def test_real_lu(self):
"""Getting factors of real matrix"""
umfpack = um.UmfpackContext("di")
for A in self.real_matrices:
umfpack.numeric(A)
(L,U,P,Q,R,do_recip) = umfpack.lu(A)
L = L.todense()
U = U.todense()
A = A.todense()
if not do_recip: R = 1.0/R
R = matrix(diag(R))
P = eye(A.shape[0])[P,:]
Q = eye(A.shape[1])[:,Q]
assert_array_almost_equal(P*R*A*Q,L*U)
# needed to speed up a few cases.
# See discussions at:
# https://groups.google.com/d/msg/scikit-image/FrM5IGP6wh4/1hp-FtVZmfcJ
# http://stackoverflow.com/questions/13977970/ignore-exceptions-printed-to-stderr-in-del/13977992?noredirect=1#comment28386412_13977992
try:
from scipy.sparse.linalg.dsolve import umfpack
old_del = umfpack.UmfpackContext.__del__
def new_del(self):
try:
old_del(self)
except AttributeError:
pass
umfpack.UmfpackContext.__del__ = new_del
UmfpackContext = umfpack.UmfpackContext()
except:
UmfpackContext = None
try:
from pyamg import ruge_stuben_solver
amg_loaded = True
except ImportError:
amg_loaded = False
from scipy.sparse.linalg import cg
from ..util import img_as_float
from ..filter import rank_order
#-----------Laplacian--------------------
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 = np.zeros((2, ), dtype=np.double)
times.append(tts)
err = np.zeros((2, 2), dtype=np.double)
errors.append(err)
print('size : %s (%d nnz)' % (mtx.shape, mtx.nnz))
sol0 = np.ones((mtx.shape[0], ), dtype=np.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 = np.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 = list(range(len(nnzs)))
for ii in xrng:
yy = y2 + 0.4 * (ax[3] - ax[2])\
* np.sin( ii * 2 * np.pi / (len( xrng ) - 1) )
if options.compare:
pylab.text(
ii + 0.02, yy, '%s\n%.2e err_umf\n%.2e err_sp' %
(sizes[ii], np.sum(
errors[ii][0, :]), np.sum(errors[ii][1, :])))
else:
pylab.text(
ii + 0.02, yy,
'%s\n%.2e err_umf' % (sizes[ii], np.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()