"""Preconditioned conjugate gradient method for the EGSZ application"""
from spuq.utils.type_check import takes, optional, returns, tuple_of
from spuq.linalg.operator import Operator
from spuq.linalg.vector import Vector, inner
from spuq.utils.forgetful_vector import ForgetfulVector
__all__ = ["pcg"]
import logging
logger = logging.getLogger(__name__)
@takes(Operator, Vector, Operator, Vector, optional(float), optional(int))
def pcg(A, f, P, w0, eps=1e-4, maxiter=100):
# for most quantities in PCG (except zeta) only the most recent
# values needs to be kept in memory
w = ForgetfulVector(1)
rho = ForgetfulVector(1)
s = ForgetfulVector(1)
v = ForgetfulVector(1)
z = ForgetfulVector(1)
alpha = ForgetfulVector(1)
zeta = ForgetfulVector(2)
w[0] = w0
rho[0] = f - A * w[0]
s[0] = P * rho[0]
v[0] = s[0]
zeta[0] = inner(rho[0], s[0])
for i in xrange(1, maxiter):
DEFAULT_BC = object()
@takes((Expression, Function), FunctionSpace)
def poisson_bilinear_form(coeff_func, V):
"""Assemble the discrete problem (i.e. the stiffness matrix)."""
# setup problem, assemble and apply boundary conditions
u = TrialFunction(V)
v = TestFunction(V)
a = inner(coeff_func * nabla_grad(u), nabla_grad(v)) * dx
return a
@takes(anything, (DirichletBC, NoneType, object), optional(FunctionSpace))
def apply_bc(fenics_obj, bc=DEFAULT_BC, V=None):
if bc is not None:
if bc is DEFAULT_BC:
if V is None:
V = fenics_obj.function_space()
bc = homogeneous_dirichlet_bc(V)
bc.apply(fenics_obj)
return fenics_obj
@takes(GenericMatrix, (DirichletBC, sequence_of(DirichletBC)))
def _remove_boundary_entries(A, bcs):
if not isinstance(bcs, DirichletBC):
for bc in bcs:
remove_boundary_entries(A, bc)
import collections
from abc import ABCMeta, abstractmethod
default_Dirichlet_boundary = lambda x, on_boundary: on_boundary
CoefficientFunction = (dolfin.Expression, dolfin.GenericFunction, ufl.expr.Expr, tuple_of((dolfin.Expression, dolfin.GenericFunction, ufl.expr.Expr, float, int)))
FormFunction = (dolfin.Argument, dolfin.Function)
LoadingFunction = (dolfin.Coefficient)
BoundaryType = (anything)
BoundaryFunction = (dolfin.Coefficient)
###################################################
# Helper functions
###################################################
@takes(anything, optional(int))
def make_list(x, length=None):
"""Make a sequence type out of some item if it not already is one"""
if not isinstance(x, collections.Sequence):
x = [x]
if length is not None:
if len(x) == 1:
x = x * length
assert len(x) == length
return x
@takes(dolfin.FunctionSpaceBase)
def zero_function(V):
if V.num_sub_spaces():
d = V.mesh().geometry().dim()
