ESMF_DGEHD2 Subroutine

subroutine ESMF_DGEHD2(N, ILO, IHI, A, LDA, TAU, WORK, INFO)

\brief \b ESMF_DGEHD2 reduces a general square matrix to upper Hessenberg form using an unblocked algorithm. \htmlonly Download ESMF_DGEHD2 + dependencies [TGZ] [ZIP] [TXT] \endhtmlonly \par Purpose:

\verbatim

ESMF_DGEHD2 reduces a real general matrix A to upper Hessenberg form H by an orthogonal similarity transformation: Q**T * A * Q = H . \endverbatim \param[in] N \verbatim N is INTEGER The order of the matrix A. N >= 0. \endverbatim

\param[in] ILO \verbatim ILO is INTEGER \endverbatim

\param[in] IHI \verbatim IHI is INTEGER

     It is assumed that A is already upper triangular in rows
     and columns 1:ILO-1 and IHI+1:N. ILO and IHI are normally
     set by a previous call to ESMF_DGEBAL; otherwise they should be
     set to 1 and N respectively. See Further Details.
     1 <= ILO <= IHI <= max(1,N).

\endverbatim

\param[in,out] A \verbatim A is DOUBLE PRECISION array, dimension (LDA,N) On entry, the n by n general matrix to be reduced. On exit, the upper triangle and the first subdiagonal of A are overwritten with the upper Hessenberg matrix H, and the elements below the first subdiagonal, 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,N). \endverbatim

\param[out] TAU \verbatim TAU is DOUBLE PRECISION array, dimension (N-1) The scalar factors of the elementary reflectors (see Further Details). \endverbatim

\param[out] WORK \verbatim WORK is DOUBLE PRECISION array, dimension (N) \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 December 2016 \ingroup doubleGEcomputational \par Further Details:

\verbatim

The matrix Q is represented as a product of (ihi-ilo) elementary reflectors

Q = H(ilo) H(ilo+1) . . . H(ihi-1).

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) = 0, v(i+1) = 1 and v(ihi+1:n) = 0; v(i+2:ihi) is stored on exit in A(i+2:ihi,i), and tau in TAU(i).

The contents of A are illustrated by the following example, with n = 7, ilo = 2 and ihi = 6:

on entry, on exit,

( a a a a a a a ) ( a a h h h h a ) ( a a a a a a ) ( a h h h h a ) ( a a a a a a ) ( h h h h h h ) ( a a a a a a ) ( v2 h h h h h ) ( a a a a a a ) ( v2 v3 h h h h ) ( a a a a a a ) ( v2 v3 v4 h h h ) ( a ) ( a )

where a denotes an element of the original matrix A, h denotes a modified element of the upper Hessenberg matrix H, and vi denotes an element of the vector defining H(i). \endverbatim

Arguments