Prototype

There is one prototype of ggqrf available, please see below.

ggqrf( MatrixA& a, VectorTAUA& taua, MatrixB& b, VectorTAUB& taub );

Description

ggqrf (short for $FRIENDLY_NAME) provides a C++ interface to LAPACK routines SGGQRF, DGGQRF, CGGQRF, and ZGGQRF. ggqrf computes a generalized QR factorization of an N-by-M matrix A and an N-by-P matrix B:

A = Q*R, B = Q*T*Z,

where Q is an N-by-N unitary matrix, Z is a P-by-P unitary matrix, and R and T assume one of the forms:

if N >= M, R = ( R11 ) M , or if N < M, R = ( R11 R12 ) N, ( 0 ) N-M N M-N M

where R11 is upper triangular, and

if N <= P, T = ( 0 T12 ) N, or if N > P, T = ( T11 ) N-P, P-N N ( T21 ) P P

where T12 or T21 is upper triangular.

In particular, if B is square and nonsingular, the GQR factorization of A and B implicitly gives the QR factorization of inv(B)*A:

inv(B)A = Z'(inv(T)*R)

where inv(B) denotes the inverse of the matrix B, and Z' denotes the conjugate transpose of matrix Z.

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.

Definition

Defined in header boost/numeric/bindings/lapack/computational/ggqrf.hpp.

Parameters or Requirements on Types

Complexity

Example

#include <boost/numeric/bindings/lapack/computational/ggqrf.hpp>
using namespace boost::numeric::bindings;

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

this will output

[5] 0 1 2 3 4 5

Notes

See Also