def trace_callback( f ):
meigs = eig( mass( f ), eigenvectors = False, method = method )
return meigs,
def find_zero_full_callback( f ):
meigs = eig( (f**2) * mass( f ), mtx_b = christoffel,
eigenvectors = False, method = method )
return meigs
def trace_full_callback( f ):
meigs, mvecs = eig( (f**2) * mass( f ), mtx_b = christoffel,
eigenvectors = True, method = method )
return meigs, mvecs
def find_zero_callback( f ):
meigs = eig( mass( f ), eigenvectors = False, method = method )
return meigs
def solve_eigen_problem1( conf, options ):
pb = ProblemDefinition.from_conf( conf )
dim = pb.domain.mesh.dim
pb.time_update()
dummy = pb.create_state_vector()
output( 'assembling lhs...' )
tt = time.clock()
mtx_a = eval_term_op( dummy, conf.equations['lhs'], pb,
dw_mode = 'matrix', tangent_matrix = pb.mtx_a )
output( '...done in %.2f s' % (time.clock() - tt) )
output( 'assembling rhs...' )
tt = time.clock()
mtx_b = eval_term_op( dummy, conf.equations['rhs'], pb,
dw_mode = 'matrix', tangent_matrix = pb.mtx_a.copy() )
output( '...done in %.2f s' % (time.clock() - tt) )
#mtxA.save( 'tmp/a.txt', format='%d %d %.12f\n' )
#mtxB.save( 'tmp/b.txt', format='%d %d %.12f\n' )
try:
n_eigs = conf.options.n_eigs
except AttributeError:
n_eigs = mtx_a.shape[0]
if n_eigs is None:
n_eigs = mtx_a.shape[0]
## mtx_a.save( 'a.txt', format='%d %d %.12f\n' )
## mtx_b.save( 'b.txt', format='%d %d %.12f\n' )
print 'computing resonance frequencies...'
eig = Solver.any_from_conf( pb.get_solver_conf( conf.options.eigen_solver ) )
eigs, mtx_s_phi = eig( mtx_a, mtx_b, conf.options.n_eigs )
from sfepy.fem.mesh import Mesh
bounding_box = Mesh.from_file("tmp/mesh.vtk").get_bounding_box()
# this assumes a box (3D), or a square (2D):
a = bounding_box[1][0] - bounding_box[0][0]
E_exact = None
if options.hydrogen or options.boron:
if options.hydrogen:
Z = 1
elif options.boron:
Z = 5
if options.dim == 2:
E_exact = [-float(Z)**2/2/(n-0.5)**2/4 for n in [1]+[2]*3+[3]*5 +\
[4]*8 + [5]*15]
elif options.dim == 3:
E_exact = [-float(Z)**2/2/n**2 for n in [1]+[2]*2**2+[3]*3**2 ]
if options.well:
if options.dim == 2:
E_exact = [pi**2/(2*a**2)*x for x in [2, 5, 5, 8, 10, 10, 13, 13,
17, 17, 18, 20, 20 ] ]
elif options.dim == 3:
E_exact = [pi**2/(2*a**2)*x for x in [3, 6, 6, 6, 9, 9, 9, 11, 11,
11, 12, 14, 14, 14, 14, 14, 14, 17, 17, 17] ]
if options.oscillator:
if options.dim == 2:
E_exact = [1] + [2]*2 + [3]*3 + [4]*4 + [5]*5 + [6]*6
elif options.dim == 3:
E_exact = [float(1)/2+x for x in [1]+[2]*3+[3]*6+[4]*10 ]
if E_exact is not None:
print "a=%f" % a
print "Energies:"
print "n exact FEM error"
for i, e in enumerate(eigs):
from numpy import NaN
if i < len(E_exact):
exact = E_exact[i]
err = 100*abs((exact - e)/exact)
else:
exact = NaN
err = NaN
print "%d: %.8f %.8f %5.2f%%" % (i, exact, e, err)
else:
print eigs
## import sfepy.base.plotutils as plu
## plu.spy( mtx_b, eps = 1e-12 )
## plu.pylab.show()
## pause()
n_eigs = eigs.shape[0]
mtx_phi = nm.empty( (pb.variables.di.ptr[-1], mtx_s_phi.shape[1]),
dtype = nm.float64 )
for ii in xrange( n_eigs ):
mtx_phi[:,ii] = pb.variables.make_full_vec( mtx_s_phi[:,ii] )
save = get_default_attr( conf.options, 'save_eig_vectors', None )
out = {}
for ii in xrange( n_eigs ):
if save is not None:
if (ii > save[0]) and (ii < (n_eigs - save[1])): continue
aux = pb.state_to_output( mtx_phi[:,ii] )
key = aux.keys()[0]
out[key+'%03d' % ii] = aux[key]
ofn_trunk = options.output_filename_trunk
pb.domain.mesh.write( ofn_trunk + '.vtk', io = 'auto', out = out )
fd = open( ofn_trunk + '_eigs.txt', 'w' )
eigs.tofile( fd, ' ' )
fd.close()
return Struct( pb = pb, eigs = eigs, mtx_phi = mtx_phi )