# CentOS 7.0 - man page for cgeqrt3 (centos section 3)

```cgeqrt3.f(3)						LAPACK						 cgeqrt3.f(3)

NAME
cgeqrt3.f -

SYNOPSIS
Functions/Subroutines
recursive subroutine cgeqrt3 (M, N, A, LDA, T, LDT, INFO)
CGEQRT3 recursively computes a QR factorization of a general real or complex matrix using the compact WY
representation of Q.

Function/Subroutine Documentation
recursive subroutine cgeqrt3 (integerM, integerN, complex, dimension( lda, * )A, integerLDA, complex, dimension(
ldt, * )T, integerLDT, integerINFO)
CGEQRT3 recursively computes a QR factorization of a general real or complex matrix using the compact WY
representation of Q.

Purpose:

CGEQRT3 recursively computes a QR factorization of a complex M-by-N matrix A,
using the compact WY representation of Q.

Based on the algorithm of Elmroth and Gustavson,
IBM J. Res. Develop. Vol 44 No. 4 July 2000.

Parameters:
M

M is INTEGER
The number of rows of the matrix A.  M >= N.

N

N is INTEGER
The number of columns of the matrix A.  N >= 0.

A

A is COMPLEX array, dimension (LDA,N)
On entry, the complex M-by-N matrix A.  On exit, the elements on and
above the diagonal contain the N-by-N upper triangular matrix R; the
elements below the diagonal are the columns of V.	See below for
further details.

LDA

LDA is INTEGER
The leading dimension of the array A.  LDA >= max(1,M).

T

T is COMPLEX array, dimension (LDT,N)
The N-by-N upper triangular factor of the block reflector.
The elements on and above the diagonal contain the block
reflector T; the elements below the diagonal are not used.
See below for further details.

LDT

LDT is INTEGER
The leading dimension of the array T.  LDT >= max(1,N).

INFO

INFO is INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value

Author:
Univ. of Tennessee

Univ. of California Berkeley

NAG Ltd.

Date:
September 2012

Further Details:

The matrix V stores the elementary reflectors H(i) in the i-th column
below the diagonal. For example, if M=5 and N=3, the matrix V is

V = (  1	 )
( v1  1	 )
( v1 v2  1 )
( v1 v2 v3 )
( v1 v2 v3 )

where the vi's represent the vectors which define H(i), which are returned
in the matrix A.  The 1's along the diagonal of V are not stored in A.  The
block reflector H is then given by

H = I - V * T * V**H

where V**H is the conjugate transpose of V.

For details of the algorithm, see Elmroth and Gustavson (cited above).

Definition at line 133 of file cgeqrt3.f.

Author
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Version 3.4.2					   Tue Sep 25 2012					 cgeqrt3.f(3)```
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