SRC/zgerq2.f(3)            Library Functions Manual            SRC/zgerq2.f(3)

NAME
       SRC/zgerq2.f

SYNOPSIS
   Functions/Subroutines
       subroutine zgerq2 (m, n, a, lda, tau, work, info)
           ZGERQ2 computes the RQ factorization of a general rectangular
           matrix using an unblocked algorithm.

Function/Subroutine Documentation
   subroutine zgerq2 (integer m, integer n, complex*16, dimension( lda, * ) a,
       integer lda, complex*16, dimension( * ) tau, complex*16, dimension( * )
       work, integer info)
       ZGERQ2 computes the RQ factorization of a general rectangular matrix
       using an unblocked algorithm.

       Purpose:


            ZGERQ2 computes an RQ factorization of a complex m by n matrix A:
            A = R * Q.

       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, if m <= n, the upper triangle of the subarray
                     A(1:m,n-m+1:n) contains the m by m upper triangular matrix R;
                     if m >= n, the elements on and above the (m-n)-th subdiagonal
                     contain the m by n upper trapezoidal matrix R; the remaining
                     elements, 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 (M)

           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 H(2)**H . . . H(k)**H, 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(n-k+i+1:n) = 0 and v(n-k+i) = 1; conjg(v(1:n-k+i-1)) is stored on
             exit in A(m-k+i,1:n-k+i-1), and tau in TAU(i).

       Definition at line 122 of file zgerq2.f.

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

LAPACK                          Version 3.12.0                 SRC/zgerq2.f(3)