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'''
This module contains all the function and class needed to wrap a PETSc Nullspace in NGSolve
'''
from petsc4py import PETSc
from ngsPETSc import VectorMapping
class NullSpace:
'''
This class creates a PETSc Null space from NGSolve vectors
:arg fes: NGSolve finite element space.
:arg span: list NGSolve grid functions spanning the null space.
'''
def __init__(self, fes, span, near=False):
constant = False
self.vecMap = VectorMapping(fes)
self.near = near
if isinstance(span, list):
nullspace = list(span)
petscNullspace = []
for vec in nullspace:
if isinstance(vec, str):
if vec == "constant":
constant = True
else:
raise ValueError("Invalid nullspace string")
else:
petscVec = self.vecMap.petscVec(vec)
petscNullspace.append(petscVec)
elif isinstance(span, str):
if span == "constant":
constant = True
petscNullspace = []
else:
raise ValueError("Invalid nullspace string")
else:
raise ValueError("Invalid nullspace type")
# Create vector space basis and orthogonalize
self.constant = constant
self.orthonormalize(petscNullspace)
self.nullspace = PETSc.NullSpace().create(constant=constant, vectors=petscNullspace)
def orthonormalize(self, basis):
"""Orthonormalize the basis."""
for i, vec in enumerate(basis):
alphas = []
for vec_ in basis[:i]:
alphas.append(vec.dot(vec_))
for alpha, vec_ in zip(alphas, basis[:i]):
vec.axpy(-alpha, vec_)
if self.constant:
# Subtract constant mode
alpha = vec.sum()
vec.array -= alpha
vec.normalize()
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