371 lines
11 KiB
C++
371 lines
11 KiB
C++
/* fortran/dlaed9.f -- translated by f2c (version 20200916).
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You must link the resulting object file with libf2c:
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on Microsoft Windows system, link with libf2c.lib;
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on Linux or Unix systems, link with .../path/to/libf2c.a -lm
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or, if you install libf2c.a in a standard place, with -lf2c -lm
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-- in that order, at the end of the command line, as in
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cc *.o -lf2c -lm
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Source for libf2c is in /netlib/f2c/libf2c.zip, e.g.,
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http://www.netlib.org/f2c/libf2c.zip
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*/
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#ifdef __cplusplus
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extern "C" {
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#endif
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#include "lmp_f2c.h"
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/* Table of constant values */
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static integer c__1 = 1;
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/* > \brief \b DLAED9 used by DSTEDC. Finds the roots of the secular equation and updates the eigenvectors. Us
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ed when the original matrix is dense. */
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/* =========== DOCUMENTATION =========== */
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/* Online html documentation available at */
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/* http://www.netlib.org/lapack/explore-html/ */
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/* > \htmlonly */
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/* > Download DLAED9 + dependencies */
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/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlaed9.
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f"> */
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/* > [TGZ]</a> */
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/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlaed9.
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f"> */
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/* > [ZIP]</a> */
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/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlaed9.
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f"> */
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/* > [TXT]</a> */
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/* > \endhtmlonly */
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/* Definition: */
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/* =========== */
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/* SUBROUTINE DLAED9( K, KSTART, KSTOP, N, D, Q, LDQ, RHO, DLAMDA, W, */
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/* S, LDS, INFO ) */
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/* .. Scalar Arguments .. */
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/* INTEGER INFO, K, KSTART, KSTOP, LDQ, LDS, N */
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/* DOUBLE PRECISION RHO */
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/* .. */
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/* .. Array Arguments .. */
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/* DOUBLE PRECISION D( * ), DLAMDA( * ), Q( LDQ, * ), S( LDS, * ), */
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/* $ W( * ) */
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/* .. */
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/* > \par Purpose: */
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/* ============= */
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/* > */
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/* > \verbatim */
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/* > */
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/* > DLAED9 finds the roots of the secular equation, as defined by the */
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/* > values in D, Z, and RHO, between KSTART and KSTOP. It makes the */
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/* > appropriate calls to DLAED4 and then stores the new matrix of */
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/* > eigenvectors for use in calculating the next level of Z vectors. */
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/* > \endverbatim */
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/* Arguments: */
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/* ========== */
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/* > \param[in] K */
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/* > \verbatim */
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/* > K is INTEGER */
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/* > The number of terms in the rational function to be solved by */
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/* > DLAED4. K >= 0. */
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/* > \endverbatim */
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/* > */
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/* > \param[in] KSTART */
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/* > \verbatim */
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/* > KSTART is INTEGER */
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/* > \endverbatim */
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/* > */
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/* > \param[in] KSTOP */
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/* > \verbatim */
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/* > KSTOP is INTEGER */
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/* > The updated eigenvalues Lambda(I), KSTART <= I <= KSTOP */
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/* > are to be computed. 1 <= KSTART <= KSTOP <= K. */
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/* > \endverbatim */
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/* > */
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/* > \param[in] N */
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/* > \verbatim */
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/* > N is INTEGER */
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/* > The number of rows and columns in the Q matrix. */
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/* > N >= K (delation may result in N > K). */
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/* > \endverbatim */
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/* > */
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/* > \param[out] D */
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/* > \verbatim */
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/* > D is DOUBLE PRECISION array, dimension (N) */
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/* > D(I) contains the updated eigenvalues */
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/* > for KSTART <= I <= KSTOP. */
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/* > \endverbatim */
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/* > */
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/* > \param[out] Q */
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/* > \verbatim */
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/* > Q is DOUBLE PRECISION array, dimension (LDQ,N) */
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/* > \endverbatim */
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/* > */
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/* > \param[in] LDQ */
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/* > \verbatim */
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/* > LDQ is INTEGER */
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/* > The leading dimension of the array Q. LDQ >= max( 1, N ). */
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/* > \endverbatim */
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/* > */
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/* > \param[in] RHO */
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/* > \verbatim */
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/* > RHO is DOUBLE PRECISION */
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/* > The value of the parameter in the rank one update equation. */
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/* > RHO >= 0 required. */
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/* > \endverbatim */
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/* > */
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/* > \param[in] DLAMDA */
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/* > \verbatim */
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/* > DLAMDA is DOUBLE PRECISION array, dimension (K) */
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/* > The first K elements of this array contain the old roots */
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/* > of the deflated updating problem. These are the poles */
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/* > of the secular equation. */
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/* > \endverbatim */
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/* > */
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/* > \param[in] W */
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/* > \verbatim */
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/* > W is DOUBLE PRECISION array, dimension (K) */
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/* > The first K elements of this array contain the components */
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/* > of the deflation-adjusted updating vector. */
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/* > \endverbatim */
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/* > */
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/* > \param[out] S */
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/* > \verbatim */
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/* > S is DOUBLE PRECISION array, dimension (LDS, K) */
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/* > Will contain the eigenvectors of the repaired matrix which */
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/* > will be stored for subsequent Z vector calculation and */
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/* > multiplied by the previously accumulated eigenvectors */
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/* > to update the system. */
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/* > \endverbatim */
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/* > */
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/* > \param[in] LDS */
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/* > \verbatim */
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/* > LDS is INTEGER */
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/* > The leading dimension of S. LDS >= max( 1, K ). */
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/* > \endverbatim */
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/* > */
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/* > \param[out] INFO */
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/* > \verbatim */
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/* > INFO is INTEGER */
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/* > = 0: successful exit. */
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/* > < 0: if INFO = -i, the i-th argument had an illegal value. */
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/* > > 0: if INFO = 1, an eigenvalue did not converge */
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/* > \endverbatim */
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/* Authors: */
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/* ======== */
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/* > \author Univ. of Tennessee */
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/* > \author Univ. of California Berkeley */
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/* > \author Univ. of Colorado Denver */
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/* > \author NAG Ltd. */
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/* > \ingroup auxOTHERcomputational */
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/* > \par Contributors: */
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/* ================== */
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/* > */
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/* > Jeff Rutter, Computer Science Division, University of California */
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/* > at Berkeley, USA */
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/* ===================================================================== */
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/* Subroutine */ int dlaed9_(integer *k, integer *kstart, integer *kstop,
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integer *n, doublereal *d__, doublereal *q, integer *ldq, doublereal *
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rho, doublereal *dlamda, doublereal *w, doublereal *s, integer *lds,
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integer *info)
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{
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/* System generated locals */
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integer q_dim1, q_offset, s_dim1, s_offset, i__1, i__2;
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doublereal d__1;
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/* Builtin functions */
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double sqrt(doublereal), d_sign(doublereal *, doublereal *);
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/* Local variables */
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integer i__, j;
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doublereal temp;
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extern doublereal dnrm2_(integer *, doublereal *, integer *);
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extern /* Subroutine */ int dcopy_(integer *, doublereal *, integer *,
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doublereal *, integer *), dlaed4_(integer *, integer *,
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doublereal *, doublereal *, doublereal *, doublereal *,
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doublereal *, integer *);
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extern doublereal dlamc3_(doublereal *, doublereal *);
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extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen);
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/* -- LAPACK computational routine -- */
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/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
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/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
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/* .. Scalar Arguments .. */
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/* .. */
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/* .. Array Arguments .. */
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/* .. */
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/* ===================================================================== */
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/* .. Local Scalars .. */
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/* .. */
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/* .. External Functions .. */
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/* .. */
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/* .. External Subroutines .. */
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/* .. */
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/* .. Intrinsic Functions .. */
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/* .. */
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/* .. Executable Statements .. */
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/* Test the input parameters. */
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/* Parameter adjustments */
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--d__;
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q_dim1 = *ldq;
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q_offset = 1 + q_dim1;
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q -= q_offset;
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--dlamda;
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--w;
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s_dim1 = *lds;
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s_offset = 1 + s_dim1;
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s -= s_offset;
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/* Function Body */
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*info = 0;
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if (*k < 0) {
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*info = -1;
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} else if (*kstart < 1 || *kstart > max(1,*k)) {
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*info = -2;
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} else if (max(1,*kstop) < *kstart || *kstop > max(1,*k)) {
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*info = -3;
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} else if (*n < *k) {
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*info = -4;
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} else if (*ldq < max(1,*k)) {
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*info = -7;
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} else if (*lds < max(1,*k)) {
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*info = -12;
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}
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if (*info != 0) {
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i__1 = -(*info);
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xerbla_((char *)"DLAED9", &i__1, (ftnlen)6);
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return 0;
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}
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/* Quick return if possible */
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if (*k == 0) {
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return 0;
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}
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/* Modify values DLAMDA(i) to make sure all DLAMDA(i)-DLAMDA(j) can */
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/* be computed with high relative accuracy (barring over/underflow). */
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/* This is a problem on machines without a guard digit in */
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/* add/subtract (Cray XMP, Cray YMP, Cray C 90 and Cray 2). */
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/* The following code replaces DLAMDA(I) by 2*DLAMDA(I)-DLAMDA(I), */
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/* which on any of these machines zeros out the bottommost */
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/* bit of DLAMDA(I) if it is 1; this makes the subsequent */
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/* subtractions DLAMDA(I)-DLAMDA(J) unproblematic when cancellation */
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/* occurs. On binary machines with a guard digit (almost all */
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/* machines) it does not change DLAMDA(I) at all. On hexadecimal */
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/* and decimal machines with a guard digit, it slightly */
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/* changes the bottommost bits of DLAMDA(I). It does not account */
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/* for hexadecimal or decimal machines without guard digits */
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/* (we know of none). We use a subroutine call to compute */
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/* 2*DLAMBDA(I) to prevent optimizing compilers from eliminating */
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/* this code. */
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i__1 = *n;
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for (i__ = 1; i__ <= i__1; ++i__) {
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dlamda[i__] = dlamc3_(&dlamda[i__], &dlamda[i__]) - dlamda[i__];
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/* L10: */
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}
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i__1 = *kstop;
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for (j = *kstart; j <= i__1; ++j) {
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dlaed4_(k, &j, &dlamda[1], &w[1], &q[j * q_dim1 + 1], rho, &d__[j],
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info);
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/* If the zero finder fails, the computation is terminated. */
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if (*info != 0) {
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goto L120;
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}
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/* L20: */
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}
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if (*k == 1 || *k == 2) {
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i__1 = *k;
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for (i__ = 1; i__ <= i__1; ++i__) {
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i__2 = *k;
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for (j = 1; j <= i__2; ++j) {
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s[j + i__ * s_dim1] = q[j + i__ * q_dim1];
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/* L30: */
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}
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/* L40: */
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}
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goto L120;
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}
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/* Compute updated W. */
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dcopy_(k, &w[1], &c__1, &s[s_offset], &c__1);
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/* Initialize W(I) = Q(I,I) */
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i__1 = *ldq + 1;
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dcopy_(k, &q[q_offset], &i__1, &w[1], &c__1);
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i__1 = *k;
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for (j = 1; j <= i__1; ++j) {
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i__2 = j - 1;
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for (i__ = 1; i__ <= i__2; ++i__) {
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w[i__] *= q[i__ + j * q_dim1] / (dlamda[i__] - dlamda[j]);
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/* L50: */
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}
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i__2 = *k;
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for (i__ = j + 1; i__ <= i__2; ++i__) {
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w[i__] *= q[i__ + j * q_dim1] / (dlamda[i__] - dlamda[j]);
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/* L60: */
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}
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/* L70: */
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}
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i__1 = *k;
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for (i__ = 1; i__ <= i__1; ++i__) {
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d__1 = sqrt(-w[i__]);
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w[i__] = d_sign(&d__1, &s[i__ + s_dim1]);
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/* L80: */
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}
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/* Compute eigenvectors of the modified rank-1 modification. */
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i__1 = *k;
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for (j = 1; j <= i__1; ++j) {
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i__2 = *k;
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for (i__ = 1; i__ <= i__2; ++i__) {
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q[i__ + j * q_dim1] = w[i__] / q[i__ + j * q_dim1];
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/* L90: */
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}
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temp = dnrm2_(k, &q[j * q_dim1 + 1], &c__1);
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i__2 = *k;
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for (i__ = 1; i__ <= i__2; ++i__) {
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s[i__ + j * s_dim1] = q[i__ + j * q_dim1] / temp;
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/* L100: */
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}
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/* L110: */
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}
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L120:
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return 0;
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/* End of DLAED9 */
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} /* dlaed9_ */
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#ifdef __cplusplus
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}
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#endif
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