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/* -- translated by f2c (version 20240504).
You must link the resulting object file with libf2c:
on Microsoft Windows system, link with libf2c.lib;
on Linux or Unix systems, link with .../path/to/libf2c.a -lm
or, if you install libf2c.a in a standard place, with -lf2c -lm
-- in that order, at the end of the command line, as in
cc *.o -lf2c -lm
Source for libf2c is in /netlib/f2c/libf2c.zip, e.g.,
http://www.netlib.org/f2c/libf2c.zip
*/
#include "f2c.h"
/* > \brief \b DLAGTS solves the system of equations (T-λI)x = y or (T-λI)Tx = y,where T is a general tridia
gonal matrix and λ a scalar, using the LU factorization computed by slagtf.
=========== DOCUMENTATION ===========
Online html documentation available at
http://www.netlib.org/lapack/explore-html/
> \htmlonly
> Download DLAGTS + dependencies
> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlagts.
f">
> [TGZ]</a>
> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlagts.
f">
> [ZIP]</a>
> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlagts.
f">
> [TXT]</a>
> \endhtmlonly
Definition:
===========
SUBROUTINE DLAGTS( JOB, N, A, B, C, D, IN, Y, TOL, INFO )
INTEGER INFO, JOB, N
DOUBLE PRECISION TOL
INTEGER IN( * )
DOUBLE PRECISION A( * ), B( * ), C( * ), D( * ), Y( * )
> \par Purpose:
=============
>
> \verbatim
>
> DLAGTS may be used to solve one of the systems of equations
>
> (T - lambda*I)*x = y or (T - lambda*I)**T*x = y,
>
> where T is an n by n tridiagonal matrix, for x, following the
> factorization of (T - lambda*I) as
>
> (T - lambda*I) = P*L*U ,
>
> by routine DLAGTF. The choice of equation to be solved is
> controlled by the argument JOB, and in each case there is an option
> to perturb zero or very small diagonal elements of U, this option
> being intended for use in applications such as inverse iteration.
> \endverbatim
Arguments:
==========
> \param[in] JOB
> \verbatim
> JOB is INTEGER
> Specifies the job to be performed by DLAGTS as follows:
> = 1: The equations (T - lambda*I)x = y are to be solved,
> but diagonal elements of U are not to be perturbed.
> = -1: The equations (T - lambda*I)x = y are to be solved
> and, if overflow would otherwise occur, the diagonal
> elements of U are to be perturbed. See argument TOL
> below.
> = 2: The equations (T - lambda*I)**Tx = y are to be solved,
> but diagonal elements of U are not to be perturbed.
> = -2: The equations (T - lambda*I)**Tx = y are to be solved
> and, if overflow would otherwise occur, the diagonal
> elements of U are to be perturbed. See argument TOL
> below.
> \endverbatim
>
> \param[in] N
> \verbatim
> N is INTEGER
> The order of the matrix T.
> \endverbatim
>
> \param[in] A
> \verbatim
> A is DOUBLE PRECISION array, dimension (N)
> On entry, A must contain the diagonal elements of U as
> returned from DLAGTF.
> \endverbatim
>
> \param[in] B
> \verbatim
> B is DOUBLE PRECISION array, dimension (N-1)
> On entry, B must contain the first super-diagonal elements of
> U as returned from DLAGTF.
> \endverbatim
>
> \param[in] C
> \verbatim
> C is DOUBLE PRECISION array, dimension (N-1)
> On entry, C must contain the sub-diagonal elements of L as
> returned from DLAGTF.
> \endverbatim
>
> \param[in] D
> \verbatim
> D is DOUBLE PRECISION array, dimension (N-2)
> On entry, D must contain the second super-diagonal elements
> of U as returned from DLAGTF.
> \endverbatim
>
> \param[in] IN
> \verbatim
> IN is INTEGER array, dimension (N)
> On entry, IN must contain details of the matrix P as returned
> from DLAGTF.
> \endverbatim
>
> \param[in,out] Y
> \verbatim
> Y is DOUBLE PRECISION array, dimension (N)
> On entry, the right hand side vector y.
> On exit, Y is overwritten by the solution vector x.
> \endverbatim
>
> \param[in,out] TOL
> \verbatim
> TOL is DOUBLE PRECISION
> On entry, with JOB .lt. 0, TOL should be the minimum
> perturbation to be made to very small diagonal elements of U.
> TOL should normally be chosen as about eps*norm(U), where eps
> is the relative machine precision, but if TOL is supplied as
> non-positive, then it is reset to eps*max( abs( u(i,j) ) ).
> If JOB .gt. 0 then TOL is not referenced.
>
> On exit, TOL is changed as described above, only if TOL is
> non-positive on entry. Otherwise TOL is unchanged.
> \endverbatim
>
> \param[out] INFO
> \verbatim
> INFO is INTEGER
> = 0 : successful exit
> .lt. 0: if INFO = -i, the i-th argument had an illegal value
> .gt. 0: overflow would occur when computing the INFO(th)
> element of the solution vector x. This can only occur
> when JOB is supplied as positive and either means
> that a diagonal element of U is very small, or that
> the elements of the right-hand side vector y are very
> large.
> \endverbatim
Authors:
========
> \author Univ. of Tennessee
> \author Univ. of California Berkeley
> \author Univ. of Colorado Denver
> \author NAG Ltd.
> \date September 2012
> \ingroup auxOTHERauxiliary
=====================================================================
Subroutine */ int igraphdlagts_(integer *job, integer *n, doublereal *a,
doublereal *b, doublereal *c__, doublereal *d__, integer *in,
doublereal *y, doublereal *tol, integer *info)
{
/* System generated locals */
integer i__1;
doublereal d__1, d__2, d__3, d__4, d__5;
/* Builtin functions */
double d_sign(doublereal *, doublereal *);
/* Local variables */
integer k;
doublereal ak, eps, temp, pert, absak, sfmin;
extern doublereal igraphdlamch_(char *);
extern /* Subroutine */ int igraphxerbla_(char *, integer *, ftnlen);
doublereal bignum;
/* -- LAPACK auxiliary routine (version 3.4.2) --
-- LAPACK is a software package provided by Univ. of Tennessee, --
-- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
September 2012
=====================================================================
Parameter adjustments */
--y;
--in;
--d__;
--c__;
--b;
--a;
/* Function Body */
*info = 0;
if (abs(*job) > 2 || *job == 0) {
*info = -1;
} else if (*n < 0) {
*info = -2;
}
if (*info != 0) {
i__1 = -(*info);
igraphxerbla_("DLAGTS", &i__1, (ftnlen)6);
return 0;
}
if (*n == 0) {
return 0;
}
eps = igraphdlamch_("Epsilon");
sfmin = igraphdlamch_("Safe minimum");
bignum = 1. / sfmin;
if (*job < 0) {
if (*tol <= 0.) {
*tol = abs(a[1]);
if (*n > 1) {
/* Computing MAX */
d__1 = *tol, d__2 = abs(a[2]), d__1 = max(d__1,d__2), d__2 =
abs(b[1]);
*tol = max(d__1,d__2);
}
i__1 = *n;
for (k = 3; k <= i__1; ++k) {
/* Computing MAX */
d__4 = *tol, d__5 = (d__1 = a[k], abs(d__1)), d__4 = max(d__4,
d__5), d__5 = (d__2 = b[k - 1], abs(d__2)), d__4 =
max(d__4,d__5), d__5 = (d__3 = d__[k - 2], abs(d__3));
*tol = max(d__4,d__5);
/* L10: */
}
*tol *= eps;
if (*tol == 0.) {
*tol = eps;
}
}
}
if (abs(*job) == 1) {
i__1 = *n;
for (k = 2; k <= i__1; ++k) {
if (in[k - 1] == 0) {
y[k] -= c__[k - 1] * y[k - 1];
} else {
temp = y[k - 1];
y[k - 1] = y[k];
y[k] = temp - c__[k - 1] * y[k];
}
/* L20: */
}
if (*job == 1) {
for (k = *n; k >= 1; --k) {
if (k <= *n - 2) {
temp = y[k] - b[k] * y[k + 1] - d__[k] * y[k + 2];
} else if (k == *n - 1) {
temp = y[k] - b[k] * y[k + 1];
} else {
temp = y[k];
}
ak = a[k];
absak = abs(ak);
if (absak < 1.) {
if (absak < sfmin) {
if (absak == 0. || abs(temp) * sfmin > absak) {
*info = k;
return 0;
} else {
temp *= bignum;
ak *= bignum;
}
} else if (abs(temp) > absak * bignum) {
*info = k;
return 0;
}
}
y[k] = temp / ak;
/* L30: */
}
} else {
for (k = *n; k >= 1; --k) {
if (k <= *n - 2) {
temp = y[k] - b[k] * y[k + 1] - d__[k] * y[k + 2];
} else if (k == *n - 1) {
temp = y[k] - b[k] * y[k + 1];
} else {
temp = y[k];
}
ak = a[k];
pert = d_sign(tol, &ak);
L40:
absak = abs(ak);
if (absak < 1.) {
if (absak < sfmin) {
if (absak == 0. || abs(temp) * sfmin > absak) {
ak += pert;
pert *= 2;
goto L40;
} else {
temp *= bignum;
ak *= bignum;
}
} else if (abs(temp) > absak * bignum) {
ak += pert;
pert *= 2;
goto L40;
}
}
y[k] = temp / ak;
/* L50: */
}
}
} else {
/* Come to here if JOB = 2 or -2 */
if (*job == 2) {
i__1 = *n;
for (k = 1; k <= i__1; ++k) {
if (k >= 3) {
temp = y[k] - b[k - 1] * y[k - 1] - d__[k - 2] * y[k - 2];
} else if (k == 2) {
temp = y[k] - b[k - 1] * y[k - 1];
} else {
temp = y[k];
}
ak = a[k];
absak = abs(ak);
if (absak < 1.) {
if (absak < sfmin) {
if (absak == 0. || abs(temp) * sfmin > absak) {
*info = k;
return 0;
} else {
temp *= bignum;
ak *= bignum;
}
} else if (abs(temp) > absak * bignum) {
*info = k;
return 0;
}
}
y[k] = temp / ak;
/* L60: */
}
} else {
i__1 = *n;
for (k = 1; k <= i__1; ++k) {
if (k >= 3) {
temp = y[k] - b[k - 1] * y[k - 1] - d__[k - 2] * y[k - 2];
} else if (k == 2) {
temp = y[k] - b[k - 1] * y[k - 1];
} else {
temp = y[k];
}
ak = a[k];
pert = d_sign(tol, &ak);
L70:
absak = abs(ak);
if (absak < 1.) {
if (absak < sfmin) {
if (absak == 0. || abs(temp) * sfmin > absak) {
ak += pert;
pert *= 2;
goto L70;
} else {
temp *= bignum;
ak *= bignum;
}
} else if (abs(temp) > absak * bignum) {
ak += pert;
pert *= 2;
goto L70;
}
}
y[k] = temp / ak;
/* L80: */
}
}
for (k = *n; k >= 2; --k) {
if (in[k - 1] == 0) {
y[k - 1] -= c__[k - 1] * y[k];
} else {
temp = y[k - 1];
y[k - 1] = y[k];
y[k] = temp - c__[k - 1] * y[k];
}
/* L90: */
}
}
/* End of DLAGTS */
return 0;
} /* igraphdlagts_ */
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