Symmetricity

Question

Hi,

Could anyone give me some hints here. I would like to know if the stiffness matrix A is symmetric. I tried two methods of estimating the symmetricity. But they give me different results.

The problem is that A.array() does not work for large matrices.

Is there an easy way to get around this issue?

Thanks!

from dolfin import *
import numpy as np

mesh = UnitSquareMesh(20,20)

parameters["linear_algebra_backend"] = "PETSc"

P2 = VectorFunctionSpace(mesh, "CG", 2)
P1 = FunctionSpace(mesh, "CG", 1)
W = MixedFunctionSpace([P2,P1])

bc = DirichletBC(W.sub(0), Constant((0,0)), DomainBoundary())

(u, p) = TrialFunctions(W)
(v, q) = TestFunctions(W)

a = inner(grad(u), grad(v))*dx 
L = inner(Constant((0,0)), v)*dx

A = PETScMatrix()

assemble(a, A)
print 'Is symmetric', np.linalg.norm(A.array() - A.array().T) < 1E-10
temp=A.mat()
print 'Is symmetric', temp.symmetric

`

Answer 1

Hello, the difference is due to tolerances. With symmetric property you are calling isSymmetric with the default 0 tolerance, see here. To get a matching answer try

from dolfin import *
import numpy as np

mesh = UnitSquareMesh(20,20)

parameters["linear_algebra_backend"] = "PETSc"

P2 = VectorFunctionSpace(mesh, "CG", 2)
P1 = FunctionSpace(mesh, "CG", 1)
W = MixedFunctionSpace([P2,P1])

bc = DirichletBC(W.sub(0), Constant((0,0)), DomainBoundary())

(u, p) = TrialFunctions(W)
(v, q) = TestFunctions(W)

a = inner(grad(u), grad(v))*dx 
L = inner(Constant((0,0)), v)*dx

A = PETScMatrix()

assemble(a, A)
print 'Is symmetric', np.linalg.norm(A.array() - A.array().T) < 1E-10
temp=A.mat()
print 'Is symmetric', temp.isSymmetric(1E-10)

Note t

Comments

Great. Thanks!