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|
"""
>>> case(fft.fft( (0,1)*4 ),
... Numeric.array([ 4.+0.j, 0.+0.j, 0.+0.j, 0.+0.j,
... -4.+0.j, 0.+0.j, 0.+0.j, 0.+0.j]))
OK
>>> case(fft.inverse_fft( fft.fft((0,1)*4)),
... Numeric.array([ 0.+0.j, 1.+0.j, 0.+0.j, 1.+0.j,
... 0.+0.j, 1.+0.j, 0.+0.j, 1.+0.j]))
OK
>>> case(fft.fft( (0,1)*4, n=16),
... Numeric.array([
... 4.00000000e+00+0.j , -1.11022302e-15-2.61312593j,
... 0.00000000e+00+0.j , -1.55431223e-15-1.0823922j ,
... 0.00000000e+00+0.j , -4.44089210e-16-1.0823922j ,
... 0.00000000e+00+0.j , -3.55271368e-15-2.61312593j,
... -4.00000000e+00+0.j , 1.11022302e-15+2.61312593j,
... 0.00000000e+00+0.j , 1.55431223e-15+1.0823922j ,
... 0.00000000e+00+0.j , 4.44089210e-16+1.0823922j ,
... 0.00000000e+00+0.j , 3.55271368e-15+2.61312593j]))
OK
>>> case(fft.fft( (0,1)*4, n=4 ),
... Numeric.array([ 2.+0.j, 0.+0.j, -2.+0.j, 0.+0.j]))
OK
>>> case(fft.fft2d( [(0,1),(1,0)] ),
... Numeric.array([[ 2.+0.j, 0.+0.j],
... [ 0.+0.j, -2.+0.j]]))
OK
>>> case(fft.inverse_fft2d (fft.fft2d( [(0, 1), (1, 0)] ) ),
... Numeric.array([[ 0.+0.j, 1.+0.j],
... [ 1.+0.j, 0.+0.j]]))
OK
>>> case(fft.real_fft2d([(0,1),(1,0)]),
... Numeric.array([[ 2.+0.j, 0.+0.j],
... [ 0.+0.j, -2.+0.j]]))
OK
>>> case(fft.real_fft2d([(1,1),(1,1)] ),
... Numeric.array([[ 4.+0.j, 0.+0.j],
... [ 0.+0.j, 0.+0.j]]))
OK
Tests for correctness.
Somewhat limited since
p (and thus q also) is real and hermite, and the dimension we're
testing is a power of 2. If someone can cook up more general data
in their head or with another program/library, splice it in!
>>> toler = 1.e-10
>>> oosq2 = 1.0/Numeric.sqrt(2.0)
>>> p = Numeric.array(((1, 1, 1, 1, 1, 1, 1, 1),
... (1, oosq2, 0, -oosq2, -1, -oosq2, 0, oosq2),
... (1, 0, -1, 0, 1, 0, -1, 0),
... (1, -oosq2, 0, oosq2, -1, oosq2, 0, -oosq2),
... (1, -1, 1, -1, 1, -1, 1, -1),
... (1, 0, 0, 0, 0, 0, 0, 0),
... (0, 0, 0, 0, 0, 0, 0, 0)))
>>> q = Numeric.array(((8,0,0,0,0,0,0,0),
... (0,4,0,0,0,0,0,4),
... (0,0,4,0,0,0,4,0),
... (0,0,0,4,0,4,0,0),
... (0,0,0,0,8,0,0,0),
... (1,1,1,1,1,1,1,1),
... (0,0,0,0,0,0,0,0)))
Correctness testing dimension -1.
>>> P = fft.fft(p)
>>> cndns(P-q) / cndns(q) > toler
0
>>> RP = fft.real_fft(p)
>>> npt = p.getshape()[-1]; rpt = npt/2 + 1
>>> qr = q[:,:rpt]; cndns(RP-qr) / cndns(qr) > toler
0
>>> I = fft.inverse_real_fft(q, npt)
>>> cndns(I-p) / cndns(p) > toler
0
Consistency testing dimension 0, length 7.
>>> dim = 0
FFT
>>> P = fft.fft(p, None, dim)
>>> Q = fft.inverse_fft(P, None, dim)
>>> cndns(Q-p) / cndns(p) > toler
0
Real FFT
>>> RP = fft.real_fft(p, None, dim)
>>> npt = p.getshape()[dim]; rpt = npt/2 + 1
>>> P = Numeric.take(P, range(rpt), axis=dim)
>>> cndns(RP-P) / cndns(RP) > toler
0
Inverse FFT
>>> P = fft.fft(p, None, dim)
>>> Q = fft.inverse_fft(P, None, dim)
>>> cndns(Q-p) / cndns(p) > toler
0
Inverse Hermite FFT
>>> hp = fft.inverse_hermite_fft(q, npt, dim)
>>> Q = fft.inverse_fft(q, None, dim)
>>> Q = Numeric.take(Q, range(rpt), axis=dim)
>>> cndns(hp-Q) / cndns(hp) > toler
0
Consistency testing dimension 1, length 8.
>>> dim = 1
FFT
>>> P = fft.fft(p, None, dim)
>>> Q = fft.inverse_fft(P, None, dim)
>>> cndns(Q-p) / cndns(p) > toler
0
Real FFT
>>> RP = fft.real_fft(p, None, dim)
>>> npt = p.getshape()[dim]; rpt = npt/2 + 1
>>> P = Numeric.take(P, range(rpt), axis=dim)
>>> cndns(RP-P) / cndns(RP) > toler
0
Inverse FFT
>>> P = fft.fft(p, None, dim)
>>> Q = fft.inverse_fft(P, None, dim)
>>> cndns(Q-p) / cndns(p) > toler
0
Inverse Hermite FFT
>>> hp = fft.inverse_hermite_fft(q, npt, dim)
>>> Q = fft.inverse_fft(q, None, dim)
>>> Q = Numeric.take(Q, range(rpt), axis=dim)
>>> cndns(hp-Q) / cndns(hp) > toler
0
Multi-dimensional tests
>>> tee = Numeric.array(((2.0, 0, 2, 0),
... (0, 2, 0, 2),
... (2, 0, 2, 0),
... (0, 2, 0, 2)))
>>> eff = Numeric.array(((16.0, 0, 0, 0),
... (0, 0, 0, 0),
... (0, 0, 16, 0),
... (0, 0, 0, 0)))
FFT N-dimensional
>>> ftest = fft.fftnd(tee)
>>> cndns(ftest - eff) / cndns(eff) > toler
0
Inverse FFT N-Dimensional
>>> cndns(fft.inverse_fftnd(ftest) - tee) / cndns(tee) > toler
0
Real FFT N-dimensional
>>> fred = fft.real_fftnd(p)
>>> npts = p.getshape()[-1]; rpts = npts/2 + 1
>>> actual = fft.fftnd(p); ract = actual[..., :rpts]
>>> cndns(fred-ract) / cndns(ract) > toler
0
Inverse Real FFT N-dimensional
>>> ethel = fft.inverse_real_fftnd(fred)
>>> cndns(p-ethel) / cndns(p) > toler
0
FFT 2D shape test:
>>> axes = (0,1); shape = (7,4); barney = Numeric.zeros(shape,'d')
>>> betty = fft.fft2d(barney); betty.shape == barney.shape
1
>>> betty = fft.fft2d(barney, None, axes); betty.shape == barney.shape
1
>>> betty = fft.fft2d(barney, shape); betty.shape == barney.shape
1
>>> betty = fft.fft2d(barney, shape, axes); betty.shape == barney.shape
1
>>> betty = fft.real_fft2d(barney); wilma = fft.inverse_real_fft2d(betty)
>>> wilma.shape == barney.shape
1
>>> wilma = fft.inverse_real_fft2d(betty, shape); wilma.shape == barney.shape
1
>>> wilma = fft.inverse_real_fft2d(betty, None, axes); wilma.shape == barney.shape
1
>>> wilma = fft.inverse_real_fft2d(betty, shape, axes); wilma.shape == barney.shape
1
Codelet order test:
>>> for size in range (1,25):
... for i in range(3):
... a = random_array.random(size)
... b = fft.real_fft(a)
... c = fft.inverse_real_fft(b,size)
... if cndns(c-a) / cndns(a) > toler:
... print "real transforms failed for size %d" % size
... a = a + random_array.random(size) * 1j
... b = fft.fft(a)
... c = fft.inverse_fft(b,size)
... if cndns(c-a) / cndns(a) > toler:
... print "complex transforms failed for size %d" % size
>>> x = Numeric.cos(Numeric.arange(30.0)/30.0*2*Numeric.pi)
>>> y = fft.real_fft(x)
>>> z = fft.inverse_real_fft(y,30)
>>> cndns(x-z)/cndns(x) > toler
0
"""
import numarray.fft as fft
import numarray.numeric as Numeric
import numarray.random_array as random_array
import sys
class DoctestError(Exception):
pass
def cndns(m):
return Numeric.maximum.reduce(Numeric.abs(m).getflat())
def case(expr, ans, eps=1e-9):
if cndns(ans-expr) < eps:
print "OK"
else:
raise DoctestError, "failed"
def test():
import dtest
import doctest
return doctest.testmod(dtest)
if __name__ == '__main__':
test()
|
