446 lines
15 KiB
Python
446 lines
15 KiB
Python
"""Includes test functions for fftpack.helper module
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Copied from fftpack.helper by Pearu Peterson, October 2005
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Modified for Array API, 2023
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"""
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from scipy.fft._helper import next_fast_len, _init_nd_shape_and_axes
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from numpy.testing import assert_equal
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from pytest import raises as assert_raises
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import pytest
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import numpy as np
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import sys
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from scipy.conftest import array_api_compatible
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from scipy._lib._array_api import xp_assert_close, SCIPY_DEVICE
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from scipy import fft
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pytestmark = [array_api_compatible, pytest.mark.usefixtures("skip_if_array_api")]
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skip_if_array_api = pytest.mark.skip_if_array_api
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_5_smooth_numbers = [
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2, 3, 4, 5, 6, 8, 9, 10,
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2 * 3 * 5,
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2**3 * 3**5,
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2**3 * 3**3 * 5**2,
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]
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def test_next_fast_len():
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for n in _5_smooth_numbers:
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assert_equal(next_fast_len(n), n)
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def _assert_n_smooth(x, n):
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x_orig = x
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if n < 2:
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assert False
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while True:
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q, r = divmod(x, 2)
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if r != 0:
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break
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x = q
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for d in range(3, n+1, 2):
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while True:
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q, r = divmod(x, d)
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if r != 0:
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break
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x = q
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assert x == 1, \
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f'x={x_orig} is not {n}-smooth, remainder={x}'
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@skip_if_array_api(np_only=True)
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class TestNextFastLen:
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def test_next_fast_len(self):
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np.random.seed(1234)
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def nums():
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yield from range(1, 1000)
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yield 2**5 * 3**5 * 4**5 + 1
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for n in nums():
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m = next_fast_len(n)
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_assert_n_smooth(m, 11)
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assert m == next_fast_len(n, False)
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m = next_fast_len(n, True)
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_assert_n_smooth(m, 5)
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def test_np_integers(self):
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ITYPES = [np.int16, np.int32, np.int64, np.uint16, np.uint32, np.uint64]
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for ityp in ITYPES:
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x = ityp(12345)
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testN = next_fast_len(x)
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assert_equal(testN, next_fast_len(int(x)))
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def testnext_fast_len_small(self):
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hams = {
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1: 1, 2: 2, 3: 3, 4: 4, 5: 5, 6: 6, 7: 8, 8: 8, 14: 15, 15: 15,
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16: 16, 17: 18, 1021: 1024, 1536: 1536, 51200000: 51200000
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}
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for x, y in hams.items():
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assert_equal(next_fast_len(x, True), y)
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@pytest.mark.xfail(sys.maxsize < 2**32,
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reason="Hamming Numbers too large for 32-bit",
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raises=ValueError, strict=True)
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def testnext_fast_len_big(self):
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hams = {
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510183360: 510183360, 510183360 + 1: 512000000,
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511000000: 512000000,
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854296875: 854296875, 854296875 + 1: 859963392,
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196608000000: 196608000000, 196608000000 + 1: 196830000000,
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8789062500000: 8789062500000, 8789062500000 + 1: 8796093022208,
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206391214080000: 206391214080000,
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206391214080000 + 1: 206624260800000,
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470184984576000: 470184984576000,
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470184984576000 + 1: 470715894135000,
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7222041363087360: 7222041363087360,
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7222041363087360 + 1: 7230196133913600,
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# power of 5 5**23
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11920928955078125: 11920928955078125,
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11920928955078125 - 1: 11920928955078125,
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# power of 3 3**34
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16677181699666569: 16677181699666569,
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16677181699666569 - 1: 16677181699666569,
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# power of 2 2**54
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18014398509481984: 18014398509481984,
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18014398509481984 - 1: 18014398509481984,
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# above this, int(ceil(n)) == int(ceil(n+1))
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19200000000000000: 19200000000000000,
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19200000000000000 + 1: 19221679687500000,
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288230376151711744: 288230376151711744,
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288230376151711744 + 1: 288325195312500000,
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288325195312500000 - 1: 288325195312500000,
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288325195312500000: 288325195312500000,
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288325195312500000 + 1: 288555831593533440,
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}
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for x, y in hams.items():
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assert_equal(next_fast_len(x, True), y)
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def test_keyword_args(self):
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assert next_fast_len(11, real=True) == 12
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assert next_fast_len(target=7, real=False) == 7
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@skip_if_array_api(cpu_only=True)
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class Test_init_nd_shape_and_axes:
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def test_py_0d_defaults(self, xp):
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x = xp.asarray(4)
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shape = None
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axes = None
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shape_expected = ()
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axes_expected = []
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shape_res, axes_res = _init_nd_shape_and_axes(x, shape, axes)
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assert shape_res == shape_expected
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assert axes_res == axes_expected
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def test_xp_0d_defaults(self, xp):
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x = xp.asarray(7.)
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shape = None
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axes = None
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shape_expected = ()
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axes_expected = []
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shape_res, axes_res = _init_nd_shape_and_axes(x, shape, axes)
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assert shape_res == shape_expected
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assert axes_res == axes_expected
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def test_py_1d_defaults(self, xp):
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x = xp.asarray([1, 2, 3])
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shape = None
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axes = None
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shape_expected = (3,)
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axes_expected = [0]
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shape_res, axes_res = _init_nd_shape_and_axes(x, shape, axes)
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assert shape_res == shape_expected
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assert axes_res == axes_expected
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def test_xp_1d_defaults(self, xp):
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x = xp.arange(0, 1, .1)
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shape = None
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axes = None
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shape_expected = (10,)
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axes_expected = [0]
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shape_res, axes_res = _init_nd_shape_and_axes(x, shape, axes)
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assert shape_res == shape_expected
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assert axes_res == axes_expected
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def test_py_2d_defaults(self, xp):
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x = xp.asarray([[1, 2, 3, 4],
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[5, 6, 7, 8]])
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shape = None
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axes = None
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shape_expected = (2, 4)
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axes_expected = [0, 1]
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shape_res, axes_res = _init_nd_shape_and_axes(x, shape, axes)
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assert shape_res == shape_expected
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assert axes_res == axes_expected
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def test_xp_2d_defaults(self, xp):
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x = xp.arange(0, 1, .1)
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x = xp.reshape(x, (5, 2))
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shape = None
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axes = None
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shape_expected = (5, 2)
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axes_expected = [0, 1]
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shape_res, axes_res = _init_nd_shape_and_axes(x, shape, axes)
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assert shape_res == shape_expected
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assert axes_res == axes_expected
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def test_xp_5d_defaults(self, xp):
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x = xp.zeros([6, 2, 5, 3, 4])
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shape = None
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axes = None
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shape_expected = (6, 2, 5, 3, 4)
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axes_expected = [0, 1, 2, 3, 4]
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shape_res, axes_res = _init_nd_shape_and_axes(x, shape, axes)
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assert shape_res == shape_expected
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assert axes_res == axes_expected
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def test_xp_5d_set_shape(self, xp):
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x = xp.zeros([6, 2, 5, 3, 4])
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shape = [10, -1, -1, 1, 4]
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axes = None
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shape_expected = (10, 2, 5, 1, 4)
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axes_expected = [0, 1, 2, 3, 4]
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shape_res, axes_res = _init_nd_shape_and_axes(x, shape, axes)
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assert shape_res == shape_expected
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assert axes_res == axes_expected
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def test_xp_5d_set_axes(self, xp):
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x = xp.zeros([6, 2, 5, 3, 4])
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shape = None
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axes = [4, 1, 2]
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shape_expected = (4, 2, 5)
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axes_expected = [4, 1, 2]
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shape_res, axes_res = _init_nd_shape_and_axes(x, shape, axes)
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assert shape_res == shape_expected
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assert axes_res == axes_expected
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def test_xp_5d_set_shape_axes(self, xp):
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x = xp.zeros([6, 2, 5, 3, 4])
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shape = [10, -1, 2]
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axes = [1, 0, 3]
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shape_expected = (10, 6, 2)
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axes_expected = [1, 0, 3]
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shape_res, axes_res = _init_nd_shape_and_axes(x, shape, axes)
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assert shape_res == shape_expected
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assert axes_res == axes_expected
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def test_shape_axes_subset(self, xp):
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x = xp.zeros((2, 3, 4, 5))
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shape, axes = _init_nd_shape_and_axes(x, shape=(5, 5, 5), axes=None)
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assert shape == (5, 5, 5)
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assert axes == [1, 2, 3]
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def test_errors(self, xp):
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x = xp.zeros(1)
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with assert_raises(ValueError, match="axes must be a scalar or "
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"iterable of integers"):
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_init_nd_shape_and_axes(x, shape=None, axes=[[1, 2], [3, 4]])
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with assert_raises(ValueError, match="axes must be a scalar or "
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"iterable of integers"):
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_init_nd_shape_and_axes(x, shape=None, axes=[1., 2., 3., 4.])
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with assert_raises(ValueError,
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match="axes exceeds dimensionality of input"):
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_init_nd_shape_and_axes(x, shape=None, axes=[1])
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with assert_raises(ValueError,
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match="axes exceeds dimensionality of input"):
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_init_nd_shape_and_axes(x, shape=None, axes=[-2])
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with assert_raises(ValueError,
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match="all axes must be unique"):
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_init_nd_shape_and_axes(x, shape=None, axes=[0, 0])
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with assert_raises(ValueError, match="shape must be a scalar or "
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"iterable of integers"):
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_init_nd_shape_and_axes(x, shape=[[1, 2], [3, 4]], axes=None)
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with assert_raises(ValueError, match="shape must be a scalar or "
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"iterable of integers"):
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_init_nd_shape_and_axes(x, shape=[1., 2., 3., 4.], axes=None)
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with assert_raises(ValueError,
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match="when given, axes and shape arguments"
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" have to be of the same length"):
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_init_nd_shape_and_axes(xp.zeros([1, 1, 1, 1]),
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shape=[1, 2, 3], axes=[1])
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with assert_raises(ValueError,
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match="invalid number of data points"
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r" \(\[0\]\) specified"):
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_init_nd_shape_and_axes(x, shape=[0], axes=None)
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with assert_raises(ValueError,
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match="invalid number of data points"
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r" \(\[-2\]\) specified"):
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_init_nd_shape_and_axes(x, shape=-2, axes=None)
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@skip_if_array_api('torch',
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reasons=['torch.fft not yet implemented by array-api-compat'])
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class TestFFTShift:
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def test_definition(self, xp):
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x = xp.asarray([0., 1, 2, 3, 4, -4, -3, -2, -1])
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y = xp.asarray([-4., -3, -2, -1, 0, 1, 2, 3, 4])
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xp_assert_close(fft.fftshift(x), y)
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xp_assert_close(fft.ifftshift(y), x)
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x = xp.asarray([0., 1, 2, 3, 4, -5, -4, -3, -2, -1])
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y = xp.asarray([-5., -4, -3, -2, -1, 0, 1, 2, 3, 4])
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xp_assert_close(fft.fftshift(x), y)
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xp_assert_close(fft.ifftshift(y), x)
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def test_inverse(self, xp):
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for n in [1, 4, 9, 100, 211]:
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x = xp.asarray(np.random.random((n,)))
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xp_assert_close(fft.ifftshift(fft.fftshift(x)), x)
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def test_axes_keyword(self, xp):
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freqs = xp.asarray([[0., 1, 2], [3, 4, -4], [-3, -2, -1]])
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shifted = xp.asarray([[-1., -3, -2], [2, 0, 1], [-4, 3, 4]])
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xp_assert_close(fft.fftshift(freqs, axes=(0, 1)), shifted)
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xp_assert_close(fft.fftshift(freqs, axes=0), fft.fftshift(freqs, axes=(0,)))
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xp_assert_close(fft.ifftshift(shifted, axes=(0, 1)), freqs)
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xp_assert_close(fft.ifftshift(shifted, axes=0),
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fft.ifftshift(shifted, axes=(0,)))
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xp_assert_close(fft.fftshift(freqs), shifted)
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xp_assert_close(fft.ifftshift(shifted), freqs)
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def test_uneven_dims(self, xp):
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""" Test 2D input, which has uneven dimension sizes """
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freqs = xp.asarray([
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[0, 1],
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[2, 3],
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[4, 5]
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], dtype=xp.float64)
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# shift in dimension 0
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shift_dim0 = xp.asarray([
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[4, 5],
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[0, 1],
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[2, 3]
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], dtype=xp.float64)
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xp_assert_close(fft.fftshift(freqs, axes=0), shift_dim0)
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xp_assert_close(fft.ifftshift(shift_dim0, axes=0), freqs)
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xp_assert_close(fft.fftshift(freqs, axes=(0,)), shift_dim0)
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xp_assert_close(fft.ifftshift(shift_dim0, axes=[0]), freqs)
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# shift in dimension 1
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shift_dim1 = xp.asarray([
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[1, 0],
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[3, 2],
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[5, 4]
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], dtype=xp.float64)
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xp_assert_close(fft.fftshift(freqs, axes=1), shift_dim1)
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xp_assert_close(fft.ifftshift(shift_dim1, axes=1), freqs)
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# shift in both dimensions
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shift_dim_both = xp.asarray([
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[5, 4],
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[1, 0],
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[3, 2]
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], dtype=xp.float64)
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xp_assert_close(fft.fftshift(freqs, axes=(0, 1)), shift_dim_both)
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xp_assert_close(fft.ifftshift(shift_dim_both, axes=(0, 1)), freqs)
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xp_assert_close(fft.fftshift(freqs, axes=[0, 1]), shift_dim_both)
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xp_assert_close(fft.ifftshift(shift_dim_both, axes=[0, 1]), freqs)
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# axes=None (default) shift in all dimensions
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xp_assert_close(fft.fftshift(freqs, axes=None), shift_dim_both)
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xp_assert_close(fft.ifftshift(shift_dim_both, axes=None), freqs)
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xp_assert_close(fft.fftshift(freqs), shift_dim_both)
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xp_assert_close(fft.ifftshift(shift_dim_both), freqs)
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@skip_if_array_api('array_api_strict', 'cupy',
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reasons=['fft not yet implemented by array-api-strict',
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'cupy.fft not yet implemented by array-api-compat'])
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class TestFFTFreq:
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def test_definition(self, xp):
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device = SCIPY_DEVICE
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try:
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x = xp.asarray([0, 1, 2, 3, 4, -4, -3, -2, -1],
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dtype=xp.float64, device=device)
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x2 = xp.asarray([0, 1, 2, 3, 4, -5, -4, -3, -2, -1],
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dtype=xp.float64, device=device)
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except TypeError:
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x = xp.asarray([0, 1, 2, 3, 4, -4, -3, -2, -1], dtype=xp.float64)
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x2 = xp.asarray([0, 1, 2, 3, 4, -5, -4, -3, -2, -1],
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dtype=xp.float64)
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y = xp.asarray(9 * fft.fftfreq(9, xp=xp), dtype=xp.float64)
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xp_assert_close(y, x)
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y = xp.asarray(9 * xp.pi * fft.fftfreq(9, xp.pi, xp=xp), dtype=xp.float64)
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xp_assert_close(y, x)
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y = xp.asarray(10 * fft.fftfreq(10, xp=xp), dtype=xp.float64)
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xp_assert_close(y, x2)
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y = xp.asarray(10 * xp.pi * fft.fftfreq(10, xp.pi, xp=xp), dtype=xp.float64)
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xp_assert_close(y, x2)
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@skip_if_array_api('array_api_strict', 'cupy',
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reasons=['fft not yet implemented by array-api-strict',
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'cupy.fft not yet implemented by array-api-compat'])
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class TestRFFTFreq:
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def test_definition(self, xp):
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device = SCIPY_DEVICE
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try:
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x = xp.asarray([0, 1, 2, 3, 4], dtype=xp.float64, device=device)
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x2 = xp.asarray([0, 1, 2, 3, 4, 5], dtype=xp.float64, device=device)
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except TypeError:
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# work around the `device` keyword not being implemented in numpy yet
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x = xp.asarray([0, 1, 2, 3, 4], dtype=xp.float64)
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x2 = xp.asarray([0, 1, 2, 3, 4, 5], dtype=xp.float64)
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y = xp.asarray(9 * fft.rfftfreq(9, xp=xp), dtype=xp.float64)
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xp_assert_close(y, x)
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y = xp.asarray(9 * xp.pi * fft.rfftfreq(9, xp.pi, xp=xp), dtype=xp.float64)
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xp_assert_close(y, x)
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y = xp.asarray(10 * fft.rfftfreq(10, xp=xp), dtype=xp.float64)
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xp_assert_close(y, x2)
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y = xp.asarray(10 * xp.pi * fft.rfftfreq(10, xp.pi, xp=xp), dtype=xp.float64)
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xp_assert_close(y, x2)
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