Fixed database typo and removed unnecessary class identifier.

venv/Lib/site-packages/scipy/signal/tests/mpsig.py

@@ -0,0 +1,122 @@
+"""
+Some signal functions implemented using mpmath.
+"""
+
+try:
+    import mpmath  # type: ignore[import]
+except ImportError:
+    mpmath = None
+
+
+def _prod(seq):
+    """Returns the product of the elements in the sequence `seq`."""
+    p = 1
+    for elem in seq:
+        p *= elem
+    return p
+
+
+def _relative_degree(z, p):
+    """
+    Return relative degree of transfer function from zeros and poles.
+
+    This is simply len(p) - len(z), which must be nonnegative.
+    A ValueError is raised if len(p) < len(z).
+    """
+    degree = len(p) - len(z)
+    if degree < 0:
+        raise ValueError("Improper transfer function. "
+                         "Must have at least as many poles as zeros.")
+    return degree
+
+
+def _zpkbilinear(z, p, k, fs):
+    """Bilinear transformation to convert a filter from analog to digital."""
+
+    degree = _relative_degree(z, p)
+
+    fs2 = 2*fs
+
+    # Bilinear transform the poles and zeros
+    z_z = [(fs2 + z1) / (fs2 - z1) for z1 in z]
+    p_z = [(fs2 + p1) / (fs2 - p1) for p1 in p]
+
+    # Any zeros that were at infinity get moved to the Nyquist frequency
+    z_z.extend([-1] * degree)
+
+    # Compensate for gain change
+    numer = _prod(fs2 - z1 for z1 in z)
+    denom = _prod(fs2 - p1 for p1 in p)
+    k_z = k * numer / denom
+
+    return z_z, p_z, k_z.real
+
+
+def _zpklp2lp(z, p, k, wo=1):
+    """Transform a lowpass filter to a different cutoff frequency."""
+
+    degree = _relative_degree(z, p)
+
+    # Scale all points radially from origin to shift cutoff frequency
+    z_lp = [wo * z1 for z1 in z]
+    p_lp = [wo * p1 for p1 in p]
+
+    # Each shifted pole decreases gain by wo, each shifted zero increases it.
+    # Cancel out the net change to keep overall gain the same
+    k_lp = k * wo**degree
+
+    return z_lp, p_lp, k_lp
+
+
+def _butter_analog_poles(n):
+    """
+    Poles of an analog Butterworth lowpass filter.
+
+    This is the same calculation as scipy.signal.buttap(n) or
+    scipy.signal.butter(n, 1, analog=True, output='zpk'), but mpmath is used,
+    and only the poles are returned.
+    """
+    poles = [-mpmath.exp(1j*mpmath.pi*k/(2*n)) for k in range(-n+1, n, 2)]
+    return poles
+
+
+def butter_lp(n, Wn):
+    """
+    Lowpass Butterworth digital filter design.
+
+    This computes the same result as scipy.signal.butter(n, Wn, output='zpk'),
+    but it uses mpmath, and the results are returned in lists instead of NumPy
+    arrays.
+    """
+    zeros = []
+    poles = _butter_analog_poles(n)
+    k = 1
+    fs = 2
+    warped = 2 * fs * mpmath.tan(mpmath.pi * Wn / fs)
+    z, p, k = _zpklp2lp(zeros, poles, k, wo=warped)
+    z, p, k = _zpkbilinear(z, p, k, fs=fs)
+    return z, p, k
+
+
+def zpkfreqz(z, p, k, worN=None):
+    """
+    Frequency response of a filter in zpk format, using mpmath.
+
+    This is the same calculation as scipy.signal.freqz, but the input is in
+    zpk format, the calculation is performed using mpath, and the results are
+    returned in lists instead of NumPy arrays.
+    """
+    if worN is None or isinstance(worN, int):
+        N = worN or 512
+        ws = [mpmath.pi * mpmath.mpf(j) / N for j in range(N)]
+    else:
+        ws = worN
+
+    h = []
+    for wk in ws:
+        zm1 = mpmath.exp(1j * wk)
+        numer = _prod([zm1 - t for t in z])
+        denom = _prod([zm1 - t for t in p])
+        hk = k * numer / denom
+        h.append(hk)
+    return ws, h

venv/Lib/site-packages/scipy/signal/tests/test_array_tools.py

@@ -0,0 +1,111 @@
+import numpy as np
+
+from numpy.testing import assert_array_equal
+from pytest import raises as assert_raises
+
+from scipy.signal._arraytools import (axis_slice, axis_reverse,
+     odd_ext, even_ext, const_ext, zero_ext)
+
+
+class TestArrayTools(object):
+
+    def test_axis_slice(self):
+        a = np.arange(12).reshape(3, 4)
+
+        s = axis_slice(a, start=0, stop=1, axis=0)
+        assert_array_equal(s, a[0:1, :])
+
+        s = axis_slice(a, start=-1, axis=0)
+        assert_array_equal(s, a[-1:, :])
+
+        s = axis_slice(a, start=0, stop=1, axis=1)
+        assert_array_equal(s, a[:, 0:1])
+
+        s = axis_slice(a, start=-1, axis=1)
+        assert_array_equal(s, a[:, -1:])
+
+        s = axis_slice(a, start=0, step=2, axis=0)
+        assert_array_equal(s, a[::2, :])
+
+        s = axis_slice(a, start=0, step=2, axis=1)
+        assert_array_equal(s, a[:, ::2])
+
+    def test_axis_reverse(self):
+        a = np.arange(12).reshape(3, 4)
+
+        r = axis_reverse(a, axis=0)
+        assert_array_equal(r, a[::-1, :])
+
+        r = axis_reverse(a, axis=1)
+        assert_array_equal(r, a[:, ::-1])
+
+    def test_odd_ext(self):
+        a = np.array([[1, 2, 3, 4, 5],
+                      [9, 8, 7, 6, 5]])
+
+        odd = odd_ext(a, 2, axis=1)
+        expected = np.array([[-1, 0, 1, 2, 3, 4, 5, 6, 7],
+                             [11, 10, 9, 8, 7, 6, 5, 4, 3]])
+        assert_array_equal(odd, expected)
+
+        odd = odd_ext(a, 1, axis=0)
+        expected = np.array([[-7, -4, -1, 2, 5],
+                             [1, 2, 3, 4, 5],
+                             [9, 8, 7, 6, 5],
+                             [17, 14, 11, 8, 5]])
+        assert_array_equal(odd, expected)
+
+        assert_raises(ValueError, odd_ext, a, 2, axis=0)
+        assert_raises(ValueError, odd_ext, a, 5, axis=1)
+
+    def test_even_ext(self):
+        a = np.array([[1, 2, 3, 4, 5],
+                      [9, 8, 7, 6, 5]])
+
+        even = even_ext(a, 2, axis=1)
+        expected = np.array([[3, 2, 1, 2, 3, 4, 5, 4, 3],
+                             [7, 8, 9, 8, 7, 6, 5, 6, 7]])
+        assert_array_equal(even, expected)
+
+        even = even_ext(a, 1, axis=0)
+        expected = np.array([[9, 8, 7, 6, 5],
+                             [1, 2, 3, 4, 5],
+                             [9, 8, 7, 6, 5],
+                             [1, 2, 3, 4, 5]])
+        assert_array_equal(even, expected)
+
+        assert_raises(ValueError, even_ext, a, 2, axis=0)
+        assert_raises(ValueError, even_ext, a, 5, axis=1)
+
+    def test_const_ext(self):
+        a = np.array([[1, 2, 3, 4, 5],
+                      [9, 8, 7, 6, 5]])
+
+        const = const_ext(a, 2, axis=1)
+        expected = np.array([[1, 1, 1, 2, 3, 4, 5, 5, 5],
+                             [9, 9, 9, 8, 7, 6, 5, 5, 5]])
+        assert_array_equal(const, expected)
+
+        const = const_ext(a, 1, axis=0)
+        expected = np.array([[1, 2, 3, 4, 5],
+                             [1, 2, 3, 4, 5],
+                             [9, 8, 7, 6, 5],
+                             [9, 8, 7, 6, 5]])
+        assert_array_equal(const, expected)
+
+    def test_zero_ext(self):
+        a = np.array([[1, 2, 3, 4, 5],
+                      [9, 8, 7, 6, 5]])
+
+        zero = zero_ext(a, 2, axis=1)
+        expected = np.array([[0, 0, 1, 2, 3, 4, 5, 0, 0],
+                             [0, 0, 9, 8, 7, 6, 5, 0, 0]])
+        assert_array_equal(zero, expected)
+
+        zero = zero_ext(a, 1, axis=0)
+        expected = np.array([[0, 0, 0, 0, 0],
+                             [1, 2, 3, 4, 5],
+                             [9, 8, 7, 6, 5],
+                             [0, 0, 0, 0, 0]])
+        assert_array_equal(zero, expected)
+

venv/Lib/site-packages/scipy/signal/tests/test_bsplines.py

@@ -0,0 +1,222 @@
+# pylint: disable=missing-docstring
+import numpy as np
+from numpy import array
+from numpy.testing import (assert_equal,
+                           assert_allclose, assert_array_equal,
+                           assert_almost_equal)
+from pytest import raises
+
+import scipy.signal.bsplines as bsp
+
+
+class TestBSplines(object):
+    """Test behaviors of B-splines. The values tested against were returned as of
+    SciPy 1.1.0 and are included for regression testing purposes"""
+
+    def test_factorial(self):
+        # can't all be zero state
+        assert_equal(bsp.factorial(1), 1)
+
+    def test_spline_filter(self):
+        np.random.seed(12457)
+        # Test the type-error branch
+        raises(TypeError, bsp.spline_filter, array([0]), 0)
+        # Test the complex branch
+        data_array_complex = np.random.rand(7, 7) + np.random.rand(7, 7)*1j
+        # make the magnitude exceed 1, and make some negative
+        data_array_complex = 10*(1+1j-2*data_array_complex)
+        result_array_complex = array(
+            [[-4.61489230e-01-1.92994022j, 8.33332443+6.25519943j,
+              6.96300745e-01-9.05576038j, 5.28294849+3.97541356j,
+              5.92165565+7.68240595j, 6.59493160-1.04542804j,
+              9.84503460-5.85946894j],
+             [-8.78262329-8.4295969j, 7.20675516+5.47528982j,
+              -8.17223072+2.06330729j, -4.38633347-8.65968037j,
+              9.89916801-8.91720295j, 2.67755103+8.8706522j,
+              6.24192142+3.76879835j],
+             [-3.15627527+2.56303072j, 9.87658501-0.82838702j,
+              -9.96930313+8.72288895j, 3.17193985+6.42474651j,
+              -4.50919819-6.84576082j, 5.75423431+9.94723988j,
+              9.65979767+6.90665293j],
+             [-8.28993416-6.61064005j, 9.71416473e-01-9.44907284j,
+              -2.38331890+9.25196648j, -7.08868170-0.77403212j,
+              4.89887714+7.05371094j, -1.37062311-2.73505688j,
+              7.70705748+2.5395329j],
+             [2.51528406-1.82964492j, 3.65885472+2.95454836j,
+              5.16786575-1.66362023j, -8.77737999e-03+5.72478867j,
+              4.10533333-3.10287571j, 9.04761887+1.54017115j,
+              -5.77960968e-01-7.87758923j],
+             [9.86398506-3.98528528j, -4.71444130-2.44316983j,
+              -1.68038976-1.12708664j, 2.84695053+1.01725709j,
+              1.14315915-8.89294529j, -3.17127085-5.42145538j,
+              1.91830420-6.16370344j],
+             [7.13875294+2.91851187j, -5.35737514+9.64132309j,
+              -9.66586399+0.70250005j, -9.87717438-2.0262239j,
+              9.93160629+1.5630846j, 4.71948051-2.22050714j,
+              9.49550819+7.8995142j]])
+        # FIXME: for complex types, the computations are done in
+        # single precision (reason unclear). When this is changed,
+        # this test needs updating.
+        assert_allclose(bsp.spline_filter(data_array_complex, 0),
+                        result_array_complex, rtol=1e-6)
+        # Test the real branch
+        np.random.seed(12457)
+        data_array_real = np.random.rand(12, 12)
+        # make the magnitude exceed 1, and make some negative
+        data_array_real = 10*(1-2*data_array_real)
+        result_array_real = array(
+            [[-.463312621, 8.33391222, .697290949, 5.28390836,
+              5.92066474, 6.59452137, 9.84406950, -8.78324188,
+              7.20675750, -8.17222994, -4.38633345, 9.89917069],
+             [2.67755154, 6.24192170, -3.15730578, 9.87658581,
+              -9.96930425, 3.17194115, -4.50919947, 5.75423446,
+              9.65979824, -8.29066885, .971416087, -2.38331897],
+             [-7.08868346, 4.89887705, -1.37062289, 7.70705838,
+              2.51526461, 3.65885497, 5.16786604, -8.77715342e-03,
+              4.10533325, 9.04761993, -.577960351, 9.86382519],
+             [-4.71444301, -1.68038985, 2.84695116, 1.14315938,
+              -3.17127091, 1.91830461, 7.13779687, -5.35737482,
+              -9.66586425, -9.87717456, 9.93160672, 4.71948144],
+             [9.49551194, -1.92958436, 6.25427993, -9.05582911,
+              3.97562282, 7.68232426, -1.04514824, -5.86021443,
+              -8.43007451, 5.47528997, 2.06330736, -8.65968112],
+             [-8.91720100, 8.87065356, 3.76879937, 2.56222894,
+              -.828387146, 8.72288903, 6.42474741, -6.84576083,
+              9.94724115, 6.90665380, -6.61084494, -9.44907391],
+             [9.25196790, -.774032030, 7.05371046, -2.73505725,
+              2.53953305, -1.82889155, 2.95454824, -1.66362046,
+              5.72478916, -3.10287679, 1.54017123, -7.87759020],
+             [-3.98464539, -2.44316992, -1.12708657, 1.01725672,
+              -8.89294671, -5.42145629, -6.16370321, 2.91775492,
+              9.64132208, .702499998, -2.02622392, 1.56308431],
+             [-2.22050773, 7.89951554, 5.98970713, -7.35861835,
+              5.45459283, -7.76427957, 3.67280490, -4.05521315,
+              4.51967507, -3.22738749, -3.65080177, 3.05630155],
+             [-6.21240584, -.296796126, -8.34800163, 9.21564563,
+              -3.61958784, -4.77120006, -3.99454057, 1.05021988e-03,
+              -6.95982829, 6.04380797, 8.43181250, -2.71653339],
+             [1.19638037, 6.99718842e-02, 6.72020394, -2.13963198,
+              3.75309875, -5.70076744, 5.92143551, -7.22150575,
+              -3.77114594, -1.11903194, -5.39151466, 3.06620093],
+             [9.86326886, 1.05134482, -7.75950607, -3.64429655,
+              7.81848957, -9.02270373, 3.73399754, -4.71962549,
+              -7.71144306, 3.78263161, 6.46034818, -4.43444731]])
+        assert_allclose(bsp.spline_filter(data_array_real, 0),
+                        result_array_real)
+
+    def test_bspline(self):
+        np.random.seed(12458)
+        assert_allclose(bsp.bspline(np.random.rand(1, 1), 2),
+                        array([[0.73694695]]))
+        data_array_complex = np.random.rand(4, 4) + np.random.rand(4, 4)*1j
+        data_array_complex = 0.1*data_array_complex
+        result_array_complex = array(
+            [[0.40882362, 0.41021151, 0.40886708, 0.40905103],
+             [0.40829477, 0.41021230, 0.40966097, 0.40939871],
+             [0.41036803, 0.40901724, 0.40965331, 0.40879513],
+             [0.41032862, 0.40925287, 0.41037754, 0.41027477]])
+        assert_allclose(bsp.bspline(data_array_complex, 10),
+                        result_array_complex)
+
+    def test_gauss_spline(self):
+        np.random.seed(12459)
+        assert_almost_equal(bsp.gauss_spline(0, 0), 1.381976597885342)
+        assert_allclose(bsp.gauss_spline(array([1.]), 1), array([0.04865217]))
+
+    def test_cubic(self):
+        np.random.seed(12460)
+        assert_array_equal(bsp.cubic([0]), array([0]))
+        data_array_complex = np.random.rand(4, 4) + np.random.rand(4, 4)*1j
+        data_array_complex = 1+1j-2*data_array_complex
+        # scaling the magnitude by 10 makes the results close enough to zero,
+        # that the assertion fails, so just make the elements have a mix of
+        # positive and negative imaginary components...
+        result_array_complex = array(
+            [[0.23056563, 0.38414406, 0.08342987, 0.06904847],
+             [0.17240848, 0.47055447, 0.63896278, 0.39756424],
+             [0.12672571, 0.65862632, 0.1116695, 0.09700386],
+             [0.3544116, 0.17856518, 0.1528841, 0.17285762]])
+        assert_allclose(bsp.cubic(data_array_complex), result_array_complex)
+
+    def test_quadratic(self):
+        np.random.seed(12461)
+        assert_array_equal(bsp.quadratic([0]), array([0]))
+        data_array_complex = np.random.rand(4, 4) + np.random.rand(4, 4)*1j
+        # scaling the magnitude by 10 makes the results all zero,
+        # so just make the elements have a mix of positive and negative
+        # imaginary components...
+        data_array_complex = (1+1j-2*data_array_complex)
+        result_array_complex = array(
+            [[0.23062746, 0.06338176, 0.34902312, 0.31944105],
+             [0.14701256, 0.13277773, 0.29428615, 0.09814697],
+             [0.52873842, 0.06484157, 0.09517566, 0.46420389],
+             [0.09286829, 0.09371954, 0.1422526, 0.16007024]])
+        assert_allclose(bsp.quadratic(data_array_complex),
+                        result_array_complex)
+
+    def test_cspline1d(self):
+        np.random.seed(12462)
+        assert_array_equal(bsp.cspline1d(array([0])), [0.])
+        c1d = array([1.21037185, 1.86293902, 2.98834059, 4.11660378,
+                     4.78893826])
+        # test lamda != 0
+        assert_allclose(bsp.cspline1d(array([1., 2, 3, 4, 5]), 1), c1d)
+        c1d0 = array([0.78683946, 2.05333735, 2.99981113, 3.94741812,
+                      5.21051638])
+        assert_allclose(bsp.cspline1d(array([1., 2, 3, 4, 5])), c1d0)
+
+    def test_qspline1d(self):
+        np.random.seed(12463)
+        assert_array_equal(bsp.qspline1d(array([0])), [0.])
+        # test lamda != 0
+        raises(ValueError, bsp.qspline1d, array([1., 2, 3, 4, 5]), 1.)
+        raises(ValueError, bsp.qspline1d, array([1., 2, 3, 4, 5]), -1.)
+        q1d0 = array([0.85350007, 2.02441743, 2.99999534, 3.97561055,
+                      5.14634135])
+        assert_allclose(bsp.qspline1d(array([1., 2, 3, 4, 5])), q1d0)
+
+    def test_cspline1d_eval(self):
+        np.random.seed(12464)
+        assert_allclose(bsp.cspline1d_eval(array([0., 0]), [0.]), array([0.]))
+        assert_array_equal(bsp.cspline1d_eval(array([1., 0, 1]), []),
+                           array([]))
+        x = [-3, -2, -1, 0, 1, 2, 3, 4, 5, 6]
+        dx = x[1]-x[0]
+        newx = [-6., -5.5, -5., -4.5, -4., -3.5, -3., -2.5, -2., -1.5, -1.,
+                -0.5, 0., 0.5, 1., 1.5, 2., 2.5, 3., 3.5, 4., 4.5, 5., 5.5, 6.,
+                6.5, 7., 7.5, 8., 8.5, 9., 9.5, 10., 10.5, 11., 11.5, 12.,
+                12.5]
+        y = array([4.216, 6.864, 3.514, 6.203, 6.759, 7.433, 7.874, 5.879,
+                   1.396, 4.094])
+        cj = bsp.cspline1d(y)
+        newy = array([6.203, 4.41570658, 3.514, 5.16924703, 6.864, 6.04643068,
+                      4.21600281, 6.04643068, 6.864, 5.16924703, 3.514,
+                      4.41570658, 6.203, 6.80717667, 6.759, 6.98971173, 7.433,
+                      7.79560142, 7.874, 7.41525761, 5.879, 3.18686814, 1.396,
+                      2.24889482, 4.094, 2.24889482, 1.396, 3.18686814, 5.879,
+                      7.41525761, 7.874, 7.79560142, 7.433, 6.98971173, 6.759,
+                      6.80717667, 6.203, 4.41570658])
+        assert_allclose(bsp.cspline1d_eval(cj, newx, dx=dx, x0=x[0]), newy)
+
+    def test_qspline1d_eval(self):
+        np.random.seed(12465)
+        assert_allclose(bsp.qspline1d_eval(array([0., 0]), [0.]), array([0.]))
+        assert_array_equal(bsp.qspline1d_eval(array([1., 0, 1]), []),
+                           array([]))
+        x = [-3, -2, -1, 0, 1, 2, 3, 4, 5, 6]
+        dx = x[1]-x[0]
+        newx = [-6., -5.5, -5., -4.5, -4., -3.5, -3., -2.5, -2., -1.5, -1.,
+                -0.5, 0., 0.5, 1., 1.5, 2., 2.5, 3., 3.5, 4., 4.5, 5., 5.5, 6.,
+                6.5, 7., 7.5, 8., 8.5, 9., 9.5, 10., 10.5, 11., 11.5, 12.,
+                12.5]
+        y = array([4.216, 6.864, 3.514, 6.203, 6.759, 7.433, 7.874, 5.879,
+                   1.396, 4.094])
+        cj = bsp.qspline1d(y)
+        newy = array([6.203, 4.49418159, 3.514, 5.18390821, 6.864, 5.91436915,
+                      4.21600002, 5.91436915, 6.864, 5.18390821, 3.514,
+                      4.49418159, 6.203, 6.71900226, 6.759, 7.03980488, 7.433,
+                      7.81016848, 7.874, 7.32718426, 5.879, 3.23872593, 1.396,
+                      2.34046013, 4.094, 2.34046013, 1.396, 3.23872593, 5.879,
+                      7.32718426, 7.874, 7.81016848, 7.433, 7.03980488, 6.759,
+                      6.71900226, 6.203, 4.49418159])
+        assert_allclose(bsp.qspline1d_eval(cj, newx, dx=dx, x0=x[0]), newy)

venv/Lib/site-packages/scipy/signal/tests/test_cont2discrete.py

@@ -0,0 +1,420 @@
+import numpy as np
+from numpy.testing import \
+                          assert_array_almost_equal, assert_almost_equal, \
+                          assert_allclose, assert_equal
+
+import pytest
+from scipy.signal import cont2discrete as c2d
+from scipy.signal import dlsim, ss2tf, ss2zpk, lsim2, lti
+from scipy.signal import tf2ss, impulse2, dimpulse, step2, dstep
+
+# Author: Jeffrey Armstrong <jeff@approximatrix.com>
+# March 29, 2011
+
+
+class TestC2D(object):
+    def test_zoh(self):
+        ac = np.eye(2)
+        bc = np.full((2, 1), 0.5)
+        cc = np.array([[0.75, 1.0], [1.0, 1.0], [1.0, 0.25]])
+        dc = np.array([[0.0], [0.0], [-0.33]])
+
+        ad_truth = 1.648721270700128 * np.eye(2)
+        bd_truth = np.full((2, 1), 0.324360635350064)
+        # c and d in discrete should be equal to their continuous counterparts
+        dt_requested = 0.5
+
+        ad, bd, cd, dd, dt = c2d((ac, bc, cc, dc), dt_requested, method='zoh')
+
+        assert_array_almost_equal(ad_truth, ad)
+        assert_array_almost_equal(bd_truth, bd)
+        assert_array_almost_equal(cc, cd)
+        assert_array_almost_equal(dc, dd)
+        assert_almost_equal(dt_requested, dt)
+
+    def test_foh(self):
+        ac = np.eye(2)
+        bc = np.full((2, 1), 0.5)
+        cc = np.array([[0.75, 1.0], [1.0, 1.0], [1.0, 0.25]])
+        dc = np.array([[0.0], [0.0], [-0.33]])
+
+        # True values are verified with Matlab
+        ad_truth = 1.648721270700128 * np.eye(2)
+        bd_truth = np.full((2, 1), 0.420839287058789)
+        cd_truth = cc
+        dd_truth = np.array([[0.260262223725224],
+                             [0.297442541400256],
+                             [-0.144098411624840]])
+        dt_requested = 0.5
+
+        ad, bd, cd, dd, dt = c2d((ac, bc, cc, dc), dt_requested, method='foh')
+
+        assert_array_almost_equal(ad_truth, ad)
+        assert_array_almost_equal(bd_truth, bd)
+        assert_array_almost_equal(cd_truth, cd)
+        assert_array_almost_equal(dd_truth, dd)
+        assert_almost_equal(dt_requested, dt)
+
+    def test_impulse(self):
+        ac = np.eye(2)
+        bc = np.full((2, 1), 0.5)
+        cc = np.array([[0.75, 1.0], [1.0, 1.0], [1.0, 0.25]])
+        dc = np.array([[0.0], [0.0], [0.0]])
+
+        # True values are verified with Matlab
+        ad_truth = 1.648721270700128 * np.eye(2)
+        bd_truth = np.full((2, 1), 0.412180317675032)
+        cd_truth = cc
+        dd_truth = np.array([[0.4375], [0.5], [0.3125]])
+        dt_requested = 0.5
+
+        ad, bd, cd, dd, dt = c2d((ac, bc, cc, dc), dt_requested,
+                                 method='impulse')
+
+        assert_array_almost_equal(ad_truth, ad)
+        assert_array_almost_equal(bd_truth, bd)
+        assert_array_almost_equal(cd_truth, cd)
+        assert_array_almost_equal(dd_truth, dd)
+        assert_almost_equal(dt_requested, dt)
+
+    def test_gbt(self):
+        ac = np.eye(2)
+        bc = np.full((2, 1), 0.5)
+        cc = np.array([[0.75, 1.0], [1.0, 1.0], [1.0, 0.25]])
+        dc = np.array([[0.0], [0.0], [-0.33]])
+
+        dt_requested = 0.5
+        alpha = 1.0 / 3.0
+
+        ad_truth = 1.6 * np.eye(2)
+        bd_truth = np.full((2, 1), 0.3)
+        cd_truth = np.array([[0.9, 1.2],
+                             [1.2, 1.2],
+                             [1.2, 0.3]])
+        dd_truth = np.array([[0.175],
+                             [0.2],
+                             [-0.205]])
+
+        ad, bd, cd, dd, dt = c2d((ac, bc, cc, dc), dt_requested,
+                                 method='gbt', alpha=alpha)
+
+        assert_array_almost_equal(ad_truth, ad)
+        assert_array_almost_equal(bd_truth, bd)
+        assert_array_almost_equal(cd_truth, cd)
+        assert_array_almost_equal(dd_truth, dd)
+
+    def test_euler(self):
+        ac = np.eye(2)
+        bc = np.full((2, 1), 0.5)
+        cc = np.array([[0.75, 1.0], [1.0, 1.0], [1.0, 0.25]])
+        dc = np.array([[0.0], [0.0], [-0.33]])
+
+        dt_requested = 0.5
+
+        ad_truth = 1.5 * np.eye(2)
+        bd_truth = np.full((2, 1), 0.25)
+        cd_truth = np.array([[0.75, 1.0],
+                             [1.0, 1.0],
+                             [1.0, 0.25]])
+        dd_truth = dc
+
+        ad, bd, cd, dd, dt = c2d((ac, bc, cc, dc), dt_requested,
+                                 method='euler')
+
+        assert_array_almost_equal(ad_truth, ad)
+        assert_array_almost_equal(bd_truth, bd)
+        assert_array_almost_equal(cd_truth, cd)
+        assert_array_almost_equal(dd_truth, dd)
+        assert_almost_equal(dt_requested, dt)
+
+    def test_backward_diff(self):
+        ac = np.eye(2)
+        bc = np.full((2, 1), 0.5)
+        cc = np.array([[0.75, 1.0], [1.0, 1.0], [1.0, 0.25]])
+        dc = np.array([[0.0], [0.0], [-0.33]])
+
+        dt_requested = 0.5
+
+        ad_truth = 2.0 * np.eye(2)
+        bd_truth = np.full((2, 1), 0.5)
+        cd_truth = np.array([[1.5, 2.0],
+                             [2.0, 2.0],
+                             [2.0, 0.5]])
+        dd_truth = np.array([[0.875],
+                             [1.0],
+                             [0.295]])
+
+        ad, bd, cd, dd, dt = c2d((ac, bc, cc, dc), dt_requested,
+                                 method='backward_diff')
+
+        assert_array_almost_equal(ad_truth, ad)
+        assert_array_almost_equal(bd_truth, bd)
+        assert_array_almost_equal(cd_truth, cd)
+        assert_array_almost_equal(dd_truth, dd)
+
+    def test_bilinear(self):
+        ac = np.eye(2)
+        bc = np.full((2, 1), 0.5)
+        cc = np.array([[0.75, 1.0], [1.0, 1.0], [1.0, 0.25]])
+        dc = np.array([[0.0], [0.0], [-0.33]])
+
+        dt_requested = 0.5
+
+        ad_truth = (5.0 / 3.0) * np.eye(2)
+        bd_truth = np.full((2, 1), 1.0 / 3.0)
+        cd_truth = np.array([[1.0, 4.0 / 3.0],
+                             [4.0 / 3.0, 4.0 / 3.0],
+                             [4.0 / 3.0, 1.0 / 3.0]])
+        dd_truth = np.array([[0.291666666666667],
+                             [1.0 / 3.0],
+                             [-0.121666666666667]])
+
+        ad, bd, cd, dd, dt = c2d((ac, bc, cc, dc), dt_requested,
+                                 method='bilinear')
+
+        assert_array_almost_equal(ad_truth, ad)
+        assert_array_almost_equal(bd_truth, bd)
+        assert_array_almost_equal(cd_truth, cd)
+        assert_array_almost_equal(dd_truth, dd)
+        assert_almost_equal(dt_requested, dt)
+
+        # Same continuous system again, but change sampling rate
+
+        ad_truth = 1.4 * np.eye(2)
+        bd_truth = np.full((2, 1), 0.2)
+        cd_truth = np.array([[0.9, 1.2], [1.2, 1.2], [1.2, 0.3]])
+        dd_truth = np.array([[0.175], [0.2], [-0.205]])
+
+        dt_requested = 1.0 / 3.0
+
+        ad, bd, cd, dd, dt = c2d((ac, bc, cc, dc), dt_requested,
+                                 method='bilinear')
+
+        assert_array_almost_equal(ad_truth, ad)
+        assert_array_almost_equal(bd_truth, bd)
+        assert_array_almost_equal(cd_truth, cd)
+        assert_array_almost_equal(dd_truth, dd)
+        assert_almost_equal(dt_requested, dt)
+
+    def test_transferfunction(self):
+        numc = np.array([0.25, 0.25, 0.5])
+        denc = np.array([0.75, 0.75, 1.0])
+
+        numd = np.array([[1.0 / 3.0, -0.427419169438754, 0.221654141101125]])
+        dend = np.array([1.0, -1.351394049721225, 0.606530659712634])
+
+        dt_requested = 0.5
+
+        num, den, dt = c2d((numc, denc), dt_requested, method='zoh')
+
+        assert_array_almost_equal(numd, num)
+        assert_array_almost_equal(dend, den)
+        assert_almost_equal(dt_requested, dt)
+
+    def test_zerospolesgain(self):
+        zeros_c = np.array([0.5, -0.5])
+        poles_c = np.array([1.j / np.sqrt(2), -1.j / np.sqrt(2)])
+        k_c = 1.0
+
+        zeros_d = [1.23371727305860, 0.735356894461267]
+        polls_d = [0.938148335039729 + 0.346233593780536j,
+                   0.938148335039729 - 0.346233593780536j]
+        k_d = 1.0
+
+        dt_requested = 0.5
+
+        zeros, poles, k, dt = c2d((zeros_c, poles_c, k_c), dt_requested,
+                                  method='zoh')
+
+        assert_array_almost_equal(zeros_d, zeros)
+        assert_array_almost_equal(polls_d, poles)
+        assert_almost_equal(k_d, k)
+        assert_almost_equal(dt_requested, dt)
+
+    def test_gbt_with_sio_tf_and_zpk(self):
+        """Test method='gbt' with alpha=0.25 for tf and zpk cases."""
+        # State space coefficients for the continuous SIO system.
+        A = -1.0
+        B = 1.0
+        C = 1.0
+        D = 0.5
+
+        # The continuous transfer function coefficients.
+        cnum, cden = ss2tf(A, B, C, D)
+
+        # Continuous zpk representation
+        cz, cp, ck = ss2zpk(A, B, C, D)
+
+        h = 1.0
+        alpha = 0.25
+
+        # Explicit formulas, in the scalar case.
+        Ad = (1 + (1 - alpha) * h * A) / (1 - alpha * h * A)
+        Bd = h * B / (1 - alpha * h * A)
+        Cd = C / (1 - alpha * h * A)
+        Dd = D + alpha * C * Bd
+
+        # Convert the explicit solution to tf
+        dnum, dden = ss2tf(Ad, Bd, Cd, Dd)
+
+        # Compute the discrete tf using cont2discrete.
+        c2dnum, c2dden, dt = c2d((cnum, cden), h, method='gbt', alpha=alpha)
+
+        assert_allclose(dnum, c2dnum)
+        assert_allclose(dden, c2dden)
+
+        # Convert explicit solution to zpk.
+        dz, dp, dk = ss2zpk(Ad, Bd, Cd, Dd)
+
+        # Compute the discrete zpk using cont2discrete.
+        c2dz, c2dp, c2dk, dt = c2d((cz, cp, ck), h, method='gbt', alpha=alpha)
+
+        assert_allclose(dz, c2dz)
+        assert_allclose(dp, c2dp)
+        assert_allclose(dk, c2dk)
+
+    def test_discrete_approx(self):
+        """
+        Test that the solution to the discrete approximation of a continuous
+        system actually approximates the solution to the continuous system.
+        This is an indirect test of the correctness of the implementation
+        of cont2discrete.
+        """
+
+        def u(t):
+            return np.sin(2.5 * t)
+
+        a = np.array([[-0.01]])
+        b = np.array([[1.0]])
+        c = np.array([[1.0]])
+        d = np.array([[0.2]])
+        x0 = 1.0
+
+        t = np.linspace(0, 10.0, 101)
+        dt = t[1] - t[0]
+        u1 = u(t)
+
+        # Use lsim2 to compute the solution to the continuous system.
+        t, yout, xout = lsim2((a, b, c, d), T=t, U=u1, X0=x0,
+                              rtol=1e-9, atol=1e-11)
+
+        # Convert the continuous system to a discrete approximation.
+        dsys = c2d((a, b, c, d), dt, method='bilinear')
+
+        # Use dlsim with the pairwise averaged input to compute the output
+        # of the discrete system.
+        u2 = 0.5 * (u1[:-1] + u1[1:])
+        t2 = t[:-1]
+        td2, yd2, xd2 = dlsim(dsys, u=u2.reshape(-1, 1), t=t2, x0=x0)
+
+        # ymid is the average of consecutive terms of the "exact" output
+        # computed by lsim2.  This is what the discrete approximation
+        # actually approximates.
+        ymid = 0.5 * (yout[:-1] + yout[1:])
+
+        assert_allclose(yd2.ravel(), ymid, rtol=1e-4)
+
+    def test_simo_tf(self):
+        # See gh-5753
+        tf = ([[1, 0], [1, 1]], [1, 1])
+        num, den, dt = c2d(tf, 0.01)
+
+        assert_equal(dt, 0.01)  # sanity check
+        assert_allclose(den, [1, -0.990404983], rtol=1e-3)
+        assert_allclose(num, [[1, -1], [1, -0.99004983]], rtol=1e-3)
+
+    def test_multioutput(self):
+        ts = 0.01  # time step
+
+        tf = ([[1, -3], [1, 5]], [1, 1])
+        num, den, dt = c2d(tf, ts)
+
+        tf1 = (tf[0][0], tf[1])
+        num1, den1, dt1 = c2d(tf1, ts)
+
+        tf2 = (tf[0][1], tf[1])
+        num2, den2, dt2 = c2d(tf2, ts)
+
+        # Sanity checks
+        assert_equal(dt, dt1)
+        assert_equal(dt, dt2)
+
+        # Check that we get the same results
+        assert_allclose(num, np.vstack((num1, num2)), rtol=1e-13)
+
+        # Single input, so the denominator should
+        # not be multidimensional like the numerator
+        assert_allclose(den, den1, rtol=1e-13)
+        assert_allclose(den, den2, rtol=1e-13)
+
+class TestC2dLti(object):
+    def test_c2d_ss(self):
+        # StateSpace
+        A = np.array([[-0.3, 0.1], [0.2, -0.7]])
+        B = np.array([[0], [1]])
+        C = np.array([[1, 0]])
+        D = 0
+
+        A_res = np.array([[0.985136404135682, 0.004876671474795],
+                          [0.009753342949590, 0.965629718236502]])
+        B_res = np.array([[0.000122937599964], [0.049135527547844]])
+
+        sys_ssc = lti(A, B, C, D)
+        sys_ssd = sys_ssc.to_discrete(0.05)
+
+        assert_allclose(sys_ssd.A, A_res)
+        assert_allclose(sys_ssd.B, B_res)
+        assert_allclose(sys_ssd.C, C)
+        assert_allclose(sys_ssd.D, D)
+
+    def test_c2d_tf(self):
+
+        sys = lti([0.5, 0.3], [1.0, 0.4])
+        sys = sys.to_discrete(0.005)
+
+        # Matlab results
+        num_res = np.array([0.5, -0.485149004980066])
+        den_res = np.array([1.0, -0.980198673306755])
+
+        # Somehow a lot of numerical errors
+        assert_allclose(sys.den, den_res, atol=0.02)
+        assert_allclose(sys.num, num_res, atol=0.02)
+
+
+class TestC2dInvariants:
+    # Some test cases for checking the invariances.
+    # Array of triplets: (system, sample time, number of samples)
+    cases = [
+        (tf2ss([1, 1], [1, 1.5, 1]), 0.25, 10),
+        (tf2ss([1, 2], [1, 1.5, 3, 1]), 0.5, 10),
+        (tf2ss(0.1, [1, 1, 2, 1]), 0.5, 10),
+    ]
+
+    # Some options for lsim2 and derived routines
+    tolerances = {'rtol': 1e-9, 'atol': 1e-11}
+
+    # Check that systems discretized with the impulse-invariant
+    # method really hold the invariant
+    @pytest.mark.parametrize("sys,sample_time,samples_number", cases)
+    def test_impulse_invariant(self, sys, sample_time, samples_number):
+        time = np.arange(samples_number) * sample_time
+        _, yout_cont = impulse2(sys, T=time, **self.tolerances)
+        _, yout_disc = dimpulse(c2d(sys, sample_time, method='impulse'),
+                                n=len(time))
+        assert_allclose(sample_time * yout_cont.ravel(), yout_disc[0].ravel())
+
+    # Step invariant should hold for ZOH discretized systems
+    @pytest.mark.parametrize("sys,sample_time,samples_number", cases)
+    def test_step_invariant(self, sys, sample_time, samples_number):
+        time = np.arange(samples_number) * sample_time
+        _, yout_cont = step2(sys, T=time, **self.tolerances)
+        _, yout_disc = dstep(c2d(sys, sample_time, method='zoh'), n=len(time))
+        assert_allclose(yout_cont.ravel(), yout_disc[0].ravel())
+
+    # Linear invariant should hold for FOH discretized systems
+    @pytest.mark.parametrize("sys,sample_time,samples_number", cases)
+    def test_linear_invariant(self, sys, sample_time, samples_number):
+        time = np.arange(samples_number) * sample_time
+        _, yout_cont, _ = lsim2(sys, T=time, U=time, **self.tolerances)
+        _, yout_disc, _ = dlsim(c2d(sys, sample_time, method='foh'), u=time)
+        assert_allclose(yout_cont.ravel(), yout_disc.ravel())

venv/Lib/site-packages/scipy/signal/tests/test_dltisys.py

@@ -0,0 +1,598 @@
+# Author: Jeffrey Armstrong <jeff@approximatrix.com>
+# April 4, 2011
+
+import numpy as np
+from numpy.testing import (assert_equal,
+                           assert_array_almost_equal, assert_array_equal,
+                           assert_allclose, assert_, assert_almost_equal,
+                           suppress_warnings)
+from pytest import raises as assert_raises
+from scipy.signal import (dlsim, dstep, dimpulse, tf2zpk, lti, dlti,
+                          StateSpace, TransferFunction, ZerosPolesGain,
+                          dfreqresp, dbode, BadCoefficients)
+
+
+class TestDLTI(object):
+
+    def test_dlsim(self):
+
+        a = np.asarray([[0.9, 0.1], [-0.2, 0.9]])
+        b = np.asarray([[0.4, 0.1, -0.1], [0.0, 0.05, 0.0]])
+        c = np.asarray([[0.1, 0.3]])
+        d = np.asarray([[0.0, -0.1, 0.0]])
+        dt = 0.5
+
+        # Create an input matrix with inputs down the columns (3 cols) and its
+        # respective time input vector
+        u = np.hstack((np.linspace(0, 4.0, num=5)[:, np.newaxis],
+                       np.full((5, 1), 0.01),
+                       np.full((5, 1), -0.002)))
+        t_in = np.linspace(0, 2.0, num=5)
+
+        # Define the known result
+        yout_truth = np.array([[-0.001,
+                                -0.00073,
+                                0.039446,
+                                0.0915387,
+                                0.13195948]]).T
+        xout_truth = np.asarray([[0, 0],
+                                 [0.0012, 0.0005],
+                                 [0.40233, 0.00071],
+                                 [1.163368, -0.079327],
+                                 [2.2402985, -0.3035679]])
+
+        tout, yout, xout = dlsim((a, b, c, d, dt), u, t_in)
+
+        assert_array_almost_equal(yout_truth, yout)
+        assert_array_almost_equal(xout_truth, xout)
+        assert_array_almost_equal(t_in, tout)
+
+        # Make sure input with single-dimension doesn't raise error
+        dlsim((1, 2, 3), 4)
+
+        # Interpolated control - inputs should have different time steps
+        # than the discrete model uses internally
+        u_sparse = u[[0, 4], :]
+        t_sparse = np.asarray([0.0, 2.0])
+
+        tout, yout, xout = dlsim((a, b, c, d, dt), u_sparse, t_sparse)
+
+        assert_array_almost_equal(yout_truth, yout)
+        assert_array_almost_equal(xout_truth, xout)
+        assert_equal(len(tout), yout.shape[0])
+
+        # Transfer functions (assume dt = 0.5)
+        num = np.asarray([1.0, -0.1])
+        den = np.asarray([0.3, 1.0, 0.2])
+        yout_truth = np.array([[0.0,
+                                0.0,
+                                3.33333333333333,
+                                -4.77777777777778,
+                                23.0370370370370]]).T
+
+        # Assume use of the first column of the control input built earlier
+        tout, yout = dlsim((num, den, 0.5), u[:, 0], t_in)
+
+        assert_array_almost_equal(yout, yout_truth)
+        assert_array_almost_equal(t_in, tout)
+
+        # Retest the same with a 1-D input vector
+        uflat = np.asarray(u[:, 0])
+        uflat = uflat.reshape((5,))
+        tout, yout = dlsim((num, den, 0.5), uflat, t_in)
+
+        assert_array_almost_equal(yout, yout_truth)
+        assert_array_almost_equal(t_in, tout)
+
+        # zeros-poles-gain representation
+        zd = np.array([0.5, -0.5])
+        pd = np.array([1.j / np.sqrt(2), -1.j / np.sqrt(2)])
+        k = 1.0
+        yout_truth = np.array([[0.0, 1.0, 2.0, 2.25, 2.5]]).T
+
+        tout, yout = dlsim((zd, pd, k, 0.5), u[:, 0], t_in)
+
+        assert_array_almost_equal(yout, yout_truth)
+        assert_array_almost_equal(t_in, tout)
+
+        # Raise an error for continuous-time systems
+        system = lti([1], [1, 1])
+        assert_raises(AttributeError, dlsim, system, u)
+
+    def test_dstep(self):
+
+        a = np.asarray([[0.9, 0.1], [-0.2, 0.9]])
+        b = np.asarray([[0.4, 0.1, -0.1], [0.0, 0.05, 0.0]])
+        c = np.asarray([[0.1, 0.3]])
+        d = np.asarray([[0.0, -0.1, 0.0]])
+        dt = 0.5
+
+        # Because b.shape[1] == 3, dstep should result in a tuple of three
+        # result vectors
+        yout_step_truth = (np.asarray([0.0, 0.04, 0.052, 0.0404, 0.00956,
+                                       -0.036324, -0.093318, -0.15782348,
+                                       -0.226628324, -0.2969374948]),
+                           np.asarray([-0.1, -0.075, -0.058, -0.04815,
+                                       -0.04453, -0.0461895, -0.0521812,
+                                       -0.061588875, -0.073549579,
+                                       -0.08727047595]),
+                           np.asarray([0.0, -0.01, -0.013, -0.0101, -0.00239,
+                                       0.009081, 0.0233295, 0.03945587,
+                                       0.056657081, 0.0742343737]))
+
+        tout, yout = dstep((a, b, c, d, dt), n=10)
+
+        assert_equal(len(yout), 3)
+
+        for i in range(0, len(yout)):
+            assert_equal(yout[i].shape[0], 10)
+            assert_array_almost_equal(yout[i].flatten(), yout_step_truth[i])
+
+        # Check that the other two inputs (tf, zpk) will work as well
+        tfin = ([1.0], [1.0, 1.0], 0.5)
+        yout_tfstep = np.asarray([0.0, 1.0, 0.0])
+        tout, yout = dstep(tfin, n=3)
+        assert_equal(len(yout), 1)
+        assert_array_almost_equal(yout[0].flatten(), yout_tfstep)
+
+        zpkin = tf2zpk(tfin[0], tfin[1]) + (0.5,)
+        tout, yout = dstep(zpkin, n=3)
+        assert_equal(len(yout), 1)
+        assert_array_almost_equal(yout[0].flatten(), yout_tfstep)
+
+        # Raise an error for continuous-time systems
+        system = lti([1], [1, 1])
+        assert_raises(AttributeError, dstep, system)
+
+    def test_dimpulse(self):
+
+        a = np.asarray([[0.9, 0.1], [-0.2, 0.9]])
+        b = np.asarray([[0.4, 0.1, -0.1], [0.0, 0.05, 0.0]])
+        c = np.asarray([[0.1, 0.3]])
+        d = np.asarray([[0.0, -0.1, 0.0]])
+        dt = 0.5
+
+        # Because b.shape[1] == 3, dimpulse should result in a tuple of three
+        # result vectors
+        yout_imp_truth = (np.asarray([0.0, 0.04, 0.012, -0.0116, -0.03084,
+                                      -0.045884, -0.056994, -0.06450548,
+                                      -0.068804844, -0.0703091708]),
+                          np.asarray([-0.1, 0.025, 0.017, 0.00985, 0.00362,
+                                      -0.0016595, -0.0059917, -0.009407675,
+                                      -0.011960704, -0.01372089695]),
+                          np.asarray([0.0, -0.01, -0.003, 0.0029, 0.00771,
+                                      0.011471, 0.0142485, 0.01612637,
+                                      0.017201211, 0.0175772927]))
+
+        tout, yout = dimpulse((a, b, c, d, dt), n=10)
+
+        assert_equal(len(yout), 3)
+
+        for i in range(0, len(yout)):
+            assert_equal(yout[i].shape[0], 10)
+            assert_array_almost_equal(yout[i].flatten(), yout_imp_truth[i])
+
+        # Check that the other two inputs (tf, zpk) will work as well
+        tfin = ([1.0], [1.0, 1.0], 0.5)
+        yout_tfimpulse = np.asarray([0.0, 1.0, -1.0])
+        tout, yout = dimpulse(tfin, n=3)
+        assert_equal(len(yout), 1)
+        assert_array_almost_equal(yout[0].flatten(), yout_tfimpulse)
+
+        zpkin = tf2zpk(tfin[0], tfin[1]) + (0.5,)
+        tout, yout = dimpulse(zpkin, n=3)
+        assert_equal(len(yout), 1)
+        assert_array_almost_equal(yout[0].flatten(), yout_tfimpulse)
+
+        # Raise an error for continuous-time systems
+        system = lti([1], [1, 1])
+        assert_raises(AttributeError, dimpulse, system)
+
+    def test_dlsim_trivial(self):
+        a = np.array([[0.0]])
+        b = np.array([[0.0]])
+        c = np.array([[0.0]])
+        d = np.array([[0.0]])
+        n = 5
+        u = np.zeros(n).reshape(-1, 1)
+        tout, yout, xout = dlsim((a, b, c, d, 1), u)
+        assert_array_equal(tout, np.arange(float(n)))
+        assert_array_equal(yout, np.zeros((n, 1)))
+        assert_array_equal(xout, np.zeros((n, 1)))
+
+    def test_dlsim_simple1d(self):
+        a = np.array([[0.5]])
+        b = np.array([[0.0]])
+        c = np.array([[1.0]])
+        d = np.array([[0.0]])
+        n = 5
+        u = np.zeros(n).reshape(-1, 1)
+        tout, yout, xout = dlsim((a, b, c, d, 1), u, x0=1)
+        assert_array_equal(tout, np.arange(float(n)))
+        expected = (0.5 ** np.arange(float(n))).reshape(-1, 1)
+        assert_array_equal(yout, expected)
+        assert_array_equal(xout, expected)
+
+    def test_dlsim_simple2d(self):
+        lambda1 = 0.5
+        lambda2 = 0.25
+        a = np.array([[lambda1, 0.0],
+                      [0.0, lambda2]])
+        b = np.array([[0.0],
+                      [0.0]])
+        c = np.array([[1.0, 0.0],
+                      [0.0, 1.0]])
+        d = np.array([[0.0],
+                      [0.0]])
+        n = 5
+        u = np.zeros(n).reshape(-1, 1)
+        tout, yout, xout = dlsim((a, b, c, d, 1), u, x0=1)
+        assert_array_equal(tout, np.arange(float(n)))
+        # The analytical solution:
+        expected = (np.array([lambda1, lambda2]) **
+                                np.arange(float(n)).reshape(-1, 1))
+        assert_array_equal(yout, expected)
+        assert_array_equal(xout, expected)
+
+    def test_more_step_and_impulse(self):
+        lambda1 = 0.5
+        lambda2 = 0.75
+        a = np.array([[lambda1, 0.0],
+                      [0.0, lambda2]])
+        b = np.array([[1.0, 0.0],
+                      [0.0, 1.0]])
+        c = np.array([[1.0, 1.0]])
+        d = np.array([[0.0, 0.0]])
+
+        n = 10
+
+        # Check a step response.
+        ts, ys = dstep((a, b, c, d, 1), n=n)
+
+        # Create the exact step response.
+        stp0 = (1.0 / (1 - lambda1)) * (1.0 - lambda1 ** np.arange(n))
+        stp1 = (1.0 / (1 - lambda2)) * (1.0 - lambda2 ** np.arange(n))
+
+        assert_allclose(ys[0][:, 0], stp0)
+        assert_allclose(ys[1][:, 0], stp1)
+
+        # Check an impulse response with an initial condition.
+        x0 = np.array([1.0, 1.0])
+        ti, yi = dimpulse((a, b, c, d, 1), n=n, x0=x0)
+
+        # Create the exact impulse response.
+        imp = (np.array([lambda1, lambda2]) **
+                            np.arange(-1, n + 1).reshape(-1, 1))
+        imp[0, :] = 0.0
+        # Analytical solution to impulse response
+        y0 = imp[:n, 0] + np.dot(imp[1:n + 1, :], x0)
+        y1 = imp[:n, 1] + np.dot(imp[1:n + 1, :], x0)
+
+        assert_allclose(yi[0][:, 0], y0)
+        assert_allclose(yi[1][:, 0], y1)
+
+        # Check that dt=0.1, n=3 gives 3 time values.
+        system = ([1.0], [1.0, -0.5], 0.1)
+        t, (y,) = dstep(system, n=3)
+        assert_allclose(t, [0, 0.1, 0.2])
+        assert_array_equal(y.T, [[0, 1.0, 1.5]])
+        t, (y,) = dimpulse(system, n=3)
+        assert_allclose(t, [0, 0.1, 0.2])
+        assert_array_equal(y.T, [[0, 1, 0.5]])
+
+
+class TestDlti(object):
+    def test_dlti_instantiation(self):
+        # Test that lti can be instantiated.
+
+        dt = 0.05
+        # TransferFunction
+        s = dlti([1], [-1], dt=dt)
+        assert_(isinstance(s, TransferFunction))
+        assert_(isinstance(s, dlti))
+        assert_(not isinstance(s, lti))
+        assert_equal(s.dt, dt)
+
+        # ZerosPolesGain
+        s = dlti(np.array([]), np.array([-1]), 1, dt=dt)
+        assert_(isinstance(s, ZerosPolesGain))
+        assert_(isinstance(s, dlti))
+        assert_(not isinstance(s, lti))
+        assert_equal(s.dt, dt)
+
+        # StateSpace
+        s = dlti([1], [-1], 1, 3, dt=dt)
+        assert_(isinstance(s, StateSpace))
+        assert_(isinstance(s, dlti))
+        assert_(not isinstance(s, lti))
+        assert_equal(s.dt, dt)
+
+        # Number of inputs
+        assert_raises(ValueError, dlti, 1)
+        assert_raises(ValueError, dlti, 1, 1, 1, 1, 1)
+
+
+class TestStateSpaceDisc(object):
+    def test_initialization(self):
+        # Check that all initializations work
+        dt = 0.05
+        StateSpace(1, 1, 1, 1, dt=dt)
+        StateSpace([1], [2], [3], [4], dt=dt)
+        StateSpace(np.array([[1, 2], [3, 4]]), np.array([[1], [2]]),
+                   np.array([[1, 0]]), np.array([[0]]), dt=dt)
+        StateSpace(1, 1, 1, 1, dt=True)
+
+    def test_conversion(self):
+        # Check the conversion functions
+        s = StateSpace(1, 2, 3, 4, dt=0.05)
+        assert_(isinstance(s.to_ss(), StateSpace))
+        assert_(isinstance(s.to_tf(), TransferFunction))
+        assert_(isinstance(s.to_zpk(), ZerosPolesGain))
+
+        # Make sure copies work
+        assert_(StateSpace(s) is not s)
+        assert_(s.to_ss() is not s)
+
+    def test_properties(self):
+        # Test setters/getters for cross class properties.
+        # This implicitly tests to_tf() and to_zpk()
+
+        # Getters
+        s = StateSpace(1, 1, 1, 1, dt=0.05)
+        assert_equal(s.poles, [1])
+        assert_equal(s.zeros, [0])
+
+
+class TestTransferFunction(object):
+    def test_initialization(self):
+        # Check that all initializations work
+        dt = 0.05
+        TransferFunction(1, 1, dt=dt)
+        TransferFunction([1], [2], dt=dt)
+        TransferFunction(np.array([1]), np.array([2]), dt=dt)
+        TransferFunction(1, 1, dt=True)
+
+    def test_conversion(self):
+        # Check the conversion functions
+        s = TransferFunction([1, 0], [1, -1], dt=0.05)
+        assert_(isinstance(s.to_ss(), StateSpace))
+        assert_(isinstance(s.to_tf(), TransferFunction))
+        assert_(isinstance(s.to_zpk(), ZerosPolesGain))
+
+        # Make sure copies work
+        assert_(TransferFunction(s) is not s)
+        assert_(s.to_tf() is not s)
+
+    def test_properties(self):
+        # Test setters/getters for cross class properties.
+        # This implicitly tests to_ss() and to_zpk()
+
+        # Getters
+        s = TransferFunction([1, 0], [1, -1], dt=0.05)
+        assert_equal(s.poles, [1])
+        assert_equal(s.zeros, [0])
+
+
+class TestZerosPolesGain(object):
+    def test_initialization(self):
+        # Check that all initializations work
+        dt = 0.05
+        ZerosPolesGain(1, 1, 1, dt=dt)
+        ZerosPolesGain([1], [2], 1, dt=dt)
+        ZerosPolesGain(np.array([1]), np.array([2]), 1, dt=dt)
+        ZerosPolesGain(1, 1, 1, dt=True)
+
+    def test_conversion(self):
+        # Check the conversion functions
+        s = ZerosPolesGain(1, 2, 3, dt=0.05)
+        assert_(isinstance(s.to_ss(), StateSpace))
+        assert_(isinstance(s.to_tf(), TransferFunction))
+        assert_(isinstance(s.to_zpk(), ZerosPolesGain))
+
+        # Make sure copies work
+        assert_(ZerosPolesGain(s) is not s)
+        assert_(s.to_zpk() is not s)
+
+
+class Test_dfreqresp(object):
+
+    def test_manual(self):
+        # Test dfreqresp() real part calculation (manual sanity check).
+        # 1st order low-pass filter: H(z) = 1 / (z - 0.2),
+        system = TransferFunction(1, [1, -0.2], dt=0.1)
+        w = [0.1, 1, 10]
+        w, H = dfreqresp(system, w=w)
+
+        # test real
+        expected_re = [1.2383, 0.4130, -0.7553]
+        assert_almost_equal(H.real, expected_re, decimal=4)
+
+        # test imag
+        expected_im = [-0.1555, -1.0214, 0.3955]
+        assert_almost_equal(H.imag, expected_im, decimal=4)
+
+    def test_auto(self):
+        # Test dfreqresp() real part calculation.
+        # 1st order low-pass filter: H(z) = 1 / (z - 0.2),
+        system = TransferFunction(1, [1, -0.2], dt=0.1)
+        w = [0.1, 1, 10, 100]
+        w, H = dfreqresp(system, w=w)
+        jw = np.exp(w * 1j)
+        y = np.polyval(system.num, jw) / np.polyval(system.den, jw)
+
+        # test real
+        expected_re = y.real
+        assert_almost_equal(H.real, expected_re)
+
+        # test imag
+        expected_im = y.imag
+        assert_almost_equal(H.imag, expected_im)
+
+    def test_freq_range(self):
+        # Test that freqresp() finds a reasonable frequency range.
+        # 1st order low-pass filter: H(z) = 1 / (z - 0.2),
+        # Expected range is from 0.01 to 10.
+        system = TransferFunction(1, [1, -0.2], dt=0.1)
+        n = 10
+        expected_w = np.linspace(0, np.pi, 10, endpoint=False)
+        w, H = dfreqresp(system, n=n)
+        assert_almost_equal(w, expected_w)
+
+    def test_pole_one(self):
+        # Test that freqresp() doesn't fail on a system with a pole at 0.
+        # integrator, pole at zero: H(s) = 1 / s
+        system = TransferFunction([1], [1, -1], dt=0.1)
+
+        with suppress_warnings() as sup:
+            sup.filter(RuntimeWarning, message="divide by zero")
+            sup.filter(RuntimeWarning, message="invalid value encountered")
+            w, H = dfreqresp(system, n=2)
+        assert_equal(w[0], 0.)  # a fail would give not-a-number
+
+    def test_error(self):
+        # Raise an error for continuous-time systems
+        system = lti([1], [1, 1])
+        assert_raises(AttributeError, dfreqresp, system)
+
+    def test_from_state_space(self):
+        # H(z) = 2 / z^3 - 0.5 * z^2
+
+        system_TF = dlti([2], [1, -0.5, 0, 0])
+
+        A = np.array([[0.5, 0, 0],
+                      [1, 0, 0],
+                      [0, 1, 0]])
+        B = np.array([[1, 0, 0]]).T
+        C = np.array([[0, 0, 2]])
+        D = 0
+
+        system_SS = dlti(A, B, C, D)
+        w = 10.0**np.arange(-3,0,.5)
+        with suppress_warnings() as sup:
+            sup.filter(BadCoefficients)
+            w1, H1 = dfreqresp(system_TF, w=w)
+            w2, H2 = dfreqresp(system_SS, w=w)
+
+        assert_almost_equal(H1, H2)
+
+    def test_from_zpk(self):
+        # 1st order low-pass filter: H(s) = 0.3 / (z - 0.2),
+        system_ZPK = dlti([],[0.2],0.3)
+        system_TF = dlti(0.3, [1, -0.2])
+        w = [0.1, 1, 10, 100]
+        w1, H1 = dfreqresp(system_ZPK, w=w)
+        w2, H2 = dfreqresp(system_TF, w=w)
+        assert_almost_equal(H1, H2)
+
+
+class Test_bode(object):
+
+    def test_manual(self):
+        # Test bode() magnitude calculation (manual sanity check).
+        # 1st order low-pass filter: H(s) = 0.3 / (z - 0.2),
+        dt = 0.1
+        system = TransferFunction(0.3, [1, -0.2], dt=dt)
+        w = [0.1, 0.5, 1, np.pi]
+        w2, mag, phase = dbode(system, w=w)
+
+        # Test mag
+        expected_mag = [-8.5329, -8.8396, -9.6162, -12.0412]
+        assert_almost_equal(mag, expected_mag, decimal=4)
+
+        # Test phase
+        expected_phase = [-7.1575, -35.2814, -67.9809, -180.0000]
+        assert_almost_equal(phase, expected_phase, decimal=4)
+
+        # Test frequency
+        assert_equal(np.array(w) / dt, w2)
+
+    def test_auto(self):
+        # Test bode() magnitude calculation.
+        # 1st order low-pass filter: H(s) = 0.3 / (z - 0.2),
+        system = TransferFunction(0.3, [1, -0.2], dt=0.1)
+        w = np.array([0.1, 0.5, 1, np.pi])
+        w2, mag, phase = dbode(system, w=w)
+        jw = np.exp(w * 1j)
+        y = np.polyval(system.num, jw) / np.polyval(system.den, jw)
+
+        # Test mag
+        expected_mag = 20.0 * np.log10(abs(y))
+        assert_almost_equal(mag, expected_mag)
+
+        # Test phase
+        expected_phase = np.rad2deg(np.angle(y))
+        assert_almost_equal(phase, expected_phase)
+
+    def test_range(self):
+        # Test that bode() finds a reasonable frequency range.
+        # 1st order low-pass filter: H(s) = 0.3 / (z - 0.2),
+        dt = 0.1
+        system = TransferFunction(0.3, [1, -0.2], dt=0.1)
+        n = 10
+        # Expected range is from 0.01 to 10.
+        expected_w = np.linspace(0, np.pi, n, endpoint=False) / dt
+        w, mag, phase = dbode(system, n=n)
+        assert_almost_equal(w, expected_w)
+
+    def test_pole_one(self):
+        # Test that freqresp() doesn't fail on a system with a pole at 0.
+        # integrator, pole at zero: H(s) = 1 / s
+        system = TransferFunction([1], [1, -1], dt=0.1)
+
+        with suppress_warnings() as sup:
+            sup.filter(RuntimeWarning, message="divide by zero")
+            sup.filter(RuntimeWarning, message="invalid value encountered")
+            w, mag, phase = dbode(system, n=2)
+        assert_equal(w[0], 0.)  # a fail would give not-a-number
+
+    def test_imaginary(self):
+        # bode() should not fail on a system with pure imaginary poles.
+        # The test passes if bode doesn't raise an exception.
+        system = TransferFunction([1], [1, 0, 100], dt=0.1)
+        dbode(system, n=2)
+
+    def test_error(self):
+        # Raise an error for continuous-time systems
+        system = lti([1], [1, 1])
+        assert_raises(AttributeError, dbode, system)
+
+
+class TestTransferFunctionZConversion(object):
+    """Test private conversions between 'z' and 'z**-1' polynomials."""
+
+    def test_full(self):
+        # Numerator and denominator same order
+        num = [2, 3, 4]
+        den = [5, 6, 7]
+        num2, den2 = TransferFunction._z_to_zinv(num, den)
+        assert_equal(num, num2)
+        assert_equal(den, den2)
+
+        num2, den2 = TransferFunction._zinv_to_z(num, den)
+        assert_equal(num, num2)
+        assert_equal(den, den2)
+
+    def test_numerator(self):
+        # Numerator lower order than denominator
+        num = [2, 3]
+        den = [5, 6, 7]
+        num2, den2 = TransferFunction._z_to_zinv(num, den)
+        assert_equal([0, 2, 3], num2)
+        assert_equal(den, den2)
+
+        num2, den2 = TransferFunction._zinv_to_z(num, den)
+        assert_equal([2, 3, 0], num2)
+        assert_equal(den, den2)
+
+    def test_denominator(self):
+        # Numerator higher order than denominator
+        num = [2, 3, 4]
+        den = [5, 6]
+        num2, den2 = TransferFunction._z_to_zinv(num, den)
+        assert_equal(num, num2)
+        assert_equal([0, 5, 6], den2)
+
+        num2, den2 = TransferFunction._zinv_to_z(num, den)
+        assert_equal(num, num2)
+        assert_equal([5, 6, 0], den2)
+

venv/Lib/site-packages/scipy/signal/tests/test_fir_filter_design.py

@@ -0,0 +1,641 @@
+import numpy as np
+from numpy.testing import (assert_almost_equal, assert_array_almost_equal,
+                           assert_equal, assert_,
+                           assert_allclose, assert_warns)
+from pytest import raises as assert_raises
+import pytest
+
+from scipy.fft import fft
+from scipy.special import sinc
+from scipy.signal import kaiser_beta, kaiser_atten, kaiserord, \
+    firwin, firwin2, freqz, remez, firls, minimum_phase
+
+
+def test_kaiser_beta():
+    b = kaiser_beta(58.7)
+    assert_almost_equal(b, 0.1102 * 50.0)
+    b = kaiser_beta(22.0)
+    assert_almost_equal(b, 0.5842 + 0.07886)
+    b = kaiser_beta(21.0)
+    assert_equal(b, 0.0)
+    b = kaiser_beta(10.0)
+    assert_equal(b, 0.0)
+
+
+def test_kaiser_atten():
+    a = kaiser_atten(1, 1.0)
+    assert_equal(a, 7.95)
+    a = kaiser_atten(2, 1/np.pi)
+    assert_equal(a, 2.285 + 7.95)
+
+
+def test_kaiserord():
+    assert_raises(ValueError, kaiserord, 1.0, 1.0)
+    numtaps, beta = kaiserord(2.285 + 7.95 - 0.001, 1/np.pi)
+    assert_equal((numtaps, beta), (2, 0.0))
+
+
+class TestFirwin(object):
+
+    def check_response(self, h, expected_response, tol=.05):
+        N = len(h)
+        alpha = 0.5 * (N-1)
+        m = np.arange(0,N) - alpha   # time indices of taps
+        for freq, expected in expected_response:
+            actual = abs(np.sum(h*np.exp(-1.j*np.pi*m*freq)))
+            mse = abs(actual-expected)**2
+            assert_(mse < tol, 'response not as expected, mse=%g > %g'
+               % (mse, tol))
+
+    def test_response(self):
+        N = 51
+        f = .5
+        # increase length just to try even/odd
+        h = firwin(N, f)  # low-pass from 0 to f
+        self.check_response(h, [(.25,1), (.75,0)])
+
+        h = firwin(N+1, f, window='nuttall')  # specific window
+        self.check_response(h, [(.25,1), (.75,0)])
+
+        h = firwin(N+2, f, pass_zero=False)  # stop from 0 to f --> high-pass
+        self.check_response(h, [(.25,0), (.75,1)])
+
+        f1, f2, f3, f4 = .2, .4, .6, .8
+        h = firwin(N+3, [f1, f2], pass_zero=False)  # band-pass filter
+        self.check_response(h, [(.1,0), (.3,1), (.5,0)])
+
+        h = firwin(N+4, [f1, f2])  # band-stop filter
+        self.check_response(h, [(.1,1), (.3,0), (.5,1)])
+
+        h = firwin(N+5, [f1, f2, f3, f4], pass_zero=False, scale=False)
+        self.check_response(h, [(.1,0), (.3,1), (.5,0), (.7,1), (.9,0)])
+
+        h = firwin(N+6, [f1, f2, f3, f4])  # multiband filter
+        self.check_response(h, [(.1,1), (.3,0), (.5,1), (.7,0), (.9,1)])
+
+        h = firwin(N+7, 0.1, width=.03)  # low-pass
+        self.check_response(h, [(.05,1), (.75,0)])
+
+        h = firwin(N+8, 0.1, pass_zero=False)  # high-pass
+        self.check_response(h, [(.05,0), (.75,1)])
+
+    def mse(self, h, bands):
+        """Compute mean squared error versus ideal response across frequency
+        band.
+          h -- coefficients
+          bands -- list of (left, right) tuples relative to 1==Nyquist of
+            passbands
+        """
+        w, H = freqz(h, worN=1024)
+        f = w/np.pi
+        passIndicator = np.zeros(len(w), bool)
+        for left, right in bands:
+            passIndicator |= (f >= left) & (f < right)
+        Hideal = np.where(passIndicator, 1, 0)
+        mse = np.mean(abs(abs(H)-Hideal)**2)
+        return mse
+
+    def test_scaling(self):
+        """
+        For one lowpass, bandpass, and highpass example filter, this test
+        checks two things:
+          - the mean squared error over the frequency domain of the unscaled
+            filter is smaller than the scaled filter (true for rectangular
+            window)
+          - the response of the scaled filter is exactly unity at the center
+            of the first passband
+        """
+        N = 11
+        cases = [
+            ([.5], True, (0, 1)),
+            ([0.2, .6], False, (.4, 1)),
+            ([.5], False, (1, 1)),
+        ]
+        for cutoff, pass_zero, expected_response in cases:
+            h = firwin(N, cutoff, scale=False, pass_zero=pass_zero, window='ones')
+            hs = firwin(N, cutoff, scale=True, pass_zero=pass_zero, window='ones')
+            if len(cutoff) == 1:
+                if pass_zero:
+                    cutoff = [0] + cutoff
+                else:
+                    cutoff = cutoff + [1]
+            assert_(self.mse(h, [cutoff]) < self.mse(hs, [cutoff]),
+                'least squares violation')
+            self.check_response(hs, [expected_response], 1e-12)
+
+
+class TestFirWinMore(object):
+    """Different author, different style, different tests..."""
+
+    def test_lowpass(self):
+        width = 0.04
+        ntaps, beta = kaiserord(120, width)
+        kwargs = dict(cutoff=0.5, window=('kaiser', beta), scale=False)
+        taps = firwin(ntaps, **kwargs)
+
+        # Check the symmetry of taps.
+        assert_array_almost_equal(taps[:ntaps//2], taps[ntaps:ntaps-ntaps//2-1:-1])
+
+        # Check the gain at a few samples where we know it should be approximately 0 or 1.
+        freq_samples = np.array([0.0, 0.25, 0.5-width/2, 0.5+width/2, 0.75, 1.0])
+        freqs, response = freqz(taps, worN=np.pi*freq_samples)
+        assert_array_almost_equal(np.abs(response),
+                                    [1.0, 1.0, 1.0, 0.0, 0.0, 0.0], decimal=5)
+
+        taps_str = firwin(ntaps, pass_zero='lowpass', **kwargs)
+        assert_allclose(taps, taps_str)
+
+    def test_highpass(self):
+        width = 0.04
+        ntaps, beta = kaiserord(120, width)
+
+        # Ensure that ntaps is odd.
+        ntaps |= 1
+
+        kwargs = dict(cutoff=0.5, window=('kaiser', beta), scale=False)
+        taps = firwin(ntaps, pass_zero=False, **kwargs)
+
+        # Check the symmetry of taps.
+        assert_array_almost_equal(taps[:ntaps//2], taps[ntaps:ntaps-ntaps//2-1:-1])
+
+        # Check the gain at a few samples where we know it should be approximately 0 or 1.
+        freq_samples = np.array([0.0, 0.25, 0.5-width/2, 0.5+width/2, 0.75, 1.0])
+        freqs, response = freqz(taps, worN=np.pi*freq_samples)
+        assert_array_almost_equal(np.abs(response),
+                                    [0.0, 0.0, 0.0, 1.0, 1.0, 1.0], decimal=5)
+
+        taps_str = firwin(ntaps, pass_zero='highpass', **kwargs)
+        assert_allclose(taps, taps_str)
+
+    def test_bandpass(self):
+        width = 0.04
+        ntaps, beta = kaiserord(120, width)
+        kwargs = dict(cutoff=[0.3, 0.7], window=('kaiser', beta), scale=False)
+        taps = firwin(ntaps, pass_zero=False, **kwargs)
+
+        # Check the symmetry of taps.
+        assert_array_almost_equal(taps[:ntaps//2], taps[ntaps:ntaps-ntaps//2-1:-1])
+
+        # Check the gain at a few samples where we know it should be approximately 0 or 1.
+        freq_samples = np.array([0.0, 0.2, 0.3-width/2, 0.3+width/2, 0.5,
+                                0.7-width/2, 0.7+width/2, 0.8, 1.0])
+        freqs, response = freqz(taps, worN=np.pi*freq_samples)
+        assert_array_almost_equal(np.abs(response),
+                [0.0, 0.0, 0.0, 1.0, 1.0, 1.0, 0.0, 0.0, 0.0], decimal=5)
+
+        taps_str = firwin(ntaps, pass_zero='bandpass', **kwargs)
+        assert_allclose(taps, taps_str)
+
+    def test_bandstop_multi(self):
+        width = 0.04
+        ntaps, beta = kaiserord(120, width)
+        kwargs = dict(cutoff=[0.2, 0.5, 0.8], window=('kaiser', beta),
+                      scale=False)
+        taps = firwin(ntaps, **kwargs)
+
+        # Check the symmetry of taps.
+        assert_array_almost_equal(taps[:ntaps//2], taps[ntaps:ntaps-ntaps//2-1:-1])
+
+        # Check the gain at a few samples where we know it should be approximately 0 or 1.
+        freq_samples = np.array([0.0, 0.1, 0.2-width/2, 0.2+width/2, 0.35,
+                                0.5-width/2, 0.5+width/2, 0.65,
+                                0.8-width/2, 0.8+width/2, 0.9, 1.0])
+        freqs, response = freqz(taps, worN=np.pi*freq_samples)
+        assert_array_almost_equal(np.abs(response),
+                [1.0, 1.0, 1.0, 0.0, 0.0, 0.0, 1.0, 1.0, 1.0, 0.0, 0.0, 0.0],
+                decimal=5)
+
+        taps_str = firwin(ntaps, pass_zero='bandstop', **kwargs)
+        assert_allclose(taps, taps_str)
+
+    def test_fs_nyq(self):
+        """Test the fs and nyq keywords."""
+        nyquist = 1000
+        width = 40.0
+        relative_width = width/nyquist
+        ntaps, beta = kaiserord(120, relative_width)
+        taps = firwin(ntaps, cutoff=[300, 700], window=('kaiser', beta),
+                        pass_zero=False, scale=False, fs=2*nyquist)
+
+        # Check the symmetry of taps.
+        assert_array_almost_equal(taps[:ntaps//2], taps[ntaps:ntaps-ntaps//2-1:-1])
+
+        # Check the gain at a few samples where we know it should be approximately 0 or 1.
+        freq_samples = np.array([0.0, 200, 300-width/2, 300+width/2, 500,
+                                700-width/2, 700+width/2, 800, 1000])
+        freqs, response = freqz(taps, worN=np.pi*freq_samples/nyquist)
+        assert_array_almost_equal(np.abs(response),
+                [0.0, 0.0, 0.0, 1.0, 1.0, 1.0, 0.0, 0.0, 0.0], decimal=5)
+
+        taps2 = firwin(ntaps, cutoff=[300, 700], window=('kaiser', beta),
+                        pass_zero=False, scale=False, nyq=nyquist)
+        assert_allclose(taps2, taps)
+
+    def test_bad_cutoff(self):
+        """Test that invalid cutoff argument raises ValueError."""
+        # cutoff values must be greater than 0 and less than 1.
+        assert_raises(ValueError, firwin, 99, -0.5)
+        assert_raises(ValueError, firwin, 99, 1.5)
+        # Don't allow 0 or 1 in cutoff.
+        assert_raises(ValueError, firwin, 99, [0, 0.5])
+        assert_raises(ValueError, firwin, 99, [0.5, 1])
+        # cutoff values must be strictly increasing.
+        assert_raises(ValueError, firwin, 99, [0.1, 0.5, 0.2])
+        assert_raises(ValueError, firwin, 99, [0.1, 0.5, 0.5])
+        # Must have at least one cutoff value.
+        assert_raises(ValueError, firwin, 99, [])
+        # 2D array not allowed.
+        assert_raises(ValueError, firwin, 99, [[0.1, 0.2],[0.3, 0.4]])
+        # cutoff values must be less than nyq.
+        assert_raises(ValueError, firwin, 99, 50.0, nyq=40)
+        assert_raises(ValueError, firwin, 99, [10, 20, 30], nyq=25)
+        assert_raises(ValueError, firwin, 99, 50.0, fs=80)
+        assert_raises(ValueError, firwin, 99, [10, 20, 30], fs=50)
+
+    def test_even_highpass_raises_value_error(self):
+        """Test that attempt to create a highpass filter with an even number
+        of taps raises a ValueError exception."""
+        assert_raises(ValueError, firwin, 40, 0.5, pass_zero=False)
+        assert_raises(ValueError, firwin, 40, [.25, 0.5])
+
+    def test_bad_pass_zero(self):
+        """Test degenerate pass_zero cases."""
+        with assert_raises(ValueError, match='pass_zero must be'):
+            firwin(41, 0.5, pass_zero='foo')
+        with assert_raises(TypeError, match='cannot be interpreted'):
+            firwin(41, 0.5, pass_zero=1.)
+        for pass_zero in ('lowpass', 'highpass'):
+            with assert_raises(ValueError, match='cutoff must have one'):
+                firwin(41, [0.5, 0.6], pass_zero=pass_zero)
+        for pass_zero in ('bandpass', 'bandstop'):
+            with assert_raises(ValueError, match='must have at least two'):
+                firwin(41, [0.5], pass_zero=pass_zero)
+
+
+class TestFirwin2(object):
+
+    def test_invalid_args(self):
+        # `freq` and `gain` have different lengths.
+        with assert_raises(ValueError, match='must be of same length'):
+            firwin2(50, [0, 0.5, 1], [0.0, 1.0])
+        # `nfreqs` is less than `ntaps`.
+        with assert_raises(ValueError, match='ntaps must be less than nfreqs'):
+            firwin2(50, [0, 0.5, 1], [0.0, 1.0, 1.0], nfreqs=33)
+        # Decreasing value in `freq`
+        with assert_raises(ValueError, match='must be nondecreasing'):
+            firwin2(50, [0, 0.5, 0.4, 1.0], [0, .25, .5, 1.0])
+        # Value in `freq` repeated more than once.
+        with assert_raises(ValueError, match='must not occur more than twice'):
+            firwin2(50, [0, .1, .1, .1, 1.0], [0.0, 0.5, 0.75, 1.0, 1.0])
+        # `freq` does not start at 0.0.
+        with assert_raises(ValueError, match='start with 0'):
+            firwin2(50, [0.5, 1.0], [0.0, 1.0])
+        # `freq` does not end at fs/2.
+        with assert_raises(ValueError, match='end with fs/2'):
+            firwin2(50, [0.0, 0.5], [0.0, 1.0])
+        # Value 0 is repeated in `freq`
+        with assert_raises(ValueError, match='0 must not be repeated'):
+            firwin2(50, [0.0, 0.0, 0.5, 1.0], [1.0, 1.0, 0.0, 0.0])
+        # Value fs/2 is repeated in `freq`
+        with assert_raises(ValueError, match='fs/2 must not be repeated'):
+            firwin2(50, [0.0, 0.5, 1.0, 1.0], [1.0, 1.0, 0.0, 0.0])
+        # Value in `freq` that is too close to a repeated number
+        with assert_raises(ValueError, match='cannot contain numbers '
+                                             'that are too close'):
+            firwin2(50, [0.0, 0.5 - np.finfo(float).eps * 0.5, 0.5, 0.5, 1.0],
+                        [1.0, 1.0, 1.0, 0.0, 0.0])
+
+        # Type II filter, but the gain at nyquist frequency is not zero.
+        with assert_raises(ValueError, match='Type II filter'):
+            firwin2(16, [0.0, 0.5, 1.0], [0.0, 1.0, 1.0])
+
+        # Type III filter, but the gains at nyquist and zero rate are not zero.
+        with assert_raises(ValueError, match='Type III filter'):
+            firwin2(17, [0.0, 0.5, 1.0], [0.0, 1.0, 1.0], antisymmetric=True)
+        with assert_raises(ValueError, match='Type III filter'):
+            firwin2(17, [0.0, 0.5, 1.0], [1.0, 1.0, 0.0], antisymmetric=True)
+        with assert_raises(ValueError, match='Type III filter'):
+            firwin2(17, [0.0, 0.5, 1.0], [1.0, 1.0, 1.0], antisymmetric=True)
+
+        # Type IV filter, but the gain at zero rate is not zero.
+        with assert_raises(ValueError, match='Type IV filter'):
+            firwin2(16, [0.0, 0.5, 1.0], [1.0, 1.0, 0.0], antisymmetric=True)
+
+    def test01(self):
+        width = 0.04
+        beta = 12.0
+        ntaps = 400
+        # Filter is 1 from w=0 to w=0.5, then decreases linearly from 1 to 0 as w
+        # increases from w=0.5 to w=1  (w=1 is the Nyquist frequency).
+        freq = [0.0, 0.5, 1.0]
+        gain = [1.0, 1.0, 0.0]
+        taps = firwin2(ntaps, freq, gain, window=('kaiser', beta))
+        freq_samples = np.array([0.0, 0.25, 0.5-width/2, 0.5+width/2,
+                                                        0.75, 1.0-width/2])
+        freqs, response = freqz(taps, worN=np.pi*freq_samples)
+        assert_array_almost_equal(np.abs(response),
+                        [1.0, 1.0, 1.0, 1.0-width, 0.5, width], decimal=5)
+
+    def test02(self):
+        width = 0.04
+        beta = 12.0
+        # ntaps must be odd for positive gain at Nyquist.
+        ntaps = 401
+        # An ideal highpass filter.
+        freq = [0.0, 0.5, 0.5, 1.0]
+        gain = [0.0, 0.0, 1.0, 1.0]
+        taps = firwin2(ntaps, freq, gain, window=('kaiser', beta))
+        freq_samples = np.array([0.0, 0.25, 0.5-width, 0.5+width, 0.75, 1.0])
+        freqs, response = freqz(taps, worN=np.pi*freq_samples)
+        assert_array_almost_equal(np.abs(response),
+                                [0.0, 0.0, 0.0, 1.0, 1.0, 1.0], decimal=5)
+
+    def test03(self):
+        width = 0.02
+        ntaps, beta = kaiserord(120, width)
+        # ntaps must be odd for positive gain at Nyquist.
+        ntaps = int(ntaps) | 1
+        freq = [0.0, 0.4, 0.4, 0.5, 0.5, 1.0]
+        gain = [1.0, 1.0, 0.0, 0.0, 1.0, 1.0]
+        taps = firwin2(ntaps, freq, gain, window=('kaiser', beta))
+        freq_samples = np.array([0.0, 0.4-width, 0.4+width, 0.45,
+                                    0.5-width, 0.5+width, 0.75, 1.0])
+        freqs, response = freqz(taps, worN=np.pi*freq_samples)
+        assert_array_almost_equal(np.abs(response),
+                    [1.0, 1.0, 0.0, 0.0, 0.0, 1.0, 1.0, 1.0], decimal=5)
+
+    def test04(self):
+        """Test firwin2 when window=None."""
+        ntaps = 5
+        # Ideal lowpass: gain is 1 on [0,0.5], and 0 on [0.5, 1.0]
+        freq = [0.0, 0.5, 0.5, 1.0]
+        gain = [1.0, 1.0, 0.0, 0.0]
+        taps = firwin2(ntaps, freq, gain, window=None, nfreqs=8193)
+        alpha = 0.5 * (ntaps - 1)
+        m = np.arange(0, ntaps) - alpha
+        h = 0.5 * sinc(0.5 * m)
+        assert_array_almost_equal(h, taps)
+
+    def test05(self):
+        """Test firwin2 for calculating Type IV filters"""
+        ntaps = 1500
+
+        freq = [0.0, 1.0]
+        gain = [0.0, 1.0]
+        taps = firwin2(ntaps, freq, gain, window=None, antisymmetric=True)
+        assert_array_almost_equal(taps[: ntaps // 2], -taps[ntaps // 2:][::-1])
+
+        freqs, response = freqz(taps, worN=2048)
+        assert_array_almost_equal(abs(response), freqs / np.pi, decimal=4)
+
+    def test06(self):
+        """Test firwin2 for calculating Type III filters"""
+        ntaps = 1501
+
+        freq = [0.0, 0.5, 0.55, 1.0]
+        gain = [0.0, 0.5, 0.0, 0.0]
+        taps = firwin2(ntaps, freq, gain, window=None, antisymmetric=True)
+        assert_equal(taps[ntaps // 2], 0.0)
+        assert_array_almost_equal(taps[: ntaps // 2], -taps[ntaps // 2 + 1:][::-1])
+
+        freqs, response1 = freqz(taps, worN=2048)
+        response2 = np.interp(freqs / np.pi, freq, gain)
+        assert_array_almost_equal(abs(response1), response2, decimal=3)
+
+    def test_fs_nyq(self):
+        taps1 = firwin2(80, [0.0, 0.5, 1.0], [1.0, 1.0, 0.0])
+        taps2 = firwin2(80, [0.0, 30.0, 60.0], [1.0, 1.0, 0.0], fs=120.0)
+        assert_array_almost_equal(taps1, taps2)
+        taps2 = firwin2(80, [0.0, 30.0, 60.0], [1.0, 1.0, 0.0], nyq=60.0)
+        assert_array_almost_equal(taps1, taps2)
+
+    def test_tuple(self):
+        taps1 = firwin2(150, (0.0, 0.5, 0.5, 1.0), (1.0, 1.0, 0.0, 0.0))
+        taps2 = firwin2(150, [0.0, 0.5, 0.5, 1.0], [1.0, 1.0, 0.0, 0.0])
+        assert_array_almost_equal(taps1, taps2)
+
+    def test_input_modyfication(self):
+        freq1 = np.array([0.0, 0.5, 0.5, 1.0])
+        freq2 = np.array(freq1)
+        firwin2(80, freq1, [1.0, 1.0, 0.0, 0.0])
+        assert_equal(freq1, freq2)
+
+
+class TestRemez(object):
+
+    def test_bad_args(self):
+        assert_raises(ValueError, remez, 11, [0.1, 0.4], [1], type='pooka')
+
+    def test_hilbert(self):
+        N = 11  # number of taps in the filter
+        a = 0.1  # width of the transition band
+
+        # design an unity gain hilbert bandpass filter from w to 0.5-w
+        h = remez(11, [a, 0.5-a], [1], type='hilbert')
+
+        # make sure the filter has correct # of taps
+        assert_(len(h) == N, "Number of Taps")
+
+        # make sure it is type III (anti-symmetric tap coefficients)
+        assert_array_almost_equal(h[:(N-1)//2], -h[:-(N-1)//2-1:-1])
+
+        # Since the requested response is symmetric, all even coefficients
+        # should be zero (or in this case really small)
+        assert_((abs(h[1::2]) < 1e-15).all(), "Even Coefficients Equal Zero")
+
+        # now check the frequency response
+        w, H = freqz(h, 1)
+        f = w/2/np.pi
+        Hmag = abs(H)
+
+        # should have a zero at 0 and pi (in this case close to zero)
+        assert_((Hmag[[0, -1]] < 0.02).all(), "Zero at zero and pi")
+
+        # check that the pass band is close to unity
+        idx = np.logical_and(f > a, f < 0.5-a)
+        assert_((abs(Hmag[idx] - 1) < 0.015).all(), "Pass Band Close To Unity")
+
+    def test_compare(self):
+        # test comparison to MATLAB
+        k = [0.024590270518440, -0.041314581814658, -0.075943803756711,
+             -0.003530911231040, 0.193140296954975, 0.373400753484939,
+             0.373400753484939, 0.193140296954975, -0.003530911231040,
+             -0.075943803756711, -0.041314581814658, 0.024590270518440]
+        h = remez(12, [0, 0.3, 0.5, 1], [1, 0], Hz=2.)
+        assert_allclose(h, k)
+        h = remez(12, [0, 0.3, 0.5, 1], [1, 0], fs=2.)
+        assert_allclose(h, k)
+
+        h = [-0.038976016082299, 0.018704846485491, -0.014644062687875,
+             0.002879152556419, 0.016849978528150, -0.043276706138248,
+             0.073641298245579, -0.103908158578635, 0.129770906801075,
+             -0.147163447297124, 0.153302248456347, -0.147163447297124,
+             0.129770906801075, -0.103908158578635, 0.073641298245579,
+             -0.043276706138248, 0.016849978528150, 0.002879152556419,
+             -0.014644062687875, 0.018704846485491, -0.038976016082299]
+        assert_allclose(remez(21, [0, 0.8, 0.9, 1], [0, 1], Hz=2.), h)
+        assert_allclose(remez(21, [0, 0.8, 0.9, 1], [0, 1], fs=2.), h)
+
+
+class TestFirls(object):
+
+    def test_bad_args(self):
+        # even numtaps
+        assert_raises(ValueError, firls, 10, [0.1, 0.2], [0, 0])
+        # odd bands
+        assert_raises(ValueError, firls, 11, [0.1, 0.2, 0.4], [0, 0, 0])
+        # len(bands) != len(desired)
+        assert_raises(ValueError, firls, 11, [0.1, 0.2, 0.3, 0.4], [0, 0, 0])
+        # non-monotonic bands
+        assert_raises(ValueError, firls, 11, [0.2, 0.1], [0, 0])
+        assert_raises(ValueError, firls, 11, [0.1, 0.2, 0.3, 0.3], [0] * 4)
+        assert_raises(ValueError, firls, 11, [0.3, 0.4, 0.1, 0.2], [0] * 4)
+        assert_raises(ValueError, firls, 11, [0.1, 0.3, 0.2, 0.4], [0] * 4)
+        # negative desired
+        assert_raises(ValueError, firls, 11, [0.1, 0.2], [-1, 1])
+        # len(weight) != len(pairs)
+        assert_raises(ValueError, firls, 11, [0.1, 0.2], [0, 0], [1, 2])
+        # negative weight
+        assert_raises(ValueError, firls, 11, [0.1, 0.2], [0, 0], [-1])
+
+    def test_firls(self):
+        N = 11  # number of taps in the filter
+        a = 0.1  # width of the transition band
+
+        # design a halfband symmetric low-pass filter
+        h = firls(11, [0, a, 0.5-a, 0.5], [1, 1, 0, 0], fs=1.0)
+
+        # make sure the filter has correct # of taps
+        assert_equal(len(h), N)
+
+        # make sure it is symmetric
+        midx = (N-1) // 2
+        assert_array_almost_equal(h[:midx], h[:-midx-1:-1])
+
+        # make sure the center tap is 0.5
+        assert_almost_equal(h[midx], 0.5)
+
+        # For halfband symmetric, odd coefficients (except the center)
+        # should be zero (really small)
+        hodd = np.hstack((h[1:midx:2], h[-midx+1::2]))
+        assert_array_almost_equal(hodd, 0)
+
+        # now check the frequency response
+        w, H = freqz(h, 1)
+        f = w/2/np.pi
+        Hmag = np.abs(H)
+
+        # check that the pass band is close to unity
+        idx = np.logical_and(f > 0, f < a)
+        assert_array_almost_equal(Hmag[idx], 1, decimal=3)
+
+        # check that the stop band is close to zero
+        idx = np.logical_and(f > 0.5-a, f < 0.5)
+        assert_array_almost_equal(Hmag[idx], 0, decimal=3)
+
+    def test_compare(self):
+        # compare to OCTAVE output
+        taps = firls(9, [0, 0.5, 0.55, 1], [1, 1, 0, 0], [1, 2])
+        # >> taps = firls(8, [0 0.5 0.55 1], [1 1 0 0], [1, 2]);
+        known_taps = [-6.26930101730182e-04, -1.03354450635036e-01,
+                      -9.81576747564301e-03, 3.17271686090449e-01,
+                      5.11409425599933e-01, 3.17271686090449e-01,
+                      -9.81576747564301e-03, -1.03354450635036e-01,
+                      -6.26930101730182e-04]
+        assert_allclose(taps, known_taps)
+
+        # compare to MATLAB output
+        taps = firls(11, [0, 0.5, 0.5, 1], [1, 1, 0, 0], [1, 2])
+        # >> taps = firls(10, [0 0.5 0.5 1], [1 1 0 0], [1, 2]);
+        known_taps = [
+            0.058545300496815, -0.014233383714318, -0.104688258464392,
+            0.012403323025279, 0.317930861136062, 0.488047220029700,
+            0.317930861136062, 0.012403323025279, -0.104688258464392,
+            -0.014233383714318, 0.058545300496815]
+        assert_allclose(taps, known_taps)
+
+        # With linear changes:
+        taps = firls(7, (0, 1, 2, 3, 4, 5), [1, 0, 0, 1, 1, 0], fs=20)
+        # >> taps = firls(6, [0, 0.1, 0.2, 0.3, 0.4, 0.5], [1, 0, 0, 1, 1, 0])
+        known_taps = [
+            1.156090832768218, -4.1385894727395849, 7.5288619164321826,
+            -8.5530572592947856, 7.5288619164321826, -4.1385894727395849,
+            1.156090832768218]
+        assert_allclose(taps, known_taps)
+
+        taps = firls(7, (0, 1, 2, 3, 4, 5), [1, 0, 0, 1, 1, 0], nyq=10)
+        assert_allclose(taps, known_taps)
+
+        with pytest.raises(ValueError, match='between 0 and 1'):
+            firls(7, [0, 1], [0, 1], nyq=0.5)
+
+    def test_rank_deficient(self):
+        # solve() runs but warns (only sometimes, so here we don't use match)
+        x = firls(21, [0, 0.1, 0.9, 1], [1, 1, 0, 0])
+        w, h = freqz(x, fs=2.)
+        assert_allclose(np.abs(h[:2]), 1., atol=1e-5)
+        assert_allclose(np.abs(h[-2:]), 0., atol=1e-6)
+        # switch to pinvh (tolerances could be higher with longer
+        # filters, but using shorter ones is faster computationally and
+        # the idea is the same)
+        x = firls(101, [0, 0.01, 0.99, 1], [1, 1, 0, 0])
+        w, h = freqz(x, fs=2.)
+        mask = w < 0.01
+        assert mask.sum() > 3
+        assert_allclose(np.abs(h[mask]), 1., atol=1e-4)
+        mask = w > 0.99
+        assert mask.sum() > 3
+        assert_allclose(np.abs(h[mask]), 0., atol=1e-4)
+
+
+class TestMinimumPhase(object):
+
+    def test_bad_args(self):
+        # not enough taps
+        assert_raises(ValueError, minimum_phase, [1.])
+        assert_raises(ValueError, minimum_phase, [1., 1.])
+        assert_raises(ValueError, minimum_phase, np.full(10, 1j))
+        assert_raises(ValueError, minimum_phase, 'foo')
+        assert_raises(ValueError, minimum_phase, np.ones(10), n_fft=8)
+        assert_raises(ValueError, minimum_phase, np.ones(10), method='foo')
+        assert_warns(RuntimeWarning, minimum_phase, np.arange(3))
+
+    def test_homomorphic(self):
+        # check that it can recover frequency responses of arbitrary
+        # linear-phase filters
+
+        # for some cases we can get the actual filter back
+        h = [1, -1]
+        h_new = minimum_phase(np.convolve(h, h[::-1]))
+        assert_allclose(h_new, h, rtol=0.05)
+
+        # but in general we only guarantee we get the magnitude back
+        rng = np.random.RandomState(0)
+        for n in (2, 3, 10, 11, 15, 16, 17, 20, 21, 100, 101):
+            h = rng.randn(n)
+            h_new = minimum_phase(np.convolve(h, h[::-1]))
+            assert_allclose(np.abs(fft(h_new)),
+                            np.abs(fft(h)), rtol=1e-4)
+
+    def test_hilbert(self):
+        # compare to MATLAB output of reference implementation
+
+        # f=[0 0.3 0.5 1];
+        # a=[1 1 0 0];
+        # h=remez(11,f,a);
+        h = remez(12, [0, 0.3, 0.5, 1], [1, 0], fs=2.)
+        k = [0.349585548646686, 0.373552164395447, 0.326082685363438,
+             0.077152207480935, -0.129943946349364, -0.059355880509749]
+        m = minimum_phase(h, 'hilbert')
+        assert_allclose(m, k, rtol=5e-3)
+
+        # f=[0 0.8 0.9 1];
+        # a=[0 0 1 1];
+        # h=remez(20,f,a);
+        h = remez(21, [0, 0.8, 0.9, 1], [0, 1], fs=2.)
+        k = [0.232486803906329, -0.133551833687071, 0.151871456867244,
+             -0.157957283165866, 0.151739294892963, -0.129293146705090,
+             0.100787844523204, -0.065832656741252, 0.035361328741024,
+             -0.014977068692269, -0.158416139047557]
+        m = minimum_phase(h, 'hilbert', n_fft=2**19)
+        assert_allclose(m, k, rtol=2e-3)

venv/Lib/site-packages/scipy/signal/tests/test_max_len_seq.py

@@ -0,0 +1,65 @@
+import numpy as np
+from numpy.testing import assert_allclose, assert_array_equal
+from pytest import raises as assert_raises
+
+from numpy.fft import fft, ifft
+
+from scipy.signal import max_len_seq
+
+
+class TestMLS(object):
+
+    def test_mls_inputs(self):
+        # can't all be zero state
+        assert_raises(ValueError, max_len_seq,
+                      10, state=np.zeros(10))
+        # wrong size state
+        assert_raises(ValueError, max_len_seq, 10,
+                      state=np.ones(3))
+        # wrong length
+        assert_raises(ValueError, max_len_seq, 10, length=-1)
+        assert_array_equal(max_len_seq(10, length=0)[0], [])
+        # unknown taps
+        assert_raises(ValueError, max_len_seq, 64)
+        # bad taps
+        assert_raises(ValueError, max_len_seq, 10, taps=[-1, 1])
+
+    def test_mls_output(self):
+        # define some alternate working taps
+        alt_taps = {2: [1], 3: [2], 4: [3], 5: [4, 3, 2], 6: [5, 4, 1], 7: [4],
+                    8: [7, 5, 3]}
+        # assume the other bit levels work, too slow to test higher orders...
+        for nbits in range(2, 8):
+            for state in [None, np.round(np.random.rand(nbits))]:
+                for taps in [None, alt_taps[nbits]]:
+                    if state is not None and np.all(state == 0):
+                        state[0] = 1  # they can't all be zero
+                    orig_m = max_len_seq(nbits, state=state,
+                                         taps=taps)[0]
+                    m = 2. * orig_m - 1.  # convert to +/- 1 representation
+                    # First, make sure we got all 1's or -1
+                    err_msg = "mls had non binary terms"
+                    assert_array_equal(np.abs(m), np.ones_like(m),
+                                       err_msg=err_msg)
+                    # Test via circular cross-correlation, which is just mult.
+                    # in the frequency domain with one signal conjugated
+                    tester = np.real(ifft(fft(m) * np.conj(fft(m))))
+                    out_len = 2**nbits - 1
+                    # impulse amplitude == test_len
+                    err_msg = "mls impulse has incorrect value"
+                    assert_allclose(tester[0], out_len, err_msg=err_msg)
+                    # steady-state is -1
+                    err_msg = "mls steady-state has incorrect value"
+                    assert_allclose(tester[1:], np.full(out_len - 1, -1),
+                                    err_msg=err_msg)
+                    # let's do the split thing using a couple options
+                    for n in (1, 2**(nbits - 1)):
+                        m1, s1 = max_len_seq(nbits, state=state, taps=taps,
+                                             length=n)
+                        m2, s2 = max_len_seq(nbits, state=s1, taps=taps,
+                                             length=1)
+                        m3, s3 = max_len_seq(nbits, state=s2, taps=taps,
+                                             length=out_len - n - 1)
+                        new_m = np.concatenate((m1, m2, m3))
+                        assert_array_equal(orig_m, new_m)
+

venv/Lib/site-packages/scipy/signal/tests/test_peak_finding.py

@@ -0,0 +1,847 @@
+import copy
+
+import numpy as np
+from numpy.testing import (
+    assert_,
+    assert_equal,
+    assert_allclose,
+    assert_array_equal
+)
+import pytest
+from pytest import raises, warns
+
+from scipy.signal._peak_finding import (
+    argrelmax,
+    argrelmin,
+    peak_prominences,
+    peak_widths,
+    _unpack_condition_args,
+    find_peaks,
+    find_peaks_cwt,
+    _identify_ridge_lines
+)
+from scipy.signal._peak_finding_utils import _local_maxima_1d, PeakPropertyWarning
+
+
+def _gen_gaussians(center_locs, sigmas, total_length):
+    xdata = np.arange(0, total_length).astype(float)
+    out_data = np.zeros(total_length, dtype=float)
+    for ind, sigma in enumerate(sigmas):
+        tmp = (xdata - center_locs[ind]) / sigma
+        out_data += np.exp(-(tmp**2))
+    return out_data
+
+
+def _gen_gaussians_even(sigmas, total_length):
+    num_peaks = len(sigmas)
+    delta = total_length / (num_peaks + 1)
+    center_locs = np.linspace(delta, total_length - delta, num=num_peaks).astype(int)
+    out_data = _gen_gaussians(center_locs, sigmas, total_length)
+    return out_data, center_locs
+
+
+def _gen_ridge_line(start_locs, max_locs, length, distances, gaps):
+    """
+    Generate coordinates for a ridge line.
+
+    Will be a series of coordinates, starting a start_loc (length 2).
+    The maximum distance between any adjacent columns will be
+    `max_distance`, the max distance between adjacent rows
+    will be `map_gap'.
+
+    `max_locs` should be the size of the intended matrix. The
+    ending coordinates are guaranteed to be less than `max_locs`,
+    although they may not approach `max_locs` at all.
+    """
+
+    def keep_bounds(num, max_val):
+        out = max(num, 0)
+        out = min(out, max_val)
+        return out
+
+    gaps = copy.deepcopy(gaps)
+    distances = copy.deepcopy(distances)
+
+    locs = np.zeros([length, 2], dtype=int)
+    locs[0, :] = start_locs
+    total_length = max_locs[0] - start_locs[0] - sum(gaps)
+    if total_length < length:
+        raise ValueError('Cannot generate ridge line according to constraints')
+    dist_int = length / len(distances) - 1
+    gap_int = length / len(gaps) - 1
+    for ind in range(1, length):
+        nextcol = locs[ind - 1, 1]
+        nextrow = locs[ind - 1, 0] + 1
+        if (ind % dist_int == 0) and (len(distances) > 0):
+            nextcol += ((-1)**ind)*distances.pop()
+        if (ind % gap_int == 0) and (len(gaps) > 0):
+            nextrow += gaps.pop()
+        nextrow = keep_bounds(nextrow, max_locs[0])
+        nextcol = keep_bounds(nextcol, max_locs[1])
+        locs[ind, :] = [nextrow, nextcol]
+
+    return [locs[:, 0], locs[:, 1]]
+
+
+class TestLocalMaxima1d(object):
+
+    def test_empty(self):
+        """Test with empty signal."""
+        x = np.array([], dtype=np.float64)
+        for array in _local_maxima_1d(x):
+            assert_equal(array, np.array([]))
+            assert_(array.base is None)
+
+    def test_linear(self):
+        """Test with linear signal."""
+        x = np.linspace(0, 100)
+        for array in _local_maxima_1d(x):
+            assert_equal(array, np.array([]))
+            assert_(array.base is None)
+
+    def test_simple(self):
+        """Test with simple signal."""
+        x = np.linspace(-10, 10, 50)
+        x[2::3] += 1
+        expected = np.arange(2, 50, 3)
+        for array in _local_maxima_1d(x):
+            # For plateaus of size 1, the edges are identical with the
+            # midpoints
+            assert_equal(array, expected)
+            assert_(array.base is None)
+
+    def test_flat_maxima(self):
+        """Test if flat maxima are detected correctly."""
+        x = np.array([-1.3, 0, 1, 0, 2, 2, 0, 3, 3, 3, 2.99, 4, 4, 4, 4, -10,
+                      -5, -5, -5, -5, -5, -10])
+        midpoints, left_edges, right_edges = _local_maxima_1d(x)
+        assert_equal(midpoints, np.array([2, 4, 8, 12, 18]))
+        assert_equal(left_edges, np.array([2, 4, 7, 11, 16]))
+        assert_equal(right_edges, np.array([2, 5, 9, 14, 20]))
+
+    @pytest.mark.parametrize('x', [
+        np.array([1., 0, 2]),
+        np.array([3., 3, 0, 4, 4]),
+        np.array([5., 5, 5, 0, 6, 6, 6]),
+    ])
+    def test_signal_edges(self, x):
+        """Test if behavior on signal edges is correct."""
+        for array in _local_maxima_1d(x):
+            assert_equal(array, np.array([]))
+            assert_(array.base is None)
+
+    def test_exceptions(self):
+        """Test input validation and raised exceptions."""
+        with raises(ValueError, match="wrong number of dimensions"):
+            _local_maxima_1d(np.ones((1, 1)))
+        with raises(ValueError, match="expected 'float64_t'"):
+            _local_maxima_1d(np.ones(1, dtype=int))
+        with raises(TypeError, match="list"):
+            _local_maxima_1d([1., 2.])
+        with raises(TypeError, match="'x' must not be None"):
+            _local_maxima_1d(None)
+
+
+class TestRidgeLines(object):
+
+    def test_empty(self):
+        test_matr = np.zeros([20, 100])
+        lines = _identify_ridge_lines(test_matr, np.full(20, 2), 1)
+        assert_(len(lines) == 0)
+
+    def test_minimal(self):
+        test_matr = np.zeros([20, 100])
+        test_matr[0, 10] = 1
+        lines = _identify_ridge_lines(test_matr, np.full(20, 2), 1)
+        assert_(len(lines) == 1)
+
+        test_matr = np.zeros([20, 100])
+        test_matr[0:2, 10] = 1
+        lines = _identify_ridge_lines(test_matr, np.full(20, 2), 1)
+        assert_(len(lines) == 1)
+
+    def test_single_pass(self):
+        distances = [0, 1, 2, 5]
+        gaps = [0, 1, 2, 0, 1]
+        test_matr = np.zeros([20, 50]) + 1e-12
+        length = 12
+        line = _gen_ridge_line([0, 25], test_matr.shape, length, distances, gaps)
+        test_matr[line[0], line[1]] = 1
+        max_distances = np.full(20, max(distances))
+        identified_lines = _identify_ridge_lines(test_matr, max_distances, max(gaps) + 1)
+        assert_array_equal(identified_lines, [line])
+
+    def test_single_bigdist(self):
+        distances = [0, 1, 2, 5]
+        gaps = [0, 1, 2, 4]
+        test_matr = np.zeros([20, 50])
+        length = 12
+        line = _gen_ridge_line([0, 25], test_matr.shape, length, distances, gaps)
+        test_matr[line[0], line[1]] = 1
+        max_dist = 3
+        max_distances = np.full(20, max_dist)
+        #This should get 2 lines, since the distance is too large
+        identified_lines = _identify_ridge_lines(test_matr, max_distances, max(gaps) + 1)
+        assert_(len(identified_lines) == 2)
+
+        for iline in identified_lines:
+            adists = np.diff(iline[1])
+            np.testing.assert_array_less(np.abs(adists), max_dist)
+
+            agaps = np.diff(iline[0])
+            np.testing.assert_array_less(np.abs(agaps), max(gaps) + 0.1)
+
+    def test_single_biggap(self):
+        distances = [0, 1, 2, 5]
+        max_gap = 3
+        gaps = [0, 4, 2, 1]
+        test_matr = np.zeros([20, 50])
+        length = 12
+        line = _gen_ridge_line([0, 25], test_matr.shape, length, distances, gaps)
+        test_matr[line[0], line[1]] = 1
+        max_dist = 6
+        max_distances = np.full(20, max_dist)
+        #This should get 2 lines, since the gap is too large
+        identified_lines = _identify_ridge_lines(test_matr, max_distances, max_gap)
+        assert_(len(identified_lines) == 2)
+
+        for iline in identified_lines:
+            adists = np.diff(iline[1])
+            np.testing.assert_array_less(np.abs(adists), max_dist)
+
+            agaps = np.diff(iline[0])
+            np.testing.assert_array_less(np.abs(agaps), max(gaps) + 0.1)
+
+    def test_single_biggaps(self):
+        distances = [0]
+        max_gap = 1
+        gaps = [3, 6]
+        test_matr = np.zeros([50, 50])
+        length = 30
+        line = _gen_ridge_line([0, 25], test_matr.shape, length, distances, gaps)
+        test_matr[line[0], line[1]] = 1
+        max_dist = 1
+        max_distances = np.full(50, max_dist)
+        #This should get 3 lines, since the gaps are too large
+        identified_lines = _identify_ridge_lines(test_matr, max_distances, max_gap)
+        assert_(len(identified_lines) == 3)
+
+        for iline in identified_lines:
+            adists = np.diff(iline[1])
+            np.testing.assert_array_less(np.abs(adists), max_dist)
+
+            agaps = np.diff(iline[0])
+            np.testing.assert_array_less(np.abs(agaps), max(gaps) + 0.1)
+
+
+class TestArgrel(object):
+
+    def test_empty(self):
+        # Regression test for gh-2832.
+        # When there are no relative extrema, make sure that
+        # the number of empty arrays returned matches the
+        # dimension of the input.
+
+        empty_array = np.array([], dtype=int)
+
+        z1 = np.zeros(5)
+
+        i = argrelmin(z1)
+        assert_equal(len(i), 1)
+        assert_array_equal(i[0], empty_array)
+
+        z2 = np.zeros((3,5))
+
+        row, col = argrelmin(z2, axis=0)
+        assert_array_equal(row, empty_array)
+        assert_array_equal(col, empty_array)
+
+        row, col = argrelmin(z2, axis=1)
+        assert_array_equal(row, empty_array)
+        assert_array_equal(col, empty_array)
+
+    def test_basic(self):
+        # Note: the docstrings for the argrel{min,max,extrema} functions
+        # do not give a guarantee of the order of the indices, so we'll
+        # sort them before testing.
+
+        x = np.array([[1, 2, 2, 3, 2],
+                      [2, 1, 2, 2, 3],
+                      [3, 2, 1, 2, 2],
+                      [2, 3, 2, 1, 2],
+                      [1, 2, 3, 2, 1]])
+
+        row, col = argrelmax(x, axis=0)
+        order = np.argsort(row)
+        assert_equal(row[order], [1, 2, 3])
+        assert_equal(col[order], [4, 0, 1])
+
+        row, col = argrelmax(x, axis=1)
+        order = np.argsort(row)
+        assert_equal(row[order], [0, 3, 4])
+        assert_equal(col[order], [3, 1, 2])
+
+        row, col = argrelmin(x, axis=0)
+        order = np.argsort(row)
+        assert_equal(row[order], [1, 2, 3])
+        assert_equal(col[order], [1, 2, 3])
+
+        row, col = argrelmin(x, axis=1)
+        order = np.argsort(row)
+        assert_equal(row[order], [1, 2, 3])
+        assert_equal(col[order], [1, 2, 3])
+
+    def test_highorder(self):
+        order = 2
+        sigmas = [1.0, 2.0, 10.0, 5.0, 15.0]
+        test_data, act_locs = _gen_gaussians_even(sigmas, 500)
+        test_data[act_locs + order] = test_data[act_locs]*0.99999
+        test_data[act_locs - order] = test_data[act_locs]*0.99999
+        rel_max_locs = argrelmax(test_data, order=order, mode='clip')[0]
+
+        assert_(len(rel_max_locs) == len(act_locs))
+        assert_((rel_max_locs == act_locs).all())
+
+    def test_2d_gaussians(self):
+        sigmas = [1.0, 2.0, 10.0]
+        test_data, act_locs = _gen_gaussians_even(sigmas, 100)
+        rot_factor = 20
+        rot_range = np.arange(0, len(test_data)) - rot_factor
+        test_data_2 = np.vstack([test_data, test_data[rot_range]])
+        rel_max_rows, rel_max_cols = argrelmax(test_data_2, axis=1, order=1)
+
+        for rw in range(0, test_data_2.shape[0]):
+            inds = (rel_max_rows == rw)
+
+            assert_(len(rel_max_cols[inds]) == len(act_locs))
+            assert_((act_locs == (rel_max_cols[inds] - rot_factor*rw)).all())
+
+
+class TestPeakProminences(object):
+
+    def test_empty(self):
+        """
+        Test if an empty array is returned if no peaks are provided.
+        """
+        out = peak_prominences([1, 2, 3], [])
+        for arr, dtype in zip(out, [np.float64, np.intp, np.intp]):
+            assert_(arr.size == 0)
+            assert_(arr.dtype == dtype)
+
+        out = peak_prominences([], [])
+        for arr, dtype in zip(out, [np.float64, np.intp, np.intp]):
+            assert_(arr.size == 0)
+            assert_(arr.dtype == dtype)
+
+    def test_basic(self):
+        """
+        Test if height of prominences is correctly calculated in signal with
+        rising baseline (peak widths are 1 sample).
+        """
+        # Prepare basic signal
+        x = np.array([-1, 1.2, 1.2, 1, 3.2, 1.3, 2.88, 2.1])
+        peaks = np.array([1, 2, 4, 6])
+        lbases = np.array([0, 0, 0, 5])
+        rbases = np.array([3, 3, 5, 7])
+        proms = x[peaks] - np.max([x[lbases], x[rbases]], axis=0)
+        # Test if calculation matches handcrafted result
+        out = peak_prominences(x, peaks)
+        assert_equal(out[0], proms)
+        assert_equal(out[1], lbases)
+        assert_equal(out[2], rbases)
+
+    def test_edge_cases(self):
+        """
+        Test edge cases.
+        """
+        # Peaks have same height, prominence and bases
+        x = [0, 2, 1, 2, 1, 2, 0]
+        peaks = [1, 3, 5]
+        proms, lbases, rbases = peak_prominences(x, peaks)
+        assert_equal(proms, [2, 2, 2])
+        assert_equal(lbases, [0, 0, 0])
+        assert_equal(rbases, [6, 6, 6])
+
+        # Peaks have same height & prominence but different bases
+        x = [0, 1, 0, 1, 0, 1, 0]
+        peaks = np.array([1, 3, 5])
+        proms, lbases, rbases = peak_prominences(x, peaks)
+        assert_equal(proms, [1, 1, 1])
+        assert_equal(lbases, peaks - 1)
+        assert_equal(rbases, peaks + 1)
+
+    def test_non_contiguous(self):
+        """
+        Test with non-C-contiguous input arrays.
+        """
+        x = np.repeat([-9, 9, 9, 0, 3, 1], 2)
+        peaks = np.repeat([1, 2, 4], 2)
+        proms, lbases, rbases = peak_prominences(x[::2], peaks[::2])
+        assert_equal(proms, [9, 9, 2])
+        assert_equal(lbases, [0, 0, 3])
+        assert_equal(rbases, [3, 3, 5])
+
+    def test_wlen(self):
+        """
+        Test if wlen actually shrinks the evaluation range correctly.
+        """
+        x = [0, 1, 2, 3, 1, 0, -1]
+        peak = [3]
+        # Test rounding behavior of wlen
+        assert_equal(peak_prominences(x, peak), [3., 0, 6])
+        for wlen, i in [(8, 0), (7, 0), (6, 0), (5, 1), (3.2, 1), (3, 2), (1.1, 2)]:
+            assert_equal(peak_prominences(x, peak, wlen), [3. - i, 0 + i, 6 - i])
+
+    def test_exceptions(self):
+        """
+        Verify that exceptions and warnings are raised.
+        """
+        # x with dimension > 1
+        with raises(ValueError, match='1-D array'):
+            peak_prominences([[0, 1, 1, 0]], [1, 2])
+        # peaks with dimension > 1
+        with raises(ValueError, match='1-D array'):
+            peak_prominences([0, 1, 1, 0], [[1, 2]])
+        # x with dimension < 1
+        with raises(ValueError, match='1-D array'):
+            peak_prominences(3, [0,])
+
+        # empty x with supplied
+        with raises(ValueError, match='not a valid index'):
+            peak_prominences([], [0])
+        # invalid indices with non-empty x
+        for p in [-100, -1, 3, 1000]:
+            with raises(ValueError, match='not a valid index'):
+                peak_prominences([1, 0, 2], [p])
+
+        # peaks is not cast-able to np.intp
+        with raises(TypeError, match='cannot safely cast'):
+            peak_prominences([0, 1, 1, 0], [1.1, 2.3])
+
+        # wlen < 3
+        with raises(ValueError, match='wlen'):
+            peak_prominences(np.arange(10), [3, 5], wlen=1)
+
+    def test_warnings(self):
+        """
+        Verify that appropriate warnings are raised.
+        """
+        msg = "some peaks have a prominence of 0"
+        for p in [0, 1, 2]:
+            with warns(PeakPropertyWarning, match=msg):
+                peak_prominences([1, 0, 2], [p,])
+        with warns(PeakPropertyWarning, match=msg):
+            peak_prominences([0, 1, 1, 1, 0], [2], wlen=2)
+
+
+class TestPeakWidths(object):
+
+    def test_empty(self):
+        """
+        Test if an empty array is returned if no peaks are provided.
+        """
+        widths = peak_widths([], [])[0]
+        assert_(isinstance(widths, np.ndarray))
+        assert_equal(widths.size, 0)
+        widths = peak_widths([1, 2, 3], [])[0]
+        assert_(isinstance(widths, np.ndarray))
+        assert_equal(widths.size, 0)
+        out = peak_widths([], [])
+        for arr in out:
+            assert_(isinstance(arr, np.ndarray))
+            assert_equal(arr.size, 0)
+
+    @pytest.mark.filterwarnings("ignore:some peaks have a width of 0")
+    def test_basic(self):
+        """
+        Test a simple use case with easy to verify results at different relative
+        heights.
+        """
+        x = np.array([1, 0, 1, 2, 1, 0, -1])
+        prominence = 2
+        for rel_height, width_true, lip_true, rip_true in [
+            (0., 0., 3., 3.),  # raises warning
+            (0.25, 1., 2.5, 3.5),
+            (0.5, 2., 2., 4.),
+            (0.75, 3., 1.5, 4.5),
+            (1., 4., 1., 5.),
+            (2., 5., 1., 6.),
+            (3., 5., 1., 6.)
+        ]:
+            width_calc, height, lip_calc, rip_calc = peak_widths(
+                x, [3], rel_height)
+            assert_allclose(width_calc, width_true)
+            assert_allclose(height, 2 - rel_height * prominence)
+            assert_allclose(lip_calc, lip_true)
+            assert_allclose(rip_calc, rip_true)
+
+    def test_non_contiguous(self):
+        """
+        Test with non-C-contiguous input arrays.
+        """
+        x = np.repeat([0, 100, 50], 4)
+        peaks = np.repeat([1], 3)
+        result = peak_widths(x[::4], peaks[::3])
+        assert_equal(result, [0.75, 75, 0.75, 1.5])
+
+    def test_exceptions(self):
+        """
+        Verify that argument validation works as intended.
+        """
+        with raises(ValueError, match='1-D array'):
+            # x with dimension > 1
+            peak_widths(np.zeros((3, 4)), np.ones(3))
+        with raises(ValueError, match='1-D array'):
+            # x with dimension < 1
+            peak_widths(3, [0])
+        with raises(ValueError, match='1-D array'):
+            # peaks with dimension > 1
+            peak_widths(np.arange(10), np.ones((3, 2), dtype=np.intp))
+        with raises(ValueError, match='1-D array'):
+            # peaks with dimension < 1
+            peak_widths(np.arange(10), 3)
+        with raises(ValueError, match='not a valid index'):
+            # peak pos exceeds x.size
+            peak_widths(np.arange(10), [8, 11])
+        with raises(ValueError, match='not a valid index'):
+            # empty x with peaks supplied
+            peak_widths([], [1, 2])
+        with raises(TypeError, match='cannot safely cast'):
+            # peak cannot be safely casted to intp
+            peak_widths(np.arange(10), [1.1, 2.3])
+        with raises(ValueError, match='rel_height'):
+            # rel_height is < 0
+            peak_widths([0, 1, 0, 1, 0], [1, 3], rel_height=-1)
+        with raises(TypeError, match='None'):
+            # prominence data contains None
+            peak_widths([1, 2, 1], [1], prominence_data=(None, None, None))
+
+    def test_warnings(self):
+        """
+        Verify that appropriate warnings are raised.
+        """
+        msg = "some peaks have a width of 0"
+        with warns(PeakPropertyWarning, match=msg):
+            # Case: rel_height is 0
+            peak_widths([0, 1, 0], [1], rel_height=0)
+        with warns(PeakPropertyWarning, match=msg):
+            # Case: prominence is 0 and bases are identical
+            peak_widths(
+                [0, 1, 1, 1, 0], [2],
+                prominence_data=(np.array([0.], np.float64),
+                                 np.array([2], np.intp),
+                                 np.array([2], np.intp))
+            )
+
+    def test_mismatching_prominence_data(self):
+        """Test with mismatching peak and / or prominence data."""
+        x = [0, 1, 0]
+        peak = [1]
+        for i, (prominences, left_bases, right_bases) in enumerate([
+            ((1.,), (-1,), (2,)),  # left base not in x
+            ((1.,), (0,), (3,)),  # right base not in x
+            ((1.,), (2,), (0,)),  # swapped bases same as peak
+            ((1., 1.), (0, 0), (2, 2)),  # array shapes don't match peaks
+            ((1., 1.), (0,), (2,)),  # arrays with different shapes
+            ((1.,), (0, 0), (2,)),  # arrays with different shapes
+            ((1.,), (0,), (2, 2))  # arrays with different shapes
+        ]):
+            # Make sure input is matches output of signal.peak_prominences
+            prominence_data = (np.array(prominences, dtype=np.float64),
+                               np.array(left_bases, dtype=np.intp),
+                               np.array(right_bases, dtype=np.intp))
+            # Test for correct exception
+            if i < 3:
+                match = "prominence data is invalid for peak"
+            else:
+                match = "arrays in `prominence_data` must have the same shape"
+            with raises(ValueError, match=match):
+                peak_widths(x, peak, prominence_data=prominence_data)
+
+    @pytest.mark.filterwarnings("ignore:some peaks have a width of 0")
+    def test_intersection_rules(self):
+        """Test if x == eval_height counts as an intersection."""
+        # Flatt peak with two possible intersection points if evaluated at 1
+        x = [0, 1, 2, 1, 3, 3, 3, 1, 2, 1, 0]
+        # relative height is 0 -> width is 0 as well, raises warning
+        assert_allclose(peak_widths(x, peaks=[5], rel_height=0),
+                        [(0.,), (3.,), (5.,), (5.,)])
+        # width_height == x counts as intersection -> nearest 1 is chosen
+        assert_allclose(peak_widths(x, peaks=[5], rel_height=2/3),
+                        [(4.,), (1.,), (3.,), (7.,)])
+
+
+def test_unpack_condition_args():
+    """
+    Verify parsing of condition arguments for `scipy.signal.find_peaks` function.
+    """
+    x = np.arange(10)
+    amin_true = x
+    amax_true = amin_true + 10
+    peaks = amin_true[1::2]
+
+    # Test unpacking with None or interval
+    assert_((None, None) == _unpack_condition_args((None, None), x, peaks))
+    assert_((1, None) == _unpack_condition_args(1, x, peaks))
+    assert_((1, None) == _unpack_condition_args((1, None), x, peaks))
+    assert_((None, 2) == _unpack_condition_args((None, 2), x, peaks))
+    assert_((3., 4.5) == _unpack_condition_args((3., 4.5), x, peaks))
+
+    # Test if borders are correctly reduced with `peaks`
+    amin_calc, amax_calc = _unpack_condition_args((amin_true, amax_true), x, peaks)
+    assert_equal(amin_calc, amin_true[peaks])
+    assert_equal(amax_calc, amax_true[peaks])
+
+    # Test raises if array borders don't match x
+    with raises(ValueError, match="array size of lower"):
+        _unpack_condition_args(amin_true, np.arange(11), peaks)
+    with raises(ValueError, match="array size of upper"):
+        _unpack_condition_args((None, amin_true), np.arange(11), peaks)
+
+
+class TestFindPeaks(object):
+
+    # Keys of optionally returned properties
+    property_keys = {'peak_heights', 'left_thresholds', 'right_thresholds',
+                     'prominences', 'left_bases', 'right_bases', 'widths',
+                     'width_heights', 'left_ips', 'right_ips'}
+
+    def test_constant(self):
+        """
+        Test behavior for signal without local maxima.
+        """
+        open_interval = (None, None)
+        peaks, props = find_peaks(np.ones(10),
+                                  height=open_interval, threshold=open_interval,
+                                  prominence=open_interval, width=open_interval)
+        assert_(peaks.size == 0)
+        for key in self.property_keys:
+            assert_(props[key].size == 0)
+
+    def test_plateau_size(self):
+        """
+        Test plateau size condition for peaks.
+        """
+        # Prepare signal with peaks with peak_height == plateau_size
+        plateau_sizes = np.array([1, 2, 3, 4, 8, 20, 111])
+        x = np.zeros(plateau_sizes.size * 2 + 1)
+        x[1::2] = plateau_sizes
+        repeats = np.ones(x.size, dtype=int)
+        repeats[1::2] = x[1::2]
+        x = np.repeat(x, repeats)
+
+        # Test full output
+        peaks, props = find_peaks(x, plateau_size=(None, None))
+        assert_equal(peaks, [1, 3, 7, 11, 18, 33, 100])
+        assert_equal(props["plateau_sizes"], plateau_sizes)
+        assert_equal(props["left_edges"], peaks - (plateau_sizes - 1) // 2)
+        assert_equal(props["right_edges"], peaks + plateau_sizes // 2)
+
+        # Test conditions
+        assert_equal(find_peaks(x, plateau_size=4)[0], [11, 18, 33, 100])
+        assert_equal(find_peaks(x, plateau_size=(None, 3.5))[0], [1, 3, 7])
+        assert_equal(find_peaks(x, plateau_size=(5, 50))[0], [18, 33])
+
+    def test_height_condition(self):
+        """
+        Test height condition for peaks.
+        """
+        x = (0., 1/3, 0., 2.5, 0, 4., 0)
+        peaks, props = find_peaks(x, height=(None, None))
+        assert_equal(peaks, np.array([1, 3, 5]))
+        assert_equal(props['peak_heights'], np.array([1/3, 2.5, 4.]))
+        assert_equal(find_peaks(x, height=0.5)[0], np.array([3, 5]))
+        assert_equal(find_peaks(x, height=(None, 3))[0], np.array([1, 3]))
+        assert_equal(find_peaks(x, height=(2, 3))[0], np.array([3]))
+
+    def test_threshold_condition(self):
+        """
+        Test threshold condition for peaks.
+        """
+        x = (0, 2, 1, 4, -1)
+        peaks, props = find_peaks(x, threshold=(None, None))
+        assert_equal(peaks, np.array([1, 3]))
+        assert_equal(props['left_thresholds'], np.array([2, 3]))
+        assert_equal(props['right_thresholds'], np.array([1, 5]))
+        assert_equal(find_peaks(x, threshold=2)[0], np.array([3]))
+        assert_equal(find_peaks(x, threshold=3.5)[0], np.array([]))
+        assert_equal(find_peaks(x, threshold=(None, 5))[0], np.array([1, 3]))
+        assert_equal(find_peaks(x, threshold=(None, 4))[0], np.array([1]))
+        assert_equal(find_peaks(x, threshold=(2, 4))[0], np.array([]))
+
+    def test_distance_condition(self):
+        """
+        Test distance condition for peaks.
+        """
+        # Peaks of different height with constant distance 3
+        peaks_all = np.arange(1, 21, 3)
+        x = np.zeros(21)
+        x[peaks_all] += np.linspace(1, 2, peaks_all.size)
+
+        # Test if peaks with "minimal" distance are still selected (distance = 3)
+        assert_equal(find_peaks(x, distance=3)[0], peaks_all)
+
+        # Select every second peak (distance > 3)
+        peaks_subset = find_peaks(x, distance=3.0001)[0]
+        # Test if peaks_subset is subset of peaks_all
+        assert_(
+            np.setdiff1d(peaks_subset, peaks_all, assume_unique=True).size == 0
+        )
+        # Test if every second peak was removed
+        assert_equal(np.diff(peaks_subset), 6)
+
+        # Test priority of peak removal
+        x = [-2, 1, -1, 0, -3]
+        peaks_subset = find_peaks(x, distance=10)[0]  # use distance > x size
+        assert_(peaks_subset.size == 1 and peaks_subset[0] == 1)
+
+    def test_prominence_condition(self):
+        """
+        Test prominence condition for peaks.
+        """
+        x = np.linspace(0, 10, 100)
+        peaks_true = np.arange(1, 99, 2)
+        offset = np.linspace(1, 10, peaks_true.size)
+        x[peaks_true] += offset
+        prominences = x[peaks_true] - x[peaks_true + 1]
+        interval = (3, 9)
+        keep = np.nonzero(
+            (interval[0] <= prominences) & (prominences <= interval[1]))
+
+        peaks_calc, properties = find_peaks(x, prominence=interval)
+        assert_equal(peaks_calc, peaks_true[keep])
+        assert_equal(properties['prominences'], prominences[keep])
+        assert_equal(properties['left_bases'], 0)
+        assert_equal(properties['right_bases'], peaks_true[keep] + 1)
+
+    def test_width_condition(self):
+        """
+        Test width condition for peaks.
+        """
+        x = np.array([1, 0, 1, 2, 1, 0, -1, 4, 0])
+        peaks, props = find_peaks(x, width=(None, 2), rel_height=0.75)
+        assert_equal(peaks.size, 1)
+        assert_equal(peaks, 7)
+        assert_allclose(props['widths'], 1.35)
+        assert_allclose(props['width_heights'], 1.)
+        assert_allclose(props['left_ips'], 6.4)
+        assert_allclose(props['right_ips'], 7.75)
+
+    def test_properties(self):
+        """
+        Test returned properties.
+        """
+        open_interval = (None, None)
+        x = [0, 1, 0, 2, 1.5, 0, 3, 0, 5, 9]
+        peaks, props = find_peaks(x,
+                                  height=open_interval, threshold=open_interval,
+                                  prominence=open_interval, width=open_interval)
+        assert_(len(props) == len(self.property_keys))
+        for key in self.property_keys:
+            assert_(peaks.size == props[key].size)
+
+    def test_raises(self):
+        """
+        Test exceptions raised by function.
+        """
+        with raises(ValueError, match="1-D array"):
+            find_peaks(np.array(1))
+        with raises(ValueError, match="1-D array"):
+            find_peaks(np.ones((2, 2)))
+        with raises(ValueError, match="distance"):
+            find_peaks(np.arange(10), distance=-1)
+
+    @pytest.mark.filterwarnings("ignore:some peaks have a prominence of 0",
+                                "ignore:some peaks have a width of 0")
+    def test_wlen_smaller_plateau(self):
+        """
+        Test behavior of prominence and width calculation if the given window
+        length is smaller than a peak's plateau size.
+
+        Regression test for gh-9110.
+        """
+        peaks, props = find_peaks([0, 1, 1, 1, 0], prominence=(None, None),
+                                  width=(None, None), wlen=2)
+        assert_equal(peaks, 2)
+        assert_equal(props["prominences"], 0)
+        assert_equal(props["widths"], 0)
+        assert_equal(props["width_heights"], 1)
+        for key in ("left_bases", "right_bases", "left_ips", "right_ips"):
+            assert_equal(props[key], peaks)
+
+
+class TestFindPeaksCwt(object):
+
+    def test_find_peaks_exact(self):
+        """
+        Generate a series of gaussians and attempt to find the peak locations.
+        """
+        sigmas = [5.0, 3.0, 10.0, 20.0, 10.0, 50.0]
+        num_points = 500
+        test_data, act_locs = _gen_gaussians_even(sigmas, num_points)
+        widths = np.arange(0.1, max(sigmas))
+        found_locs = find_peaks_cwt(test_data, widths, gap_thresh=2, min_snr=0,
+                                         min_length=None)
+        np.testing.assert_array_equal(found_locs, act_locs,
+                        "Found maximum locations did not equal those expected")
+
+    def test_find_peaks_withnoise(self):
+        """
+        Verify that peak locations are (approximately) found
+        for a series of gaussians with added noise.
+        """
+        sigmas = [5.0, 3.0, 10.0, 20.0, 10.0, 50.0]
+        num_points = 500
+        test_data, act_locs = _gen_gaussians_even(sigmas, num_points)
+        widths = np.arange(0.1, max(sigmas))
+        noise_amp = 0.07
+        np.random.seed(18181911)
+        test_data += (np.random.rand(num_points) - 0.5)*(2*noise_amp)
+        found_locs = find_peaks_cwt(test_data, widths, min_length=15,
+                                         gap_thresh=1, min_snr=noise_amp / 5)
+
+        np.testing.assert_equal(len(found_locs), len(act_locs), 'Different number' +
+                                'of peaks found than expected')
+        diffs = np.abs(found_locs - act_locs)
+        max_diffs = np.array(sigmas) / 5
+        np.testing.assert_array_less(diffs, max_diffs, 'Maximum location differed' +
+                                     'by more than %s' % (max_diffs))
+
+    def test_find_peaks_nopeak(self):
+        """
+        Verify that no peak is found in
+        data that's just noise.
+        """
+        noise_amp = 1.0
+        num_points = 100
+        np.random.seed(181819141)
+        test_data = (np.random.rand(num_points) - 0.5)*(2*noise_amp)
+        widths = np.arange(10, 50)
+        found_locs = find_peaks_cwt(test_data, widths, min_snr=5, noise_perc=30)
+        np.testing.assert_equal(len(found_locs), 0)
+
+    def test_find_peaks_window_size(self):
+        """
+        Verify that window_size is passed correctly to private function and
+        affects the result.
+        """
+        sigmas = [2.0, 2.0]
+        num_points = 1000
+        test_data, act_locs = _gen_gaussians_even(sigmas, num_points)
+        widths = np.arange(0.1, max(sigmas), 0.2)
+        noise_amp = 0.05
+        np.random.seed(18181911)
+        test_data += (np.random.rand(num_points) - 0.5)*(2*noise_amp)
+
+        # Possibly contrived negative region to throw off peak finding
+        # when window_size is too large
+        test_data[250:320] -= 1
+
+        found_locs = find_peaks_cwt(test_data, widths, gap_thresh=2, min_snr=3,
+                                    min_length=None, window_size=None)
+        with pytest.raises(AssertionError):
+            assert found_locs.size == act_locs.size
+
+        found_locs = find_peaks_cwt(test_data, widths, gap_thresh=2, min_snr=3,
+                                    min_length=None, window_size=20)
+        assert found_locs.size == act_locs.size

venv/Lib/site-packages/scipy/signal/tests/test_savitzky_golay.py

@@ -0,0 +1,301 @@
+import numpy as np
+from numpy.testing import (assert_allclose, assert_equal,
+                           assert_almost_equal, assert_array_equal,
+                           assert_array_almost_equal)
+
+from scipy.ndimage import convolve1d
+
+from scipy.signal import savgol_coeffs, savgol_filter
+from scipy.signal._savitzky_golay import _polyder
+
+
+def check_polyder(p, m, expected):
+    dp = _polyder(p, m)
+    assert_array_equal(dp, expected)
+
+
+def test_polyder():
+    cases = [
+        ([5], 0, [5]),
+        ([5], 1, [0]),
+        ([3, 2, 1], 0, [3, 2, 1]),
+        ([3, 2, 1], 1, [6, 2]),
+        ([3, 2, 1], 2, [6]),
+        ([3, 2, 1], 3, [0]),
+        ([[3, 2, 1], [5, 6, 7]], 0, [[3, 2, 1], [5, 6, 7]]),
+        ([[3, 2, 1], [5, 6, 7]], 1, [[6, 2], [10, 6]]),
+        ([[3, 2, 1], [5, 6, 7]], 2, [[6], [10]]),
+        ([[3, 2, 1], [5, 6, 7]], 3, [[0], [0]]),
+    ]
+    for p, m, expected in cases:
+        check_polyder(np.array(p).T, m, np.array(expected).T)
+
+
+#--------------------------------------------------------------------
+# savgol_coeffs tests
+#--------------------------------------------------------------------
+
+def alt_sg_coeffs(window_length, polyorder, pos):
+    """This is an alternative implementation of the SG coefficients.
+
+    It uses numpy.polyfit and numpy.polyval. The results should be
+    equivalent to those of savgol_coeffs(), but this implementation
+    is slower.
+
+    window_length should be odd.
+
+    """
+    if pos is None:
+        pos = window_length // 2
+    t = np.arange(window_length)
+    unit = (t == pos).astype(int)
+    h = np.polyval(np.polyfit(t, unit, polyorder), t)
+    return h
+
+
+def test_sg_coeffs_trivial():
+    # Test a trivial case of savgol_coeffs: polyorder = window_length - 1
+    h = savgol_coeffs(1, 0)
+    assert_allclose(h, [1])
+
+    h = savgol_coeffs(3, 2)
+    assert_allclose(h, [0, 1, 0], atol=1e-10)
+
+    h = savgol_coeffs(5, 4)
+    assert_allclose(h, [0, 0, 1, 0, 0], atol=1e-10)
+
+    h = savgol_coeffs(5, 4, pos=1)
+    assert_allclose(h, [0, 0, 0, 1, 0], atol=1e-10)
+
+    h = savgol_coeffs(5, 4, pos=1, use='dot')
+    assert_allclose(h, [0, 1, 0, 0, 0], atol=1e-10)
+
+
+def compare_coeffs_to_alt(window_length, order):
+    # For the given window_length and order, compare the results
+    # of savgol_coeffs and alt_sg_coeffs for pos from 0 to window_length - 1.
+    # Also include pos=None.
+    for pos in [None] + list(range(window_length)):
+        h1 = savgol_coeffs(window_length, order, pos=pos, use='dot')
+        h2 = alt_sg_coeffs(window_length, order, pos=pos)
+        assert_allclose(h1, h2, atol=1e-10,
+                        err_msg=("window_length = %d, order = %d, pos = %s" %
+                                 (window_length, order, pos)))
+
+
+def test_sg_coeffs_compare():
+    # Compare savgol_coeffs() to alt_sg_coeffs().
+    for window_length in range(1, 8, 2):
+        for order in range(window_length):
+            compare_coeffs_to_alt(window_length, order)
+
+
+def test_sg_coeffs_exact():
+    polyorder = 4
+    window_length = 9
+    halflen = window_length // 2
+
+    x = np.linspace(0, 21, 43)
+    delta = x[1] - x[0]
+
+    # The data is a cubic polynomial.  We'll use an order 4
+    # SG filter, so the filtered values should equal the input data
+    # (except within half window_length of the edges).
+    y = 0.5 * x ** 3 - x
+    h = savgol_coeffs(window_length, polyorder)
+    y0 = convolve1d(y, h)
+    assert_allclose(y0[halflen:-halflen], y[halflen:-halflen])
+
+    # Check the same input, but use deriv=1.  dy is the exact result.
+    dy = 1.5 * x ** 2 - 1
+    h = savgol_coeffs(window_length, polyorder, deriv=1, delta=delta)
+    y1 = convolve1d(y, h)
+    assert_allclose(y1[halflen:-halflen], dy[halflen:-halflen])
+
+    # Check the same input, but use deriv=2. d2y is the exact result.
+    d2y = 3.0 * x
+    h = savgol_coeffs(window_length, polyorder, deriv=2, delta=delta)
+    y2 = convolve1d(y, h)
+    assert_allclose(y2[halflen:-halflen], d2y[halflen:-halflen])
+
+
+def test_sg_coeffs_deriv():
+    # The data in `x` is a sampled parabola, so using savgol_coeffs with an
+    # order 2 or higher polynomial should give exact results.
+    i = np.array([-2.0, 0.0, 2.0, 4.0, 6.0])
+    x = i ** 2 / 4
+    dx = i / 2
+    d2x = np.full_like(i, 0.5)
+    for pos in range(x.size):
+        coeffs0 = savgol_coeffs(5, 3, pos=pos, delta=2.0, use='dot')
+        assert_allclose(coeffs0.dot(x), x[pos], atol=1e-10)
+        coeffs1 = savgol_coeffs(5, 3, pos=pos, delta=2.0, use='dot', deriv=1)
+        assert_allclose(coeffs1.dot(x), dx[pos], atol=1e-10)
+        coeffs2 = savgol_coeffs(5, 3, pos=pos, delta=2.0, use='dot', deriv=2)
+        assert_allclose(coeffs2.dot(x), d2x[pos], atol=1e-10)
+
+
+def test_sg_coeffs_deriv_gt_polyorder():
+    """
+    If deriv > polyorder, the coefficients should be all 0.
+    This is a regression test for a bug where, e.g.,
+        savgol_coeffs(5, polyorder=1, deriv=2)
+    raised an error.
+    """
+    coeffs = savgol_coeffs(5, polyorder=1, deriv=2)
+    assert_array_equal(coeffs, np.zeros(5))
+    coeffs = savgol_coeffs(7, polyorder=4, deriv=6)
+    assert_array_equal(coeffs, np.zeros(7))
+
+
+def test_sg_coeffs_large():
+    # Test that for large values of window_length and polyorder the array of
+    # coefficients returned is symmetric. The aim is to ensure that
+    # no potential numeric overflow occurs.
+    coeffs0 = savgol_coeffs(31, 9)
+    assert_array_almost_equal(coeffs0, coeffs0[::-1])
+    coeffs1 = savgol_coeffs(31, 9, deriv=1)
+    assert_array_almost_equal(coeffs1, -coeffs1[::-1])
+
+
+#--------------------------------------------------------------------
+# savgol_filter tests
+#--------------------------------------------------------------------
+
+
+def test_sg_filter_trivial():
+    """ Test some trivial edge cases for savgol_filter()."""
+    x = np.array([1.0])
+    y = savgol_filter(x, 1, 0)
+    assert_equal(y, [1.0])
+
+    # Input is a single value. With a window length of 3 and polyorder 1,
+    # the value in y is from the straight-line fit of (-1,0), (0,3) and
+    # (1, 0) at 0. This is just the average of the three values, hence 1.0.
+    x = np.array([3.0])
+    y = savgol_filter(x, 3, 1, mode='constant')
+    assert_almost_equal(y, [1.0], decimal=15)
+
+    x = np.array([3.0])
+    y = savgol_filter(x, 3, 1, mode='nearest')
+    assert_almost_equal(y, [3.0], decimal=15)
+
+    x = np.array([1.0] * 3)
+    y = savgol_filter(x, 3, 1, mode='wrap')
+    assert_almost_equal(y, [1.0, 1.0, 1.0], decimal=15)
+
+
+def test_sg_filter_basic():
+    # Some basic test cases for savgol_filter().
+    x = np.array([1.0, 2.0, 1.0])
+    y = savgol_filter(x, 3, 1, mode='constant')
+    assert_allclose(y, [1.0, 4.0 / 3, 1.0])
+
+    y = savgol_filter(x, 3, 1, mode='mirror')
+    assert_allclose(y, [5.0 / 3, 4.0 / 3, 5.0 / 3])
+
+    y = savgol_filter(x, 3, 1, mode='wrap')
+    assert_allclose(y, [4.0 / 3, 4.0 / 3, 4.0 / 3])
+
+
+def test_sg_filter_2d():
+    x = np.array([[1.0, 2.0, 1.0],
+                  [2.0, 4.0, 2.0]])
+    expected = np.array([[1.0, 4.0 / 3, 1.0],
+                         [2.0, 8.0 / 3, 2.0]])
+    y = savgol_filter(x, 3, 1, mode='constant')
+    assert_allclose(y, expected)
+
+    y = savgol_filter(x.T, 3, 1, mode='constant', axis=0)
+    assert_allclose(y, expected.T)
+
+
+def test_sg_filter_interp_edges():
+    # Another test with low degree polynomial data, for which we can easily
+    # give the exact results. In this test, we use mode='interp', so
+    # savgol_filter should match the exact solution for the entire data set,
+    # including the edges.
+    t = np.linspace(-5, 5, 21)
+    delta = t[1] - t[0]
+    # Polynomial test data.
+    x = np.array([t,
+                  3 * t ** 2,
+                  t ** 3 - t])
+    dx = np.array([np.ones_like(t),
+                   6 * t,
+                   3 * t ** 2 - 1.0])
+    d2x = np.array([np.zeros_like(t),
+                    np.full_like(t, 6),
+                    6 * t])
+
+    window_length = 7
+
+    y = savgol_filter(x, window_length, 3, axis=-1, mode='interp')
+    assert_allclose(y, x, atol=1e-12)
+
+    y1 = savgol_filter(x, window_length, 3, axis=-1, mode='interp',
+                       deriv=1, delta=delta)
+    assert_allclose(y1, dx, atol=1e-12)
+
+    y2 = savgol_filter(x, window_length, 3, axis=-1, mode='interp',
+                       deriv=2, delta=delta)
+    assert_allclose(y2, d2x, atol=1e-12)
+
+    # Transpose everything, and test again with axis=0.
+
+    x = x.T
+    dx = dx.T
+    d2x = d2x.T
+
+    y = savgol_filter(x, window_length, 3, axis=0, mode='interp')
+    assert_allclose(y, x, atol=1e-12)
+
+    y1 = savgol_filter(x, window_length, 3, axis=0, mode='interp',
+                       deriv=1, delta=delta)
+    assert_allclose(y1, dx, atol=1e-12)
+
+    y2 = savgol_filter(x, window_length, 3, axis=0, mode='interp',
+                       deriv=2, delta=delta)
+    assert_allclose(y2, d2x, atol=1e-12)
+
+
+def test_sg_filter_interp_edges_3d():
+    # Test mode='interp' with a 3-D array.
+    t = np.linspace(-5, 5, 21)
+    delta = t[1] - t[0]
+    x1 = np.array([t, -t])
+    x2 = np.array([t ** 2, 3 * t ** 2 + 5])
+    x3 = np.array([t ** 3, 2 * t ** 3 + t ** 2 - 0.5 * t])
+    dx1 = np.array([np.ones_like(t), -np.ones_like(t)])
+    dx2 = np.array([2 * t, 6 * t])
+    dx3 = np.array([3 * t ** 2, 6 * t ** 2 + 2 * t - 0.5])
+
+    # z has shape (3, 2, 21)
+    z = np.array([x1, x2, x3])
+    dz = np.array([dx1, dx2, dx3])
+
+    y = savgol_filter(z, 7, 3, axis=-1, mode='interp', delta=delta)
+    assert_allclose(y, z, atol=1e-10)
+
+    dy = savgol_filter(z, 7, 3, axis=-1, mode='interp', deriv=1, delta=delta)
+    assert_allclose(dy, dz, atol=1e-10)
+
+    # z has shape (3, 21, 2)
+    z = np.array([x1.T, x2.T, x3.T])
+    dz = np.array([dx1.T, dx2.T, dx3.T])
+
+    y = savgol_filter(z, 7, 3, axis=1, mode='interp', delta=delta)
+    assert_allclose(y, z, atol=1e-10)
+
+    dy = savgol_filter(z, 7, 3, axis=1, mode='interp', deriv=1, delta=delta)
+    assert_allclose(dy, dz, atol=1e-10)
+
+    # z has shape (21, 3, 2)
+    z = z.swapaxes(0, 1).copy()
+    dz = dz.swapaxes(0, 1).copy()
+
+    y = savgol_filter(z, 7, 3, axis=0, mode='interp', delta=delta)
+    assert_allclose(y, z, atol=1e-10)
+
+    dy = savgol_filter(z, 7, 3, axis=0, mode='interp', deriv=1, delta=delta)
+    assert_allclose(dy, dz, atol=1e-10)

venv/Lib/site-packages/scipy/signal/tests/test_upfirdn.py

@@ -0,0 +1,273 @@
+# Code adapted from "upfirdn" python library with permission:
+#
+# Copyright (c) 2009, Motorola, Inc
+#
+# All Rights Reserved.
+#
+# Redistribution and use in source and binary forms, with or without
+# modification, are permitted provided that the following conditions are
+# met:
+#
+# * Redistributions of source code must retain the above copyright notice,
+# this list of conditions and the following disclaimer.
+#
+# * Redistributions in binary form must reproduce the above copyright
+# notice, this list of conditions and the following disclaimer in the
+# documentation and/or other materials provided with the distribution.
+#
+# * Neither the name of Motorola nor the names of its contributors may be
+# used to endorse or promote products derived from this software without
+# specific prior written permission.
+#
+# THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS
+# IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO,
+# THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
+# PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR
+# CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
+# EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
+# PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
+# PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
+# LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
+# NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
+# SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+
+
+import numpy as np
+from itertools import product
+
+from numpy.testing import assert_equal, assert_allclose
+from pytest import raises as assert_raises
+import pytest
+
+from scipy.signal import upfirdn, firwin
+from scipy.signal._upfirdn import _output_len, _upfirdn_modes
+from scipy.signal._upfirdn_apply import _pad_test
+
+
+def upfirdn_naive(x, h, up=1, down=1):
+    """Naive upfirdn processing in Python.
+
+    Note: arg order (x, h) differs to facilitate apply_along_axis use.
+    """
+    h = np.asarray(h)
+    out = np.zeros(len(x) * up, x.dtype)
+    out[::up] = x
+    out = np.convolve(h, out)[::down][:_output_len(len(h), len(x), up, down)]
+    return out
+
+
+class UpFIRDnCase(object):
+    """Test _UpFIRDn object"""
+    def __init__(self, up, down, h, x_dtype):
+        self.up = up
+        self.down = down
+        self.h = np.atleast_1d(h)
+        self.x_dtype = x_dtype
+        self.rng = np.random.RandomState(17)
+
+    def __call__(self):
+        # tiny signal
+        self.scrub(np.ones(1, self.x_dtype))
+        # ones
+        self.scrub(np.ones(10, self.x_dtype))  # ones
+        # randn
+        x = self.rng.randn(10).astype(self.x_dtype)
+        if self.x_dtype in (np.complex64, np.complex128):
+            x += 1j * self.rng.randn(10)
+        self.scrub(x)
+        # ramp
+        self.scrub(np.arange(10).astype(self.x_dtype))
+        # 3D, random
+        size = (2, 3, 5)
+        x = self.rng.randn(*size).astype(self.x_dtype)
+        if self.x_dtype in (np.complex64, np.complex128):
+            x += 1j * self.rng.randn(*size)
+        for axis in range(len(size)):
+            self.scrub(x, axis=axis)
+        x = x[:, ::2, 1::3].T
+        for axis in range(len(size)):
+            self.scrub(x, axis=axis)
+
+    def scrub(self, x, axis=-1):
+        yr = np.apply_along_axis(upfirdn_naive, axis, x,
+                                 self.h, self.up, self.down)
+        want_len = _output_len(len(self.h), x.shape[axis], self.up, self.down)
+        assert yr.shape[axis] == want_len
+        y = upfirdn(self.h, x, self.up, self.down, axis=axis)
+        assert y.shape[axis] == want_len
+        assert y.shape == yr.shape
+        dtypes = (self.h.dtype, x.dtype)
+        if all(d == np.complex64 for d in dtypes):
+            assert_equal(y.dtype, np.complex64)
+        elif np.complex64 in dtypes and np.float32 in dtypes:
+            assert_equal(y.dtype, np.complex64)
+        elif all(d == np.float32 for d in dtypes):
+            assert_equal(y.dtype, np.float32)
+        elif np.complex128 in dtypes or np.complex64 in dtypes:
+            assert_equal(y.dtype, np.complex128)
+        else:
+            assert_equal(y.dtype, np.float64)
+        assert_allclose(yr, y)
+
+
+_UPFIRDN_TYPES = (int, np.float32, np.complex64, float, complex)
+
+
+class TestUpfirdn(object):
+
+    def test_valid_input(self):
+        assert_raises(ValueError, upfirdn, [1], [1], 1, 0)  # up or down < 1
+        assert_raises(ValueError, upfirdn, [], [1], 1, 1)  # h.ndim != 1
+        assert_raises(ValueError, upfirdn, [[1]], [1], 1, 1)
+
+    @pytest.mark.parametrize('len_h', [1, 2, 3, 4, 5])
+    @pytest.mark.parametrize('len_x', [1, 2, 3, 4, 5])
+    def test_singleton(self, len_h, len_x):
+        # gh-9844: lengths producing expected outputs
+        h = np.zeros(len_h)
+        h[len_h // 2] = 1.  # make h a delta
+        x = np.ones(len_x)
+        y = upfirdn(h, x, 1, 1)
+        want = np.pad(x, (len_h // 2, (len_h - 1) // 2), 'constant')
+        assert_allclose(y, want)
+
+    def test_shift_x(self):
+        # gh-9844: shifted x can change values?
+        y = upfirdn([1, 1], [1.], 1, 1)
+        assert_allclose(y, [1, 1])  # was [0, 1] in the issue
+        y = upfirdn([1, 1], [0., 1.], 1, 1)
+        assert_allclose(y, [0, 1, 1])
+
+    # A bunch of lengths/factors chosen because they exposed differences
+    # between the "old way" and new way of computing length, and then
+    # got `expected` from MATLAB
+    @pytest.mark.parametrize('len_h, len_x, up, down, expected', [
+        (2, 2, 5, 2, [1, 0, 0, 0]),
+        (2, 3, 6, 3, [1, 0, 1, 0, 1]),
+        (2, 4, 4, 3, [1, 0, 0, 0, 1]),
+        (3, 2, 6, 2, [1, 0, 0, 1, 0]),
+        (4, 11, 3, 5, [1, 0, 0, 1, 0, 0, 1]),
+    ])
+    def test_length_factors(self, len_h, len_x, up, down, expected):
+        # gh-9844: weird factors
+        h = np.zeros(len_h)
+        h[0] = 1.
+        x = np.ones(len_x)
+        y = upfirdn(h, x, up, down)
+        assert_allclose(y, expected)
+
+    @pytest.mark.parametrize('down, want_len', [  # lengths from MATLAB
+        (2, 5015),
+        (11, 912),
+        (79, 127),
+    ])
+    def test_vs_convolve(self, down, want_len):
+        # Check that up=1.0 gives same answer as convolve + slicing
+        random_state = np.random.RandomState(17)
+        try_types = (int, np.float32, np.complex64, float, complex)
+        size = 10000
+
+        for dtype in try_types:
+            x = random_state.randn(size).astype(dtype)
+            if dtype in (np.complex64, np.complex128):
+                x += 1j * random_state.randn(size)
+
+            h = firwin(31, 1. / down, window='hamming')
+            yl = upfirdn_naive(x, h, 1, down)
+            y = upfirdn(h, x, up=1, down=down)
+            assert y.shape == (want_len,)
+            assert yl.shape[0] == y.shape[0]
+            assert_allclose(yl, y, atol=1e-7, rtol=1e-7)
+
+    @pytest.mark.parametrize('x_dtype', _UPFIRDN_TYPES)
+    @pytest.mark.parametrize('h', (1., 1j))
+    @pytest.mark.parametrize('up, down', [(1, 1), (2, 2), (3, 2), (2, 3)])
+    def test_vs_naive_delta(self, x_dtype, h, up, down):
+        UpFIRDnCase(up, down, h, x_dtype)()
+
+    @pytest.mark.parametrize('x_dtype', _UPFIRDN_TYPES)
+    @pytest.mark.parametrize('h_dtype', _UPFIRDN_TYPES)
+    @pytest.mark.parametrize('p_max, q_max',
+                             list(product((10, 100), (10, 100))))
+    def test_vs_naive(self, x_dtype, h_dtype, p_max, q_max):
+        tests = self._random_factors(p_max, q_max, h_dtype, x_dtype)
+        for test in tests:
+            test()
+
+    def _random_factors(self, p_max, q_max, h_dtype, x_dtype):
+        n_rep = 3
+        longest_h = 25
+        random_state = np.random.RandomState(17)
+        tests = []
+
+        for _ in range(n_rep):
+            # Randomize the up/down factors somewhat
+            p_add = q_max if p_max > q_max else 1
+            q_add = p_max if q_max > p_max else 1
+            p = random_state.randint(p_max) + p_add
+            q = random_state.randint(q_max) + q_add
+
+            # Generate random FIR coefficients
+            len_h = random_state.randint(longest_h) + 1
+            h = np.atleast_1d(random_state.randint(len_h))
+            h = h.astype(h_dtype)
+            if h_dtype == complex:
+                h += 1j * random_state.randint(len_h)
+
+            tests.append(UpFIRDnCase(p, q, h, x_dtype))
+
+        return tests
+
+    @pytest.mark.parametrize('mode', _upfirdn_modes)
+    def test_extensions(self, mode):
+        """Test vs. manually computed results for modes not in numpy's pad."""
+        x = np.array([1, 2, 3, 1], dtype=float)
+        npre, npost = 6, 6
+        y = _pad_test(x, npre=npre, npost=npost, mode=mode)
+        if mode == 'antisymmetric':
+            y_expected = np.asarray(
+                [3, 1, -1, -3, -2, -1, 1, 2, 3, 1, -1, -3, -2, -1, 1, 2])
+        elif mode == 'antireflect':
+            y_expected = np.asarray(
+                [1, 2, 3, 1, -1, 0, 1, 2, 3, 1, -1, 0, 1, 2, 3, 1])
+        elif mode == 'smooth':
+            y_expected = np.asarray(
+                [-5, -4, -3, -2, -1, 0, 1, 2, 3, 1, -1, -3, -5, -7, -9, -11])
+        elif mode == "line":
+            lin_slope = (x[-1] - x[0]) / (len(x) - 1)
+            left = x[0] + np.arange(-npre, 0, 1) * lin_slope
+            right = x[-1] + np.arange(1, npost + 1) * lin_slope
+            y_expected = np.concatenate((left, x, right))
+        else:
+            y_expected = np.pad(x, (npre, npost), mode=mode)
+        assert_allclose(y, y_expected)
+
+    @pytest.mark.parametrize(
+        'size, h_len, mode, dtype',
+        product(
+            [8],
+            [4, 5, 26],  # include cases with h_len > 2*size
+            _upfirdn_modes,
+            [np.float32, np.float64, np.complex64, np.complex128],
+        )
+    )
+    def test_modes(self, size, h_len, mode, dtype):
+        random_state = np.random.RandomState(5)
+        x = random_state.randn(size).astype(dtype)
+        if dtype in (np.complex64, np.complex128):
+            x += 1j * random_state.randn(size)
+        h = np.arange(1, 1 + h_len, dtype=x.real.dtype)
+
+        y = upfirdn(h, x, up=1, down=1, mode=mode)
+        # expected result: pad the input, filter with zero padding, then crop
+        npad = h_len - 1
+        if mode in ['antisymmetric', 'antireflect', 'smooth', 'line']:
+            # use _pad_test test function for modes not supported by np.pad.
+            xpad = _pad_test(x, npre=npad, npost=npad, mode=mode)
+        else:
+            xpad = np.pad(x, npad, mode=mode)
+        ypad = upfirdn(h, xpad, up=1, down=1, mode='constant')
+        y_expected = ypad[npad:-npad]
+
+        atol = rtol = np.finfo(dtype).eps * 1e2
+        assert_allclose(y, y_expected, atol=atol, rtol=rtol)

venv/Lib/site-packages/scipy/signal/tests/test_waveforms.py

@@ -0,0 +1,351 @@
+import numpy as np
+from numpy.testing import (assert_almost_equal, assert_equal,
+                           assert_, assert_allclose, assert_array_equal)
+from pytest import raises as assert_raises
+
+import scipy.signal.waveforms as waveforms
+
+
+# These chirp_* functions are the instantaneous frequencies of the signals
+# returned by chirp().
+
+def chirp_linear(t, f0, f1, t1):
+    f = f0 + (f1 - f0) * t / t1
+    return f
+
+
+def chirp_quadratic(t, f0, f1, t1, vertex_zero=True):
+    if vertex_zero:
+        f = f0 + (f1 - f0) * t**2 / t1**2
+    else:
+        f = f1 - (f1 - f0) * (t1 - t)**2 / t1**2
+    return f
+
+
+def chirp_geometric(t, f0, f1, t1):
+    f = f0 * (f1/f0)**(t/t1)
+    return f
+
+
+def chirp_hyperbolic(t, f0, f1, t1):
+    f = f0*f1*t1 / ((f0 - f1)*t + f1*t1)
+    return f
+
+
+def compute_frequency(t, theta):
+    """
+    Compute theta'(t)/(2*pi), where theta'(t) is the derivative of theta(t).
+    """
+    # Assume theta and t are 1-D NumPy arrays.
+    # Assume that t is uniformly spaced.
+    dt = t[1] - t[0]
+    f = np.diff(theta)/(2*np.pi) / dt
+    tf = 0.5*(t[1:] + t[:-1])
+    return tf, f
+
+
+class TestChirp(object):
+
+    def test_linear_at_zero(self):
+        w = waveforms.chirp(t=0, f0=1.0, f1=2.0, t1=1.0, method='linear')
+        assert_almost_equal(w, 1.0)
+
+    def test_linear_freq_01(self):
+        method = 'linear'
+        f0 = 1.0
+        f1 = 2.0
+        t1 = 1.0
+        t = np.linspace(0, t1, 100)
+        phase = waveforms._chirp_phase(t, f0, t1, f1, method)
+        tf, f = compute_frequency(t, phase)
+        abserr = np.max(np.abs(f - chirp_linear(tf, f0, f1, t1)))
+        assert_(abserr < 1e-6)
+
+    def test_linear_freq_02(self):
+        method = 'linear'
+        f0 = 200.0
+        f1 = 100.0
+        t1 = 10.0
+        t = np.linspace(0, t1, 100)
+        phase = waveforms._chirp_phase(t, f0, t1, f1, method)
+        tf, f = compute_frequency(t, phase)
+        abserr = np.max(np.abs(f - chirp_linear(tf, f0, f1, t1)))
+        assert_(abserr < 1e-6)
+
+    def test_quadratic_at_zero(self):
+        w = waveforms.chirp(t=0, f0=1.0, f1=2.0, t1=1.0, method='quadratic')
+        assert_almost_equal(w, 1.0)
+
+    def test_quadratic_at_zero2(self):
+        w = waveforms.chirp(t=0, f0=1.0, f1=2.0, t1=1.0, method='quadratic',
+                            vertex_zero=False)
+        assert_almost_equal(w, 1.0)
+
+    def test_quadratic_freq_01(self):
+        method = 'quadratic'
+        f0 = 1.0
+        f1 = 2.0
+        t1 = 1.0
+        t = np.linspace(0, t1, 2000)
+        phase = waveforms._chirp_phase(t, f0, t1, f1, method)
+        tf, f = compute_frequency(t, phase)
+        abserr = np.max(np.abs(f - chirp_quadratic(tf, f0, f1, t1)))
+        assert_(abserr < 1e-6)
+
+    def test_quadratic_freq_02(self):
+        method = 'quadratic'
+        f0 = 20.0
+        f1 = 10.0
+        t1 = 10.0
+        t = np.linspace(0, t1, 2000)
+        phase = waveforms._chirp_phase(t, f0, t1, f1, method)
+        tf, f = compute_frequency(t, phase)
+        abserr = np.max(np.abs(f - chirp_quadratic(tf, f0, f1, t1)))
+        assert_(abserr < 1e-6)
+
+    def test_logarithmic_at_zero(self):
+        w = waveforms.chirp(t=0, f0=1.0, f1=2.0, t1=1.0, method='logarithmic')
+        assert_almost_equal(w, 1.0)
+
+    def test_logarithmic_freq_01(self):
+        method = 'logarithmic'
+        f0 = 1.0
+        f1 = 2.0
+        t1 = 1.0
+        t = np.linspace(0, t1, 10000)
+        phase = waveforms._chirp_phase(t, f0, t1, f1, method)
+        tf, f = compute_frequency(t, phase)
+        abserr = np.max(np.abs(f - chirp_geometric(tf, f0, f1, t1)))
+        assert_(abserr < 1e-6)
+
+    def test_logarithmic_freq_02(self):
+        method = 'logarithmic'
+        f0 = 200.0
+        f1 = 100.0
+        t1 = 10.0
+        t = np.linspace(0, t1, 10000)
+        phase = waveforms._chirp_phase(t, f0, t1, f1, method)
+        tf, f = compute_frequency(t, phase)
+        abserr = np.max(np.abs(f - chirp_geometric(tf, f0, f1, t1)))
+        assert_(abserr < 1e-6)
+
+    def test_logarithmic_freq_03(self):
+        method = 'logarithmic'
+        f0 = 100.0
+        f1 = 100.0
+        t1 = 10.0
+        t = np.linspace(0, t1, 10000)
+        phase = waveforms._chirp_phase(t, f0, t1, f1, method)
+        tf, f = compute_frequency(t, phase)
+        abserr = np.max(np.abs(f - chirp_geometric(tf, f0, f1, t1)))
+        assert_(abserr < 1e-6)
+
+    def test_hyperbolic_at_zero(self):
+        w = waveforms.chirp(t=0, f0=10.0, f1=1.0, t1=1.0, method='hyperbolic')
+        assert_almost_equal(w, 1.0)
+
+    def test_hyperbolic_freq_01(self):
+        method = 'hyperbolic'
+        t1 = 1.0
+        t = np.linspace(0, t1, 10000)
+        #           f0     f1
+        cases = [[10.0, 1.0],
+                 [1.0, 10.0],
+                 [-10.0, -1.0],
+                 [-1.0, -10.0]]
+        for f0, f1 in cases:
+            phase = waveforms._chirp_phase(t, f0, t1, f1, method)
+            tf, f = compute_frequency(t, phase)
+            expected = chirp_hyperbolic(tf, f0, f1, t1)
+            assert_allclose(f, expected)
+
+    def test_hyperbolic_zero_freq(self):
+        # f0=0 or f1=0 must raise a ValueError.
+        method = 'hyperbolic'
+        t1 = 1.0
+        t = np.linspace(0, t1, 5)
+        assert_raises(ValueError, waveforms.chirp, t, 0, t1, 1, method)
+        assert_raises(ValueError, waveforms.chirp, t, 1, t1, 0, method)
+
+    def test_unknown_method(self):
+        method = "foo"
+        f0 = 10.0
+        f1 = 20.0
+        t1 = 1.0
+        t = np.linspace(0, t1, 10)
+        assert_raises(ValueError, waveforms.chirp, t, f0, t1, f1, method)
+
+    def test_integer_t1(self):
+        f0 = 10.0
+        f1 = 20.0
+        t = np.linspace(-1, 1, 11)
+        t1 = 3.0
+        float_result = waveforms.chirp(t, f0, t1, f1)
+        t1 = 3
+        int_result = waveforms.chirp(t, f0, t1, f1)
+        err_msg = "Integer input 't1=3' gives wrong result"
+        assert_equal(int_result, float_result, err_msg=err_msg)
+
+    def test_integer_f0(self):
+        f1 = 20.0
+        t1 = 3.0
+        t = np.linspace(-1, 1, 11)
+        f0 = 10.0
+        float_result = waveforms.chirp(t, f0, t1, f1)
+        f0 = 10
+        int_result = waveforms.chirp(t, f0, t1, f1)
+        err_msg = "Integer input 'f0=10' gives wrong result"
+        assert_equal(int_result, float_result, err_msg=err_msg)
+
+    def test_integer_f1(self):
+        f0 = 10.0
+        t1 = 3.0
+        t = np.linspace(-1, 1, 11)
+        f1 = 20.0
+        float_result = waveforms.chirp(t, f0, t1, f1)
+        f1 = 20
+        int_result = waveforms.chirp(t, f0, t1, f1)
+        err_msg = "Integer input 'f1=20' gives wrong result"
+        assert_equal(int_result, float_result, err_msg=err_msg)
+
+    def test_integer_all(self):
+        f0 = 10
+        t1 = 3
+        f1 = 20
+        t = np.linspace(-1, 1, 11)
+        float_result = waveforms.chirp(t, float(f0), float(t1), float(f1))
+        int_result = waveforms.chirp(t, f0, t1, f1)
+        err_msg = "Integer input 'f0=10, t1=3, f1=20' gives wrong result"
+        assert_equal(int_result, float_result, err_msg=err_msg)
+
+
+class TestSweepPoly(object):
+
+    def test_sweep_poly_quad1(self):
+        p = np.poly1d([1.0, 0.0, 1.0])
+        t = np.linspace(0, 3.0, 10000)
+        phase = waveforms._sweep_poly_phase(t, p)
+        tf, f = compute_frequency(t, phase)
+        expected = p(tf)
+        abserr = np.max(np.abs(f - expected))
+        assert_(abserr < 1e-6)
+
+    def test_sweep_poly_const(self):
+        p = np.poly1d(2.0)
+        t = np.linspace(0, 3.0, 10000)
+        phase = waveforms._sweep_poly_phase(t, p)
+        tf, f = compute_frequency(t, phase)
+        expected = p(tf)
+        abserr = np.max(np.abs(f - expected))
+        assert_(abserr < 1e-6)
+
+    def test_sweep_poly_linear(self):
+        p = np.poly1d([-1.0, 10.0])
+        t = np.linspace(0, 3.0, 10000)
+        phase = waveforms._sweep_poly_phase(t, p)
+        tf, f = compute_frequency(t, phase)
+        expected = p(tf)
+        abserr = np.max(np.abs(f - expected))
+        assert_(abserr < 1e-6)
+
+    def test_sweep_poly_quad2(self):
+        p = np.poly1d([1.0, 0.0, -2.0])
+        t = np.linspace(0, 3.0, 10000)
+        phase = waveforms._sweep_poly_phase(t, p)
+        tf, f = compute_frequency(t, phase)
+        expected = p(tf)
+        abserr = np.max(np.abs(f - expected))
+        assert_(abserr < 1e-6)
+
+    def test_sweep_poly_cubic(self):
+        p = np.poly1d([2.0, 1.0, 0.0, -2.0])
+        t = np.linspace(0, 2.0, 10000)
+        phase = waveforms._sweep_poly_phase(t, p)
+        tf, f = compute_frequency(t, phase)
+        expected = p(tf)
+        abserr = np.max(np.abs(f - expected))
+        assert_(abserr < 1e-6)
+
+    def test_sweep_poly_cubic2(self):
+        """Use an array of coefficients instead of a poly1d."""
+        p = np.array([2.0, 1.0, 0.0, -2.0])
+        t = np.linspace(0, 2.0, 10000)
+        phase = waveforms._sweep_poly_phase(t, p)
+        tf, f = compute_frequency(t, phase)
+        expected = np.poly1d(p)(tf)
+        abserr = np.max(np.abs(f - expected))
+        assert_(abserr < 1e-6)
+
+    def test_sweep_poly_cubic3(self):
+        """Use a list of coefficients instead of a poly1d."""
+        p = [2.0, 1.0, 0.0, -2.0]
+        t = np.linspace(0, 2.0, 10000)
+        phase = waveforms._sweep_poly_phase(t, p)
+        tf, f = compute_frequency(t, phase)
+        expected = np.poly1d(p)(tf)
+        abserr = np.max(np.abs(f - expected))
+        assert_(abserr < 1e-6)
+
+
+class TestGaussPulse(object):
+
+    def test_integer_fc(self):
+        float_result = waveforms.gausspulse('cutoff', fc=1000.0)
+        int_result = waveforms.gausspulse('cutoff', fc=1000)
+        err_msg = "Integer input 'fc=1000' gives wrong result"
+        assert_equal(int_result, float_result, err_msg=err_msg)
+
+    def test_integer_bw(self):
+        float_result = waveforms.gausspulse('cutoff', bw=1.0)
+        int_result = waveforms.gausspulse('cutoff', bw=1)
+        err_msg = "Integer input 'bw=1' gives wrong result"
+        assert_equal(int_result, float_result, err_msg=err_msg)
+
+    def test_integer_bwr(self):
+        float_result = waveforms.gausspulse('cutoff', bwr=-6.0)
+        int_result = waveforms.gausspulse('cutoff', bwr=-6)
+        err_msg = "Integer input 'bwr=-6' gives wrong result"
+        assert_equal(int_result, float_result, err_msg=err_msg)
+
+    def test_integer_tpr(self):
+        float_result = waveforms.gausspulse('cutoff', tpr=-60.0)
+        int_result = waveforms.gausspulse('cutoff', tpr=-60)
+        err_msg = "Integer input 'tpr=-60' gives wrong result"
+        assert_equal(int_result, float_result, err_msg=err_msg)
+
+
+class TestUnitImpulse(object):
+
+    def test_no_index(self):
+        assert_array_equal(waveforms.unit_impulse(7), [1, 0, 0, 0, 0, 0, 0])
+        assert_array_equal(waveforms.unit_impulse((3, 3)),
+                           [[1, 0, 0], [0, 0, 0], [0, 0, 0]])
+
+    def test_index(self):
+        assert_array_equal(waveforms.unit_impulse(10, 3),
+                           [0, 0, 0, 1, 0, 0, 0, 0, 0, 0])
+        assert_array_equal(waveforms.unit_impulse((3, 3), (1, 1)),
+                           [[0, 0, 0], [0, 1, 0], [0, 0, 0]])
+
+        # Broadcasting
+        imp = waveforms.unit_impulse((4, 4), 2)
+        assert_array_equal(imp, np.array([[0, 0, 0, 0],
+                                          [0, 0, 0, 0],
+                                          [0, 0, 1, 0],
+                                          [0, 0, 0, 0]]))
+
+    def test_mid(self):
+        assert_array_equal(waveforms.unit_impulse((3, 3), 'mid'),
+                           [[0, 0, 0], [0, 1, 0], [0, 0, 0]])
+        assert_array_equal(waveforms.unit_impulse(9, 'mid'),
+                           [0, 0, 0, 0, 1, 0, 0, 0, 0])
+
+    def test_dtype(self):
+        imp = waveforms.unit_impulse(7)
+        assert_(np.issubdtype(imp.dtype, np.floating))
+
+        imp = waveforms.unit_impulse(5, 3, dtype=int)
+        assert_(np.issubdtype(imp.dtype, np.integer))
+
+        imp = waveforms.unit_impulse((5, 2), (3, 1), dtype=complex)
+        assert_(np.issubdtype(imp.dtype, np.complexfloating))

venv/Lib/site-packages/scipy/signal/tests/test_wavelets.py

@@ -0,0 +1,152 @@
+import numpy as np
+from numpy.testing import assert_equal, \
+    assert_array_equal, assert_array_almost_equal, assert_array_less, assert_
+
+from scipy.signal import wavelets
+
+
+class TestWavelets(object):
+    def test_qmf(self):
+        assert_array_equal(wavelets.qmf([1, 1]), [1, -1])
+
+    def test_daub(self):
+        for i in range(1, 15):
+            assert_equal(len(wavelets.daub(i)), i * 2)
+
+    def test_cascade(self):
+        for J in range(1, 7):
+            for i in range(1, 5):
+                lpcoef = wavelets.daub(i)
+                k = len(lpcoef)
+                x, phi, psi = wavelets.cascade(lpcoef, J)
+                assert_(len(x) == len(phi) == len(psi))
+                assert_equal(len(x), (k - 1) * 2 ** J)
+
+    def test_morlet(self):
+        x = wavelets.morlet(50, 4.1, complete=True)
+        y = wavelets.morlet(50, 4.1, complete=False)
+        # Test if complete and incomplete wavelet have same lengths:
+        assert_equal(len(x), len(y))
+        # Test if complete wavelet is less than incomplete wavelet:
+        assert_array_less(x, y)
+
+        x = wavelets.morlet(10, 50, complete=False)
+        y = wavelets.morlet(10, 50, complete=True)
+        # For large widths complete and incomplete wavelets should be
+        # identical within numerical precision:
+        assert_equal(x, y)
+
+        # miscellaneous tests:
+        x = np.array([1.73752399e-09 + 9.84327394e-25j,
+                      6.49471756e-01 + 0.00000000e+00j,
+                      1.73752399e-09 - 9.84327394e-25j])
+        y = wavelets.morlet(3, w=2, complete=True)
+        assert_array_almost_equal(x, y)
+
+        x = np.array([2.00947715e-09 + 9.84327394e-25j,
+                      7.51125544e-01 + 0.00000000e+00j,
+                      2.00947715e-09 - 9.84327394e-25j])
+        y = wavelets.morlet(3, w=2, complete=False)
+        assert_array_almost_equal(x, y, decimal=2)
+
+        x = wavelets.morlet(10000, s=4, complete=True)
+        y = wavelets.morlet(20000, s=8, complete=True)[5000:15000]
+        assert_array_almost_equal(x, y, decimal=2)
+
+        x = wavelets.morlet(10000, s=4, complete=False)
+        assert_array_almost_equal(y, x, decimal=2)
+        y = wavelets.morlet(20000, s=8, complete=False)[5000:15000]
+        assert_array_almost_equal(x, y, decimal=2)
+
+        x = wavelets.morlet(10000, w=3, s=5, complete=True)
+        y = wavelets.morlet(20000, w=3, s=10, complete=True)[5000:15000]
+        assert_array_almost_equal(x, y, decimal=2)
+
+        x = wavelets.morlet(10000, w=3, s=5, complete=False)
+        assert_array_almost_equal(y, x, decimal=2)
+        y = wavelets.morlet(20000, w=3, s=10, complete=False)[5000:15000]
+        assert_array_almost_equal(x, y, decimal=2)
+
+        x = wavelets.morlet(10000, w=7, s=10, complete=True)
+        y = wavelets.morlet(20000, w=7, s=20, complete=True)[5000:15000]
+        assert_array_almost_equal(x, y, decimal=2)
+
+        x = wavelets.morlet(10000, w=7, s=10, complete=False)
+        assert_array_almost_equal(x, y, decimal=2)
+        y = wavelets.morlet(20000, w=7, s=20, complete=False)[5000:15000]
+        assert_array_almost_equal(x, y, decimal=2)
+
+    def test_morlet2(self):
+        w = wavelets.morlet2(1.0, 0.5)
+        expected = (np.pi**(-0.25) * np.sqrt(1/0.5)).astype(complex)
+        assert_array_equal(w, expected)
+
+        lengths = [5, 11, 15, 51, 101]
+        for length in lengths:
+            w = wavelets.morlet2(length, 1.0)
+            assert_(len(w) == length)
+            max_loc = np.argmax(w)
+            assert_(max_loc == (length // 2))
+
+        points = 100
+        w = abs(wavelets.morlet2(points, 2.0))
+        half_vec = np.arange(0, points // 2)
+        assert_array_almost_equal(w[half_vec], w[-(half_vec + 1)])
+
+        x = np.array([5.03701224e-09 + 2.46742437e-24j,
+                      1.88279253e+00 + 0.00000000e+00j,
+                      5.03701224e-09 - 2.46742437e-24j])
+        y = wavelets.morlet2(3, s=1/(2*np.pi), w=2)
+        assert_array_almost_equal(x, y)
+
+    def test_ricker(self):
+        w = wavelets.ricker(1.0, 1)
+        expected = 2 / (np.sqrt(3 * 1.0) * (np.pi ** 0.25))
+        assert_array_equal(w, expected)
+
+        lengths = [5, 11, 15, 51, 101]
+        for length in lengths:
+            w = wavelets.ricker(length, 1.0)
+            assert_(len(w) == length)
+            max_loc = np.argmax(w)
+            assert_(max_loc == (length // 2))
+
+        points = 100
+        w = wavelets.ricker(points, 2.0)
+        half_vec = np.arange(0, points // 2)
+        #Wavelet should be symmetric
+        assert_array_almost_equal(w[half_vec], w[-(half_vec + 1)])
+
+        #Check zeros
+        aas = [5, 10, 15, 20, 30]
+        points = 99
+        for a in aas:
+            w = wavelets.ricker(points, a)
+            vec = np.arange(0, points) - (points - 1.0) / 2
+            exp_zero1 = np.argmin(np.abs(vec - a))
+            exp_zero2 = np.argmin(np.abs(vec + a))
+            assert_array_almost_equal(w[exp_zero1], 0)
+            assert_array_almost_equal(w[exp_zero2], 0)
+
+    def test_cwt(self):
+        widths = [1.0]
+        delta_wavelet = lambda s, t: np.array([1])
+        len_data = 100
+        test_data = np.sin(np.pi * np.arange(0, len_data) / 10.0)
+
+        #Test delta function input gives same data as output
+        cwt_dat = wavelets.cwt(test_data, delta_wavelet, widths)
+        assert_(cwt_dat.shape == (len(widths), len_data))
+        assert_array_almost_equal(test_data, cwt_dat.flatten())
+
+        #Check proper shape on output
+        widths = [1, 3, 4, 5, 10]
+        cwt_dat = wavelets.cwt(test_data, wavelets.ricker, widths)
+        assert_(cwt_dat.shape == (len(widths), len_data))
+
+        widths = [len_data * 10]
+        #Note: this wavelet isn't defined quite right, but is fine for this test
+        flat_wavelet = lambda l, w: np.full(w, 1 / w)
+        cwt_dat = wavelets.cwt(test_data, flat_wavelet, widths)
+        assert_array_almost_equal(cwt_dat, np.mean(test_data))
+