LinearOperator<double> epetraMatrixMatrixProduct(
const LinearOperator<double>& A,
const LinearOperator<double>& B)
{
/* Extract the underlying Epetra matrix for A. Type checking is done
* ny rcp_dynamic_cast, so we need no error check here. */
RCP<const Epetra_CrsMatrix> A_crs = EpetraMatrix::getConcretePtr(A);
/* Extract the underlying Epetra matrix for A. Type checking is done
* ny rcp_dynamic_cast, so we need no error check here. */
RCP<const Epetra_CrsMatrix> B_crs = EpetraMatrix::getConcretePtr(B);
bool transA = false;
bool transB = false;
/* Get the row map from A. We will need this to build the target matrix C */
const Epetra_Map* rowmap
= transA ? &(A_crs->DomainMap()) : &(A_crs->RowMap());
/* make the target matrix */
RCP<Epetra_CrsMatrix> C = rcp(new Epetra_CrsMatrix(Copy, *rowmap, 1));
/* Carry out the multiplication */
int ierr
= EpetraExt::MatrixMatrix::Multiply(*A_crs, transA, *B_crs, transB, *C);
TEUCHOS_TEST_FOR_EXCEPTION(ierr != 0, RuntimeError,
"EpetraExt Matrix-matrix multiply failed with error code ierr=" << ierr);
/* Prepare an operator object for the scaled matrix */
RCP<LinearOperatorBase<double> > rtn
= rcp(new EpetraMatrix(C, B.domain(), A.range()));
return rtn;
}
virtual Preconditioner <Scalar>
createPreconditioner(const LinearOperator<Scalar>& A) const
{
/* In order for ICC factorization to work, the operator A must
* implement the ICCFactorizableOp interface. We cast A's pointer
* to a ICCFactorizableOp ptr. If the cast fails, throw a spoke. */
const ICCFactorizableOp<Scalar>* fop
= dynamic_cast<const ICCFactorizableOp<Scalar>*>(A.ptr().get());
TEUCHOS_TEST_FOR_EXCEPTION(fop==0, std::runtime_error,
"ICCPreconditionerFactory attempted to "
"create an ICC preconditioner for an operator type "
"that does not implement the ICCFactorizableOp "
"interface. The op is " << A.description());
/* Now we can delegate the construction of the ICC factors to
* the factorizable op. */
Preconditioner<Scalar> P;
fop->getICCPreconditioner(fillLevels_,
overlapFill_,
relaxationValue_,
relativeThreshold_,
absoluteThreshold_,
P);
/* Return the preconditioner */
return P;
}
Epetra_TSFOperator::Epetra_TSFOperator(const LinearOperator<double>& A,
const LinearSolver<double>& solver)
: A_(A), solver_(solver), useTranspose_(false), comm_(), domain_(), range_(),
isNativeEpetra_(false), isCompoundEpetra_(false), label_(A.description())
{
const EpetraMatrix* em = dynamic_cast<const EpetraMatrix*>(A.ptr().get());
const EpetraVectorSpace* ed = dynamic_cast<const EpetraVectorSpace*>(A.domain().ptr().get());
const EpetraVectorSpace* er = dynamic_cast<const EpetraVectorSpace*>(A.range().ptr().get());
if (em)
{
isNativeEpetra_ = true;
const Epetra_CrsMatrix* crs = em->crsMatrix();
domain_ = rcp(new Epetra_Map(crs->OperatorDomainMap()));
range_ = rcp(new Epetra_Map(crs->OperatorRangeMap()));
useTranspose_ = crs->UseTranspose();
comm_ = rcp(crs->Comm().Clone());
}
else if (er != 0 && ed != 0)
{
domain_ = ed->epetraMap();
range_ = er->epetraMap();
comm_ = rcp(domain_->Comm().Clone());
isCompoundEpetra_ = true;
}
else
{
TEST_FOR_EXCEPT(true);
}
}
/**
* Construct a InverseLTIOp that takes <t>numTimesteps</t> steps
* with the operator \f$ A\f$.
*/
InverseLTIOp(int numTimesteps, const LinearOperator<Scalar>& A,
const LinearOperator<Scalar>& At)
: HomogeneouslyBlockedLinearOp<Scalar>(
A.domain(), numTimesteps,
A.range(), numTimesteps),
A_(A), At_(At)
{}
LinearOperator<double> createW() const
{
static LinearOperator<double> J = prob_.allocateJacobian();
TEST_FOR_EXCEPTION(J.ptr().get()==0, RuntimeError,
"null Jacobian");
return J;
}
//============================================================================
KrylovSolverStatus CGNR_Solver::
solve(const LinearOperator &A, const double *rhs, double *result,
const LinearOperator *preconditioner, bool use_given_initial_guess)
{
const int m=A.m, n=A.n;
assert(preconditioner==0 || (preconditioner->m==n && preconditioner->n==n));
if((int)s.size()!=n){
r.resize(n);
z.resize(n);
s.resize(n);
u.resize(m);
}
// convergence tolerance
A.apply_transpose(rhs, &r[0]); // form A^T*rhs in r
double tol=tolerance_factor*BLAS::abs_max(r);
// initial guess
if(use_given_initial_guess){
A.apply_and_subtract(result, rhs, &u[0]);
A.apply_transpose(u, r);
}else{
BLAS::set_zero(n, result);
}
// check instant convergence
iteration=0;
residual_norm=BLAS::abs_max(r);
if(residual_norm==0) return status=KRYLOV_CONVERGED;
// set up CG
double rho;
if(preconditioner) preconditioner->apply(r, z); else BLAS::copy(r, z);
rho=BLAS::dot(r, z);
if(rho<=0 || rho!=rho) return status=KRYLOV_BREAKDOWN;
BLAS::copy(z, s);
// and iterate
for(iteration=1; iteration<max_iterations; ++iteration){
double alpha;
A.apply(s, u);
A.apply_transpose(u, z);
double sz=BLAS::dot(u, u);
if(sz<=0 || sz!=sz) return status=KRYLOV_BREAKDOWN;
alpha=rho/sz;
BLAS::add_scaled(n, alpha, &s[0], result);
BLAS::add_scaled(-alpha, z, r);
residual_norm=BLAS::abs_max(r);
if(residual_norm<=tol) return status=KRYLOV_CONVERGED;
if(preconditioner) preconditioner->apply(r, z); else BLAS::copy(r, z);
double rho_new=BLAS::dot(r, z);
if(rho_new<=0 || rho_new!=rho_new) return status=KRYLOV_BREAKDOWN;
double beta=rho_new/rho;
BLAS::add_scaled(beta, s, z); s.swap(z); // s=beta*s+z
rho=rho_new;
if ( iteration % 5000 == 0 )
{
std::cout << "CGNR_Solver --- residual_norm: " << residual_norm << std::endl;
}
}
return status=KRYLOV_EXCEEDED_MAX_ITERATIONS;
}
//============================================================================
KrylovSolverStatus MINRES_CR_Solver::
solve(const LinearOperator &A, const double *rhs, double *result,
const LinearOperator *preconditioner, bool use_given_initial_guess)
{
const int n=A.m;
assert(A.n==n);
assert(preconditioner==0 || (preconditioner->m==n && preconditioner->n==n));
if((int)s.size()!=n){
r.resize(n);
z.resize(n);
q.resize(n);
s.resize(n);
t.resize(n);
}
// convergence tolerance
double tol=tolerance_factor*BLAS::abs_max(n, rhs);
// initial guess
if(use_given_initial_guess){
A.apply_and_subtract(result, rhs, &r[0]);
}else{
BLAS::set_zero(n, result);
BLAS::copy(n, rhs, &r[0]);
}
// check instant convergence
iteration=0;
residual_norm=BLAS::abs_max(r);
if(residual_norm==0) return status=KRYLOV_CONVERGED;
// set up CR
double rho;
if(preconditioner) preconditioner->apply(r, z); else BLAS::copy(r, s);
A.apply(s, t);
rho=BLAS::dot(r, t);
if(rho==0 || rho!=rho) return status=KRYLOV_BREAKDOWN;
// and iterate
for(iteration=1; iteration<max_iterations; ++iteration){
double alpha;
double tt=BLAS::dot(t, t);
if(tt==0 || tt!=tt) return status=KRYLOV_BREAKDOWN;
alpha=rho/tt;
BLAS::add_scaled(n, alpha, &s[0], result);
BLAS::add_scaled(-alpha, t, r);
residual_norm=BLAS::abs_max(r);
if(residual_norm<=tol) return KRYLOV_CONVERGED;
if(preconditioner) preconditioner->apply(r, z);
else BLAS::copy(r, z);
A.apply(z, q);
double rho_new=BLAS::dot(r, q);
if(rho_new==0 || rho_new!=rho_new) return KRYLOV_BREAKDOWN;
double beta=rho_new/rho;
BLAS::add_scaled(beta, s, z); s.swap(z); // s=beta*s+z
BLAS::add_scaled(beta, t, q); t.swap(q); // t=beta*t+q
rho=rho_new;
}
return KRYLOV_EXCEEDED_MAX_ITERATIONS;
}
bool runit(const VectorType<double>& vecType,
const LinearSolver<double>& solver)
{
typedef Teuchos::ScalarTraits<double> ST;
/* create the range space */
int nLocalRows = 10;
MatrixLaplacian1D builder(nLocalRows, vecType);
LinearOperator<double> A = builder.getOp();
Out::root() << "matrix is " << std::endl;
Out::os() << A << std::endl;
Vector<double> x = A.domain().createMember();
x.randomize();
Out::root() << "input is " << std::endl;
Out::os() << x << std::endl;
Vector<double> y = A*x;
Out::root() << "rhs is " << std::endl;
Out::os() << y << std::endl;
Vector<double> ans = A.range().createMember();
Out::root() << "slot for solution is " << std::endl;
Out::os() << ans << std::endl;
LinearOperator<double> AInv = inverse(A, solver);
ans = AInv * y;
Out::root() << "answer is " << std::endl;
Out::os() << ans << std::endl;
double err = (x-ans).norm2();
Out::root() << "error norm = " << err << std::endl;
double tol = 1.0e-7;
if (err <= tol)
{
Out::root() << "Poisson solve test PASSED" << std::endl;
return true;
}
else
{
Out::root() << "Poisson solve test FAILED" << std::endl;
return false;
}
}
void NLOp::
computeJacobianAndFunction(LinearOperator<double>& J,
Vector<double>& resid) const
{
/* Set the vector underlying the discrete
* function to the evaluation point*/
TEST_FOR_EXCEPTION(discreteU0_==0, RuntimeError,
"null discrete function pointer in "
"NLOp::jacobian()");
TEST_FOR_EXCEPTION(currentEvalPt().ptr().get()==0, RuntimeError,
"null evaluation point in "
"NLOp::jacobian()");
TEST_FOR_EXCEPTION(J.ptr().get()==0, RuntimeError,
"null Jacobian pointer in "
"NLOp::jacobian()");
TEST_FOR_EXCEPTION(resid.ptr().get()==0, RuntimeError,
"null residual pointer in "
"NLOp::jacobian()");
discreteU0_->setVector(currentEvalPt());
Array<Vector<double> > mv(1);
mv[0] = resid;
assembler_->assemble(J, mv);
resid.acceptCopyOf(mv[0]);
J_ = J;
}
LinearOperator<double> PartitionedMatrixFactory::createMatrix() const
{
RCP<LinearOpBase<double> > op
= rcp(new TSFExtended::LoadableBlockOperator<double>(domain_, lowestLocalCol_, isBCCol_, remoteBCCols_, range_, lowestLocalRow_, isBCRow_));
LinearOperator<double> A = op;
LinearOperator<double> A_ii = blockFactory_[0][0]->createMatrix();
LinearOperator<double> A_ib = blockFactory_[0][1]->createMatrix();
LinearOperator<double> A_bb = blockFactory_[1][1]->createMatrix();
A.setBlock(0,0,A_ii);
A.setBlock(0,1,A_ib);
A.setBlock(1,1,A_bb);
A.endBlockFill();
return A;
}
void TestOpGradient::testCall() {
const size_t n = 40;
const double tol = 1e-8;
LinearOperator * op = new OpGradient(n);
_ASSERT_EQ(n, op->dimensionIn().first);
_ASSERT_EQ(n - 1, op->dimensionOut().first);
_ASSERT_NOT(op->isSelfAdjoint());
Matrix x(n, 1);
Matrix y(n - 1, 1);
for (size_t i = 0; i < n; i++) {
x.set(i, 0, i + 1);
}
for (size_t i = 0; i < n - 1; i++) {
y.set(i, 0, 3 * i + 1);
}
Matrix Tx = op->call(x);
Matrix Tstar_y = op->callAdjoint(y);
Matrix err = y * Tx;
Matrix temp = x*Tstar_y;
Matrix::add(err, -1.0, temp, 1.0);
_ASSERT(std::abs(err.get(0, 0)) < tol);
delete op;
}
LinearOperator<double> epetraLeftScale(
const Vector<double>& d,
const LinearOperator<double>& A)
{
/* Extract the underlying Epetra matrix. Type checking is done
* ny rcp_dynamic_cast, so we need no error check here. */
RCP<const Epetra_CrsMatrix> A_crs = EpetraMatrix::getConcretePtr(A);
/* Make a deep copy of A */
RCP<Epetra_CrsMatrix> mtxCopy = rcp(new Epetra_CrsMatrix(*A_crs));
/* Extract the underlying Epetra vector. Type checking is done
* internally, so we need no error check here. */
const Epetra_Vector& epv = EpetraVector::getConcrete(d);
/* Scale the copy */
mtxCopy->LeftScale(epv);
RCP<LinearOperatorBase<double> > rtn
= rcp(new EpetraMatrix(mtxCopy, A.domain(), A.range()));
return rtn;
}
void constructPreconditionerAndSolve(LinearOperator& linearOperator,
Vector& x, Vector& istlb,
const POrComm& parallelInformation_arg,
Dune::InverseOperatorResult& result) const
{
// Construct scalar product.
typedef Dune::ScalarProductChooser<Vector, POrComm, category> ScalarProductChooser;
typedef std::unique_ptr<typename ScalarProductChooser::ScalarProduct> SPPointer;
SPPointer sp(ScalarProductChooser::construct(parallelInformation_arg));
// Communicate if parallel.
parallelInformation_arg.copyOwnerToAll(istlb, istlb);
#if ! HAVE_UMFPACK
if( parameters_.linear_solver_use_amg_ )
{
typedef ISTLUtility::CPRSelector< Matrix, Vector, Vector, POrComm> CPRSelectorType;
typedef typename CPRSelectorType::AMG AMG;
typedef typename CPRSelectorType::Operator MatrixOperator;
std::unique_ptr< AMG > amg;
std::unique_ptr< MatrixOperator > opA;
if( ! std::is_same< LinearOperator, MatrixOperator > :: value )
{
// create new operator in case linear operator and matrix operator differ
opA.reset( CPRSelectorType::makeOperator( linearOperator.getmat(), parallelInformation_arg ) );
}
const double relax = 1.0;
// Construct preconditioner.
constructAMGPrecond( linearOperator, parallelInformation_arg, amg, opA, relax );
// Solve.
solve(linearOperator, x, istlb, *sp, *amg, result);
}
else
#endif
{
// Construct preconditioner.
auto precond = constructPrecond(linearOperator, parallelInformation_arg);
// Solve.
solve(linearOperator, x, istlb, *sp, *precond, result);
}
}
::Spacy::Real LinearOperator::operator()( const LinearOperator& dx ) const
{
return Real( get() * dx.get() );
}
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);
VectorType<double> vecType = new SerialVectorType();
VectorSpace<double> domain
= vecType.createEvenlyPartitionedSpace(MPIComm::world(), 3);
VectorSpace<double> range
= vecType.createEvenlyPartitionedSpace(MPIComm::world(), 5);
RCP<MatrixFactory<double> > mf
= vecType.createMatrixFactory(domain, range);
LinearOperator<double> A = mf->createMatrix();
RCP<DenseSerialMatrix> APtr
= rcp_dynamic_cast<DenseSerialMatrix>(A.ptr());
APtr->setRow(0, tuple(1.0, 2.0, 3.0));
APtr->setRow(1, tuple(4.0, 5.0, 6.0));
APtr->setRow(2, tuple(7.0, 8.0, 9.0));
APtr->setRow(3, tuple(10.0, 11.0, 12.0));
APtr->setRow(4, tuple(13.0, 14.0, 15.0));
Out::os() << "A = " << std::endl;
A.setVerb(10);
Out::os() << A << std::endl;
LinearOperator<double> U;
LinearOperator<double> Vt;
Vector<double> sigma;
denseSVD(A, U, sigma, Vt);
Out::os() << "U = " << std::endl;
U.setVerb(10);
Out::os() << U << std::endl;
Out::os() << "sigma = " << std::endl;
Out::os() << sigma << std::endl;
Out::os() << "Vt = " << std::endl;
Vt.setVerb(10);
Out::os() << Vt << std::endl;
int nSamples = 10;
bool allOK = true;
double tol = 1.0e-13;
for (int i=0; i<nSamples; i++)
{
Out::os() << "Sample #" << i << " of " << nSamples << std::endl;
Vector<double> x = domain.createMember();
x.randomize();
U.setVerb(0);
Vt.setVerb(0);
A.setVerb(0);
LinearOperator<double> Sigma = diagonalOperator(sigma);
Vector<double> z = (U * Sigma * Vt)*x - A*x;
double ez = z.norm2();
Out::os() << "|| (U Sigma Vt - A)*x || = " << ez << std::endl;
Vector<double> y = (U.transpose() * U)*x - x;
double ey = y.norm2();
Out::os() << "|| (U^T U - I)*x || = " << ey << std::endl;
Vector<double> w = (Vt * Vt.transpose())*x - x;
double ew = w.norm2();
Out::os() << "|| (V^T*V - I)*x || = " << ew << std::endl;
if (ew > tol || ez > tol || ey > tol) allOK = false;
}
if (allOK)
{
Out::os() << "SVD test PASSED" << std::endl;
}
else
{
Out::os() << "SVD test FAILED" << std::endl;
stat = -1;
}
}
catch(std::exception& e)
{
stat = -1;
Out::os() << "Caught exception: " << e.what() << std::endl;
}
return stat;
}
int main(int argc, char *argv[])
{
typedef Teuchos::ScalarTraits<double> ST;
try
{
GlobalMPISession session(&argc, &argv);
MPIComm::world().synchronize();
VectorType<double> type = new EpetraVectorType();
/* create the range space */
int nLocalRows = 10;
MatrixLaplacian1D builder(nLocalRows, type);
LinearOperator<double> A = builder.getOp();
int nBlocks = 3;
Array<Vector<double> > x(nBlocks);
Array<VectorSpace<double> > space(nBlocks);
for (int i=0; i<nBlocks; i++)
{
space[i] = A.domain();
x[i] = A.domain().createMember();
Thyra::randomize(-ST::one(),+ST::one(),x[i].ptr().ptr());
}
VectorSpace<double> blockSpace = productSpace(space);
LinearOperator<double> bigA = makeBlockOperator(blockSpace, blockSpace);
Vector<double> bigRHS = blockSpace.createMember();
Vector<double> bigX = blockSpace.createMember();
for (int i=0; i<nBlocks; i++)
{
bigX.setBlock(i, x[i]);
for (int j=i; j<nBlocks; j++)
{
MatrixLaplacian1D builder(nLocalRows, type);
LinearOperator<double> Aij = builder.getOp();
bigA.setBlock(i,j,Aij);
}
}
bigA.endBlockFill();
bigRHS = bigA * bigX;
Vector<double> bigSoln = blockSpace.createMember();
#ifdef HAVE_CONFIG_H
ParameterXMLFileReader reader(Sundance::searchForFile("SolverParameters/poissonParams.xml"));
#else
ParameterXMLFileReader reader("poissonParams.xml");
#endif
ParameterList solverParams = reader.getParameters();
LinearSolver<double> solver
= LinearSolverBuilder::createSolver(solverParams);
LinearSolver<double> blockSolver
= new BlockTriangularSolver<double>(solver);
SolverState<double> state = blockSolver.solve(bigA, bigRHS, bigSoln);
std::cerr << state << std::endl;
double err = (bigSoln - bigX).norm2();
std::cerr << "error norm = " << err << std::endl;
double tol = 1.0e-8;
if (err > tol)
{
std::cerr << "Poisson solve test FAILED" << std::endl;
return 1;
}
else
{
std::cerr << "Poisson solve test PASSED" << std::endl;
return 0;
}
}
catch(std::exception& e)
{
std::cerr << "Caught exception: " << e.what() << std::endl;
return -1;
}
return 0;
}
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;
}
int main(int argc, char *argv[])
{
typedef Teuchos::ScalarTraits<double> ST;
try
{
GlobalMPISession session(&argc, &argv);
MPIComm::world().synchronize();
VectorType<double> type = new EpetraVectorType();
ParameterXMLFileReader reader("anasazi-ml.xml");
ParameterList solverParams = reader.getParameters().sublist("Eigensolver");
/* create the range space */
int nLocalRows = 40;
MatrixLaplacian1D builder(nLocalRows, type);
typedef Anasazi::MultiVec<double> MV;
typedef Anasazi::Operator<double> OP;
LinearOperator<double> A = builder.getOp();
LinearOperator<double> M;
Teuchos::RCP<Anasazi::OutputManager<double> > MyOM = Teuchos::rcp( new Anasazi::BasicOutputManager<double>() );
MyOM->setVerbosity(Anasazi::Warnings);
int nv = 1;
RCP<const Array<Vector<double> > > initMV = rcp(new Array<Vector<double> >(nv));
RCP<Array<Vector<double> > > nc
= rcp_const_cast<Array<Vector<double> > >(initMV);
for (int i=0; i<nv; i++)
{
(*nc)[i] = A.domain().createMember();
(*nc)[i].randomize();
}
#ifdef BLARF
bool mvPass = Anasazi::TestMultiVecTraits<double,Array<Vector<double> > >(MyOM,initMV);
if (mvPass) Out::os() << "******* MV unit test PASSED ******* " << endl;
else Out::os() << "******* MV unit test FAILED ******* " << endl;
RCP<const LinearOperator<double> > APtr = rcp(&A, false);
bool opPass = Anasazi::TestOperatorTraits<double, Array<Vector<double> >, LinearOperator<double> >(MyOM, initMV, APtr);
if (opPass) Out::os() << "******* OP unit test PASSED ******* " << endl;
else Out::os() << "******* OP unit test FAILED ******* " << endl;
#endif
Eigensolver<double> solver = new AnasaziEigensolver<double>(solverParams);
Array<Vector<double> > ev;
Array<std::complex<double> > ew;
solver.solve(A, M, ev, ew);
Out::os() << "Eigenvalues are " << ew << endl;
const double pi = 4.0*atan(1.0);
double err = 0.0;
for (int i=0; i<ev.size(); i++)
{
double x = (i+1)*pi;
err += ::fabs(ew[i].real()-x*x)/x/x;
}
err = err / ew.size();
Out::os() << "error = " << err << endl;
if (err < 0.01)
{
cout << "Belos poisson solve test PASSED" << std::endl;
return 0;
}
else
{
cout << "Belos poisson solve test FAILED" << std::endl;
return 1;
}
}
catch(std::exception& e)
{
cout << "Caught exception: " << e.what() << std::endl;
return -1;
}
}
inline bool LinearCombinationTester<Scalar>
::selfModifyingOpTests() const
{
bool pass = true;
RandomSparseMatrixBuilder<double> ABuilder(nLocalRows_, nLocalRows_,
onProcDensity_, offProcDensity_,
vecType_);
RandomSparseMatrixBuilder<double> BBuilder(nLocalRows_, nLocalRows_,
onProcDensity_, offProcDensity_,
vecType_);
RandomSparseMatrixBuilder<double> CBuilder(nLocalRows_, nLocalRows_,
onProcDensity_, offProcDensity_,
vecType_);
LinearOperator<double> A = ABuilder.getOp();
LinearOperator<double> B = BBuilder.getOp();
LinearOperator<double> C = CBuilder.getOp();
VectorSpace<Scalar> vs = A.domain();
A = identityOperator(vs);
B = identityOperator(vs);
C = identityOperator(vs);
Vector<Scalar> x = A.domain().createMember();
Vector<Scalar> y = A.domain().createMember();
Vector<Scalar> z = A.domain().createMember();
this->randomizeVec(x);
this->randomizeVec(y);
this->randomizeVec(z);
Vector<Scalar> a = x.copy();
Vector<Scalar> b = y.copy();
Vector<Scalar> c = z.copy();
Out::os() << "starting linear combination tests" << std::endl;
x = 2.0*A*x;
Scalar err = (x - 2.0*A*a).norm2();
if (!this->checkTest(spec_, err, "x=2.0*A*x")) pass = false;
a = x.copy();
x = x + y;
err = (x - (a + y)).norm2();
if (!this->checkTest(spec_, err, "x=x+y")) pass = false;
a = x.copy();
x = y + x;
err = (x - (y + a)).norm2();
if (!this->checkTest(spec_, err, "x=y+x")) pass = false;
a = x.copy();
x = A*x + B*y;
err = (x - (A*a + B*y)).norm2();
if (!this->checkTest(spec_, err, "x=A*x+B*y")) pass = false;
a = x.copy();
x = B*y + A*x;
err = (x - (B*y + A*a)).norm2();
if (!this->checkTest(spec_, err, "x=B*y+A*x")) pass = false;
a = x.copy();
x = A*x + (B*y + C*x);
err = (x - (A*a + (B*y + C*a))).norm2();
if (!this->checkTest(spec_, err, "x=A*x + (B*y + C*x)")) pass = false;
a = x.copy();
x = (A*x + B*y) + C*x;
err = (x - ((A*a + B*y) + C*a)).norm2();
if (!this->checkTest(spec_, err, "x=(A*x + B*y) + C*x")) pass = false;
/* test assignment of OpTimesLC into empty and non-empty vectors */
Vector<Scalar> u;
u = 2.0*A*B*x;
err = (u - 2.0*A*B*x).norm2();
if (!this->checkTest(spec_, err, "(empty) u=2*A*B*x")) pass = false;
u = 2.0*A*B*x;
err = (u - 2.0*A*B*x).norm2();
if (!this->checkTest(spec_, err, "(non-empty) u=2*A*B*x")) pass = false;
/* test assignment of LC2 into empty and non-empty vectors */
Vector<Scalar> v;
v = 2.0*x + 3.0*y;
err = (v - (2.0*x + 3.0*y)).norm2();
if (!this->checkTest(spec_, err, "(empty) v=2*x + 3*y")) pass = false;
v = 2.0*x + 3.0*y;
err = (v - (2.0*x + 3.0*y)).norm2();
if (!this->checkTest(spec_, err, "(non-empty) v=2*x + 3*y")) pass = false;
/* test assignment of LC3 into empty and non-empty vectors */
Vector<Scalar> w;
w = 2.0*x + 3.0*y + 5.0*z;
err = (w - (2.0*x + 3.0*y + 5.0*z)).norm2();
if (!this->checkTest(spec_, err, "(empty) w=2*x + 3*y + 5*z")) pass = false;
w = 2.0*x + 3.0*y + 5.0*z;
err = (w - (2.0*x + 3.0*y + 5.0*z)).norm2();
if (!this->checkTest(spec_, err, "(non-empty) w=2*x + 3*y + 5*z")) pass = false;
/* test assignment of LC4 into empty and non-empty vectors */
Vector<Scalar> w2;
w2 = 2.0*x + 3.0*y + 5.0*z + 7.0*u;
err = (w2 - (2.0*x + 3.0*y + 5.0*z + 7.0*u)).norm2();
if (!this->checkTest(spec_, err,
"(empty) w2=2*x + 3*y + 5*z + 7*u")) pass = false;
w2 = 2.0*x + 3.0*y + 5.0*z + 7.0*u;
err = (w2 - (2.0*x + 3.0*y + 5.0*z + 7.0*u)).norm2();
if (!this->checkTest(spec_, err,
"(non-empty) w2=2*x + 3*y + 5*z + 7*u")) pass = false;
/* test assignment of LC3 into one of the operands */
x = 2.0*x + 3.0*y + 5.0*z;
err = (w - x).norm2(); // Note: w contains 2x + 3y + 5z
if (!this->checkTest(spec_, err, "x=2*x + 3*y + 5*z")) pass = false;
return pass;
}
inline bool LinearCombinationTester<Scalar>
::nonModifyingOpTests() const
{
bool pass = true;
RandomSparseMatrixBuilder<double> ABuilder(nLocalRows_, nLocalRows_,
onProcDensity_, offProcDensity_,
vecType_);
RandomSparseMatrixBuilder<double> BBuilder(nLocalRows_, nLocalRows_,
onProcDensity_, offProcDensity_,
vecType_);
RandomSparseMatrixBuilder<double> CBuilder(nLocalRows_, nLocalRows_,
onProcDensity_, offProcDensity_,
vecType_);
LinearOperator<double> A = ABuilder.getOp();
LinearOperator<Scalar> B = BBuilder.getOp();
LinearOperator<Scalar> C = CBuilder.getOp();
Vector<Scalar> x = A.domain().createMember();
Vector<Scalar> y = A.domain().createMember();
Vector<Scalar> z = A.domain().createMember();
this->randomizeVec(x);
this->randomizeVec(y);
this->randomizeVec(z);
TESTER(x*2.0, 2.0*x);
TESTER(2.0*(x + y), 2.0*x + 2.0*y);
TESTER(2.0*(x - y), 2.0*x - 2.0*y);
TESTER((2.0*x + y) - y, 2.0*x);
TESTER(-1.0*y + (2.0*x + y), 2.0*x);
TESTER((x + y)*2.0, 2.0*x + 2.0*y);
TESTER((x - y)*2.0, 2.0*x - 2.0*y);
TESTER(2.0*(x - y), -2.0*(y - x));
TESTER(0.25*(2.0*(x + y) - 2.0*(x - y)), y);
TESTER((2.0*A)*x, 2.0*(A*x));
TESTER(2.0*(A*x), (A*x)*2.0);
TESTER(A*(B*x), (A*B)*x);
TESTER(2.0*A*(B*x), A*(B*(2.0*x)));
TESTER(3.0*(2.0*A)*x, 6.0*(A*x));
TESTER(y + A*x, A*x + y);
TESTER(z + (A*x + B*y), (B*y + A*x) + z);
TESTER(z - (A*x + B*y), -1.0*((B*y + A*x) - z));
TESTER(C*z + (A*x + B*y), (B*y + A*x) + C*z);
TESTER(C*z - (A*x + B*y), -1.0*((B*y + A*x) - C*z));
TESTER(2.0*z + (A*x + B*y), (B*y + A*x) + 2.0*z);
TESTER(2.0*z - (A*x + B*y), -1.0*((B*y + A*x) - 2.0*z));
TESTER(A*x - y, -1.0*(y - A*x));
TESTER(A*x + B*y, B*y + A*x);
TESTER(A*x - B*y - A*x + B*y +z, z);
TESTER(2.0*(A*x + y), 2.0*A*x + 2.0*y);
TESTER(2.0*(A*x + B*y), A*x + B*y + A*x + B*y);
TESTER(2.0*(y + A*x), 2.0*y + 2.0*(A*x));
TESTER(x + 2.0*A*y, x + 2.0*(A*y));
TESTER(2.0*A*y + x, 2.0*(A*y) + x);
TESTER(2.0*A*(3.0*B)*y, 6.0*(A*B*y));
TESTER(2.0*A*(3.0*B)*y, 6.0*(A*(B*y)));
TESTER(2.0*A*(3.0*B + 2.0*A)*x, 6.0*A*B*x + 4.0*A*A*x );
TESTER(2.0*(A*x + B*y), 2.0*A*x + 2.0*B*y);
TESTER(2.0*(A*x - B*y), 2.0*A*x - 2.0*B*y);
TESTER(2.0*(A*x + B*y + z), 2.0*A*x + 2.0*B*y + 2.0*z);
TESTER(2.0*(A*x + 3.0*B*y), 2.0*A*x + 6.0*B*y);
TESTER(2.0*(A*x + 3.0*(z + B*y)), 2.0*A*x + 6.0*B*y + 6.0*z);
TESTER(2.0*(z + A*x + B*y + z), 2.0*A*x + 2.0*B*y + 4.0*z);
TESTER(2.0*(3.0*(z + A*x) + B*y), 6.0*z + 6.0*A*x + 2.0*B*y);
TESTER(2.0*(3.0*(z + A*x) + 4.0*(B*y + z)), 6.0*z + 6.0*A*x + 8.0*B*y + 8.0*z);
TESTER((A*x + B*y) + (A*y + B*x), (A + B)*x + (A+B)*y);
TESTER((A*x + B*y) - (A*y + B*x), A*x - A*y + B*y - B*x);
TESTER((A*x + B*y) + 2.0*(A*y + B*x), A*(x + 2.0*y) + B*(2.0*x + y));
TESTER((A*x + B*y) - 2.0*(A*y + B*x), A*(x - 2.0*y) + B*(y - 2.0*x));
return pass;
}
void run( Vector<Real> &x, LinearOperator<Real> &A, const Vector<Real> &b,
LinearOperator<Real> &M, int &iter, int &flag ) {
using Teuchos::RCP;
flag = 0;
Real zero = 0.0;
Real one = 1.0;
if ( !isInitialized_ ) {
r_ = b.clone();
w_ = b.clone();
z_ = x.clone();
isInitialized_ = true;
}
Real itol = std::sqrt(ROL_EPSILON<Real>());
// Compute initial residual
if(useInitialGuess_) {
A.apply(*r_,x,itol);
r_->scale(-1.0);
r_->plus(b); // r = b-Ax
}
else {
x.zero();
r_->set(b);
}
Real temp = 0;
std::vector<RCP<Vector<Real > > > V;
std::vector<RCP<Vector<Real > > > Z;
(*res_)[0] = r_->norm();
Real rtol = std::min(absTol_,relTol_*(*res_)[0]);
V.push_back(b.clone());
(V[0])->set(*r_);
(V[0])->scale(one/(*res_)[0]);
(*s_)(0) = (*res_)[0];
for( iter=0; iter<maxit_; ++iter ) {
// std::cout << (*res_)[iter] << std::endl;
if( useInexact_ ) {
itol = rtol/(maxit_*(*res_)[iter]);
}
Z.push_back(x.clone());
// Apply right preconditioner
M.applyInverse(*(Z[iter]),*(V[iter]),itol);
// Apply operator
A.apply(*w_,*(Z[iter]),itol);
// Evaluate coefficients and orthogonalize using Gram-Schmidt
for( int k=0; k<=iter; ++k ) {
(*H_)(k,iter) = w_->dot(*(V[k]));
w_->axpy( -(*H_)(k,iter), *(V[k]) );
}
(*H_)(iter+1,iter) = w_->norm();
V.push_back( b.clone() );
(V[iter+1])->set(*w_);
(V[iter+1])->scale(one/((*H_)(iter+1,iter)));
// Apply Givens rotations
for( int k=0; k<=iter-1; ++k ) {
temp = (*cs_)(k)*(*H_)(k,iter) + (*sn_)(k)*(*H_)(k+1,iter);
(*H_)(k+1,iter) = -(*sn_)(k)*(*H_)(k,iter) + (*cs_)(k)*(*H_)(k+1,iter);
(*H_)(k,iter) = temp;
}
// Form i-th rotation matrix
if( (*H_)(iter+1,iter) == zero ) {
(*cs_)(iter) = one;
(*sn_)(iter) = zero;
}
else if ( std::abs((*H_)(iter+1,iter)) > std::abs((*H_)(iter,iter)) ) {
temp = (*H_)(iter,iter) / (*H_)(iter+1,iter);
(*sn_)(iter) = one / std::sqrt( one + temp*temp );
(*cs_)(iter) = temp*(*sn_)(iter);
}
else {
temp = (*H_)(iter+1,iter) / (*H_)(iter,iter);
(*cs_)(iter) = one / std::sqrt( one + temp*temp );
(*sn_)(iter) = temp*(*cs_)(iter);
}
// Approximate residual norm
temp = (*cs_)(iter)*(*s_)(iter);
(*s_)(iter+1) = -(*sn_)(iter)*(*s_)(iter);
(*s_)(iter) = temp;
(*H_)(iter,iter) = (*cs_)(iter)*(*H_)(iter,iter) + (*sn_)(iter)*(*H_)(iter+1,iter);
(*H_)(iter+1,iter) = zero;
(*res_)[iter+1] = std::abs((*s_)(iter+1));
// Update solution approximation.
const char uplo = 'U';
const char trans = 'N';
const char diag = 'N';
const char normin = 'N';
Real scaling = zero;
int info = 0;
*y_ = *s_;
lapack_.LATRS(uplo, trans, diag, normin, iter+1, H_->values(), maxit_+1, y_->values(), &scaling, cnorm_->values(), &info);
z_->zero();
for( int k=0; k<=iter;++k ) {
z_->axpy((*y_)(k),*(Z[k]));
}
if( (*res_)[iter+1] <= rtol ) {
// Update solution vector
x.plus(*z_);
break;
}
if(iter == maxit_) {
flag = 1;
}
} // loop over iter
}
SolverState<double> BelosSolver::solve(const LinearOperator<double>& A,
const Vector<double>& rhs,
Vector<double>& soln) const
{
typedef Anasazi::SimpleMV MV;
typedef LinearOperator<double> OP;
typedef Belos::LinearProblem<double, MV, OP> LP;
TEUCHOS_TEST_FOR_EXCEPT(!A.ptr().get());
TEUCHOS_TEST_FOR_EXCEPT(!rhs.ptr().get());
if (!soln.ptr().get())
{
soln = rhs.copy();
/* KRL 8 Jun 2012: set x0 to zero to workaround bug in Belos */
soln.zero();
}
if (rhs.norm2()==0.0)
{
soln.zero();
SolverStatusCode code = SolveConverged;
SolverState<double> state(code, "Detected trivial solution", 0, 0.0);
return state;
}
RCP<OP> APtr = rcp(new LinearOperator<double>(A));
RCP<MV> bPtr = rcp(new MV(1));
(*bPtr)[0] = rhs;
RCP<MV> ansPtr = rcp(new MV(1));
(*ansPtr)[0] = soln;
RCP<LP> prob = rcp(new LP(APtr, ansPtr, bPtr));
TEUCHOS_TEST_FOR_EXCEPT(!prob->setProblem());
if (pf_.ptr().get())
{
Preconditioner<double> P = pf_.createPreconditioner(A);
if (P.hasLeft())
{
prob->setLeftPrec(rcp(new OP(P.left())));
}
if (P.hasRight())
{
prob->setRightPrec(rcp(new OP(P.right())));
}
}
if (!hasSolver_)
{
ParameterList plist = parameters();
RCP<ParameterList> belosList = rcp(&plist, false);
std::string solverType = parameters().get<string>("Method");
if (solverType=="GMRES")
{
solver_=rcp(new Belos::BlockGmresSolMgr<double, MV, OP>(prob, belosList));
}
else if (solverType=="CG")
{
solver_=rcp(new Belos::BlockCGSolMgr<double, MV, OP>(prob, belosList));
}
else if (solverType=="TFQMR")
{
solver_=rcp(new Belos::TFQMRSolMgr<double, MV, OP>(prob, belosList));
}
else if (solverType=="GCRODR")
{
solver_=rcp(new Belos::GCRODRSolMgr<double, MV, OP>(prob, belosList));
hasSolver_ = true; // only cache recycling solvers
}
else if (solverType=="RCG")
{
solver_=rcp(new Belos::RCGSolMgr<double, MV, OP>(prob, belosList));
hasSolver_ = true; // only cache recycling solvers
}
else
{
TEUCHOS_TEST_FOR_EXCEPT(!(solverType=="GMRES" || solverType=="CG"));
}
}
else // reset problem
{
solver_->setProblem( prob );
}
Belos::ReturnType rtn = solver_->solve();
int numIters = solver_->getNumIters();
double resid = solver_->achievedTol();
SolverStatusCode code = SolveFailedToConverge;
if (rtn==Belos::Converged) code = SolveConverged;
SolverState<double> state(code, "Belos solver completed", numIters, resid);
return state;
}
int main(int argc, char *argv[])
{
typedef Teuchos::ScalarTraits<double> ST;
try
{
GlobalMPISession session(&argc, &argv);
MPIComm::world().synchronize();
VectorType<double> type = new EpetraVectorType();
#ifdef HAVE_CONFIG_H
ParameterXMLFileReader reader(Sundance::searchForFile("SolverParameters/userPrecParams.xml"));
#else
ParameterXMLFileReader reader("userPrecParams.xml");
#endif
ParameterList solverParams = reader.getParameters();
ParameterList innerSolverParams = solverParams.sublist("Inner Solve");
ParameterList outerSolverParams = solverParams.sublist("Outer Solve");
/* create the range space */
int nLocalRows = solverParams.get<int>("nLocal");
MatrixLaplacian1D builder(nLocalRows, type);
LinearOperator<double> A = builder.getOp();
Vector<double> x = A.domain().createMember();
int myRank = MPIComm::world().getRank();
int nProcs = MPIComm::world().getNProc();
Thyra::randomize(-ST::one(),+ST::one(),x.ptr().ptr());
#ifdef TRILINOS_6
if (myRank==0) x[0] = 0.0;
if (myRank==nProcs-1) x[nProcs * nLocalRows - 1] = 0.0;
// need to fix operator[] routine
#else
if (myRank==0) x.setElement(0, 0);
if (myRank==nProcs-1) x.setElement(nProcs * nLocalRows - 1, 0.0);
#endif
cout << "x=" << std::endl;
x.print(cout);
Vector<double> y = A*x;
cout << "y=" << std::endl;
y.print(cout);
Vector<double> ans = A.range().createMember();
LinearSolver<double> innerSolver
= LinearSolverBuilder::createSolver(innerSolverParams);
LinearSolver<double> outerSolver
= LinearSolverBuilder::createSolver(outerSolverParams);
/* call the setUserPrec() function to set the operator and solver
* to be used for preconditioning */
outerSolver.setUserPrec(A, innerSolver);
LinearOperator<double> AInv = inverse(A, outerSolver);
ans = AInv * y;
// SolverState<double> state = solver.solve(A, y, ans);
// cout << state << std::endl;
cout << "answer is " << std::endl;
ans.print(cout);
double err = (x-ans).norm2();
cout << "error norm = " << err << std::endl;
double tol = 1.0e-8;
if (err > tol)
{
cout << "User-defined preconditioner test FAILED" << std::endl;
return 1;
}
else
{
cout << "User-defined preconditioner test PASSED" << std::endl;
return 0;
}
}
catch(std::exception& e)
{
cout << "Caught exception: " << e.what() << std::endl;
return -1;
}
}
SolverState<double> BelosSolver::solve(const LinearOperator<double>& A,
const Vector<double>& rhs,
Vector<double>& soln) const
{
typedef Thyra::MultiVectorBase<double> MV;
typedef Thyra::LinearOpBase<double> OP;
typedef Belos::LinearProblem<double, MV, OP> LP;
TEST_FOR_EXCEPT(!A.ptr().get());
TEST_FOR_EXCEPT(!rhs.ptr().get());
/* get Thyra objects */
RCP<OP> APtr = A.ptr();
RCP<MV> bPtr = rhs.ptr();
if (!soln.ptr().get()) soln = rhs.copy();
RCP<MV> ansPtr = soln.ptr();
RCP<LP> prob = rcp(new LP(APtr, ansPtr, bPtr));
TEST_FOR_EXCEPT(!prob->setProblem());
if (pf_.ptr().get())
{
Preconditioner<double> P = pf_.createPreconditioner(A);
if (P.hasLeft())
{
prob->setLeftPrec(P.left().ptr());
}
if (P.hasRight())
{
prob->setRightPrec(P.right().ptr());
}
}
ParameterList plist = parameters();
RCP<ParameterList> belosList = rcp(&plist, false);
RCP<Belos::SolverManager<double, MV, OP> > solver ;
std::string solverType = parameters().get<string>("Method");
if (solverType=="GMRES")
{
solver=rcp(new Belos::BlockGmresSolMgr<double, MV, OP>(prob, belosList));
}
else if (solverType=="CG")
{
solver=rcp(new Belos::BlockCGSolMgr<double, MV, OP>(prob, belosList));
}
else
{
TEST_FOR_EXCEPT(!(solverType=="GMRES" || solverType=="CG"));
}
Belos::ReturnType rtn = solver->solve();
int numIters = solver->getNumIters();
double resid = -1.0;
SolverStatusCode code = SolveFailedToConverge;
if (rtn==Belos::Converged) code = SolveConverged;
SolverState<double> state(code, "Belos solver completed", numIters, resid);
return state;
}
bool DuffingFloquet()
{
int np = MPIComm::world().getNProc();
TEUCHOS_TEST_FOR_EXCEPT(np != 1);
const double pi = 4.0*atan(1.0);
/* We will do our linear algebra using Epetra */
VectorType<double> vecType = new EpetraVectorType();
/* Create a periodic mesh */
int nx = 128;
MeshType meshType = new PeriodicMeshType1D();
MeshSource mesher = new PeriodicLineMesher(0.0, 2.0*pi, nx, meshType);
Mesh mesh = mesher.getMesh();
/* Create a cell filter that will identify the maximal cells
* in the interior of the domain */
CellFilter interior = new MaximalCellFilter();
CellFilter pts = new DimensionalCellFilter(0);
CellFilter left = pts.subset(new CoordinateValueCellPredicate(0,0.0));
CellFilter right = pts.subset(new CoordinateValueCellPredicate(0,2.0*pi));
/* Create unknown and test functions, discretized using first-order
* Lagrange interpolants */
Expr u1 = new UnknownFunction(new Lagrange(1), "u1");
Expr u2 = new UnknownFunction(new Lagrange(1), "u2");
Expr v1 = new TestFunction(new Lagrange(1), "v1");
Expr v2 = new TestFunction(new Lagrange(1), "v2");
/* Create differential operator and coordinate function */
Expr dx = new Derivative(0);
Expr x = new CoordExpr(0);
/* We need a quadrature rule for doing the integrations */
QuadratureFamily quad = new GaussianQuadrature(4);
double F0 = 0.5;
double gamma = 2.0/3.0;
double a0 = 1.0;
double w0 = 1.0;
double eps = 0.5;
Expr u1Guess = -0.75*cos(x) + 0.237*sin(x);
Expr u2Guess = 0.237*cos(x) + 0.75*sin(x);
DiscreteSpace discSpace(mesh,
List(new Lagrange(1), new Lagrange(1)),
vecType);
L2Projector proj(discSpace, List(u1Guess, u2Guess));
Expr u0 = proj.project();
Expr rhs1 = u2;
Expr rhs2 = -w0*w0*u1 - gamma*u2 - eps*w0*w0*pow(u1,3.0)/a0/a0
+ F0*w0*w0*sin(x);
/* Define the weak form */
Expr eqn = Integral(interior,
v1*(dx*u1 - rhs1) + v2*(dx*u2 - rhs2),
quad);
Expr dummyBC ;
NonlinearProblem prob(mesh, eqn, dummyBC, List(v1,v2), List(u1,u2),
u0, vecType);
ParameterXMLFileReader reader("nox.xml");
ParameterList solverParams = reader.getParameters();
Out::root() << "finding periodic solution" << endl;
NOXSolver solver(solverParams);
prob.solve(solver);
/* unfold the solution onto a non-periodic mesh */
Expr uP = unfoldPeriodicDiscreteFunction(u0, "u_p");
Out::root() << "uP=" << uP << endl;
Mesh unfoldedMesh = DiscreteFunction::discFunc(uP)->mesh();
DiscreteSpace unfDiscSpace = DiscreteFunction::discFunc(uP)->discreteSpace();
FieldWriter writer = new MatlabWriter("Floquet.dat");
writer.addMesh(unfoldedMesh);
writer.addField("u_p[0]", new ExprFieldWrapper(uP[0]));
writer.addField("u_p[1]", new ExprFieldWrapper(uP[1]));
Array<Expr> a(2);
a[0] = new Sundance::Parameter(0.0, "a1");
a[1] = new Sundance::Parameter(0.0, "a2");
Expr bc = EssentialBC(left, v1*(u1-uP[0]-a[0]) + v2*(u2-uP[1]-a[1]), quad);
NonlinearProblem unfProb(unfoldedMesh, eqn, bc,
List(v1,v2), List(u1,u2), uP, vecType);
unfProb.setEvalPoint(uP);
LinearOperator<double> J = unfProb.allocateJacobian();
Vector<double> b = J.domain().createMember();
LinearSolver<double> linSolver
= LinearSolverBuilder::createSolver("amesos.xml");
SerialDenseMatrix<int, double> F(a.size(), a.size());
for (int i=0; i<a.size(); i++)
{
Out::root() << "doing perturbed orbit #" << i << endl;
for (int j=0; j<a.size(); j++)
{
if (i==j) a[j].setParameterValue(1.0);
else a[j].setParameterValue(0.0);
}
unfProb.computeJacobianAndFunction(J, b);
Vector<double> w = b.copy();
linSolver.solve(J, b, w);
Expr w_i = new DiscreteFunction(unfDiscSpace, w);
for (int j=0; j<a.size(); j++)
{
Out::root() << "postprocessing" << i << endl;
writer.addField("w[" + Teuchos::toString(i)
+ ", " + Teuchos::toString(j) + "]", new ExprFieldWrapper(w_i[j]));
Expr g = Integral(right, w_i[j], quad);
F(j,i) = evaluateIntegral(unfoldedMesh, g);
}
}
writer.write();
Out::root() << "Floquet matrix = " << endl
<< F << endl;
Out::root() << "doing eigenvalue analysis" << endl;
Array<double> ew_r(a.size());
Array<double> ew_i(a.size());
int lWork = 6*a.size();
Array<double> work(lWork);
int info = 0;
LAPACK<int, double> lapack;
lapack.GEEV('N','N', a.size(), F.values(),
a.size(), &(ew_r[0]), &(ew_i[0]), 0, 1, 0, 1, &(work[0]), lWork,
&info);
TEUCHOS_TEST_FOR_EXCEPTION(info != 0,
std::runtime_error,
"LAPACK GEEV returned error code =" << info);
Array<double> ew(a.size());
for (int i=0; i<a.size(); i++)
{
ew[i] = sqrt(ew_r[i]*ew_r[i]+ew_i[i]*ew_i[i]);
Out::root() << setw(5) << i
<< setw(16) << ew_r[i]
<< setw(16) << ew_i[i]
<< setw(16) << ew[i]
<< endl;
}
double err = ::fabs(ew[0] - 0.123);
return SundanceGlobal::checkTest(err, 0.001);
}
int main(int argc, char *argv[])
{
int stat = 0;
try
{
GlobalMPISession session(&argc, &argv);
/* create a distributed vector space for the multivector's vectors */
VectorType<double> rowType = new EpetraVectorType();
int nLocalRows = 2;
VectorSpace<double> space
= rowType.createEvenlyPartitionedSpace(MPIComm::world(), nLocalRows);
/* create a replicated vector space for the small space of columns */
int nVecs = 3;
VectorType<double> colType = new SerialVectorType();
VectorSpace<double> replSpace
= colType.createEvenlyPartitionedSpace(MPIComm::world(), nVecs);
/* create some random vectors */
Teuchos::Array<Vector<double> > vecs(nVecs);
for (int i=0; i<nVecs; i++)
{
vecs[i] = space.createMember();
vecs[i].randomize();
}
/* Test multiplication by a multivector operator. We will compute
* y1 by directly summing columns, and y2 by applying the operator */
LinearOperator<double> A = multiVectorOperator<double>(vecs, replSpace);
Vector<double> y1 = space.createMember();
Vector<double> y2 = space.createMember();
y1.zero();
y2.zero();
/* Sum columns, putting the weights into x */
Vector<double> x = replSpace.createMember();
Out::os() << "A=" << A << std::endl;
for (int j=0; j<replSpace.numLocalElements(); j++)
{
x[j] = 2.0*(drand48()-0.5);
y1 = y1 + x[j] * vecs[j];
Out::os() << "x[" << j << "]=" << x[j] << std::endl;
Out::os() << "vecs[j]=" << vecs[j] << std::endl;
}
Out::os() << "y1=" << std::endl << y1 << std::endl;
/* Apply the operator to the vector of weights */
y2 = A * x;
Out::os() << "y2=A*x=" << std::endl << y2 << std::endl;
Vector<double> y12 = y1-y2;
Vector<double> y21 = y2-y1;
Out::os() << "y1-y2=" << std::endl << y12 << std::endl;
Out::os() << "y2-y1=" << std::endl << y21 << std::endl;
double errA = (y1-y2).norm2();
Out::root() << "error in A*x = " << errA << std::endl;
/* Now test z = A^T * y */
LinearOperator<double> At = A.transpose();
Vector<double> z1 = replSpace.createMember();
z1.zero();
Vector<double> z2 = replSpace.createMember();
z2.zero();
Vector<double> y = y1.copy();
/* compute by vectorwise multiplication */
for (int j=0; j<replSpace.numLocalElements(); j++)
{
z1[j] = vecs[j].dot(y);
}
/* compute with operator */
z2 = At * y;
double errAt = (z1-z2).normInf();
Out::root() << "error in At*y = " << errA << std::endl;
double tol = 1.0e-13;
bool pass = errA + errAt < tol;
pass = globalAnd(pass);
if (pass)
{
Out::root() << "multivector op test PASSED" << std::endl;
}
else
{
stat = -1;
Out::root() << "multivector op test FAILED" << std::endl;
}
}
catch(std::exception& e)
{
stat = -1;
std::cerr << "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);
}
