Prototype

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

ggsvp( const char jobu, const char jobv, const char jobq, MatrixA& a,
        MatrixB& b, const Scalar >, const Scalar >, int_t& k,
        int_t& l, MatrixU& u, MatrixV& v, MatrixQ& q );

Description

ggsvp (short for $FRIENDLY_NAME) provides a C++ interface to LAPACK routines SGGSVP, DGGSVP, CGGSVP, and ZGGSVP. ggsvp computes unitary matrices U, V and Q such that

N-K-L K L U'*A*Q = K ( 0 A12 A13 ) if M-K-L >= 0; L ( 0 0 A23 ) M-K-L ( 0 0 0 )

N-K-L K L = K ( 0 A12 A13 ) if M-K-L < 0; M-K ( 0 0 A23 )

N-K-L K L V'*B*Q = L ( 0 0 B13 ) P-L ( 0 0 0 )

where the K-by-K matrix A12 and L-by-L matrix B13 are nonsingular upper triangular; A23 is L-by-L upper triangular if M-K-L >= 0, otherwise A23 is (M-K)-by-L upper trapezoidal. K+L = the effective numerical rank of the (M+P)-by-N matrix (A',B')'. Z' denotes the conjugate transpose of Z.

This decomposition is the preprocessing step for computing the Generalized Singular Value Decomposition (GSVD), see subroutine ZGGSVD.

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/computational/ggsvp.hpp.

Parameters or Requirements on Types

Complexity

Example

#include <boost/numeric/bindings/lapack/computational/ggsvp.hpp>
using namespace boost::numeric::bindings;

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

this will output

[5] 0 1 2 3 4 5

Notes

See Also