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#!/usr/bin/env python
# Created by: Robert Cimrman, 05.12.2005
"""Benchamrks for umfpack module"""
from optparse import OptionParser
import scipy.linsolve.umfpack as um
import numpy as nm
#import scipy.io as io
import scipy.sparse as sp
import scipy.linalg as nla
#import pylab
import time
import urllib
import gzip
defaultURL = 'http://www.cise.ufl.edu/research/sparse/HBformat/'
usage = """%%prog [options] <matrix file name> [<matrix file name>, ...]
<matrix file name> can be a local or distant (gzipped) file
default url is:
%s
supported formats are:
triplet .. [nRow, nCol, nItem] followed by 'nItem' * [ir, ic, value]
hb .. Harwell-Boeing format N/A
""" % defaultURL
##
# 05.12.2005, c
def read_triplet( fd ):
nRow, nCol = map( int, fd.readline().split() )
nItem = int( fd.readline() )
ij = nm.zeros( (nItem,2), nm.int32 )
val = nm.zeros( (nItem,), nm.float64 )
for ii, row in enumerate( fd.readlines() ):
aux = row.split()
ij[ii] = int( aux[0] ), int( aux[1] )
val[ii] = float( aux[2] )
mtx = sp.csc_matrix( (val, ij), dims = (nRow, nCol), nzmax = nItem )
return mtx
##
# 06.12.2005, c
def read_triplet2( fd ):
nRow, nCol = map( int, fd.readline().split() )
nItem = int( fd.readline() )
ij, val = io.read_array( fd,
columns = [(0,1), (2,)],
atype = (nm.int32, nm.float64),
rowsize = nItem )
mtx = sp.csc_matrix( (val, ij), dims = (nRow, nCol), nzmax = nItem )
return mtx
formatMap = {'triplet' : read_triplet}
##
# 05.12.2005, c
def readMatrix( matrixName, options ):
if options.default_url:
matrixName = defaultURL + matrixName
print 'url:', matrixName
if matrixName[:7] == 'http://':
fileName, status = urllib.urlretrieve( matrixName )
## print status
else:
fileName = matrixName
print 'file:', fileName
try:
readMatrix = formatMap[options.format]
except:
raise ValueError, 'unsupported format: %s' % options.format
print 'format:', options.format
print 'reading...'
if fileName[-3:] == '.gz':
fd = gzip.open( fileName )
else:
fd = open( fileName )
mtx = readMatrix( fd )
fd.close()
print 'ok'
return mtx
##
# 05.12.2005, c
def main():
parser = OptionParser( usage = usage )
parser.add_option( "-c", "--compare",
action = "store_true", dest = "compare",
default = False,
help = "compare with default scipy.sparse solver [default: %default]" )
parser.add_option( "-p", "--plot",
action = "store_true", dest = "plot",
default = False,
help = "plot time statistics [default: %default]" )
parser.add_option( "-d", "--default-url",
action = "store_true", dest = "default_url",
default = False,
help = "use default url [default: %default]" )
parser.add_option( "-f", "--format", type = type( '' ),
dest = "format", default = 'triplet',
help = "matrix format [default: %default]" )
(options, args) = parser.parse_args()
if (len( args ) >= 1):
matrixNames = args;
else:
parser.print_help(),
return
sizes, nnzs, times, errors = [], [], [], []
legends = ['umfpack', 'sparse.solve']
for ii, matrixName in enumerate( matrixNames ):
print '*' * 50
mtx = readMatrix( matrixName, options )
sizes.append( mtx.shape )
nnzs.append( mtx.nnz )
tts = nm.zeros( (2,), dtype = nm.double )
times.append( tts )
err = nm.zeros( (2,2), dtype = nm.double )
errors.append( err )
print 'size : %s (%d nnz)' % (mtx.shape, mtx.nnz)
sol0 = nm.ones( (mtx.shape[0],), dtype = nm.double )
rhs = mtx * sol0
umfpack = um.UmfpackContext()
tt = time.clock()
sol = umfpack( um.UMFPACK_A, mtx, rhs, autoTranspose = True )
tts[0] = time.clock() - tt
print "umfpack : %.2f s" % tts[0]
error = mtx * sol - rhs
err[0,0] = nla.norm( error )
print '||Ax-b|| :', err[0,0]
error = sol0 - sol
err[0,1] = nla.norm( error )
print '||x - x_{exact}|| :', err[0,1]
if options.compare:
tt = time.clock()
sol = sp.solve( mtx, rhs )
tts[1] = time.clock() - tt
print "sparse.solve : %.2f s" % tts[1]
error = mtx * sol - rhs
err[1,0] = nla.norm( error )
print '||Ax-b|| :', err[1,0]
error = sol0 - sol
err[1,1] = nla.norm( error )
print '||x - x_{exact}|| :', err[1,1]
if options.plot:
try:
import pylab
except ImportError:
raise ImportError, "could not import pylab"
times = nm.array( times )
print times
pylab.plot( times[:,0], 'b-o' )
if options.compare:
pylab.plot( times[:,1], 'r-s' )
else:
del legends[1]
print legends
ax = pylab.axis()
y2 = 0.5 * (ax[3] - ax[2])
xrng = range( len( nnzs ) )
for ii in xrng:
yy = y2 + 0.4 * (ax[3] - ax[2])\
* nm.sin( ii * 2 * nm.pi / (len( xrng ) - 1) )
if options.compare:
pylab.text( ii+0.02, yy,
'%s\n%.2e err_umf\n%.2e err_sp'
% (sizes[ii], nm.sum( errors[ii][0,:] ),
nm.sum( errors[ii][1,:] )) )
else:
pylab.text( ii+0.02, yy,
'%s\n%.2e err_umf'
% (sizes[ii], nm.sum( errors[ii][0,:] )) )
pylab.plot( [ii, ii], [ax[2], ax[3]], 'k:' )
pylab.xticks( xrng, ['%d' % (nnzs[ii] ) for ii in xrng] )
pylab.xlabel( 'nnz' )
pylab.ylabel( 'time [s]' )
pylab.legend( legends )
pylab.axis( [ax[0] - 0.05, ax[1] + 1, ax[2], ax[3]] )
pylab.show()
if __name__ == '__main__':
main()
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