def getBasis(self):
"""
Construct a basis for the subspace by orthonormalization of
the input vectors using Singular Value Decomposition. The
basis consists of a sequence of
:class:`~MMTK.ParticleProperties.ParticleVector`
objects that are orthonormal in configuration space.
:returns: the basis
"""
if self._basis is None:
basis = N.array([v.array for v in self.vectors], N.Float)
shape = basis.shape
nvectors = shape[0]
natoms = shape[1]
basis.shape = (nvectors, 3*natoms)
sv = N.zeros((min(nvectors, 3*natoms),), N.Float)
min_n_m = min(3*natoms, nvectors)
vt = N.zeros((nvectors, min_n_m), N.Float)
work = N.zeros((1,), N.Float)
iwork = N.zeros((8*min_n_m,), int_type)
if 3*natoms >= nvectors:
result = dgesdd('O', 3*natoms, nvectors, basis, 3*natoms,
sv, basis, 3*natoms, vt, min_n_m,
work, -1, iwork, 0)
work = N.zeros((int(work[0]),), N.Float)
result = dgesdd('O', 3*natoms, nvectors, basis, 3*natoms,
sv, basis, 3*natoms, vt, min_n_m,
work, work.shape[0], iwork, 0)
u = basis
else:
u = N.zeros((min_n_m, 3*natoms), N.Float)
result = dgesdd('S', 3*natoms, nvectors, basis, 3*natoms,
sv, u, 3*natoms, vt, min_n_m,
work, -1, iwork, 0)
work = N.zeros((int(work[0]),), N.Float)
result = dgesdd('S', 3*natoms, nvectors, basis, 3*natoms,
sv, u, 3*natoms, vt, min_n_m,
work, work.shape[0], iwork, 0)
if result['info'] != 0:
raise ValueError('Lapack SVD: ' + `result['info']`)
svmax = N.maximum.reduce(sv)
nvectors = N.add.reduce(N.greater(sv, 1.e-10*svmax))
u = u[:nvectors]
u.shape = (nvectors, natoms, 3)
self._basis = ParticleVectorSet(self.universe, u)
return self._basis
def _setupBasis(self):
if type(self.basis) is type(()):
excluded, basis = self.basis
else:
excluded = []
basis = self.basis
nexcluded = len(excluded)
nmodes = len(basis)
ntotal = nexcluded + nmodes
natoms = len(basis[0])
sv = N.zeros((min(ntotal, 3 * natoms), ), N.Float)
work_size = N.zeros((1, ), N.Float)
if nexcluded > 0:
self.basis = N.zeros((ntotal, 3 * natoms), N.Float)
for i in range(nexcluded):
self.basis[i] = N.ravel(excluded[i].array * self.weights)
min_n_m = min(3 * natoms, nexcluded)
vt = N.zeros((nexcluded, min_n_m), N.Float)
iwork = N.zeros((8 * min_n_m, ), int_type)
if 3 * natoms >= nexcluded:
result = dgesdd('O', 3 * natoms, nexcluded, self.basis,
3 * natoms, sv, self.basis, 3 * natoms, vt,
min_n_m, work_size, -1, iwork, 0)
work = N.zeros((int(work_size[0]), ), N.Float)
result = dgesdd('O', 3 * natoms, nexcluded, self.basis,
3 * natoms, sv, self.basis, 3 * natoms, vt,
min_n_m, work, work.shape[0], iwork, 0)
else:
u = N.zeros((min_n_m, 3 * natoms), N.Float)
result = dgesdd('S', 3 * natoms, nexcluded, self.basis,
3 * natoms, sv, u, 3 * natoms, vt, min_n_m,
work_size, -1, iwork, 0)
work = N.zeros((int(work_size[0]), ), N.Float)
result = dgesdd('S', 3 * natoms, nexcluded, self.basis,
3 * natoms, sv, u, 3 * natoms, vt, min_n_m,
work, work.shape[0], iwork, 0)
self.basis[:min_n_m] = u
if result['info'] != 0:
raise ValueError('Lapack SVD: ' + ` result['info'] `)
svmax = N.maximum.reduce(sv)
nexcluded = N.add.reduce(N.greater(sv, 1.e-10 * svmax))
ntotal = nexcluded + nmodes
for i in range(nmodes):
self.basis[i + nexcluded] = N.ravel(basis[i].array *
self.weights)
min_n_m = min(3 * natoms, ntotal)
vt = N.zeros((ntotal, min_n_m), N.Float)
if 3 * natoms >= ntotal:
result = dgesdd('O', 3 * natoms, ntotal, self.basis,
3 * natoms, sv, self.basis, 3 * natoms, vt,
min_n_m, work_size, -1, iwork, 0)
if int(work_size[0]) > work.shape[0]:
work = N.zeros((int(work_size[0]), ), N.Float)
result = dgesdd('O', 3 * natoms, ntotal, self.basis,
3 * natoms, sv, self.basis, 3 * natoms, vt,
min_n_m, work, work.shape[0], iwork, 0)
else:
u = N.zeros((min_n_m, 3 * natoms), N.Float)
result = dgesdd('S', 3 * natoms, ntotal, self.basis,
3 * natoms, sv, u, 3 * natoms, vt, min_n_m,
work_size, -1, iwork, 0)
if int(work_size[0]) > work.shape[0]:
work = N.zeros((int(work_size[0]), ), N.Float)
result = dgesdd('S', 3 * natoms, ntotal, self.basis,
3 * natoms, sv, u, 3 * natoms, vt, min_n_m,
work, work.shape[0], iwork, 0)
self.basis[:min_n_m] = u
if result['info'] != 0:
raise ValueError('Lapack SVD: ' + ` result['info'] `)
svmax = N.maximum.reduce(sv)
ntotal = N.add.reduce(N.greater(sv, 1.e-10 * svmax))
nmodes = ntotal - nexcluded
else:
if hasattr(self.basis, 'may_modify') and \
hasattr(self.basis, 'array'):
self.basis = self.basis.array
else:
self.basis = N.array(map(lambda v: v.array, basis))
N.multiply(self.basis, self.weights, self.basis)
self.basis.shape = (nmodes, 3 * natoms)
min_n_m = min(3 * natoms, nmodes)
vt = N.zeros((nmodes, min_n_m), N.Float)
iwork = N.zeros((8 * min_n_m, ), int_type)
if 3 * natoms >= nmodes:
result = dgesdd('O', 3 * natoms, nmodes, self.basis,
3 * natoms, sv, self.basis, 3 * natoms, vt,
min_n_m, work_size, -1, iwork, 0)
work = N.zeros((int(work_size[0]), ), N.Float)
result = dgesdd('O', 3 * natoms, nmodes, self.basis,
3 * natoms, sv, self.basis, 3 * natoms, vt,
min_n_m, work, work.shape[0], iwork, 0)
else:
u = N.zeros((min_n_m, 3 * natoms), N.Float)
result = dgesdd('S', 3 * natoms, nmodes, self.basis,
3 * natoms, sv, u, 3 * natoms, vt, min_n_m,
work_size, -1, iwork, 0)
work = N.zeros((int(work_size[0]), ), N.Float)
result = dgesdd('S', 3 * natoms, nmodes, self.basis,
3 * natoms, sv, u, 3 * natoms, vt, min_n_m,
work, work.shape[0], iwork, 0)
self.basis[:min_n_m] = u
if result['info'] != 0:
raise ValueError('Lapack SVD: ' + ` result['info'] `)
svmax = N.maximum.reduce(sv)
nmodes = N.add.reduce(N.greater(sv, 1.e-10 * svmax))
ntotal = nmodes
self.basis = self.basis[nexcluded:ntotal, :]
n = 1
array = N.zeros((n, n), N.Float)
sv = N.zeros((n,), N.Float)
u = N.zeros((n, n), N.Float)
vt = N.zeros((n, n), N.Float)
work = N.zeros((1,), N.Float)
int_types = [N.Int, N.Int8, N.Int16, N.Int32]
try:
int_types.append(N.Int64)
int_types.append(N.Int128)
except AttributeError:
pass
for int_type in int_types:
iwork = N.zeros((1,), int_type)
try:
dgesdd('S', n, n, array, n, sv, u, n, vt, n, work, -1, iwork, 0)
break
except LapackError:
pass
del n, array, sv, u, vt, work, iwork, int_types
del array_package
#
# A set of particle vectors that define a subspace
#
class ParticleVectorSet(object):
def __init__(self, universe, data):
self.universe = universe
if type(data) == N.arraytype:
def _setupBasis(self):
if type(self.basis) is type(()):
excluded, basis = self.basis
else:
excluded = []
basis = self.basis
nexcluded = len(excluded)
nmodes = len(basis)
ntotal = nexcluded + nmodes
natoms = len(basis[0])
sv = N.zeros((min(ntotal, 3*natoms),), N.Float)
work_size = N.zeros((1,), N.Float)
if nexcluded > 0:
self.basis = N.zeros((ntotal, 3*natoms), N.Float)
for i in range(nexcluded):
self.basis[i] = N.ravel(excluded[i].array*self.weights)
min_n_m = min(3*natoms, nexcluded)
vt = N.zeros((nexcluded, min_n_m), N.Float)
iwork = N.zeros((8*min_n_m,), int_type)
if 3*natoms >= nexcluded:
result = dgesdd('O', 3*natoms, nexcluded, self.basis,
3*natoms, sv, self.basis, 3*natoms, vt, min_n_m,
work_size, -1, iwork, 0)
work = N.zeros((int(work_size[0]),), N.Float)
result = dgesdd('O', 3*natoms, nexcluded, self.basis,
3*natoms, sv, self.basis, 3*natoms, vt, min_n_m,
work, work.shape[0], iwork, 0)
else:
u = N.zeros((min_n_m, 3*natoms), N.Float)
result = dgesdd('S', 3*natoms, nexcluded, self.basis,
3*natoms, sv, u, 3*natoms, vt, min_n_m,
work_size, -1, iwork, 0)
work = N.zeros((int(work_size[0]),), N.Float)
result = dgesdd('S', 3*natoms, nexcluded, self.basis,
3*natoms, sv, u, 3*natoms, vt, min_n_m,
work, work.shape[0], iwork, 0)
self.basis[:min_n_m] = u
if result['info'] != 0:
raise ValueError('Lapack SVD: ' + `result['info']`)
svmax = N.maximum.reduce(sv)
nexcluded = N.add.reduce(N.greater(sv, 1.e-10*svmax))
ntotal = nexcluded + nmodes
for i in range(nmodes):
self.basis[i+nexcluded] = N.ravel(basis[i].array*self.weights)
min_n_m = min(3*natoms, ntotal)
vt = N.zeros((ntotal, min_n_m), N.Float)
if 3*natoms >= ntotal:
result = dgesdd('O', 3*natoms, ntotal, self.basis, 3*natoms,
sv, self.basis, 3*natoms, vt, min_n_m,
work_size, -1, iwork, 0)
if int(work_size[0]) > work.shape[0]:
work = N.zeros((int(work_size[0]),), N.Float)
result = dgesdd('O', 3*natoms, ntotal, self.basis, 3*natoms,
sv, self.basis, 3*natoms, vt, min_n_m,
work, work.shape[0], iwork, 0)
else:
u = N.zeros((min_n_m, 3*natoms), N.Float)
result = dgesdd('S', 3*natoms, ntotal, self.basis, 3*natoms,
sv, u, 3*natoms, vt, min_n_m,
work_size, -1, iwork, 0)
if int(work_size[0]) > work.shape[0]:
work = N.zeros((int(work_size[0]),), N.Float)
result = dgesdd('S', 3*natoms, ntotal, self.basis, 3*natoms,
sv, u, 3*natoms, vt, min_n_m,
work, work.shape[0], iwork, 0)
self.basis[:min_n_m] = u
if result['info'] != 0:
raise ValueError('Lapack SVD: ' + `result['info']`)
svmax = N.maximum.reduce(sv)
ntotal = N.add.reduce(N.greater(sv, 1.e-10*svmax))
nmodes = ntotal - nexcluded
else:
if hasattr(self.basis, 'may_modify') and \
hasattr(self.basis, 'array'):
self.basis = self.basis.array
else:
self.basis = N.array(map(lambda v: v.array, basis))
N.multiply(self.basis, self.weights, self.basis)
self.basis.shape = (nmodes, 3*natoms)
min_n_m = min(3*natoms, nmodes)
vt = N.zeros((nmodes, min_n_m), N.Float)
iwork = N.zeros((8*min_n_m,), int_type)
if 3*natoms >= nmodes:
result = dgesdd('O', 3*natoms, nmodes, self.basis, 3*natoms,
sv, self.basis, 3*natoms, vt, min_n_m,
work_size, -1, iwork, 0)
work = N.zeros((int(work_size[0]),), N.Float)
result = dgesdd('O', 3*natoms, nmodes, self.basis, 3*natoms,
sv, self.basis, 3*natoms, vt, min_n_m,
work, work.shape[0], iwork, 0)
else:
u = N.zeros((min_n_m, 3*natoms), N.Float)
result = dgesdd('S', 3*natoms, nmodes, self.basis, 3*natoms,
sv, u, 3*natoms, vt, min_n_m,
work_size, -1, iwork, 0)
work = N.zeros((int(work_size[0]),), N.Float)
result = dgesdd('S', 3*natoms, nmodes, self.basis, 3*natoms,
sv, u, 3*natoms, vt, min_n_m,
work, work.shape[0], iwork, 0)
self.basis[:min_n_m] = u
if result['info'] != 0:
raise ValueError('Lapack SVD: ' + `result['info']`)
svmax = N.maximum.reduce(sv)
nmodes = N.add.reduce(N.greater(sv, 1.e-10*svmax))
ntotal = nmodes
self.basis = self.basis[nexcluded:ntotal, :]