CGERQF(3)      LAPACK routine of NEC Numeric Library Collection      CGERQF(3)



NAME
       CGERQF

SYNOPSIS
       SUBROUTINE CGERQF (M, N, A, LDA, TAU, WORK, LWORK, INFO)



PURPOSE
            CGERQF computes an RQ factorization of a complex M-by-N matrix A:
            A = R * Q.




ARGUMENTS
           M         (input)
                     M is INTEGER
                     The number of rows of the matrix A.  M >= 0.

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

           A         (input/output)
                     A is COMPLEX 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 min(m,n) elementary
                     reflectors (see Further Details).

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

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

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

           LWORK     (input)
                     LWORK is INTEGER
                     The dimension of the array WORK.  LWORK >= max(1,M).
                     For optimum performance LWORK >= M*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      (output)
                     INFO is INTEGER
                     = 0:  successful exit
                     < 0:  if INFO = -i, the i-th argument had an illegal value






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).



LAPACK routine                  31 October 2017                      CGERQF(3)