##### tzrzf

###### Prototype

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

    tzrzf( MatrixA& a, VectorTAU& tau );

###### Description

`tzrzf` (short for $FRIENDLY_NAME) provides a C++ interface to LAPACK routines STZRZF, DTZRZF, CTZRZF, and ZTZRZF. `tzrzf` reduces the M-by-N ( M<=N ) complex upper trapezoidal matrix A to upper triangular form by means of unitary transformations.

The upper trapezoidal matrix A is factored as

A = ( R 0 ) * Z,

where Z is an N-by-N unitary matrix and R is an M-by-M upper triangular matrix.

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 1.206. Dispatching of tzrzf

Value type of MatrixA | LAPACK routine
--- | ---
`float` | STZRZF
`double` | DTZRZF
`complex<float>` | CTZRZF
`complex<double>` | ZTZRZF

###### Definition

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

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

this will output

    [5] 0 1 2 3 4 5

###### Notes

###### See Also

- Originating Fortran source files stzrzf.f, dtzrzf.f, ctzrzf.f, and ztzrzf.f at Netlib.