ESMF_DGELQ2 Subroutine

subroutine ESMF_DGELQ2(M, N, A, LDA, TAU, WORK, INFO)

\brief \b ESMF_DGELQ2 \htmlonly Download ESMF_DGELQ2 + dependencies [TGZ] [ZIP] [TXT] \endhtmlonly \par Purpose:

\verbatim

ESMF_DGELQ2 computes an LQ factorization of a real m by n matrix A: A = L * Q. \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 below the diagonal of the array contain the m by min(m,n) lower trapezoidal matrix L (L is lower triangular if m <= n); the elements above the diagonal, with the array TAU, represent the orthogonal matrix Q as a product of 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 (M) \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(k) . . . H(2) H(1), 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:n) is stored on exit in A(i,i+1:n), and tau in TAU(i). \endverbatim

Arguments