# dgeqrt3 (3) - Linux Manuals

dgeqrt3.f -

## SYNOPSIS

### Functions/Subroutines

recursive subroutine dgeqrt3 (M, N, A, LDA, T, LDT, INFO)
DGEQRT3 recursively computes a QR factorization of a general real or complex matrix using the compact WY representation of Q.

## Function/Subroutine Documentation

### recursive subroutine dgeqrt3 (integerM, integerN, double precision, dimension( lda, * )A, integerLDA, double precision, dimension( ldt, * )T, integerLDT, integerINFO)

DGEQRT3 recursively computes a QR factorization of a general real or complex matrix using the compact WY representation of Q.

Purpose:

DGEQRT3 recursively computes a QR factorization of a real 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 DOUBLE PRECISION array, dimension (LDA,N)
On entry, the real 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 DOUBLE PRECISION 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**T

where V**T is the transpose of V.

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

Definition at line 133 of file dgeqrt3.f.

## Author

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