template <typename F> GpuQmrCs<F>::GpuQmrCs (const OpenCL::StubPool& pool, const std::vector<cl::CommandQueue>& queues, const DDAParams<ftype>& ddaParams, GpuMatVec<ftype>& matVec, csize_t maxIter, OpenCL::VectorAccounting& accounting) :
GpuIterativeSolver<F> (pool, queues, ddaParams, matVec, 50000, maxIter, accounting),
varsVec (pool, 1, accounting, "vars"),
vars (varsVec.pointer ()),
tmpVec2_ (pool, queues, g (), accounting, "tmpVec2"),
tmpVec3_ (pool, queues, g (), accounting, "tmpVec3"),
tmpVec4_ (pool, queues, g (), accounting, "tmpVec4")
{
this->Avecbuffer ().setToZero (queues);
this->rvec ().setToZero (queues);
this->xvec ().setToZero (queues);
this->tmpVec1 ().setToZero (queues);
tmpVec2 ().setToZero (queues);
tmpVec3 ().setToZero (queues);
tmpVec4 ().setToZero (queues);
}
int SVD(Mat3d & F, Mat3d & U, Vec3d & Sigma, Mat3d & V, double singularValue_eps, int modifiedSVD)
{
// The code handles the following special situations:
//---------------------------------------------------------
// 1. det(V) == -1
// - multiply the first column of V by -1
//---------------------------------------------------------
// 2. An entry of Sigma is near zero
//---------------------------------------------------------
// (if modifiedSVD == 1) :
// 3. negative determinant (Tet is inverted in solid mechanics).
// - check if det(U) == -1
// - If yes, then negate the minimal element of Sigma
// and the corresponding column of U
//---------------------------------------------------------
// form F^T F and do eigendecomposition
Mat3d normalEq = trans(F) * F;
Vec3d eigenValues;
Vec3d eigenVectors[3];
eigen_sym(normalEq, eigenValues, eigenVectors);
V.set(eigenVectors[0][0], eigenVectors[1][0], eigenVectors[2][0],
eigenVectors[0][1], eigenVectors[1][1], eigenVectors[2][1],
eigenVectors[0][2], eigenVectors[1][2], eigenVectors[2][2]);
/*
printf("--- original V ---\n");
V.print();
printf("--- eigenValues ---\n");
printf("%G %G %G\n", eigenValues[0], eigenValues[1], eigenValues[2]);
*/
// Handle situation:
// 1. det(V) == -1
// - multiply the first column of V by -1
if (det(V) < 0.0)
{
// convert V into a rotation (multiply column 1 by -1)
V[0][0] *= -1.0;
V[1][0] *= -1.0;
V[2][0] *= -1.0;
}
Sigma[0] = (eigenValues[0] > 0.0) ? sqrt(eigenValues[0]) : 0.0;
Sigma[1] = (eigenValues[1] > 0.0) ? sqrt(eigenValues[1]) : 0.0;
Sigma[2] = (eigenValues[2] > 0.0) ? sqrt(eigenValues[2]) : 0.0;
//printf("--- Sigma ---\n");
//printf("%G %G %G\n", Sigma[0][0], Sigma[1][1], Sigma[2][2]);
// compute inverse of singular values
// also check if singular values are close to zero
Vec3d SigmaInverse;
SigmaInverse[0] = (Sigma[0] > singularValue_eps) ? (1.0 / Sigma[0]) : 0.0;
SigmaInverse[1] = (Sigma[1] > singularValue_eps) ? (1.0 / Sigma[1]) : 0.0;
SigmaInverse[2] = (Sigma[2] > singularValue_eps) ? (1.0 / Sigma[2]) : 0.0;
// compute U using the formula:
// U = F * V * diag(SigmaInverse)
U = F * V;
U.multiplyDiagRight(SigmaInverse);
// In theory, U is now orthonormal, U^T U = U U^T = I .. it may be a rotation or a reflection, depending on F.
// But in practice, if singular values are small or zero, it may not be orthonormal, so we need to fix it.
// Handle situation:
// 2. An entry of Sigma is near zero
// ---------------------------------------------------------
/*
printf("--- SigmaInverse ---\n");
SigmaInverse.print();
printf(" --- U ---\n");
U.print();
*/
if ((Sigma[0] < singularValue_eps) && (Sigma[1] < singularValue_eps) && (Sigma[2] < singularValue_eps))
{
// extreme case, all singular values are small, material has collapsed almost to a point
// see [Irving 04], p. 4
U.set(1.0, 0.0, 0.0,
0.0, 1.0, 0.0,
0.0, 0.0, 1.0);
}
else
{
// handle the case where two singular values are small, but the third one is not
// handle it by computing two (arbitrary) vectors orthogonal to the eigenvector for the large singular value
int done = 0;
for(int dim=0; dim<3; dim++)
{
int dimA = dim;
int dimB = (dim + 1) % 3;
int dimC = (dim + 2) % 3;
if ((Sigma[dimB] < singularValue_eps) && (Sigma[dimC] < singularValue_eps))
{
// only the column dimA can be trusted, columns dimB and dimC correspond to tiny singular values
Vec3d tmpVec1(U[0][dimA], U[1][dimA], U[2][dimA]); // column dimA
Vec3d tmpVec2;
tmpVec2 = tmpVec1.findOrthonormalVector();
Vec3d tmpVec3 = norm(cross(tmpVec1, tmpVec2));
U[0][dimB] = tmpVec2[0];
U[1][dimB] = tmpVec2[1];
U[2][dimB] = tmpVec2[2];
U[0][dimC] = tmpVec3[0];
U[1][dimC] = tmpVec3[1];
U[2][dimC] = tmpVec3[2];
if (det(U) < 0.0)
{
U[0][dimB] *= -1.0;
U[1][dimB] *= -1.0;
U[2][dimB] *= -1.0;
}
done = 1;
break; // out of for
}
}
// handle the case where one singular value is small, but the other two are not
// handle it by computing the cross product of the two eigenvectors for the two large singular values
if (!done)
{
for(int dim=0; dim<3; dim++)
{
int dimA = dim;
int dimB = (dim + 1) % 3;
int dimC = (dim + 2) % 3;
if (Sigma[dimA] < singularValue_eps)
{
// columns dimB and dimC are both good, but column dimA corresponds to a tiny singular value
Vec3d tmpVec1(U[0][dimB], U[1][dimB], U[2][dimB]); // column dimB
Vec3d tmpVec2(U[0][dimC], U[1][dimC], U[2][dimC]); // column dimC
Vec3d tmpVec3 = norm(cross(tmpVec1, tmpVec2));
U[0][dimA] = tmpVec3[0];
U[1][dimA] = tmpVec3[1];
U[2][dimA] = tmpVec3[2];
if (det(U) < 0.0)
{
U[0][dimA] *= -1.0;
U[1][dimA] *= -1.0;
U[2][dimA] *= -1.0;
}
done = 1;
break; // out of for
}
}
}
if ((!done) && (modifiedSVD == 1))
{
// Handle situation:
// 3. negative determinant (Tet is inverted in solid mechanics)
// - check if det(U) == -1
// - If yes, then negate the minimal element of Sigma
// and the corresponding column of U
double detU = det(U);
if (detU < 0.0)
{
// negative determinant
// find the smallest singular value (they are all non-negative)
int smallestSingularValueIndex = 0;
for(int dim=1; dim<3; dim++)
if (Sigma[dim] < Sigma[smallestSingularValueIndex])
smallestSingularValueIndex = dim;
// negate the smallest singular value
Sigma[smallestSingularValueIndex] *= -1.0;
U[0][smallestSingularValueIndex] *= -1.0;
U[1][smallestSingularValueIndex] *= -1.0;
U[2][smallestSingularValueIndex] *= -1.0;
}
}
}
/*
printf("U = \n");
U.print();
printf("Sigma = \n");
Sigma.print();
printf("V = \n");
V.print();
*/
return 0;
}
GcmJointTildeInfo<S_V,S_M,D_V,D_M,P_V,P_M,Q_V,Q_M>::GcmJointTildeInfo(
const GpmsaComputerModelOptions& gcmOptionsObj,
const GcmExperimentInfo<S_V,S_M,D_V,D_M,P_V,P_M>& e,
const GcmJointInfo<S_V,S_M,D_V,D_M,P_V,P_M,Q_V,Q_M>& jj)
:
m_env (jj.m_env),
m_Bmat_tilde (m_env,e.m_y_space.map(),jj.m_Bmat_rank),
m_Bmat_tilde_rank (0),
m_vu_tilde_space (m_env, "vu_tilde_", jj.m_Bmat_rank, NULL), // rr0 check
m_Lbmat (m_env,m_vu_tilde_space.map(),jj.m_Bmat_with_permut->numCols()), // rr0 check
m_Btildet_Wy_Btilde (m_vu_tilde_space.zeroVector()),
m_Btildet_Wy_Btilde_inv(m_vu_tilde_space.zeroVector()),
m_Zvec_tilde_hat_vu (m_vu_tilde_space.zeroVector()),
m_a_y_modifier_tilde (0),
m_b_y_modifier_tilde (0)
{
std::set<unsigned int> tmpSet;
tmpSet.insert(m_env.subId());
//******************************************************************************
// Tilde situation: form 'm_Bmat_tilde'
// Tilde situation: form 'm_vu_tilde_space'
// Tilde situation: form 'm_Lbmat'
//******************************************************************************
if (jj.m_Bmat_with_permut->numRowsGlobal() >= jj.m_Bmat_with_permut->numCols()) {
D_M matbU(m_env,e.m_y_space.map(),jj.m_vu_size); // same as m_Bmat
matbU = jj.m_Bmat_with_permut->svdMatU();
unsigned int buMatRank = matbU.rank(0.,1.e-8 ); // todo: should be an option
unsigned int buMatRank14 = matbU.rank(0.,1.e-14);
if (m_env.subDisplayFile()) {
*m_env.subDisplayFile() << "In GcmJointTildeInfo<S_V,S_M,D_V,D_M,P_V,P_M,Q_V,Q_M>::constructor()"
<< ": matbU.numRowsLocal() = " << matbU.numRowsLocal()
<< ", matbU.numCols() = " << matbU.numCols()
<< ", matbU.rank(0.,1.e-8) = " << buMatRank
<< ", matbU.rank(0.,1.e-14) = " << buMatRank14
<< std::endl;
}
if (m_env.checkingLevel() >= 1) {
D_M matbUcheck(jj.m_vu_space.zeroVector());
D_V vecI(e.m_y_space.zeroVector());
D_V vecJ(e.m_y_space.zeroVector());
for (unsigned int i = 0; i < matbU.numCols(); ++i) {
matbU.getColumn(i,vecI);
for (unsigned int j = i; j < matbU.numCols(); ++j) {
matbU.getColumn(j,vecJ);
matbUcheck(i,j) = scalarProduct(vecI,vecJ);
}
}
matbUcheck.setPrintHorizontally(false);
if (m_env.subDisplayFile()) {
*m_env.subDisplayFile() << "In GcmJointTildeInfo<S_V,S_M,D_V,D_M,P_V,P_M,Q_V,Q_M>::constructor()"
<< ": m_Bmat_with_permut->numRowsLocal() = " << jj.m_Bmat_with_permut->numRowsLocal()
<< ", m_Bmat_with_permut->numCols() = " << jj.m_Bmat_with_permut->numCols()
<< ", m_Bmat_rank = " << jj.m_Bmat_rank
<< ", matbU.numRowsLocal() = " << matbU.numRowsLocal()
<< ", matbU.numCols() = " << matbU.numCols()
<< ", buMatrank(0.,1.e-8) = " << buMatRank
<< ", buMatrank(0.,1.e-14) = " << buMatRank14
<< ", matbUcheck.numRowsLocal() = " << matbUcheck.numRowsLocal()
<< ", matbUcheck.numCols() = " << matbUcheck.numCols()
<< ", matbUcheck =\n" << matbUcheck
<< std::endl;
}
}
D_V vecbJ(e.m_y_space.zeroVector());
for (unsigned int j = 0; j < jj.m_Bmat_rank; ++j) {
matbU.getColumn(j,vecbJ);
m_Bmat_tilde.setColumn(j,vecbJ);
}
if (gcmOptionsObj.m_ov.m_dataOutputAllowedSet.find(m_env.subId()) != gcmOptionsObj.m_ov.m_dataOutputAllowedSet.end()) {
m_Bmat_tilde.subWriteContents("Btilde",
"Btilde1",
"m",
tmpSet);
}
if (m_env.subDisplayFile()) {
*m_env.subDisplayFile() << "In GcmJointTildeInfo<S_V,S_M,D_V,D_M,P_V,P_M,Q_V,Q_M>::constructor()"
<< ": m_Bmat_tilde computed (1)"
<< std::endl;
}
}
else {
D_M Bmat_t(m_env,jj.m_vu_space.map(),e.m_paper_n_y); // same as m_Bmat^T
Bmat_t.fillWithTranspose(0,0,*jj.m_Bmat_with_permut,true,true);
D_M matbV(e.m_y_space.zeroVector());
matbV = Bmat_t.svdMatV();
unsigned int bvMatRank = matbV.rank(0.,1.e-8); // todo: should be an option
unsigned int bvMatRank14 = matbV.rank(0.,1.e-14);
if (m_env.subDisplayFile()) {
*m_env.subDisplayFile() << "In GcmJointTildeInfo<S_V,S_M,D_V,D_M,P_V,P_M,Q_V,Q_M>::constructor()"
<< ": matbV.numRowsLocal() = " << matbV.numRowsLocal()
<< ", matbV.numCols() = " << matbV.numCols()
<< ", matbV.rank(0.,1.e-8) = " << bvMatRank
<< ", matbV.rank(0.,1.e-14) = " << bvMatRank14
<< std::endl;
}
if (m_env.checkingLevel() >= 1) {
D_M matbVcheck(e.m_y_space.zeroVector());
D_V vecI(e.m_y_space.zeroVector());
D_V vecJ(e.m_y_space.zeroVector());
for (unsigned int i = 0; i < matbV.numCols(); ++i) {
matbV.getColumn(i,vecI);
for (unsigned int j = i; j < matbV.numCols(); ++j) {
matbV.getColumn(j,vecJ);
matbVcheck(i,j) = scalarProduct(vecI,vecJ);
}
}
matbVcheck.setPrintHorizontally(false);
if (m_env.subDisplayFile()) {
*m_env.subDisplayFile() << "In GcmJointTildeInfo<S_V,S_M,D_V,D_M,P_V,P_M,Q_V,Q_M>::constructor()"
<< ": m_Bmat_with_permut->numRowsLocal() = " << jj.m_Bmat_with_permut->numRowsLocal()
<< ", m_Bmat_with_permut->numCols() = " << jj.m_Bmat_with_permut->numCols()
<< ", m_Bmat_rank = " << jj.m_Bmat_rank
<< ", matbV.numRowsLocal() = " << matbV.numRowsLocal()
<< ", matbV.numCols() = " << matbV.numCols()
<< ", bvMatrank(0.,1.e-8) = " << bvMatRank
<< ", bvMatrank(0.,1.e-14) = " << bvMatRank14
<< ", matbVcheck.numRowsLocal() = " << matbVcheck.numRowsLocal()
<< ", matbVcheck.numCols() = " << matbVcheck.numCols()
<< ", matbVcheck =\n" << matbVcheck
<< std::endl;
}
}
D_V vecbJ(e.m_y_space.zeroVector());
for (unsigned int j = 0; j < jj.m_Bmat_rank; ++j) {
matbV.getColumn(j,vecbJ);
m_Bmat_tilde.setColumn(j,vecbJ);
}
if (gcmOptionsObj.m_ov.m_dataOutputAllowedSet.find(m_env.subId()) != gcmOptionsObj.m_ov.m_dataOutputAllowedSet.end()) {
m_Bmat_tilde.subWriteContents("Btilde",
"Btilde2",
"m",
tmpSet);
}
if (m_env.subDisplayFile()) {
*m_env.subDisplayFile() << "In GcmJointTildeInfo<S_V,S_M,D_V,D_M,P_V,P_M,Q_V,Q_M>::constructor()"
<< ": m_Bmat_tilde computed (2)"
<< std::endl;
}
}
if (m_env.subDisplayFile()) {
*m_env.subDisplayFile() << "In GcmJointTildeInfo<S_V,S_M,D_V,D_M,P_V,P_M,Q_V,Q_M>::constructor()"
<< ": finished forming 'm_Bmat_tilde'"
<< ", m_Bmat_tilde.numRowsLocal() = " << m_Bmat_tilde.numRowsLocal()
<< ", m_Bmat_tilde.numCols() = " << m_Bmat_tilde.numCols()
<< std::endl;
}
m_Bmat_tilde.svdSolve(*jj.m_Bmat_with_permut,m_Lbmat);
if (gcmOptionsObj.m_ov.m_dataOutputAllowedSet.find(m_env.subId()) != gcmOptionsObj.m_ov.m_dataOutputAllowedSet.end()) {
m_Lbmat.subWriteContents("Lbmat",
"Lbmat",
"m",
tmpSet);
}
if (m_env.subDisplayFile()) {
*m_env.subDisplayFile() << "In GcmJointTildeInfo<S_V,S_M,D_V,D_M,P_V,P_M,Q_V,Q_M>::constructor()"
<< ": m_Lbmat_tilde computed"
<< std::endl;
}
//********************************************************************************
// Form 'Btilde^T' matrix
//********************************************************************************
D_M Btildet(m_env,m_vu_tilde_space.map(),e.m_paper_n_y);
Btildet.fillWithTranspose(0,0,m_Bmat_tilde,true,true);
if (m_env.checkingLevel() >= 1) {
// Check transpose operation
D_M Btildett(m_env,e.m_y_space.map(),m_vu_tilde_space.dimGlobal());
Btildett.fillWithTranspose(0,0,Btildet,true,true);
Btildett -= m_Bmat_tilde;
double btDiffNorm = Btildett.normFrob();
if (m_env.subDisplayFile()) {
*m_env.subDisplayFile() << "In GcmJointTildeInfo<S_V,S_M,D_V,D_M,P_V,P_M,Q_V,Q_M>::constructor()"
<< ": ||Btildett - Btilde||_2 = " << btDiffNorm
<< std::endl;
}
}
//********************************************************************************
// Compute 'Btilde' rank
//********************************************************************************
double bTildeRank14 = 0.;
if (m_Bmat_tilde.numRowsGlobal() >= m_Bmat_tilde.numCols()) {
m_Bmat_tilde_rank = m_Bmat_tilde.rank(0.,1.e-8 ); // todo: should be an option
bTildeRank14 = m_Bmat_tilde.rank(0.,1.e-14);
}
else {
m_Bmat_tilde_rank = Btildet.rank(0.,1.e-8 ); // todo: should be an option
bTildeRank14 = Btildet.rank(0.,1.e-14);
}
if (m_env.subDisplayFile()) {
*m_env.subDisplayFile() << "In GcmJointTildeInfo<S_V,S_M,D_V,D_M,P_V,P_M,Q_V,Q_M>::constructor()"
<< ": m_Bmat_tilde.numRowsLocal() = " << m_Bmat_tilde.numRowsLocal()
<< ", m_Bmat_tilde.numCols() = " << m_Bmat_tilde.numCols()
<< ", m_Bmat_tilde.rank(0.,1.e-8) = " << m_Bmat_tilde_rank
<< ", m_Bmat_tilde.rank(0.,1.e-14) = " << bTildeRank14
<< std::endl;
}
queso_require_equal_to_msg(m_Bmat_tilde_rank, std::min(m_Bmat_tilde.numRowsGlobal(),m_Bmat_tilde.numCols()), "'m_Bmat_tilde' does not have a proper rank");
//******************************************************************************
// Tilde situation: compute 'Btilde^T W_y Btilde' matrix, and its inverse
//******************************************************************************
m_Btildet_Wy_Btilde = Btildet * (*e.m_Wy * m_Bmat_tilde); // todo: add 1.e-4 to diagonal
if (m_env.subDisplayFile()) {
*m_env.subDisplayFile() << "In GcmJointTildeInfo<S_V,S_M,D_V,D_M,P_V,P_M,Q_V,Q_M>::constructor()"
<< ": finished computing 'm_Btildet_Wy_Btilde'"
<< std::endl;
}
if (gcmOptionsObj.m_ov.m_dataOutputAllowedSet.find(m_env.subId()) != gcmOptionsObj.m_ov.m_dataOutputAllowedSet.end()) {
m_Btildet_Wy_Btilde.subWriteContents("Btildet_Wy_Btilde",
"Btildet_Wy_Btilde",
"m",
tmpSet);
}
if (m_env.subDisplayFile()) {
*m_env.subDisplayFile() << "In GcmJointTildeInfo<S_V,S_M,D_V,D_M,P_V,P_M,Q_V,Q_M>::constructor()"
<< ": m_Btildet_Wy_Btilde computed"
<< std::endl;
}
double btildetWyBtildeLnDeterminant = m_Btildet_Wy_Btilde.lnDeterminant();
unsigned int btildetWyBtildeRank = m_Btildet_Wy_Btilde.rank(0.,1.e-8 ); // todo: should be an option
unsigned int btildetWyBtildeRank14 = m_Btildet_Wy_Btilde.rank(0.,1.e-14);
if (m_env.subDisplayFile()) {
*m_env.subDisplayFile() << "In GcmJointTildeInfo<S_V,S_M,D_V,D_M,P_V,P_M,Q_V,Q_M>::constructor()"
<< ": m_Btildet_Wy_Btilde.numRowsLocal() = " << m_Btildet_Wy_Btilde.numRowsLocal()
<< ", m_Btildet_Wy_Btilde.numCols() = " << m_Btildet_Wy_Btilde.numCols()
<< ", m_Btildet_Wy_Btilde.lnDeterminant() = " << btildetWyBtildeLnDeterminant
<< ": m_Btildet_Wy_Btilde.rank(0.,1.e-8) = " << btildetWyBtildeRank
<< ": m_Btildet_Wy_Btilde.rank(0.,1.e-14) = " << btildetWyBtildeRank14
<< std::endl;
}
m_Btildet_Wy_Btilde_inv = m_Btildet_Wy_Btilde.inverse(); // todo: add 1.e-6 to diagonal
if (m_env.subDisplayFile()) {
*m_env.subDisplayFile() << "In GcmJointTildeInfo<S_V,S_M,D_V,D_M,P_V,P_M,Q_V,Q_M>::constructor()"
<< ": finished computing 'm_Btildet_Wy_Btilde_inv'"
<< ", m_Btildet_Wy_Btilde_inv.lnDeterminant() = " << m_Btildet_Wy_Btilde_inv.lnDeterminant()
<< std::endl;
}
if (gcmOptionsObj.m_ov.m_dataOutputAllowedSet.find(m_env.subId()) != gcmOptionsObj.m_ov.m_dataOutputAllowedSet.end()) {
m_Btildet_Wy_Btilde_inv.subWriteContents("Btildet_Wy_Btilde_inv",
"Btildet_Wy_Btilde_inv",
"m",
tmpSet);
}
if (m_env.subDisplayFile()) {
*m_env.subDisplayFile() << "In GcmJointTildeInfo<S_V,S_M,D_V,D_M,P_V,P_M,Q_V,Q_M>::constructor()"
<< ": m_Btildet_Wy_Btilde_inv computed"
<< std::endl;
}
double btildetWyBtildeInvLnDeterminant = m_Btildet_Wy_Btilde_inv.lnDeterminant();
unsigned int btildetWyBtildeInvRank = m_Btildet_Wy_Btilde_inv.rank(0.,1.e-8 ); // todo: should be an option
unsigned int btildetWyBtildeInvRank14 = m_Btildet_Wy_Btilde_inv.rank(0.,1.e-14);
if (m_env.subDisplayFile()) {
*m_env.subDisplayFile() << "In GcmJointTildeInfo<S_V,S_M,D_V,D_M,P_V,P_M,Q_V,Q_M>::constructor()"
<< ": m_Btildet_Wy_Btilde_inv.numRowsLocal() = " << m_Btildet_Wy_Btilde_inv.numRowsLocal()
<< ", m_Btildet_Wy_Btilde_inv.numCols() = " << m_Btildet_Wy_Btilde_inv.numCols()
<< ": m_Btildet_Wy_Btilde_inv.lnDeterminant() = " << btildetWyBtildeInvLnDeterminant
<< ": m_Btildet_Wy_Btilde_inv.rank(0.,1.e-8) = " << btildetWyBtildeInvRank
<< ": m_Btildet_Wy_Btilde_inv.rank(0.,1.e-14) = " << btildetWyBtildeInvRank14
<< std::endl;
}
//********************************************************************************
// Compute 'tilde' exponent modifiers
//********************************************************************************
m_a_y_modifier_tilde = ((double) (e.m_paper_n_y - m_Bmat_tilde_rank)) / 2.;
if (m_env.subDisplayFile()) {
*m_env.subDisplayFile() << "In GcmJointTildeInfo<S_V,S_M,D_V,D_M,P_V,P_M,Q_V,Q_M>::constructor()"
<< ": m_a_y_modifier_tilde = " << m_a_y_modifier_tilde
<< std::endl;
}
D_V yVec_transformed(e.m_experimentStorage.yVec_transformed());
if (m_env.subDisplayFile()) {
*m_env.subDisplayFile() << "In GcmJointTildeInfo<S_V,S_M,D_V,D_M,P_V,P_M,Q_V,Q_M>::constructor()"
<< ": m_Zvec_tilde_hat_vu.sizeLocal() = " << m_Zvec_tilde_hat_vu.sizeLocal()
<< ", m_Btildet_Wy_Btilde_inv.numRowsLocal() = " << m_Btildet_Wy_Btilde_inv.numRowsLocal()
<< ", m_Btildet_Wy_Btilde_inv.numCols() = " << m_Btildet_Wy_Btilde_inv.numCols()
<< ", Btildet.numRowsLocal() = " << Btildet.numRowsLocal()
<< ", Btildet.numCols() = " << Btildet.numCols()
<< ", m_Wy->numRowsLocal() = " << e.m_Wy->numRowsLocal()
<< ", m_Wy->numCols() = " << e.m_Wy->numCols()
<< ", yVec_transformed.sizeLocal() = " << yVec_transformed.sizeLocal()
<< std::endl;
}
m_Zvec_tilde_hat_vu = m_Btildet_Wy_Btilde_inv * (Btildet * (*e.m_Wy * yVec_transformed));
D_V tmpVec2(yVec_transformed - (m_Bmat_tilde * m_Zvec_tilde_hat_vu));
tmpVec2 = *e.m_Wy * tmpVec2;
m_b_y_modifier_tilde = scalarProduct(yVec_transformed,tmpVec2) / 2.;
if (m_env.subDisplayFile()) {
*m_env.subDisplayFile() << "In GcmJointTildeInfo<S_V,S_M,D_V,D_M,P_V,P_M,Q_V,Q_M>::constructor()"
<< ": m_b_y_modifier_tilde = " << m_b_y_modifier_tilde
<< std::endl;
}
if (m_env.subDisplayFile()) {
*m_env.subDisplayFile() << "In GcmJointTildeInfo<S_V,S_M,D_V,D_M,P_V,P_M,Q_V,Q_M>::constructor()"
<< ": finished computing 'tilde' exponent modifiers"
<< std::endl;
}
}
int ReducedStVKCubatureForceModel::ModifiedSVD(Mat3d & F, Mat3d & U, Vec3d & Fhat, Mat3d & V) const
{
// The code handles the following necessary special situations (see the code below) :
//---------------------------------------------------------
// 1. det(V) == -1
// - simply multiply a column of V by -1
//---------------------------------------------------------
// 2. An entry of Fhat is near zero
//---------------------------------------------------------
// 3. Tet is inverted.
// - check if det(U) == -1
// - If yes, then negate the minimal element of Fhat
// and the corresponding column of U
//---------------------------------------------------------
double modifiedSVD_singularValue_eps = 1e-8;
// form F^T F and do eigendecomposition
Mat3d normalEq = trans(F) * F;
Vec3d eigenValues;
Vec3d eigenVectors[3];
// note that normalEq is changed after calling eigen_sym
eigen_sym(normalEq, eigenValues, eigenVectors);
V.set(eigenVectors[0][0], eigenVectors[1][0], eigenVectors[2][0],
eigenVectors[0][1], eigenVectors[1][1], eigenVectors[2][1],
eigenVectors[0][2], eigenVectors[1][2], eigenVectors[2][2]);
/*
printf("--- original V ---\n");
V.print();
printf("--- eigenValues ---\n");
printf("%G %G %G\n", eigenValues[0], eigenValues[1], eigenValues[2]);
*/
// Handle situation:
// 1. det(V) == -1
// - simply multiply a column of V by -1
if (det(V) < 0.0)
{
// convert V into a rotation (multiply column 1 by -1)
V[0][0] *= -1.0;
V[1][0] *= -1.0;
V[2][0] *= -1.0;
}
Fhat[0] = (eigenValues[0] > 0.0) ? sqrt(eigenValues[0]) : 0.0;
Fhat[1] = (eigenValues[1] > 0.0) ? sqrt(eigenValues[1]) : 0.0;
Fhat[2] = (eigenValues[2] > 0.0) ? sqrt(eigenValues[2]) : 0.0;
//printf("--- Fhat ---\n");
//printf("%G %G %G\n", Fhat[0][0], Fhat[1][1], Fhat[2][2]);
// compute inverse of singular values
// also check if singular values are close to zero
Vec3d FhatInverse;
FhatInverse[0] = (Fhat[0] > modifiedSVD_singularValue_eps) ? (1.0 / Fhat[0]) : 0.0;
FhatInverse[1] = (Fhat[1] > modifiedSVD_singularValue_eps) ? (1.0 / Fhat[1]) : 0.0;
FhatInverse[2] = (Fhat[2] > modifiedSVD_singularValue_eps) ? (1.0 / Fhat[2]) : 0.0;
// compute U using the formula:
// U = F * V * diag(FhatInverse)
U = F * V;
U.multiplyDiagRight(FhatInverse);
// In theory, U is now orthonormal, U^T U = U U^T = I .. it may be a rotation or a reflection, depending on F.
// But in practice, if singular values are small or zero, it may not be orthonormal, so we need to fix it.
// Handle situation:
// 2. An entry of Fhat is near zero
// ---------------------------------------------------------
/*
printf("--- FhatInverse ---\n");
FhatInverse.print();
printf(" --- U ---\n");
U.print();
*/
if ((Fhat[0] < modifiedSVD_singularValue_eps) && (Fhat[1] < modifiedSVD_singularValue_eps) && (Fhat[2] < modifiedSVD_singularValue_eps))
{
// extreme case, material has collapsed almost to a point
// see [Irving 04], p. 4
U.set(1.0, 0.0, 0.0,
0.0, 1.0, 0.0,
0.0, 0.0, 1.0);
}
else
{
int done = 0;
for(int dim=0; dim<3; dim++)
{
int dimA = dim;
int dimB = (dim + 1) % 3;
int dimC = (dim + 2) % 3;
if ((Fhat[dimB] < modifiedSVD_singularValue_eps) && (Fhat[dimC] < modifiedSVD_singularValue_eps))
{
// only the column dimA can be trusted, columns dimB and dimC correspond to tiny singular values
Vec3d tmpVec1(U[0][dimA], U[1][dimA], U[2][dimA]); // column dimA
Vec3d tmpVec2;
FindOrthonormalVector(tmpVec1, tmpVec2);
Vec3d tmpVec3 = norm(cross(tmpVec1, tmpVec2));
U[0][dimB] = tmpVec2[0];
U[1][dimB] = tmpVec2[1];
U[2][dimB] = tmpVec2[2];
U[0][dimC] = tmpVec3[0];
U[1][dimC] = tmpVec3[1];
U[2][dimC] = tmpVec3[2];
if (det(U) < 0.0)
{
U[0][dimB] *= -1.0;
U[1][dimB] *= -1.0;
U[2][dimB] *= -1.0;
}
done = 1;
break; // out of for
}
}
if (!done)
{
for(int dim=0; dim<3; dim++)
{
int dimA = dim;
int dimB = (dim + 1) % 3;
int dimC = (dim + 2) % 3;
if (Fhat[dimA] < modifiedSVD_singularValue_eps)
{
// columns dimB and dimC are both good, but column dimA corresponds to a tiny singular value
Vec3d tmpVec1(U[0][dimB], U[1][dimB], U[2][dimB]); // column dimB
Vec3d tmpVec2(U[0][dimC], U[1][dimC], U[2][dimC]); // column dimC
Vec3d tmpVec3 = norm(cross(tmpVec1, tmpVec2));
U[0][dimA] = tmpVec3[0];
U[1][dimA] = tmpVec3[1];
U[2][dimA] = tmpVec3[2];
if (det(U) < 0.0)
{
U[0][dimA] *= -1.0;
U[1][dimA] *= -1.0;
U[2][dimA] *= -1.0;
}
done = 1;
break; // out of for
}
}
}
if (!done)
{
// Handle situation:
// 3. Tet is inverted.
// - check if det(U) == -1
// - If yes, then negate the minimal element of Fhat
// and the corresponding column of U
double detU = det(U);
if (detU < 0.0)
{
// tet is inverted
// find smallest singular value (they are all non-negative)
int smallestSingularValueIndex = 0;
for(int dim=1; dim<3; dim++)
if (Fhat[dim] < Fhat[smallestSingularValueIndex])
smallestSingularValueIndex = dim;
// negate smallest singular value
Fhat[smallestSingularValueIndex] *= -1.0;
U[0][smallestSingularValueIndex] *= -1.0;
U[1][smallestSingularValueIndex] *= -1.0;
U[2][smallestSingularValueIndex] *= -1.0;
}
}
}
/*
printf("U = \n");
U.print();
printf("Fhat = \n");
Fhat.print();
printf("V = \n");
V.print();
*/
return 0;
}