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/* eispack/otqlrat.f -- translated by f2c (version 20050501).
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
*/
#ifdef __cplusplus
extern "C" {
#endif
#include "v3p_netlib.h"
/* Table of constant values */
static doublereal c_b11 = 1.;
/*< subroutine tqlrat(n,d,e2,ierr) >*/
/* Subroutine */ int tqlrat_(integer *n, doublereal *d__, doublereal *e2,
integer *ierr)
{
/* System generated locals */
integer i__1, i__2;
doublereal d__1, d__2;
/* Builtin functions */
double sqrt(doublereal), d_sign(doublereal *, doublereal *);
/* Local variables */
doublereal b=0, c__=0, f, g, h__;
integer i__, j, l, m;
doublereal p, r__, s, t;
integer l1, ii, mml;
extern doublereal pythag_(doublereal *, doublereal *), epslon_(doublereal
*);
/*< integer i,j,l,m,n,ii,l1,mml,ierr >*/
/*< double precision d(n),e2(n) >*/
/*< double precision b,c,f,g,h,p,r,s,t,epslon,pythag >*/
/* this subroutine is a translation of the algol procedure tqlrat, */
/* algorithm 464, comm. acm 16, 689(1973) by reinsch. */
/* this subroutine finds the eigenvalues of a symmetric */
/* tridiagonal matrix by the rational ql method. */
/* on input */
/* n is the order of the matrix. */
/* d contains the diagonal elements of the input matrix. */
/* e2 contains the squares of the subdiagonal elements of the */
/* input matrix in its last n-1 positions. e2(1) is arbitrary. */
/* on output */
/* d contains the eigenvalues in ascending order. if an */
/* error exit is made, the eigenvalues are correct and */
/* ordered for indices 1,2,...ierr-1, but may not be */
/* the smallest eigenvalues. */
/* e2 has been destroyed. */
/* ierr is set to */
/* zero for normal return, */
/* j if the j-th eigenvalue has not been */
/* determined after 30 iterations. */
/* calls pythag for dsqrt(a*a + b*b) . */
/* questions and comments should be directed to burton s. garbow, */
/* mathematics and computer science div, argonne national laboratory */
/* this version dated august 1983. */
/* ------------------------------------------------------------------ */
/*< ierr = 0 >*/
/* Parameter adjustments */
--e2;
--d__;
/* Function Body */
*ierr = 0;
/*< if (n .eq. 1) go to 1001 >*/
if (*n == 1) {
goto L1001;
}
/*< do 100 i = 2, n >*/
i__1 = *n;
for (i__ = 2; i__ <= i__1; ++i__) {
/*< 100 e2(i-1) = e2(i) >*/
/* L100: */
e2[i__ - 1] = e2[i__];
}
/*< f = 0.0d0 >*/
f = 0.;
/*< t = 0.0d0 >*/
t = 0.;
/*< e2(n) = 0.0d0 >*/
e2[*n] = 0.;
/*< do 290 l = 1, n >*/
i__1 = *n;
for (l = 1; l <= i__1; ++l) {
/*< j = 0 >*/
j = 0;
/*< h = dabs(d(l)) + dsqrt(e2(l)) >*/
h__ = (d__1 = d__[l], abs(d__1)) + sqrt(e2[l]);
/*< if (t .gt. h) go to 105 >*/
if (t > h__) {
goto L105;
}
/*< t = h >*/
t = h__;
/*< b = epslon(t) >*/
b = epslon_(&t);
/*< c = b * b >*/
c__ = b * b;
/* .......... look for small squared sub-diagonal element .......... */
/*< 105 do 110 m = l, n >*/
L105:
i__2 = *n;
for (m = l; m <= i__2; ++m) {
/*< if (e2(m) .le. c) go to 120 >*/
if (e2[m] <= c__) {
goto L120;
}
/* .......... e2(n) is always zero, so there is no exit */
/* through the bottom of the loop .......... */
/*< 110 continue >*/
/* L110: */
}
/*< 120 if (m .eq. l) go to 210 >*/
L120:
if (m == l) {
goto L210;
}
/*< 130 if (j .eq. 30) go to 1000 >*/
L130:
if (j == 30) {
goto L1000;
}
/*< j = j + 1 >*/
++j;
/* .......... form shift .......... */
/*< l1 = l + 1 >*/
l1 = l + 1;
/*< s = dsqrt(e2(l)) >*/
s = sqrt(e2[l]);
/*< g = d(l) >*/
g = d__[l];
/*< p = (d(l1) - g) / (2.0d0 * s) >*/
p = (d__[l1] - g) / (s * 2.);
/*< r = pythag(p,1.0d0) >*/
r__ = pythag_(&p, &c_b11);
/*< d(l) = s / (p + dsign(r,p)) >*/
d__[l] = s / (p + d_sign(&r__, &p));
/*< h = g - d(l) >*/
h__ = g - d__[l];
/*< do 140 i = l1, n >*/
i__2 = *n;
for (i__ = l1; i__ <= i__2; ++i__) {
/*< 140 d(i) = d(i) - h >*/
/* L140: */
d__[i__] -= h__;
}
/*< f = f + h >*/
f += h__;
/* .......... rational ql transformation .......... */
/*< g = d(m) >*/
g = d__[m];
/*< if (g .eq. 0.0d0) g = b >*/
if (g == 0.) {
g = b;
}
/*< h = g >*/
h__ = g;
/*< s = 0.0d0 >*/
s = 0.;
/*< mml = m - l >*/
mml = m - l;
/* .......... for i=m-1 step -1 until l do -- .......... */
/*< do 200 ii = 1, mml >*/
i__2 = mml;
for (ii = 1; ii <= i__2; ++ii) {
/*< i = m - ii >*/
i__ = m - ii;
/*< p = g * h >*/
p = g * h__;
/*< r = p + e2(i) >*/
r__ = p + e2[i__];
/*< e2(i+1) = s * r >*/
e2[i__ + 1] = s * r__;
/*< s = e2(i) / r >*/
s = e2[i__] / r__;
/*< d(i+1) = h + s * (h + d(i)) >*/
d__[i__ + 1] = h__ + s * (h__ + d__[i__]);
/*< g = d(i) - e2(i) / g >*/
g = d__[i__] - e2[i__] / g;
/*< if (g .eq. 0.0d0) g = b >*/
if (g == 0.) {
g = b;
}
/*< h = g * p / r >*/
h__ = g * p / r__;
/*< 200 continue >*/
/* L200: */
}
/*< e2(l) = s * g >*/
e2[l] = s * g;
/*< d(l) = h >*/
d__[l] = h__;
/* .......... guard against underflow in convergence test .......... */
/*< if (h .eq. 0.0d0) go to 210 >*/
if (h__ == 0.) {
goto L210;
}
/*< if (dabs(e2(l)) .le. dabs(c/h)) go to 210 >*/
if ((d__1 = e2[l], abs(d__1)) <= (d__2 = c__ / h__, abs(d__2))) {
goto L210;
}
/*< e2(l) = h * e2(l) >*/
e2[l] = h__ * e2[l];
/*< if (e2(l) .ne. 0.0d0) go to 130 >*/
if (e2[l] != 0.) {
goto L130;
}
/*< 210 p = d(l) + f >*/
L210:
p = d__[l] + f;
/* .......... order eigenvalues .......... */
/*< if (l .eq. 1) go to 250 >*/
if (l == 1) {
goto L250;
}
/* .......... for i=l step -1 until 2 do -- .......... */
/*< do 230 ii = 2, l >*/
i__2 = l;
for (ii = 2; ii <= i__2; ++ii) {
/*< i = l + 2 - ii >*/
i__ = l + 2 - ii;
/*< if (p .ge. d(i-1)) go to 270 >*/
if (p >= d__[i__ - 1]) {
goto L270;
}
/*< d(i) = d(i-1) >*/
d__[i__] = d__[i__ - 1];
/*< 230 continue >*/
/* L230: */
}
/*< 250 i = 1 >*/
L250:
i__ = 1;
/*< 270 d(i) = p >*/
L270:
d__[i__] = p;
/*< 290 continue >*/
/* L290: */
}
/*< go to 1001 >*/
goto L1001;
/* .......... set error -- no convergence to an */
/* eigenvalue after 30 iterations .......... */
/*< 1000 ierr = l >*/
L1000:
*ierr = l;
/*< 1001 return >*/
L1001:
return 0;
/*< end >*/
} /* tqlrat_ */
#ifdef __cplusplus
}
#endif
|
