void LOCA::TurningPoint::MooreSpence::ExtendedGroup::lTransNorm( const NOX::Abstract::MultiVector& n, NOX::Abstract::MultiVector::DenseMatrix& result) const { n.multiply(1.0 / lengthVec->length(), *lengthMultiVec, result); }
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); }
NOX::Abstract::Group::ReturnType LOCA::MultiContinuation::ConstraintInterfaceMVDX::multiplyDX( double alpha, const NOX::Abstract::MultiVector& input_x, NOX::Abstract::MultiVector::DenseMatrix& result_p) const { if (!isDXZero()) { const NOX::Abstract::MultiVector* dgdx = getDX(); input_x.multiply(alpha, *dgdx, result_p); } else result_p.putScalar(0.0); return NOX::Abstract::Group::Ok; }
void LOCA::BorderedSolver::HouseholderQR::applyHouseholderVector( const NOX::Abstract::MultiVector::DenseMatrix& V1, const NOX::Abstract::MultiVector& V2, double beta, NOX::Abstract::MultiVector::DenseMatrix& A1, NOX::Abstract::MultiVector& A2) { int nColsA = A2.numVectors(); // Compute u = V2^T * A2 NOX::Abstract::MultiVector::DenseMatrix u(1, nColsA); A2.multiply(1.0, V2, u); // Compute u = u + V1^T * A_P u.multiply(Teuchos::TRANS, Teuchos::NO_TRANS, 1.0, V1, A1, 1.0); // Compute A1 = A1 - b*V1*u A1.multiply(Teuchos::NO_TRANS, Teuchos::NO_TRANS, -beta, V1, u, 1.0); // Compute A2 = A2 - b*V2*u A2.update(Teuchos::NO_TRANS, -beta, V2, u, 1.0); }
// 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; }