Commit 9918b72b authored by Martin Reinecke's avatar Martin Reinecke

tweak docstrings; simplify tests

parent ee5193a5
......@@ -597,11 +597,18 @@ axes : list of integers
inorm : int
Normalization type
0 : no normalization
1 : divide by sqrt(N)
1 : make transform orthogonal and divide by sqrt(N)
2 : divide by N
where N is the product of n_i for every transformed axis i.
n_i is 2*(<axis_length>-1 for type 1 and 2*<axis length>
for types 2, 3, 4.
Making the transform orthogonal involves the following additional steps
for every 1D sub-transform:
Type 1 : multiply first and last input value by sqrt(2)
divide first and last output value by sqrt(2)
Type 2 : divide first output value by sqrt(2)
Type 3 : multiply first input value by sqrt(2)
Type 4 : nothing
out : numpy.ndarray (same shape and data type as `a`)
May be identical to `a`, but if it isn't, it must not overlap with `a`.
If None, a new array is allocated to store the output.
......@@ -629,11 +636,17 @@ axes : list of integers
inorm : int
Normalization type
0 : no normalization
1 : divide by sqrt(N)
1 : make transform orthogonal and divide by sqrt(N)
2 : divide by N
where N is the product of n_i for every transformed axis i.
n_i is 2*(<axis_length>+1 for type 1 and 2*<axis length>
for types 2, 3, 4.
Making the transform orthogonal involves the following additional steps
for every 1D sub-transform:
Type 1 : nothing
Type 2 : divide first output value by sqrt(2)
Type 3 : multiply first input value by sqrt(2)
Type 4 : nothing
out : numpy.ndarray (same shape and data type as `a`)
May be identical to `a`, but if it isn't, it must not overlap with `a`.
If None, a new array is allocated to store the output.
......
......@@ -55,36 +55,27 @@ def irfft_scipy(a, axis, inorm=0, out=None, nthreads=1):
forward=False, inorm=inorm, out=out,
nthreads=nthreads)
tol = {np.float32: 6e-7, np.float64: 1.5e-15, np.longfloat: 1e-18}
ctype = {np.float32: np.complex64, np.float64: np.complex128, np.longfloat: np.longcomplex}
@pmp("len", len1D)
@pmp("inorm", [0, 1, 2])
def test1D(len, inorm):
@pmp("dtype", [np.float32, np.float64, np.longfloat])
def test1D(len, inorm, dtype):
a = np.random.rand(len)-0.5 + 1j*np.random.rand(len)-0.5j
b = a.astype(np.complex64)
c = a.astype(np.complex256)
_assert_close(a, ifftn(fftn(c, inorm=inorm), inorm=2-inorm), 1e-18)
assert_(_l2error(a, ifftn(fftn(a, inorm=inorm), inorm=2-inorm)) < 1.5e-15)
a = a.astype(ctype[dtype])
eps = tol[dtype]
assert_(_l2error(a, ifftn(fftn(a, inorm=inorm), inorm=2-inorm)) < eps)
assert_(_l2error(a.real, ifftn(fftn(a.real, inorm=inorm), inorm=2-inorm))
< 1.5e-15)
< eps)
assert_(_l2error(a.real, fftn(ifftn(a.real, inorm=inorm), inorm=2-inorm))
< 1.5e-15)
< eps)
assert_(_l2error(a.real, irfftn(rfftn(a.real, inorm=inorm),
inorm=2-inorm, lastsize=len)) < 1.5e-15)
inorm=2-inorm, lastsize=len)) < eps)
tmp = a.copy()
assert_(ifftn(fftn(tmp, out=tmp, inorm=inorm), out=tmp, inorm=2-inorm)
is tmp)
assert_(_l2error(tmp, a) < 1.5e-15)
assert_(_l2error(b, ifftn(fftn(b, inorm=inorm), inorm=2-inorm)) < 6e-7)
assert_(_l2error(b.real, ifftn(fftn(b.real, inorm=inorm), inorm=2-inorm))
< 6e-7)
assert_(_l2error(b.real, fftn(ifftn(b.real, inorm=inorm), inorm=2-inorm))
< 6e-7)
assert_(_l2error(b.real, irfftn(rfftn(b.real, inorm=inorm), lastsize=len,
inorm=2-inorm)) < 6e-7)
tmp = b.copy()
assert_(ifftn(fftn(tmp, out=tmp, inorm=inorm), out=tmp, inorm=2-inorm)
is tmp)
assert_(_l2error(tmp, b) < 6e-7)
assert_(_l2error(tmp, a) < eps)
@pmp("shp", shapes)
......@@ -206,54 +197,17 @@ def test_genuine_hartley_2D(shp, axes):
@pmp("len", len1D)
@pmp("inorm", [0, 1, 2])
@pmp("type", [1, 2, 3])
def testdcst1D(len, inorm, type):
a = np.random.rand(len)-0.5
b = a.astype(np.float32)
c = a.astype(np.float128)
itp = (0, 1, 3, 2, 4)
itype = itp[type]
if type != 1 or len > 1:
_assert_close(a, pypocketfft.dct(pypocketfft.dct(c, inorm=inorm, type=type), inorm=2-inorm, type=itype), 2e-18)
_assert_close(a, pypocketfft.dct(pypocketfft.dct(a, inorm=inorm, type=type), inorm=2-inorm, type=itype), 1.5e-15)
_assert_close(b, pypocketfft.dct(pypocketfft.dct(b, inorm=inorm, type=type), inorm=2-inorm, type=itype), 6e-7)
_assert_close(a, pypocketfft.dst(pypocketfft.dst(c, inorm=inorm, type=type), inorm=2-inorm, type=itype), 2e-18)
_assert_close(a, pypocketfft.dst(pypocketfft.dst(a, inorm=inorm, type=type), inorm=2-inorm, type=itype), 1.5e-15)
_assert_close(b, pypocketfft.dst(pypocketfft.dst(b, inorm=inorm, type=type), inorm=2-inorm, type=itype), 6e-7)
@pmp("len", len1D)
@pmp("type", [1, 2, 3])
def testdcst1Dortho(len, type):
a = np.random.rand(len)-0.5
b = a.astype(np.float32)
c = a.astype(np.float128)
itp = (0, 1, 3, 2, 4)
itype = itp[type]
if type != 1 or len > 1:
_assert_close(a, pypocketfft.dct(pypocketfft.dct(c, inorm=1, type=type), inorm=1, type=itype), 2e-18)
_assert_close(a, pypocketfft.dct(pypocketfft.dct(a, inorm=1, type=type), inorm=1, type=itype), 1.5e-15)
_assert_close(b, pypocketfft.dct(pypocketfft.dct(b, inorm=1, type=type), inorm=1, type=itype), 6e-7)
if type != 1:
_assert_close(a, pypocketfft.dst(pypocketfft.dst(c, inorm=1, type=type), inorm=1, type=itype), 2e-18)
_assert_close(a, pypocketfft.dst(pypocketfft.dst(a, inorm=1, type=type), inorm=1, type=itype), 1.5e-15)
_assert_close(b, pypocketfft.dst(pypocketfft.dst(b, inorm=1, type=type), inorm=1, type=itype), 6e-7)
# TEMPORARY: separate test for DCT/DST IV, since they are less accurate
@pmp("len", len1D)
@pmp("inorm", [0, 1, 2])
@pmp("type", [4])
def testdcst1D4(len, inorm, type):
a = np.random.rand(len)-0.5
b = a.astype(np.float32)
c = a.astype(np.float128)
@pmp("inorm", [0, 1]) # inorm==2 not needed, tested via inverse
@pmp("type", [1, 2, 3, 4])
@pmp("dtype", [np.float32, np.float64, np.longfloat])
def testdcst1D(len, inorm, type, dtype):
a = (np.random.rand(len)-0.5).astype(dtype)
eps = tol[dtype]
itp = (0, 1, 3, 2, 4)
if type==4 and len%2 == 1: # relaxed accuracies for odd-length type 4 transforms
special_tol = {np.float32: 4e-5, np.float64: 6e-14, np.longfloat: 4e-17}
eps = special_tol[dtype]
itype = itp[type]
if type != 1 or len > 1:
_assert_close(a, pypocketfft.dct(pypocketfft.dct(c, inorm=inorm, type=type), inorm=2-inorm, type=itype), 2e-16)
_assert_close(a, pypocketfft.dct(pypocketfft.dct(a, inorm=inorm, type=type), inorm=2-inorm, type=itype), 1.5e-13)
_assert_close(b, pypocketfft.dct(pypocketfft.dct(b, inorm=inorm, type=type), inorm=2-inorm, type=itype), 6e-5)
_assert_close(a, pypocketfft.dst(pypocketfft.dst(c, inorm=inorm, type=type), inorm=2-inorm, type=itype), 2e-16)
_assert_close(a, pypocketfft.dst(pypocketfft.dst(a, inorm=inorm, type=type), inorm=2-inorm, type=itype), 1.5e-13)
_assert_close(b, pypocketfft.dst(pypocketfft.dst(b, inorm=inorm, type=type), inorm=2-inorm, type=itype), 6e-5)
if type != 1 or len > 1: # there are no length-1 type 1 DCTs
_assert_close(a, pypocketfft.dct(pypocketfft.dct(a, inorm=inorm, type=type), inorm=2-inorm, type=itype), eps)
_assert_close(a, pypocketfft.dst(pypocketfft.dst(a, inorm=inorm, type=type), inorm=2-inorm, type=itype), eps)
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