SGERQ2 (3lapack)

compute an RQ factorization of a real m by n matrix A

SYNOPSIS

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

      INTEGER        INFO, LDA, M, N

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

PURPOSE

  SGERQ2 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 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) REAL array, dimension (M)

  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).