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[section gglse]

[heading Prototype]
There is one prototype of `gglse` available, please see below.
``
gglse( MatrixA& a, MatrixB& b, VectorC& c, VectorD& d, VectorX& x );
``


[heading Description]

`gglse` (short for $FRIENDLY_NAME) provides a C++
interface to LAPACK routines SGGLSE, DGGLSE, CGGLSE, and ZGGLSE. 
`gglse` solves the linear equality-constrained least squares (LSE)
problem:

minimize || c - A*x ||_2 subject to B*x = d

where A is an M-by-N matrix, B is a P-by-N matrix, c is a given
M-vector, and d is a given P-vector. It is assumed that
P <= N <= M+P, and

rank(B) = P and rank( ( A ) ) = N.
( ( B ) )

These conditions ensure that the LSE problem has a unique solution,
which is obtained using a generalized RQ factorization of the
matrices (B, A) given by

B = (0 R)*Q, A = Z*T*Q.

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 Dispatching of gglse
[  [ Value type of MatrixA ] [LAPACK routine] ]
[  [`float`][SGGLSE] ]
[  [`double`][DGGLSE] ]
[  [`complex<float>`][CGGLSE] ]
[  [`complex<double>`][ZGGLSE] ]

]


[heading Definition]
Defined in header [headerref boost/numeric/bindings/lapack/driver/gglse.hpp].


[heading Parameters or Requirements on Types]

[variablelist Parameters
    [[MatrixA] [The definition of term 1]]
    [[MatrixB] [The definition of term 2]]
    [[MatrixC] [
    The definition of term 3.

    Definitions may contain paragraphs.
    ]]
]


[heading Complexity]


[heading Example]
``
#include <boost/numeric/bindings/lapack/driver/gglse.hpp>
using namespace boost::numeric::bindings;

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

``

this will output

``
[5] 0 1 2 3 4 5
``



[heading Notes]


[heading See Also]

* Originating Fortran source files [@http://www.netlib.org/lapack/single/sgglse.f sgglse.f], [@http://www.netlib.org/lapack/double/dgglse.f dgglse.f], [@http://www.netlib.org/lapack/complex/cgglse.f cgglse.f], and [@http://www.netlib.org/lapack/complex16/zgglse.f zgglse.f] at Netlib.

[endsect]
