int main(int argc, char* argv[])
{
#ifdef HAVE_MPI
MPI_Init(&argc,&argv);
#endif
// Creating an instance of the LAPACK class for double-precision routines looks like:
Teuchos::LAPACK<int, double> lapack;
// This instance provides the access to all the LAPACK routines.
Teuchos::SerialDenseMatrix<int, double> My_Matrix(4,4);
Teuchos::SerialDenseVector<int, double> My_Vector(4);
My_Matrix.random();
My_Vector.random();
// Perform an LU factorization of this matrix.
int ipiv[4], info;
char TRANS = 'N';
lapack.GETRF( 4, 4, My_Matrix.values(), My_Matrix.stride(), ipiv, &info );
// Solve the linear system.
lapack.GETRS( TRANS, 4, 1, My_Matrix.values(), My_Matrix.stride(),
ipiv, My_Vector.values(), My_Vector.stride(), &info );
// Print out the solution.
cout << My_Vector << endl;
#ifdef HAVE_MPI
MPI_Finalize();
#endif
return 0;
}
void solve_state(std::vector<std::vector<Real> > &U, const std::vector<Real> &z) {
// Get Diagonal and Off-Diagonal Entries of PDE Jacobian
std::vector<Real> d(nx_,4.0*dx_/6.0 + dt_*2.0/dx_);
d[0] = dx_/3.0 + dt_/dx_;
d[nx_-1] = dx_/3.0 + dt_/dx_;
std::vector<Real> o(nx_-1,dx_/6.0 - dt_/dx_);
// Perform LDL factorization
Teuchos::LAPACK<int,Real> lp;
int info;
int ldb = nx_;
int nhrs = 1;
lp.PTTRF(nx_,&d[0],&o[0],&info);
// Initialize State Storage
U.clear();
U.resize(nt_+1);
(U[0]).assign(u0_.begin(),u0_.end());
// Time Step Using Implicit Euler
std::vector<Real> b(nx_,0.0);
for ( uint t = 0; t < nt_; t++ ) {
// Get Right Hand Side
apply_mass(b,U[t]);
b[nx_-1] += dt_*z[t];
// Solve Tridiagonal System Using LAPACK's SPD Tridiagonal Solver
lp.PTTRS(nx_,nhrs,&d[0],&o[0],&b[0],ldb,&info);
// Update State Storage
(U[t+1]).assign(b.begin(),b.end());
}
}
void solve_adjoint_sensitivity(std::vector<std::vector<Real> > &P, const std::vector<std::vector<Real> > &U) {
// Get Diagonal and Off-Diagonal Entries of PDE Jacobian
std::vector<Real> d(nx_,4.0*dx_/6.0 + dt_*2.0/dx_);
d[0] = dx_/3.0 + dt_/dx_;
d[nx_-1] = dx_/3.0 + dt_/dx_;
std::vector<Real> o(nx_-1,dx_/6.0 - dt_/dx_);
// Perform LDL factorization
Teuchos::LAPACK<int,Real> lp;
int info;
int ldb = nx_;
int nhrs = 1;
lp.PTTRF(nx_,&d[0],&o[0],&info);
// Initialize State Storage
P.clear();
P.resize(nt_);
// Time Step Using Implicit Euler
std::vector<Real> b(nx_,0.0);
for ( uint t = nt_; t > 0; t-- ) {
// Get Right Hand Side
if ( t == nt_ ) {
apply_mass(b,U[t-1]);
}
else {
apply_mass(b,P[t]);
}
// Solve Tridiagonal System Using LAPACK's SPD Tridiagonal Solver
lp.PTTRS(nx_,nhrs,&d[0],&o[0],&b[0],ldb,&info);
// Update State Storage
(P[t-1]).assign(b.begin(),b.end());
}
}
KOKKOS_INLINE_FUNCTION
int
Chol<Uplo::Upper,
AlgoChol::ExternalLapack,Variant::One>
::invoke(PolicyType &policy,
const MemberType &member,
DenseExecViewTypeA &A) {
// static_assert( Kokkos::Impl::is_same<
// typename DenseMatrixTypeA::space_type,
// Kokkos::Cuda
// >::value,
// "Cuda space is not available for calling external BLAS" );
//typedef typename DenseExecViewTypeA::space_type space_type;
typedef typename DenseExecViewTypeA::ordinal_type ordinal_type;
typedef typename DenseExecViewTypeA::value_type value_type;
int r_val = 0;
if (member.team_rank() == 0) {
#ifdef HAVE_SHYLUTACHO_TEUCHOS
Teuchos::LAPACK<ordinal_type,value_type> lapack;
lapack.POTRF('U',
A.NumRows(),
A.ValuePtr(), A.BaseObject().ColStride(),
&r_val);
#else
TACHO_TEST_FOR_ABORT( true, MSG_NOT_HAVE_PACKAGE("Teuchos") );
#endif
}
return r_val;
}
MxDimMatrix<T, DIM> MxDimMatrix<T, DIM>::inv() const {
MxDimMatrix<T, DIM> thisT = this->transpose();
MxDimMatrix<T, DIM> solnT(MxDimVector<T, DIM>(1));
int info;
int ipiv[DIM];
Teuchos::LAPACK<int, T> lapack;
lapack.GESV(DIM, DIM, &thisT(0, 0), DIM, ipiv, &solnT(0, 0), DIM, &info);
if (info != 0)
std::cout << "MxDimMatrix::inv(): error in lapack routine. Return code: " << info << ".\n";
return solnT.transpose();
}
int MxDimMatrix<T, DIM>::eig(MxDimVector<std::complex<T>, DIM> & evals,
MxDimMatrix<std::complex<T>, DIM> & levecs,
MxDimMatrix<std::complex<T>, DIM> & revecs) const {
MxDimMatrix<T, DIM> thisT = this->transpose();
MxDimVector<T, DIM> rva, iva;
MxDimMatrix<T, DIM> rve, lve;
int info;
int lwork = 5 * DIM;
T work[lwork];
Teuchos::LAPACK<int, T> lapack;
lapack.GEEV('V', 'V', DIM, &thisT(0, 0), DIM, &rva[0], &iva[0], &lve(0, 0), DIM, &rve(0, 0), DIM, work, lwork, &info);
if (info != 0)
std::cout << "MxDimMatrix::eig(): error in lapack routine. Return code: " << info << ".\n";
// gather results
for (size_t i = 0; i < DIM; ++i) {
if (iva[i] != 0) {
for (size_t k = 0; k < 2; ++k) {
evals[i + k].real() = rva[i + k];
evals[i + k].imag() = iva[i + k];
for (size_t j = 0; j < DIM; ++j) {
levecs(i + k, j).real() = lve(j, i);
levecs(i + k, j).imag() = (k == 0 ? 1.0 : -1.0) * lve(j, i + 1);
revecs(i + k, j).real() = rve(j, i);
revecs(i + k, j).imag() = (k == 0 ? 1.0 : -1.0) * rve(j, i + 1);
}
}
i++;
}
else {
evals[i].real() = rva[i];
evals[i].imag() = iva[i];
for (size_t j = 0; j < DIM; ++j) {
levecs(i, j).real() = lve(j, i);
revecs(i, j).real() = rve(j, i);
}
}
}
return info;
}
void Constraint<Scalar, LocalOrdinal, GlobalOrdinal, Node, LocalMatOps>::Setup(const MultiVector& B, const MultiVector& Bc, RCP<const CrsGraph> Ppattern) {
Ppattern_ = Ppattern;
const RCP<const Map> uniqueMap = Ppattern_->getDomainMap();
const RCP<const Map> nonUniqueMap = Ppattern_->getColMap();
RCP<const Import> importer = ImportFactory::Build(uniqueMap, nonUniqueMap);
const size_t NSDim = Bc.getNumVectors();
X_ = MultiVectorFactory::Build(nonUniqueMap, NSDim);
X_->doImport(Bc, *importer, Xpetra::INSERT);
size_t numRows = Ppattern_->getNodeNumRows();
XXtInv_.resize(numRows);
Teuchos::SerialDenseVector<LO,SC> BcRow(NSDim, false);
for (size_t i = 0; i < numRows; i++) {
Teuchos::ArrayView<const LO> indices;
Ppattern_->getLocalRowView(i, indices);
size_t nnz = indices.size();
Teuchos::SerialDenseMatrix<LO,SC> locX(NSDim, nnz, false);
for (size_t j = 0; j < nnz; j++) {
for (size_t k = 0; k < NSDim; k++)
BcRow[k] = X_->getData(k)[indices[j]];
Teuchos::setCol(BcRow, (LO)j, locX);
}
XXtInv_[i] = Teuchos::SerialDenseMatrix<LO,SC>(NSDim, NSDim, false);
Teuchos::BLAS<LO,SC> blas;
blas.GEMM(Teuchos::NO_TRANS, Teuchos::CONJ_TRANS, NSDim, NSDim, nnz,
Teuchos::ScalarTraits<SC>::one(), locX.values(), locX.stride(),
locX.values(), locX.stride(), Teuchos::ScalarTraits<SC>::zero(),
XXtInv_[i].values(), XXtInv_[i].stride());
Teuchos::LAPACK<LO,SC> lapack;
LO info, lwork = 3*NSDim;
ArrayRCP<LO> IPIV(NSDim);
ArrayRCP<SC> WORK(lwork);
lapack.GETRF(NSDim, NSDim, XXtInv_[i].values(), XXtInv_[i].stride(), IPIV.get(), &info);
lapack.GETRI(NSDim, XXtInv_[i].values(), XXtInv_[i].stride(), IPIV.get(), WORK.get(), lwork, &info);
}
}
int MxDimMatrix<T, DIM>::solve(MxDimVector<T, DIM> & x, const MxDimVector<T, DIM> & b) const {
x = b;
MxDimMatrix<T, DIM> copy(*this);
Teuchos::LAPACK<int, T> lapack;
MxDimVector<int, DIM> ipiv;
//int ipiv[DIM];
int info;
lapack.GETRF(DIM, DIM, ©(0, 0), DIM, &ipiv[0], &info);
if (info != 0)
std::cout << "MxDimMatrix::solve(...): error in lapack routine getrf. Return code: " << info << ".\n";
lapack.GETRS('T', DIM, 1, ©(0, 0), DIM, &ipiv[0], &x[0], DIM, &info);
if (info != 0)
std::cout << "MxDimMatrix::solve(...): error in lapack routine getrs. Return code: " << info << ".\n";
return info;
}
void updateGuess(Teuchos::SerialDenseVector<int, std::complex<double> >& myCurrentGuess,
Teuchos::SerialDenseVector<int, std::complex<double> >& myTargetsCalculated,
Teuchos::SerialDenseMatrix<int, std::complex<double> >& myJacobian,
Teuchos::LAPACK<int, std::complex<double> >& myLAPACK
)
{
//v = J(inverse) * (-F(x))
//new guess = v + old guess
myTargetsCalculated *= -1.0;
//Perform an LU factorization of this matrix.
int ipiv[NUMDIMENSIONS], info;
char TRANS = 'N';
myLAPACK.GETRF( NUMDIMENSIONS, NUMDIMENSIONS, myJacobian.values(), myJacobian.stride(), ipiv, &info );
// Solve the linear system.
myLAPACK.GETRS( TRANS, NUMDIMENSIONS, 1, myJacobian.values(), myJacobian.stride(),
ipiv, myTargetsCalculated.values(), myTargetsCalculated.stride(), &info );
//We have overwritten myTargetsCalculated with guess update values
//myBLAS.AXPY(NUMDIMENSIONS, 1.0, myGuessAdjustment.values(), 1, myCurrentGuess.values(), 1);
myCurrentGuess += myTargetsCalculated;
}
void DenseContainer<MatrixType, LocalScalarType>::factor ()
{
Teuchos::LAPACK<int, local_scalar_type> lapack;
int INFO = 0;
lapack.GETRF (diagBlock_.numRows (), diagBlock_.numCols (),
diagBlock_.values (), diagBlock_.stride (),
ipiv_.getRawPtr (), &INFO);
// INFO < 0 is a bug.
TEUCHOS_TEST_FOR_EXCEPTION(
INFO < 0, std::logic_error, "Ifpack2::DenseContainer::factor: "
"LAPACK's _GETRF (LU factorization with partial pivoting) was called "
"incorrectly. INFO = " << INFO << " < 0. "
"Please report this bug to the Ifpack2 developers.");
// INFO > 0 means the matrix is singular. This is probably an issue
// either with the choice of rows the rows we extracted, or with the
// input matrix itself.
TEUCHOS_TEST_FOR_EXCEPTION(
INFO > 0, std::runtime_error, "Ifpack2::DenseContainer::factor: "
"LAPACK's _GETRF (LU factorization with partial pivoting) reports that the "
"computed U factor is exactly singular. U(" << INFO << "," << INFO << ") "
"(one-based index i) is exactly zero. This probably means that the input "
"matrix has a singular diagonal block.");
}
NOX::Abstract::Group::ReturnType
LOCA::EigenvalueSort::LargestMagnitude::sort(int n, double* r_evals,
double* i_evals,
std::vector<int>* perm) const
{
int i, j;
int tempord = 0;
double temp, tempr, tempi;
Teuchos::LAPACK<int,double> lapack;
//
// Reset the index
if (perm) {
for (i=0; i < n; i++) {
(*perm)[i] = i;
}
}
//---------------------------------------------------------------
// Sort eigenvalues in decreasing order of magnitude
//---------------------------------------------------------------
for (j=1; j < n; ++j) {
tempr = r_evals[j]; tempi = i_evals[j];
if (perm)
tempord = (*perm)[j];
temp=lapack.LAPY2(r_evals[j],i_evals[j]);
for (i=j-1; i>=0 && lapack.LAPY2(r_evals[i],i_evals[i])<temp; --i) {
r_evals[i+1]=r_evals[i]; i_evals[i+1]=i_evals[i];
if (perm)
(*perm)[i+1]=(*perm)[i];
}
r_evals[i+1] = tempr; i_evals[i+1] = tempi;
if (perm)
(*perm)[i+1] = tempord;
}
return NOX::Abstract::Group::Ok;
}
void gauss( const Teuchos::LAPACK<int,Real> &lapack,
const ROL::Vector<Real> &a,
const ROL::Vector<Real> &b,
ROL::Vector<Real> &x,
ROL::Vector<Real> &w ) {
int INFO;
Teuchos::RCP<const std::vector<Real> > ap =
(Teuchos::dyn_cast<ROL::StdVector<Real> >(const_cast<ROL::Vector<Real> &>(a))).getVector();
Teuchos::RCP<const std::vector<Real> > bp =
(Teuchos::dyn_cast<ROL::StdVector<Real> >(const_cast<ROL::Vector<Real> &>(b))).getVector();
Teuchos::RCP<std::vector<Real> > xp =
Teuchos::rcp_const_cast<std::vector<Real> >((Teuchos::dyn_cast<ROL::StdVector<Real> >(x)).getVector());
Teuchos::RCP<std::vector<Real> > wp =
Teuchos::rcp_const_cast<std::vector<Real> >((Teuchos::dyn_cast<ROL::StdVector<Real> >(w)).getVector());
const int N = ap->size();
const int LDZ = N;
const char COMPZ = 'I';
Teuchos::RCP<std::vector<Real> > Dp = Teuchos::rcp(new std::vector<Real>(N,0.0));
Teuchos::RCP<std::vector<Real> > Ep = Teuchos::rcp(new std::vector<Real>(N,0.0));
Teuchos::RCP<std::vector<Real> > WORKp = Teuchos::rcp(new std::vector<Real>(4*N,0.0));
// Column-stacked matrix of eigenvectors needed for weights
Teuchos::RCP<std::vector<Real> > Zp = Teuchos::rcp(new std::vector<Real>(N*N,0));
// D = a
std::copy(ap->begin(),ap->end(),Dp->begin());
for(int i=0;i<N-1;++i) {
(*Ep)[i] = sqrt((*bp)[i+1]);
}
// Eigenvalue Decomposition
lapack.STEQR(COMPZ,N,&(*Dp)[0],&(*Ep)[0],&(*Zp)[0],LDZ,&(*WORKp)[0],&INFO);
for(int i=0;i<N;++i){
(*xp)[i] = (*Dp)[i];
(*wp)[i] = (*bp)[0]*pow((*Zp)[N*i],2);
}
}
Stokhos::MonoProjPCEBasis<ordinal_type, value_type>::
MonoProjPCEBasis(
ordinal_type p,
const Stokhos::OrthogPolyApprox<ordinal_type, value_type>& pce,
const Stokhos::Quadrature<ordinal_type, value_type>& quad,
const Stokhos::Sparse3Tensor<ordinal_type, value_type>& Cijk,
bool limit_integration_order_) :
RecurrenceBasis<ordinal_type, value_type>("Monomial Projection", p, true),
limit_integration_order(limit_integration_order_),
pce_sz(pce.basis()->size()),
pce_norms(pce.basis()->norm_squared()),
a(pce_sz),
b(pce_sz),
basis_vecs(pce_sz, p+1),
new_pce(p+1)
{
// If the original basis is normalized, we can use the standard QR
// factorization. For simplicity, we renormalize the PCE coefficients
// for a normalized basis
Stokhos::OrthogPolyApprox<ordinal_type, value_type> normalized_pce(pce);
for (ordinal_type i=0; i<pce_sz; i++) {
pce_norms[i] = std::sqrt(pce_norms[i]);
normalized_pce[i] *= pce_norms[i];
}
// Evaluate PCE at quad points
ordinal_type nqp = quad.size();
Teuchos::Array<value_type> pce_vals(nqp);
const Teuchos::Array<value_type>& weights = quad.getQuadWeights();
const Teuchos::Array< Teuchos::Array<value_type> >& quad_points =
quad.getQuadPoints();
const Teuchos::Array< Teuchos::Array<value_type> >& basis_values =
quad.getBasisAtQuadPoints();
for (ordinal_type i=0; i<nqp; i++) {
pce_vals[i] = normalized_pce.evaluate(quad_points[i], basis_values[i]);
}
// Form Kylov matrix up to order pce_sz
matrix_type K(pce_sz, pce_sz);
// Compute matrix
matrix_type A(pce_sz, pce_sz);
typedef Stokhos::Sparse3Tensor<ordinal_type, value_type> Cijk_type;
for (typename Cijk_type::k_iterator k_it = Cijk.k_begin();
k_it != Cijk.k_end(); ++k_it) {
ordinal_type k = index(k_it);
for (typename Cijk_type::kj_iterator j_it = Cijk.j_begin(k_it);
j_it != Cijk.j_end(k_it); ++j_it) {
ordinal_type j = index(j_it);
value_type val = 0;
for (typename Cijk_type::kji_iterator i_it = Cijk.i_begin(j_it);
i_it != Cijk.i_end(j_it); ++i_it) {
ordinal_type i = index(i_it);
value_type c = value(i_it) / (pce_norms[j]*pce_norms[k]);
val += pce[i]*c;
}
A(k,j) = val;
}
}
// Each column i is given by projection of the i-th order monomial
// onto original basis
vector_type u0 = Teuchos::getCol(Teuchos::View, K, 0);
u0(0) = 1.0;
for (ordinal_type i=1; i<pce_sz; i++)
u0(i) = 0.0;
for (ordinal_type k=1; k<pce_sz; k++) {
vector_type u = Teuchos::getCol(Teuchos::View, K, k);
vector_type up = Teuchos::getCol(Teuchos::View, K, k-1);
u.multiply(Teuchos::NO_TRANS, Teuchos::NO_TRANS, 1.0, A, up, 0.0);
}
/*
for (ordinal_type j=0; j<pce_sz; j++) {
for (ordinal_type i=0; i<pce_sz; i++) {
value_type val = 0.0;
for (ordinal_type k=0; k<nqp; k++)
val += weights[k]*std::pow(pce_vals[k],j)*basis_values[k][i];
K(i,j) = val;
}
}
*/
std::cout << K << std::endl << std::endl;
// Compute QR factorization of K
ordinal_type ws_size, info;
value_type ws_size_query;
Teuchos::Array<value_type> tau(pce_sz);
Teuchos::LAPACK<ordinal_type,value_type> lapack;
lapack.GEQRF(pce_sz, pce_sz, K.values(), K.stride(), &tau[0],
&ws_size_query, -1, &info);
TEUCHOS_TEST_FOR_EXCEPTION(info != 0, std::logic_error,
"GEQRF returned value " << info);
ws_size = static_cast<ordinal_type>(ws_size_query);
Teuchos::Array<value_type> work(ws_size);
lapack.GEQRF(pce_sz, pce_sz, K.values(), K.stride(), &tau[0],
&work[0], ws_size, &info);
TEUCHOS_TEST_FOR_EXCEPTION(info != 0, std::logic_error,
"GEQRF returned value " << info);
// Get Q
lapack.ORGQR(pce_sz, pce_sz, pce_sz, K.values(), K.stride(), &tau[0],
&ws_size_query, -1, &info);
TEUCHOS_TEST_FOR_EXCEPTION(info != 0, std::logic_error,
"ORGQR returned value " << info);
ws_size = static_cast<ordinal_type>(ws_size_query);
work.resize(ws_size);
lapack.ORGQR(pce_sz, pce_sz, pce_sz, K.values(), K.stride(), &tau[0],
&work[0], ws_size, &info);
TEUCHOS_TEST_FOR_EXCEPTION(info != 0, std::logic_error,
"ORGQR returned value " << info);
// Get basis vectors
for (ordinal_type j=0; j<p+1; j++)
for (ordinal_type i=0; i<pce_sz; i++)
basis_vecs(i,j) = K(i,j);
// Compute T = Q'*A*Q
matrix_type prod(pce_sz,pce_sz);
prod.multiply(Teuchos::TRANS, Teuchos::NO_TRANS, 1.0, K, A, 0.0);
matrix_type T(pce_sz,pce_sz);
T.multiply(Teuchos::NO_TRANS, Teuchos::NO_TRANS, 1.0, prod, K, 0.0);
//std::cout << T << std::endl;
// Recursion coefficients are diagonal and super diagonal
b[0] = 1.0;
for (ordinal_type i=0; i<pce_sz-1; i++) {
a[i] = T(i,i);
b[i+1] = T(i,i+1);
}
a[pce_sz-1] = T(pce_sz-1,pce_sz-1);
// Setup rest of basis
this->setup();
// Project original PCE into the new basis
vector_type u(pce_sz);
for (ordinal_type i=0; i<pce_sz; i++)
u[i] = normalized_pce[i];
new_pce.multiply(Teuchos::TRANS, Teuchos::NO_TRANS, 1.0, basis_vecs, u,
0.0);
for (ordinal_type i=0; i<=p; i++)
new_pce[i] /= this->norms[i];
}
int main(int argc, char *argv[]) {
Teuchos::GlobalMPISession mpiSession(&argc, &argv);
Kokkos::initialize();
// This little trick lets us print to std::cout only if
// a (dummy) command-line argument is provided.
int iprint = argc - 1;
Teuchos::RCP<std::ostream> outStream;
Teuchos::oblackholestream bhs; // outputs nothing
if (iprint > 0)
outStream = Teuchos::rcp(&std::cout, false);
else
outStream = Teuchos::rcp(&bhs, false);
// Save the format state of the original std::cout.
Teuchos::oblackholestream oldFormatState;
oldFormatState.copyfmt(std::cout);
*outStream \
<< "===============================================================================\n" \
<< "| |\n" \
<< "| Unit Test (Basis_HGRAD_HEX_In_FEM) |\n" \
<< "| |\n" \
<< "| 1) Patch test involving H(div) matrices |\n" \
<< "| for the Dirichlet problem on a hexahedron |\n" \
<< "| Omega with boundary Gamma. |\n" \
<< "| |\n" \
<< "| Questions? Contact Pavel Bochev ([email protected]), |\n" \
<< "| Robert Kirby ([email protected]), |\n" \
<< "| Denis Ridzal ([email protected]), |\n" \
<< "| Kara Peterson ([email protected]). |\n" \
<< "| |\n" \
<< "| Intrepid's website: http://trilinos.sandia.gov/packages/intrepid |\n" \
<< "| Trilinos website: http://trilinos.sandia.gov |\n" \
<< "| |\n" \
<< "===============================================================================\n" \
<< "| TEST 1: Patch test |\n" \
<< "===============================================================================\n";
int errorFlag = 0;
outStream -> precision(16);
try {
DefaultCubatureFactory<double> cubFactory; // create cubature factory
shards::CellTopology cell(shards::getCellTopologyData< shards::Hexahedron<> >()); // create parent cell topology
shards::CellTopology side(shards::getCellTopologyData< shards::Quadrilateral<> >()); // create relevant subcell (side) topology
shards::CellTopology line(shards::getCellTopologyData< shards::Line<> >() ); // for getting points to construct the basis
int cellDim = cell.getDimension();
int sideDim = side.getDimension();
int min_order = 0;
int max_order = 3;
int numIntervals = 2;
int numInterpPoints = (numIntervals + 1)*(numIntervals + 1)*(numIntervals+1);
FieldContainer<double> interp_points_ref(numInterpPoints, cellDim);
int counter = 0;
for (int k=0;k<numIntervals;k++) {
for (int j=0; j<=numIntervals; j++) {
for (int i=0; i<=numIntervals; i++) {
interp_points_ref(counter,0) = i*(1.0/numIntervals);
interp_points_ref(counter,1) = j*(1.0/numIntervals);
interp_points_ref(counter,2) = k*(1.0/numIntervals);
counter++;
}
}
}
for (int basis_order=min_order;basis_order<=max_order;basis_order++) {
// create bases
// get the points for the vector basis
Teuchos::RCP<Basis<double,FieldContainer<double> > > vectorBasis =
Teuchos::rcp(new Basis_HDIV_HEX_In_FEM<double,FieldContainer<double> >(basis_order+1,POINTTYPE_SPECTRAL) );
Teuchos::RCP<Basis<double,FieldContainer<double> > > scalarBasis =
Teuchos::rcp(new Basis_HGRAD_HEX_Cn_FEM<double,FieldContainer<double> >(basis_order,POINTTYPE_SPECTRAL) );
int numVectorFields = vectorBasis->getCardinality();
int numScalarFields = scalarBasis->getCardinality();
int numTotalFields = numVectorFields + numScalarFields;
// create cubatures
Teuchos::RCP<Cubature<double> > cellCub = cubFactory.create(cell, 2*(basis_order+1));
Teuchos::RCP<Cubature<double> > sideCub = cubFactory.create(side, 2*(basis_order+1));
int numCubPointsCell = cellCub->getNumPoints();
int numCubPointsSide = sideCub->getNumPoints();
// hold cubature information
FieldContainer<double> cub_points_cell(numCubPointsCell, cellDim);
FieldContainer<double> cub_weights_cell(numCubPointsCell);
FieldContainer<double> cub_points_side( numCubPointsSide, sideDim );
FieldContainer<double> cub_weights_side( numCubPointsSide );
FieldContainer<double> cub_points_side_refcell( numCubPointsSide , cellDim );
// hold basis function information on refcell
FieldContainer<double> value_of_v_basis_at_cub_points_cell(numVectorFields, numCubPointsCell, cellDim );
FieldContainer<double> w_value_of_v_basis_at_cub_points_cell(1, numVectorFields, numCubPointsCell, cellDim);
FieldContainer<double> div_of_v_basis_at_cub_points_cell( numVectorFields, numCubPointsCell );
FieldContainer<double> w_div_of_v_basis_at_cub_points_cell( 1, numVectorFields , numCubPointsCell );
FieldContainer<double> value_of_s_basis_at_cub_points_cell(numScalarFields,numCubPointsCell);
FieldContainer<double> w_value_of_s_basis_at_cub_points_cell(1,numScalarFields,numCubPointsCell);
// containers for side integration:
// I just need the normal component of the vector basis
// and the exact solution at the cub points
FieldContainer<double> value_of_v_basis_at_cub_points_side(numVectorFields,numCubPointsSide,cellDim);
FieldContainer<double> n_of_v_basis_at_cub_points_side(numVectorFields,numCubPointsSide);
FieldContainer<double> w_n_of_v_basis_at_cub_points_side(1,numVectorFields,numCubPointsSide);
FieldContainer<double> diri_data_at_cub_points_side(1,numCubPointsSide);
FieldContainer<double> side_normal(cellDim);
// holds rhs data
FieldContainer<double> rhs_at_cub_points_cell(1,numCubPointsCell);
// FEM matrices and vectors
FieldContainer<double> fe_matrix_M(1,numVectorFields,numVectorFields);
FieldContainer<double> fe_matrix_B(1,numVectorFields,numScalarFields);
FieldContainer<double> fe_matrix(1,numTotalFields,numTotalFields);
FieldContainer<double> rhs_vector_vec(1,numVectorFields);
FieldContainer<double> rhs_vector_scal(1,numScalarFields);
FieldContainer<double> rhs_and_soln_vec(1,numTotalFields);
FieldContainer<int> ipiv(numTotalFields);
FieldContainer<double> value_of_s_basis_at_interp_points( numScalarFields , numInterpPoints);
FieldContainer<double> interpolant( 1 , numInterpPoints );
// set test tolerance
double zero = (basis_order+1)*(basis_order+1)*1000.0*INTREPID_TOL;
// build matrices outside the loop, and then just do the rhs
// for each iteration
cellCub->getCubature(cub_points_cell, cub_weights_cell);
sideCub->getCubature(cub_points_side, cub_weights_side);
// need the vector basis & its divergences
vectorBasis->getValues(value_of_v_basis_at_cub_points_cell,
cub_points_cell,
OPERATOR_VALUE);
vectorBasis->getValues(div_of_v_basis_at_cub_points_cell,
cub_points_cell,
OPERATOR_DIV);
// need the scalar basis as well
scalarBasis->getValues(value_of_s_basis_at_cub_points_cell,
cub_points_cell,
OPERATOR_VALUE);
// construct mass matrix
cub_weights_cell.resize(1,numCubPointsCell);
FunctionSpaceTools::multiplyMeasure<double>(w_value_of_v_basis_at_cub_points_cell ,
cub_weights_cell ,
value_of_v_basis_at_cub_points_cell );
cub_weights_cell.resize(numCubPointsCell);
value_of_v_basis_at_cub_points_cell.resize( 1 , numVectorFields , numCubPointsCell , cellDim );
FunctionSpaceTools::integrate<double>(fe_matrix_M,
w_value_of_v_basis_at_cub_points_cell ,
value_of_v_basis_at_cub_points_cell ,
COMP_BLAS );
value_of_v_basis_at_cub_points_cell.resize( numVectorFields , numCubPointsCell , cellDim );
// div matrix
cub_weights_cell.resize(1,numCubPointsCell);
FunctionSpaceTools::multiplyMeasure<double>(w_div_of_v_basis_at_cub_points_cell,
cub_weights_cell,
div_of_v_basis_at_cub_points_cell);
cub_weights_cell.resize(numCubPointsCell);
value_of_s_basis_at_cub_points_cell.resize(1,numScalarFields,numCubPointsCell);
FunctionSpaceTools::integrate<double>(fe_matrix_B,
w_div_of_v_basis_at_cub_points_cell ,
value_of_s_basis_at_cub_points_cell ,
COMP_BLAS );
value_of_s_basis_at_cub_points_cell.resize(numScalarFields,numCubPointsCell);
for (int x_order=0;x_order<=basis_order;x_order++) {
for (int y_order=0;y_order<=basis_order;y_order++) {
for (int z_order=0;z_order<=basis_order;z_order++) {
// reset global matrix since I destroyed it in LU factorization.
fe_matrix.initialize();
// insert mass matrix into global matrix
for (int i=0;i<numVectorFields;i++) {
for (int j=0;j<numVectorFields;j++) {
fe_matrix(0,i,j) = fe_matrix_M(0,i,j);
}
}
// insert div matrix into global matrix
for (int i=0;i<numVectorFields;i++) {
for (int j=0;j<numScalarFields;j++) {
fe_matrix(0,i,numVectorFields+j)=-fe_matrix_B(0,i,j);
fe_matrix(0,j+numVectorFields,i)=fe_matrix_B(0,i,j);
}
}
// clear old vector data
rhs_vector_vec.initialize();
rhs_vector_scal.initialize();
rhs_and_soln_vec.initialize();
// now get rhs vector
// rhs_vector_scal is just (rhs,w) for w in the scalar basis
// I already have the scalar basis tabulated.
cub_points_cell.resize(1,numCubPointsCell,cellDim);
rhsFunc(rhs_at_cub_points_cell,
cub_points_cell,
x_order,
y_order,
z_order);
cub_points_cell.resize(numCubPointsCell,cellDim);
cub_weights_cell.resize(1,numCubPointsCell);
FunctionSpaceTools::multiplyMeasure<double>(w_value_of_s_basis_at_cub_points_cell,
cub_weights_cell,
value_of_s_basis_at_cub_points_cell);
cub_weights_cell.resize(numCubPointsCell);
FunctionSpaceTools::integrate<double>(rhs_vector_scal,
rhs_at_cub_points_cell,
w_value_of_s_basis_at_cub_points_cell,
COMP_BLAS);
for (int i=0;i<numScalarFields;i++) {
rhs_and_soln_vec(0,numVectorFields+i) = rhs_vector_scal(0,i);
}
// now get <u,v.n> on boundary
for (unsigned side_cur=0;side_cur<6;side_cur++) {
// map side cubature to current side
CellTools<double>::mapToReferenceSubcell( cub_points_side_refcell ,
cub_points_side ,
sideDim ,
(int)side_cur ,
cell );
// Evaluate dirichlet data
cub_points_side_refcell.resize(1,numCubPointsSide,cellDim);
u_exact(diri_data_at_cub_points_side,
cub_points_side_refcell,x_order,y_order,z_order);
cub_points_side_refcell.resize(numCubPointsSide,cellDim);
// get normal direction, this has the edge weight factored into it already
CellTools<double>::getReferenceSideNormal(side_normal ,
(int)side_cur,cell );
// v.n at cub points on side
vectorBasis->getValues(value_of_v_basis_at_cub_points_side ,
cub_points_side_refcell ,
OPERATOR_VALUE );
for (int i=0;i<numVectorFields;i++) {
for (int j=0;j<numCubPointsSide;j++) {
n_of_v_basis_at_cub_points_side(i,j) = 0.0;
for (int k=0;k<cellDim;k++) {
n_of_v_basis_at_cub_points_side(i,j) += side_normal(k) *
value_of_v_basis_at_cub_points_side(i,j,k);
}
}
}
cub_weights_side.resize(1,numCubPointsSide);
FunctionSpaceTools::multiplyMeasure<double>(w_n_of_v_basis_at_cub_points_side,
cub_weights_side,
n_of_v_basis_at_cub_points_side);
cub_weights_side.resize(numCubPointsSide);
FunctionSpaceTools::integrate<double>(rhs_vector_vec,
diri_data_at_cub_points_side,
w_n_of_v_basis_at_cub_points_side,
COMP_BLAS,
false);
for (int i=0;i<numVectorFields;i++) {
rhs_and_soln_vec(0,i) -= rhs_vector_vec(0,i);
}
}
// solve linear system
int info = 0;
Teuchos::LAPACK<int, double> solver;
solver.GESV(numTotalFields, 1, &fe_matrix(0,0,0), numTotalFields, &ipiv(0), &rhs_and_soln_vec(0,0),
numTotalFields, &info);
// compute interpolant; the scalar entries are last
scalarBasis->getValues(value_of_s_basis_at_interp_points,
interp_points_ref,
OPERATOR_VALUE);
for (int pt=0;pt<numInterpPoints;pt++) {
interpolant(0,pt)=0.0;
for (int i=0;i<numScalarFields;i++) {
interpolant(0,pt) += rhs_and_soln_vec(0,numVectorFields+i)
* value_of_s_basis_at_interp_points(i,pt);
}
}
interp_points_ref.resize(1,numInterpPoints,cellDim);
// get exact solution for comparison
FieldContainer<double> exact_solution(1,numInterpPoints);
u_exact( exact_solution , interp_points_ref , x_order, y_order, z_order);
interp_points_ref.resize(numInterpPoints,cellDim);
RealSpaceTools<double>::add(interpolant,exact_solution);
double nrm= RealSpaceTools<double>::vectorNorm(&interpolant(0,0),interpolant.dimension(1), NORM_TWO);
*outStream << "\nNorm-2 error between scalar components of exact solution of order ("
<< x_order << ", " << y_order << ", " << z_order
<< ") and finite element interpolant of order " << basis_order << ": "
<< nrm << "\n";
if (nrm > zero) {
*outStream << "\n\nPatch test failed for solution polynomial order ("
<< x_order << ", " << y_order << ", " << z_order << ") and basis order (scalar, vector) ("
<< basis_order << ", " << basis_order+1 << ")\n\n";
errorFlag++;
}
}
}
}
}
}
catch (std::logic_error err) {
*outStream << err.what() << "\n\n";
errorFlag = -1000;
};
if (errorFlag != 0)
std::cout << "End Result: TEST FAILED\n";
else
std::cout << "End Result: TEST PASSED\n";
// reset format state of std::cout
std::cout.copyfmt(oldFormatState);
Kokkos::finalize();
return errorFlag;
}
NOX::StatusTest::StatusType NOX::Solver::AndersonAcceleration::step()
{
prePostOperator.runPreIterate(*this);
Teuchos::ParameterList lsParams = paramsPtr->sublist("Direction").sublist("Newton").sublist("Linear Solver");
// On the first step, do some initializations
if (nIter == 0) {
// Compute F of initital guess
NOX::Abstract::Group::ReturnType rtype = solnPtr->computeF();
if (rtype != NOX::Abstract::Group::Ok) {
utilsPtr->out() << "NOX::Solver::AndersonAcceleration::init - "
<< "Unable to compute F" << std::endl;
throw "NOX Error";
}
// Test the initial guess
status = testPtr->checkStatus(*this, checkType);
if ((status == NOX::StatusTest::Converged) &&
(utilsPtr->isPrintType(NOX::Utils::Warning))) {
utilsPtr->out() << "Warning: NOX::Solver::AndersonAcceleration::init() - "
<< "The solution passed into the solver (either "
<< "through constructor or reset method) "
<< "is already converged! The solver wil not "
<< "attempt to solve this system since status is "
<< "flagged as converged." << std::endl;
}
printUpdate();
// First check status
if (status != NOX::StatusTest::Unconverged) {
prePostOperator.runPostIterate(*this);
printUpdate();
return status;
}
// Apply preconditioner if enabled
if (precond) {
if (recomputeJacobian)
solnPtr->computeJacobian();
solnPtr->applyRightPreconditioning(false, lsParams, solnPtr->getF(), *oldPrecF);
}
else
*oldPrecF = solnPtr->getF();
// Copy initial guess to old soln
*oldSolnPtr = *solnPtr;
// Compute step then first iterate with a line search.
workVec->update(mixParam,*oldPrecF);
bool ok = lineSearchPtr->compute(*solnPtr, stepSize, *workVec, *this);
if (!ok)
{
if (stepSize == 0.0)
{
utilsPtr->out() << "NOX::Solver::AndersonAcceleratino::iterate - line search failed" << std::endl;
status = NOX::StatusTest::Failed;
prePostOperator.runPostIterate(*this);
printUpdate();
return status;
}
else if (utilsPtr->isPrintType(NOX::Utils::Warning))
utilsPtr->out() << "NOX::Solver::AndersonAcceleration::iterate - using recovery step for line search" << std::endl;
}
// Compute F for the first iterate in case it isn't in the line search
rtype = solnPtr->computeF();
if (rtype != NOX::Abstract::Group::Ok)
{
utilsPtr->out() << "NOX::Solver::AndersonAcceleration::iterate - unable to compute F" << std::endl;
status = NOX::StatusTest::Failed;
prePostOperator.runPostIterate(*this);
printUpdate();
return status;
}
// Evaluate the current status.
status = testPtr->checkStatus(*this, checkType);
//Update iteration count
nIter++;
prePostOperator.runPostIterate(*this);
printUpdate();
return status;
}
// First check status
if (status != NOX::StatusTest::Unconverged) {
prePostOperator.runPostIterate(*this);
printUpdate();
return status;
}
// Apply preconditioner if enabled
if (precond) {
if (recomputeJacobian)
solnPtr->computeJacobian();
solnPtr->applyRightPreconditioning(false, lsParams, solnPtr->getF(), *precF);
}
else
*precF = solnPtr->getF();
// Manage the matrices of past iterates and QR factors
if (storeParam > 0) {
if (nIter == accelerationStartIteration) {
// Initialize
nStore = 0;
rMat.shape(0,0);
oldPrecF->update(1.0, *precF, -1.0);
qrAdd(*oldPrecF);
xMat[0]->update(1.0, solnPtr->getX(), -1.0, oldSolnPtr->getX(), 0.0);
}
else if (nIter > accelerationStartIteration) {
if (nStore == storeParam) {
Teuchos::RCP<NOX::Abstract::Vector> tempPtr = xMat[0];
for (int ii = 0; ii<nStore-1; ii++)
xMat[ii] = xMat[ii+1];
xMat[nStore-1] = tempPtr;
qrDelete();
}
oldPrecF->update(1.0, *precF, -1.0);
qrAdd(*oldPrecF);
xMat[nStore-1]->update(1.0, solnPtr->getX(), -1.0, oldSolnPtr->getX(), 0.0);
}
}
// Reorthogonalize
if ( (nStore > 1) && (orthoFrequency > 0) )
if (nIter % orthoFrequency == 0)
reorthogonalize();
// Copy current soln to the old soln.
*oldSolnPtr = *solnPtr;
*oldPrecF = *precF;
// Adjust for condition number
if (nStore > 0) {
Teuchos::LAPACK<int,double> lapack;
char normType = '1';
double invCondNum = 0.0;
int info = 0;
if ( WORK.size() < static_cast<std::size_t>(4*nStore) )
WORK.resize(4*nStore);
if (IWORK.size() < static_cast<std::size_t>(nStore))
IWORK.resize(nStore);
lapack.GECON(normType,nStore,rMat.values(),nStore,rMat.normOne(),&invCondNum,&WORK[0],&IWORK[0],&info);
if (utilsPtr->isPrintType(Utils::Details))
utilsPtr->out() << " R condition number estimate ("<< nStore << ") = " << 1.0/invCondNum << std::endl;
if (adjustForConditionNumber) {
while ( (1.0/invCondNum > dropTolerance) && (nStore > 1) ) {
Teuchos::RCP<NOX::Abstract::Vector> tempPtr = xMat[0];
for (int ii = 0; ii<nStore-1; ii++)
xMat[ii] = xMat[ii+1];
xMat[nStore-1] = tempPtr;
qrDelete();
lapack.GECON(normType,nStore,rMat.values(),nStore,rMat.normOne(),&invCondNum,&WORK[0],&IWORK[0],&info);
if (utilsPtr->isPrintType(Utils::Details))
utilsPtr->out() << " Adjusted R condition number estimate ("<< nStore << ") = " << 1.0/invCondNum << std::endl;
}
}
}
// Solve the least-squares problem.
Teuchos::SerialDenseMatrix<int,double> gamma(nStore,1), RHS(nStore,1), Rgamma(nStore,1);
for (int ii = 0; ii<nStore; ii++)
RHS(ii,0) = precF->innerProduct( *(qMat[ii]) );
//Back-solve for gamma
for (int ii = nStore-1; ii>=0; ii--) {
gamma(ii,0) = RHS(ii,0);
for (int jj = ii+1; jj<nStore; jj++) {
gamma(ii,0) -= rMat(ii,jj)*gamma(jj,0);
}
gamma(ii,0) /= rMat(ii,ii);
}
if (nStore > 0)
Rgamma.multiply(Teuchos::NO_TRANS,Teuchos::NO_TRANS,mixParam,rMat,gamma,0.0);
// Compute the step and new solution using the line search.
workVec->update(mixParam,*precF);
for (int ii=0; ii<nStore; ii++)
workVec->update(-gamma(ii,0), *(xMat[ii]), -Rgamma(ii,0),*(qMat[ii]),1.0);
bool ok = lineSearchPtr->compute(*solnPtr, stepSize, *workVec, *this);
if (!ok)
{
if (stepSize == 0.0)
{
utilsPtr->out() << "NOX::Solver::AndersonAcceleratino::iterate - line search failed" << std::endl;
status = NOX::StatusTest::Failed;
prePostOperator.runPostIterate(*this);
printUpdate();
return status;
}
else if (utilsPtr->isPrintType(NOX::Utils::Warning))
utilsPtr->out() << "NOX::Solver::AndersonAcceleration::iterate - using recovery step for line search" << std::endl;
}
// Compute F for new current solution in case the line search didn't .
NOX::Abstract::Group::ReturnType rtype = solnPtr->computeF();
if (rtype != NOX::Abstract::Group::Ok)
{
utilsPtr->out() << "NOX::Solver::AndersonAcceleration::iterate - unable to compute F" << std::endl;
status = NOX::StatusTest::Failed;
prePostOperator.runPostIterate(*this);
printUpdate();
return status;
}
// Update iteration count
nIter++;
// Evaluate the current status.
status = testPtr->checkStatus(*this, checkType);
prePostOperator.runPostIterate(*this);
printUpdate();
return status;
}
//==============================================================================
int Ifpack_Polynomial::Compute()
{
if (!IsInitialized())
IFPACK_CHK_ERR(Initialize());
Time_->ResetStartTime();
// reset values
IsComputed_ = false;
Condest_ = -1.0;
if (PolyDegree_ <= 0)
IFPACK_CHK_ERR(-2); // at least one application
#ifdef HAVE_IFPACK_EPETRAEXT
// Check to see if we can run in block mode
if(IsRowMatrix_ && InvDiagonal_ == Teuchos::null && UseBlockMode_){
const Epetra_CrsMatrix *CrsMatrix=dynamic_cast<const Epetra_CrsMatrix*>(&*Matrix_);
// If we don't have CrsMatrix, we can't use the block preconditioner
if(!CrsMatrix) UseBlockMode_=false;
else{
int ierr;
InvBlockDiagonal_=Teuchos::rcp(new EpetraExt_PointToBlockDiagPermute(*CrsMatrix));
if(InvBlockDiagonal_==Teuchos::null) IFPACK_CHK_ERR(-6);
ierr=InvBlockDiagonal_->SetParameters(BlockList_);
if(ierr) IFPACK_CHK_ERR(-7);
ierr=InvBlockDiagonal_->Compute();
if(ierr) IFPACK_CHK_ERR(-8);
}
}
#endif
if (IsRowMatrix_ && InvDiagonal_ == Teuchos::null && !UseBlockMode_)
{
InvDiagonal_ = Teuchos::rcp( new Epetra_Vector(Matrix().Map()) );
if (InvDiagonal_ == Teuchos::null)
IFPACK_CHK_ERR(-5);
IFPACK_CHK_ERR(Matrix().ExtractDiagonalCopy(*InvDiagonal_));
// Inverse diagonal elements
// Replace zeros with 1.0
for (int i = 0 ; i < NumMyRows_ ; ++i) {
double diag = (*InvDiagonal_)[i];
if (IFPACK_ABS(diag) < MinDiagonalValue_)
(*InvDiagonal_)[i] = MinDiagonalValue_;
else
(*InvDiagonal_)[i] = 1.0 / diag;
}
}
// Automatically compute maximum eigenvalue estimate of D^{-1}A if user hasn't provided one
double lambda_real_min, lambda_real_max, lambda_imag_min, lambda_imag_max;
if (LambdaRealMax_ == -1) {
//PowerMethod(Matrix(), *InvDiagonal_, EigMaxIters_, lambda_max);
GMRES(Matrix(), *InvDiagonal_, EigMaxIters_, lambda_real_min, lambda_real_max, lambda_imag_min, lambda_imag_max);
LambdaRealMin_=lambda_real_min; LambdaImagMin_=lambda_imag_min;
LambdaRealMax_=lambda_real_max; LambdaImagMax_=lambda_imag_max;
//std::cout<<"LambdaRealMin: "<<LambdaRealMin_<<std::endl;
//std::cout<<"LambdaRealMax: "<<LambdaRealMax_<<std::endl;
//std::cout<<"LambdaImagMin: "<<LambdaImagMin_<<std::endl;
//std::cout<<"LambdaImagMax: "<<LambdaImagMax_<<std::endl;
}
// find least squares polynomial for (LSPointsReal_*LSPointsImag_) zeros
// on a rectangle in the complex plane defined as
// [LambdaRealMin_,LambdaRealMax_] x [LambdaImagMin_,LambdaImagMax_]
const std::complex<double> zero(0.0,0.0);
// Compute points in complex plane
double lenx = LambdaRealMax_-LambdaRealMin_;
int nx = ceil(lenx*((double) LSPointsReal_));
if (nx<2) { nx = 2; }
double hx = lenx/((double) nx);
std::vector<double> xs;
if(abs(lenx)>1.0e-8) {
for( int pt=0; pt<=nx; pt++ ) {
xs.push_back(hx*pt+LambdaRealMin_);
}
}
else {
xs.push_back(LambdaRealMax_);
nx=1;
}
double leny = LambdaImagMax_-LambdaImagMin_;
int ny = ceil(leny*((double) LSPointsImag_));
if (ny<2) { ny = 2; }
double hy = leny/((double) ny);
std::vector<double> ys;
if(abs(leny)>1.0e-8) {
for( int pt=0; pt<=ny; pt++ ) {
ys.push_back(hy*pt+LambdaImagMin_);
}
}
else {
ys.push_back(LambdaImagMax_);
ny=1;
}
std::vector< std::complex<double> > cpts;
for( int jj=0; jj<ny; jj++ ) {
for( int ii=0; ii<nx; ii++ ) {
std::complex<double> cpt(xs[ii],ys[jj]);
cpts.push_back(cpt);
}
}
cpts.push_back(zero);
#ifdef HAVE_TEUCHOS_COMPLEX
const std::complex<double> one(1.0,0.0);
// Construct overdetermined Vandermonde matrix
Teuchos::SerialDenseMatrix<int, std::complex<double> > Vmatrix(cpts.size(),PolyDegree_+1);
Vmatrix.putScalar(zero);
for (int jj = 0; jj <= PolyDegree_; ++jj) {
for (int ii = 0; ii < static_cast<int> (cpts.size ()) - 1; ++ii) {
if (jj > 0) {
Vmatrix(ii,jj) = pow(cpts[ii],jj);
}
else {
Vmatrix(ii,jj) = one;
}
}
}
Vmatrix(cpts.size()-1,0)=one;
// Right hand side: all zero except last entry
Teuchos::SerialDenseMatrix< int,std::complex<double> > RHS(cpts.size(),1);
RHS.putScalar(zero);
RHS(cpts.size()-1,0)=one;
// Solve least squares problem using LAPACK
Teuchos::LAPACK< int, std::complex<double> > lapack;
const int N = Vmatrix.numCols();
Teuchos::Array<double> singularValues(N);
Teuchos::Array<double> rwork(1);
rwork.resize (std::max (1, 5 * N));
std::complex<double> lworkScalar(1.0,0.0);
int info = 0;
lapack.GELS('N', Vmatrix.numRows(), Vmatrix.numCols(), RHS.numCols(),
Vmatrix.values(), Vmatrix.numRows(), RHS.values(), RHS.numRows(),
&lworkScalar, -1, &info);
TEUCHOS_TEST_FOR_EXCEPTION(info != 0, std::logic_error,
"_GELSS workspace query returned INFO = "
<< info << " != 0.");
const int lwork = static_cast<int> (real(lworkScalar));
TEUCHOS_TEST_FOR_EXCEPTION(lwork < 0, std::logic_error,
"_GELSS workspace query returned LWORK = "
<< lwork << " < 0.");
// Allocate workspace. Size > 0 means &work[0] makes sense.
Teuchos::Array< std::complex<double> > work (std::max (1, lwork));
// Solve the least-squares problem.
lapack.GELS('N', Vmatrix.numRows(), Vmatrix.numCols(), RHS.numCols(),
Vmatrix.values(), Vmatrix.numRows(), RHS.values(), RHS.numRows(),
&work[0], lwork, &info);
coeff_.resize(PolyDegree_+1);
std::complex<double> c0=RHS(0,0);
for(int ii=0; ii<=PolyDegree_; ii++) {
// test that the imaginary part is nonzero
//TEUCHOS_TEST_FOR_EXCEPTION(abs(imag(RHS(ii,0))) > 1e-8, std::logic_error,
// "imaginary part of polynomial coefficients is nonzero! coeff = "
// << RHS(ii,0));
coeff_[ii]=real(RHS(ii,0)/c0);
//std::cout<<"coeff["<<ii<<"]="<<coeff_[ii]<<std::endl;
}
#else
// Construct overdetermined Vandermonde matrix
Teuchos::SerialDenseMatrix< int, double > Vmatrix(xs.size()+1,PolyDegree_+1);
Vmatrix.putScalar(0.0);
for( int jj=0; jj<=PolyDegree_; jj++) {
for( std::vector<double>::size_type ii=0; ii<xs.size(); ii++) {
if(jj>0) {
Vmatrix(ii,jj)=pow(xs[ii],jj);
}
else {
Vmatrix(ii,jj)=1.0;
}
}
}
Vmatrix(xs.size(),0)=1.0;
// Right hand side: all zero except last entry
Teuchos::SerialDenseMatrix< int, double > RHS(xs.size()+1,1);
RHS.putScalar(0.0);
RHS(xs.size(),0)=1.0;
// Solve least squares problem using LAPACK
Teuchos::LAPACK< int, double > lapack;
const int N = Vmatrix.numCols();
Teuchos::Array<double> singularValues(N);
Teuchos::Array<double> rwork(1);
rwork.resize (std::max (1, 5 * N));
double lworkScalar(1.0);
int info = 0;
lapack.GELS('N', Vmatrix.numRows(), Vmatrix.numCols(), RHS.numCols(),
Vmatrix.values(), Vmatrix.numRows(), RHS.values(), RHS.numRows(),
&lworkScalar, -1, &info);
TEUCHOS_TEST_FOR_EXCEPTION(info != 0, std::logic_error,
"_GELSS workspace query returned INFO = "
<< info << " != 0.");
const int lwork = static_cast<int> (lworkScalar);
TEUCHOS_TEST_FOR_EXCEPTION(lwork < 0, std::logic_error,
"_GELSS workspace query returned LWORK = "
<< lwork << " < 0.");
// Allocate workspace. Size > 0 means &work[0] makes sense.
Teuchos::Array< double > work (std::max (1, lwork));
// Solve the least-squares problem.
lapack.GELS('N', Vmatrix.numRows(), Vmatrix.numCols(), RHS.numCols(),
Vmatrix.values(), Vmatrix.numRows(), RHS.values(), RHS.numRows(),
&work[0], lwork, &info);
coeff_.resize(PolyDegree_+1);
double c0=RHS(0,0);
for(int ii=0; ii<=PolyDegree_; ii++) {
// test that the imaginary part is nonzero
//TEUCHOS_TEST_FOR_EXCEPTION(abs(imag(RHS(ii,0))) > 1e-8, std::logic_error,
// "imaginary part of polynomial coefficients is nonzero! coeff = "
// << RHS(ii,0));
coeff_[ii]=RHS(ii,0)/c0;
}
#endif
#ifdef IFPACK_FLOPCOUNTERS
ComputeFlops_ += NumMyRows_;
#endif
++NumCompute_;
ComputeTime_ += Time_->ElapsedTime();
IsComputed_ = true;
return(0);
}
int main(int argc, char *argv[]) {
Teuchos::GlobalMPISession mpiSession(&argc, &argv);
// This little trick lets us print to std::cout only if
// a (dummy) command-line argument is provided.
int iprint = argc - 1;
Teuchos::RCP<std::ostream> outStream;
Teuchos::oblackholestream bhs; // outputs nothing
if (iprint > 0)
outStream = Teuchos::rcp(&std::cout, false);
else
outStream = Teuchos::rcp(&bhs, false);
// Save the format state of the original std::cout.
Teuchos::oblackholestream oldFormatState;
oldFormatState.copyfmt(std::cout);
*outStream \
<< "===============================================================================\n" \
<< "| |\n" \
<< "| Unit Test (Basis_HGRAD_QUAD_C2_FEM) |\n" \
<< "| |\n" \
<< "| 1) Patch test involving mass and stiffness matrices, |\n" \
<< "| for the Neumann problem on a physical parallelogram |\n" \
<< "| AND a reference quad Omega with boundary Gamma. |\n" \
<< "| |\n" \
<< "| - div (grad u) + u = f in Omega, (grad u) . n = g on Gamma |\n" \
<< "| |\n" \
<< "| For a generic parallelogram, the basis recovers a complete |\n" \
<< "| polynomial space of order 2. On a (scaled and/or translated) |\n" \
<< "| reference quad, the basis recovers a complete tensor product |\n" \
<< "| space of order 2 (i.e. incl. the x^2*y, x*y^2, x^2*y^2 terms). |\n" \
<< "| |\n" \
<< "| Questions? Contact Pavel Bochev ([email protected]), |\n" \
<< "| Denis Ridzal ([email protected]), |\n" \
<< "| Kara Peterson ([email protected]). |\n" \
<< "| |\n" \
<< "| Intrepid's website: http://trilinos.sandia.gov/packages/intrepid |\n" \
<< "| Trilinos website: http://trilinos.sandia.gov |\n" \
<< "| |\n" \
<< "===============================================================================\n"\
<< "| TEST 1: Patch test |\n"\
<< "===============================================================================\n";
int errorFlag = 0;
outStream -> precision(16);
try {
int max_order = 2; // max total order of polynomial solution
DefaultCubatureFactory<double> cubFactory; // create cubature factory
shards::CellTopology cell(shards::getCellTopologyData< shards::Quadrilateral<> >()); // create parent cell topology
shards::CellTopology side(shards::getCellTopologyData< shards::Line<> >()); // create relevant subcell (side) topology
int cellDim = cell.getDimension();
int sideDim = side.getDimension();
// Define array containing points at which the solution is evaluated, in reference cell.
int numIntervals = 10;
int numInterpPoints = (numIntervals + 1)*(numIntervals + 1);
FieldContainer<double> interp_points_ref(numInterpPoints, 2);
int counter = 0;
for (int j=0; j<=numIntervals; j++) {
for (int i=0; i<=numIntervals; i++) {
interp_points_ref(counter,0) = i*(2.0/numIntervals)-1.0;
interp_points_ref(counter,1) = j*(2.0/numIntervals)-1.0;
counter++;
}
}
/* Parent cell definition. */
FieldContainer<double> cell_nodes[2];
cell_nodes[0].resize(1, 4, cellDim);
cell_nodes[1].resize(1, 4, cellDim);
// Generic parallelogram.
cell_nodes[0](0, 0, 0) = -5.0;
cell_nodes[0](0, 0, 1) = -1.0;
cell_nodes[0](0, 1, 0) = 4.0;
cell_nodes[0](0, 1, 1) = 1.0;
cell_nodes[0](0, 2, 0) = 8.0;
cell_nodes[0](0, 2, 1) = 3.0;
cell_nodes[0](0, 3, 0) = -1.0;
cell_nodes[0](0, 3, 1) = 1.0;
// Reference quad.
cell_nodes[1](0, 0, 0) = -1.0;
cell_nodes[1](0, 0, 1) = -1.0;
cell_nodes[1](0, 1, 0) = 1.0;
cell_nodes[1](0, 1, 1) = -1.0;
cell_nodes[1](0, 2, 0) = 1.0;
cell_nodes[1](0, 2, 1) = 1.0;
cell_nodes[1](0, 3, 0) = -1.0;
cell_nodes[1](0, 3, 1) = 1.0;
std::stringstream mystream[2];
mystream[0].str("\n>> Now testing basis on a generic parallelogram ...\n");
mystream[1].str("\n>> Now testing basis on the reference quad ...\n");
for (int pcell = 0; pcell < 2; pcell++) {
*outStream << mystream[pcell].str();
FieldContainer<double> interp_points(1, numInterpPoints, cellDim);
CellTools<double>::mapToPhysicalFrame(interp_points, interp_points_ref, cell_nodes[pcell], cell);
interp_points.resize(numInterpPoints, cellDim);
for (int x_order=0; x_order <= max_order; x_order++) {
int max_y_order = max_order;
if (pcell == 0) {
max_y_order -= x_order;
}
for (int y_order=0; y_order <= max_y_order; y_order++) {
// evaluate exact solution
FieldContainer<double> exact_solution(1, numInterpPoints);
u_exact(exact_solution, interp_points, x_order, y_order);
int basis_order = 2;
// set test tolerance
double zero = basis_order*basis_order*100*INTREPID_TOL;
//create basis
Teuchos::RCP<Basis<double,FieldContainer<double> > > basis =
Teuchos::rcp(new Basis_HGRAD_QUAD_C2_FEM<double,FieldContainer<double> >() );
int numFields = basis->getCardinality();
// create cubatures
Teuchos::RCP<Cubature<double> > cellCub = cubFactory.create(cell, 2*basis_order);
Teuchos::RCP<Cubature<double> > sideCub = cubFactory.create(side, 2*basis_order);
int numCubPointsCell = cellCub->getNumPoints();
int numCubPointsSide = sideCub->getNumPoints();
/* Computational arrays. */
/* Section 1: Related to parent cell integration. */
FieldContainer<double> cub_points_cell(numCubPointsCell, cellDim);
FieldContainer<double> cub_points_cell_physical(1, numCubPointsCell, cellDim);
FieldContainer<double> cub_weights_cell(numCubPointsCell);
FieldContainer<double> jacobian_cell(1, numCubPointsCell, cellDim, cellDim);
FieldContainer<double> jacobian_inv_cell(1, numCubPointsCell, cellDim, cellDim);
FieldContainer<double> jacobian_det_cell(1, numCubPointsCell);
FieldContainer<double> weighted_measure_cell(1, numCubPointsCell);
FieldContainer<double> value_of_basis_at_cub_points_cell(numFields, numCubPointsCell);
FieldContainer<double> transformed_value_of_basis_at_cub_points_cell(1, numFields, numCubPointsCell);
FieldContainer<double> weighted_transformed_value_of_basis_at_cub_points_cell(1, numFields, numCubPointsCell);
FieldContainer<double> grad_of_basis_at_cub_points_cell(numFields, numCubPointsCell, cellDim);
FieldContainer<double> transformed_grad_of_basis_at_cub_points_cell(1, numFields, numCubPointsCell, cellDim);
FieldContainer<double> weighted_transformed_grad_of_basis_at_cub_points_cell(1, numFields, numCubPointsCell, cellDim);
FieldContainer<double> fe_matrix(1, numFields, numFields);
FieldContainer<double> rhs_at_cub_points_cell_physical(1, numCubPointsCell);
FieldContainer<double> rhs_and_soln_vector(1, numFields);
/* Section 2: Related to subcell (side) integration. */
unsigned numSides = 4;
FieldContainer<double> cub_points_side(numCubPointsSide, sideDim);
FieldContainer<double> cub_weights_side(numCubPointsSide);
FieldContainer<double> cub_points_side_refcell(numCubPointsSide, cellDim);
FieldContainer<double> cub_points_side_physical(1, numCubPointsSide, cellDim);
FieldContainer<double> jacobian_side_refcell(1, numCubPointsSide, cellDim, cellDim);
FieldContainer<double> jacobian_det_side_refcell(1, numCubPointsSide);
FieldContainer<double> weighted_measure_side_refcell(1, numCubPointsSide);
FieldContainer<double> value_of_basis_at_cub_points_side_refcell(numFields, numCubPointsSide);
FieldContainer<double> transformed_value_of_basis_at_cub_points_side_refcell(1, numFields, numCubPointsSide);
FieldContainer<double> weighted_transformed_value_of_basis_at_cub_points_side_refcell(1, numFields, numCubPointsSide);
FieldContainer<double> neumann_data_at_cub_points_side_physical(1, numCubPointsSide);
FieldContainer<double> neumann_fields_per_side(1, numFields);
/* Section 3: Related to global interpolant. */
FieldContainer<double> value_of_basis_at_interp_points(numFields, numInterpPoints);
FieldContainer<double> transformed_value_of_basis_at_interp_points(1, numFields, numInterpPoints);
FieldContainer<double> interpolant(1, numInterpPoints);
FieldContainer<int> ipiv(numFields);
/******************* START COMPUTATION ***********************/
// get cubature points and weights
cellCub->getCubature(cub_points_cell, cub_weights_cell);
// compute geometric cell information
CellTools<double>::setJacobian(jacobian_cell, cub_points_cell, cell_nodes[pcell], cell);
CellTools<double>::setJacobianInv(jacobian_inv_cell, jacobian_cell);
CellTools<double>::setJacobianDet(jacobian_det_cell, jacobian_cell);
// compute weighted measure
FunctionSpaceTools::computeCellMeasure<double>(weighted_measure_cell, jacobian_det_cell, cub_weights_cell);
///////////////////////////
// Computing mass matrices:
// tabulate values of basis functions at (reference) cubature points
basis->getValues(value_of_basis_at_cub_points_cell, cub_points_cell, OPERATOR_VALUE);
// transform values of basis functions
FunctionSpaceTools::HGRADtransformVALUE<double>(transformed_value_of_basis_at_cub_points_cell,
value_of_basis_at_cub_points_cell);
// multiply with weighted measure
FunctionSpaceTools::multiplyMeasure<double>(weighted_transformed_value_of_basis_at_cub_points_cell,
weighted_measure_cell,
transformed_value_of_basis_at_cub_points_cell);
// compute mass matrices
FunctionSpaceTools::integrate<double>(fe_matrix,
transformed_value_of_basis_at_cub_points_cell,
weighted_transformed_value_of_basis_at_cub_points_cell,
COMP_BLAS);
///////////////////////////
////////////////////////////////
// Computing stiffness matrices:
// tabulate gradients of basis functions at (reference) cubature points
basis->getValues(grad_of_basis_at_cub_points_cell, cub_points_cell, OPERATOR_GRAD);
// transform gradients of basis functions
FunctionSpaceTools::HGRADtransformGRAD<double>(transformed_grad_of_basis_at_cub_points_cell,
jacobian_inv_cell,
grad_of_basis_at_cub_points_cell);
// multiply with weighted measure
FunctionSpaceTools::multiplyMeasure<double>(weighted_transformed_grad_of_basis_at_cub_points_cell,
weighted_measure_cell,
transformed_grad_of_basis_at_cub_points_cell);
// compute stiffness matrices and sum into fe_matrix
FunctionSpaceTools::integrate<double>(fe_matrix,
transformed_grad_of_basis_at_cub_points_cell,
weighted_transformed_grad_of_basis_at_cub_points_cell,
COMP_BLAS,
true);
////////////////////////////////
///////////////////////////////
// Computing RHS contributions:
// map cell (reference) cubature points to physical space
CellTools<double>::mapToPhysicalFrame(cub_points_cell_physical, cub_points_cell, cell_nodes[pcell], cell);
// evaluate rhs function
rhsFunc(rhs_at_cub_points_cell_physical, cub_points_cell_physical, x_order, y_order);
// compute rhs
FunctionSpaceTools::integrate<double>(rhs_and_soln_vector,
rhs_at_cub_points_cell_physical,
weighted_transformed_value_of_basis_at_cub_points_cell,
COMP_BLAS);
// compute neumann b.c. contributions and adjust rhs
sideCub->getCubature(cub_points_side, cub_weights_side);
for (unsigned i=0; i<numSides; i++) {
// compute geometric cell information
CellTools<double>::mapToReferenceSubcell(cub_points_side_refcell, cub_points_side, sideDim, (int)i, cell);
CellTools<double>::setJacobian(jacobian_side_refcell, cub_points_side_refcell, cell_nodes[pcell], cell);
CellTools<double>::setJacobianDet(jacobian_det_side_refcell, jacobian_side_refcell);
// compute weighted edge measure
FunctionSpaceTools::computeEdgeMeasure<double>(weighted_measure_side_refcell,
jacobian_side_refcell,
cub_weights_side,
i,
cell);
// tabulate values of basis functions at side cubature points, in the reference parent cell domain
basis->getValues(value_of_basis_at_cub_points_side_refcell, cub_points_side_refcell, OPERATOR_VALUE);
// transform
FunctionSpaceTools::HGRADtransformVALUE<double>(transformed_value_of_basis_at_cub_points_side_refcell,
value_of_basis_at_cub_points_side_refcell);
// multiply with weighted measure
FunctionSpaceTools::multiplyMeasure<double>(weighted_transformed_value_of_basis_at_cub_points_side_refcell,
weighted_measure_side_refcell,
transformed_value_of_basis_at_cub_points_side_refcell);
// compute Neumann data
// map side cubature points in reference parent cell domain to physical space
CellTools<double>::mapToPhysicalFrame(cub_points_side_physical, cub_points_side_refcell, cell_nodes[pcell], cell);
// now compute data
neumann(neumann_data_at_cub_points_side_physical, cub_points_side_physical, jacobian_side_refcell,
cell, (int)i, x_order, y_order);
FunctionSpaceTools::integrate<double>(neumann_fields_per_side,
neumann_data_at_cub_points_side_physical,
weighted_transformed_value_of_basis_at_cub_points_side_refcell,
COMP_BLAS);
// adjust RHS
RealSpaceTools<double>::add(rhs_and_soln_vector, neumann_fields_per_side);;
}
///////////////////////////////
/////////////////////////////
// Solution of linear system:
int info = 0;
Teuchos::LAPACK<int, double> solver;
solver.GESV(numFields, 1, &fe_matrix[0], numFields, &ipiv(0), &rhs_and_soln_vector[0], numFields, &info);
/////////////////////////////
////////////////////////
// Building interpolant:
// evaluate basis at interpolation points
basis->getValues(value_of_basis_at_interp_points, interp_points_ref, OPERATOR_VALUE);
// transform values of basis functions
FunctionSpaceTools::HGRADtransformVALUE<double>(transformed_value_of_basis_at_interp_points,
value_of_basis_at_interp_points);
FunctionSpaceTools::evaluate<double>(interpolant, rhs_and_soln_vector, transformed_value_of_basis_at_interp_points);
////////////////////////
/******************* END COMPUTATION ***********************/
RealSpaceTools<double>::subtract(interpolant, exact_solution);
*outStream << "\nRelative norm-2 error between exact solution polynomial of order ("
<< x_order << ", " << y_order << ") and finite element interpolant of order " << basis_order << ": "
<< RealSpaceTools<double>::vectorNorm(&interpolant[0], interpolant.dimension(1), NORM_TWO) /
RealSpaceTools<double>::vectorNorm(&exact_solution[0], exact_solution.dimension(1), NORM_TWO) << "\n";
if (RealSpaceTools<double>::vectorNorm(&interpolant[0], interpolant.dimension(1), NORM_TWO) /
RealSpaceTools<double>::vectorNorm(&exact_solution[0], exact_solution.dimension(1), NORM_TWO) > zero) {
*outStream << "\n\nPatch test failed for solution polynomial order ("
<< x_order << ", " << y_order << ") and basis order " << basis_order << "\n\n";
errorFlag++;
}
} // end for y_order
} // end for x_order
} // end for pcell
}
// Catch unexpected errors
catch (std::logic_error err) {
*outStream << err.what() << "\n\n";
errorFlag = -1000;
};
if (errorFlag != 0)
std::cout << "End Result: TEST FAILED\n";
else
std::cout << "End Result: TEST PASSED\n";
// reset format state of std::cout
std::cout.copyfmt(oldFormatState);
return errorFlag;
}
void RCGIter<ScalarType,MV,OP>::iterate()
{
TEUCHOS_TEST_FOR_EXCEPTION( initialized_ == false, RCGIterFailure,
"Belos::RCGIter::iterate(): RCGIter class not initialized." );
// We'll need LAPACK
Teuchos::LAPACK<int,ScalarType> lapack;
// Create convenience variables for zero and one.
ScalarType one = Teuchos::ScalarTraits<ScalarType>::one();
ScalarType zero = Teuchos::ScalarTraits<ScalarType>::zero();
// Allocate memory for scalars
std::vector<int> index(1);
Teuchos::SerialDenseMatrix<int,ScalarType> pAp(1,1), rTz(1,1);
// Get the current solution std::vector.
Teuchos::RCP<MV> cur_soln_vec = lp_->getCurrLHSVec();
// Check that the current solution std::vector only has one column.
TEUCHOS_TEST_FOR_EXCEPTION( MVT::GetNumberVecs(*cur_soln_vec) != 1, RCGIterFailure,
"Belos::RCGIter::iterate(): current linear system has more than one std::vector!" );
// Compute the current search dimension.
int searchDim = numBlocks_+1;
// index of iteration within current cycle
int i_ = 0;
////////////////////////////////////////////////////////////////
// iterate until the status test tells us to stop.
//
// also break if our basis is full
//
Teuchos::RCP<const MV> p_ = Teuchos::null;
Teuchos::RCP<MV> pnext_ = Teuchos::null;
while (stest_->checkStatus(this) != Passed && curDim_+1 <= searchDim) {
// Ap = A*p;
index.resize( 1 );
index[0] = i_;
p_ = MVT::CloneView( *P_, index );
lp_->applyOp( *p_, *Ap_ );
// d = p'*Ap;
MVT::MvTransMv( one, *p_, *Ap_, pAp );
(*D_)(i_,0) = pAp(0,0);
// alpha = rTz_old / pAp
(*Alpha_)(i_,0) = (*rTz_old_)(0,0) / pAp(0,0);
// Check that alpha is a positive number
TEUCHOS_TEST_FOR_EXCEPTION( SCT::real(pAp(0,0)) <= zero, RCGIterFailure, "Belos::RCGIter::iterate(): non-positive value for p^H*A*p encountered!" );
// x = x + (alpha * p);
MVT::MvAddMv( one, *cur_soln_vec, (*Alpha_)(i_,0), *p_, *cur_soln_vec );
lp_->updateSolution();
// r = r - (alpha * Ap);
MVT::MvAddMv( one, *r_, -(*Alpha_)(i_,0), *Ap_, *r_ );
std::vector<MagnitudeType> norm(1);
MVT::MvNorm( *r_, norm );
//printf("i = %i\tnorm(r) = %e\n",i_,norm[0]);
// z = M\r
if ( lp_->getLeftPrec() != Teuchos::null ) {
lp_->applyLeftPrec( *r_, *z_ );
}
else if ( lp_->getRightPrec() != Teuchos::null ) {
lp_->applyRightPrec( *r_, *z_ );
}
else {
z_ = r_;
}
// rTz_new = r'*z;
MVT::MvTransMv( one, *r_, *z_, rTz );
// beta = rTz_new/rTz_old;
(*Beta_)(i_,0) = rTz(0,0) / (*rTz_old_)(0,0);
// rTz_old = rTz_new;
(*rTz_old_)(0,0) = rTz(0,0);
// get pointer for next p
index.resize( 1 );
index[0] = i_+1;
pnext_ = MVT::CloneViewNonConst( *P_, index );
if (existU_) {
// mu = UTAU \ (AU'*z);
Teuchos::SerialDenseMatrix<int,ScalarType> mu( Teuchos::View, *Delta_, recycleBlocks_, 1, 0, i_ );
MVT::MvTransMv( one, *AU_, *z_, mu );
char TRANS = 'N';
int info;
lapack.GETRS( TRANS, recycleBlocks_, 1, LUUTAU_->values(), LUUTAU_->stride(), &(*ipiv_)[0], mu.values(), mu.stride(), &info );
TEUCHOS_TEST_FOR_EXCEPTION(info != 0, RCGIterLAPACKFailure,
"Belos::RCGIter::solve(): LAPACK GETRS failed to compute a solution.");
// p = -(U*mu) + (beta*p) + z (in two steps)
// p = (beta*p) + z;
MVT::MvAddMv( (*Beta_)(i_,0), *p_, one, *z_, *pnext_ );
// pnext = -(U*mu) + (one)*pnext;
MVT::MvTimesMatAddMv( -one, *U_, mu, one, *pnext_ );
}
else {
// p = (beta*p) + z;
MVT::MvAddMv( (*Beta_)(i_,0), *p_, one, *z_, *pnext_ );
}
// Done with this view; release pointer
p_ = Teuchos::null;
pnext_ = Teuchos::null;
// increment iteration count and dimension index
i_++;
iter_++;
curDim_++;
} // end while (statusTest == false)
}
// ***********************************************************
int DG_Prob::Eigenvectors(const double Dt,
const Epetra_Map & Map)
{
printf("Entrou em Eigenvectors\n");
#ifdef HAVE_MPI
Epetra_MpiComm Comm(MPI_COMM_WORLD);
#else
Epetra_SerialComm Comm;
#endif
//MPI::COMM_WORLD.Barrier();
Comm.Barrier();
Teuchos::RCP<Epetra_FECrsMatrix> M = Teuchos::rcp(new Epetra_FECrsMatrix(Copy, Map,0));//&NNz[0]);
Teuchos::RCP<Epetra_FEVector> RHS = Teuchos::rcp(new Epetra_FEVector(Map,1));
DG_MatrizVetor_Epetra(Dt,M,RHS);
Teuchos::RCP<Epetra_CrsMatrix> A = Teuchos::rcp(new Epetra_CrsMatrix(Copy, Map,0
/* &NNz[0]*/) );
Epetra_Export Exporter(Map,Map);
A->PutScalar(0.0);
A->Export(*(M.ptr()),Exporter,Add);
A->FillComplete();
using std::cout;
// int nx = 5;
bool boolret;
int MyPID = Comm.MyPID();
bool verbose = true;
bool debug = false;
std::string which("LR");
Teuchos::CommandLineProcessor cmdp(false,true);
cmdp.setOption("verbose","quiet",&verbose,"Print messages and results.");
cmdp.setOption("debug","nodebug",&debug,"Print debugging information.");
cmdp.setOption("sort",&which,"Targetted eigenvalues (SM,LM,SR,LR,SI,or LI).");
typedef double ScalarType;
typedef Teuchos::ScalarTraits<ScalarType> SCT;
typedef SCT::magnitudeType MagnitudeType;
typedef Epetra_MultiVector MV;
typedef Epetra_Operator OP;
typedef Anasazi::MultiVecTraits<ScalarType,MV> MVT;
typedef Anasazi::OperatorTraits<ScalarType,MV,OP> OPT;
// double rho = 2*nx+1;
// Compute coefficients for discrete convection-diffution operator
// const double one = 1.0;
// int NumEntries, info;
//************************************
// Start the block Arnoldi iteration
//***********************************
//
// Variables used for the Block Krylov Schur Method
//
int nev = 10;
int blockSize = 1;
int numBlocks = 20;
int maxRestarts = 500;
//int stepSize = 5;
double tol = 1e-8;
// Create a sort manager to pass into the block Krylov-Schur solver manager
// --> Make sure the reference-counted pointer is of type Anasazi::SortManager<>
// --> The block Krylov-Schur solver manager uses Anasazi::BasicSort<> by default,
// so you can also pass in the parameter "Which", instead of a sort manager.
Teuchos::RCP<Anasazi::SortManager<MagnitudeType> > MySort =
Teuchos::rcp( new Anasazi::BasicSort<MagnitudeType>( which ) );
// Set verbosity level
int verbosity = Anasazi::Errors + Anasazi::Warnings;
if (verbose) {
verbosity += Anasazi::FinalSummary + Anasazi::TimingDetails;
}
if (debug) {
verbosity += Anasazi::Debug;
}
//
// Create parameter list to pass into solver manager
//
Teuchos::ParameterList MyPL;
MyPL.set( "Verbosity", verbosity );
MyPL.set( "Sort Manager", MySort );
//MyPL.set( "Which", which );
MyPL.set( "Block Size", blockSize );
MyPL.set( "Num Blocks", numBlocks );
MyPL.set( "Maximum Restarts", maxRestarts );
//MyPL.set( "Step Size", stepSize );
MyPL.set( "Convergence Tolerance", tol );
// Create an Epetra_MultiVector for an initial vector to start the solver.
// Note: This needs to have the same number of columns as the blocksize.
Teuchos::RCP<Epetra_MultiVector> ivec = Teuchos::rcp( new Epetra_MultiVector(Map, blockSize) );
ivec->Random();
// Create the eigenproblem.
Teuchos::RCP<Anasazi::BasicEigenproblem<double, MV, OP> > MyProblem =
Teuchos::rcp( new Anasazi::BasicEigenproblem<double, MV, OP>(A, ivec) );
// Inform the eigenproblem that the operator A is symmetric
//MyProblem->setHermitian(rho==0.0);
// Set the number of eigenvalues requested
MyProblem->setNEV( nev );
// Inform the eigenproblem that you are finishing passing it information
boolret = MyProblem->setProblem();
if (boolret != true) {
if (verbose && MyPID == 0) {
cout << "Anasazi::BasicEigenproblem::setProblem() returned with error." << endl;
}
#ifdef HAVE_MPI
MPI_Finalize() ;
#endif
return -1;
}
// Initialize the Block Arnoldi solver
Anasazi::BlockKrylovSchurSolMgr<double, MV, OP> MySolverMgr(MyProblem, MyPL);
// Solve the problem to the specified tolerances or length
Anasazi::ReturnType returnCode = MySolverMgr.solve();
if (returnCode != Anasazi::Converged && MyPID==0 && verbose) {
cout << "Anasazi::EigensolverMgr::solve() returned unconverged." << endl;
}
// Get the Ritz values from the eigensolver
std::vector<Anasazi::Value<double> > ritzValues = MySolverMgr.getRitzValues();
// Output computed eigenvalues and their direct residuals
if (verbose && MyPID==0) {
int numritz = (int)ritzValues.size();
cout.setf(std::ios_base::right, std::ios_base::adjustfield);
cout<<endl<< "Computed Ritz Values"<< endl;
if (MyProblem->isHermitian()) {
cout<< std::setw(16) << "Real Part"
<< endl;
cout<<"-----------------------------------------------------------"<<endl;
for (int i=0; i<numritz; i++) {
cout<< std::setw(16) << ritzValues[i].realpart
<< endl;
}
cout<<"-----------------------------------------------------------"<<endl;
}
else {
cout<< std::setw(16) << "Real Part"
<< std::setw(16) << "Imag Part"
<< endl;
cout<<"-----------------------------------------------------------"<<endl;
for (int i=0; i<numritz; i++) {
cout<< std::setw(16) << ritzValues[i].realpart
<< std::setw(16) << ritzValues[i].imagpart
<< endl;
}
cout<<"-----------------------------------------------------------"<<endl;
}
}
// Get the eigenvalues and eigenvectors from the eigenproblem
Anasazi::Eigensolution<ScalarType,MV> sol = MyProblem->getSolution();
std::vector<Anasazi::Value<ScalarType> > evals = sol.Evals;
Teuchos::RCP<MV> evecs = sol.Evecs;
std::vector<int> index = sol.index;
int numev = sol.numVecs;
if (numev > 0) {
// Compute residuals.
Teuchos::LAPACK<int,double> lapack;
std::vector<double> normA(numev);
if (MyProblem->isHermitian()) {
// Get storage
Epetra_MultiVector Aevecs(Map,numev);
Teuchos::SerialDenseMatrix<int,double> B(numev,numev);
B.putScalar(0.0);
for (int i=0; i<numev; i++) {B(i,i) = evals[i].realpart;}
// Compute A*evecs
OPT::Apply( *A, *evecs, Aevecs );
// Compute A*evecs - lambda*evecs and its norm
MVT::MvTimesMatAddMv( -1.0, *evecs, B, 1.0, Aevecs );
MVT::MvNorm( Aevecs, normA );
// Scale the norms by the eigenvalue
for (int i=0; i<numev; i++) {
normA[i] /= Teuchos::ScalarTraits<double>::magnitude( evals[i].realpart );
}
} else {
// The problem is non-Hermitian.
int i=0;
std::vector<int> curind(1);
std::vector<double> resnorm(1), tempnrm(1);
Teuchos::RCP<MV> tempAevec;
Teuchos::RCP<const MV> evecr, eveci;
Epetra_MultiVector Aevec(Map,numev);
// Compute A*evecs
OPT::Apply( *A, *evecs, Aevec );
Teuchos::SerialDenseMatrix<int,double> Breal(1,1), Bimag(1,1);
while (i<numev) {
if (index[i]==0) {
// Get a view of the current eigenvector (evecr)
curind[0] = i;
evecr = MVT::CloneView( *evecs, curind );
// Get a copy of A*evecr
tempAevec = MVT::CloneCopy( Aevec, curind );
// Compute A*evecr - lambda*evecr
Breal(0,0) = evals[i].realpart;
MVT::MvTimesMatAddMv( -1.0, *evecr, Breal, 1.0, *tempAevec );
// Compute the norm of the residual and increment counter
MVT::MvNorm( *tempAevec, resnorm );
normA[i] = resnorm[0]/Teuchos::ScalarTraits<MagnitudeType>::magnitude( evals[i].realpart );
i++;
} else {
// Get a view of the real part of the eigenvector (evecr)
curind[0] = i;
evecr = MVT::CloneView( *evecs, curind );
// Get a copy of A*evecr
tempAevec = MVT::CloneCopy( Aevec, curind );
// Get a view of the imaginary part of the eigenvector (eveci)
curind[0] = i+1;
eveci = MVT::CloneView( *evecs, curind );
// Set the eigenvalue into Breal and Bimag
Breal(0,0) = evals[i].realpart;
Bimag(0,0) = evals[i].imagpart;
// Compute A*evecr - evecr*lambdar + eveci*lambdai
MVT::MvTimesMatAddMv( -1.0, *evecr, Breal, 1.0, *tempAevec );
MVT::MvTimesMatAddMv( 1.0, *eveci, Bimag, 1.0, *tempAevec );
MVT::MvNorm( *tempAevec, tempnrm );
// Get a copy of A*eveci
tempAevec = MVT::CloneCopy( Aevec, curind );
// Compute A*eveci - eveci*lambdar - evecr*lambdai
MVT::MvTimesMatAddMv( -1.0, *evecr, Bimag, 1.0, *tempAevec );
MVT::MvTimesMatAddMv( -1.0, *eveci, Breal, 1.0, *tempAevec );
MVT::MvNorm( *tempAevec, resnorm );
// Compute the norms and scale by magnitude of eigenvalue
normA[i] = lapack.LAPY2( tempnrm[i], resnorm[i] ) /
lapack.LAPY2( evals[i].realpart, evals[i].imagpart );
normA[i+1] = normA[i];
i=i+2;
}
}
}
// Output computed eigenvalues and their direct residuals
if (verbose && MyPID==0) {
cout.setf(std::ios_base::right, std::ios_base::adjustfield);
cout<<endl<< "Actual Residuals"<<endl;
if (MyProblem->isHermitian()) {
cout<< std::setw(16) << "Real Part"
<< std::setw(20) << "Direct Residual"<< endl;
cout<<"-----------------------------------------------------------"<<endl;
for (int i=0; i<numev; i++) {
cout<< std::setw(16) << evals[i].realpart
<< std::setw(20) << normA[i] << endl;
}
cout<<"-----------------------------------------------------------"<<endl;
}
else {
cout<< std::setw(16) << "Real Part"
<< std::setw(16) << "Imag Part"
<< std::setw(20) << "Direct Residual"<< endl;
cout<<"-----------------------------------------------------------"<<endl;
for (int i=0; i<numev; i++) {
cout<< std::setw(16) << evals[i].realpart
<< std::setw(16) << evals[i].imagpart
<< std::setw(20) << normA[i] << endl;
}
cout<<"-----------------------------------------------------------"<<endl;
}
}
}
#ifdef EPETRA_MPI
MPI_Finalize();
#endif
return 0;
}
int main(int argc, char *argv[]) {
int i, j, info;
const double one = 1.0;
const double zero = 0.0;
Teuchos::LAPACK<int,double> lapack;
#ifdef EPETRA_MPI
// Initialize MPI
MPI_Init(&argc,&argv);
Epetra_MpiComm Comm(MPI_COMM_WORLD);
#else
Epetra_SerialComm Comm;
#endif
int MyPID = Comm.MyPID();
// Dimension of the matrix
int m = 500;
int n = 100;
// Construct a Map that puts approximately the same number of
// equations on each processor.
Epetra_Map RowMap(m, 0, Comm);
Epetra_Map ColMap(n, 0, Comm);
// Get update list and number of local equations from newly created Map.
int NumMyRowElements = RowMap.NumMyElements();
std::vector<int> MyGlobalRowElements(NumMyRowElements);
RowMap.MyGlobalElements(&MyGlobalRowElements[0]);
/* We are building an m by n matrix with entries
A(i,j) = k*(si)*(tj - 1) if i <= j
= k*(tj)*(si - 1) if i > j
where si = i/(m+1) and tj = j/(n+1) and k = 1/(n+1).
*/
// Create an Epetra_Matrix
Teuchos::RCP<Epetra_CrsMatrix> A = Teuchos::rcp( new Epetra_CrsMatrix(Copy, RowMap, n) );
// Compute coefficients for discrete integral operator
std::vector<double> Values(n);
std::vector<int> Indices(n);
double inv_mp1 = one/(m+1);
double inv_np1 = one/(n+1);
for (i=0; i<n; i++) { Indices[i] = i; }
for (i=0; i<NumMyRowElements; i++) {
//
for (j=0; j<n; j++) {
//
if ( MyGlobalRowElements[i] <= j ) {
Values[j] = inv_np1 * ( (MyGlobalRowElements[i]+one)*inv_mp1 ) * ( (j+one)*inv_np1 - one ); // k*(si)*(tj-1)
}
else {
Values[j] = inv_np1 * ( (j+one)*inv_np1 ) * ( (MyGlobalRowElements[i]+one)*inv_mp1 - one ); // k*(tj)*(si-1)
}
}
info = A->InsertGlobalValues(MyGlobalRowElements[i], n, &Values[0], &Indices[0]);
assert( info==0 );
}
// Finish up
info = A->FillComplete(ColMap, RowMap);
assert( info==0 );
info = A->OptimizeStorage();
assert( info==0 );
A->SetTracebackMode(1); // Shutdown Epetra Warning tracebacks
//************************************
// Start the block Arnoldi iteration
//***********************************
//
// Variables used for the Block Arnoldi Method
//
int nev = 4;
int blockSize = 1;
int numBlocks = 10;
int maxRestarts = 20;
int verbosity = Anasazi::Errors + Anasazi::Warnings + Anasazi::FinalSummary;
double tol = lapack.LAMCH('E');
std::string which = "LM";
//
// Create parameter list to pass into solver
//
Teuchos::ParameterList MyPL;
MyPL.set( "Verbosity", verbosity );
MyPL.set( "Which", which );
MyPL.set( "Block Size", blockSize );
MyPL.set( "Num Blocks", numBlocks );
MyPL.set( "Maximum Restarts", maxRestarts );
MyPL.set( "Convergence Tolerance", tol );
typedef Anasazi::MultiVec<double> MV;
typedef Anasazi::Operator<double> OP;
// Create an Anasazi::EpetraMultiVec for an initial vector to start the solver.
// Note: This needs to have the same number of columns as the blocksize.
Teuchos::RCP<Anasazi::EpetraMultiVec> ivec = Teuchos::rcp( new Anasazi::EpetraMultiVec(ColMap, blockSize) );
ivec->MvRandom();
// Call the constructor for the (A^T*A) operator
Teuchos::RCP<Anasazi::EpetraSymOp> Amat = Teuchos::rcp( new Anasazi::EpetraSymOp(A) );
Teuchos::RCP<Anasazi::BasicEigenproblem<double, MV, OP> > MyProblem =
Teuchos::rcp( new Anasazi::BasicEigenproblem<double, MV, OP>(Amat, ivec) );
// Inform the eigenproblem that the matrix A is symmetric
MyProblem->setHermitian(true);
// Set the number of eigenvalues requested and the blocksize the solver should use
MyProblem->setNEV( nev );
// Inform the eigenproblem that you are finished passing it information
bool boolret = MyProblem->setProblem();
if (boolret != true) {
if (MyPID == 0) {
cout << "Anasazi::BasicEigenproblem::setProblem() returned with error." << endl;
}
#ifdef HAVE_MPI
MPI_Finalize() ;
#endif
return -1;
}
// Initialize the Block Arnoldi solver
Anasazi::BlockKrylovSchurSolMgr<double, MV, OP> MySolverMgr(MyProblem, MyPL);
// Solve the problem to the specified tolerances or length
Anasazi::ReturnType returnCode = MySolverMgr.solve();
if (returnCode != Anasazi::Converged && MyPID==0) {
cout << "Anasazi::EigensolverMgr::solve() returned unconverged." << endl;
}
// Get the eigenvalues and eigenvectors from the eigenproblem
Anasazi::Eigensolution<double,MV> sol = MyProblem->getSolution();
std::vector<Anasazi::Value<double> > evals = sol.Evals;
int numev = sol.numVecs;
if (numev > 0) {
// Compute singular values/vectors and direct residuals.
//
// Compute singular values which are the square root of the eigenvalues
if (MyPID==0) {
cout<<"------------------------------------------------------"<<endl;
cout<<"Computed Singular Values: "<<endl;
cout<<"------------------------------------------------------"<<endl;
}
for (i=0; i<numev; i++) { evals[i].realpart = Teuchos::ScalarTraits<double>::squareroot( evals[i].realpart ); }
//
// Compute left singular vectors : u = Av/sigma
//
std::vector<double> tempnrm(numev), directnrm(numev);
std::vector<int> index(numev);
for (i=0; i<numev; i++) { index[i] = i; }
Anasazi::EpetraMultiVec Av(RowMap,numev), u(RowMap,numev);
Anasazi::EpetraMultiVec* evecs = dynamic_cast<Anasazi::EpetraMultiVec* >(sol.Evecs->CloneViewNonConst( index ));
Teuchos::SerialDenseMatrix<int,double> S(numev,numev);
A->Apply( *evecs, Av );
Av.MvNorm( tempnrm );
for (i=0; i<numev; i++) { S(i,i) = one/tempnrm[i]; };
u.MvTimesMatAddMv( one, Av, S, zero );
//
// Compute direct residuals : || Av - sigma*u ||
//
for (i=0; i<numev; i++) { S(i,i) = evals[i].realpart; }
Av.MvTimesMatAddMv( -one, u, S, one );
Av.MvNorm( directnrm );
if (MyPID==0) {
cout.setf(std::ios_base::right, std::ios_base::adjustfield);
cout<<std::setw(16)<<"Singular Value"
<<std::setw(20)<<"Direct Residual"
<<endl;
cout<<"------------------------------------------------------"<<endl;
for (i=0; i<numev; i++) {
cout<<std::setw(16)<<evals[i].realpart
<<std::setw(20)<<directnrm[i]
<<endl;
}
cout<<"------------------------------------------------------"<<endl;
}
}
#ifdef EPETRA_MPI
MPI_Finalize() ;
#endif
return 0;
}
void DenseContainer<MatrixType, LocalScalarType>::
applyImpl (const local_mv_type& X,
local_mv_type& Y,
Teuchos::ETransp mode,
LocalScalarType alpha,
LocalScalarType beta) const
{
using Teuchos::ArrayRCP;
using Teuchos::RCP;
using Teuchos::rcp;
using Teuchos::rcpFromRef;
TEUCHOS_TEST_FOR_EXCEPTION(
X.getLocalLength () != Y.getLocalLength (),
std::logic_error, "Ifpack2::DenseContainer::applyImpl: X and Y have "
"incompatible dimensions (" << X.getLocalLength () << " resp. "
<< Y.getLocalLength () << "). Please report this bug to "
"the Ifpack2 developers.");
TEUCHOS_TEST_FOR_EXCEPTION(
localMap_->getNodeNumElements () != X.getLocalLength (),
std::logic_error, "Ifpack2::DenseContainer::applyImpl: The inverse "
"operator and X have incompatible dimensions (" <<
localMap_->getNodeNumElements () << " resp. "
<< X.getLocalLength () << "). Please report this bug to "
"the Ifpack2 developers.");
TEUCHOS_TEST_FOR_EXCEPTION(
localMap_->getNodeNumElements () != Y.getLocalLength (),
std::logic_error, "Ifpack2::DenseContainer::applyImpl: The inverse "
"operator and Y have incompatible dimensions (" <<
localMap_->getNodeNumElements () << " resp. "
<< Y.getLocalLength () << "). Please report this bug to "
"the Ifpack2 developers.");
TEUCHOS_TEST_FOR_EXCEPTION(
X.getLocalLength () != static_cast<size_t> (diagBlock_.numRows ()),
std::logic_error, "Ifpack2::DenseContainer::applyImpl: The input "
"multivector X has incompatible dimensions from those of the "
"inverse operator (" << X.getLocalLength () << " vs. "
<< (mode == Teuchos::NO_TRANS ? diagBlock_.numCols () : diagBlock_.numRows ())
<< "). Please report this bug to the Ifpack2 developers.");
TEUCHOS_TEST_FOR_EXCEPTION(
X.getLocalLength () != static_cast<size_t> (diagBlock_.numRows ()),
std::logic_error, "Ifpack2::DenseContainer::applyImpl: The output "
"multivector Y has incompatible dimensions from those of the "
"inverse operator (" << Y.getLocalLength () << " vs. "
<< (mode == Teuchos::NO_TRANS ? diagBlock_.numRows () : diagBlock_.numCols ())
<< "). Please report this bug to the Ifpack2 developers.");
typedef Teuchos::ScalarTraits<local_scalar_type> STS;
const int numVecs = static_cast<int> (X.getNumVectors ());
if (alpha == STS::zero ()) { // don't need to solve the linear system
if (beta == STS::zero ()) {
// Use BLAS AXPY semantics for beta == 0: overwrite, clobbering
// any Inf or NaN values in Y (rather than multiplying them by
// zero, resulting in NaN values).
Y.putScalar (STS::zero ());
}
else { // beta != 0
Y.scale (beta);
}
}
else { // alpha != 0; must solve the linear system
Teuchos::LAPACK<int, local_scalar_type> lapack;
// If beta is nonzero or Y is not constant stride, we have to use
// a temporary output multivector. It gets a (deep) copy of X,
// since GETRS overwrites its (multi)vector input with its output.
RCP<local_mv_type> Y_tmp;
if (beta == STS::zero () ) {
Tpetra::deep_copy (Y, X);
Y_tmp = rcpFromRef (Y);
}
else {
Y_tmp = rcp (new local_mv_type (X, Teuchos::Copy));
}
const int Y_stride = static_cast<int> (Y_tmp->getStride ());
ArrayRCP<local_scalar_type> Y_view = Y_tmp->get1dViewNonConst ();
local_scalar_type* const Y_ptr = Y_view.getRawPtr ();
int INFO = 0;
const char trans =
(mode == Teuchos::CONJ_TRANS ? 'C' : (mode == Teuchos::TRANS ? 'T' : 'N'));
lapack.GETRS (trans, diagBlock_.numRows (), numVecs,
diagBlock_.values (), diagBlock_.stride (),
ipiv_.getRawPtr (), Y_ptr, Y_stride, &INFO);
TEUCHOS_TEST_FOR_EXCEPTION(
INFO != 0, std::runtime_error, "Ifpack2::DenseContainer::applyImpl: "
"LAPACK's _GETRS (solve using LU factorization with partial pivoting) "
"failed with INFO = " << INFO << " != 0.");
if (beta != STS::zero ()) {
Y.update (alpha, *Y_tmp, beta);
}
else if (! Y.isConstantStride ()) {
Tpetra::deep_copy (Y, *Y_tmp);
}
}
}
// Solves turning point equations via Phipps modified bordering
// The first m columns of input_x and input_null store the RHS while
// the last column stores df/dp, d(Jn)/dp respectively. Note however
// input_param has only m columns (not m+1). result_x, result_null,
// are result_param have the same dimensions as their input counterparts
NOX::Abstract::Group::ReturnType
LOCA::TurningPoint::MooreSpence::PhippsBordering::solveContiguous(
Teuchos::ParameterList& params,
const NOX::Abstract::MultiVector& input_x,
const NOX::Abstract::MultiVector& input_null,
const NOX::Abstract::MultiVector::DenseMatrix& input_param,
NOX::Abstract::MultiVector& result_x,
NOX::Abstract::MultiVector& result_null,
NOX::Abstract::MultiVector::DenseMatrix& result_param) const
{
std::string callingFunction =
"LOCA::TurningPoint::MooreSpence::PhippsBordering::solveContiguous()";
NOX::Abstract::Group::ReturnType finalStatus = NOX::Abstract::Group::Ok;
NOX::Abstract::Group::ReturnType status;
int m = input_x.numVectors()-2;
std::vector<int> index_input(m);
std::vector<int> index_input_dp(m+1);
std::vector<int> index_null(1);
std::vector<int> index_dp(1);
for (int i=0; i<m; i++) {
index_input[i] = i;
index_input_dp[i] = i;
}
index_input_dp[m] = m;
index_dp[0] = m;
index_null[0] = m+1;
NOX::Abstract::MultiVector::DenseMatrix tmp_mat_1(1, m+1);
NOX::Abstract::MultiVector::DenseMatrix tmp_mat_2(1, m+2);
// Create view of first m+1 columns of input_x, result_x
Teuchos::RCP<NOX::Abstract::MultiVector> input_x_view =
input_x.subView(index_input_dp);
Teuchos::RCP<NOX::Abstract::MultiVector> result_x_view =
result_x.subView(index_input_dp);
// verify underlying Jacobian is valid
if (!group->isJacobian()) {
status = group->computeJacobian();
finalStatus =
globalData->locaErrorCheck->combineAndCheckReturnTypes(status,
finalStatus,
callingFunction);
}
// Solve |J u||A B| = |F df/dp|
// |v^T 0||a b| |0 0 |
status = borderedSolver->applyInverse(params, input_x_view.get(), NULL,
*result_x_view, tmp_mat_1);
finalStatus =
globalData->locaErrorCheck->combineAndCheckReturnTypes(status, finalStatus,
callingFunction);
Teuchos::RCP<NOX::Abstract::MultiVector> A =
result_x.subView(index_input);
Teuchos::RCP<NOX::Abstract::MultiVector> B =
result_x.subView(index_dp);
double b = tmp_mat_1(0,m);
// compute (Jv)_x[A B v]
result_x[m+1] = *nullVector;
Teuchos::RCP<NOX::Abstract::MultiVector> tmp =
result_x.clone(NOX::ShapeCopy);
status = group->computeDJnDxaMulti(*nullVector, *JnVector, result_x,
*tmp);
finalStatus =
globalData->locaErrorCheck->combineAndCheckReturnTypes(status, finalStatus,
callingFunction);
// compute (Jv)_x[A B v] - [G d(Jn)/dp 0]
tmp->update(-1.0, input_null, 1.0);
// verify underlying Jacobian is valid
if (!group->isJacobian()) {
status = group->computeJacobian();
finalStatus =
globalData->locaErrorCheck->combineAndCheckReturnTypes(status,
finalStatus,
callingFunction);
}
// Solve |J u||C D E| = |(Jv)_x A - G (Jv)_x B - d(Jv)/dp (Jv)_x v|
// |v^T 0||c d e| | 0 0 0 |
status = borderedSolver->applyInverse(params, tmp.get(), NULL, result_null,
tmp_mat_2);
finalStatus =
globalData->locaErrorCheck->combineAndCheckReturnTypes(status, finalStatus,
callingFunction);
Teuchos::RCP<NOX::Abstract::MultiVector> C =
result_null.subView(index_input);
Teuchos::RCP<NOX::Abstract::MultiVector> D =
result_null.subView(index_dp);
Teuchos::RCP<NOX::Abstract::MultiVector> E =
result_null.subView(index_null);
double d = tmp_mat_2(0, m);
double e = tmp_mat_2(0, m+1);
// Fill coefficient arrays
double M[9];
M[0] = s; M[1] = e; M[2] = -tpGroup->lTransNorm((*E)[0]);
M[3] = 0.0; M[4] = s; M[5] = tpGroup->lTransNorm(*nullVector);
M[6] = b; M[7] = -d; M[8] = tpGroup->lTransNorm((*D)[0]);
// compute h + phi^T C
tpGroup->lTransNorm(*C, result_param);
result_param += input_param;
double *R = new double[3*m];
for (int i=0; i<m; i++) {
R[3*i] = tmp_mat_1(0,i);
R[3*i+1] = -tmp_mat_2(0,i);
R[3*i+2] = result_param(0,i);
}
// Solve M*P = R
int three = 3;
int piv[3];
int info;
Teuchos::LAPACK<int,double> L;
L.GESV(three, m, M, three, piv, R, three, &info);
if (info != 0) {
globalData->locaErrorCheck->throwError(
callingFunction,
"Solve of 3x3 coefficient matrix failed!");
return NOX::Abstract::Group::Failed;
}
NOX::Abstract::MultiVector::DenseMatrix alpha(1,m);
NOX::Abstract::MultiVector::DenseMatrix beta(1,m);
for (int i=0; i<m; i++) {
alpha(0,i) = R[3*i];
beta(0,i) = R[3*i+1];
result_param(0,i) = R[3*i+2];
}
// compute A = A - B*z + v*alpha (remember A is a sub-view of result_x)
A->update(Teuchos::NO_TRANS, -1.0, *B, result_param, 1.0);
A->update(Teuchos::NO_TRANS, 1.0, *nullMultiVector, alpha, 1.0);
// compute C = -C + d*z - E*alpha + v*beta
// (remember C is a sub-view of result_null)
C->update(Teuchos::NO_TRANS, 1.0, *D, result_param, -1.0);
C->update(Teuchos::NO_TRANS, -1.0, *E, alpha, 1.0);
C->update(Teuchos::NO_TRANS, 1.0, *nullMultiVector, beta, 1.0);
delete [] R;
return finalStatus;
}
Basis_HGRAD_LINE_Cn_FEM<SpT,OT,PT>::
Basis_HGRAD_LINE_Cn_FEM( const ordinal_type order,
const EPointType pointType ) {
this->basisCardinality_ = order+1;
this->basisDegree_ = order;
this->basisCellTopology_ = shards::CellTopology(shards::getCellTopologyData<shards::Line<2> >() );
this->basisType_ = BASIS_FEM_FIAT;
this->basisCoordinates_ = COORDINATES_CARTESIAN;
const ordinal_type card = this->basisCardinality_;
// points are computed in the host and will be copied
Kokkos::DynRankView<typename scalarViewType::value_type,typename SpT::array_layout,Kokkos::HostSpace>
dofCoords("Hgrad::Line::Cn::dofCoords", card, 1);
switch (pointType) {
case POINTTYPE_EQUISPACED:
case POINTTYPE_WARPBLEND: {
// lattice ordering
{
const ordinal_type offset = 0;
PointTools::getLattice( dofCoords,
this->basisCellTopology_,
order, offset,
pointType );
}
// topological order
// {
// // two vertices
// dofCoords(0,0) = -1.0;
// dofCoords(1,0) = 1.0;
// // internal points
// typedef Kokkos::pair<ordinal_type,ordinal_type> range_type;
// auto pts = Kokkos::subview(dofCoords, range_type(2, card), Kokkos::ALL());
// const auto offset = 1;
// PointTools::getLattice( pts,
// this->basisCellTopology_,
// order, offset,
// pointType );
// }
break;
}
case POINTTYPE_GAUSS: {
// internal points only
PointTools::getGaussPoints( dofCoords,
order );
break;
}
default: {
INTREPID2_TEST_FOR_EXCEPTION( !isValidPointType(pointType),
std::invalid_argument ,
">>> ERROR: (Intrepid2::Basis_HGRAD_LINE_Cn_FEM) invalid pointType." );
}
}
this->dofCoords_ = Kokkos::create_mirror_view(typename SpT::memory_space(), dofCoords);
Kokkos::deep_copy(this->dofCoords_, dofCoords);
// form Vandermonde matrix; actually, this is the transpose of the VDM,
// this matrix is used in LAPACK so it should be column major and left layout
const ordinal_type lwork = card*card;
Kokkos::DynRankView<typename scalarViewType::value_type,Kokkos::LayoutLeft,Kokkos::HostSpace>
vmat("Hgrad::Line::Cn::vmat", card, card),
work("Hgrad::Line::Cn::work", lwork),
ipiv("Hgrad::Line::Cn::ipiv", card);
const double alpha = 0.0, beta = 0.0;
Impl::Basis_HGRAD_LINE_Cn_FEM_JACOBI::
getValues<Kokkos::HostSpace::execution_space,Parameters::MaxNumPtsPerBasisEval>
(vmat, dofCoords, order, alpha, beta, OPERATOR_VALUE);
ordinal_type info = 0;
Teuchos::LAPACK<ordinal_type,typename scalarViewType::value_type> lapack;
lapack.GETRF(card, card,
vmat.data(), vmat.stride_1(),
(ordinal_type*)ipiv.data(),
&info);
INTREPID2_TEST_FOR_EXCEPTION( info != 0,
std::runtime_error ,
">>> ERROR: (Intrepid2::Basis_HGRAD_LINE_Cn_FEM) lapack.GETRF returns nonzero info." );
lapack.GETRI(card,
vmat.data(), vmat.stride_1(),
(ordinal_type*)ipiv.data(),
work.data(), lwork,
&info);
INTREPID2_TEST_FOR_EXCEPTION( info != 0,
std::runtime_error ,
">>> ERROR: (Intrepid2::Basis_HGRAD_LINE_Cn_FEM) lapack.GETRI returns nonzero info." );
// create host mirror
Kokkos::DynRankView<typename scalarViewType::value_type,typename SpT::array_layout,Kokkos::HostSpace>
vinv("Hgrad::Line::Cn::vinv", card, card);
for (ordinal_type i=0;i<card;++i)
for (ordinal_type j=0;j<card;++j)
vinv(i,j) = vmat(j,i);
this->vinv_ = Kokkos::create_mirror_view(typename SpT::memory_space(), vinv);
Kokkos::deep_copy(this->vinv_ , vinv);
// initialize tags
{
const bool is_vertex_included = (pointType != POINTTYPE_GAUSS);
// Basis-dependent initializations
const ordinal_type tagSize = 4; // size of DoF tag, i.e., number of fields in the tag
const ordinal_type posScDim = 0; // position in the tag, counting from 0, of the subcell dim
const ordinal_type posScOrd = 1; // position in the tag, counting from 0, of the subcell ordinal
const ordinal_type posDfOrd = 2; // position in the tag, counting from 0, of DoF ordinal relative to the subcell
ordinal_type tags[Parameters::MaxOrder+1][4];
// now we check the points for association
if (is_vertex_included) {
// lattice order
{
const auto v0 = 0;
tags[v0][0] = 0; // vertex dof
tags[v0][1] = 0; // vertex id
tags[v0][2] = 0; // local dof id
tags[v0][3] = 1; // total number of dofs in this vertex
const ordinal_type iend = card - 2;
for (ordinal_type i=0;i<iend;++i) {
const auto e = i + 1;
tags[e][0] = 1; // edge dof
tags[e][1] = 0; // edge id
tags[e][2] = i; // local dof id
tags[e][3] = iend; // total number of dofs in this edge
}
const auto v1 = card -1;
tags[v1][0] = 0; // vertex dof
tags[v1][1] = 1; // vertex id
tags[v1][2] = 0; // local dof id
tags[v1][3] = 1; // total number of dofs in this vertex
}
// topological order
// {
// tags[0][0] = 0; // vertex dof
// tags[0][1] = 0; // vertex id
// tags[0][2] = 0; // local dof id
// tags[0][3] = 1; // total number of dofs in this vertex
// tags[1][0] = 0; // vertex dof
// tags[1][1] = 1; // vertex id
// tags[1][2] = 0; // local dof id
// tags[1][3] = 1; // total number of dofs in this vertex
// const ordinal_type iend = card - 2;
// for (ordinal_type i=0;i<iend;++i) {
// const auto ii = i + 2;
// tags[ii][0] = 1; // edge dof
// tags[ii][1] = 0; // edge id
// tags[ii][2] = i; // local dof id
// tags[ii][3] = iend; // total number of dofs in this edge
// }
// }
} else {
for (ordinal_type i=0;i<card;++i) {
tags[i][0] = 1; // edge dof
tags[i][1] = 0; // edge id
tags[i][2] = i; // local dof id
tags[i][3] = card; // total number of dofs in this edge
}
}
ordinal_type_array_1d_host tagView(&tags[0][0], card*4);
// Basis-independent function sets tag and enum data in tagToOrdinal_ and ordinalToTag_ arrays:
// tags are constructed on host
this->setOrdinalTagData(this->tagToOrdinal_,
this->ordinalToTag_,
tagView,
this->basisCardinality_,
tagSize,
posScDim,
posScOrd,
posDfOrd);
}
}
// Solves turning point equations via classic Salinger bordering
// The first m columns of input_x and input_null store the RHS while
// the last column stores df/dp, d(Jn)/dp respectively. Note however
// input_param has only m columns (not m+1). result_x, result_null,
// are result_param have the same dimensions as their input counterparts
NOX::Abstract::Group::ReturnType
LOCA::TurningPoint::MooreSpence::PhippsBordering::solveTransposeContiguous(
Teuchos::ParameterList& params,
const NOX::Abstract::MultiVector& input_x,
const NOX::Abstract::MultiVector& input_null,
const NOX::Abstract::MultiVector::DenseMatrix& input_param,
NOX::Abstract::MultiVector& result_x,
NOX::Abstract::MultiVector& result_null,
NOX::Abstract::MultiVector::DenseMatrix& result_param) const
{
std::string callingFunction =
"LOCA::TurningPoint::MooreSpence::PhippsBordering::solveTransposeContiguous()";
NOX::Abstract::Group::ReturnType finalStatus = NOX::Abstract::Group::Ok;
NOX::Abstract::Group::ReturnType status;
int m = input_x.numVectors()-2;
std::vector<int> index_input(m);
std::vector<int> index_input_dp(m+1);
std::vector<int> index_null(1);
std::vector<int> index_dp(1);
for (int i=0; i<m; i++) {
index_input[i] = i;
index_input_dp[i] = i;
}
index_input_dp[m] = m;
index_dp[0] = m;
index_null[0] = m+1;
NOX::Abstract::MultiVector::DenseMatrix tmp_mat_1(1, m+1);
NOX::Abstract::MultiVector::DenseMatrix tmp_mat_2(1, m+2);
// Create view of first m+1 columns of input_null, result_null
Teuchos::RCP<NOX::Abstract::MultiVector> input_null_view =
input_null.subView(index_input_dp);
Teuchos::RCP<NOX::Abstract::MultiVector> result_null_view =
result_null.subView(index_input_dp);
// verify underlying Jacobian is valid
if (!group->isJacobian()) {
status = group->computeJacobian();
finalStatus =
globalData->locaErrorCheck->combineAndCheckReturnTypes(status,
finalStatus,
callingFunction);
}
// Solve |J^T v||A B| = |G -phi|
// |u^T 0||a b| |0 0 |
status =
transposeBorderedSolver->applyInverseTranspose(params,
input_null_view.get(),
NULL,
*result_null_view,
tmp_mat_1);
finalStatus =
globalData->locaErrorCheck->combineAndCheckReturnTypes(status, finalStatus,
callingFunction);
Teuchos::RCP<NOX::Abstract::MultiVector> A =
result_null.subView(index_input);
Teuchos::RCP<NOX::Abstract::MultiVector> B =
result_null.subView(index_dp);
double b = tmp_mat_1(0,m);
// compute (Jv)_x^T[A B u]
result_null[m+1] = *uVector;
Teuchos::RCP<NOX::Abstract::MultiVector> tmp =
result_null.clone(NOX::ShapeCopy);
status = group->computeDwtJnDxMulti(result_null, *nullVector, *tmp);
finalStatus =
globalData->locaErrorCheck->combineAndCheckReturnTypes(status,
finalStatus,
callingFunction);
// compute [F 0 0] - (Jv)_x^T[A B u]
tmp->update(1.0, input_x, -1.0);
// verify underlying Jacobian is valid
if (!group->isJacobian()) {
status = group->computeJacobian();
finalStatus =
globalData->locaErrorCheck->combineAndCheckReturnTypes(status,
finalStatus,
callingFunction);
}
// Solve |J^T v||C D E| = |F - (Jv)_x^T A -(Jv)_x^T B -(Jv)_x^T u|
// |u^T 0||c d e| | 0 0 0 |
status =
transposeBorderedSolver->applyInverseTranspose(params,
tmp.get(),
NULL,
result_x,
tmp_mat_2);
finalStatus =
globalData->locaErrorCheck->combineAndCheckReturnTypes(status, finalStatus,
callingFunction);
Teuchos::RCP<NOX::Abstract::MultiVector> C =
result_x.subView(index_input);
Teuchos::RCP<NOX::Abstract::MultiVector> D =
result_x.subView(index_dp);
Teuchos::RCP<NOX::Abstract::MultiVector> E =
result_x.subView(index_null);
double d = tmp_mat_2(0, m);
double e = tmp_mat_2(0, m+1);
// compute (Jv)_p^T*[A B u]
NOX::Abstract::MultiVector::DenseMatrix t1(1,m+2);
result_null.multiply(1.0, *dJndp, t1);
// compute f_p^T*[C D E]
NOX::Abstract::MultiVector::DenseMatrix t2(1,m+2);
result_x.multiply(1.0, *dfdp, t2);
// compute f_p^T*u
double fptu = uVector->innerProduct((*dfdp)[0]);
// Fill coefficient arrays
double M[9];
M[0] = st; M[1] = -e; M[2] = t1(0,m+1) + t2(0,m+1);
M[3] = 0.0; M[4] = st; M[5] = fptu;
M[6] = -b; M[7] = -d; M[8] = t1(0,m) + t2(0,m);
// Compute RHS
double *R = new double[3*m];
for (int i=0; i<m; i++) {
R[3*i] = tmp_mat_1(0,i);
R[3*i+1] = tmp_mat_2(0,i);
R[3*i+2] = result_param(0,i) - t1(0,i) - t2(0,i);
}
// Solve M*P = R
int three = 3;
int piv[3];
int info;
Teuchos::LAPACK<int,double> L;
L.GESV(three, m, M, three, piv, R, three, &info);
if (info != 0) {
globalData->locaErrorCheck->throwError(
callingFunction,
"Solve of 3x3 coefficient matrix failed!");
return NOX::Abstract::Group::Failed;
}
NOX::Abstract::MultiVector::DenseMatrix alpha(1,m);
NOX::Abstract::MultiVector::DenseMatrix beta(1,m);
for (int i=0; i<m; i++) {
alpha(0,i) = R[3*i];
beta(0,i) = R[3*i+1];
result_param(0,i) = R[3*i+2];
}
// compute A = A + B*z + alpha*u (remember A is a sub-view of result_null)
A->update(Teuchos::NO_TRANS, 1.0, *B, result_param, 1.0);
A->update(Teuchos::NO_TRANS, 1.0, *uMultiVector, alpha, 1.0);
// compute C = C + D*z + alpha*E + beta*u
// (remember C is a sub-view of result_x)
C->update(Teuchos::NO_TRANS, 1.0, *D, result_param, 1.0);
C->update(Teuchos::NO_TRANS, 1.0, *E, alpha, 1.0);
C->update(Teuchos::NO_TRANS, 1.0, *uMultiVector, beta, 1.0);
delete [] R;
return finalStatus;
}
NOX::Abstract::Group::ReturnType
LOCA::BorderedSolver::LowerTriangularBlockElimination::
solve(Teuchos::ParameterList& params,
const LOCA::BorderedSolver::AbstractOperator& op,
const LOCA::MultiContinuation::ConstraintInterface& B,
const NOX::Abstract::MultiVector::DenseMatrix& C,
const NOX::Abstract::MultiVector* F,
const NOX::Abstract::MultiVector::DenseMatrix* G,
NOX::Abstract::MultiVector& X,
NOX::Abstract::MultiVector::DenseMatrix& Y) const
{
string callingFunction =
"LOCA::BorderedSolver::LowerTriangularBlockElimination::solve()";
NOX::Abstract::Group::ReturnType finalStatus = NOX::Abstract::Group::Ok;
NOX::Abstract::Group::ReturnType status;
// Determine if X or Y is zero
bool isZeroF = (F == NULL);
bool isZeroG = (G == NULL);
bool isZeroB = B.isDXZero();
bool isZeroX = isZeroF;
bool isZeroY = isZeroG && (isZeroB || isZeroX);
// First compute X
if (isZeroX)
X.init(0.0);
else {
// Solve X = J^-1 F, note F must be nonzero
status = op.applyInverse(params, *F, X);
finalStatus =
globalData->locaErrorCheck->combineAndCheckReturnTypes(status,
finalStatus,
callingFunction);
}
// Now compute Y
if (isZeroY)
Y.putScalar(0.0);
else {
// Compute G - B^T*X and store in Y
if (isZeroG)
B.multiplyDX(-1.0, X, Y);
else {
Y.assign(*G);
if (!isZeroB && !isZeroX) {
NOX::Abstract::MultiVector::DenseMatrix T(Y.numRows(),Y.numCols());
B.multiplyDX(1.0, X, T);
Y -= T;
}
}
// Overwrite Y with Y = C^-1 * (G - B^T*X)
NOX::Abstract::MultiVector::DenseMatrix M(C);
int *ipiv = new int[M.numRows()];
Teuchos::LAPACK<int,double> L;
int info;
L.GETRF(M.numRows(), M.numCols(), M.values(), M.stride(), ipiv, &info);
if (info != 0) {
status = NOX::Abstract::Group::Failed;
finalStatus =
globalData->locaErrorCheck->combineAndCheckReturnTypes(
status,
finalStatus,
callingFunction);
}
L.GETRS('N', M.numRows(), Y.numCols(), M.values(), M.stride(), ipiv,
Y.values(), Y.stride(), &info);
delete [] ipiv;
if (info != 0) {
status = NOX::Abstract::Group::Failed;
finalStatus =
globalData->locaErrorCheck->combineAndCheckReturnTypes(
status,
finalStatus,
callingFunction);
}
}
return finalStatus;
}
// ----------------------------------------------------------------------
// Main
//
//
int main(int argc, char *argv[]) {
Teuchos::GlobalMPISession mpiSession(&argc, &argv);
Kokkos::initialize();
// This little trick lets us print to std::cout only if a (dummy) command-line argument is provided.
int iprint = argc - 1;
for (int i=0;i<argc;++i) {
if ((strcmp(argv[i],"--nelement") == 0)) { nelement = atoi(argv[++i]); continue;}
if ((strcmp(argv[i],"--apply-orientation") == 0)) { apply_orientation = atoi(argv[++i]); continue;}
if ((strcmp(argv[i],"--verbose") == 0)) { verbose = atoi(argv[++i]); continue;}
if ((strcmp(argv[i],"--maxp") == 0)) { maxp = atoi(argv[++i]); continue;}
}
Teuchos::RCP<std::ostream> outStream;
Teuchos::oblackholestream bhs; // outputs nothing
if (iprint > 0)
outStream = Teuchos::rcp(&std::cout, false);
else
outStream = Teuchos::rcp(&bhs, false);
// Save the format state of the original std::cout.
Teuchos::oblackholestream oldFormatState;
oldFormatState.copyfmt(std::cout);
*outStream << std::scientific;
*outStream \
<< "===============================================================================\n" \
<< "| |\n" \
<< "| Unit Test (Basis_HGRAD_TRI_Cn_FEM) |\n" \
<< "| |\n" \
<< "| 1) Patch test involving mass and stiffness matrices, |\n" \
<< "| for the Neumann problem on a triangular patch |\n" \
<< "| Omega with boundary Gamma. |\n" \
<< "| |\n" \
<< "| - div (grad u) + u = f in Omega, (grad u) . n = g on Gamma |\n" \
<< "| |\n" \
<< "| Questions? Contact Pavel Bochev ([email protected]), |\n" \
<< "| Denis Ridzal ([email protected]), |\n" \
<< "| Kara Peterson ([email protected]). |\n" \
<< "| Kyungjoo Kim ([email protected]). |\n" \
<< "| |\n" \
<< "| Intrepid's website: http://trilinos.sandia.gov/packages/intrepid |\n" \
<< "| Trilinos website: http://trilinos.sandia.gov |\n" \
<< "| |\n" \
<< "===============================================================================\n" \
<< "| TEST 4: Patch test for high order assembly |\n" \
<< "===============================================================================\n";
int r_val = 0;
// precision control
outStream->precision(3);
#if defined( INTREPID_USING_EXPERIMENTAL_HIGH_ORDER )
try {
// test setup
const int ndim = 2;
FieldContainer<value_type> base_nodes(1, 4, ndim);
base_nodes(0, 0, 0) = 0.0;
base_nodes(0, 0, 1) = 0.0;
base_nodes(0, 1, 0) = 1.0;
base_nodes(0, 1, 1) = 0.0;
base_nodes(0, 2, 0) = 0.0;
base_nodes(0, 2, 1) = 1.0;
base_nodes(0, 3, 0) = 1.0;
base_nodes(0, 3, 1) = 1.0;
// element 0 has globally permuted edge node
const int elt_0[2][3] = { { 0, 1, 2 },
{ 0, 2, 1 } };
// element 1 is locally permuted
int elt_1[3] = { 1, 2, 3 };
DefaultCubatureFactory<value_type> cubature_factory;
// for all test orders
for (int nx=0;nx<=maxp;++nx) {
for (int ny=0;ny<=maxp-nx;++ny) {
// polynomial order of approximation
const int minp = std::max(nx+ny, 1);
// test for all basis above order p
const EPointType pointtype[] = { POINTTYPE_EQUISPACED, POINTTYPE_WARPBLEND };
for (int ptype=0;ptype<2;++ptype) {
for (int p=minp;p<=maxp;++p) {
*outStream << "\n" \
<< "===============================================================================\n" \
<< " Order (nx,ny,p) = " << nx << ", " << ny << ", " << p << " , PointType = " << EPointTypeToString(pointtype[ptype]) << "\n" \
<< "===============================================================================\n";
BasisSet_HGRAD_TRI_Cn_FEM<value_type,FieldContainer<value_type> > basis_set(p, pointtype[ptype]);
const auto& basis = basis_set.getCellBasis();
const shards::CellTopology cell = basis.getBaseCellTopology();
const int nbf = basis.getCardinality();
const int nvert = cell.getVertexCount();
const int nedge = cell.getEdgeCount();
FieldContainer<value_type> nodes(1, 4, ndim);
FieldContainer<value_type> cell_nodes(1, nvert, ndim);
// ignore the subdimension; the matrix is always considered as 1D array
FieldContainer<value_type> A(1, nbf, nbf), b(1, nbf);
// ***** Test for different orientations *****
for (int conf0=0;conf0<2;++conf0) {
for (int ino=0;ino<3;++ino) {
nodes(0, elt_0[conf0][ino], 0) = base_nodes(0, ino, 0);
nodes(0, elt_0[conf0][ino], 1) = base_nodes(0, ino, 1);
}
nodes(0, 3, 0) = base_nodes(0, 3, 0);
nodes(0, 3, 1) = base_nodes(0, 3, 1);
// reset element connectivity
elt_1[0] = 1;
elt_1[1] = 2;
elt_1[2] = 3;
// for all permuations of element 1
for (int conf1=0;conf1<6;++conf1) {
// filter out left handed element
fill_cell_nodes(cell_nodes,
nodes,
elt_1,
nvert, ndim);
if (OrientationTools<value_type>::isLeftHandedCell(cell_nodes)) {
// skip left handed
} else {
const int *element[2] = { elt_0[conf0], elt_1 };
*outStream << "\n" \
<< " Element 0 is configured " << conf0 << " "
<< "(" << element[0][0] << ","<< element[0][1] << "," << element[0][2] << ")"
<< " Element 1 is configured " << conf1 << " "
<< "(" << element[1][0] << ","<< element[1][1] << "," << element[1][2] << ")"
<< "\n";
if (verbose) {
*outStream << " - Element nodal connectivity - \n";
for (int iel=0;iel<nelement;++iel)
*outStream << " iel = " << std::setw(4) << iel
<< ", nodes = "
<< std::setw(4) << element[iel][0]
<< std::setw(4) << element[iel][1]
<< std::setw(4) << element[iel][2]
<< "\n";
}
// Step 0: count one-to-one mapping between high order nodes and dofs
Example::ToyMesh mesh;
int local2global[2][8][2], boundary[2][3], off_global = 0;
const int nnodes_per_element
= cell.getVertexCount()
+ cell.getEdgeCount()
+ 1;
for (int iel=0;iel<nelement;++iel)
mesh.getLocalToGlobalMap(local2global[iel], off_global, basis, element[iel]);
for (int iel=0;iel<nelement;++iel)
mesh.getBoundaryFlags(boundary[iel], cell, element[iel]);
if (verbose) {
*outStream << " - Element one-to-one local2global map -\n";
for (int iel=0;iel<nelement;++iel) {
*outStream << " iel = " << std::setw(4) << iel << "\n";
for (int i=0;i<(nnodes_per_element+1);++i) {
*outStream << " local = " << std::setw(4) << local2global[iel][i][0]
<< " global = " << std::setw(4) << local2global[iel][i][1]
<< "\n";
}
}
*outStream << " - Element boundary flags -\n";
const int nside = cell.getSideCount();
for (int iel=0;iel<nelement;++iel) {
*outStream << " iel = " << std::setw(4) << iel << "\n";
for (int i=0;i<nside;++i) {
*outStream << " side = " << std::setw(4) << i
<< " boundary = " << std::setw(4) << boundary[iel][i]
<< "\n";
}
}
}
// Step 1: assembly
const int ndofs = off_global;
FieldContainer<value_type> A_asm(1, ndofs, ndofs), b_asm(1, ndofs);
for (int iel=0;iel<nelement;++iel) {
// Step 1.1: create element matrices
Orientation ort = Orientation::getOrientation(cell, element[iel]);
// set element nodal coordinates
fill_cell_nodes(cell_nodes,
nodes,
element[iel],
nvert, ndim);
build_element_matrix_and_rhs(A, b,
cubature_factory,
basis_set,
element[iel],
boundary[iel],
cell_nodes,
ort,
nx, ny);
// if p is bigger than 4, not worth to look at the matrix
if (verbose && p < 5) {
*outStream << " - Element matrix and rhs, iel = " << iel << "\n";
*outStream << std::showpos;
for (int i=0;i<nbf;++i) {
for (int j=0;j<nbf;++j)
*outStream << MatVal(A, i, j) << " ";
*outStream << ":: " << MatVal(b, i, 0) << "\n";
}
*outStream << std::noshowpos;
}
// Step 1.2: assemble high order elements
assemble_element_matrix_and_rhs(A_asm, b_asm,
A, b,
local2global[iel],
nnodes_per_element);
}
if (verbose && p < 5) {
*outStream << " - Assembled element matrix and rhs -\n";
*outStream << std::showpos;
for (int i=0;i<ndofs;++i) {
for (int j=0;j<ndofs;++j)
*outStream << MatVal(A_asm, i, j) << " ";
*outStream << ":: " << MatVal(b_asm, i, 0) << "\n";
}
*outStream << std::noshowpos;
}
// Step 2: solve the system of equations
int info = 0;
Teuchos::LAPACK<int,value_type> lapack;
FieldContainer<int> ipiv(ndofs);
lapack.GESV(ndofs, 1, &A_asm(0,0,0), ndofs, &ipiv(0,0), &b_asm(0,0), ndofs, &info);
TEUCHOS_TEST_FOR_EXCEPTION( info != 0, std::runtime_error,
">>> ERROR (Intrepid::HGRAD_TRI_Cn::Test 04): " \
"LAPACK solve fails");
// Step 3: construct interpolant and check solutions
magnitude_type interpolation_error = 0, solution_norm =0;
for (int iel=0;iel<nelement;++iel) {
retrieve_element_solution(b,
b_asm,
local2global[iel],
nnodes_per_element);
if (verbose && p < 5) {
*outStream << " - Element solution, iel = " << iel << "\n";
*outStream << std::showpos;
for (int i=0;i<nbf;++i) {
*outStream << MatVal(b, i, 0) << "\n";
}
*outStream << std::noshowpos;
}
magnitude_type
element_interpolation_error = 0,
element_solution_norm = 0;
Orientation ort = Orientation::getOrientation(cell, element[iel]);
// set element nodal coordinates
fill_cell_nodes(cell_nodes,
nodes,
element[iel],
nvert, ndim);
compute_element_error(element_interpolation_error,
element_solution_norm,
element[iel],
cell_nodes,
basis_set,
b,
ort,
nx, ny);
interpolation_error += element_interpolation_error;
solution_norm += element_solution_norm;
{
int edge_orts[3];
ort.getEdgeOrientation(edge_orts, nedge);
*outStream << " iel = " << std::setw(4) << iel
<< ", orientation = "
<< edge_orts[0]
<< edge_orts[1]
<< edge_orts[2]
<< " , error = " << element_interpolation_error
<< " , solution norm = " << element_solution_norm
<< " , relative error = " << (element_interpolation_error/element_solution_norm)
<< "\n";
}
const magnitude_type relative_error = interpolation_error/solution_norm;
const magnitude_type tol = p*p*100*INTREPID_TOL;
if (relative_error > tol) {
++r_val;
*outStream << "\n\nPatch test failed: \n"
<< " exact polynomial (nx, ny) = " << std::setw(4) << nx << ", " << std::setw(4) << ny << "\n"
<< " basis order = " << std::setw(4) << p << "\n"
<< " orientation configuration = " << std::setw(4) << conf0 << std::setw(4) << conf1 << "\n"
<< " relative error = " << std::setw(4) << relative_error << "\n"
<< " tolerance = " << std::setw(4) << tol << "\n";
}
}
}
// for next iteration
std::next_permutation(elt_1, elt_1+3);
} // end of conf1
} // end of conf0
} // end of p
} // end of point type
} // end of ny
} // end of nx
}
catch (std::logic_error err) {
*outStream << err.what() << "\n\n";
r_val = -1000;
};
#else
*outStream << "\t This test is for high order element assembly. \n"
<< "\t Use -D INTREPID_USING_EXPERIMENTAL_HIGH_ORDER in CMAKE_CXX_FLAGS \n";
#endif
if (r_val != 0)
std::cout << "End Result: TEST FAILED :: r_val = " << r_val << "\n";
else
std::cout << "End Result: TEST PASSED\n";
// reset format state of std::cout
std::cout.copyfmt(oldFormatState);
Kokkos::finalize();
return r_val;
}
int main(int argc, char *argv[]) {
Teuchos::GlobalMPISession mpiSession(&argc, &argv);
Kokkos::initialize();
// This little trick lets us print to std::cout only if
// a (dummy) command-line argument is provided.
int iprint = argc - 1;
Teuchos::RCP<std::ostream> outStream;
Teuchos::oblackholestream bhs; // outputs nothing
if (iprint > 0)
outStream = Teuchos::rcp(&std::cout, false);
else
outStream = Teuchos::rcp(&bhs, false);
// Save the format state of the original std::cout.
Teuchos::oblackholestream oldFormatState;
oldFormatState.copyfmt(std::cout);
*outStream \
<< "===============================================================================\n" \
<< "| |\n" \
<< "| Unit Test (Basis_HGRAD_LINE_C1_FEM) |\n" \
<< "| |\n" \
<< "| 1) Patch test involving mass and stiffness matrices, |\n" \
<< "| for the Neumann problem on a REFERENCE line: |\n" \
<< "| |\n" \
<< "| - u'' + u = f in (-1,1), u' = g at -1,1 |\n" \
<< "| |\n" \
<< "| Questions? Contact Pavel Bochev ([email protected]), |\n" \
<< "| Denis Ridzal ([email protected]), |\n" \
<< "| Kara Peterson ([email protected]). |\n" \
<< "| |\n" \
<< "| Intrepid's website: http://trilinos.sandia.gov/packages/intrepid |\n" \
<< "| Trilinos website: http://trilinos.sandia.gov |\n" \
<< "| |\n" \
<< "===============================================================================\n"\
<< "| TEST 1: Patch test |\n"\
<< "===============================================================================\n";
int errorFlag = 0;
double zero = 100*INTREPID_TOL;
outStream -> precision(20);
try {
int max_order = 1; // max total order of polynomial solution
// Define array containing points at which the solution is evaluated
int numIntervals = 100;
int numInterpPoints = numIntervals + 1;
FieldContainer<double> interp_points(numInterpPoints, 1);
for (int i=0; i<numInterpPoints; i++) {
interp_points(i,0) = -1.0+(2.0*(double)i)/(double)numIntervals;
}
DefaultCubatureFactory<double> cubFactory; // create factory
shards::CellTopology line(shards::getCellTopologyData< shards::Line<> >()); // create cell topology
//create basis
Teuchos::RCP<Basis<double,FieldContainer<double> > > lineBasis =
Teuchos::rcp(new Basis_HGRAD_LINE_C1_FEM<double,FieldContainer<double> >() );
int numFields = lineBasis->getCardinality();
int basis_order = lineBasis->getDegree();
// create cubature
Teuchos::RCP<Cubature<double> > lineCub = cubFactory.create(line, 2);
int numCubPoints = lineCub->getNumPoints();
int spaceDim = lineCub->getDimension();
for (int soln_order=0; soln_order <= max_order; soln_order++) {
// evaluate exact solution
FieldContainer<double> exact_solution(1, numInterpPoints);
u_exact(exact_solution, interp_points, soln_order);
/* Computational arrays. */
FieldContainer<double> cub_points(numCubPoints, spaceDim);
FieldContainer<double> cub_points_physical(1, numCubPoints, spaceDim);
FieldContainer<double> cub_weights(numCubPoints);
FieldContainer<double> cell_nodes(1, 2, spaceDim);
FieldContainer<double> jacobian(1, numCubPoints, spaceDim, spaceDim);
FieldContainer<double> jacobian_inv(1, numCubPoints, spaceDim, spaceDim);
FieldContainer<double> jacobian_det(1, numCubPoints);
FieldContainer<double> weighted_measure(1, numCubPoints);
FieldContainer<double> value_of_basis_at_cub_points(numFields, numCubPoints);
FieldContainer<double> transformed_value_of_basis_at_cub_points(1, numFields, numCubPoints);
FieldContainer<double> weighted_transformed_value_of_basis_at_cub_points(1, numFields, numCubPoints);
FieldContainer<double> grad_of_basis_at_cub_points(numFields, numCubPoints, spaceDim);
FieldContainer<double> transformed_grad_of_basis_at_cub_points(1, numFields, numCubPoints, spaceDim);
FieldContainer<double> weighted_transformed_grad_of_basis_at_cub_points(1, numFields, numCubPoints, spaceDim);
FieldContainer<double> fe_matrix(1, numFields, numFields);
FieldContainer<double> rhs_at_cub_points_physical(1, numCubPoints);
FieldContainer<double> rhs_and_soln_vector(1, numFields);
FieldContainer<double> one_point(1, 1);
FieldContainer<double> value_of_basis_at_one(numFields, 1);
FieldContainer<double> value_of_basis_at_minusone(numFields, 1);
FieldContainer<double> bc_neumann(2, numFields);
FieldContainer<double> value_of_basis_at_interp_points(numFields, numInterpPoints);
FieldContainer<double> transformed_value_of_basis_at_interp_points(1, numFields, numInterpPoints);
FieldContainer<double> interpolant(1, numInterpPoints);
FieldContainer<int> ipiv(numFields);
/******************* START COMPUTATION ***********************/
// get cubature points and weights
lineCub->getCubature(cub_points, cub_weights);
// fill cell vertex array
cell_nodes(0, 0, 0) = -1.0;
cell_nodes(0, 1, 0) = 1.0;
// compute geometric cell information
CellTools<double>::setJacobian(jacobian, cub_points, cell_nodes, line);
CellTools<double>::setJacobianInv(jacobian_inv, jacobian);
CellTools<double>::setJacobianDet(jacobian_det, jacobian);
// compute weighted measure
FunctionSpaceTools::computeCellMeasure<double>(weighted_measure, jacobian_det, cub_weights);
///////////////////////////
// Computing mass matrices:
// tabulate values of basis functions at (reference) cubature points
lineBasis->getValues(value_of_basis_at_cub_points, cub_points, OPERATOR_VALUE);
// transform values of basis functions
FunctionSpaceTools::HGRADtransformVALUE<double>(transformed_value_of_basis_at_cub_points,
value_of_basis_at_cub_points);
// multiply with weighted measure
FunctionSpaceTools::multiplyMeasure<double>(weighted_transformed_value_of_basis_at_cub_points,
weighted_measure,
transformed_value_of_basis_at_cub_points);
// compute mass matrices
FunctionSpaceTools::integrate<double>(fe_matrix,
transformed_value_of_basis_at_cub_points,
weighted_transformed_value_of_basis_at_cub_points,
COMP_CPP);
///////////////////////////
////////////////////////////////
// Computing stiffness matrices:
// tabulate gradients of basis functions at (reference) cubature points
lineBasis->getValues(grad_of_basis_at_cub_points, cub_points, OPERATOR_GRAD);
// transform gradients of basis functions
FunctionSpaceTools::HGRADtransformGRAD<double>(transformed_grad_of_basis_at_cub_points,
jacobian_inv,
grad_of_basis_at_cub_points);
// multiply with weighted measure
FunctionSpaceTools::multiplyMeasure<double>(weighted_transformed_grad_of_basis_at_cub_points,
weighted_measure,
transformed_grad_of_basis_at_cub_points);
// compute stiffness matrices and sum into fe_matrix
FunctionSpaceTools::integrate<double>(fe_matrix,
transformed_grad_of_basis_at_cub_points,
weighted_transformed_grad_of_basis_at_cub_points,
COMP_CPP,
true);
////////////////////////////////
///////////////////////////////
// Computing RHS contributions:
// map (reference) cubature points to physical space
CellTools<double>::mapToPhysicalFrame(cub_points_physical, cub_points, cell_nodes, line);
// evaluate rhs function
rhsFunc(rhs_at_cub_points_physical, cub_points_physical, soln_order);
// compute rhs
FunctionSpaceTools::integrate<double>(rhs_and_soln_vector,
rhs_at_cub_points_physical,
weighted_transformed_value_of_basis_at_cub_points,
COMP_CPP);
// compute neumann b.c. contributions and adjust rhs
one_point(0,0) = 1.0; lineBasis->getValues(value_of_basis_at_one, one_point, OPERATOR_VALUE);
one_point(0,0) = -1.0; lineBasis->getValues(value_of_basis_at_minusone, one_point, OPERATOR_VALUE);
neumann(bc_neumann, value_of_basis_at_minusone, value_of_basis_at_one, soln_order);
for (int i=0; i<numFields; i++) {
rhs_and_soln_vector(0, i) -= bc_neumann(0, i);
rhs_and_soln_vector(0, i) += bc_neumann(1, i);
}
///////////////////////////////
/////////////////////////////
// Solution of linear system:
int info = 0;
Teuchos::LAPACK<int, double> solver;
//solver.GESV(numRows, 1, &fe_mat(0,0), numRows, &ipiv(0), &fe_vec(0), numRows, &info);
solver.GESV(numFields, 1, &fe_matrix[0], numFields, &ipiv(0), &rhs_and_soln_vector[0], numFields, &info);
/////////////////////////////
////////////////////////
// Building interpolant:
// evaluate basis at interpolation points
lineBasis->getValues(value_of_basis_at_interp_points, interp_points, OPERATOR_VALUE);
// transform values of basis functions
FunctionSpaceTools::HGRADtransformVALUE<double>(transformed_value_of_basis_at_interp_points,
value_of_basis_at_interp_points);
FunctionSpaceTools::evaluate<double>(interpolant, rhs_and_soln_vector, transformed_value_of_basis_at_interp_points);
////////////////////////
/******************* END COMPUTATION ***********************/
RealSpaceTools<double>::subtract(interpolant, exact_solution);
*outStream << "\nNorm-2 difference between exact solution polynomial of order "
<< soln_order << " and finite element interpolant of order " << basis_order << ": "
<< RealSpaceTools<double>::vectorNorm(&interpolant[0], interpolant.dimension(1), NORM_TWO) << "\n";
if (RealSpaceTools<double>::vectorNorm(&interpolant[0], interpolant.dimension(1), NORM_TWO) > zero) {
*outStream << "\n\nPatch test failed for solution polynomial order "
<< soln_order << " and basis order " << basis_order << "\n\n";
errorFlag++;
}
} // end for soln_order
}
// Catch unexpected errors
catch (std::logic_error err) {
*outStream << err.what() << "\n\n";
errorFlag = -1000;
};
if (errorFlag != 0)
std::cout << "End Result: TEST FAILED\n";
else
std::cout << "End Result: TEST PASSED\n";
// reset format state of std::cout
std::cout.copyfmt(oldFormatState);
Kokkos::finalize();
return errorFlag;
}
int main(int argc, char *argv[]) {
#ifdef EPETRA_MPI
// Initialize MPI
MPI_Init(&argc,&argv);
Epetra_MpiComm Comm(MPI_COMM_WORLD);
#else
Epetra_SerialComm Comm;
#endif
bool testFailed;
bool boolret;
int MyPID = Comm.MyPID();
bool verbose = true;
bool debug = false;
std::string which("SM");
Teuchos::CommandLineProcessor cmdp(false,true);
cmdp.setOption("verbose","quiet",&verbose,"Print messages and results.");
cmdp.setOption("debug","nodebug",&debug,"Print debugging information.");
cmdp.setOption("sort",&which,"Targetted eigenvalues (SM,LM,SR,LR,SI,or LI).");
if (cmdp.parse(argc,argv) != Teuchos::CommandLineProcessor::PARSE_SUCCESSFUL) {
#ifdef HAVE_MPI
MPI_Finalize();
#endif
return -1;
}
typedef double ScalarType;
typedef Teuchos::ScalarTraits<ScalarType> ScalarTypeTraits;
typedef ScalarTypeTraits::magnitudeType MagnitudeType;
typedef Epetra_MultiVector MV;
typedef Epetra_Operator OP;
typedef Anasazi::MultiVecTraits<ScalarType,MV> MVTraits;
typedef Anasazi::OperatorTraits<ScalarType,MV,OP> OpTraits;
// Dimension of the matrix
int nx = 10; // Discretization points in any one direction.
int NumGlobalElements = nx*nx; // Size of matrix nx*nx
// Construct a Map that puts approximately the same number of
// equations on each processor.
Epetra_Map Map(NumGlobalElements, 0, Comm);
// Get update list and number of local equations from newly created Map.
int NumMyElements = Map.NumMyElements();
std::vector<int> MyGlobalElements(NumMyElements);
Map.MyGlobalElements(&MyGlobalElements[0]);
// Create an integer vector NumNz that is used to build the Petra Matrix.
// NumNz[i] is the Number of OFF-DIAGONAL term for the ith global equation
// on this processor
std::vector<int> NumNz(NumMyElements);
/* We are building a matrix of block structure:
| T -I |
|-I T -I |
| -I T |
| ... -I|
| -I T|
where each block is dimension nx by nx and the matrix is on the order of
nx*nx. The block T is a tridiagonal matrix.
*/
for (int i=0; i<NumMyElements; i++) {
if (MyGlobalElements[i] == 0 || MyGlobalElements[i] == NumGlobalElements-1 ||
MyGlobalElements[i] == nx-1 || MyGlobalElements[i] == nx*(nx-1) ) {
NumNz[i] = 3;
}
else if (MyGlobalElements[i] < nx || MyGlobalElements[i] > nx*(nx-1) ||
MyGlobalElements[i]%nx == 0 || (MyGlobalElements[i]+1)%nx == 0) {
NumNz[i] = 4;
}
else {
NumNz[i] = 5;
}
}
// Create an Epetra_Matrix
Teuchos::RCP<Epetra_CrsMatrix> A = Teuchos::rcp( new Epetra_CrsMatrix(Copy, Map, &NumNz[0]) );
// Diffusion coefficient, can be set by user.
// When rho*h/2 <= 1, the discrete convection-diffusion operator has real eigenvalues.
// When rho*h/2 > 1, the operator has complex eigenvalues.
double rho = 2*(nx+1);
// Compute coefficients for discrete convection-diffution operator
const double one = 1.0;
std::vector<double> Values(4);
std::vector<int> Indices(4);
double h = one /(nx+1);
double h2 = h*h;
double c = 5.0e-01*rho/ h;
Values[0] = -one/h2 - c; Values[1] = -one/h2 + c; Values[2] = -one/h2; Values[3]= -one/h2;
double diag = 4.0 / h2;
int NumEntries, info;
for (int i=0; i<NumMyElements; i++)
{
if (MyGlobalElements[i]==0)
{
Indices[0] = 1;
Indices[1] = nx;
NumEntries = 2;
info = A->InsertGlobalValues(MyGlobalElements[i], NumEntries, &Values[1], &Indices[0]);
assert( info==0 );
}
else if (MyGlobalElements[i] == nx*(nx-1))
{
Indices[0] = nx*(nx-1)+1;
Indices[1] = nx*(nx-2);
NumEntries = 2;
info = A->InsertGlobalValues(MyGlobalElements[i], NumEntries, &Values[1], &Indices[0]);
assert( info==0 );
}
else if (MyGlobalElements[i] == nx-1)
{
Indices[0] = nx-2;
NumEntries = 1;
info = A->InsertGlobalValues(MyGlobalElements[i], NumEntries, &Values[0], &Indices[0]);
assert( info==0 );
Indices[0] = 2*nx-1;
info = A->InsertGlobalValues(MyGlobalElements[i], NumEntries, &Values[2], &Indices[0]);
assert( info==0 );
}
else if (MyGlobalElements[i] == NumGlobalElements-1)
{
Indices[0] = NumGlobalElements-2;
NumEntries = 1;
info = A->InsertGlobalValues(MyGlobalElements[i], NumEntries, &Values[0], &Indices[0]);
assert( info==0 );
Indices[0] = nx*(nx-1)-1;
info = A->InsertGlobalValues(MyGlobalElements[i], NumEntries, &Values[2], &Indices[0]);
assert( info==0 );
}
else if (MyGlobalElements[i] < nx)
{
Indices[0] = MyGlobalElements[i]-1;
Indices[1] = MyGlobalElements[i]+1;
Indices[2] = MyGlobalElements[i]+nx;
NumEntries = 3;
info = A->InsertGlobalValues(MyGlobalElements[i], NumEntries, &Values[0], &Indices[0]);
assert( info==0 );
}
else if (MyGlobalElements[i] > nx*(nx-1))
{
Indices[0] = MyGlobalElements[i]-1;
Indices[1] = MyGlobalElements[i]+1;
Indices[2] = MyGlobalElements[i]-nx;
NumEntries = 3;
info = A->InsertGlobalValues(MyGlobalElements[i], NumEntries, &Values[0], &Indices[0]);
assert( info==0 );
}
else if (MyGlobalElements[i]%nx == 0)
{
Indices[0] = MyGlobalElements[i]+1;
Indices[1] = MyGlobalElements[i]-nx;
Indices[2] = MyGlobalElements[i]+nx;
NumEntries = 3;
info = A->InsertGlobalValues(MyGlobalElements[i], NumEntries, &Values[1], &Indices[0]);
assert( info==0 );
}
else if ((MyGlobalElements[i]+1)%nx == 0)
{
Indices[0] = MyGlobalElements[i]-nx;
Indices[1] = MyGlobalElements[i]+nx;
NumEntries = 2;
info = A->InsertGlobalValues(MyGlobalElements[i], NumEntries, &Values[2], &Indices[0]);
assert( info==0 );
Indices[0] = MyGlobalElements[i]-1;
NumEntries = 1;
info = A->InsertGlobalValues(MyGlobalElements[i], NumEntries, &Values[0], &Indices[0]);
assert( info==0 );
}
else
{
Indices[0] = MyGlobalElements[i]-1;
Indices[1] = MyGlobalElements[i]+1;
Indices[2] = MyGlobalElements[i]-nx;
Indices[3] = MyGlobalElements[i]+nx;
NumEntries = 4;
info = A->InsertGlobalValues(MyGlobalElements[i], NumEntries, &Values[0], &Indices[0]);
assert( info==0 );
}
// Put in the diagonal entry
info = A->InsertGlobalValues(MyGlobalElements[i], 1, &diag, &MyGlobalElements[i]);
assert( info==0 );
}
// Finish up
info = A->FillComplete();
assert( info==0 );
A->SetTracebackMode(1); // Shutdown Epetra Warning tracebacks
//************************************
// Start the block Davidson iteration
//***********************************
//
// Variables used for the Generalized Davidson Method
//
int nev = 4;
int blockSize = 1;
int maxDim = 50;
int restartDim = 10;
int maxRestarts = 500;
double tol = 1e-10;
// Set verbosity level
int verbosity = Anasazi::Errors + Anasazi::Warnings;
if (verbose) {
verbosity += Anasazi::FinalSummary + Anasazi::TimingDetails;
}
if (debug) {
verbosity += Anasazi::Debug;
}
//
// Create parameter list to pass into solver manager
//
Teuchos::ParameterList MyPL;
MyPL.set( "Verbosity", verbosity );
MyPL.set( "Which", which );
MyPL.set( "Block Size", blockSize );
MyPL.set( "Maximum Subspace Dimension", maxDim);
MyPL.set( "Restart Dimension", restartDim);
MyPL.set( "Maximum Restarts", maxRestarts );
MyPL.set( "Convergence Tolerance", tol );
MyPL.set( "Relative Convergence Tolerance", true );
MyPL.set( "Initial Guess", "User" );
// Create an Epetra_MultiVector for an initial vector to start the solver.
// Note: This needs to have the same number of columns as the blocksize.
Teuchos::RCP<Epetra_MultiVector> ivec = Teuchos::rcp( new Epetra_MultiVector(Map, blockSize) );
ivec->Random();
// Create the eigenproblem.
Teuchos::RCP<Anasazi::BasicEigenproblem<double, MV, OP> > MyProblem = Teuchos::rcp(
new Anasazi::BasicEigenproblem<double,MV,OP>() );
MyProblem->setA(A);
MyProblem->setInitVec(ivec);
// Inform the eigenproblem that the operator A is non-Hermitian
MyProblem->setHermitian(false);
// Set the number of eigenvalues requested
MyProblem->setNEV( nev );
// Inform the eigenproblem that you are finishing passing it information
boolret = MyProblem->setProblem();
if (boolret != true) {
if (verbose && MyPID == 0) {
std::cout << "Anasazi::BasicEigenproblem::setProblem() returned with error." << std::endl;
}
#ifdef HAVE_MPI
MPI_Finalize() ;
#endif
return -1;
}
// Initialize the Block Arnoldi solver
Anasazi::GeneralizedDavidsonSolMgr<double, MV, OP> MySolverMgr(MyProblem, MyPL);
// Solve the problem to the specified tolerances or length
Anasazi::ReturnType returnCode = MySolverMgr.solve();
testFailed = false;
if (returnCode != Anasazi::Converged && MyPID==0 && verbose) {
testFailed = true;
}
// Get the eigenvalues and eigenvectors from the eigenproblem
Anasazi::Eigensolution<ScalarType,MV> sol = MyProblem->getSolution();
std::vector<Anasazi::Value<ScalarType> > evals = sol.Evals;
Teuchos::RCP<MV> evecs = sol.Evecs;
std::vector<int> index = sol.index;
int numev = sol.numVecs;
// Output computed eigenvalues and their direct residuals
if (verbose && MyPID==0) {
int numritz = (int)evals.size();
std::cout.setf(std::ios_base::right, std::ios_base::adjustfield);
std::cout<<std::endl<< "Computed Ritz Values"<< std::endl;
std::cout<< std::setw(16) << "Real Part"
<< std::setw(16) << "Imag Part"
<< std::endl;
std::cout<<"-----------------------------------------------------------"<<std::endl;
for (int i=0; i<numritz; i++) {
std::cout<< std::setw(16) << evals[i].realpart
<< std::setw(16) << evals[i].imagpart
<< std::endl;
}
std::cout<<"-----------------------------------------------------------"<<std::endl;
}
if (numev > 0) {
// Compute residuals.
Teuchos::LAPACK<int,double> lapack;
std::vector<double> normA(numev);
// The problem is non-Hermitian.
int i=0;
std::vector<int> curind(1);
std::vector<double> resnorm(1), tempnrm(1);
Teuchos::RCP<MV> tempAevec;
Teuchos::RCP<const MV> evecr, eveci;
Epetra_MultiVector Aevec(Map,numev);
// Compute A*evecs
OpTraits::Apply( *A, *evecs, Aevec );
Teuchos::SerialDenseMatrix<int,double> Breal(1,1), Bimag(1,1);
while (i<numev) {
if (index[i]==0) {
// Get a view of the current eigenvector (evecr)
curind[0] = i;
evecr = MVTraits::CloneView( *evecs, curind );
// Get a copy of A*evecr
tempAevec = MVTraits::CloneCopy( Aevec, curind );
// Compute A*evecr - lambda*evecr
Breal(0,0) = evals[i].realpart;
MVTraits::MvTimesMatAddMv( -1.0, *evecr, Breal, 1.0, *tempAevec );
// Compute the norm of the residual and increment counter
MVTraits::MvNorm( *tempAevec, resnorm );
normA[i] = resnorm[0] / Teuchos::ScalarTraits<MagnitudeType>::magnitude( evals[i].realpart );
i++;
} else {
// Get a view of the real part of the eigenvector (evecr)
curind[0] = i;
evecr = MVTraits::CloneView( *evecs, curind );
// Get a copy of A*evecr
tempAevec = MVTraits::CloneCopy( Aevec, curind );
// Get a view of the imaginary part of the eigenvector (eveci)
curind[0] = i+1;
eveci = MVTraits::CloneView( *evecs, curind );
// Set the eigenvalue into Breal and Bimag
Breal(0,0) = evals[i].realpart;
Bimag(0,0) = evals[i].imagpart;
// Compute A*evecr - evecr*lambdar + eveci*lambdai
MVTraits::MvTimesMatAddMv( -1.0, *evecr, Breal, 1.0, *tempAevec );
MVTraits::MvTimesMatAddMv( 1.0, *eveci, Bimag, 1.0, *tempAevec );
MVTraits::MvNorm( *tempAevec, tempnrm );
// Get a copy of A*eveci
tempAevec = MVTraits::CloneCopy( Aevec, curind );
// Compute A*eveci - eveci*lambdar - evecr*lambdai
MVTraits::MvTimesMatAddMv( -1.0, *evecr, Bimag, 1.0, *tempAevec );
MVTraits::MvTimesMatAddMv( -1.0, *eveci, Breal, 1.0, *tempAevec );
MVTraits::MvNorm( *tempAevec, resnorm );
// Compute the norms and scale by magnitude of eigenvalue
normA[i] = lapack.LAPY2( tempnrm[0], resnorm[0] ) /
lapack.LAPY2( evals[i].realpart, evals[i].imagpart );
normA[i+1] = normA[i];
i=i+2;
}
}
// Output computed eigenvalues and their direct residuals
if (verbose && MyPID==0) {
std::cout.setf(std::ios_base::right, std::ios_base::adjustfield);
std::cout<<std::endl<< "Actual Residuals"<<std::endl;
std::cout<< std::setw(16) << "Real Part"
<< std::setw(16) << "Imag Part"
<< std::setw(20) << "Direct Residual"<< std::endl;
std::cout<<"-----------------------------------------------------------"<<std::endl;
for (int j=0; j<numev; j++) {
std::cout<< std::setw(16) << evals[j].realpart
<< std::setw(16) << evals[j].imagpart
<< std::setw(20) << normA[j] << std::endl;
if ( normA[j] > tol ) {
testFailed = true;
}
}
std::cout<<"-----------------------------------------------------------"<<std::endl;
}
}
#ifdef EPETRA_MPI
MPI_Finalize();
#endif
if (testFailed) {
if (verbose && MyPID==0) {
std::cout << "End Result: TEST FAILED" << std::endl;
}
return -1;
}
//
// Default return value
//
if (verbose && MyPID==0) {
std::cout << "End Result: TEST PASSED" << std::endl;
}
return 0;
}
int main(int argc, char *argv[]) {
Teuchos::GlobalMPISession mpiSession(&argc, &argv);
Kokkos::initialize();
// This little trick lets us print to std::cout only if
// a (dummy) command-line argument is provided.
int iprint = argc - 1;
Teuchos::RCP<std::ostream> outStream;
Teuchos::oblackholestream bhs; // outputs nothing
if (iprint > 0)
outStream = Teuchos::rcp(&std::cout, false);
else
outStream = Teuchos::rcp(&bhs, false);
// Save the format state of the original std::cout.
Teuchos::oblackholestream oldFormatState;
oldFormatState.copyfmt(std::cout);
*outStream \
<< "===============================================================================\n" \
<< "| |\n" \
<< "| Unit Test (Basis_HGRAD_TET_Cn_FEM) |\n" \
<< "| |\n" \
<< "| 1) Patch test involving mass and stiffness matrices, |\n" \
<< "| for the Neumann problem on a tetrahedral patch |\n" \
<< "| Omega with boundary Gamma. |\n" \
<< "| |\n" \
<< "| - div (grad u) + u = f in Omega, (grad u) . n = g on Gamma |\n" \
<< "| |\n" \
<< "| Questions? Contact Pavel Bochev ([email protected]), |\n" \
<< "| Denis Ridzal ([email protected]), |\n" \
<< "| Kara Peterson ([email protected]). |\n" \
<< "| |\n" \
<< "| Intrepid's website: http://trilinos.sandia.gov/packages/intrepid |\n" \
<< "| Trilinos website: http://trilinos.sandia.gov |\n" \
<< "| |\n" \
<< "===============================================================================\n"\
<< "| TEST 1: Patch test |\n"\
<< "===============================================================================\n";
int errorFlag = 0;
outStream -> precision(16);
try {
int max_order = 5; // max total order of polynomial solution
DefaultCubatureFactory<double> cubFactory; // create factory
shards::CellTopology cell(shards::getCellTopologyData< shards::Tetrahedron<> >()); // create parent cell topology
shards::CellTopology side(shards::getCellTopologyData< shards::Triangle<> >()); // create relevant subcell (side) topology
int cellDim = cell.getDimension();
int sideDim = side.getDimension();
// Define array containing points at which the solution is evaluated, on the reference tet.
int numIntervals = 10;
int numInterpPoints = ((numIntervals + 1)*(numIntervals + 2)*(numIntervals + 3))/6;
FieldContainer<double> interp_points_ref(numInterpPoints, 3);
int counter = 0;
for (int k=0; k<=numIntervals; k++) {
for (int j=0; j<=numIntervals; j++) {
for (int i=0; i<=numIntervals; i++) {
if (i+j+k <= numIntervals) {
interp_points_ref(counter,0) = i*(1.0/numIntervals);
interp_points_ref(counter,1) = j*(1.0/numIntervals);
interp_points_ref(counter,2) = k*(1.0/numIntervals);
counter++;
}
}
}
}
/* Definition of parent cell. */
FieldContainer<double> cell_nodes(1, 4, cellDim);
// funky tet
cell_nodes(0, 0, 0) = -1.0;
cell_nodes(0, 0, 1) = -2.0;
cell_nodes(0, 0, 2) = 0.0;
cell_nodes(0, 1, 0) = 6.0;
cell_nodes(0, 1, 1) = 2.0;
cell_nodes(0, 1, 2) = 0.0;
cell_nodes(0, 2, 0) = -5.0;
cell_nodes(0, 2, 1) = 1.0;
cell_nodes(0, 2, 2) = 0.0;
cell_nodes(0, 3, 0) = -4.0;
cell_nodes(0, 3, 1) = -1.0;
cell_nodes(0, 3, 2) = 3.0;
// perturbed reference tet
/*cell_nodes(0, 0, 0) = 0.1;
cell_nodes(0, 0, 1) = -0.1;
cell_nodes(0, 0, 2) = 0.2;
cell_nodes(0, 1, 0) = 1.2;
cell_nodes(0, 1, 1) = -0.1;
cell_nodes(0, 1, 2) = 0.05;
cell_nodes(0, 2, 0) = 0.0;
cell_nodes(0, 2, 1) = 0.9;
cell_nodes(0, 2, 2) = 0.1;
cell_nodes(0, 3, 0) = 0.1;
cell_nodes(0, 3, 1) = -0.1;
cell_nodes(0, 3, 2) = 1.1;*/
// reference tet
/*cell_nodes(0, 0, 0) = 0.0;
cell_nodes(0, 0, 1) = 0.0;
cell_nodes(0, 0, 2) = 0.0;
cell_nodes(0, 1, 0) = 1.0;
cell_nodes(0, 1, 1) = 0.0;
cell_nodes(0, 1, 2) = 0.0;
cell_nodes(0, 2, 0) = 0.0;
cell_nodes(0, 2, 1) = 1.0;
cell_nodes(0, 2, 2) = 0.0;
cell_nodes(0, 3, 0) = 0.0;
cell_nodes(0, 3, 1) = 0.0;
cell_nodes(0, 3, 2) = 1.0;*/
FieldContainer<double> interp_points(1, numInterpPoints, cellDim);
CellTools<double>::mapToPhysicalFrame(interp_points, interp_points_ref, cell_nodes, cell);
interp_points.resize(numInterpPoints, cellDim);
// we test two types of bases
EPointType pointtype[] = {POINTTYPE_EQUISPACED, POINTTYPE_WARPBLEND};
for (int ptype=0; ptype < 2; ptype++) {
*outStream << "\nTesting bases with " << EPointTypeToString(pointtype[ptype]) << ":\n";
for (int x_order=0; x_order <= max_order; x_order++) {
for (int y_order=0; y_order <= max_order-x_order; y_order++) {
for (int z_order=0; z_order <= max_order-x_order-y_order; z_order++) {
// evaluate exact solution
FieldContainer<double> exact_solution(1, numInterpPoints);
u_exact(exact_solution, interp_points, x_order, y_order, z_order);
int total_order = std::max(x_order + y_order + z_order, 1);
for (int basis_order=total_order; basis_order <= max_order; basis_order++) {
// set test tolerance;
double zero = basis_order*basis_order*basis_order*100*INTREPID_TOL;
//create basis
Teuchos::RCP<Basis<double,FieldContainer<double> > > basis =
Teuchos::rcp(new Basis_HGRAD_TET_Cn_FEM<double,FieldContainer<double> >(basis_order, pointtype[ptype]) );
int numFields = basis->getCardinality();
// create cubatures
Teuchos::RCP<Cubature<double> > cellCub = cubFactory.create(cell, 2*basis_order);
Teuchos::RCP<Cubature<double> > sideCub = cubFactory.create(side, 2*basis_order);
int numCubPointsCell = cellCub->getNumPoints();
int numCubPointsSide = sideCub->getNumPoints();
/* Computational arrays. */
/* Section 1: Related to parent cell integration. */
FieldContainer<double> cub_points_cell(numCubPointsCell, cellDim);
FieldContainer<double> cub_points_cell_physical(1, numCubPointsCell, cellDim);
FieldContainer<double> cub_weights_cell(numCubPointsCell);
FieldContainer<double> jacobian_cell(1, numCubPointsCell, cellDim, cellDim);
FieldContainer<double> jacobian_inv_cell(1, numCubPointsCell, cellDim, cellDim);
FieldContainer<double> jacobian_det_cell(1, numCubPointsCell);
FieldContainer<double> weighted_measure_cell(1, numCubPointsCell);
FieldContainer<double> value_of_basis_at_cub_points_cell(numFields, numCubPointsCell);
FieldContainer<double> transformed_value_of_basis_at_cub_points_cell(1, numFields, numCubPointsCell);
FieldContainer<double> weighted_transformed_value_of_basis_at_cub_points_cell(1, numFields, numCubPointsCell);
FieldContainer<double> grad_of_basis_at_cub_points_cell(numFields, numCubPointsCell, cellDim);
FieldContainer<double> transformed_grad_of_basis_at_cub_points_cell(1, numFields, numCubPointsCell, cellDim);
FieldContainer<double> weighted_transformed_grad_of_basis_at_cub_points_cell(1, numFields, numCubPointsCell, cellDim);
FieldContainer<double> fe_matrix(1, numFields, numFields);
FieldContainer<double> rhs_at_cub_points_cell_physical(1, numCubPointsCell);
FieldContainer<double> rhs_and_soln_vector(1, numFields);
/* Section 2: Related to subcell (side) integration. */
unsigned numSides = 4;
FieldContainer<double> cub_points_side(numCubPointsSide, sideDim);
FieldContainer<double> cub_weights_side(numCubPointsSide);
FieldContainer<double> cub_points_side_refcell(numCubPointsSide, cellDim);
FieldContainer<double> cub_points_side_physical(1, numCubPointsSide, cellDim);
FieldContainer<double> jacobian_side_refcell(1, numCubPointsSide, cellDim, cellDim);
FieldContainer<double> jacobian_det_side_refcell(1, numCubPointsSide);
FieldContainer<double> weighted_measure_side_refcell(1, numCubPointsSide);
FieldContainer<double> value_of_basis_at_cub_points_side_refcell(numFields, numCubPointsSide);
FieldContainer<double> transformed_value_of_basis_at_cub_points_side_refcell(1, numFields, numCubPointsSide);
FieldContainer<double> weighted_transformed_value_of_basis_at_cub_points_side_refcell(1, numFields, numCubPointsSide);
FieldContainer<double> neumann_data_at_cub_points_side_physical(1, numCubPointsSide);
FieldContainer<double> neumann_fields_per_side(1, numFields);
/* Section 3: Related to global interpolant. */
FieldContainer<double> value_of_basis_at_interp_points_ref(numFields, numInterpPoints);
FieldContainer<double> transformed_value_of_basis_at_interp_points_ref(1, numFields, numInterpPoints);
FieldContainer<double> interpolant(1, numInterpPoints);
FieldContainer<int> ipiv(numFields);
/******************* START COMPUTATION ***********************/
// get cubature points and weights
cellCub->getCubature(cub_points_cell, cub_weights_cell);
// compute geometric cell information
CellTools<double>::setJacobian(jacobian_cell, cub_points_cell, cell_nodes, cell);
CellTools<double>::setJacobianInv(jacobian_inv_cell, jacobian_cell);
CellTools<double>::setJacobianDet(jacobian_det_cell, jacobian_cell);
// compute weighted measure
FunctionSpaceTools::computeCellMeasure<double>(weighted_measure_cell, jacobian_det_cell, cub_weights_cell);
///////////////////////////
// Computing mass matrices:
// tabulate values of basis functions at (reference) cubature points
basis->getValues(value_of_basis_at_cub_points_cell, cub_points_cell, OPERATOR_VALUE);
// transform values of basis functions
FunctionSpaceTools::HGRADtransformVALUE<double>(transformed_value_of_basis_at_cub_points_cell,
value_of_basis_at_cub_points_cell);
// multiply with weighted measure
FunctionSpaceTools::multiplyMeasure<double>(weighted_transformed_value_of_basis_at_cub_points_cell,
weighted_measure_cell,
transformed_value_of_basis_at_cub_points_cell);
// compute mass matrices
FunctionSpaceTools::integrate<double>(fe_matrix,
transformed_value_of_basis_at_cub_points_cell,
weighted_transformed_value_of_basis_at_cub_points_cell,
COMP_BLAS);
///////////////////////////
////////////////////////////////
// Computing stiffness matrices:
// tabulate gradients of basis functions at (reference) cubature points
basis->getValues(grad_of_basis_at_cub_points_cell, cub_points_cell, OPERATOR_GRAD);
// transform gradients of basis functions
FunctionSpaceTools::HGRADtransformGRAD<double>(transformed_grad_of_basis_at_cub_points_cell,
jacobian_inv_cell,
grad_of_basis_at_cub_points_cell);
// multiply with weighted measure
FunctionSpaceTools::multiplyMeasure<double>(weighted_transformed_grad_of_basis_at_cub_points_cell,
weighted_measure_cell,
transformed_grad_of_basis_at_cub_points_cell);
// compute stiffness matrices and sum into fe_matrix
FunctionSpaceTools::integrate<double>(fe_matrix,
transformed_grad_of_basis_at_cub_points_cell,
weighted_transformed_grad_of_basis_at_cub_points_cell,
COMP_BLAS,
true);
////////////////////////////////
///////////////////////////////
// Computing RHS contributions:
// map cell (reference) cubature points to physical space
CellTools<double>::mapToPhysicalFrame(cub_points_cell_physical, cub_points_cell, cell_nodes, cell);
// evaluate rhs function
rhsFunc(rhs_at_cub_points_cell_physical, cub_points_cell_physical, x_order, y_order, z_order);
// compute rhs
FunctionSpaceTools::integrate<double>(rhs_and_soln_vector,
rhs_at_cub_points_cell_physical,
weighted_transformed_value_of_basis_at_cub_points_cell,
COMP_BLAS);
// compute neumann b.c. contributions and adjust rhs
sideCub->getCubature(cub_points_side, cub_weights_side);
for (unsigned i=0; i<numSides; i++) {
// compute geometric cell information
CellTools<double>::mapToReferenceSubcell(cub_points_side_refcell, cub_points_side, sideDim, (int)i, cell);
CellTools<double>::setJacobian(jacobian_side_refcell, cub_points_side_refcell, cell_nodes, cell);
CellTools<double>::setJacobianDet(jacobian_det_side_refcell, jacobian_side_refcell);
// compute weighted face measure
FunctionSpaceTools::computeFaceMeasure<double>(weighted_measure_side_refcell,
jacobian_side_refcell,
cub_weights_side,
i,
cell);
// tabulate values of basis functions at side cubature points, in the reference parent cell domain
basis->getValues(value_of_basis_at_cub_points_side_refcell, cub_points_side_refcell, OPERATOR_VALUE);
// transform
FunctionSpaceTools::HGRADtransformVALUE<double>(transformed_value_of_basis_at_cub_points_side_refcell,
value_of_basis_at_cub_points_side_refcell);
// multiply with weighted measure
FunctionSpaceTools::multiplyMeasure<double>(weighted_transformed_value_of_basis_at_cub_points_side_refcell,
weighted_measure_side_refcell,
transformed_value_of_basis_at_cub_points_side_refcell);
// compute Neumann data
// map side cubature points in reference parent cell domain to physical space
CellTools<double>::mapToPhysicalFrame(cub_points_side_physical, cub_points_side_refcell, cell_nodes, cell);
// now compute data
neumann(neumann_data_at_cub_points_side_physical, cub_points_side_physical, jacobian_side_refcell,
cell, (int)i, x_order, y_order, z_order);
FunctionSpaceTools::integrate<double>(neumann_fields_per_side,
neumann_data_at_cub_points_side_physical,
weighted_transformed_value_of_basis_at_cub_points_side_refcell,
COMP_BLAS);
// adjust RHS
RealSpaceTools<double>::add(rhs_and_soln_vector, neumann_fields_per_side);;
}
///////////////////////////////
/////////////////////////////
// Solution of linear system:
int info = 0;
Teuchos::LAPACK<int, double> solver;
solver.GESV(numFields, 1, &fe_matrix[0], numFields, &ipiv(0), &rhs_and_soln_vector[0], numFields, &info);
/////////////////////////////
////////////////////////
// Building interpolant:
// evaluate basis at interpolation points
basis->getValues(value_of_basis_at_interp_points_ref, interp_points_ref, OPERATOR_VALUE);
// transform values of basis functions
FunctionSpaceTools::HGRADtransformVALUE<double>(transformed_value_of_basis_at_interp_points_ref,
value_of_basis_at_interp_points_ref);
FunctionSpaceTools::evaluate<double>(interpolant, rhs_and_soln_vector, transformed_value_of_basis_at_interp_points_ref);
////////////////////////
/******************* END COMPUTATION ***********************/
RealSpaceTools<double>::subtract(interpolant, exact_solution);
*outStream << "\nRelative norm-2 error between exact solution polynomial of order ("
<< x_order << ", " << y_order << ", " << z_order
<< ") and finite element interpolant of order " << basis_order << ": "
<< RealSpaceTools<double>::vectorNorm(&interpolant[0], interpolant.dimension(1), NORM_TWO) /
RealSpaceTools<double>::vectorNorm(&exact_solution[0], exact_solution.dimension(1), NORM_TWO) << "\n";
if (RealSpaceTools<double>::vectorNorm(&interpolant[0], interpolant.dimension(1), NORM_TWO) /
RealSpaceTools<double>::vectorNorm(&exact_solution[0], exact_solution.dimension(1), NORM_TWO) > zero) {
*outStream << "\n\nPatch test failed for solution polynomial order ("
<< x_order << ", " << y_order << ", " << z_order << ") and basis order " << basis_order << "\n\n";
errorFlag++;
}
} // end for basis_order
} // end for z_order
} // end for y_order
} // end for x_order
} // end for ptype
}
// Catch unexpected errors
catch (std::logic_error err) {
*outStream << err.what() << "\n\n";
errorFlag = -1000;
};
if (errorFlag != 0)
std::cout << "End Result: TEST FAILED\n";
else
std::cout << "End Result: TEST PASSED\n";
// reset format state of std::cout
std::cout.copyfmt(oldFormatState);
Kokkos::finalize();
return errorFlag;
}
void Constraint<Scalar, LocalOrdinal, GlobalOrdinal, Node>::Setup(const MultiVector& B, const MultiVector& Bc, RCP<const CrsGraph> Ppattern) {
const size_t NSDim = Bc.getNumVectors();
Ppattern_ = Ppattern;
size_t numRows = Ppattern_->getNodeNumRows();
XXtInv_.resize(numRows);
RCP<const Import> importer = Ppattern_->getImporter();
X_ = MultiVectorFactory::Build(Ppattern_->getColMap(), NSDim);
if (!importer.is_null())
X_->doImport(Bc, *importer, Xpetra::INSERT);
else
*X_ = Bc;
std::vector<const SC*> Xval(NSDim);
for (size_t j = 0; j < NSDim; j++)
Xval[j] = X_->getData(j).get();
SC zero = Teuchos::ScalarTraits<SC>::zero();
SC one = Teuchos::ScalarTraits<SC>::one();
Teuchos::BLAS <LO,SC> blas;
Teuchos::LAPACK<LO,SC> lapack;
LO lwork = 3*NSDim;
ArrayRCP<LO> IPIV(NSDim);
ArrayRCP<SC> WORK(lwork);
for (size_t i = 0; i < numRows; i++) {
Teuchos::ArrayView<const LO> indices;
Ppattern_->getLocalRowView(i, indices);
size_t nnz = indices.size();
XXtInv_[i] = Teuchos::SerialDenseMatrix<LO,SC>(NSDim, NSDim, false/*zeroOut*/);
Teuchos::SerialDenseMatrix<LO,SC>& XXtInv = XXtInv_[i];
if (NSDim == 1) {
SC d = zero;
for (size_t j = 0; j < nnz; j++)
d += Xval[0][indices[j]] * Xval[0][indices[j]];
XXtInv(0,0) = one/d;
} else {
Teuchos::SerialDenseMatrix<LO,SC> locX(NSDim, nnz, false/*zeroOut*/);
for (size_t j = 0; j < nnz; j++)
for (size_t k = 0; k < NSDim; k++)
locX(k,j) = Xval[k][indices[j]];
// XXtInv_ = (locX*locX^T)^{-1}
blas.GEMM(Teuchos::NO_TRANS, Teuchos::CONJ_TRANS, NSDim, NSDim, nnz,
one, locX.values(), locX.stride(),
locX.values(), locX.stride(),
zero, XXtInv.values(), XXtInv.stride());
LO info;
// Compute LU factorization using partial pivoting with row exchanges
lapack.GETRF(NSDim, NSDim, XXtInv.values(), XXtInv.stride(), IPIV.get(), &info);
// Use the computed factorization to compute the inverse
lapack.GETRI(NSDim, XXtInv.values(), XXtInv.stride(), IPIV.get(), WORK.get(), lwork, &info);
}
}
}