//============================================================================
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;
}
//============================================================================
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;
}