Alternate partitioning method

[Steven Dalton]

I've been playing around with the partitioning example and LOBPCG.

It's great when it works but unpredictable at times. I've attached an alternative method

based on isoperimetric partitioning that works well though the results may not be as

desirable since it doesn't guarantee connectivity of one of the partitions. The method

randomly selects a node and assigns it to a partition which makes the system nonsingular

and uses CG to solve for the resulting partition.

Anyway, just an idea for a alternative example.

Here's a link to the paper:

http://cns.bu.edu/~lgrady/grady2006isoperimetric_siam.pdf

Regards,

  Steve

[Steven Dalton]

It's not based on any well posed principles but the following code seems to allow LOBPCG to execute without failure from my tests.

# small random perturbation of A diagonals

N = A.shape[0]

data = 10.0**-numpy.random.randint(8,16,size=N)

D = coo_matrix((data,(numpy.arange(N),numpy.arange(N))),A.shape)

A = A + D

# construct preconditioner

ml = smoothed_aggregation_solver(A, coarse_solver='pinv2',max_coarse=10)

M = ml.aspreconditioner()

# solve for lowest two modes: constant vector and Fiedler vector

X = scipy.rand(A.shape[0], 2)

# specify lowest constant eigenvector and orthonormalize Fiedler against it

X[:,0] = numpy.ones((A.shape[0],))

X = numpy.linalg.qr(X, mode='full')[0]

(eval,evec,res) = lobpcg(A, X, M=M, tol=1e-12, largest=False, \

        verbosityLevel=0, retResidualNormsHistory=True)