//============================================================================
KrylovSolverStatus MINRES_CR_Solver::
solve(const LinearOperator &A, const double *rhs, double *result,
const LinearOperator *preconditioner, bool use_given_initial_guess)
{
const int n=A.m;
assert(A.n==n);
assert(preconditioner==0 || (preconditioner->m==n && preconditioner->n==n));
if((int)s.size()!=n){
r.resize(n);
z.resize(n);
q.resize(n);
s.resize(n);
t.resize(n);
}
// convergence tolerance
double tol=tolerance_factor*BLAS::abs_max(n, rhs);
// initial guess
if(use_given_initial_guess){
A.apply_and_subtract(result, rhs, &r[0]);
}else{
BLAS::set_zero(n, result);
BLAS::copy(n, rhs, &r[0]);
}
// check instant convergence
iteration=0;
residual_norm=BLAS::abs_max(r);
if(residual_norm==0) return status=KRYLOV_CONVERGED;
// set up CR
double rho;
if(preconditioner) preconditioner->apply(r, z); else BLAS::copy(r, s);
A.apply(s, t);
rho=BLAS::dot(r, t);
if(rho==0 || rho!=rho) return status=KRYLOV_BREAKDOWN;
// and iterate
for(iteration=1; iteration<max_iterations; ++iteration){
double alpha;
double tt=BLAS::dot(t, t);
if(tt==0 || tt!=tt) return status=KRYLOV_BREAKDOWN;
alpha=rho/tt;
BLAS::add_scaled(n, alpha, &s[0], result);
BLAS::add_scaled(-alpha, t, r);
residual_norm=BLAS::abs_max(r);
if(residual_norm<=tol) return KRYLOV_CONVERGED;
if(preconditioner) preconditioner->apply(r, z);
else BLAS::copy(r, z);
A.apply(z, q);
double rho_new=BLAS::dot(r, q);
if(rho_new==0 || rho_new!=rho_new) return KRYLOV_BREAKDOWN;
double beta=rho_new/rho;
BLAS::add_scaled(beta, s, z); s.swap(z); // s=beta*s+z
BLAS::add_scaled(beta, t, q); t.swap(q); // t=beta*t+q
rho=rho_new;
}
return KRYLOV_EXCEEDED_MAX_ITERATIONS;
}
//============================================================================
KrylovSolverStatus CGNR_Solver::
solve(const LinearOperator &A, const double *rhs, double *result,
const LinearOperator *preconditioner, bool use_given_initial_guess)
{
const int m=A.m, n=A.n;
assert(preconditioner==0 || (preconditioner->m==n && preconditioner->n==n));
if((int)s.size()!=n){
r.resize(n);
z.resize(n);
s.resize(n);
u.resize(m);
}
// convergence tolerance
A.apply_transpose(rhs, &r[0]); // form A^T*rhs in r
double tol=tolerance_factor*BLAS::abs_max(r);
// initial guess
if(use_given_initial_guess){
A.apply_and_subtract(result, rhs, &u[0]);
A.apply_transpose(u, r);
}else{
BLAS::set_zero(n, result);
}
// check instant convergence
iteration=0;
residual_norm=BLAS::abs_max(r);
if(residual_norm==0) return status=KRYLOV_CONVERGED;
// set up CG
double rho;
if(preconditioner) preconditioner->apply(r, z); else BLAS::copy(r, z);
rho=BLAS::dot(r, z);
if(rho<=0 || rho!=rho) return status=KRYLOV_BREAKDOWN;
BLAS::copy(z, s);
// and iterate
for(iteration=1; iteration<max_iterations; ++iteration){
double alpha;
A.apply(s, u);
A.apply_transpose(u, z);
double sz=BLAS::dot(u, u);
if(sz<=0 || sz!=sz) return status=KRYLOV_BREAKDOWN;
alpha=rho/sz;
BLAS::add_scaled(n, alpha, &s[0], result);
BLAS::add_scaled(-alpha, z, r);
residual_norm=BLAS::abs_max(r);
if(residual_norm<=tol) return status=KRYLOV_CONVERGED;
if(preconditioner) preconditioner->apply(r, z); else BLAS::copy(r, z);
double rho_new=BLAS::dot(r, z);
if(rho_new<=0 || rho_new!=rho_new) return status=KRYLOV_BREAKDOWN;
double beta=rho_new/rho;
BLAS::add_scaled(beta, s, z); s.swap(z); // s=beta*s+z
rho=rho_new;
if ( iteration % 5000 == 0 )
{
std::cout << "CGNR_Solver --- residual_norm: " << residual_norm << std::endl;
}
}
return status=KRYLOV_EXCEEDED_MAX_ITERATIONS;
}
void run( Vector<Real> &x, LinearOperator<Real> &A, const Vector<Real> &b,
LinearOperator<Real> &M, int &iter, int &flag ) {
using Teuchos::RCP;
flag = 0;
Real zero = 0.0;
Real one = 1.0;
if ( !isInitialized_ ) {
r_ = b.clone();
w_ = b.clone();
z_ = x.clone();
isInitialized_ = true;
}
Real itol = std::sqrt(ROL_EPSILON<Real>());
// Compute initial residual
if(useInitialGuess_) {
A.apply(*r_,x,itol);
r_->scale(-1.0);
r_->plus(b); // r = b-Ax
}
else {
x.zero();
r_->set(b);
}
Real temp = 0;
std::vector<RCP<Vector<Real > > > V;
std::vector<RCP<Vector<Real > > > Z;
(*res_)[0] = r_->norm();
Real rtol = std::min(absTol_,relTol_*(*res_)[0]);
V.push_back(b.clone());
(V[0])->set(*r_);
(V[0])->scale(one/(*res_)[0]);
(*s_)(0) = (*res_)[0];
for( iter=0; iter<maxit_; ++iter ) {
// std::cout << (*res_)[iter] << std::endl;
if( useInexact_ ) {
itol = rtol/(maxit_*(*res_)[iter]);
}
Z.push_back(x.clone());
// Apply right preconditioner
M.applyInverse(*(Z[iter]),*(V[iter]),itol);
// Apply operator
A.apply(*w_,*(Z[iter]),itol);
// Evaluate coefficients and orthogonalize using Gram-Schmidt
for( int k=0; k<=iter; ++k ) {
(*H_)(k,iter) = w_->dot(*(V[k]));
w_->axpy( -(*H_)(k,iter), *(V[k]) );
}
(*H_)(iter+1,iter) = w_->norm();
V.push_back( b.clone() );
(V[iter+1])->set(*w_);
(V[iter+1])->scale(one/((*H_)(iter+1,iter)));
// Apply Givens rotations
for( int k=0; k<=iter-1; ++k ) {
temp = (*cs_)(k)*(*H_)(k,iter) + (*sn_)(k)*(*H_)(k+1,iter);
(*H_)(k+1,iter) = -(*sn_)(k)*(*H_)(k,iter) + (*cs_)(k)*(*H_)(k+1,iter);
(*H_)(k,iter) = temp;
}
// Form i-th rotation matrix
if( (*H_)(iter+1,iter) == zero ) {
(*cs_)(iter) = one;
(*sn_)(iter) = zero;
}
else if ( std::abs((*H_)(iter+1,iter)) > std::abs((*H_)(iter,iter)) ) {
temp = (*H_)(iter,iter) / (*H_)(iter+1,iter);
(*sn_)(iter) = one / std::sqrt( one + temp*temp );
(*cs_)(iter) = temp*(*sn_)(iter);
}
else {
temp = (*H_)(iter+1,iter) / (*H_)(iter,iter);
(*cs_)(iter) = one / std::sqrt( one + temp*temp );
(*sn_)(iter) = temp*(*cs_)(iter);
}
// Approximate residual norm
temp = (*cs_)(iter)*(*s_)(iter);
(*s_)(iter+1) = -(*sn_)(iter)*(*s_)(iter);
(*s_)(iter) = temp;
(*H_)(iter,iter) = (*cs_)(iter)*(*H_)(iter,iter) + (*sn_)(iter)*(*H_)(iter+1,iter);
(*H_)(iter+1,iter) = zero;
(*res_)[iter+1] = std::abs((*s_)(iter+1));
// Update solution approximation.
const char uplo = 'U';
const char trans = 'N';
const char diag = 'N';
const char normin = 'N';
Real scaling = zero;
int info = 0;
*y_ = *s_;
lapack_.LATRS(uplo, trans, diag, normin, iter+1, H_->values(), maxit_+1, y_->values(), &scaling, cnorm_->values(), &info);
z_->zero();
for( int k=0; k<=iter;++k ) {
z_->axpy((*y_)(k),*(Z[k]));
}
if( (*res_)[iter+1] <= rtol ) {
// Update solution vector
x.plus(*z_);
break;
}
if(iter == maxit_) {
flag = 1;
}
} // loop over iter
}