There is one prototype of gbsvx
available, please see below.
gbsvx( const char fact, MatrixAB& ab, MatrixAFB& afb, VectorIPIV& ipiv, char& equed, VectorR& r, VectorC& c, MatrixB& b, MatrixX& x, Scalar >, VectorFERR& ferr, VectorBERR& berr );
gbsvx
(short for $FRIENDLY_NAME)
provides a C++ interface to LAPACK routines SGBSVX, DGBSVX, CGBSVX, and
ZGBSVX. gbsvx
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 band matrix of order N with KL subdiagonals and
KU superdiagonals, and X and B are N-by-NRHS matrices.
Error bounds on the solution and a condition estimate are also provided.
Description =
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The following steps are performed by this subroutine:
1. If FACT = 'E', real scaling factors are computed to equilibrate the system: TRANS = 'N': diag(R)*A*diag(C) *inv(diag(C))*X = diag(R)*B TRANS = 'T': (diag(R)A*diag(C))*T *inv(diag(R))*X = diag(C)*B TRANS = 'C': (diag(R)A*diag(C))*H *inv(diag(R))*X = diag(C)*B Whether or not the system will be equilibrated depends on the scaling of the matrix A, but if equilibration is used, A is overwritten by diag(R)*A*diag(C) and B by diag(R)*B (if TRANS='N') or diag(C)*B (if TRANS = 'T' or 'C').
2. If FACT = 'N' or 'E', the LU decomposition is used to factor the matrix A (after equilibration if FACT = 'E') as A = L * U, where L is a product of permutation and unit lower triangular matrices with KL subdiagonals, and U is upper triangular with KL+KU superdiagonals.
3. 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.
4. The system of equations is solved for X using the factored form of A.
5. Iterative refinement is applied to improve the computed solution matrix and calculate error bounds and backward error estimates for it.
6. If equilibration was used, the matrix X is premultiplied by diag(C) (if TRANS = 'N') or diag(R) (if TRANS = 'T' or 'C') so that it solves the original system before equilibration.
The selection of the LAPACK routine is done during compile-time, and
is determined by the type of values contained in type MatrixAB
.
The type of values is obtained through the value_type
meta-function typename value_type<MatrixAB>::type
. The dispatching table below illustrates
to which specific routine the code path will be generated.
Table 1.127. Dispatching of gbsvx
Value type of MatrixAB |
LAPACK routine |
---|---|
|
SGBSVX |
|
DGBSVX |
|
CGBSVX |
|
ZGBSVX |
Defined in header boost/numeric/bindings/lapack/driver/gbsvx.hpp
.
Parameters
The definition of term 1
The definition of term 2
The definition of term 3.
Definitions may contain paragraphs.
#include <boost/numeric/bindings/lapack/driver/gbsvx.hpp> using namespace boost::numeric::bindings; lapack::gbsvx( x, y, z );
this will output
[5] 0 1 2 3 4 5