352 lines
9.3 KiB
C
352 lines
9.3 KiB
C
/* dlagts.f -- translated by f2c (version 20061008).
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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 "clapack.h"
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/* Subroutine */ int dlagts_(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 dlamch_(char *);
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extern /* Subroutine */ int xerbla_(char *, integer *);
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doublereal bignum;
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/* -- LAPACK auxiliary routine (version 3.2) -- */
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/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
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/* November 2006 */
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/* .. Scalar Arguments .. */
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/* .. */
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/* .. Array Arguments .. */
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/* .. */
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/* Purpose */
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/* ======= */
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/* DLAGTS may be used to solve one of the systems of equations */
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/* (T - lambda*I)*x = y or (T - lambda*I)'*x = y, */
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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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/* (T - lambda*I) = P*L*U , */
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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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/* Arguments */
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/* ========= */
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/* JOB (input) 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)'x = 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)'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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/* N (input) INTEGER */
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/* The order of the matrix T. */
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/* A (input) 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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/* B (input) 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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/* C (input) 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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/* D (input) 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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/* IN (input) 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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/* Y (input/output) 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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/* TOL (input/output) 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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/* 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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/* INFO (output) 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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/* ===================================================================== */
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/* .. Parameters .. */
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/* .. */
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/* .. Local Scalars .. */
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/* .. */
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/* .. Intrinsic Functions .. */
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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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/* .. Executable Statements .. */
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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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xerbla_("DLAGTS", &i__1);
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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 = dlamch_("Epsilon");
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sfmin = dlamch_("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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} /* dlagts_ */
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