##### gesdd

###### Prototype

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

    gesdd( const char jobz, MatrixA& a, VectorS& s, MatrixU& u,
            MatrixVT& vt );

###### Description

`gesdd` (short for $FRIENDLY_NAME) provides a C++ interface to LAPACK routines SGESDD, DGESDD, CGESDD, and ZGESDD. `gesdd` computes the singular value decomposition (SVD) of a complex M-by-N matrix A, optionally computing the left and/or right singular vectors, by using divide-and-conquer method. 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 VT = V**H, not V.

The divide and conquer algorithm makes very mild assumptions about floating point arithmetic. It will work on machines with a guard digit in add/subtract, or on those binary machines without guard digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or Cray-2. It could conceivably fail on hexadecimal or decimal machines without guard digits, but we know of none.

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 1.155. Dispatching of gesdd

Value type of MatrixA | LAPACK routine
--- | ---
`float` | SGESDD
`double` | DGESDD
`complex<float>` | CGESDD
`complex<double>` | ZGESDD

###### Definition

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

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

this will output

    [5] 0 1 2 3 4 5

###### Notes

###### See Also

- Originating Fortran source files sgesdd.f, dgesdd.f, cgesdd.f, and zgesdd.f at Netlib.