##### ggsvp

###### 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.

Table 1.339. Dispatching of ggsvp

Value type of MatrixA | LAPACK routine
--- | ---
`float` | SGGSVP
`double` | DGGSVP
`complex<float>` | CGGSVP
`complex<double>` | ZGGSVP

###### Definition

Defined in header `boost/numeric/bindings/lapack/computational/ggsvp.hpp`.

###### Parameters or Requirements on Types

Parameters

MatrixA

  The definition of term 1

MatrixB

  The definition of term 2

MatrixC

  The definition of term 3.

  Definitions may contain paragraphs.

###### 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

- Originating Fortran source files sggsvp.f, dggsvp.f, cggsvp.f, and zggsvp.f at Netlib.