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# ex4.py: Singular value decomposition of the Lauchli matrix
# ==========================================================
#
# This example illustrates the use of the SVD solver in slepc4py. It
# computes singular values and vectors of the Lauchli matrix, whose
# condition number depends on a parameter ``mu``.
#
# The full source code for this demo can be `downloaded here
# <../_static/ex4.py>`__.
# Initialization is similar to previous examples.
try: range = xrange
except: pass
import sys, slepc4py
slepc4py.init(sys.argv)
from petsc4py import PETSc
from slepc4py import SLEPc
# This example takes two command-line arguments, the matrix size ``n``
# and the ``mu`` parameter.
opts = PETSc.Options()
n = opts.getInt('n', 30)
mu = opts.getReal('mu', 1e-6)
PETSc.Sys.Print( "Lauchli singular value decomposition, (%d x %d) mu=%g\n" % (n+1,n,mu) )
# Create the matrix and fill its nonzero entries. Every MPI process will
# insert its locally owned part only.
A = PETSc.Mat(); A.create()
A.setSizes([n+1, n])
A.setFromOptions()
rstart, rend = A.getOwnershipRange()
for i in range(rstart, rend):
if i==0:
for j in range(n):
A[0,j] = 1.0
else:
A[i,i-1] = mu
A.assemble()
# The singular value solver is similar to the eigensolver used in previous
# examples. In this case, we select the thick-restart Lanczos
# bidiagonalization method.
S = SLEPc.SVD(); S.create()
S.setOperator(A)
S.setType(S.Type.TRLANCZOS)
S.setFromOptions()
S.solve()
# After solve, we print some informative data and extract the computed
# solution, showing the list of singular values and the corresponding
# residual errors.
Print = PETSc.Sys.Print
Print( "******************************" )
Print( "*** SLEPc Solution Results ***" )
Print( "******************************\n" )
svd_type = S.getType()
Print( "Solution method: %s" % svd_type )
its = S.getIterationNumber()
Print( "Number of iterations of the method: %d" % its )
nsv, ncv, mpd = S.getDimensions()
Print( "Number of requested singular values: %d" % nsv )
tol, maxit = S.getTolerances()
Print( "Stopping condition: tol=%.4g, maxit=%d" % (tol, maxit) )
nconv = S.getConverged()
Print( "Number of converged approximate singular triplets %d" % nconv )
if nconv > 0:
v, u = A.createVecs()
Print()
Print(" sigma residual norm ")
Print("------------- ---------------")
for i in range(nconv):
sigma = S.getSingularTriplet(i, u, v)
error = S.computeError(i)
Print( " %6f %12g" % (sigma, error) )
Print()
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