ESMF_DGEQRF Subroutine

subroutine ESMF_DGEQRF(M, N, A, LDA, TAU, WORK, LWORK, INFO)

\brief \b ESMF_DGEQRF \htmlonly Download ESMF_DGEQRF + dependencies [TGZ] [ZIP] [TXT] \endhtmlonly \par Purpose:

\verbatim

ESMF_DGEQRF computes a QR factorization of a real M-by-N matrix A: A = Q * R. \endverbatim \param[in] M \verbatim M is INTEGER The number of rows of the matrix A. M >= 0. \endverbatim

\param[in] N \verbatim N is INTEGER The number of columns of the matrix A. N >= 0. \endverbatim

\param[in,out] A \verbatim A is 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). \endverbatim

\param[in] LDA \verbatim LDA is INTEGER The leading dimension of the array A. LDA >= max(1,M). \endverbatim

\param[out] TAU \verbatim TAU is DOUBLE PRECISION array, dimension (min(M,N)) The scalar factors of the elementary reflectors (see Further Details). \endverbatim

\param[out] WORK \verbatim WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)) On exit, if INFO = 0, WORK(1) returns the optimal LWORK. \endverbatim

\param[in] LWORK \verbatim LWORK is INTEGER The dimension of the array WORK. LWORK >= max(1,N). For optimum performance LWORK >= N*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 ESMF_XERBLA.

\endverbatim

\param[out] INFO \verbatim INFO is INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value \endverbatim \author Univ. of Tennessee \author Univ. of California Berkeley \author Univ. of Colorado Denver \author NAG Ltd. \date November 2011 \ingroup doubleGEcomputational \par Further Details:

\verbatim

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(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). \endverbatim

Arguments