def set_pmr_solver(K, M):
# =========================== Solver setting ===========================
# define solver
# How to use
# SLEPcEigenSolver(A): Create eigenvalue solver for Ax = \lambda x
# SLEPcEigenSolver(A, B): Create eigenvalue solver Ax = \lambda Bx (Generalized Hermitian eigenvalue problem)
eigensolver = df.SLEPcEigenSolver(K, M) # Ku = \lambda Mu
# print( help(SLEPcEigenSolver) )
# print( help(eigensolver.get_options_prefix ) )
# monitor SLEP solver
# PETScOptions.set("eps_view")
# PETScOptions.set("ksp_type", "cg")
# PETScOptions.set("pc_type", "none")
# PETScOptions.set("ksp_monitor_singular_value", "")
# print(help(PETScOptions.set))
# set solver's parameters
pmr = eigensolver.parameters
# solver setup 1
pmr["problem_type"] = "gen_hermitian"
pmr["tolerance"] = 1e-14
pmr["spectral_transform"] = "shift-and-invert" # needed
pmr["spectral_shift"] = 0.0
pmr["solver"] = "krylov-schur"
#pmr['solver'] = 'lanczos' # too long, even parallelism is used
return eigensolver
def compute_eig(M, filename):
eigsolver = dl.SLEPcEigenSolver(M)
eigsolver.solve()
eig = []
for ii in range(eigsolver.get_number_converged()):
eig.append(eigsolver.get_eigenvalue(ii)[0])
eig.sort()
np.savetxt(filename, np.array(eig))
def eigen_xct(V, A, B=None, k=100, spect='LM', **kwargs):
"""
Get eigen-pairs of A (or generalized eigen-pairs for (A,B)) for the first k in the spectrum spect.
"""
if 'mpi_comm' in kwargs:
mpi_comm = kwargs['mpi_comm']
else:
mpi_comm = df.mpi_comm_world()
# mixed functions to store eigenfunctions
try:
M = df.FunctionSpace(V.mesh(), df.MixedElement([V.ufl_element()] * k))
except:
print('Warning: '
'MixedFunctionSpace'
' has been deprecated after DOLFIN version 1.6.0.')
M = df.MixedFunctionSpace([V] * k)
# Extract subfunction dofs
eigf_dofs = [M.sub(i).dofmap().dofs() for i in range(k)]
eigf = df.Function(M)
# try reading eigen-pairs from file
eig_files = [
f for f in os.listdir(os.getcwd())
if f.startswith('prior_' + spect + 'eig')
]
found_eigv = False
found_eigf = False
if any(eig_files):
for f_i in eig_files:
if int(f_i.split("_k")[-1].split(".")[0]) >= k:
if f_i.endswith('.txt'):
try:
eigv_ = np.loadtxt(os.path.join(os.getcwd(), f_i),
delimiter=',')
eigv = eigv_[:k]
found_eigv = True
except:
pass
if f_i.endswith('.h5'):
try:
f = df.HDF5File(mpi_comm,
os.path.join(os.getcwd(), f_i), "r")
eigf_i = df.Function(V, name='eigenfunction')
for i, dof_i in enumerate(eigf_dofs):
f.read(eigf_i, 'eigf_{0}'.format(i))
eigf.vector()[dof_i] = eigf_i.vector()
f.close()
found_eigf = True
except:
f.close()
pass
if found_eigv and found_eigf:
break
if found_eigv and found_eigf:
print('Read the first %d eigen-pairs with ' % k + {
'LM': 'largest magnitude',
'SM': 'smallest magnitude'
}[spect] + ' successfully!')
return (eigv, eigf), eigf_dofs
else:
# solve the associated eigen-problem
f = df.HDF5File(
mpi_comm,
os.path.join(os.getcwd(),
'prior_' + spect + 'eigf_k' + str(k) + '.h5'), "w")
eigf_i = df.Function(V, name='eigenfunction')
if type(A) is df.PETScMatrix and df.has_slepc():
# using SLEPc
print("Computing the first %d eigenvalues with " % k + {
'LM': 'largest magnitude',
'SM': 'smallest magnitude'
}[spect] + "...")
# Create eigen-solver
if B is not None and type(B) is df.PETScMatrix:
eigen = df.SLEPcEigenSolver(A, B)
eigen.parameters['problem_type'] = 'gen_hermitian'
else:
eigen = df.SLEPcEigenSolver(A)
# eigen.parameters['problem_type']='hermitian'
eigen.parameters['spectrum'] = {
'LM': 'largest magnitude',
'SM': 'smallest magnitude'
}[spect]
if spect is 'SM':
eigen.parameters['tolerance'] = 1e-10
eigen.parameters['maximum_iterations'] = 100
eigen.parameters['spectral_transform'] = 'shift-and-invert'
eigen.parameters['spectral_shift'] = 10.0 * df.DOLFIN_EPS
eigen.solve(k)
print(
'Total number of iterations: %d, and total number of convergences: %d.'
% (eigen.get_iteration_number(), eigen.get_number_converged()))
# get eigen-pairs
eigv = np.zeros(k)
for i, dof_i in enumerate(eigf_dofs):
eigv[i], _, eigf_vec_i, _ = eigen.get_eigenpair(i)
eigf_i.vector()[:] = eigf_vec_i[:]
f.write(eigf_i, 'eigf_{0}'.format(i))
eigf.vector()[dof_i] = eigf_i.vector()
else:
warnings.warn(
'petsc4py or SLEPc not found! Using scipy.sparse.linalg.eigsh...'
)
import scipy.sparse.linalg as spsla
eigv, eigf_vec = spsla.eigsh(A, k=k, M=B, which=spect)
dsc_ord = eigv.argsort()[::-1]
eigv = eigv[dsc_ord]
eigf_vec = eigf_vec[:, dsc_ord]
for i, dof_i in enumerate(eigf_dofs):
eigf_i.vector()[:] = eigf_vec[:, i]
f.write(eigf_i, 'eigf_{0}'.format(i))
eigf.vector()[dof_i] = eigf_i.vector()
f.close()
np.savetxt(os.path.join(os.getcwd(),
'prior_' + spect + 'eigv_k' + str(k) + '.txt'),
eigv,
delimiter=',')
return (eigv, eigf), eigf_dofs
dolfin.assemble(t, tensor=T)
print(S.size(1))
markers=dolfin.MeshFunction('size_t',mesh,1)
markers.set_all(0)
dolfin.DomainBoundary().mark(markers,1)
electric_wall = dolfin.DirichletBC(V,
dolfin.Constant(0.0),
markers,
1)
electric_wall.apply(S)
electric_wall.apply(T)
#from scipy.linalg import eig
#lambds, vectors=eig(S.array(),T.array())
# Solve the eigensystem
esolver = dolfin.SLEPcEigenSolver(S,T)
esolver.solve(S.size(1))
res=[esolver.get_eigenpair(i) for i in range(esolver.get_number_converged())]
res.sort(key=lambda tup: tup[0])
lambds=np.array([r[0] for r in res])
vect=[r[2] for r in res]
#lambds=np.sort(np.array(lambds))
plt.close('all')
plt.figure()
plt.plot(lambds, '.', color='g')
for lambd in lambds_real[:20]:
plt.plot([0,len(lambds)],[lambd, lambd], '--', color='r')
plt.ylim([-1,lambds_real[20]+1])
bb[:] = b
lu.solve(xx, bb)
return xx[:]
M_matvec = lambda x: M * x
arpack_eigs, v = speigs.ARPACK_gen_eigs(M_matvec,
sigma_solve,
M.size(0),
sigma,
51,
ncv=91)
# Create eigensolver
esolver = dol.SLEPcEigenSolver(S, M)
esolver.parameters["spectrum"] = "smallest real"
esolver.parameters["solver"] = "arnoldi"
esolver.parameters["spectral_shift"] = sigma
esolver.parameters["spectral_transform"] = "shift-and-invert"
esolver.solve()
eigs = [esolver.get_eigenvalue(i)[0] for i in range(4)]
filtered_eigs = []
for i in range(S.size(0)):
ev_r, ev_i = esolver.get_eigenvalue(i)
if ev_r > 0.001:
filtered_eigs.append(ev_r)
print sorted(arpack_eigs)[0:4]
print eigs[0:4]