class Poisson1dTestCase(unittest.TestCase):
def setUp(self):
self.n = 50000
self.B = PysparseMatrix( matrix=poisson.poisson1d(self.n) )
self.x_exact = numpy.ones(self.n)/math.sqrt(self.n)
self.normx = 1.0/math.sqrt(self.n)
self.b = self.B * self.x_exact
lmbd_min = 4.0 * math.sin(math.pi/2.0/self.n) ** 2
lmbd_max = 4.0 * math.sin((self.n - 1)*math.pi/2.0/self.n) ** 2
cond = lmbd_max/lmbd_min
self.tol = cond * macheps()
self.relerr = 0.0
self.nnz = self.B.getNnz()
self.LU = None
self.fmt = '\t%8.2e %8.2e %8d %8d %8d %6.2f %6.2f\n'
def computeError(self, x):
absErr = numpy.linalg.norm(x - self.x_exact, ord=numpy.inf)
self.relerr = absErr/(1 + self.normx)
return self.relerr
def tearDown(self):
self.LU.fetch_lunz()
sys.stdout.write(self.fmt % (self.relerr, self.tol, self.nnz,
self.LU.lnz, self.LU.unz,
self.LU.factorizationTime,
self.LU.solutionTime))
def testPoisson1dDefault(self):
self.LU = PysparseUmfpackSolver(self.B)
self.LU.solve(self.b)
self.failUnless(self.computeError(self.LU.sol) < self.tol)
def testPoisson1dUnsymmetric(self):
self.LU = PysparseUmfpackSolver(self.B, strategy='unsymmetric')
self.LU.solve(self.b)
self.failUnless(self.computeError(self.LU.sol) < self.tol)
def testPoisson1dSymmetric(self):
self.LU = PysparseUmfpackSolver(self.B, strategy='symmetric')
self.LU.solve(self.b)
self.failUnless(self.computeError(self.LU.sol) < self.tol)
def testPoisson1d2by2(self):
self.LU = PysparseUmfpackSolver(self.B, strategy='2by2')
self.LU.solve(self.b)
self.failUnless(self.computeError(self.LU.sol) < self.tol)
def testPoisson1dNoScaling(self):
self.LU = PysparseUmfpackSolver(self.B, scale='none')
self.LU.solve(self.b)
self.failUnless(self.computeError(self.LU.sol) < self.tol)
def testPoisson1dScaleMax(self):
self.LU = PysparseUmfpackSolver(self.B, scale='max')
self.LU.solve(self.b)
self.failUnless(self.computeError(self.LU.sol) < self.tol)
def setUp(self):
self.n = 50000
self.A = PysparseMatrix(matrix=poisson.poisson1d_sym(self.n))
self.x_exact = numpy.ones(self.n)/math.sqrt(self.n)
self.normx = 1.0/math.sqrt(self.n)
self.b = self.A * self.x_exact
lmbd_min = 4.0 * math.sin(math.pi/2.0/self.n) ** 2
lmbd_max = 4.0 * math.sin((self.n - 1)*math.pi/2.0/self.n) ** 2
cond = lmbd_max/lmbd_min
self.tol = cond * macheps()
self.LU = None
self.relerr = 0.0
self.descr = ''
self.fmt = '\t%10s %8.2e %8.2e %8d %8d %6.2f %6.2f\n'
def setUp(self):
self.n = 200
self.A = PysparseMatrix(matrix=poisson.poisson2d_sym_blk(self.n))
self.x_exact = numpy.ones(self.n*self.n)/self.n
self.normx = 1.0/self.n
self.b = self.A * self.x_exact
h = 1.0 / self.n
lmbd_min = 4.0/h/h * (math.sin(math.pi*h/2.0) ** 2 +
math.sin(math.pi*h/2.0) ** 2)
lmbd_max = 4.0/h/h * (math.sin((self.n - 1)*math.pi*h/2.0) ** 2 +
math.sin((self.n - 1)*math.pi*h/2.0) ** 2)
cond = lmbd_max/lmbd_min
self.tol = cond * macheps()
self.LU = None
self.relerr = 0.0
self.descr = ''
self.fmt = '\t%10s %8.2e %8.2e %8d %8d %6.2f %6.2f\n'
class Poisson1dTestCase(unittest.TestCase):
def setUp(self):
self.n = 50000
self.A = PysparseMatrix(matrix=poisson.poisson1d_sym(self.n))
self.x_exact = numpy.ones(self.n)/math.sqrt(self.n)
self.normx = 1.0/math.sqrt(self.n)
self.b = self.A * self.x_exact
lmbd_min = 4.0 * math.sin(math.pi/2.0/self.n) ** 2
lmbd_max = 4.0 * math.sin((self.n - 1)*math.pi/2.0/self.n) ** 2
cond = lmbd_max/lmbd_min
self.tol = cond * macheps()
self.LU = None
self.relerr = 0.0
self.descr = ''
self.fmt = '\t%10s %8.2e %8.2e %8d %8d %6.2f %6.2f\n'
def tearDown(self):
self.LU.fetch_lunz()
sys.stdout.write(self.fmt % (self.descr, self.relerr, self.tol,
self.A.getNnz(),
self.LU.lunz, self.LU.factorizationTime,
self.LU.solutionTime))
def computeError(self, x):
absErr = numpy.linalg.norm(x-self.x_exact, ord=numpy.inf)
self.relerr = absErr/(1+self.normx)
return self.relerr
def testPoisson1dDefault(self):
self.descr = 'poi1d-dflt'
self.LU = PysparseSuperLUSolver(self.A)
self.LU.solve(self.b)
self.failUnless(self.computeError(self.LU.sol) < self.tol)
def testPoisson1dThresh(self):
self.descr = 'poi1d-trsh'
self.LU = PysparseSuperLUSolver(self.A, diag_pivot_thresh=0.5)
self.LU.solve(self.b)
self.failUnless(self.computeError(self.LU.sol) < self.tol)
def testPoisson1dRelax(self):
self.descr = 'poi1d-relx'
self.LU = PysparseSuperLUSolver(self.A, relax=20)
self.LU.solve(self.b)
self.failUnless(self.computeError(self.LU.sol) < self.tol)
def testPoisson1dPanel(self):
self.descr = 'poi1d-size'
self.LU = PysparseSuperLUSolver(self.A, panel_size=1)
self.LU.solve(self.b)
self.failUnless(self.computeError(self.LU.sol) < self.tol)
def testPoisson1dperm0(self):
self.descr = 'poi1d-prm0'
self.LU = PysparseSuperLUSolver(self.A, permc_spec=0)
self.LU.solve(self.b)
self.failUnless(self.computeError(self.LU.sol) < self.tol)
def testPoisson1dperm1(self):
self.descr = 'poi1d-prm1'
self.LU = PysparseSuperLUSolver(self.A, permc_spec=1)
self.LU.solve(self.b)
self.failUnless(self.computeError(self.LU.sol) < self.tol)
def testPoisson1dperm2(self):
self.descr = 'poi1d-prm2'
self.LU = PysparseSuperLUSolver(self.A, permc_spec=2)
self.LU.solve(self.b)
self.failUnless(self.computeError(self.LU.sol) < self.tol)
def testPoisson1dperm3(self):
self.descr = 'poi1d-prm3'
self.LU = PysparseSuperLUSolver(self.A, permc_spec=3)
self.LU.solve(self.b)
self.failUnless(self.computeError(self.LU.sol) < self.tol)