NAME

       sgerqf.f -

SYNOPSIS

   Functions/Subroutines
       subroutine sgerqf (M, N, A, LDA, TAU, WORK, LWORK, INFO)
           SGERQF

Function/Subroutine Documentation

   subroutine sgerqf (integerM, integerN, real, dimension( lda, * )A, integerLDA, real,
       dimension( * )TAU, real, dimension( * )WORK, integerLWORK, integerINFO)
       SGERQF

       Purpose:

            SGERQF computes an RQ factorization of a real 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 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 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 REAL array, dimension (min(M,N))
                     The scalar factors of the elementary reflectors (see Further
                     Details).

           WORK

                     WORK is REAL 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.  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

                     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**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).

       Definition at line 139 of file sgerqf.f.

Author

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