca, fspa = mlab.psd(x=self.y,
|
||
|
|
NFFT=self.NFFT_density,
|
||
|
|
Fs=self.Fs,
|
||
|
|
noverlap=self.nover_density,
|
||
|
|
pad_to=self.pad_to_density,
|
||
|
|
sides=self.sides,
|
||
|
|
window=win)
|
||
|
|
specb, fspb = mlab.psd(x=self.y,
|
||
|
|
NFFT=self.NFFT_density,
|
||
|
|
Fs=self.Fs,
|
||
|
|
noverlap=self.nover_density,
|
||
|
|
pad_to=self.pad_to_density,
|
||
|
|
sides=self.sides)
|
||
|
|
assert_array_equal(fspa, fspb)
|
||
|
|
assert_allclose(speca, specb, atol=1e-08)
|
||
|
|
|
||
|
|
|
||
|
|
# extra test for cohere...
|
||
|
|
def test_cohere():
|
||
|
|
N = 1024
|
||
|
|
np.random.seed(19680801)
|
||
|
|
x = np.random.randn(N)
|
||
|
|
# phase offset
|
||
|
|
y = np.roll(x, 20)
|
||
|
|
# high-freq roll-off
|
||
|
|
y = np.convolve(y, np.ones(20) / 20., mode='same')
|
||
|
|
cohsq, f = mlab.cohere(x, y, NFFT=256, Fs=2, noverlap=128)
|
||
|
|
assert_allclose(np.mean(cohsq), 0.837, atol=1.e-3)
|
||
|
|
assert np.isreal(np.mean(cohsq))
|
||
|
|
|
||
|
|
|
||
|
|
# *****************************************************************
|
||
|
|
# These Tests were taken from SCIPY with some minor modifications
|
||
|
|
# this can be retrieved from:
|
||
|
|
# https://github.com/scipy/scipy/blob/master/scipy/stats/tests/test_kdeoth.py
|
||
|
|
# *****************************************************************
|
||
|
|
|
||
|
|
class TestGaussianKDE:
|
||
|
|
|
||
|
|
def test_kde_integer_input(self):
|
||
|
|
"""Regression test for #1181."""
|
||
|
|
x1 = np.arange(5)
|
||
|
|
kde = mlab.GaussianKDE(x1)
|
||
|
|
y_expected = [0.13480721, 0.18222869, 0.19514935, 0.18222869,
|
||
|
|
0.13480721]
|
||
|
|
np.testing.assert_array_almost_equal(kde(x1), y_expected, decimal=6)
|
||
|
|
|
||
|
|
def test_gaussian_kde_covariance_caching(self):
|
||
|
|
x1 = np.array([-7, -5, 1, 4, 5], dtype=float)
|
||
|
|
xs = np.linspace(-10, 10, num=5)
|
||
|
|
# These expected values are from scipy 0.10, before some changes to
|
||
|
|
# gaussian_kde. They were not compared with any external reference.
|
||
|
|
y_expected = [0.02463386, 0.04689208, 0.05395444, 0.05337754,
|
||
|
|
0.01664475]
|
||
|
|
|
||
|
|
# set it to the default bandwidth.
|
||
|
|
kde2 = mlab.GaussianKDE(x1, 'scott')
|
||
|
|
y2 = kde2(xs)
|
||
|
|
|
||
|
|
np.testing.assert_array_almost_equal(y_expected, y2, decimal=7)
|
||
|
|
|
||
|
|
def test_kde_bandwidth_method(self):
|
||
|
|
|
||
|
|
np.random.seed(8765678)
|
||
|
|
n_basesample = 50
|
||
|
|
xn = np.random.randn(n_basesample)
|
||
|
|
|
||
|
|
# Default
|
||
|
|
gkde = mlab.GaussianKDE(xn)
|
||
|
|
# Supply a callable
|
||
|
|
gkde2 = mlab.GaussianKDE(xn, 'scott')
|
||
|
|
# Supply a scalar
|
||
|
|
gkde3 = mlab.GaussianKDE(xn, bw_method=gkde.factor)
|
||
|
|
|
||
|
|
xs = np.linspace(-7, 7, 51)
|
||
|
|
kdepdf = gkde.evaluate(xs)
|
||
|
|
kdepdf2 = gkde2.evaluate(xs)
|
||
|
|
assert kdepdf.all() == kdepdf2.all()
|
||
|
|
kdepdf3 = gkde3.evaluate(xs)
|
||
|
|
assert kdepdf.all() == kdepdf3.all()
|
||
|
|
|
||
|
|
|
||
|
|
class TestGaussianKDECustom:
|
||
|
|
def test_no_data(self):
|
||
|
|
"""Pass no data into the GaussianKDE class."""
|
||
|
|
with pytest.raises(ValueError):
|
||
|
|
mlab.GaussianKDE([])
|
||
|
|
|
||
|
|
def test_single_dataset_element(self):
|
||
|
|
"""Pass a single dataset element into the GaussianKDE class."""
|
||
|
|
with pytest.raises(ValueError):
|
||
|
|
mlab.GaussianKDE([42])
|
||
|
|
|
||
|
|
def test_silverman_multidim_dataset(self):
|
||
|
|
"""Test silverman's for a multi-dimensional array."""
|
||
|
|
x1 = np.array([[1, 2, 3], [4, 5, 6], [7, 8, 9]])
|
||
|
|
with pytest.raises(np.linalg.LinAlgError):
|
||
|
|
mlab.GaussianKDE(x1, "silverman")
|
||
|
|
|
||
|
|
def test_silverman_singledim_dataset(self):
|
||
|
|
"""Test silverman's output for a single dimension list."""
|
||
|
|
x1 = np.array([-7, -5, 1, 4, 5])
|
||
|
|
mygauss = mlab.GaussianKDE(x1, "silverman")
|
||
|
|
y_expected = 0.76770389927475502
|
||
|
|
assert_almost_equal(mygauss.covariance_factor(), y_expected, 7)
|
||
|
|
|
||
|
|
def test_scott_multidim_dataset(self):
|
||
|
|
"""Test scott's output for a multi-dimensional array."""
|
||
|
|
x1 = np.array([[1, 2, 3], [4, 5, 6], [7, 8, 9]])
|
||
|
|
with pytest.raises(np.linalg.LinAlgError):
|
||
|
|
mlab.GaussianKDE(x1, "scott")
|
||
|
|
|
||
|
|
def test_scott_singledim_dataset(self):
|
||
|
|
"""Test scott's output a single-dimensional array."""
|
||
|
|
x1 = np.array([-7, -5, 1, 4, 5])
|
||
|
|
mygauss = mlab.GaussianKDE(x1, "scott")
|
||
|
|
y_expected = 0.72477966367769553
|
||
|
|
assert_almost_equal(mygauss.covariance_factor(), y_expected, 7)
|
||
|
|
|
||
|
|
def test_scalar_empty_dataset(self):
|
||
|
|
"""Test the scalar's cov factor for an empty array."""
|
||
|
|
with pytest.raises(ValueError):
|
||
|
|
mlab.GaussianKDE([], bw_method=5)
|
||
|
|
|
||
|
|
def test_scalar_covariance_dataset(self):
|
||
|
|
"""Test a scalar's cov factor."""
|
||
|
|
np.random.seed(8765678)
|
||
|
|
n_basesample = 50
|
||
|
|
multidim_data = [np.random.randn(n_basesample) for i in range(5)]
|
||
|
|
|
||
|
|
kde = mlab.GaussianKDE(multidim_data, bw_method=0.5)
|
||
|
|
assert kde.covariance_factor() == 0.5
|
||
|
|
|
||
|
|
def test_callable_covariance_dataset(self):
|
||
|
|
"""Test the callable's cov factor for a multi-dimensional array."""
|
||
|
|
np.random.seed(8765678)
|
||
|
|
n_basesample = 50
|
||
|
|
multidim_data = [np.random.randn(n_basesample) for i in range(5)]
|
||
|
|
|
||
|
|
def callable_fun(x):
|
||
|
|
return 0.55
|
||
|
|
kde = mlab.GaussianKDE(multidim_data, bw_method=callable_fun)
|
||
|
|
assert kde.covariance_factor() == 0.55
|
||
|
|
|
||
|
|
def test_callable_singledim_dataset(self):
|
||
|
|
"""Test the callable's cov factor for a single-dimensional array."""
|
||
|
|
np.random.seed(8765678)
|
||
|
|
n_basesample = 50
|
||
|
|
multidim_data = np.random.randn(n_basesample)
|
||
|
|
|
||
|
|
kde = mlab.GaussianKDE(multidim_data, bw_method='silverman')
|
||
|
|
y_expected = 0.48438841363348911
|
||
|
|
assert_almost_equal(kde.covariance_factor(), y_expected, 7)
|
||
|
|
|
||
|
|
def test_wrong_bw_method(self):
|
||
|
|
"""Test the error message that should be called when bw is invalid."""
|
||
|
|
np.random.seed(8765678)
|
||
|
|
n_basesample = 50
|
||
|
|
data = np.random.randn(n_basesample)
|
||
|
|
with pytest.raises(ValueError):
|
||
|
|
mlab.GaussianKDE(data, bw_method="invalid")
|
||
|
|
|
||
|
|
|
||
|
|
class TestGaussianKDEEvaluate:
|
||
|
|
|
||
|
|
def test_evaluate_diff_dim(self):
|
||
|
|
"""
|
||
|
|
Test the evaluate method when the dim's of dataset and points have
|
||
|
|
different dimensions.
|
||
|
|
"""
|
||
|
|
x1 = np.arange(3, 10, 2)
|
||
|
|
kde = mlab.GaussianKDE(x1)
|
||
|
|
x2 = np.arange(3, 12, 2)
|
||
|
|
y_expected = [
|
||
|
|
0.08797252, 0.11774109, 0.11774109, 0.08797252, 0.0370153
|
||
|
|
]
|
||
|
|
y = kde.evaluate(x2)
|
||
|
|
np.testing.assert_array_almost_equal(y, y_expected, 7)
|
||
|
|
|
||
|
|
def test_evaluate_inv_dim(self):
|
||
|
|
"""
|
||
|
|
Invert the dimensions; i.e., for a dataset of dimension 1 [3, 2, 4],
|
||
|
|
the points should have a dimension of 3 [[3], [2], [4]].
|
||
|
|
"""
|
||
|
|
np.random.seed(8765678)
|
||
|
|
n_basesample = 50
|
||
|
|
multidim_data = np.random.randn(n_basesample)
|
||
|
|
kde = mlab.GaussianKDE(multidim_data)
|
||
|
|
x2 = [[1], [2], [3]]
|
||
|
|
with pytest.raises(ValueError):
|
||
|
|
kde.evaluate(x2)
|
||
|
|
|
||
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def test_evaluate_dim_and_num(self):
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"""Tests if evaluated against a one by one array"""
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x1 = np.arange(3, 10, 2)
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x2 = np.array([3])
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kde = mlab.GaussianKDE(x1)
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y_expected = [0.08797252]
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y = kde.evaluate(x2)
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np.testing.assert_array_almost_equal(y, y_expected, 7)
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def test_evaluate_point_dim_not_one(self):
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x1 = np.arange(3, 10, 2)
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x2 = [np.arange(3, 10, 2), np.arange(3, 10, 2)]
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kde = mlab.GaussianKDE(x1)
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with pytest.raises(ValueError):
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kde.evaluate(x2)
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def test_evaluate_equal_dim_and_num_lt(self):
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x1 = np.arange(3, 10, 2)
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x2 = np.arange(3, 8, 2)
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kde = mlab.GaussianKDE(x1)
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y_expected = [0.08797252, 0.11774109, 0.11774109]
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y = kde.evaluate(x2)
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np.testing.assert_array_almost_equal(y, y_expected, 7)
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def test_psd_onesided_norm():
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u = np.array([0, 1, 2, 3, 1, 2, 1])
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dt = 1.0
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Su = np.abs(np.fft.fft(u) * dt)**2 / (dt * u.size)
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P, f = mlab.psd(u, NFFT=u.size, Fs=1/dt, window=mlab.window_none,
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detrend=mlab.detrend_none, noverlap=0, pad_to=None,
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scale_by_freq=None,
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sides='onesided')
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Su_1side = np.append([Su[0]], Su[1:4] + Su[4:][::-1])
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assert_allclose(P, Su_1side, atol=1e-06)
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def test_psd_oversampling():
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"""Test the case len(x) < NFFT for psd()."""
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u = np.array([0, 1, 2, 3, 1, 2, 1])
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dt = 1.0
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||
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|
Su = np.abs(np.fft.fft(u) * dt)**2 / (dt * u.size)
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P, f = mlab.psd(u, NFFT=u.size*2, Fs=1/dt, window=mlab.window_none,
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||
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detrend=mlab.detrend_none, noverlap=0, pad_to=None,
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|
scale_by_freq=None,
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||
|
|
sides='onesided')
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||
|
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Su_1side = np.append([Su[0]], Su[1:4] + Su[4:][::-1])
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assert_almost_equal(np.sum(P), np.sum(Su_1side)) # same energy
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