cgelqt3.f man page

cgelqt3.f

Synopsis

Functions/Subroutines

recursive subroutine cgelqt3 (M, N, A, LDA, T, LDT, INFO)

Function/Subroutine Documentation

recursive subroutine cgelqt3 (integer M, integer N, complex, dimension( lda, * ) A, integer LDA, complex, dimension( ldt, * ) T, integer LDT, integer INFO)

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 real 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.

Date:

November 2017

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 116 of file cgelqt3.f.

Author

Generated automatically by Doxygen for LAPACK from the source code.

Referenced By

The man page cgelqt3(3) is an alias of cgelqt3.f(3).

Tue Nov 14 2017 Version 3.8.0 LAPACK