Add graph references
This commit is contained in:
Abdelrahman Said
+453
@@ -0,0 +1,453 @@
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/* -- translated by f2c (version 20240504).
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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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#include "f2c.h"
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/* > \brief \b DLASQ3 checks for deflation, computes a shift and calls dqds. Used by sbdsqr.
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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 DLASQ3 + dependencies
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> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlasq3.
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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/dlasq3.
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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/dlasq3.
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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 DLASQ3( I0, N0, Z, PP, DMIN, SIGMA, DESIG, QMAX, NFAIL,
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ITER, NDIV, IEEE, TTYPE, DMIN1, DMIN2, DN, DN1,
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DN2, G, TAU )
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LOGICAL IEEE
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INTEGER I0, ITER, N0, NDIV, NFAIL, PP
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DOUBLE PRECISION DESIG, DMIN, DMIN1, DMIN2, DN, DN1, DN2, G,
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$ QMAX, SIGMA, TAU
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DOUBLE PRECISION Z( * )
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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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> DLASQ3 checks for deflation, computes a shift (TAU) and calls dqds.
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> In case of failure it changes shifts, and tries again until output
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> is positive.
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> \endverbatim
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Arguments:
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==========
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> \param[in] I0
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> \verbatim
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> I0 is INTEGER
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> First index.
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> \endverbatim
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>
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> \param[in,out] N0
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> \verbatim
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> N0 is INTEGER
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> Last index.
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> \endverbatim
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>
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> \param[in] Z
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> \verbatim
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> Z is DOUBLE PRECISION array, dimension ( 4*N )
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> Z holds the qd array.
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> \endverbatim
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>
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> \param[in,out] PP
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> \verbatim
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> PP is INTEGER
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> PP=0 for ping, PP=1 for pong.
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> PP=2 indicates that flipping was applied to the Z array
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> and that the initial tests for deflation should not be
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> performed.
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> \endverbatim
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>
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> \param[out] DMIN
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> \verbatim
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> DMIN is DOUBLE PRECISION
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> Minimum value of d.
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> \endverbatim
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>
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> \param[out] SIGMA
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> \verbatim
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> SIGMA is DOUBLE PRECISION
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> Sum of shifts used in current segment.
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> \endverbatim
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>
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> \param[in,out] DESIG
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> \verbatim
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> DESIG is DOUBLE PRECISION
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> Lower order part of SIGMA
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> \endverbatim
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>
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> \param[in] QMAX
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> \verbatim
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> QMAX is DOUBLE PRECISION
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> Maximum value of q.
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> \endverbatim
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>
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> \param[out] NFAIL
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> \verbatim
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> NFAIL is INTEGER
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> Number of times shift was too big.
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> \endverbatim
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>
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> \param[out] ITER
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> \verbatim
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> ITER is INTEGER
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> Number of iterations.
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> \endverbatim
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>
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> \param[out] NDIV
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> \verbatim
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> NDIV is INTEGER
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> Number of divisions.
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> \endverbatim
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>
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> \param[in] IEEE
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> \verbatim
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> IEEE is LOGICAL
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> Flag for IEEE or non IEEE arithmetic (passed to DLASQ5).
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> \endverbatim
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>
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> \param[in,out] TTYPE
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> \verbatim
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> TTYPE is INTEGER
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> Shift type.
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> \endverbatim
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>
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> \param[in,out] DMIN1
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> \verbatim
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> DMIN1 is DOUBLE PRECISION
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> \endverbatim
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>
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> \param[in,out] DMIN2
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> \verbatim
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> DMIN2 is DOUBLE PRECISION
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> \endverbatim
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>
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> \param[in,out] DN
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> \verbatim
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> DN is DOUBLE PRECISION
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> \endverbatim
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>
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> \param[in,out] DN1
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> \verbatim
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> DN1 is DOUBLE PRECISION
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> \endverbatim
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>
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> \param[in,out] DN2
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> \verbatim
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> DN2 is DOUBLE PRECISION
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> \endverbatim
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>
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> \param[in,out] G
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> \verbatim
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> G is DOUBLE PRECISION
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> \endverbatim
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>
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> \param[in,out] TAU
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> \verbatim
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> TAU is DOUBLE PRECISION
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>
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> These are passed as arguments in order to save their values
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> between calls to DLASQ3.
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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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> \date September 2012
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> \ingroup auxOTHERcomputational
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=====================================================================
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Subroutine */ int igraphdlasq3_(integer *i0, integer *n0, doublereal *z__,
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integer *pp, doublereal *dmin__, doublereal *sigma, doublereal *desig,
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doublereal *qmax, integer *nfail, integer *iter, integer *ndiv,
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logical *ieee, integer *ttype, doublereal *dmin1, doublereal *dmin2,
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doublereal *dn, doublereal *dn1, doublereal *dn2, doublereal *g,
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doublereal *tau)
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{
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/* System generated locals */
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integer i__1;
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doublereal d__1, d__2;
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/* Builtin functions */
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double sqrt(doublereal);
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/* Local variables */
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doublereal s, t;
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integer j4, nn;
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doublereal eps, tol;
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integer n0in, ipn4;
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doublereal tol2, temp;
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extern /* Subroutine */ int igraphdlasq4_(integer *, integer *, doublereal *,
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integer *, integer *, doublereal *, doublereal *, doublereal *,
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doublereal *, doublereal *, doublereal *, doublereal *, integer *,
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doublereal *), igraphdlasq5_(integer *, integer *, doublereal *,
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integer *, doublereal *, doublereal *, doublereal *, doublereal *,
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doublereal *, doublereal *, doublereal *, doublereal *, logical *
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, doublereal *), igraphdlasq6_(integer *, integer *, doublereal *,
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integer *, doublereal *, doublereal *, doublereal *, doublereal *,
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doublereal *, doublereal *);
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extern doublereal igraphdlamch_(char *);
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extern logical igraphdisnan_(doublereal *);
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/* -- LAPACK computational routine (version 3.4.2) --
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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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September 2012
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=====================================================================
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Parameter adjustments */
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--z__;
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/* Function Body */
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n0in = *n0;
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eps = igraphdlamch_("Precision");
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tol = eps * 100.;
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/* Computing 2nd power */
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d__1 = tol;
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tol2 = d__1 * d__1;
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/* Check for deflation. */
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L10:
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if (*n0 < *i0) {
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return 0;
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}
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if (*n0 == *i0) {
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goto L20;
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}
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nn = (*n0 << 2) + *pp;
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if (*n0 == *i0 + 1) {
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goto L40;
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}
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/* Check whether E(N0-1) is negligible, 1 eigenvalue. */
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if (z__[nn - 5] > tol2 * (*sigma + z__[nn - 3]) && z__[nn - (*pp << 1) -
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4] > tol2 * z__[nn - 7]) {
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goto L30;
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}
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L20:
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z__[(*n0 << 2) - 3] = z__[(*n0 << 2) + *pp - 3] + *sigma;
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--(*n0);
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goto L10;
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/* Check whether E(N0-2) is negligible, 2 eigenvalues. */
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L30:
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if (z__[nn - 9] > tol2 * *sigma && z__[nn - (*pp << 1) - 8] > tol2 * z__[
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nn - 11]) {
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goto L50;
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}
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L40:
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if (z__[nn - 3] > z__[nn - 7]) {
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s = z__[nn - 3];
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z__[nn - 3] = z__[nn - 7];
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z__[nn - 7] = s;
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}
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t = (z__[nn - 7] - z__[nn - 3] + z__[nn - 5]) * .5;
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if (z__[nn - 5] > z__[nn - 3] * tol2 && t != 0.) {
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s = z__[nn - 3] * (z__[nn - 5] / t);
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if (s <= t) {
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s = z__[nn - 3] * (z__[nn - 5] / (t * (sqrt(s / t + 1.) + 1.)));
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} else {
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s = z__[nn - 3] * (z__[nn - 5] / (t + sqrt(t) * sqrt(t + s)));
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}
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t = z__[nn - 7] + (s + z__[nn - 5]);
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z__[nn - 3] *= z__[nn - 7] / t;
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z__[nn - 7] = t;
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}
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z__[(*n0 << 2) - 7] = z__[nn - 7] + *sigma;
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z__[(*n0 << 2) - 3] = z__[nn - 3] + *sigma;
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*n0 += -2;
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goto L10;
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L50:
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if (*pp == 2) {
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*pp = 0;
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}
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/* Reverse the qd-array, if warranted. */
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if (*dmin__ <= 0. || *n0 < n0in) {
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if (z__[(*i0 << 2) + *pp - 3] * 1.5 < z__[(*n0 << 2) + *pp - 3]) {
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ipn4 = *i0 + *n0 << 2;
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i__1 = *i0 + *n0 - 1 << 1;
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for (j4 = *i0 << 2; j4 <= i__1; j4 += 4) {
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temp = z__[j4 - 3];
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z__[j4 - 3] = z__[ipn4 - j4 - 3];
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z__[ipn4 - j4 - 3] = temp;
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temp = z__[j4 - 2];
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z__[j4 - 2] = z__[ipn4 - j4 - 2];
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z__[ipn4 - j4 - 2] = temp;
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temp = z__[j4 - 1];
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z__[j4 - 1] = z__[ipn4 - j4 - 5];
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z__[ipn4 - j4 - 5] = temp;
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temp = z__[j4];
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z__[j4] = z__[ipn4 - j4 - 4];
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z__[ipn4 - j4 - 4] = temp;
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/* L60: */
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}
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if (*n0 - *i0 <= 4) {
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z__[(*n0 << 2) + *pp - 1] = z__[(*i0 << 2) + *pp - 1];
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z__[(*n0 << 2) - *pp] = z__[(*i0 << 2) - *pp];
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}
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/* Computing MIN */
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d__1 = *dmin2, d__2 = z__[(*n0 << 2) + *pp - 1];
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*dmin2 = min(d__1,d__2);
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/* Computing MIN */
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d__1 = z__[(*n0 << 2) + *pp - 1], d__2 = z__[(*i0 << 2) + *pp - 1]
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, d__1 = min(d__1,d__2), d__2 = z__[(*i0 << 2) + *pp + 3];
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z__[(*n0 << 2) + *pp - 1] = min(d__1,d__2);
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/* Computing MIN */
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d__1 = z__[(*n0 << 2) - *pp], d__2 = z__[(*i0 << 2) - *pp], d__1 =
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min(d__1,d__2), d__2 = z__[(*i0 << 2) - *pp + 4];
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z__[(*n0 << 2) - *pp] = min(d__1,d__2);
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/* Computing MAX */
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d__1 = *qmax, d__2 = z__[(*i0 << 2) + *pp - 3], d__1 = max(d__1,
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d__2), d__2 = z__[(*i0 << 2) + *pp + 1];
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*qmax = max(d__1,d__2);
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*dmin__ = -0.;
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}
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}
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/* Choose a shift. */
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igraphdlasq4_(i0, n0, &z__[1], pp, &n0in, dmin__, dmin1, dmin2, dn, dn1, dn2,
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tau, ttype, g);
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/* Call dqds until DMIN > 0. */
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L70:
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igraphdlasq5_(i0, n0, &z__[1], pp, tau, sigma, dmin__, dmin1, dmin2, dn, dn1,
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dn2, ieee, &eps);
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*ndiv += *n0 - *i0 + 2;
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++(*iter);
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/* Check status. */
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if (*dmin__ >= 0. && *dmin1 >= 0.) {
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/* Success. */
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goto L90;
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} else if (*dmin__ < 0. && *dmin1 > 0. && z__[(*n0 - 1 << 2) - *pp] < tol
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* (*sigma + *dn1) && abs(*dn) < tol * *sigma) {
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/* Convergence hidden by negative DN. */
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z__[(*n0 - 1 << 2) - *pp + 2] = 0.;
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*dmin__ = 0.;
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goto L90;
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} else if (*dmin__ < 0.) {
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/* TAU too big. Select new TAU and try again. */
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++(*nfail);
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if (*ttype < -22) {
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/* Failed twice. Play it safe. */
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*tau = 0.;
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} else if (*dmin1 > 0.) {
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/* Late failure. Gives excellent shift. */
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*tau = (*tau + *dmin__) * (1. - eps * 2.);
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*ttype += -11;
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} else {
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/* Early failure. Divide by 4. */
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*tau *= .25;
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*ttype += -12;
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}
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goto L70;
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} else if (igraphdisnan_(dmin__)) {
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/* NaN. */
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if (*tau == 0.) {
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goto L80;
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} else {
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*tau = 0.;
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goto L70;
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}
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} else {
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/* Possible underflow. Play it safe. */
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goto L80;
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}
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/* Risk of underflow. */
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L80:
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igraphdlasq6_(i0, n0, &z__[1], pp, dmin__, dmin1, dmin2, dn, dn1, dn2);
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*ndiv += *n0 - *i0 + 2;
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++(*iter);
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*tau = 0.;
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L90:
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if (*tau < *sigma) {
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*desig += *tau;
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t = *sigma + *desig;
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*desig -= t - *sigma;
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} else {
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t = *sigma + *tau;
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*desig = *sigma - (t - *tau) + *desig;
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}
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*sigma = t;
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return 0;
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/* End of DLASQ3 */
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} /* igraphdlasq3_ */
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Block a user