DGEQRF (3lapack)

compute a QR factorization of a real M-by-N matrix A

SYNOPSIS

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

      INTEGER        INFO, LDA, LWORK, M, N

      DOUBLE         PRECISION A( LDA, * ), TAU( * ), WORK( LWORK )

PURPOSE

  DGEQRF computes a QR factorization of a real M-by-N matrix A: A = Q * R.

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) DOUBLE PRECISION array, dimension (LDA,N)
          On entry, the M-by-N matrix A.  On exit, the elements on and above
          the diagonal of the array contain the min(M,N)-by-N upper
          trapezoidal matrix R (R is upper triangular if m >= n); the
          elements below the diagonal, 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) DOUBLE PRECISION array, dimension (min(M,N))
          The scalar factors of the elementary reflectors (see Further
          Details).

  WORK    (workspace/output) DOUBLE PRECISION 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,N).  For optimum
          performance LWORK >= N*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(1:i-1) = 0 and v(i) = 1; v(i+1:m) is stored on exit in A(i+1:m,i), and
  tau in TAU(i).