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[section gels]

[heading Prototype]
There is one prototype of `gels` available, please see below.
``
gels( MatrixA& a, MatrixB& b );
``


[heading Description]

`gels` (short for $FRIENDLY_NAME) provides a C++
interface to LAPACK routines SGELS, DGELS, CGELS, and ZGELS. 
`gels` solves overdetermined or underdetermined complex linear systems
involving an M-by-N matrix A, or its conjugate-transpose, using a QR
or LQ factorization of A. It is assumed that A has full rank.

The following options are provided:

1. If TRANS = 'N' and m >= n: find the least squares solution of
an overdetermined system, i.e., solve the least squares problem
minimize || B - A*X ||.

2. If TRANS = 'N' and m < n: find the minimum norm solution of
an underdetermined system A * X = B.

3. If TRANS = 'C' and m >= n: find the minimum norm solution of
an undetermined system A**H * X = B.

4. If TRANS = 'C' and m < n: find the least squares solution of
an overdetermined system, i.e., solve the least squares problem
minimize || B - A**H * X ||.

Several right hand side vectors b and solution vectors x can be
handled in a single call; they are stored as the columns of the
M-by-NRHS right hand side matrix B and the N-by-NRHS solution
matrix X.

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 gels
[  [ Value type of MatrixA ] [LAPACK routine] ]
[  [`float`][SGELS] ]
[  [`double`][DGELS] ]
[  [`complex<float>`][CGELS] ]
[  [`complex<double>`][ZGELS] ]

]


[heading Definition]
Defined in header [headerref boost/numeric/bindings/lapack/driver/gels.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/gels.hpp>
using namespace boost::numeric::bindings;

lapack::gels( 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/sgels.f sgels.f], [@http://www.netlib.org/lapack/double/dgels.f dgels.f], [@http://www.netlib.org/lapack/complex/cgels.f cgels.f], and [@http://www.netlib.org/lapack/complex16/zgels.f zgels.f] at Netlib.

[endsect]
