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references/igraph-1.0.1/vendor/lapack/dlagtf.c
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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 DLAGTF computes an LU factorization of a matrix T-λI, where T is a general tridiagonal matrix,
and λ a scalar, using partial pivoting with row interchanges.
=========== DOCUMENTATION ===========
Online html documentation available at
http://www.netlib.org/lapack/explore-html/
> \htmlonly
> Download DLAGTF + dependencies
> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlagtf.
f">
> [TGZ]</a>
> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlagtf.
f">
> [ZIP]</a>
> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlagtf.
f">
> [TXT]</a>
> \endhtmlonly
Definition:
===========
SUBROUTINE DLAGTF( N, A, LAMBDA, B, C, TOL, D, IN, INFO )
INTEGER INFO, N
DOUBLE PRECISION LAMBDA, TOL
INTEGER IN( * )
DOUBLE PRECISION A( * ), B( * ), C( * ), D( * )
> \par Purpose:
=============
>
> \verbatim
>
> DLAGTF factorizes the matrix (T - lambda*I), where T is an n by n
> tridiagonal matrix and lambda is a scalar, as
>
> T - lambda*I = PLU,
>
> where P is a permutation matrix, L is a unit lower tridiagonal matrix
> with at most one non-zero sub-diagonal elements per column and U is
> an upper triangular matrix with at most two non-zero super-diagonal
> elements per column.
>
> The factorization is obtained by Gaussian elimination with partial
> pivoting and implicit row scaling.
>
> The parameter LAMBDA is included in the routine so that DLAGTF may
> be used, in conjunction with DLAGTS, to obtain eigenvectors of T by
> inverse iteration.
> \endverbatim
Arguments:
==========
> \param[in] N
> \verbatim
> N is INTEGER
> The order of the matrix T.
> \endverbatim
>
> \param[in,out] A
> \verbatim
> A is DOUBLE PRECISION array, dimension (N)
> On entry, A must contain the diagonal elements of T.
>
> On exit, A is overwritten by the n diagonal elements of the
> upper triangular matrix U of the factorization of T.
> \endverbatim
>
> \param[in] LAMBDA
> \verbatim
> LAMBDA is DOUBLE PRECISION
> On entry, the scalar lambda.
> \endverbatim
>
> \param[in,out] B
> \verbatim
> B is DOUBLE PRECISION array, dimension (N-1)
> On entry, B must contain the (n-1) super-diagonal elements of
> T.
>
> On exit, B is overwritten by the (n-1) super-diagonal
> elements of the matrix U of the factorization of T.
> \endverbatim
>
> \param[in,out] C
> \verbatim
> C is DOUBLE PRECISION array, dimension (N-1)
> On entry, C must contain the (n-1) sub-diagonal elements of
> T.
>
> On exit, C is overwritten by the (n-1) sub-diagonal elements
> of the matrix L of the factorization of T.
> \endverbatim
>
> \param[in] TOL
> \verbatim
> TOL is DOUBLE PRECISION
> On entry, a relative tolerance used to indicate whether or
> not the matrix (T - lambda*I) is nearly singular. TOL should
> normally be chose as approximately the largest relative error
> in the elements of T. For example, if the elements of T are
> correct to about 4 significant figures, then TOL should be
> set to about 5*10**(-4). If TOL is supplied as less than eps,
> where eps is the relative machine precision, then the value
> eps is used in place of TOL.
> \endverbatim
>
> \param[out] D
> \verbatim
> D is DOUBLE PRECISION array, dimension (N-2)
> On exit, D is overwritten by the (n-2) second super-diagonal
> elements of the matrix U of the factorization of T.
> \endverbatim
>
> \param[out] IN
> \verbatim
> IN is INTEGER array, dimension (N)
> On exit, IN contains details of the permutation matrix P. If
> an interchange occurred at the kth step of the elimination,
> then IN(k) = 1, otherwise IN(k) = 0. The element IN(n)
> returns the smallest positive integer j such that
>
> abs( u(j,j) ).le. norm( (T - lambda*I)(j) )*TOL,
>
> where norm( A(j) ) denotes the sum of the absolute values of
> the jth row of the matrix A. If no such j exists then IN(n)
> is returned as zero. If IN(n) is returned as positive, then a
> diagonal element of U is small, indicating that
> (T - lambda*I) is singular or nearly singular,
> \endverbatim
>
> \param[out] INFO
> \verbatim
> INFO is INTEGER
> = 0 : successful exit
> .lt. 0: if INFO = -k, the kth argument had an illegal value
> \endverbatim
Authors:
========
> \author Univ. of Tennessee
> \author Univ. of California Berkeley
> \author Univ. of Colorado Denver
> \author NAG Ltd.
> \date September 2012
> \ingroup auxOTHERcomputational
=====================================================================
Subroutine */ int igraphdlagtf_(integer *n, doublereal *a, doublereal *lambda,
doublereal *b, doublereal *c__, doublereal *tol, doublereal *d__,
integer *in, integer *info)
{
/* System generated locals */
integer i__1;
doublereal d__1, d__2;
/* Local variables */
integer k;
doublereal tl, eps, piv1, piv2, temp, mult, scale1, scale2;
extern doublereal igraphdlamch_(char *);
extern /* Subroutine */ int igraphxerbla_(char *, integer *, ftnlen);
/* -- LAPACK computational 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 */
--in;
--d__;
--c__;
--b;
--a;
/* Function Body */
*info = 0;
if (*n < 0) {
*info = -1;
i__1 = -(*info);
igraphxerbla_("DLAGTF", &i__1, (ftnlen)6);
return 0;
}
if (*n == 0) {
return 0;
}
a[1] -= *lambda;
in[*n] = 0;
if (*n == 1) {
if (a[1] == 0.) {
in[1] = 1;
}
return 0;
}
eps = igraphdlamch_("Epsilon");
tl = max(*tol,eps);
scale1 = abs(a[1]) + abs(b[1]);
i__1 = *n - 1;
for (k = 1; k <= i__1; ++k) {
a[k + 1] -= *lambda;
scale2 = (d__1 = c__[k], abs(d__1)) + (d__2 = a[k + 1], abs(d__2));
if (k < *n - 1) {
scale2 += (d__1 = b[k + 1], abs(d__1));
}
if (a[k] == 0.) {
piv1 = 0.;
} else {
piv1 = (d__1 = a[k], abs(d__1)) / scale1;
}
if (c__[k] == 0.) {
in[k] = 0;
piv2 = 0.;
scale1 = scale2;
if (k < *n - 1) {
d__[k] = 0.;
}
} else {
piv2 = (d__1 = c__[k], abs(d__1)) / scale2;
if (piv2 <= piv1) {
in[k] = 0;
scale1 = scale2;
c__[k] /= a[k];
a[k + 1] -= c__[k] * b[k];
if (k < *n - 1) {
d__[k] = 0.;
}
} else {
in[k] = 1;
mult = a[k] / c__[k];
a[k] = c__[k];
temp = a[k + 1];
a[k + 1] = b[k] - mult * temp;
if (k < *n - 1) {
d__[k] = b[k + 1];
b[k + 1] = -mult * d__[k];
}
b[k] = temp;
c__[k] = mult;
}
}
if (max(piv1,piv2) <= tl && in[*n] == 0) {
in[*n] = k;
}
/* L10: */
}
if ((d__1 = a[*n], abs(d__1)) <= scale1 * tl && in[*n] == 0) {
in[*n] = *n;
}
return 0;
/* End of DLAGTF */
} /* igraphdlagtf_ */