SRC/cgelqt3.f(3)           Library Functions Manual           SRC/cgelqt3.f(3)

NAME
       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
       Generated automatically by Doxygen for LAPACK from the source code.

LAPACK                          Version 3.12.0                SRC/cgelqt3.f(3)