Add graph references
This commit is contained in:
Abdelrahman Said
+415
@@ -0,0 +1,415 @@
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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 DLAGTS solves the system of equations (T-λI)x = y or (T-λI)Tx = y,where T is a general tridia
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gonal matrix and λ a scalar, using the LU factorization computed by slagtf.
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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 DLAGTS + dependencies
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> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlagts.
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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/dlagts.
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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/dlagts.
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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 DLAGTS( JOB, N, A, B, C, D, IN, Y, TOL, INFO )
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INTEGER INFO, JOB, N
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DOUBLE PRECISION TOL
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INTEGER IN( * )
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DOUBLE PRECISION A( * ), B( * ), C( * ), D( * ), Y( * )
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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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> DLAGTS may be used to solve one of the systems of equations
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>
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> (T - lambda*I)*x = y or (T - lambda*I)**T*x = y,
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>
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> where T is an n by n tridiagonal matrix, for x, following the
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> factorization of (T - lambda*I) as
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>
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> (T - lambda*I) = P*L*U ,
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>
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> by routine DLAGTF. The choice of equation to be solved is
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> controlled by the argument JOB, and in each case there is an option
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> to perturb zero or very small diagonal elements of U, this option
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> being intended for use in applications such as inverse iteration.
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> \endverbatim
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Arguments:
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==========
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> \param[in] JOB
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> \verbatim
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> JOB is INTEGER
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> Specifies the job to be performed by DLAGTS as follows:
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> = 1: The equations (T - lambda*I)x = y are to be solved,
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> but diagonal elements of U are not to be perturbed.
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> = -1: The equations (T - lambda*I)x = y are to be solved
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> and, if overflow would otherwise occur, the diagonal
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> elements of U are to be perturbed. See argument TOL
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> below.
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> = 2: The equations (T - lambda*I)**Tx = y are to be solved,
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> but diagonal elements of U are not to be perturbed.
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> = -2: The equations (T - lambda*I)**Tx = y are to be solved
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> and, if overflow would otherwise occur, the diagonal
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> elements of U are to be perturbed. See argument TOL
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> below.
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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 order of the matrix T.
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> \endverbatim
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>
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> \param[in] A
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> \verbatim
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> A is DOUBLE PRECISION array, dimension (N)
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> On entry, A must contain the diagonal elements of U as
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> returned from DLAGTF.
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> \endverbatim
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>
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> \param[in] B
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> \verbatim
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> B is DOUBLE PRECISION array, dimension (N-1)
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> On entry, B must contain the first super-diagonal elements of
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> U as returned from DLAGTF.
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> \endverbatim
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>
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> \param[in] C
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> \verbatim
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> C is DOUBLE PRECISION array, dimension (N-1)
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> On entry, C must contain the sub-diagonal elements of L as
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> returned from DLAGTF.
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> \endverbatim
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>
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> \param[in] D
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> \verbatim
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> D is DOUBLE PRECISION array, dimension (N-2)
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> On entry, D must contain the second super-diagonal elements
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> of U as returned from DLAGTF.
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> \endverbatim
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>
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> \param[in] IN
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> \verbatim
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> IN is INTEGER array, dimension (N)
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> On entry, IN must contain details of the matrix P as returned
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> from DLAGTF.
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> \endverbatim
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>
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> \param[in,out] Y
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> \verbatim
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> Y is DOUBLE PRECISION array, dimension (N)
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> On entry, the right hand side vector y.
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> On exit, Y is overwritten by the solution vector x.
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> \endverbatim
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>
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> \param[in,out] TOL
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> \verbatim
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> TOL is DOUBLE PRECISION
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> On entry, with JOB .lt. 0, TOL should be the minimum
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> perturbation to be made to very small diagonal elements of U.
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> TOL should normally be chosen as about eps*norm(U), where eps
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> is the relative machine precision, but if TOL is supplied as
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> non-positive, then it is reset to eps*max( abs( u(i,j) ) ).
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> If JOB .gt. 0 then TOL is not referenced.
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>
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> On exit, TOL is changed as described above, only if TOL is
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> non-positive on entry. Otherwise TOL is unchanged.
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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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> .lt. 0: if INFO = -i, the i-th argument had an illegal value
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> .gt. 0: overflow would occur when computing the INFO(th)
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> element of the solution vector x. This can only occur
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> when JOB is supplied as positive and either means
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> that a diagonal element of U is very small, or that
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> the elements of the right-hand side vector y are very
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> large.
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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 auxOTHERauxiliary
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=====================================================================
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Subroutine */ int igraphdlagts_(integer *job, integer *n, doublereal *a,
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doublereal *b, doublereal *c__, doublereal *d__, integer *in,
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doublereal *y, doublereal *tol, integer *info)
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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, d__3, d__4, d__5;
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/* Builtin functions */
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double d_sign(doublereal *, doublereal *);
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/* Local variables */
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integer k;
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doublereal ak, eps, temp, pert, absak, sfmin;
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extern doublereal igraphdlamch_(char *);
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extern /* Subroutine */ int igraphxerbla_(char *, integer *, ftnlen);
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doublereal bignum;
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/* -- LAPACK auxiliary 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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--y;
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--in;
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--d__;
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--c__;
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--b;
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--a;
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/* Function Body */
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*info = 0;
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if (abs(*job) > 2 || *job == 0) {
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*info = -1;
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} else if (*n < 0) {
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*info = -2;
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}
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if (*info != 0) {
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i__1 = -(*info);
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igraphxerbla_("DLAGTS", &i__1, (ftnlen)6);
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return 0;
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}
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if (*n == 0) {
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return 0;
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}
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eps = igraphdlamch_("Epsilon");
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sfmin = igraphdlamch_("Safe minimum");
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bignum = 1. / sfmin;
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if (*job < 0) {
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if (*tol <= 0.) {
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*tol = abs(a[1]);
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if (*n > 1) {
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/* Computing MAX */
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d__1 = *tol, d__2 = abs(a[2]), d__1 = max(d__1,d__2), d__2 =
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abs(b[1]);
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*tol = max(d__1,d__2);
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}
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i__1 = *n;
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for (k = 3; k <= i__1; ++k) {
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/* Computing MAX */
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d__4 = *tol, d__5 = (d__1 = a[k], abs(d__1)), d__4 = max(d__4,
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d__5), d__5 = (d__2 = b[k - 1], abs(d__2)), d__4 =
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max(d__4,d__5), d__5 = (d__3 = d__[k - 2], abs(d__3));
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*tol = max(d__4,d__5);
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/* L10: */
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}
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*tol *= eps;
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if (*tol == 0.) {
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*tol = eps;
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}
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}
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}
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if (abs(*job) == 1) {
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i__1 = *n;
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for (k = 2; k <= i__1; ++k) {
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if (in[k - 1] == 0) {
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y[k] -= c__[k - 1] * y[k - 1];
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} else {
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temp = y[k - 1];
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y[k - 1] = y[k];
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y[k] = temp - c__[k - 1] * y[k];
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}
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/* L20: */
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}
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if (*job == 1) {
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for (k = *n; k >= 1; --k) {
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if (k <= *n - 2) {
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temp = y[k] - b[k] * y[k + 1] - d__[k] * y[k + 2];
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} else if (k == *n - 1) {
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temp = y[k] - b[k] * y[k + 1];
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} else {
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temp = y[k];
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}
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ak = a[k];
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absak = abs(ak);
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if (absak < 1.) {
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if (absak < sfmin) {
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if (absak == 0. || abs(temp) * sfmin > absak) {
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*info = k;
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return 0;
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} else {
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temp *= bignum;
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ak *= bignum;
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}
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} else if (abs(temp) > absak * bignum) {
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*info = k;
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return 0;
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}
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}
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y[k] = temp / ak;
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/* L30: */
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}
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} else {
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for (k = *n; k >= 1; --k) {
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if (k <= *n - 2) {
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temp = y[k] - b[k] * y[k + 1] - d__[k] * y[k + 2];
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} else if (k == *n - 1) {
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temp = y[k] - b[k] * y[k + 1];
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} else {
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temp = y[k];
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}
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ak = a[k];
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pert = d_sign(tol, &ak);
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L40:
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absak = abs(ak);
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if (absak < 1.) {
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if (absak < sfmin) {
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if (absak == 0. || abs(temp) * sfmin > absak) {
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ak += pert;
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pert *= 2;
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goto L40;
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} else {
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temp *= bignum;
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ak *= bignum;
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}
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} else if (abs(temp) > absak * bignum) {
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ak += pert;
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pert *= 2;
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goto L40;
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}
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}
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y[k] = temp / ak;
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/* L50: */
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}
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}
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} else {
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/* Come to here if JOB = 2 or -2 */
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if (*job == 2) {
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i__1 = *n;
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for (k = 1; k <= i__1; ++k) {
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if (k >= 3) {
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temp = y[k] - b[k - 1] * y[k - 1] - d__[k - 2] * y[k - 2];
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} else if (k == 2) {
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temp = y[k] - b[k - 1] * y[k - 1];
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} else {
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temp = y[k];
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}
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ak = a[k];
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absak = abs(ak);
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if (absak < 1.) {
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if (absak < sfmin) {
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if (absak == 0. || abs(temp) * sfmin > absak) {
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*info = k;
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return 0;
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} else {
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temp *= bignum;
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ak *= bignum;
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}
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} else if (abs(temp) > absak * bignum) {
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*info = k;
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return 0;
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}
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}
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y[k] = temp / ak;
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/* L60: */
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}
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} else {
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i__1 = *n;
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for (k = 1; k <= i__1; ++k) {
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if (k >= 3) {
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temp = y[k] - b[k - 1] * y[k - 1] - d__[k - 2] * y[k - 2];
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} else if (k == 2) {
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temp = y[k] - b[k - 1] * y[k - 1];
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} else {
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temp = y[k];
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}
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ak = a[k];
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pert = d_sign(tol, &ak);
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L70:
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absak = abs(ak);
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if (absak < 1.) {
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if (absak < sfmin) {
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if (absak == 0. || abs(temp) * sfmin > absak) {
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ak += pert;
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pert *= 2;
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goto L70;
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} else {
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temp *= bignum;
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ak *= bignum;
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}
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} else if (abs(temp) > absak * bignum) {
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ak += pert;
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pert *= 2;
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goto L70;
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}
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}
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y[k] = temp / ak;
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/* L80: */
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}
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}
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for (k = *n; k >= 2; --k) {
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if (in[k - 1] == 0) {
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y[k - 1] -= c__[k - 1] * y[k];
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} else {
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temp = y[k - 1];
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y[k - 1] = y[k];
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y[k] = temp - c__[k - 1] * y[k];
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}
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/* L90: */
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}
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}
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/* End of DLAGTS */
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return 0;
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} /* igraphdlagts_ */
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Reference in New Issue
Block a user