225 lines
6.5 KiB
C
225 lines
6.5 KiB
C
/* dlagtf.f -- translated by f2c (version 20061008).
|
|
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 "clapack.h"
|
|
|
|
|
|
/* Subroutine */ int dlagtf_(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 dlamch_(char *);
|
|
extern /* Subroutine */ int xerbla_(char *, integer *);
|
|
|
|
|
|
/* -- LAPACK routine (version 3.2) -- */
|
|
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
|
|
/* November 2006 */
|
|
|
|
/* .. Scalar Arguments .. */
|
|
/* .. */
|
|
/* .. Array Arguments .. */
|
|
/* .. */
|
|
|
|
/* Purpose */
|
|
/* ======= */
|
|
|
|
/* 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. */
|
|
|
|
/* Arguments */
|
|
/* ========= */
|
|
|
|
/* N (input) INTEGER */
|
|
/* The order of the matrix T. */
|
|
|
|
/* A (input/output) 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. */
|
|
|
|
/* LAMBDA (input) DOUBLE PRECISION */
|
|
/* On entry, the scalar lambda. */
|
|
|
|
/* B (input/output) 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. */
|
|
|
|
/* C (input/output) 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. */
|
|
|
|
/* TOL (input) 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. */
|
|
|
|
/* D (output) 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. */
|
|
|
|
/* IN (output) 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, */
|
|
|
|
/* INFO (output) INTEGER */
|
|
/* = 0 : successful exit */
|
|
/* .lt. 0: if INFO = -k, the kth argument had an illegal value */
|
|
|
|
/* ===================================================================== */
|
|
|
|
/* .. Parameters .. */
|
|
/* .. */
|
|
/* .. Local Scalars .. */
|
|
/* .. */
|
|
/* .. Intrinsic Functions .. */
|
|
/* .. */
|
|
/* .. External Functions .. */
|
|
/* .. */
|
|
/* .. External Subroutines .. */
|
|
/* .. */
|
|
/* .. Executable Statements .. */
|
|
|
|
/* Parameter adjustments */
|
|
--in;
|
|
--d__;
|
|
--c__;
|
|
--b;
|
|
--a;
|
|
|
|
/* Function Body */
|
|
*info = 0;
|
|
if (*n < 0) {
|
|
*info = -1;
|
|
i__1 = -(*info);
|
|
xerbla_("DLAGTF", &i__1);
|
|
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 = dlamch_("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 */
|
|
|
|
} /* dlagtf_ */
|