SRC/zgeqr2.f(3)            Library Functions Manual            SRC/zgeqr2.f(3)

NAME
       SRC/zgeqr2.f

SYNOPSIS
   Functions/Subroutines
       subroutine zgeqr2 (m, n, a, lda, tau, work, info)
           ZGEQR2 computes the QR factorization of a general rectangular
           matrix using an unblocked algorithm.

Function/Subroutine Documentation
   subroutine zgeqr2 (integer m, integer n, complex*16, dimension( lda, * ) a,
       integer lda, complex*16, dimension( * ) tau, complex*16, dimension( * )
       work, integer info)
       ZGEQR2 computes the QR factorization of a general rectangular matrix
       using an unblocked algorithm.

       Purpose:


            ZGEQR2 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 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 (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 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 129 of file zgeqr2.f.

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

LAPACK                          Version 3.12.0                 SRC/zgeqr2.f(3)