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from __future__ import print_function
from time import time
import numpy as np
from scipy.fftpack import dctn as scipy_dctn
from scipy.fftpack import dstn as scipy_dstn
import scipy.fftpack # pylint: disable=unused-import
from mpi4py_fft import fftw
has_pyfftw = True
try:
import pyfftw
except ImportError:
has_pyfftw = False
abstol = dict(f=5e-4, d=1e-12, g=1e-14)
kinds = {'dst4': fftw.FFTW_RODFT11, # no scipy to compare with
'dct4': fftw.FFTW_REDFT11, # no scipy to compare with
'dst3': fftw.FFTW_RODFT01,
'dct3': fftw.FFTW_REDFT01,
'dct2': fftw.FFTW_REDFT10,
'dst2': fftw.FFTW_RODFT10,
'dct1': fftw.FFTW_REDFT00,
'dst1': fftw.FFTW_RODFT00}
rkinds = {val: key for key, val in kinds.items()}
def allclose(a, b):
atol = abstol[a.dtype.char.lower()]
return np.allclose(a, b, rtol=0, atol=atol)
def test_fftw():
from itertools import product
dims = (1, 2, 3)
sizes = (7, 8, 10)
types = ''
for t in 'fdg':
if fftw.get_fftw_lib(t):
types += t
fflags = (fftw.FFTW_ESTIMATE, fftw.FFTW_DESTROY_INPUT)
iflags = (fftw.FFTW_ESTIMATE, fftw.FFTW_DESTROY_INPUT)
for threads in (1, 2):
for typecode in types:
for dim in dims:
for shape in product(*([sizes]*dim)):
allaxes = tuple(reversed(range(dim)))
for i in range(dim):
for j in range(i+1, dim):
axes = allaxes[i:j]
#print(shape, axes, typecode, threads)
# r2c - c2r
input_array = fftw.aligned(shape, dtype=typecode)
outshape = list(shape)
outshape[axes[-1]] = shape[axes[-1]]//2+1
output_array = fftw.aligned(outshape, dtype=typecode.upper())
oa = output_array if typecode == 'd' else None # Test for both types of signature
rfftn = fftw.rfftn(input_array, None, axes, threads, fflags, output_array=oa)
A = np.random.random(shape).astype(typecode)
input_array[:] = A
B = rfftn()
assert id(B) == id(rfftn.output_array)
if has_pyfftw:
B2 = pyfftw.interfaces.numpy_fft.rfftn(input_array, axes=axes)
assert allclose(B, B2), np.linalg.norm(B-B2)
ia = input_array if typecode == 'd' else None
sa = np.take(input_array.shape, axes) if shape[axes[-1]] % 2 == 1 else None
irfftn = fftw.irfftn(output_array, sa, axes, threads, iflags, output_array=ia)
irfftn.input_array[...] = B
A2 = irfftn(normalize=True)
assert allclose(A, A2), np.linalg.norm(A-A2)
hfftn = fftw.hfftn(output_array, sa, axes, threads, fflags, output_array=ia)
hfftn.input_array[...] = B
AC = hfftn().copy()
ihfftn = fftw.ihfftn(input_array, None, axes, threads, iflags, output_array=oa)
A2 = ihfftn(AC, implicit=False, normalize=True)
assert allclose(A2, B), print(np.linalg.norm(A2-B))
# c2c
input_array = fftw.aligned(shape, dtype=typecode.upper())
output_array = fftw.aligned_like(input_array)
oa = output_array if typecode=='d' else None
fftn = fftw.fftn(input_array, None, axes, threads, fflags, output_array=oa)
C = np.random.random(shape).astype(typecode.upper())
fftn.input_array[...] = C
D = fftn().copy()
ifftn = fftw.ifftn(input_array, None, axes, threads, iflags, output_array=oa)
ifftn.input_array[...] = D
C2 = ifftn(normalize=True)
assert allclose(C, C2), np.linalg.norm(C-C2)
if has_pyfftw:
D2 = pyfftw.interfaces.numpy_fft.fftn(C, axes=axes)
assert allclose(D, D2), np.linalg.norm(D-D2)
# r2r
input_array = fftw.aligned(shape, dtype=typecode)
output_array = fftw.aligned_like(input_array)
oa = output_array if typecode =='d' else None
for type in (1, 2, 3, 4):
dct = fftw.dctn(input_array, None, axes, type, threads, fflags, output_array=oa)
B = dct(A).copy()
idct = fftw.idctn(input_array, None, axes, type, threads, iflags, output_array=oa)
A2 = idct(B, implicit=True, normalize=True)
assert allclose(A, A2), np.linalg.norm(A-A2)
if typecode != 'g' and type != 4:
B2 = scipy_dctn(A, axes=axes, type=type)
assert allclose(B, B2), np.linalg.norm(B-B2)
dst = fftw.dstn(input_array, None, axes, type, threads, fflags, output_array=oa)
B = dst(A).copy()
idst = fftw.idstn(input_array, None, axes, type, threads, iflags, output_array=oa)
A2 = idst(B, implicit=True, normalize=True)
assert allclose(A, A2), np.linalg.norm(A-A2)
if typecode != 'g' and type != 4:
B2 = scipy_dstn(A, axes=axes, type=type)
assert allclose(B, B2), np.linalg.norm(B-B2)
# Different r2r transforms along all axes. Just pick
# any naxes transforms and compare with scipy
naxes = len(axes)
kds = np.random.randint(3, 11, size=naxes) # get naxes random transforms
tsf = [rkinds[k] for k in kds]
T = fftw.get_planned_FFT(input_array, input_array.copy(), axes=axes,
kind=kds, threads=threads, flags=fflags)
C = T(A)
TI = fftw.get_planned_FFT(input_array.copy(), input_array.copy(), axes=axes,
kind=list([fftw.inverse[kd] for kd in kds]),
threads=threads, flags=iflags)
C2 = TI(C)
M = fftw.get_normalization(kds, input_array.shape, axes)
assert allclose(C2*M, A)
# Test vs scipy for transforms available in scipy
if typecode != 'g' and not any(f in kds for f in (fftw.FFTW_RODFT11, fftw.FFTW_REDFT11)):
for m, ts in enumerate(tsf):
A = eval('scipy.fftpack.'+ts[:-1])(A, axis=axes[m], type=int(ts[-1]))
assert allclose(C, A), np.linalg.norm(C-A)
def test_wisdom():
# Test a simple export/import call
fftw.export_wisdom('newwisdom.dat')
fftw.import_wisdom('newwisdom.dat')
fftw.forget_wisdom()
def test_timelimit():
limit = 0.01
input_array = fftw.aligned((128, 128), dtype='d')
t0 = time()
fftw.rfftn(input_array, flags=fftw.FFTW_PATIENT)
t1 = time()-t0
fftw.forget_wisdom()
fftw.set_timelimit(limit)
t0 = time()
fftw.rfftn(input_array, flags=fftw.FFTW_PATIENT)
t2 = time()-t0
assert t1 > t2
assert abs(t2-limit) < limit, print(abs(t2-limit), limit)
fftw.cleanup()
if __name__ == '__main__':
test_fftw()
test_wisdom()
test_timelimit()
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