##### gesvd

###### Prototype

There is one prototype of `gesvd` available, please see below.

    gesvd( const char jobu, const char jobvt, MatrixA& a, VectorS& s,
            MatrixU& u, MatrixVT& vt );

###### Description

`gesvd` (short for $FRIENDLY_NAME) provides a C++ interface to LAPACK routines SGESVD, DGESVD, CGESVD, and ZGESVD. `gesvd` computes the singular value decomposition (SVD) of a complex M-by-N matrix A, optionally computing the left and/or right singular vectors. The SVD is written

A = U * SIGMA * conjugate-transpose(V)

where SIGMA is an M-by-N matrix which is zero except for its min(m,n) diagonal elements, U is an M-by-M unitary matrix, and V is an N-by-N unitary matrix. The diagonal elements of SIGMA are the singular values of A; they are real and non-negative, and are returned in descending order. The first min(m,n) columns of U and V are the left and right singular vectors of A.

Note that the routine returns V**H, not V.

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 1.156. Dispatching of gesvd

Value type of MatrixA | LAPACK routine
--- | ---
`float` | SGESVD
`double` | DGESVD
`complex<float>` | CGESVD
`complex<double>` | ZGESVD

###### Definition

Defined in header `boost/numeric/bindings/lapack/driver/gesvd.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/driver/gesvd.hpp>
    using namespace boost::numeric::bindings;

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

this will output

    [5] 0 1 2 3 4 5

###### Notes

###### See Also

- Originating Fortran source files sgesvd.f, dgesvd.f, cgesvd.f, and zgesvd.f at Netlib.