571 lines
20 KiB
Python
571 lines
20 KiB
Python
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"""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, prev_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 (
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xp_assert_close, get_xp_devices, device, array_namespace
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)
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from scipy import fft
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pytestmark = [array_api_compatible, pytest.mark.usefixtures("skip_xp_backends")]
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skip_xp_backends = pytest.mark.skip_xp_backends
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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_xp_backends(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_xp_backends(np_only=True)
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class TestPrevFastLen:
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def test_prev_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 = prev_fast_len(n)
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_assert_n_smooth(m, 11)
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assert m == prev_fast_len(n, False)
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m = prev_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,
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np.uint64]
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for ityp in ITYPES:
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x = ityp(12345)
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testN = prev_fast_len(x)
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assert_equal(testN, prev_fast_len(int(x)))
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testN = prev_fast_len(x, real=True)
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assert_equal(testN, prev_fast_len(int(x), real=True))
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def testprev_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: 6, 8: 8, 14: 12, 15: 15,
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16: 16, 17: 16, 1021: 1000, 1536: 1536, 51200000: 51200000
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}
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for x, y in hams.items():
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assert_equal(prev_fast_len(x, True), y)
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hams = {
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1: 1, 2: 2, 3: 3, 4: 4, 5: 5, 6: 6, 7: 7, 8: 8, 9: 9, 10: 10,
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11: 11, 12: 12, 13: 12, 14: 14, 15: 15, 16: 16, 17: 16, 18: 18,
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19: 18, 20: 20, 21: 21, 22: 22, 120: 120, 121: 121, 122: 121,
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1021: 1008, 1536: 1536, 51200000: 51200000
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}
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for x, y in hams.items():
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assert_equal(prev_fast_len(x, False), 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 testprev_fast_len_big(self):
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hams = {
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# 2**6 * 3**13 * 5**1
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510183360: 510183360,
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510183360 + 1: 510183360,
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510183360 - 1: 509607936, # 2**21 * 3**5
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# 2**6 * 5**6 * 7**1 * 73**1
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511000000: 510183360,
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511000000 + 1: 510183360,
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511000000 - 1: 510183360, # 2**6 * 3**13 * 5**1
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# 3**7 * 5**8
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854296875: 854296875,
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854296875 + 1: 854296875,
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854296875 - 1: 850305600, # 2**6 * 3**12 * 5**2
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# 2**22 * 3**1 * 5**6
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196608000000: 196608000000,
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196608000000 + 1: 196608000000,
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196608000000 - 1: 195910410240, # 2**13 * 3**14 * 5**1
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# 2**5 * 3**2 * 5**15
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8789062500000: 8789062500000,
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8789062500000 + 1: 8789062500000,
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8789062500000 - 1: 8748000000000, # 2**11 * 3**7 * 5**9
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# 2**24 * 3**9 * 5**4
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206391214080000: 206391214080000,
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206391214080000 + 1: 206391214080000,
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206391214080000 - 1: 206158430208000, # 2**39 * 3**1 * 5**3
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# 2**18 * 3**15 * 5**3
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470184984576000: 470184984576000,
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470184984576000 + 1: 470184984576000,
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470184984576000 - 1: 469654673817600, # 2**33 * 3**7 **5**2
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# 2**25 * 3**16 * 5**1
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7222041363087360: 7222041363087360,
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7222041363087360 + 1: 7222041363087360,
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7222041363087360 - 1: 7213895789838336, # 2**40 * 3**8
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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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11920928955078125 - 1: 11901557422080000, # 2**14 * 3**19 * 5**4
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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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16677181699666569 - 1: 16607531250000000, # 2**7 * 3**12 * 5**12
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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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18014398509481984 - 1: 18000000000000000, # 2**16 * 3**2 * 5**15
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# 2**20 * 3**1 * 5**14
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19200000000000000: 19200000000000000,
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19200000000000000 + 1: 19200000000000000,
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19200000000000000 - 1: 19131876000000000, # 2**11 * 3**14 * 5**9
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# 2**58
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288230376151711744: 288230376151711744,
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288230376151711744 + 1: 288230376151711744,
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288230376151711744 - 1: 288000000000000000, # 2**20 * 3**2 * 5**15
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# 2**5 * 3**10 * 5**16
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288325195312500000: 288325195312500000,
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288325195312500000 + 1: 288325195312500000,
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288325195312500000 - 1: 288230376151711744, # 2**58
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}
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for x, y in hams.items():
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assert_equal(prev_fast_len(x, True), y)
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def test_keyword_args(self):
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assert prev_fast_len(11, real=True) == 10
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assert prev_fast_len(target=7, real=False) == 7
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@skip_xp_backends(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])
|
||
|
|
shape = [10, -1, -1, 1, 4]
|
||
|
|
axes = None
|
||
|
|
|
||
|
|
shape_expected = (10, 2, 5, 1, 4)
|
||
|
|
axes_expected = [0, 1, 2, 3, 4]
|
||
|
|
|
||
|
|
shape_res, axes_res = _init_nd_shape_and_axes(x, shape, axes)
|
||
|
|
|
||
|
|
assert shape_res == shape_expected
|
||
|
|
assert axes_res == axes_expected
|
||
|
|
|
||
|
|
def test_xp_5d_set_axes(self, xp):
|
||
|
|
x = xp.zeros([6, 2, 5, 3, 4])
|
||
|
|
shape = None
|
||
|
|
axes = [4, 1, 2]
|
||
|
|
|
||
|
|
shape_expected = (4, 2, 5)
|
||
|
|
axes_expected = [4, 1, 2]
|
||
|
|
|
||
|
|
shape_res, axes_res = _init_nd_shape_and_axes(x, shape, axes)
|
||
|
|
|
||
|
|
assert shape_res == shape_expected
|
||
|
|
assert axes_res == axes_expected
|
||
|
|
|
||
|
|
def test_xp_5d_set_shape_axes(self, xp):
|
||
|
|
x = xp.zeros([6, 2, 5, 3, 4])
|
||
|
|
shape = [10, -1, 2]
|
||
|
|
axes = [1, 0, 3]
|
||
|
|
|
||
|
|
shape_expected = (10, 6, 2)
|
||
|
|
axes_expected = [1, 0, 3]
|
||
|
|
|
||
|
|
shape_res, axes_res = _init_nd_shape_and_axes(x, shape, axes)
|
||
|
|
|
||
|
|
assert shape_res == shape_expected
|
||
|
|
assert axes_res == axes_expected
|
||
|
|
|
||
|
|
def test_shape_axes_subset(self, xp):
|
||
|
|
x = xp.zeros((2, 3, 4, 5))
|
||
|
|
shape, axes = _init_nd_shape_and_axes(x, shape=(5, 5, 5), axes=None)
|
||
|
|
|
||
|
|
assert shape == (5, 5, 5)
|
||
|
|
assert axes == [1, 2, 3]
|
||
|
|
|
||
|
|
def test_errors(self, xp):
|
||
|
|
x = xp.zeros(1)
|
||
|
|
with assert_raises(ValueError, match="axes must be a scalar or "
|
||
|
|
"iterable of integers"):
|
||
|
|
_init_nd_shape_and_axes(x, shape=None, axes=[[1, 2], [3, 4]])
|
||
|
|
|
||
|
|
with assert_raises(ValueError, match="axes must be a scalar or "
|
||
|
|
"iterable of integers"):
|
||
|
|
_init_nd_shape_and_axes(x, shape=None, axes=[1., 2., 3., 4.])
|
||
|
|
|
||
|
|
with assert_raises(ValueError,
|
||
|
|
match="axes exceeds dimensionality of input"):
|
||
|
|
_init_nd_shape_and_axes(x, shape=None, axes=[1])
|
||
|
|
|
||
|
|
with assert_raises(ValueError,
|
||
|
|
match="axes exceeds dimensionality of input"):
|
||
|
|
_init_nd_shape_and_axes(x, shape=None, axes=[-2])
|
||
|
|
|
||
|
|
with assert_raises(ValueError,
|
||
|
|
match="all axes must be unique"):
|
||
|
|
_init_nd_shape_and_axes(x, shape=None, axes=[0, 0])
|
||
|
|
|
||
|
|
with assert_raises(ValueError, match="shape must be a scalar or "
|
||
|
|
"iterable of integers"):
|
||
|
|
_init_nd_shape_and_axes(x, shape=[[1, 2], [3, 4]], axes=None)
|
||
|
|
|
||
|
|
with assert_raises(ValueError, match="shape must be a scalar or "
|
||
|
|
"iterable of integers"):
|
||
|
|
_init_nd_shape_and_axes(x, shape=[1., 2., 3., 4.], axes=None)
|
||
|
|
|
||
|
|
with assert_raises(ValueError,
|
||
|
|
match="when given, axes and shape arguments"
|
||
|
|
" have to be of the same length"):
|
||
|
|
_init_nd_shape_and_axes(xp.zeros([1, 1, 1, 1]),
|
||
|
|
shape=[1, 2, 3], axes=[1])
|
||
|
|
|
||
|
|
with assert_raises(ValueError,
|
||
|
|
match="invalid number of data points"
|
||
|
|
r" \(\[0\]\) specified"):
|
||
|
|
_init_nd_shape_and_axes(x, shape=[0], axes=None)
|
||
|
|
|
||
|
|
with assert_raises(ValueError,
|
||
|
|
match="invalid number of data points"
|
||
|
|
r" \(\[-2\]\) specified"):
|
||
|
|
_init_nd_shape_and_axes(x, shape=-2, axes=None)
|
||
|
|
|
||
|
|
|
||
|
|
class TestFFTShift:
|
||
|
|
|
||
|
|
def test_definition(self, xp):
|
||
|
|
x = xp.asarray([0., 1, 2, 3, 4, -4, -3, -2, -1])
|
||
|
|
y = xp.asarray([-4., -3, -2, -1, 0, 1, 2, 3, 4])
|
||
|
|
xp_assert_close(fft.fftshift(x), y)
|
||
|
|
xp_assert_close(fft.ifftshift(y), x)
|
||
|
|
x = xp.asarray([0., 1, 2, 3, 4, -5, -4, -3, -2, -1])
|
||
|
|
y = xp.asarray([-5., -4, -3, -2, -1, 0, 1, 2, 3, 4])
|
||
|
|
xp_assert_close(fft.fftshift(x), y)
|
||
|
|
xp_assert_close(fft.ifftshift(y), x)
|
||
|
|
|
||
|
|
def test_inverse(self, xp):
|
||
|
|
for n in [1, 4, 9, 100, 211]:
|
||
|
|
x = xp.asarray(np.random.random((n,)))
|
||
|
|
xp_assert_close(fft.ifftshift(fft.fftshift(x)), x)
|
||
|
|
|
||
|
|
def test_axes_keyword(self, xp):
|
||
|
|
freqs = xp.asarray([[0., 1, 2], [3, 4, -4], [-3, -2, -1]])
|
||
|
|
shifted = xp.asarray([[-1., -3, -2], [2, 0, 1], [-4, 3, 4]])
|
||
|
|
xp_assert_close(fft.fftshift(freqs, axes=(0, 1)), shifted)
|
||
|
|
xp_assert_close(fft.fftshift(freqs, axes=0), fft.fftshift(freqs, axes=(0,)))
|
||
|
|
xp_assert_close(fft.ifftshift(shifted, axes=(0, 1)), freqs)
|
||
|
|
xp_assert_close(fft.ifftshift(shifted, axes=0),
|
||
|
|
fft.ifftshift(shifted, axes=(0,)))
|
||
|
|
xp_assert_close(fft.fftshift(freqs), shifted)
|
||
|
|
xp_assert_close(fft.ifftshift(shifted), freqs)
|
||
|
|
|
||
|
|
def test_uneven_dims(self, xp):
|
||
|
|
""" Test 2D input, which has uneven dimension sizes """
|
||
|
|
freqs = xp.asarray([
|
||
|
|
[0, 1],
|
||
|
|
[2, 3],
|
||
|
|
[4, 5]
|
||
|
|
], dtype=xp.float64)
|
||
|
|
|
||
|
|
# shift in dimension 0
|
||
|
|
shift_dim0 = xp.asarray([
|
||
|
|
[4, 5],
|
||
|
|
[0, 1],
|
||
|
|
[2, 3]
|
||
|
|
], dtype=xp.float64)
|
||
|
|
xp_assert_close(fft.fftshift(freqs, axes=0), shift_dim0)
|
||
|
|
xp_assert_close(fft.ifftshift(shift_dim0, axes=0), freqs)
|
||
|
|
xp_assert_close(fft.fftshift(freqs, axes=(0,)), shift_dim0)
|
||
|
|
xp_assert_close(fft.ifftshift(shift_dim0, axes=[0]), freqs)
|
||
|
|
|
||
|
|
# shift in dimension 1
|
||
|
|
shift_dim1 = xp.asarray([
|
||
|
|
[1, 0],
|
||
|
|
[3, 2],
|
||
|
|
[5, 4]
|
||
|
|
], dtype=xp.float64)
|
||
|
|
xp_assert_close(fft.fftshift(freqs, axes=1), shift_dim1)
|
||
|
|
xp_assert_close(fft.ifftshift(shift_dim1, axes=1), freqs)
|
||
|
|
|
||
|
|
# shift in both dimensions
|
||
|
|
shift_dim_both = xp.asarray([
|
||
|
|
[5, 4],
|
||
|
|
[1, 0],
|
||
|
|
[3, 2]
|
||
|
|
], dtype=xp.float64)
|
||
|
|
xp_assert_close(fft.fftshift(freqs, axes=(0, 1)), shift_dim_both)
|
||
|
|
xp_assert_close(fft.ifftshift(shift_dim_both, axes=(0, 1)), freqs)
|
||
|
|
xp_assert_close(fft.fftshift(freqs, axes=[0, 1]), shift_dim_both)
|
||
|
|
xp_assert_close(fft.ifftshift(shift_dim_both, axes=[0, 1]), freqs)
|
||
|
|
|
||
|
|
# axes=None (default) shift in all dimensions
|
||
|
|
xp_assert_close(fft.fftshift(freqs, axes=None), shift_dim_both)
|
||
|
|
xp_assert_close(fft.ifftshift(shift_dim_both, axes=None), freqs)
|
||
|
|
xp_assert_close(fft.fftshift(freqs), shift_dim_both)
|
||
|
|
xp_assert_close(fft.ifftshift(shift_dim_both), freqs)
|
||
|
|
|
||
|
|
|
||
|
|
@skip_xp_backends("cupy", "jax.numpy",
|
||
|
|
reasons=["CuPy has not implemented the `device` param",
|
||
|
|
"JAX has not implemented the `device` param"])
|
||
|
|
class TestFFTFreq:
|
||
|
|
|
||
|
|
def test_definition(self, xp):
|
||
|
|
x = xp.asarray([0, 1, 2, 3, 4, -4, -3, -2, -1], dtype=xp.float64)
|
||
|
|
x2 = xp.asarray([0, 1, 2, 3, 4, -5, -4, -3, -2, -1], dtype=xp.float64)
|
||
|
|
|
||
|
|
# default dtype varies across backends
|
||
|
|
|
||
|
|
y = 9 * fft.fftfreq(9, xp=xp)
|
||
|
|
xp_assert_close(y, x, check_dtype=False, check_namespace=True)
|
||
|
|
|
||
|
|
y = 9 * xp.pi * fft.fftfreq(9, xp.pi, xp=xp)
|
||
|
|
xp_assert_close(y, x, check_dtype=False)
|
||
|
|
|
||
|
|
y = 10 * fft.fftfreq(10, xp=xp)
|
||
|
|
xp_assert_close(y, x2, check_dtype=False)
|
||
|
|
|
||
|
|
y = 10 * xp.pi * fft.fftfreq(10, xp.pi, xp=xp)
|
||
|
|
xp_assert_close(y, x2, check_dtype=False)
|
||
|
|
|
||
|
|
def test_device(self, xp):
|
||
|
|
xp_test = array_namespace(xp.empty(0))
|
||
|
|
devices = get_xp_devices(xp)
|
||
|
|
for d in devices:
|
||
|
|
y = fft.fftfreq(9, xp=xp, device=d)
|
||
|
|
x = xp_test.empty(0, device=d)
|
||
|
|
assert device(y) == device(x)
|
||
|
|
|
||
|
|
|
||
|
|
@skip_xp_backends("cupy", "jax.numpy",
|
||
|
|
reasons=["CuPy has not implemented the `device` param",
|
||
|
|
"JAX has not implemented the `device` param"])
|
||
|
|
class TestRFFTFreq:
|
||
|
|
|
||
|
|
def test_definition(self, xp):
|
||
|
|
x = xp.asarray([0, 1, 2, 3, 4], dtype=xp.float64)
|
||
|
|
x2 = xp.asarray([0, 1, 2, 3, 4, 5], dtype=xp.float64)
|
||
|
|
|
||
|
|
# default dtype varies across backends
|
||
|
|
|
||
|
|
y = 9 * fft.rfftfreq(9, xp=xp)
|
||
|
|
xp_assert_close(y, x, check_dtype=False, check_namespace=True)
|
||
|
|
|
||
|
|
y = 9 * xp.pi * fft.rfftfreq(9, xp.pi, xp=xp)
|
||
|
|
xp_assert_close(y, x, check_dtype=False)
|
||
|
|
|
||
|
|
y = 10 * fft.rfftfreq(10, xp=xp)
|
||
|
|
xp_assert_close(y, x2, check_dtype=False)
|
||
|
|
|
||
|
|
y = 10 * xp.pi * fft.rfftfreq(10, xp.pi, xp=xp)
|
||
|
|
xp_assert_close(y, x2, check_dtype=False)
|
||
|
|
|
||
|
|
def test_device(self, xp):
|
||
|
|
xp_test = array_namespace(xp.empty(0))
|
||
|
|
devices = get_xp_devices(xp)
|
||
|
|
for d in devices:
|
||
|
|
y = fft.rfftfreq(9, xp=xp, device=d)
|
||
|
|
x = xp_test.empty(0, device=d)
|
||
|
|
assert device(y) == device(x)
|