SGERQF (3lapack)

compute an RQ factorization of a real M-by-N matrix A

SYNOPSIS

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

      INTEGER        INFO, LDA, LWORK, M, N

      REAL           A( LDA, * ), TAU( * ), WORK( LWORK )

PURPOSE

  SGERQF computes an RQ factorization of a real M-by-N matrix A: A = R * Q.

ARGUMENTS

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

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

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

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

  WORK    (workspace/output) REAL array, dimension (LWORK)
          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

  LWORK   (input) INTEGER
          The dimension of the array WORK.  LWORK >= max(1,M).  For optimum
          performance LWORK >= M*NB, where NB is the optimal blocksize.

  INFO    (output) 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'

  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).