There is one prototype of spsvx
available, please see below.
spsvx( const char fact, const MatrixAP& ap, MatrixAFP& afp, VectorIPIV& ipiv, const MatrixB& b, MatrixX& x, Scalar >, VectorFERR& ferr, VectorBERR& berr );
spsvx
(short for $FRIENDLY_NAME)
provides a C++ interface to LAPACK routines SSPSVX, DSPSVX, CSPSVX, and
ZSPSVX. spsvx
uses the
diagonal pivoting factorization A = UD*U*T
or A = LD*L*T to compute the solution
to a complex system of linear equations A * X = B, where A is an N-by-N
symmetric matrix stored in packed format 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 diagonal pivoting method is used to factor A as A = U * D * U*T, if UPLO = 'U', or A = L * D * L*T, if UPLO = 'L', where U (or L) is a product of permutation and unit upper (lower) triangular matrices and D is symmetric and block diagonal with 1-by-1 and 2-by-2 diagonal blocks.
2. If some D(i,i)=0, so that D 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 MatrixAP
.
The type of values is obtained through the value_type
meta-function typename value_type<MatrixAP>::type
. The dispatching table below illustrates
to which specific routine the code path will be generated.
Table 1.148. Dispatching of spsvx
Value type of MatrixAP |
LAPACK routine |
---|---|
|
SSPSVX |
|
DSPSVX |
|
CSPSVX |
|
ZSPSVX |
Defined in header boost/numeric/bindings/lapack/driver/spsvx.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/spsvx.hpp> using namespace boost::numeric::bindings; lapack::spsvx( x, y, z );
this will output
[5] 0 1 2 3 4 5