void
LOCA::Homotopy::DeflatedGroup::
extractParameterComponent(bool use_transpose,
const NOX::Abstract::MultiVector& v,
NOX::Abstract::MultiVector::DenseMatrix& v_p) const
{
// cast v to an extended multi-vec
const LOCA::MultiContinuation::ExtendedMultiVector& mc_v =
dynamic_cast<const LOCA::MultiContinuation::ExtendedMultiVector&>(v);
// get solution and parameter components
Teuchos::RCP<const NOX::Abstract::MultiVector> mc_v_x =
mc_v.getXMultiVec();
Teuchos::RCP<const NOX::Abstract::MultiVector::DenseMatrix> mc_v_p =
mc_v.getScalars();
// If the underlying system isn't bordered, we're done
if (!isBordered) {
if (!use_transpose)
v_p.assign(*mc_v_p);
else
for (int j=0; j<v_p.numCols(); j++)
for (int i=0; i<v_p.numRows(); i++)
v_p(i,j) = (*mc_v_p)(j,i);
return;
}
int w = bordered_grp->getBorderedWidth();
if (!use_transpose) {
// Split v_p into 2 block rows, the top to store mc_v_x_p and the bottom
// to store mc_v_p
int num_cols = v_p.numCols();
NOX::Abstract::MultiVector::DenseMatrix v_p_1(Teuchos::View, v_p,
w, num_cols, 0, 0);
NOX::Abstract::MultiVector::DenseMatrix v_p_2(Teuchos::View, v_p,
1, num_cols, w, 0);
// Decompose mc_v_x
bordered_grp->extractParameterComponent(use_transpose,*mc_v_x, v_p_1);
v_p_2.assign(*mc_v_p);
}
else {
// Split v_p into 2 block columns, the first to store mc_v_x_p^t and the
// the second to store mc_v_p^T
int num_rows = v_p.numRows();
NOX::Abstract::MultiVector::DenseMatrix v_p_1(Teuchos::View, v_p,
num_rows, w, 0, 0);
NOX::Abstract::MultiVector::DenseMatrix v_p_2(Teuchos::View, v_p,
num_rows, 1, 0, w);
// Decompose mc_v_x
bordered_grp->extractParameterComponent(use_transpose,*mc_v_x, v_p_1);
for (int j=0; j<1; j++)
for (int i=0; i<num_rows; i++)
v_p_2(i,j) = (*mc_v_p)(j,i);
}
}
void
LOCA::Extended::MultiVector::multiply(
double alpha,
const LOCA::Extended::MultiVector& y,
NOX::Abstract::MultiVector::DenseMatrix& b) const
{
// Verify dimensions are consistent
if (y.numMultiVecRows != numMultiVecRows || y.numColumns != b.numRows() ||
y.numScalarRows != numScalarRows || numColumns != b.numCols())
globalData->locaErrorCheck->throwError(
"LOCA::Extended::MultiVector::multiply()",
"Size of supplied multivector/matrix is incompatible with this multivector");
// Zero out b
b.putScalar(0.0);
// Create temporary matrix to hold product for each multivec
NOX::Abstract::MultiVector::DenseMatrix tmp(b);
// Compute and sum products for each multivec
for (int i=0; i<numMultiVecRows; i++) {
multiVectorPtrs[i]->multiply(alpha, *(y.multiVectorPtrs[i]), tmp);
b += tmp;
}
// Compute and add in product for scalars
if (numScalarRows > 0)
b.multiply(Teuchos::TRANS, Teuchos::NO_TRANS, alpha, *y.scalarsPtr,
*scalarsPtr, 1.0);
}
int
NOX::TestCompare::testMatrix(
const NOX::Abstract::MultiVector::DenseMatrix& mat,
const NOX::Abstract::MultiVector::DenseMatrix& mat_expected,
double rtol, double atol,
const std::string& name)
{
bool passed;
NOX::Abstract::MultiVector::DenseMatrix tmp(mat_expected.numRows(),
mat_expected.numCols());
for (int j=0; j<mat_expected.numCols(); j++)
for (int i=0; i<mat_expected.numRows(); i++)
tmp(i,j) = fabs(mat(i,j)-mat_expected(i,j)) /
(atol + rtol * fabs(mat_expected(i,j)));
double inf_norm = tmp.normInf();
if (inf_norm < 1)
passed = true;
else
passed = false;
if (utils.isPrintType(NOX::Utils::TestDetails)) {
os << std::endl
<< "\tChecking " << name << ": ";
if (passed)
os << "Passed." << std::endl;
else
os << "Failed." << std::endl;
os << "\t\tComputed norm: " << utils.sciformat(inf_norm)
<< std::endl
<< "\t\tRelative Tolerance: " << utils.sciformat(rtol)
<< std::endl
<< "\t\tAbsolute Tolerance: " << utils.sciformat(rtol)
<< std::endl;
}
if (passed)
return 0;
else
return 1;
}
void
LOCA::BorderedSolver::HouseholderQR::applyCompactWY(
const NOX::Abstract::MultiVector::DenseMatrix& Y1,
const NOX::Abstract::MultiVector& Y2,
const NOX::Abstract::MultiVector::DenseMatrix& T,
NOX::Abstract::MultiVector::DenseMatrix& X1,
NOX::Abstract::MultiVector& X2,
bool isZeroX1, bool isZeroX2,
bool useTranspose) const
{
if (isZeroX1 && isZeroX2) {
X1.putScalar(0.0);
X2.init(0.0);
return;
}
int m = Y2.numVectors();
Teuchos::ETransp T_flag;
if (useTranspose)
T_flag = Teuchos::TRANS;
else
T_flag = Teuchos::NO_TRANS;
NOX::Abstract::MultiVector::DenseMatrix tmp(m, X2.numVectors());
// Compute Y1^T*X1 + Y2^T*X2
if (!isZeroX2)
X2.multiply(1.0, Y2, tmp);
// Opportunity for optimization here since Y1 is a lower-triangular
// matrix with unit diagonal
if (!isZeroX2 && !isZeroX1)
tmp.multiply(Teuchos::TRANS, Teuchos::NO_TRANS, 1.0, Y1, X1, 1.0);
else if (!isZeroX1)
tmp.multiply(Teuchos::TRANS, Teuchos::NO_TRANS, 1.0, Y1, X1, 0.0);
// Compute op(T)*(Y1^T*X1 + Y2^T*X2)
dblas.TRMM(Teuchos::LEFT_SIDE, Teuchos::UPPER_TRI, T_flag,
Teuchos::NON_UNIT_DIAG, tmp.numRows(), tmp.numCols(), 1.0,
T.values(), T.numRows(), tmp.values(), tmp.numRows());
// Compute X1 = X1 + Y1*op(T)*(Y1^T*X1 + Y2^T*X2)
// Opportunity for optimization here since Y1 is a lower-triangular
// matrix with unit diagonal
if (isZeroX1)
X1.multiply(Teuchos::NO_TRANS, Teuchos::NO_TRANS, 1.0, Y1, tmp, 0.0);
else
X1.multiply(Teuchos::NO_TRANS, Teuchos::NO_TRANS, 1.0, Y1, tmp, 1.0);
// Compute X2 = X2 + Y1*op(T)*(Y1^T*X1 + Y2^T*X2)
if (isZeroX2)
X2.update(Teuchos::NO_TRANS, 1.0, Y2, tmp, 0.0);
else
X2.update(Teuchos::NO_TRANS, 1.0, Y2, tmp, 1.0);
}
LOCA::MultiContinuation::ExtendedMultiVector::ExtendedMultiVector(
const Teuchos::RCP<LOCA::GlobalData>& global_data,
const NOX::Abstract::MultiVector& xVec,
const NOX::Abstract::MultiVector::DenseMatrix& params) :
LOCA::Extended::MultiVector(global_data, xVec.numVectors(), 1,
params.numRows())
{
LOCA::Extended::MultiVector::setMultiVectorPtr(0, xVec.clone(NOX::DeepCopy));
LOCA::Extended::MultiVector::getScalars()->assign(params);
}
void
LOCA::BorderedSolver::HouseholderQR::computeHouseholderVector(
int col,
const NOX::Abstract::MultiVector::DenseMatrix& A1,
const NOX::Abstract::MultiVector& A2,
NOX::Abstract::MultiVector::DenseMatrix& V1,
NOX::Abstract::MultiVector& V2,
double& beta)
{
double houseP = A1(col,col);
V1(0,0) = 1.0;
V2[0] = A2[col];
double sigma = A2[col].innerProduct(A2[col]);
for (int i=col+1; i<A1.numRows(); i++)
sigma += A1(i,col)*A1(i,col);
if (sigma == 0.0)
beta = 0.0;
else {
double mu = sqrt(houseP*houseP + sigma);
if (houseP <= 0.0)
houseP = houseP - mu;
else
houseP = -sigma / (houseP + mu);
beta = 2.0*houseP*houseP/(sigma + houseP*houseP);
V2.scale(1.0/houseP);
for (int i=1; i<V1.numRows(); i++)
V1(i,0) = A1(i+col,col) / houseP;
}
return;
}
void
NOX::Thyra::MultiVector::
multiply(double alpha,
const NOX::Abstract::MultiVector& y,
NOX::Abstract::MultiVector::DenseMatrix& b) const
{
const NOX::Thyra::MultiVector& yy =
dynamic_cast<const NOX::Thyra::MultiVector&>(y);
int m = b.numRows();
int n = b.numCols();
Teuchos::RCP< ::Thyra::MultiVectorBase<double> > bb =
::Thyra::createMembersView(
yy.thyraMultiVec->domain(),
RTOpPack::SubMultiVectorView<double>(0, m, 0, n,
Teuchos::arcp(b.values(), 0, b.stride()*b.numCols(), false),
b.stride()
)
);
::Thyra::apply(*yy.thyraMultiVec, ::Thyra::CONJTRANS, *thyraMultiVec,
bb.ptr(), alpha, 0.0);
}
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;
}