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LinearSolver.cpp
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Sat, Aug 24, 21:37

LinearSolver.cpp
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// Header file for this class
#include "LinearSolver.h"
#include <sstream>
using std::stringstream;
namespace ATC {
const double kPenalty = 1.0e4;
const double kTol = 1.0e-8;
const int kMaxDirect = 1000;
// ====================================================================
// LinearSolver
// ====================================================================
LinearSolver::LinearSolver(
const SPAR_MAT & A,
const BC_SET & bcs,
const int solverType,
const int constraintHandlerType,
bool parallel
)
: solverType_(solverType),
constraintHandlerType_(constraintHandlerType),
nVariables_(0),
initialized_(false),
initializedMatrix_(false),
initializedInverse_(false),
matrixModified_(false),
allowReinitialization_(false),
homogeneousBCs_(false),
bcs_(&bcs),
rhs_(NULL),
rhsDense_(),
b_(NULL),
matrix_(A),
matrixDense_(),
matrixFreeFree_(), matrixFreeFixed_(),matrixInverse_(),
penalty_(0),maxIterations_(0), maxRestarts_(0), tol_(0),
parallel_(parallel)
{
// deep copy
matrixCopy_ = A;
matrixSparse_ = &matrixCopy_;
setup();
}
LinearSolver::LinearSolver(
const SPAR_MAT & A,
const int solverType,
bool parallel
)
: solverType_(solverType),
constraintHandlerType_(NO_CONSTRAINTS),
nVariables_(0),
initialized_(false),
initializedMatrix_(true),
initializedInverse_(false),
matrixModified_(false),
allowReinitialization_(false),
homogeneousBCs_(false),
bcs_(NULL), // null implies no contraints will be added later
rhs_(NULL),
rhsDense_(), b_(NULL),
matrix_(A),
matrixDense_(),
matrixFreeFree_(), matrixFreeFixed_(),matrixInverse_(),
penalty_(0),maxIterations_(0), maxRestarts_(0), tol_(0),
parallel_(parallel)
{
// shallow copy
matrixSparse_ = &A;
setup();
}
// --------------------------------------------------------------------
// Setup
// --------------------------------------------------------------------
void LinearSolver::setup(void)
{
penalty_ = kPenalty; // relative to matrix diagonal
tol_ = kTol;
nVariables_ = matrix_.nRows();
maxIterations_=2*nVariables_;
maxRestarts_=nVariables_;
// switch method based on size
if (solverType_ < 0) {
if (nVariables_ > kMaxDirect ) {
solverType_ = ITERATIVE_SOLVE_SYMMETRIC;
constraintHandlerType_ = PENALIZE_CONSTRAINTS;
}
else {
solverType_ = DIRECT_SOLVE;
}
}
if (constraintHandlerType_ < 0) {
constraintHandlerType_ = PENALIZE_CONSTRAINTS;
if (solverType_ == DIRECT_SOLVE) constraintHandlerType_ = CONDENSE_CONSTRAINTS;
}
if ( solverType_ == DIRECT_SOLVE && constraintHandlerType_ == CONDENSE_CONSTRAINTS ) allowReinitialization_ = true;
if ( solverType_ == ITERATIVE_SOLVE_SYMMETRIC && constraintHandlerType_ == CONDENSE_CONSTRAINTS )
throw ATC_Error("LinearSolver::unimplemented method");
}
// --------------------------------------------------------------------
// Initialize
// --------------------------------------------------------------------
void LinearSolver::allow_reinitialization(void)
{
if (constraintHandlerType_ == PENALIZE_CONSTRAINTS) {
if (matrixModified_ ) throw ATC_Error("LinearSolver: can't allow reinitialization after matrix has been modified");
matrixOriginal_ = *matrixSparse_;
}
allowReinitialization_ = true;
}
void LinearSolver::initialize(const BC_SET * bcs)
{
if (bcs) {
if (! allowReinitialization_ ) throw ATC_Error("LinearSolver: reinitialization not allowed");
//if (! bcs_ ) throw ATC_Error("LinearSolver: adding constraints after constructing without constraints is not allowed");
// shallow --> deep copy
if (! bcs_ ) { // constraintHandlerType_ == NO_CONSTRAINTS
if (matrixModified_) {
throw ATC_Error("LinearSolver: adding constraints after constructing without constraints is not allowed if matrix has been modified");
}
else {
matrixCopy_ = *matrixSparse_;
matrixSparse_ = &matrixCopy_;
constraintHandlerType_ = -1;
setup();
}
}
bcs_ = bcs;
initializedMatrix_ = false;
initializedInverse_ = false;
if (matrixModified_) {
matrixCopy_ = matrixOriginal_;
matrixSparse_ = &matrixCopy_;
}
}
initialize_matrix();
initialize_inverse();
initialize_rhs();
initialized_ = true;
}
// --------------------------------------------------------------------
// initialize_matrix
// --------------------------------------------------------------------
void LinearSolver::initialize_matrix(void)
{
if ( initializedMatrix_ ) return;
if (constraintHandlerType_ == PENALIZE_CONSTRAINTS) {
add_matrix_penalty();
}
else if (constraintHandlerType_ == CONDENSE_CONSTRAINTS) {
partition_matrix();
}
initializedMatrix_ = true;
}
// --------------------------------------------------------------------
// initialize_inverse
// --------------------------------------------------------------------
void LinearSolver::initialize_inverse(void)
{
if ( initializedInverse_ ) return;
if (solverType_ == ITERATIVE_SOLVE_SYMMETRIC
|| solverType_ == ITERATIVE_SOLVE ) {
matrixDiagonal_ = matrixSparse_->diag(); // preconditioner
}
else { // DIRECT_SOLVE
if (constraintHandlerType_ == CONDENSE_CONSTRAINTS) {
if( num_unknowns() > 0 ) {
matrixInverse_ = inv(matrixFreeFree_);
}
}
else { // NO_CONSTRAINTS || PENALIZE_CONSTRAINTS
matrixDense_ = matrixSparse_->dense_copy(); // need dense for lapack
matrixInverse_ = inv(matrixDense_);
}
}
initializedInverse_ = true;
}
// --------------------------------------------------------------------
// initialize_rhs
// --------------------------------------------------------------------
void LinearSolver::initialize_rhs(void)
{
if (! rhs_ ) return;
if (! bcs_ ) {
b_ = rhs_;
return;
}
if (constraintHandlerType_ == PENALIZE_CONSTRAINTS) {
add_rhs_penalty();
}
else if (constraintHandlerType_ == CONDENSE_CONSTRAINTS) {
add_rhs_influence();
}
}
// --------------------------------------------------------------------
// add matrix penalty
// - change matrix for Dirichlet conditions: add penalty
// --------------------------------------------------------------------
void LinearSolver::add_matrix_penalty(void)
{
SPAR_MAT & A = matrixCopy_;
penalty_ *= (A.diag()).maxabs();
BC_SET::const_iterator itr;
for (itr = bcs_->begin(); itr != bcs_->end(); itr++) {
int i = itr->first;
A.add(i,i,penalty_); // modifies matrix
}
A.compress();
matrixModified_ = true;
}
// --------------------------------------------------------------------
// partition matrix
// - partition matrix based on Dirichlet constraints
// --------------------------------------------------------------------
void LinearSolver::partition_matrix(void)
{
fixedSet_.clear();
BC_SET::const_iterator itr;
for (itr = bcs_->begin(); itr != bcs_->end(); itr++) {
int i = itr->first;
fixedSet_.insert(i);
}
freeSet_.clear();
freeGlobalToCondensedMap_.clear();
int j = 0; // local index
for (int i = 0; i < nVariables_; i++) {
if (fixedSet_.find(i) == fixedSet_.end() ) {
freeSet_.insert(i);
freeGlobalToCondensedMap_[i] = j++;
}
}
if (matrixDense_.nRows() == 0) matrixDense_ =matrixSparse_->dense_copy();
DENS_MAT & K = matrixDense_;
K.row_partition(freeSet_,matrixFreeFree_,matrixFreeFixed_);
}
// --------------------------------------------------------------------
// add_rhs_penalty
// --------------------------------------------------------------------
void LinearSolver::add_rhs_penalty()
{
// deep copy
VECTOR & b = rhsDense_;
const VECTOR & r = *rhs_;
int size = r.nRows();
b.reset(size);
for (int i = 0; i < size; i++) {
b(i) = r(i);
}
if ( ! homogeneousBCs_ ){
BC_SET::const_iterator itr;
for (itr = bcs_->begin(); itr != bcs_->end(); itr++) {
int i = itr->first;
double v = itr->second;
b(i) += penalty_ * v;
}
}
b_ = &rhsDense_;
}
// --------------------------------------------------------------------
// add_rhs_influence
// --------------------------------------------------------------------
void LinearSolver::add_rhs_influence()
{
if (! initializedMatrix_ ) partition_matrix();
// rhs = rhs + K_free,fixed * x_fixed
int nbcs = bcs_->size();
if (nbcs == 0) { // no bcs to handle
b_ = rhs_;
}
else {
DENS_VEC & b = rhsDense_;
if ( ! homogeneousBCs_ ){
DENS_VEC xFixed(nbcs);
BC_SET::const_iterator itr;
int i = 0;
for (itr = bcs_->begin(); itr != bcs_->end(); itr++,i++) {
double v = itr->second;
xFixed(i,0) = -v;
}
b = matrixFreeFixed_*xFixed; // matrix and bcs have same ordering
}
else {
b.reset(matrixFreeFixed_.nRows());
}
const VECTOR & r = *rhs_;
set<int>::const_iterator iter;
int i = 0;
for (iter = freeSet_.begin(); iter != freeSet_.end(); iter++,i++) {
b(i) += r(*iter);
}
b_ = &rhsDense_;
}
}
// --------------------------------------------------------------------
// set fixed values
// - {x_i = y_i}
// --------------------------------------------------------------------
void LinearSolver::set_fixed_values(VECTOR & X)
{
BC_SET::const_iterator itr;
for (itr = bcs_->begin(); itr != bcs_->end(); itr++) {
int i = itr->first;
double v = 0;
if ( ! homogeneousBCs_ ) v = itr->second;
X(i) = v;
}
}
// --------------------------------------------------------------------
// Eigensystem
// --------------------------------------------------------------------
// calls lapack
void LinearSolver::eigen_system( DENS_MAT & eigenvalues, DENS_MAT & eigenvectors, const DENS_MAT * M) /* const */
{
initialize_matrix(); // no inverse needed
const DENS_MAT * Kp = NULL;
const DENS_MAT * Mp =M;
DENS_MAT MM;
DENS_MAT KM;
if (constraintHandlerType_ == CONDENSE_CONSTRAINTS) {
Kp = &matrixFreeFree_;
if (M) {
DENS_MAT MfreeFixed; // not used
M->row_partition(freeSet_,MM,MfreeFixed);
Mp = &MM;
}
}
else {
if (matrixDense_.nRows() == 0) matrixDense_ =matrixSparse_->dense_copy();
Kp = &matrixDense_;
}
if (!M) {
MM.identity(Kp->nRows());
Mp = &MM;
}
DENS_MAT eVecs, eVals;
eVecs = eigensystem(*Kp,*Mp,eVals);
eigenvalues.reset(nVariables_,1);
eigenvectors.reset(nVariables_,nVariables_);
set<int>::const_iterator itr;
for (int i = 0; i < Kp->nRows(); i++) { // ordering is by energy not node
eigenvalues(i,0) = eVals(i,0);
int j = 0;
for (itr = freeSet_.begin(); itr != freeSet_.end(); itr++,j++) {
int jj = *itr;
eigenvectors(jj,i) = eVecs(j,i); // transpose
}
}
}
// --------------------------------------------------------------------
// solve
// - solves A x = b
// - if a "b" is provided it is used as the new rhs
// --------------------------------------------------------------------
bool LinearSolver::solve(VECTOR & x, const VECTOR & b)
{
SPAR_MAT * A = NULL;
rhs_ = &b;
initialized_ = false;
initialize();
if (num_unknowns() == 0) {
set_fixed_values(x);
return true;
}
const VECTOR & r = *b_;
if (solverType_ == ITERATIVE_SOLVE_SYMMETRIC) {
if (parallel_) {
A = new PAR_SPAR_MAT(LammpsInterface::instance()->world(), *matrixSparse_);
}
else {
A = new SPAR_MAT(*matrixSparse_);
}
DIAG_MAT & PC = matrixDiagonal_;
int niter = maxIterations_;
double tol = tol_;
int convergence = CG(*A, x, r, PC, niter, tol);// CG changes niter, tol
if (convergence>0) {
stringstream ss;
ss << "CG solve did not converge,";
ss << " iterations: " << niter;
ss << " residual: " << tol;
throw ATC_Error(ss.str());
}
}
else if (solverType_ == ITERATIVE_SOLVE) {
if (parallel_) {
A = new PAR_SPAR_MAT(LammpsInterface::instance()->world(), *matrixSparse_);
}
else {
A = new SPAR_MAT(*matrixSparse_);
}
const DIAG_MAT & PC = matrixDiagonal_;
int iterations = maxIterations_;
int restarts = maxRestarts_;
double tol = tol_;
DENS_MAT H(maxRestarts_+1, maxRestarts_);
DENS_VEC xx(nVariables_);
DENS_VEC bb;
bb = b;
int convergence = GMRES(*A, xx, bb, PC, H, restarts, iterations, tol);
if (convergence>0) {
stringstream ss;
ss << "GMRES greens_function solve did not converge,";
ss << " iterations: " << iterations;
ss << " residual: " << tol;
throw ATC_Error(ss.str());
}
x.copy(xx.ptr(),xx.nRows());
}
else { // DIRECT_SOLVE
const DENS_MAT & invA = matrixInverse_;
if (constraintHandlerType_ == CONDENSE_CONSTRAINTS) {
DENS_MAT xx = invA*r;
int i = 0;
set<int>::const_iterator itr;
for (itr = freeSet_.begin(); itr != freeSet_.end(); itr++,i++) {
int ii = *itr;
x(ii) = xx(i,0);
}
set_fixed_values(x);
}
else {
DENS_VEC xx = invA*r;
for (int i = 0; i < xx.nRows(); i++) {
x(i) = xx(i);
}
}
}
delete A;
return true;
}
// --------------------------------------------------------------------
// greens function
// - returns the solution to a Kronecker delta rhs b = {0 0 .. 1 .. 0 0}
// and with homogeneous constraints {x_i = 0}
// --------------------------------------------------------------------
void LinearSolver::greens_function(int I, VECTOR & G_I)
{
SPAR_MAT * A = NULL;
initialize_matrix();
initialize_inverse();
G_I.reset(nVariables_);
VECTOR & x = G_I;
if (solverType_ == ITERATIVE_SOLVE_SYMMETRIC) {
DENS_VEC b(nVariables_); b = 0.0; b(I) = 1.0;
if (parallel_) {
A = new PAR_SPAR_MAT(LammpsInterface::instance()->world(), *matrixSparse_);
}
else {
A = new SPAR_MAT(*matrixSparse_);
}
const DIAG_MAT & PC = matrixDiagonal_;
int niter = maxIterations_;
double tol = tol_;
int convergence = CG(*A, x, b, PC, niter, tol);
if (convergence>0) {
stringstream ss;
ss << "CG greens_function solve did not converge,";
ss << " iterations: " << niter;
ss << " residual: " << tol;
throw ATC_Error(ss.str());
}
}
else if (solverType_ == ITERATIVE_SOLVE) {
DENS_VEC b(nVariables_); b = 0.0; b(I) = 1.0;
// VECTOR & bb = b;
if (parallel_) {
A = new PAR_SPAR_MAT(LammpsInterface::instance()->world(), *matrixSparse_);
}
else {
A = new SPAR_MAT(*matrixSparse_);
}
// const DENS_MAT A = matrixSparse_->dense_copy();
const DIAG_MAT & PC = matrixDiagonal_;
int iterations = maxIterations_;
int restarts = maxRestarts_;
double tol = tol_;
DENS_MAT H(maxRestarts_+1, maxRestarts_);
DENS_VEC xx(nVariables_);
int convergence = GMRES(*A, xx, b, PC, H, restarts, iterations, tol);
if (convergence>0) {
stringstream ss;
ss << "GMRES greens_function solve did not converge,";
ss << " iterations: " << iterations;
ss << " residual: " << tol;
throw ATC_Error(ss.str());
}
x.copy(xx.ptr(),xx.nRows());
}
else {
const DENS_MAT & invA = matrixInverse_;
if (constraintHandlerType_ == CONDENSE_CONSTRAINTS) {
set<int>::const_iterator itr;
for (itr = fixedSet_.begin(); itr != fixedSet_.end(); itr++) {
int ii = *itr;
x(ii) = 0;
}
itr = freeSet_.find(I);
if (itr !=freeSet_.end() ) {
int j = freeGlobalToCondensedMap_[I];
int i = 0;
for (itr = freeSet_.begin(); itr != freeSet_.end(); itr++,i++) {
int ii = *itr;
x(ii) = invA(j,i);
}
}
}
else {
for (int i = 0; i < nVariables_; ++i) x(i) = invA(I,i);
}
}
delete A;
}
} // namespace ATC

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