// 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;
}
// 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;
}
// Solves pitchfork equations via Phipps modified bordering
// The first m columns of input_x and input_null store the RHS,
// column m+1 stores df/dp, d(Jn)/dp, column m+2 stores psi and 0,
// and the last column provides space for solving (Jv_x) v. Note however
// input_param has only m columns. result_x, result_null,
// are result_param have the same dimensions as their input counterparts
NOX::Abstract::Group::ReturnType
LOCA::Pitchfork::MooreSpence::PhippsBordering::solveContiguous(
Teuchos::ParameterList& params,
const NOX::Abstract::MultiVector& input_x,
const NOX::Abstract::MultiVector& input_null,
const NOX::Abstract::MultiVector::DenseMatrix& input_slack,
const NOX::Abstract::MultiVector::DenseMatrix& input_param,
NOX::Abstract::MultiVector& result_x,
NOX::Abstract::MultiVector& result_null,
NOX::Abstract::MultiVector::DenseMatrix& result_slack,
NOX::Abstract::MultiVector::DenseMatrix& result_param) const
{
string callingFunction =
"LOCA::Pitchfork::MooreSpence::PhippsBordering::solveContiguous()";
NOX::Abstract::Group::ReturnType finalStatus = NOX::Abstract::Group::Ok;
NOX::Abstract::Group::ReturnType status;
int m = input_x.numVectors()-3;
vector<int> index_input(m);
vector<int> index_input_dp(m+2);
vector<int> index_null(1);
vector<int> index_dp(1);
vector<int> index_s(1);
for (int i=0; i<m; i++) {
index_input[i] = i;
index_input_dp[i] = i;
}
index_input_dp[m] = m;
index_input_dp[m+1] = m+1;
index_dp[0] = m;
index_s[0] = m+1;
index_null[0] = m+2;
NOX::Abstract::MultiVector::DenseMatrix tmp_mat_1(1, m+2);
NOX::Abstract::MultiVector::DenseMatrix tmp_mat_2(1, m+3);
// Create view of first m+2 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 C| = |F df/dp psi|
// |v^T 0||a b c| |0 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);
Teuchos::RCP<NOX::Abstract::MultiVector> C =
result_x.subView(index_s);
double b = tmp_mat_1(0,m);
double c = tmp_mat_1(0,m+1);
// compute (Jv)_x[A B C v]
result_x[m+2] = *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 [G d(Jn)/dp 0 0] - (Jv)_x[A B C v]
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||D E K L| = |G-(Jv)_xA d(Jv)/dp-(Jv)_xB -(Jv)_xC -(Jv)_xv|
// |v^T 0||d e k l| | 0 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> D =
result_null.subView(index_input);
Teuchos::RCP<NOX::Abstract::MultiVector> E =
result_null.subView(index_dp);
Teuchos::RCP<NOX::Abstract::MultiVector> K =
result_null.subView(index_s);
Teuchos::RCP<NOX::Abstract::MultiVector> L =
result_null.subView(index_null);
double e = tmp_mat_2(0, m);
double k = tmp_mat_2(0, m+1);
double l = tmp_mat_2(0, m+2);
double ltE = pfGroup->lTransNorm((*E)[0]);
double ltK = pfGroup->lTransNorm((*K)[0]);
double ltL = pfGroup->lTransNorm((*L)[0]);
double ltv = pfGroup->lTransNorm(*nullVector);
double ipv = group->innerProduct(*nullVector, *asymVector);
double ipB = group->innerProduct((*B)[0], *asymVector);
double ipC = group->innerProduct((*C)[0], *asymVector);
// Fill coefficient arrays
double M[16];
M[0] = sigma; M[1] = -l; M[2] = ipv; M[3] = ltL;
M[4] = 0.0; M[5] = sigma; M[6] = 0.0; M[7] = ltv;
M[8] = b; M[9] = e; M[10] = -ipB; M[11] = -ltE;
M[12] = c; M[13] = k; M[14] = -ipC; M[15] = -ltK;
// compute s - <A,psi>
NOX::Abstract::MultiVector::DenseMatrix tmp_mat_3(1, m);
group->innerProduct(*asymMultiVector, *A, tmp_mat_3);
tmp_mat_3 -= input_slack;
tmp_mat_3.scale(-1.0);
// compute h - phi^T D
NOX::Abstract::MultiVector::DenseMatrix tmp_mat_4(1, m);
pfGroup->lTransNorm(*D, tmp_mat_4);
tmp_mat_4 -= input_param;
tmp_mat_4.scale(-1.0);
double *R = new double[4*m];
for (int i=0; i<m; i++) {
R[4*i] = tmp_mat_1(0,i);
R[4*i+1] = tmp_mat_2(0,i);
R[4*i+2] = tmp_mat_3(0,i);
R[4*i+3] = tmp_mat_4(0,i);
}
// Solve M*P = R
int piv[4];
int info;
Teuchos::LAPACK<int,double> dlapack;
dlapack.GESV(4, m, M, 4, piv, R, 4, &info);
if (info != 0) {
globalData->locaErrorCheck->throwError(
callingFunction,
"Solve of 4x4 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[4*i];
beta(0,i) = R[4*i+1];
result_param(0,i) = R[4*i+2];
result_slack(0,i) = R[4*i+3];
}
// compute A = A - B*z -C*w + 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, *C, result_slack, 1.0);
A->update(Teuchos::NO_TRANS, 1.0, *nullMultiVector, alpha, 1.0);
// compute D = D - E*z - K*w + L*alpha + v*beta
// (remember D is a sub-view of result_null)
D->update(Teuchos::NO_TRANS, -1.0, *E, result_param, 1.0);
D->update(Teuchos::NO_TRANS, -1.0, *K, result_slack, 1.0);
D->update(Teuchos::NO_TRANS, 1.0, *L, alpha, 1.0);
D->update(Teuchos::NO_TRANS, 1.0, *nullMultiVector, beta, 1.0);
delete [] R;
return finalStatus;
}