##### bdsdc

###### Prototype

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

    bdsdc( const char uplo, const char compq, const int_t n,
            VectorD& d, VectorE& e, MatrixU& u, MatrixVT& vt, VectorQ& q,
            VectorIQ& iq );

###### Description

`bdsdc` (short for $FRIENDLY_NAME) provides a C++ interface to LAPACK routines SBDSDC and DBDSDC. `bdsdc` computes the singular value decomposition (SVD) of a real N-by-N (upper or lower) bidiagonal matrix B: B = U * S * VT, using a divide and conquer method, where S is a diagonal matrix with non-negative diagonal elements (the singular values of B), and U and VT are orthogonal matrices of left and right singular vectors, respectively. `bdsdc` can be used to compute all singular values, and optionally, singular vectors or singular vectors in compact form.

This code 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. See DLASD3 for details.

The code currently calls DLASDQ if singular values only are desired. However, it can be slightly modified to compute singular values using the divide and conquer method.

The selection of the LAPACK routine is done during compile-time, and is determined by the type of values contained in type `VectorD`. The type of values is obtained through the `value_type` meta-function `typename value_type<VectorD>::type`. The dispatching table below illustrates to which specific routine the code path will be generated.

Table 1.216. Dispatching of bdsdc

Value type of VectorD | LAPACK routine
--- | ---
`float` | SBDSDC
`double` | DBDSDC

###### Definition

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

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

this will output

    [5] 0 1 2 3 4 5

###### Notes

###### See Also

- Originating Fortran source files sbdsdc.f and dbdsdc.f at Netlib.