cgelqt3.f - Man Page
SRC/cgelqt3.f
Synopsis
Functions/Subroutines
recursive subroutine cgelqt3 (m, n, a, lda, t, ldt, info)
CGELQT3
Function/Subroutine Documentation
recursive subroutine cgelqt3 (integer m, integer n, complex, dimension( lda, * ) a, integer lda, complex, dimension( ldt, * ) t, integer ldt, integer info)
CGELQT3
Purpose:
CGELQT3 recursively computes a LQ 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 below the diagonal contain the N-by-N lower triangular matrix L; the elements above the diagonal are the rows 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.
Further Details:
The matrix V stores the elementary reflectors H(i) in the i-th row above the diagonal. For example, if M=5 and N=3, the matrix V is V = ( 1 v1 v1 v1 v1 ) ( 1 v2 v2 v2 ) ( 1 v3 v3 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 115 of file cgelqt3.f.
Author
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Referenced By
The man page cgelqt3(3) is an alias of cgelqt3.f(3).
Tue Nov 28 2023 12:08:41 Version 3.12.0 LAPACK