Prototype

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

gtsvx( const char fact, const VectorDL& dl, const VectorD& d,
        const VectorDU& du, VectorDLF& dlf, VectorDF& df, VectorDUF& duf,
        VectorDU2& du2, VectorIPIV& ipiv, const MatrixB& b, MatrixX& x,
        Scalar >, VectorFERR& ferr, VectorBERR& berr );

Description

gtsvx (short for $FRIENDLY_NAME) provides a C++ interface to LAPACK routines SGTSVX, DGTSVX, CGTSVX, and ZGTSVX. gtsvx uses the LU factorization to compute the solution to a complex system of linear equations A * X = B, A*T * X = B, or A*H * X = B, where A is a tridiagonal matrix of order N and X and B are N-by-NRHS matrices.

Error bounds on the solution and a condition estimate are also provided.

Description =====

The following steps are performed:

1. If FACT = 'N', the LU decomposition is used to factor the matrix A as A = L * U, where L is a product of permutation and unit lower bidiagonal matrices and U is upper triangular with nonzeros in only the main diagonal and first two superdiagonals.

2. If some U(i,i)=0, so that U is exactly singular, then the routine returns with INFO = i. Otherwise, the factored form of A is used to estimate the condition number of the matrix A. If the reciprocal of the condition number is less than machine precision, INFO = N+1 is returned as a warning, but the routine still goes on to solve for X and compute error bounds as described below.

3. The system of equations is solved for X using the factored form of A.

4. Iterative refinement is applied to improve the computed solution matrix and calculate error bounds and backward error estimates for it.

The selection of the LAPACK routine is done during compile-time, and is determined by the type of values contained in type VectorDL. The type of values is obtained through the value_type meta-function typename value_type<VectorDL>::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/gtsvx.hpp.

Parameters or Requirements on Types

Complexity

Example

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

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

this will output

[5] 0 1 2 3 4 5

Notes

See Also