dgeqrt3.f man page

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

Univ. of Colorado Denver

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

Generated automatically by Doxygen for LAPACK from the source code.

Referenced By

dgeqrt3(3) is an alias of dgeqrt3.f(3).

Sat Nov 16 2013 Version 3.4.2 LAPACK