def assemble_matrices(define, mod, pars, set_wave_dir, options, wdir=None):
"""
Assemble the blocks of dispersion eigenvalue problem matrices.
"""
define_dict = define(filename_mesh=options.mesh_filename,
pars=pars,
approx_order=options.order,
refinement_level=options.refine,
solver_conf=options.solver_conf,
plane=options.plane,
post_process=options.post_process,
**options.define_kwargs)
conf = ProblemConf.from_dict(define_dict, mod)
pb = Problem.from_conf(conf)
pb.dispersion_options = options
pb.set_output_dir(options.output_dir)
dim = pb.domain.shape.dim
# Set the normalized wave vector direction to the material(s).
if wdir is None:
wdir = nm.asarray(options.wave_dir[:dim], dtype=nm.float64)
wdir = wdir / nm.linalg.norm(wdir)
set_wave_dir(pb, wdir)
bbox = pb.domain.mesh.get_bounding_box()
size = (bbox[1] - bbox[0]).max()
scaling0 = apply_unit_multipliers([1.0], ['length'],
options.unit_multipliers)[0]
scaling = scaling0
if options.mesh_size is not None:
scaling *= options.mesh_size / size
output('scaling factor of periodic cell mesh coordinates:', scaling)
output('new mesh size with applied unit multipliers:', scaling * size)
pb.domain.mesh.coors[:] *= scaling
pb.set_mesh_coors(pb.domain.mesh.coors, update_fields=True)
bzone = 2.0 * nm.pi / (scaling * size)
output('1. Brillouin zone size:', bzone * scaling0)
output('1. Brillouin zone size with applied unit multipliers:', bzone)
pb.time_update()
pb.update_materials()
# Assemble the matrices.
mtxs = {}
for key, eq in pb.equations.iteritems():
mtxs[key] = mtx = pb.mtx_a.copy()
mtx = eq.evaluate(mode='weak', dw_mode='matrix', asm_obj=mtx)
mtx.eliminate_zeros()
output_array_stats(mtx.data, 'nonzeros in %s' % key)
output('symmetry checks:')
output('%s - %s^T:' % (key, key), max_diff_csr(mtx, mtx.T))
output('%s - %s^H:' % (key, key), max_diff_csr(mtx, mtx.H))
return pb, wdir, bzone, mtxs
def assemble_matrices(define, mod, pars, set_wave_dir, options):
"""
Assemble the blocks of dispersion eigenvalue problem matrices.
"""
define_problem = functools.partial(define,
filename_mesh=options.mesh_filename,
pars=pars,
approx_order=options.order,
refinement_level=options.refine,
solver_conf=options.solver_conf,
plane=options.plane,
post_process=options.post_process)
conf = ProblemConf.from_dict(define_problem(), mod)
pb = Problem.from_conf(conf)
pb.dispersion_options = options
pb.set_output_dir(options.output_dir)
dim = pb.domain.shape.dim
# Set the normalized wave vector direction to the material(s).
wdir = nm.asarray(options.wave_dir[:dim], dtype=nm.float64)
wdir = wdir / nm.linalg.norm(wdir)
set_wave_dir(pb, wdir)
bbox = pb.domain.mesh.get_bounding_box()
size = (bbox[1] - bbox[0]).max()
scaling0 = apply_unit_multipliers([1.0], ['length'],
options.unit_multipliers)[0]
scaling = scaling0
if options.mesh_size is not None:
scaling *= options.mesh_size / size
output('scaling factor of periodic cell mesh coordinates:', scaling)
output('new mesh size with applied unit multipliers:', scaling * size)
pb.domain.mesh.coors[:] *= scaling
pb.set_mesh_coors(pb.domain.mesh.coors, update_fields=True)
bzone = 2.0 * nm.pi / (scaling * size)
output('1. Brillouin zone size:', bzone * scaling0)
output('1. Brillouin zone size with applied unit multipliers:', bzone)
pb.time_update()
pb.update_materials()
# Assemble the matrices.
mtxs = {}
for key, eq in pb.equations.iteritems():
mtxs[key] = mtx = pb.mtx_a.copy()
mtx = eq.evaluate(mode='weak', dw_mode='matrix', asm_obj=mtx)
mtx.eliminate_zeros()
output_array_stats(mtx.data, 'nonzeros in %s' % key)
output('symmetry checks:')
output('%s - %s^T:' % (key, key), max_diff_csr(mtx, mtx.T))
output('%s - %s^H:' % (key, key), max_diff_csr(mtx, mtx.H))
return pb, wdir, bzone, mtxs
def build_evp_matrices(mtxs, val, mode, pb):
"""
Build the matrices of the dispersion eigenvalue problem.
"""
if mode == 'omega':
mtx_a = mtxs['K'] + val**2 * mtxs['S'] + val * mtxs['R']
output('A - A^H:', max_diff_csr(mtx_a, mtx_a.H))
evp_mtxs = (mtx_a, mtxs['M'])
else:
evp_mtxs = (mtxs['S'], mtxs['R'], mtxs['K'] - val**2 * mtxs['M'])
return evp_mtxs
def build_evp_matrices(mtxs, val, mode, pb):
"""
Build the matrices of the dispersion eigenvalue problem.
"""
if mode == 'omega':
mtx_a = mtxs['K'] + val**2 * mtxs['S'] + val * mtxs['R']
output('A - A^H:', max_diff_csr(mtx_a, mtx_a.H))
evp_mtxs = (mtx_a, mtxs['M'])
else:
evp_mtxs = (mtxs['S'], mtxs['R'], mtxs['K'] - val**2 * mtxs['M'])
return evp_mtxs
def __call__(self,
mtx_m,
mtx_d,
mtx_k,
n_eigs=None,
eigenvectors=None,
status=None,
conf=None):
if conf.debug:
ssym = status['matrix_info'] = {}
ssym['|M - M^T|'] = max_diff_csr(mtx_m, mtx_m.T)
ssym['|D - D^T|'] = max_diff_csr(mtx_d, mtx_d.T)
ssym['|K - K^T|'] = max_diff_csr(mtx_k, mtx_k.T)
ssym['|M - M^H|'] = max_diff_csr(mtx_m, mtx_m.H)
ssym['|D - D^H|'] = max_diff_csr(mtx_d, mtx_d.H)
ssym['|K - K^H|'] = max_diff_csr(mtx_k, mtx_k.H)
if conf.method == 'companion':
mtx_eye = -sps.eye(mtx_m.shape[0], dtype=mtx_m.dtype)
mtx_a = sps.bmat([[mtx_d, mtx_k], [mtx_eye, None]])
mtx_b = sps.bmat([[-mtx_m, None], [None, mtx_eye]])
elif conf.method == 'cholesky':
from sksparse.cholmod import cholesky
factor = cholesky(mtx_m)
perm = factor.P()
ir = nm.arange(len(perm))
mtx_p = sps.coo_matrix((nm.ones_like(perm), (ir, perm)))
mtx_l = mtx_p.T * factor.L()
if conf.debug:
ssym['|S - LL^T|'] = max_diff_csr(mtx_m, mtx_l * mtx_l.T)
mtx_eye = sps.eye(mtx_l.shape[0], dtype=nm.float64)
mtx_a = sps.bmat([[-mtx_k, None], [None, mtx_eye]])
mtx_b = sps.bmat([[mtx_d, mtx_l], [mtx_l.T, None]])
else:
raise ValueError('unknown method! (%s)' % conf.method)
if conf.debug:
ssym['|A - A^T|'] = max_diff_csr(mtx_a, mtx_a.T)
ssym['|A - A^H|'] = max_diff_csr(mtx_a, mtx_a.H)
ssym['|B - B^T|'] = max_diff_csr(mtx_b, mtx_b.T)
ssym['|B - B^H|'] = max_diff_csr(mtx_b, mtx_b.H)
for key, val in sorted(ssym.items()):
output('{}: {}'.format(key, val))
if conf.mode == 'normal':
out = self.solver(mtx_a,
mtx_b,
n_eigs=n_eigs,
eigenvectors=eigenvectors,
status=status)
if eigenvectors:
eigs, vecs = out
out = (eigs, vecs[:mtx_m.shape[0], :])
if conf.debug:
res = mtx_a.dot(vecs) - eigs * mtx_b.dot(vecs)
status['lin. error'] = nm.linalg.norm(res, nm.inf)
else:
out = self.solver(mtx_b,
mtx_a,
n_eigs=n_eigs,
eigenvectors=eigenvectors,
status=status)
if eigenvectors:
eigs, vecs = out
out = (1.0 / eigs, vecs[:mtx_m.shape[0], :])
if conf.debug:
res = (1.0 / eigs) * mtx_b.dot(vecs) - mtx_a.dot(vecs)
status['lin. error'] = nm.linalg.norm(res, nm.inf)
else:
out = 1.0 / out
if conf.debug and eigenvectors:
eigs, vecs = out
res = ((eigs**2 * (mtx_m.dot(vecs))) + (eigs * (mtx_d.dot(vecs))) +
(mtx_k.dot(vecs)))
status['error'] = nm.linalg.norm(res, nm.inf)
return out
def __call__(self, mtx_m, mtx_d, mtx_k, n_eigs=None,
eigenvectors=None, status=None, conf=None):
if conf.debug:
ssym = status['matrix_info'] = {}
ssym['|M - M^T|'] = max_diff_csr(mtx_m, mtx_m.T)
ssym['|D - D^T|'] = max_diff_csr(mtx_d, mtx_d.T)
ssym['|K - K^T|'] = max_diff_csr(mtx_k, mtx_k.T)
ssym['|M - M^H|'] = max_diff_csr(mtx_m, mtx_m.H)
ssym['|D - D^H|'] = max_diff_csr(mtx_d, mtx_d.H)
ssym['|K - K^H|'] = max_diff_csr(mtx_k, mtx_k.H)
if conf.method == 'companion':
mtx_eye = -sps.eye(mtx_m.shape[0], dtype=mtx_m.dtype)
mtx_a = sps.bmat([[mtx_d, mtx_k],
[mtx_eye, None]])
mtx_b = sps.bmat([[-mtx_m, None],
[None, mtx_eye]])
elif conf.method == 'cholesky':
from sksparse.cholmod import cholesky
factor = cholesky(mtx_m)
perm = factor.P()
ir = nm.arange(len(perm))
mtx_p = sps.coo_matrix((nm.ones_like(perm), (ir, perm)))
mtx_l = mtx_p.T * factor.L()
if conf.debug:
ssym['|S - LL^T|'] = max_diff_csr(mtx_m, mtx_l * mtx_l.T)
mtx_eye = sps.eye(mtx_l.shape[0], dtype=nm.float64)
mtx_a = sps.bmat([[-mtx_k, None],
[None, mtx_eye]])
mtx_b = sps.bmat([[mtx_d, mtx_l],
[mtx_l.T, None]])
else:
raise ValueError('unknown method! (%s)' % conf.method)
if conf.debug:
ssym['|A - A^T|'] = max_diff_csr(mtx_a, mtx_a.T)
ssym['|A - A^H|'] = max_diff_csr(mtx_a, mtx_a.H)
ssym['|B - B^T|'] = max_diff_csr(mtx_b, mtx_b.T)
ssym['|B - B^H|'] = max_diff_csr(mtx_b, mtx_b.H)
for key, val in sorted(ssym.items()):
output('{}: {}'.format(key, val))
if conf.mode == 'normal':
out = self.solver(mtx_a, mtx_b, n_eigs=n_eigs,
eigenvectors=eigenvectors, status=status)
if eigenvectors:
eigs, vecs = out
out = (eigs, vecs[:mtx_m.shape[0], :])
if conf.debug:
res = mtx_a.dot(vecs) - eigs * mtx_b.dot(vecs)
status['lin. error'] = nm.linalg.norm(res, nm.inf)
else:
out = self.solver(mtx_b, mtx_a, n_eigs=n_eigs,
eigenvectors=eigenvectors, status=status)
if eigenvectors:
eigs, vecs = out
out = (1.0 / eigs, vecs[:mtx_m.shape[0], :])
if conf.debug:
res = (1.0 / eigs) * mtx_b.dot(vecs) - mtx_a.dot(vecs)
status['lin. error'] = nm.linalg.norm(res, nm.inf)
else:
out = 1.0 / out
if conf.debug and eigenvectors:
eigs, vecs = out
res = ((eigs**2 * (mtx_m.dot(vecs)))
+ (eigs * (mtx_d.dot(vecs)))
+ (mtx_k.dot(vecs)))
status['error'] = nm.linalg.norm(res, nm.inf)
return out