def makeKvecs(self, kmag2, S, orthogonal=True):
"""Make k-vectors needed for space fourier transform.
`orthogonal` is a a keyword indicating that we will only use
(k,0,0), (0,k,0), (0,0,k) as our vectors, instead of that in
addition to all diagonal vectors consistent with a certain
angle. This is because in a cubic lattice, diagonals pointing
in different directions (0,0,3) vs (1,2,2) do not have the
same symmetry properties. Default to only using orthogonal
vectors (orthogonal=True)
"""
if orthogonal:
kmag = int(math.sqrt(kmag2))
# If we didn't get an exact integer used with orthogonal,
# is is incorrect. We could just round it, but likely the
# user did not want that, since most likely they are using
# all values of integer $k^2$ instead of all values of
# integer $k$.
if kmag != math.sqrt(kmag2):
raise NoKvecsException
if len(S.physicalShape) == 1:
kvecs = numpy.asarray([(kmag, ),
],
dtype=saiga12.c_double)
elif len(S.physicalShape) == 2:
kvecs = numpy.asarray([(kmag, 0. ),
(0. , kmag),
],
dtype=saiga12.c_double)
elif len(S.physicalShape) == 3:
kvecs = numpy.asarray([(kmag, 0. , 0. ),
(0. , kmag, 0. ),
(0. , 0. , kmag),
],
dtype=saiga12.c_double)
else:
import shelve
cachepar = str((kmag2, len(S.physicalShape)))
kmax = int(math.ceil(math.sqrt(kmag2)))
useCache = False
if _kvecCache.has_key(cachepar): # memory cache always used
kvecs = _kvecCache[cachepar]
else:
cache = shelve.open("kvecCache")
if cache.get('version', 0) < 1:
for k in cache.keys(): del cache[k]
cache['version'] = 1
if cache.has_key(cachepar) and useCache:
kvecs = cache[cachepar]
_kvecCache[cachepar] = kvecs
else:
# kvecs is a list of all k-vectors consistent with our
# magnitude.
full = [ x for x in range(-kmax+1, kmax+1) ]
half = [ x for x in range(0, kmax+1) ]
if len(S.physicalShape) == 1:
kvecs = cartesianproduct(half, )
elif len(S.physicalShape) == 2:
kvecs = cartesianproduct(full, half)
elif len(S.physicalShape) == 3:
kvecs = cartesianproduct(full, full, half)
kvecs = numpy.asarray([ _ for _ in kvecs
# the following lines limits to only
# orthogonal vectors, which is handled
# at the very first of this method
#if numpy.max(numpy.abs(_))**2 == kmag2
],
dtype=saiga12.c_double)
magnitudes2 = numpy.sum(kvecs * kvecs, axis=1)
kvecs = kvecs[magnitudes2 == kmag2]
if len(kvecs) == 0:
raise NoKvecsException
if useCache:
cache[cachepar] = kvecs
_kvecCache[cachepar] = kvecs # memory cache always
del cache
self.kvecs = kvecs
def makeKvecs(n, orthogonal, dim):
n2 = n**2
if orthogonal:
if dim == 2:
kvecs = numpy.asarray([(n , 0. ),
(0., n),
],
dtype=saiga12.c_double)
return kvecs
elif dim == 3:
kvecs = numpy.asarray([(n , 0., 0.),
(0., n , 0.),
(0., 0., n ),
],
dtype=saiga12.c_double)
return kvecs
else:
raise Exception("dimensions must be 2 or 3.")
else:
import shelve
cachepar = str((n2, dim))
nmax = int(math.ceil(math.sqrt(n2)))
useCache = False
if _kvecCache.has_key(cachepar): # memory cache always used
kvecs = _kvecCache[cachepar]
else:
cache = shelve.open("kvecCache")
if cache.get('version', 0) < 1:
for k in cache.keys(): del cache[k]
cache['version'] = 1
if cache.has_key(cachepar) and useCache:
kvecs = cache[cachepar]
_kvecCache[cachepar] = kvecs
else:
# kvecs is a list of all k-vectors consistent with our
# magnitude.
full = [ x for x in range(-nmax+1, nmax+1) ]
half = [ x for x in range(0, nmax+1) ]
if dim == 1:
kvecs = cartesianproduct(half, )
elif dim == 2:
kvecs = cartesianproduct(full, half)
elif dim == 3:
kvecs = cartesianproduct(full, full, half)
kvecs = numpy.asarray([ _ for _ in kvecs
# the following lines limits to only
# orthogonal vectors, which is handled
# at the very first of this method
#if numpy.max(numpy.abs(_))**2 == kmag2
],
dtype=saiga12.c_double)
magnitudes2 = numpy.sum(kvecs * kvecs, axis=1)
kvecs = kvecs[magnitudes2 == n2]
if len(kvecs) == 0:
raise NoKvecsException
if useCache:
cache[cachepar] = kvecs
_kvecCache[cachepar] = kvecs # memory cache always
del cache
return kvecs