ESMF_DLAIC1 Subroutine

subroutine ESMF_DLAIC1(JOB, J, X, SEST, W, GAMMA, SESTPR, S, C)

\brief \b ESMF_DLAIC1 \htmlonly Download ESMF_DLAIC1 + dependencies [TGZ] [ZIP] [TXT] \endhtmlonly \par Purpose:

\verbatim

ESMF_DLAIC1 applies one step of incremental condition estimation in its simplest version:

Let x, twonorm(x) = 1, be an approximate singular vector of an j-by-j lower triangular matrix L, such that twonorm(Lx) = sest Then ESMF_DLAIC1 computes sestpr, s, c such that the vector [ sx ] xhat = [ c ] is an approximate singular vector of [ L 0 ] Lhat = [ w*T gamma ] in the sense that twonorm(Lhatxhat) = sestpr.

Depending on JOB, an estimate for the largest or smallest singular value is computed.

Note that [s c]T and sestpr2 is an eigenpair of the system

diag(sest*sest, 0) + [alpha  gamma] * [ alpha ]
                                      [ gamma ]

where alpha = x*Tw. \endverbatim \param[in] JOB \verbatim JOB is INTEGER = 1: an estimate for the largest singular value is computed. = 2: an estimate for the smallest singular value is computed. \endverbatim

\param[in] J \verbatim J is INTEGER Length of X and W \endverbatim

\param[in] X \verbatim X is DOUBLE PRECISION array, dimension (J) The j-vector x. \endverbatim

\param[in] SEST \verbatim SEST is DOUBLE PRECISION Estimated singular value of j by j matrix L \endverbatim

\param[in] W \verbatim W is DOUBLE PRECISION array, dimension (J) The j-vector w. \endverbatim

\param[in] GAMMA \verbatim GAMMA is DOUBLE PRECISION The diagonal element gamma. \endverbatim

\param[out] SESTPR \verbatim SESTPR is DOUBLE PRECISION Estimated singular value of (j+1) by (j+1) matrix Lhat. \endverbatim

\param[out] S \verbatim S is DOUBLE PRECISION Sine needed in forming xhat. \endverbatim

\param[out] C \verbatim C is DOUBLE PRECISION Cosine needed in forming xhat. \endverbatim \author Univ. of Tennessee \author Univ. of California Berkeley \author Univ. of Colorado Denver \author NAG Ltd. \date November 2011 \ingroup doubleOTHERauxiliary

Arguments