SGERQ2(3)      LAPACK routine of NEC Numeric Library Collection      SGERQ2(3)



NAME
       SGERQ2

SYNOPSIS
       SUBROUTINE SGERQ2 (M, N, A, LDA, TAU, WORK, INFO)



PURPOSE
            SGERQ2 computes an RQ factorization of a real 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 REAL 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 orthogonal matrix
                     Q as a product of 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 REAL array, dimension (min(M,N))
                     The scalar factors of the elementary reflectors (see Further
                     Details).

           WORK      (output)
                     WORK is REAL array, dimension (M)

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

             Each H(i) has the form

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

             where tau is a real scalar, and v is a real vector with
             v(n-k+i+1:n) = 0 and v(n-k+i) = 1; 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                      SGERQ2(3)