def test_zi_some_singleton_dims(self):
# lfilter doesn't really broadcast (no prepending of 1's). But does
# do singleton expansion if x and zi have the same ndim. This was
# broken only if a subset of the axes were singletons (gh-4681).
x = self.convert_dtype(np.zeros((3, 2, 5), 'l'))
b = self.convert_dtype(np.ones(5, 'l'))
a = self.convert_dtype(np.array([1, 0, 0]))
zi = np.ones((3, 1, 4), 'l')
zi[1, :, :] *= 2
zi[2, :, :] *= 3
zi = self.convert_dtype(zi)
zf_expected = self.convert_dtype(np.zeros((3, 2, 4), 'l'))
y_expected = np.zeros((3, 2, 5), 'l')
y_expected[:, :, :4] = [[[1]], [[2]], [[3]]]
y_expected = self.convert_dtype(y_expected)
# IIR
y_iir, zf_iir = lfilter(b, a, x, -1, zi)
assert_array_almost_equal(y_iir, y_expected)
assert_array_almost_equal(zf_iir, zf_expected)
# FIR
y_fir, zf_fir = lfilter(b, a[0], x, -1, zi)
assert_array_almost_equal(y_fir, y_expected)
assert_array_almost_equal(zf_fir, zf_expected)
def test_rank_3_FIR(self):
x = self.generate((4, 3, 2))
b = self.convert_dtype([1, 0, -1])
a = self.convert_dtype([1])
for axis in range(x.ndim):
y = lfilter(b, a, x, axis)
y_r = np.apply_along_axis(lambda w: lfilter(b, a, w), axis, x)
assert_array_almost_equal(y, y_r)
def test_rank_3_FIR_init_cond(self):
x = self.generate((4, 3, 2))
b = self.convert_dtype([1, 0, -1])
a = self.convert_dtype([1])
for axis in range(x.ndim):
zi_shape = list(x.shape)
zi_shape[axis] = 2
zi = self.convert_dtype(np.ones(zi_shape))
zi1 = self.convert_dtype([1, 1])
y, zf = lfilter(b, a, x, axis, zi)
lf0 = lambda w: lfilter(b, a, w, zi=zi1)[0]
lf1 = lambda w: lfilter(b, a, w, zi=zi1)[1]
y_r = np.apply_along_axis(lf0, axis, x)
zf_r = np.apply_along_axis(lf1, axis, x)
assert_array_almost_equal(y, y_r)
assert_array_almost_equal(zf, zf_r)
def test_rank_2_IIR_axis_1(self):
x = self.generate((4, 3))
b = self.convert_dtype([1, -1])
a = self.convert_dtype([0.5, 0.5])
y_r2_a1 = self.convert_dtype([[0, 2, 0], [6, -4, 6], [12, -10, 12],
[18, -16, 18]])
y = lfilter(b, a, x, axis=1)
assert_array_almost_equal(y_r2_a1, y)
def test_rank_2_IIR_axis_0(self):
x = self.generate((4, 3))
b = self.convert_dtype([1, -1])
a = self.convert_dtype([0.5, 0.5])
y_r2_a0 = self.convert_dtype([[0, 2, 4], [6, 4, 2], [0, 2, 4],
[6, 4, 2]])
y = lfilter(b, a, x, axis=0)
assert_array_almost_equal(y_r2_a0, y)
def test_scalar_a(self):
# a can be a scalar.
x = self.generate(6)
b = self.convert_dtype([1, 0, -1])
a = self.convert_dtype([1])
y_r = self.convert_dtype([0, 1, 2, 2, 2, 2])
y = lfilter(b, a[0], x)
assert_array_almost_equal(y, y_r)
def test_empty_zi(self):
# Regression test for #880: empty array for zi crashes.
x = self.generate((5, ))
a = self.convert_dtype([1])
b = self.convert_dtype([1])
zi = self.convert_dtype([])
y, zf = lfilter(b, a, x, zi=zi)
assert_array_almost_equal(y, x)
assert_equal(zf.dtype, self.dtype)
assert_equal(zf.size, 0)
def test_rank_1_FIR_init_cond(self):
x = self.generate((6, ))
b = self.convert_dtype([1, 1, 1])
a = self.convert_dtype([1])
zi = self.convert_dtype([1, 1])
y_r = self.convert_dtype([1, 2, 3, 6, 9, 12.])
zf_r = self.convert_dtype([9, 5])
y, zf = lfilter(b, a, x, zi=zi)
assert_array_almost_equal(y, y_r)
assert_array_almost_equal(zf, zf_r)
def test_rank_1_IIR_init_cond(self):
x = self.generate((6, ))
b = self.convert_dtype([1, 0, -1])
a = self.convert_dtype([0.5, -0.5])
zi = self.convert_dtype([1, 2])
y_r = self.convert_dtype([1, 5, 9, 13, 17, 21])
zf_r = self.convert_dtype([13, -10])
y, zf = lfilter(b, a, x, zi=zi)
assert_array_almost_equal(y, y_r)
assert_array_almost_equal(zf, zf_r)
def test_zi_pseudobroadcast(self):
x = self.generate((4, 5, 20))
b, a = butter(8, 0.2, output='ba')
b = self.convert_dtype(b)
a = self.convert_dtype(a)
zi_size = b.shape[0] - 1
# lfilter requires x.ndim == zi.ndim exactly. However, zi can have
# length 1 dimensions.
zi_full = self.convert_dtype(np.ones((4, 5, zi_size)))
zi_sing = self.convert_dtype(np.ones((1, 1, zi_size)))
y_full, zf_full = lfilter(b, a, x, zi=zi_full)
y_sing, zf_sing = lfilter(b, a, x, zi=zi_sing)
assert_array_almost_equal(y_sing, y_full)
assert_array_almost_equal(zf_full, zf_sing)
# lfilter does not prepend ones
assert_raises(ValueError, lfilter, b, a, x, -1, np.ones(zi_size))
def test_do_not_modify_a_b_FIR(self):
x = self.generate((6, ))
b = self.convert_dtype([1, 0, 1])
b0 = b.copy()
a = self.convert_dtype([2])
a0 = a.copy()
y_r = self.convert_dtype([0, 0.5, 1, 2, 3, 4.])
y_f = lfilter(b, a, x)
assert_array_almost_equal(y_f, y_r)
assert_equal(b, b0)
assert_equal(a, a0)
def test_do_not_modify_a_b_IIR(self):
x = self.generate((6, ))
b = self.convert_dtype([1, -1])
b0 = b.copy()
a = self.convert_dtype([0.5, -0.5])
a0 = a.copy()
y_r = self.convert_dtype([0, 2, 4, 6, 8, 10.])
y_f = lfilter(b, a, x)
assert_array_almost_equal(y_f, y_r)
assert_equal(b, b0)
assert_equal(a, a0)
def test_short_x_IIR(self):
# regression test for #5116
# x shorter than b, with non None zi fails
a = self.convert_dtype([1, 1])
b = self.convert_dtype([1, 0, -1])
zi = self.convert_dtype([2, 7])
x = self.convert_dtype([72])
ye = self.convert_dtype([74])
zfe = self.convert_dtype([-67, -72])
y, zf = lfilter(b, a, x, zi=zi)
assert_array_almost_equal(y, ye)
assert_array_almost_equal(zf, zfe)
def test_rank_2_IIR_axis_0_init_cond(self):
x = self.generate((4, 3))
b = self.convert_dtype([1, -1])
a = self.convert_dtype([0.5, 0.5])
zi = self.convert_dtype(np.ones((4, 1)))
y_r2_a0_1 = self.convert_dtype([[1, 1, 1], [7, -5, 7], [13, -11, 13],
[19, -17, 19]])
zf_r = self.convert_dtype([-5, -17, -29, -41])[:, np.newaxis]
y, zf = lfilter(b, a, x, axis=1, zi=zi)
assert_array_almost_equal(y_r2_a0_1, y)
assert_array_almost_equal(zf, zf_r)
def test_rank_2_IIR_axis_1_init_cond(self):
x = self.generate((4, 3))
b = self.convert_dtype([1, -1])
a = self.convert_dtype([0.5, 0.5])
zi = self.convert_dtype(np.ones((1, 3)))
y_r2_a0_0 = self.convert_dtype([[1, 3, 5], [5, 3, 1], [1, 3, 5],
[5, 3, 1]])
zf_r = self.convert_dtype([[-23, -23, -23]])
y, zf = lfilter(b, a, x, axis=0, zi=zi)
assert_array_almost_equal(y_r2_a0_0, y)
assert_array_almost_equal(zf, zf_r)
def test_rank_1_IIR(self):
x = self.generate((6, ))
b = self.convert_dtype([1, -1])
a = self.convert_dtype([0.5, -0.5])
y_r = self.convert_dtype([0, 2, 4, 6, 8, 10.])
assert_array_almost_equal(lfilter(b, a, x), y_r)
def test_rank_1_FIR(self):
x = self.generate((6, ))
b = self.convert_dtype([1, 1])
a = self.convert_dtype([1])
y_r = self.convert_dtype([0, 1, 3, 5, 7, 9.])
assert_array_almost_equal(lfilter(b, a, x), y_r)
