/usr/include/trilinos/ROL_Lanczos.hpp is in libtrilinos-rol-dev 12.12.1-5.
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// ************************************************************************
//
// Rapid Optimization Library (ROL) Package
// Copyright (2014) Sandia Corporation
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#ifndef ROL_LANCZOS_H
#define ROL_LANCZOS_H
#include "ROL_Krylov.hpp"
#include "ROL_LinearOperator.hpp"
#include "ROL_Vector.hpp"
#include "ROL_Types.hpp"
#include "Teuchos_LAPACK.hpp"
namespace ROL {
/** \class ROL::Lanczos
\brief Interface for computing the Lanczos vectors
and approximate solutions to symmetric indefinite
linear systems
*/
template<class Real>
class Lanczos {
template <typename T> using RCP = Teuchos::RCP<T>;
template <typename T> using vector = std::vector<T>;
template typename vector<Real> size_type uint;
typedef Vector<Real> V;
typedef LinearOperator<Real> OP;
typedef Teuchos::ParameterList PL;
private:
Teuchos::LAPACK<int,Real> lapack_;
vector<RCP<V> > Q_; // Orthogonal basis
vector<Real> alpha_; // Diagonal recursion coefficients
vector<Real> beta_; // Sub/super-diagonal recursion coefficients
// Temporary vectors for factorizations, linear solves, and eigenvalue calculations
vector<Real> dl_;
vector<Real> d_;
vector<Real> du_;
vector<Real> du2_;
vector<Real> y_; // Arnoldi expansion coefficients
vector<Real> work_; // Scratch space for eigenvalue decomposition
vector<int> ipiv_; // Pivots for LU
RCP<V> u_; // An auxilliary vector
Real max_beta_; // maximum beta encountered
Real tol_beta_; // relative smallest beta allowed
Real tol_ortho_; // Maximum orthogonality loss tolerance
int maxit_; // Maximum number of vectors to store
int k_; // current iterate number
// Allocte memory for Arnoldi vectors and recurions coefficients
void allocate( void ) {
u_ = b.clone();
alpha_.reserve(maxit_);
beta_.reserve(maxit_);
dl_.reserve(maxit_);
d_.reserve(maxit_);
du_.reserve(maxit_);
du2_.reserve(maxit_);
work_.reserve(4*maxit_);
ipiv_.reserve(maxit_);
y_.reserve(maxit_);
alpha_.reserve(maxit_);
beta_.reserve(maxit_);
for( uint j=0; j<maxit_; ++j ) {
Q_.push_back(b.clone());
}
}
public:
enum class FLAG_ITERATE : unsigned {
ITERATE_SUCCESS = 0,
ITERATE_SMALL_BETA, // Beta too small to continue
ITERATE_MAX_REACHED, // Reached maximum number of iterations
ITERATE_ORTHO_TOL, // Reached maximim orthogonality loss
ITERATE_LAST
};
enum class FLAG_SOLVE : unsigned {
SOLVE_SUCCESS = 0,
SOLVE_ILLEGAL_VALUE,
SOLVE_SINGULAR_U,
SOLVE_LAST
};
Lanczos( Teuchos::ParameterList &PL ) {
PL &krylovList = parlist.sublist("General").sublist("Krylov");
PL &lanczosList = krylovList.sublist("Lanczos");
Real tol_default = std::sqrt(ROL_EPSILON<Real>());
maxit_ = krylovList_.get("Iteration Limit",10);
tol_beta_ = lanczosList.get("Beta Relative Tolerance", tol_default);
tol_ortho_ = lanczosList.get("Orthogonality Tolerance", tol_default);
}
void initialize( const V& b ) {
allocate();
reset(b);
}
void initialize( const V &x0, const V &b, const LO &A, Real &tol ) {
allocate();
reset(x0,b,A,tol);
}
void reset( const V &b ) {
k_ = 0;
max_beta_ = 0;
Q_[0]->set(b);
beta_[0] = Q_[0]->norm();
max_beta_ = std::max(max_beta_,beta_[0]);
Q_[0]->scale(1.0/beta_[0]);
}
void reset( const V &x0, const V &b, const LO &A, Real &tol ) {
k_ = 0;
max_beta_ = 0;
Q_[0]->set(b);
A.apply(*u_,x0,tol);
Q_[0]->axpy(-1.0,*u_);
beta_[0] = Q_[0]->norm();
max_beta_ = std::max(max_beta_,beta_[0]);
Q_[0]->scale(1.0/beta_[0]);
}
FLAG_ITERATE iterate( const OP &A, Real &tol ) {
if( k_ == maxit_ ) {
return ITERATE_MAX_REACHED;
}
A.apply(*u_,*(Q_[k]),tol);
Real delta;
if( k_>0 ) {
u_->axpy(-beta_[k],V_[k_-1]);
}
alpha_[k] = u_->dot(*(V_[k]));
u_->axpy(alpha_[k],V_[k_]);
if( k_>0 ) {
delta = u_->dot(*(V_[k-1]));
u_->axpy(-delta,*(V_[k-1]));
}
delta = u_->dot(*(V_[k]));
alpha_[k] += delta;
if( k_ < maxit_-1 ) {
u_->axpy(-delta,*(V_[k_]));
beta_[k+1] = u_->norm();
max_beta_ = std::max(max_beta_,beta_[k+1]);
if(beta_[k+1] < tol_beta_*max_beta_) {
return ITERATE_SMALL_BETA;
}
V_[k+1]->set(*u_);
V_[k+1]->scale(1.0/beta_[k+1]);
// Check orthogonality
Real dotprod = V_[k+1]->dot(*(V_[0]));
if( std::sqrt(dotprod) > tol_ortho_ ) {
return ITERATE_ORTHO_TOL;
}
}
++k_;
return ITERATE_SUCCESS;
}
// Compute the eigenvalues of the tridiagonal matrix T
void eigenvalues( std::vector<Real> &E ) {
std::vector<Real> Z(1,0); // Don't compute eigenvectors
int INFO;
int LDZ = 0;
const char COMPZ = 'N':
d_ = alpha_;
du_ = beta_;
lapack_->STEQR(COMPZ,k_,&d_[0],&du_[0],&Z[0],LDZ,&work_[0],&INFO);
if( INFO < 0 ) {
return SOLVE_ILLEGAL_VALUE;
}
else if( INFO > 0 ) {
return SOLVE_SINGULAR_U;
}
}
FLAG_SOLVE solve( V &x, Real tau=0 ) {
const char TRANS = 'N';
const int NRHS = 1;
int INFO;
// Fill arrays
for(uint j=0;j<k_;++j) {
d_[j] = alpha_[j]+tau;
}
dl_ = beta_;
du_ = beta_;
du2_.assign(maxit_,0);
// Do Tridiagonal LU factorization
lapack_->GTTRF(k_,&dl_[0],&d_[0],&du_[0],&du2_[0],&ipiv_[0],&INFO);
// Solve the factorized system for Arnoldi expansion coefficients
lapack_->GTTRS(TRANS,k_,1,&dl[0],&d_[0],&du_[0],&du2_[0],&ipiv_[0],&y_[0],k_,&INFO);
}
}; // class LanczosFactorization
} // namespace ROL
#endif // ROL_LANCZOS_H
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