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
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**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
Generated automatically by Doxygen for LAPACK from the source code.
Version 3.4.2 Tue Sep 25 2012 cgeqrt3.f(3)
