template <class Scalar> inline
SolverState<Scalar> BlockTriangularSolver<Scalar>
::solve(const LinearOperator<Scalar>& op,
const Vector<Scalar>& rhs,
Vector<Scalar>& soln) const
{
int nRows = op.numBlockRows();
int nCols = op.numBlockCols();
soln = op.domain().createMember();
// bool converged = false;
TEST_FOR_EXCEPTION(nRows != rhs.space().numBlocks(), std::runtime_error,
"number of rows in operator " << op
<< " not equal to number of blocks on RHS "
<< rhs);
TEST_FOR_EXCEPTION(nRows != nCols, std::runtime_error,
"nonsquare block structure in block triangular "
"solver: nRows=" << nRows << " nCols=" << nCols);
bool isUpper = false;
bool isLower = false;
for (int r=0; r<nRows; r++)
{
for (int c=0; c<nCols; c++)
{
if (op.getBlock(r,c).ptr().get() == 0 ||
dynamic_cast<const SimpleZeroOp<Scalar>* >(op.getBlock(r,c).ptr().get()))
{
TEST_FOR_EXCEPTION(r==c, std::runtime_error,
"zero diagonal block (" << r << ", " << c
<< " detected in block "
"triangular solver. Operator is " << op);
continue;
}
else
{
if (r < c) isUpper = true;
if (c < r) isLower = true;
}
}
}
TEST_FOR_EXCEPTION(isUpper && isLower, std::runtime_error,
"block triangular solver detected non-triangular operator "
<< op);
bool oneSolverFitsAll = false;
if ((int) solvers_.size() == 1 && nRows != 1)
{
oneSolverFitsAll = true;
}
for (int i=0; i<nRows; i++)
{
int r = i;
if (isUpper) r = nRows - 1 - i;
Vector<Scalar> rhs_r = rhs.getBlock(r);
for (int j=0; j<i; j++)
{
int c = j;
if (isUpper) c = nCols - 1 - j;
if (op.getBlock(r,c).ptr().get() != 0)
{
rhs_r = rhs_r - op.getBlock(r,c) * soln.getBlock(c);
}
}
SolverState<Scalar> state;
Vector<Scalar> soln_r;
if (oneSolverFitsAll)
{
state = solvers_[0].solve(op.getBlock(r,r), rhs_r, soln_r);
}
else
{
state = solvers_[r].solve(op.getBlock(r,r), rhs_r, soln_r);
}
if (nRows > 1) soln.setBlock(r, soln_r);
else soln = soln_r;
if (state.finalState() != SolveConverged)
{
return state;
}
}
return SolverState<Scalar>(SolveConverged, "block solves converged",
0, ScalarTraits<Scalar>::zero());
}
int main(int argc, char *argv[])
{
int stat = 0;
try
{
GlobalMPISession session(&argc, &argv);
MPIComm::world().synchronize();
Out::os() << "go!" << std::endl;
VectorType<double> type = new EpetraVectorType();
Array<int> domainBlockSizes = tuple(2,3,4);
Array<int> rangeBlockSizes = tuple(2,2);
Array<VectorSpace<double> > domainBlocks(domainBlockSizes.size());
Array<VectorSpace<double> > rangeBlocks(rangeBlockSizes.size());
for (int i=0; i<domainBlocks.size(); i++)
{
domainBlocks[i] = type.createEvenlyPartitionedSpace(MPIComm::world(),
domainBlockSizes[i]);
}
for (int i=0; i<rangeBlocks.size(); i++)
{
rangeBlocks[i] = type.createEvenlyPartitionedSpace(MPIComm::world(),
rangeBlockSizes[i]);
}
VectorSpace<double> domain = blockSpace(domainBlocks);
VectorSpace<double> range = blockSpace(rangeBlocks);
double blockDensity = 0.75;
double onProcDensity = 0.5;
double offProcDensity = 0.1;
RandomBlockMatrixBuilder<double> builder(domain, range,
blockDensity,
onProcDensity,
offProcDensity,
type);
LinearOperator<double> A = builder.getOp();
Out::os() << "A num block rows = " << A.numBlockRows() << std::endl;
Out::os() << "A num block cols = " << A.numBlockCols() << std::endl;
Vector<double> x = domain.createMember();
Out::os() << "randomizing trial vector" << std::endl;
x.randomize();
Array<Vector<double> > xBlock(domain.numBlocks());
for (int i=0; i<xBlock.size(); i++)
{
xBlock[i] = x.getBlock(i);
}
Vector<double> xx = x.copy();
Out::os() << "------------------------------------------------------------" << std::endl;
Out::os() << "computing A*x..." << std::endl;
Vector<double> y0 = A * x;
for (int i=0; i<y0.space().numBlocks(); i++)
{
Out::os() << "y0[" << i << "] = " << std::endl << y0.getBlock(i) << std::endl;
}
Vector<double> y1 = range.createMember();
Out::os() << "------------------------------------------------------------" << std::endl;
Out::os() << "computing A*x block-by-block..." << std::endl;
Array<Vector<double> > yBlock(range.numBlocks());
for (int i=0; i<yBlock.size(); i++)
{
yBlock[i] = range.getBlock(i).createMember();
yBlock[i].zero();
for (int j=0; j<xBlock.size(); j++)
{
LinearOperator<double> Aij = A.getBlock(i,j);
if (Aij.ptr().get() != 0)
{
Out::os() << "A(" << i << ", " << j << ") = " << std::endl
<< Aij << std::endl;
}
else
{
Out::os() << "A(" << i << ", " << j << ") = 0 " << std::endl;
}
Out::os() << "x[" << j << "] = " << std::endl << xBlock[j] << std::endl;
if (Aij.ptr().get()==0) continue;
yBlock[i] = yBlock[i] + Aij * xBlock[j];
}
y1.setBlock(i, yBlock[i]);
}
for (int i=0; i<y1.space().numBlocks(); i++)
{
Out::os() << "y1[" << i << "] = " << std::endl << y1.getBlock(i) << std::endl;
}
double err = (y1 - y0).norm2();
Out::os() << "error = " << err << std::endl;
double tol = 1.0e-13;
if (err < tol)
{
Out::os() << "block op test PASSED" << std::endl;
}
else
{
stat = -1;
Out::os() << "block op test FAILED" << std::endl;
}
}
catch(std::exception& e)
{
stat = -1;
Out::os() << "Caught exception: " << e.what() << std::endl;
}
return stat;
}
Preconditioner<double>
PCDPreconditionerFactory::
createPreconditioner(const LinearOperator<double>& K) const
{
Tabs tab;
LinearOperator<double> F = K.getBlock(0,0);
// F.setName("F");
LinearOperator<double> FInv = inverse(F, FSolver_);
// FInv.setName("FInv");
LinearOperator<double> Bt = K.getBlock(0,1);
// Bt.setName("Bt");
LinearOperator<double> Fp = FpProb_.getOperator();
LinearOperator<double> Mp = MpProb_.getOperator();
// Mp.setName("Mp");
LinearOperator<double> MpInv = inverse(Mp, MpSolver_);
// MpInv.setName("MpInv");
LinearOperator<double> Ap = ApProb_.getOperator();
// Ap.setName("Ap");
LinearOperator<double> ApInv = inverse(Ap, ApSolver_);
// ApInv.setName("ApInv");
VectorSpace<double> pDomain = Bt.domain();
VectorSpace<double> uDomain = F.domain();
LinearOperator<double> Iu = identityOperator(uDomain);
// Iu.setName("Iu");
LinearOperator<double> Ip = identityOperator(pDomain);
// Ip.setName("Ip");
LinearOperator<double> XInv = MpInv * Fp * ApInv;
VectorSpace<double> rowSpace = K.range();
VectorSpace<double> colSpace = K.domain();
LinearOperator<double> Q1 = makeBlockOperator(colSpace, rowSpace);
// Q1.setName("Q1");
LinearOperator<double> Q2 = makeBlockOperator(colSpace, rowSpace);
// Q2.setName("Q2");
LinearOperator<double> Q3 = makeBlockOperator(colSpace, rowSpace);
//Q3.setName("Q3");
Q1.setBlock(0, 0, FInv);
Q1.setBlock(1, 1, Ip);
Q1.endBlockFill();
Q2.setBlock(0, 0, Iu);
Q2.setBlock(0, 1, -1.0*Bt);
Q2.setBlock(1, 1, Ip);
Q2.endBlockFill();
Q3.setBlock(0, 0, Iu);
Q3.setBlock(1, 1, -1.0*XInv);
Q3.endBlockFill();
LinearOperator<double> P1 = Q2 * Q3;
LinearOperator<double> PInv = Q1 * P1;
return new GenericRightPreconditioner<double>(PInv);
}