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

NAME
       SRC/zgeqrf.f

SYNOPSIS
   Functions/Subroutines
       subroutine zgeqrf (m, n, a, lda, tau, work, lwork, info)
           ZGEQRF

Function/Subroutine Documentation
   subroutine zgeqrf (integer m, integer n, complex*16, dimension( lda, * ) a,
       integer lda, complex*16, dimension( * ) tau, complex*16, dimension( * )
       work, integer lwork, integer info)
       ZGEQRF

       Purpose:


            ZGEQRF computes a QR factorization of a complex M-by-N matrix A:

               A = Q * ( R ),
                       ( 0 )

            where:

               Q is a M-by-M orthogonal matrix;
               R is an upper-triangular N-by-N matrix;
               0 is a (M-N)-by-N zero matrix, if M > N.

       Parameters
           M

                     M is INTEGER
                     The number of rows of the matrix A.  M >= 0.

           N

                     N is INTEGER
                     The number of columns of the matrix A.  N >= 0.

           A

                     A is COMPLEX*16 array, dimension (LDA,N)
                     On entry, the M-by-N matrix A.
                     On exit, the elements on and above the diagonal of the array
                     contain the min(M,N)-by-N upper trapezoidal matrix R (R is
                     upper triangular if m >= n); the elements below the diagonal,
                     with the array TAU, represent the unitary matrix Q as a
                     product of min(m,n) elementary reflectors (see Further
                     Details).

           LDA

                     LDA is INTEGER
                     The leading dimension of the array A.  LDA >= max(1,M).

           TAU

                     TAU is COMPLEX*16 array, dimension (min(M,N))
                     The scalar factors of the elementary reflectors (see Further
                     Details).

           WORK

                     WORK is COMPLEX*16 array, dimension (MAX(1,LWORK))
                     On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

           LWORK

                     LWORK is INTEGER
                     The dimension of the array WORK.
                     LWORK >= 1, if MIN(M,N) = 0, and LWORK >= N, otherwise.
                     For optimum performance LWORK >= N*NB, where NB is
                     the optimal blocksize.

                     If LWORK = -1, then a workspace query is assumed; the routine
                     only calculates the optimal size of the WORK array, returns
                     this value as the first entry of the WORK array, and no error
                     message related to LWORK is issued by XERBLA.

           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 Q is represented as a product of elementary reflectors

                Q = H(1) H(2) . . . H(k), where k = min(m,n).

             Each H(i) has the form

                H(i) = I - tau * v * v**H

             where tau is a complex scalar, and v is a complex vector with
             v(1:i-1) = 0 and v(i) = 1; v(i+1:m) is stored on exit in A(i+1:m,i),
             and tau in TAU(i).

       Definition at line 145 of file zgeqrf.f.

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

LAPACK                          Version 3.12.0                 SRC/zgeqrf.f(3)