Prototype

There is one prototype of iter_posv available, please see below.

iter_posv( MatrixA& a, const MatrixB& b, MatrixX& x,
        int_t& iter );

Description

iter_posv (short for $FRIENDLY_NAME) provides a C++ interface to LAPACK routines DSPOSV and ZCPOSV. iter_posv computes the solution to a complex system of linear equations A * X = B, where A is an N-by-N Hermitian positive definite matrix and X and B are N-by-NRHS matrices.

iter_posv first attempts to factorize the matrix in COMPLEX and use this factorization within an iterative refinement procedure to produce a solution with COMPLEX*16 normwise backward error quality (see below). If the approach fails the method switches to a COMPLEX*16 factorization and solve.

The iterative refinement is not going to be a winning strategy if the ratio COMPLEX performance over COMPLEX*16 performance is too small. A reasonable strategy should take the number of right-hand sides and the size of the matrix into account. This might be done with a call to ILAENV in the future. Up to now, we always try iterative refinement.

The iterative refinement process is stopped if ITER > ITERMAX or for all the RHS we have: RNRM < SQRT(N)*XNRM*ANRM*EPS*BWDMAX where o ITER is the number of the current iteration in the iterative refinement process o RNRM is the infinity-norm of the residual o XNRM is the infinity-norm of the solution o ANRM is the infinity-operator-norm of the matrix A o EPS is the machine epsilon returned by DLAMCH('Epsilon') The value ITERMAX and BWDMAX are fixed to 30 and 1.0D+00 respectively.

The selection of the LAPACK routine is done during compile-time, and is determined by the type of values contained in type MatrixA. The type of values is obtained through the value_type meta-function typename value_type<MatrixA>::type. The dispatching table below illustrates to which specific routine the code path will be generated.

Definition

Defined in header boost/numeric/bindings/lapack/driver/iter_posv.hpp.

Parameters or Requirements on Types

Complexity

Example

#include <boost/numeric/bindings/lapack/driver/iter_posv.hpp>
using namespace boost::numeric::bindings;

lapack::iter_posv( x, y, z );

this will output

[5] 0 1 2 3 4 5

Notes

See Also