
sgeqrt3.f(3) LAPACK sgeqrt3.f(3)
NAME
sgeqrt3.f 
SYNOPSIS
Functions/Subroutines
recursive subroutine sgeqrt3 (M, N, A, LDA, T, LDT, INFO)
SGEQRT3 recursively computes a QR factorization of a general real or complex matrix
using the compact WY representation of Q.
Function/Subroutine Documentation
recursive subroutine sgeqrt3 (integerM, integerN, real, dimension( lda, * )A, integerLDA,
real, dimension( ldt, * )T, integerLDT, integerINFO)
SGEQRT3 recursively computes a QR factorization of a general real or complex matrix using
the compact WY representation of Q.
Purpose:
SGEQRT3 recursively computes a QR factorization of a real MbyN
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 REAL array, dimension (LDA,N)
On entry, the real MbyN matrix A. On exit, the elements on and
above the diagonal contain the NbyN 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 REAL array, dimension (LDT,N)
The NbyN 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 ith 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 ith 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 sgeqrt3.f.
Author
Generated automatically by Doxygen for LAPACK from the source code.
Version 3.4.2 Tue Sep 25 2012 sgeqrt3.f(3) 
