def test_Arnoldifyer():
vs = [numpy.ones((10, 1)),
numpy.r_[numpy.ones((3, 1)), numpy.zeros((7, 1))]
]
for matrix in test_utils.get_matrices():
A_norm = numpy.linalg.norm(matrix, 2)
numpy.random.seed(0)
Ms = [None, numpy.diag(range(1, 11))]
Wt_sels = ['none', 'smallest', 'largest']
for A, v, M, Wt_sel in \
itertools.product(test_utils.get_operators(matrix),
vs, Ms, Wt_sels):
if M is None:
Minv = None
else:
Minv = numpy.linalg.inv(M)
ls = krypy.linsys.LinearSystem(A, v, M=M, Minv=Minv)
evals, evecs = scipy.linalg.eig(ls.M*matrix)
sort = numpy.argsort(numpy.abs(evals))
evecs = evecs[:, sort]
Us = [numpy.zeros((10, 0)),
evecs[:, -2:],
evecs[:, -2:] + 1e-2*numpy.random.rand(10, 2)
]
for U in Us:
yield run_Arnoldifyer, ls, U, A_norm, Wt_sel
def test_linsys_herm_indef():
A = test_utils.get_matrix_herm_indef()
Ainv = numpy.linalg.inv(A)
# solution
x = (1.+1.j)*numpy.ones((10,1))
# preconditioner
m = numpy.array(range(1,11))
m[-1] = 1.
M, Minv = numpy.diag(m), numpy.diag(1./m)
params_adds = [
{ 'M': [ None ] + test_utils.get_operators(Minv) },
{ 'Ml': [ None, Ainv ] + test_utils.get_operators(Minv) },
{ 'Mr': [ None, Ainv ] + test_utils.get_operators(Minv) }
]
solvers = [ krypy.linsys.minres, krypy.linsys.gmres ]
for case in produce_cases(A, x, params_adds, solvers):
yield case
def test_linsys_comp_nonsymm():
A = test_utils.get_matrix_comp_nonsymm()
Ainv = numpy.linalg.inv(A)
# solution
x = (1.j+1)*numpy.ones((10,1))
# preconditioner
m = numpy.array(range(1,11))
m[-1] = 1.
M, Minv = numpy.diag(m), numpy.diag(1./m)
params_adds = [
{ 'maxiter': [5], 'max_restarts': [20] },
{ 'M': [ None ] + test_utils.get_operators(Minv) },
{ 'Ml': [ None, Ainv ] + test_utils.get_operators(Minv) },
{ 'Mr': [ None, Ainv ] + test_utils.get_operators(Minv) }
]
solvers = [ krypy.linsys.gmres ]
for case in produce_cases(A, x, params_adds, solvers):
yield case
def test_linsys_symm_indef():
A = test_utils.get_matrix_symm_indef()
Ainv = numpy.linalg.inv(A)
# solution
x = numpy.ones((10, 1))
# preconditioner
m = numpy.array(range(1, 11))
m[-1] = 1.
M, Minv = numpy.diag(m), numpy.diag(1. / m)
params_adds = [{
'M': [None] + test_utils.get_operators(Minv)
}, {
'Ml': [None, Ainv] + test_utils.get_operators(Minv)
}, {
'Mr': [None, Ainv] + test_utils.get_operators(Minv)
}]
solvers = [krypy.linsys.minres, krypy.linsys.gmres]
for case in produce_cases(A, x, params_adds, solvers):
yield case
def test_linsys_comp_nonsymm():
A = test_utils.get_matrix_comp_nonsymm()
Ainv = numpy.linalg.inv(A)
# solution
x = (1.j + 1) * numpy.ones((10, 1))
# preconditioner
m = numpy.array(range(1, 11))
m[-1] = 1.
M, Minv = numpy.diag(m), numpy.diag(1. / m)
params_adds = [{
'maxiter': [5],
'max_restarts': [20]
}, {
'M': [None] + test_utils.get_operators(Minv)
}, {
'Ml': [None, Ainv] + test_utils.get_operators(Minv)
}, {
'Mr': [None, Ainv] + test_utils.get_operators(Minv)
}]
solvers = [krypy.linsys.gmres]
for case in produce_cases(A, x, params_adds, solvers):
yield case
def produce_cases(A, x, params_adds, solvers):
b = numpy.dot(A, x)
params_base = {
'A': test_utils.get_operators(A),
'b': test_utils.get_vecs(b),
'x0': [ None, numpy.zeros(b.shape), x ] + test_utils.get_vecs(numpy.ones(b.shape)),
'tol': [ 1e-14, 1e-5, 1e-2 ],
'maxiter': [ 15 ],
'M': [ None ],
'Ml': [ None ],
'Mr': [ None ],
'inner_product': [ krypy.utils.ip_euclid ],
'exact_solution': [ None ] + test_utils.get_vecs(x)
}
for params_add in params_adds:
params = dict( list(params_base.items()) + list(params_add.items()))
for solver, param in itertools.product(solvers, dictproduct(params)):
yield run_case, solver, param
def produce_cases(A, x, params_adds, solvers):
b = numpy.dot(A, x)
params_base = {
'A':
test_utils.get_operators(A),
'b':
test_utils.get_vecs(b),
'x0': [None, numpy.zeros(b.shape), x] +
test_utils.get_vecs(numpy.ones(b.shape)),
'tol': [1e-14, 1e-5, 1e-2],
'maxiter': [15],
'M': [None],
'Ml': [None],
'Mr': [None],
'inner_product': [krypy.utils.ip_euclid],
'exact_solution': [None] + test_utils.get_vecs(x)
}
for params_add in params_adds:
params = dict(list(params_base.items()) + list(params_add.items()))
for solver, param in itertools.product(solvers, dictproduct(params)):
yield run_case, solver, param