def solve_eigensystem(M, C, K):
# Setup the eigensolver
Q = SLEPc.PEP().create()
A = []
A.append(K)
A.append(C)
A.append(M)
Q.setOperators(A)
Q.setDimensions(6)
Q.setProblemType(SLEPc.PEP.ProblemType.GENERAL)
Q.setFromOptions()
# Solve the eigensystem
Q.solve()
# Create the results vectors
xr, tmp = K.getVecs()
xi, tmp = K.getVecs()
its = Q.getIterationNumber()
Print("Number of iterations of the method: %i" % its)
sol_type = Q.getType()
Print("Solution method: %s" % sol_type)
nev, ncv, mpd = Q.getDimensions()
Print("")
Print("Number of requested eigenvalues: %i" % nev)
tol, maxit = Q.getTolerances()
Print("Stopping condition: tol=%.4g, maxit=%d" % (tol, maxit))
nconv = Q.getConverged()
Print("Number of converged approximate eigenpairs: %d" % nconv)
if nconv > 0:
Print("")
Print(" k ||(k^2M+Ck+K)x||/||kx|| ")
Print("-------------------- -------------------------")
for i in range(nconv):
k = Q.getEigenpair(i, xr, xi)
error = Q.computeError(i)
if k.imag != 0.0:
Print("%9f%+9f j %12g" % (k.real, k.imag, error))
else:
Print("%12f %12g" % (k.real, error))
Print("")
V = FunctionSpace(mesh, 'CG', 1) u = TrialFunction(V) v = TestFunction(V) bc = DirichletBC(V, Constant(0), DomainBoundary()) a = inner(grad(u), grad(v)) * dx m = inner(u, v) * dx L = inner(Constant(1), v) * dx A, M = PETScMatrix(), PETScMatrix() b = PETScVector() # See that assemble + bc.apply does not imply symmetry assemble(a, A) bc.apply(A) print 'Is symmetric?', np.linalg.norm(A.array() - A.array().T) < 1E-10 # But assemble system does assemble_system(a, L, bc, A_tensor=A, b_tensor=b) assemble_system(m, L, bc, A_tensor=M, b_tensor=b) print 'Is symmetric?', np.linalg.norm(A.array() - A.array().T) < 1E-10 print 'Is symmetric?', np.linalg.norm(M.array() - M.array().T) < 1E-10 from slepc4py import SLEPc E = SLEPc.PEP().create() E.setOperators([A.mat(), M.mat(), A.mat()])
def help(args=None):
import sys
# program name
try:
prog = sys.argv[0]
except Exception:
prog = getattr(sys, 'executable', 'python')
# arguments
if args is None:
args = sys.argv[1:]
elif isinstance(args, str):
args = args.split()
else:
args = [str(a) for a in args]
# initialization
import slepc4py
slepc4py.init([prog, '-help'] + args)
from slepc4py import SLEPc
# and finally ...
COMM = SLEPc.COMM_SELF
if 'eps' in args:
eps = SLEPc.EPS().create(comm=COMM)
eps.setFromOptions()
eps.destroy()
del eps
if 'svd' in args:
svd = SLEPc.SVD().create(comm=COMM)
svd.setFromOptions()
svd.destroy()
del svd
if 'pep' in args:
pep = SLEPc.PEP().create(comm=COMM)
pep.setFromOptions()
pep.destroy()
del pep
if 'nep' in args:
nep = SLEPc.NEP().create(comm=COMM)
nep.setFromOptions()
nep.destroy()
del nep
if 'mfn' in args:
mfn = SLEPc.MFN().create(comm=COMM)
mfn.setFromOptions()
mfn.destroy()
del mfn
if 'st' in args:
st = SLEPc.ST().create(comm=COMM)
st.setFromOptions()
st.destroy()
del st
if 'bv' in args:
bv = SLEPc.BV().create(comm=COMM)
bv.setFromOptions()
bv.destroy()
del bv
if 'rg' in args:
rg = SLEPc.RG().create(comm=COMM)
rg.setFromOptions()
rg.destroy()
del rg
if 'fn' in args:
fn = SLEPc.FN().create(comm=COMM)
fn.setFromOptions()
fn.destroy()
del fn
if 'ds' in args:
ds = SLEPc.DS().create(comm=COMM)
ds.setFromOptions()
ds.destroy()
del ds