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# --------------------------------------------------------------------
from petsc4py import PETSc
# --------------------------------------------------------------------
OptDB = PETSc.Options()
INFO = OptDB.hasName('info')
def LOG(arg):
if INFO:
print(arg)
# --------------------------------------------------------------------
class Laplace1D(object):
def create(self, A):
LOG('Laplace1D.create()')
M, N = A.getSize()
assert M == N
def destroy(self, A):
LOG('Laplace1D.destroy()')
def view(self, A, vw):
LOG('Laplace1D.view()')
def setFromOptions(self, A):
LOG('Laplace1D.setFromOptions()')
def setUp(self, A):
LOG('Laplace1D.setUp()')
def assemblyBegin(self, A, flag):
LOG('Laplace1D.assemblyBegin()')
def assemblyEnd(self, A, flag):
LOG('Laplace1D.assemblyEnd()')
def getDiagonal(self, A, d):
LOG('Laplace1D.getDiagonal()')
M, N = A.getSize()
h = 1.0/(M-1)
d.set(2.0/h**2)
def mult(self, A, x, y):
LOG('Laplace1D.mult()')
M, N = A.getSize()
xx = x.getArray(readonly=1) # to numpy array
yy = y.getArray(readonly=0) # to numpy array
yy[0] = 2.0*xx[0] - xx[1]
yy[1:-1] = - xx[:-2] + 2.0*xx[1:-1] - xx[2:]
yy[-1] = - xx[-2] + 2.0*xx[-1]
h = 1.0/(M-1)
yy *= 1.0/h**2
def multTranspose(self, A, x, y):
LOG('Laplace1D.multTranspose()')
self.mult(A, x, y)
# --------------------------------------------------------------------
class Jacobi(object):
def create(self, pc):
LOG('Jacobi.create()')
self.diag = None
def destroy(self, pc):
LOG('Jacobi.destroy()')
if self.diag:
self.diag.destroy()
def view(self, pc, vw):
LOG('Jacobi.view()')
def setFromOptions(self, pc):
LOG('Jacobi.setFromOptions()')
def setUp(self, pc):
LOG('Jacobi.setUp()')
A, B = pc.getOperators()
self.diag = B.getDiagonal(self.diag)
def apply(self, pc, x, y):
LOG('Jacobi.apply()')
y.pointwiseDivide(x, self.diag)
def applyTranspose(self, pc, x, y):
LOG('Jacobi.applyTranspose()')
self.apply(pc, x, y)
# --------------------------------------------------------------------
class ConjGrad(object):
def create(self, ksp):
LOG('ConjGrad.create()')
self.work = []
def destroy(self, ksp):
LOG('ConjGrad.destroy()')
for vec in self.work:
if vec:
vec.destroy()
self.work = []
def view(self, ksp, viewer):
LOG('ConjGrad.view()')
def setUp(self, ksp):
LOG('ConjGrad.setUp()')
self.work[:] = ksp.getWorkVecs(right=3, left=None)
def solve(self, ksp, b, x):
LOG('ConjGrad.solve()')
A, P = get_op_pc(ksp, transpose=False)
pcg(ksp, A, P, b, x, *self.work)
def solveTranspose(self, ksp, b, x):
LOG('ConjGrad.solveTranspose()')
A, P = get_op_pc(ksp, transpose=True)
pcg(ksp, A, P, b, x, *self.work)
def get_op_pc(ksp, transpose=False):
op, _ = ksp.getOperators()
pc = ksp.getPC()
if not transpose:
A = op.mult
P = pc.apply
else:
A = op.multTranspose
P = pc.applyTranspose
return A, P
def do_loop(ksp, r):
its = ksp.getIterationNumber()
rnorm = r.norm()
ksp.setResidualNorm(rnorm)
ksp.logConvergenceHistory(rnorm)
ksp.monitor(its, rnorm)
reason = ksp.callConvergenceTest(its, rnorm)
if not reason:
ksp.setIterationNumber(its+1)
else:
ksp.setConvergedReason(reason)
return reason
def pcg(ksp, A, P, b, x, r, z, p):
A(x, r)
r.aypx(-1, b)
P(r, z)
delta = r.dot(z)
z.copy(p)
while not do_loop(ksp, z):
A(p, z)
alpha = delta / z.dot(p)
x.axpy(+alpha, p)
r.axpy(-alpha, z)
P(r, z)
delta_old = delta
delta = r.dot(z)
beta = delta / delta_old
p.aypx(beta, z)
def richardson(ksp, A, P, b, x, r, z):
A(x, r)
r.aypx(-1, b)
P(r, z)
x.axpy(1, z)
while not do_loop(ksp, z):
A(x, r)
r.aypx(-1, b)
P(r, z)
x.axpy(1, z)
# --------------------------------------------------------------------
|
