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NAME

       zgeqrf.f -

SYNOPSIS

   Functions/Subroutines
       subroutine zgeqrf (M, N, A, LDA, TAU, WORK, LWORK, INFO)
           ZGEQRF VARIANT: left-looking Level 3 BLAS of the algorithm.

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 VARIANT: left-looking Level 3 BLAS of the algorithm. Purpose:

        ZGEQRF computes a QR factorization of a real M-by-N matrix A:
        A = Q * R.

        This is the left-looking Level 3 BLAS version of the algorithm.

       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 orthogonal 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. The dimension can be divided into three parts.

                     1) The part for the triangular factor T. If the very last T is not bigger
                        than any of the rest, then this part is NB x ceiling(K/NB), otherwise,
                        NB x (K-NT), where K = min(M,N) and NT is the dimension of the very last T

                     2) The part for the very last T when T is bigger than any of the rest T.
                        The size of this part is NT x NT, where NT = K - ceiling ((K-NX)/NB) x NB,
                        where K = min(M,N), NX is calculated by
                              NX = MAX( 0, ILAENV( 3, 'ZGEQRF', ' ', M, N, -1, -1 ) )

                     3) The part for dlarfb is of size max((N-M)*K, (N-M)*NB, K*NB, NB*NB)

                     So LWORK = part1 + part2 + part3

                     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.

       Date:
           November 2011

       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'

         where tau is a real scalar, and v is a real 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).

Author

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