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/* eispack/tql1.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_b10 = 1.;
/*< subroutine tql1(n,d,e,ierr) >*/
/* Subroutine */ int tql1_(integer *n, doublereal *d__, doublereal *e,
integer *ierr)
{
/* System generated locals */
integer i__1, i__2;
doublereal d__1, d__2;
/* Builtin functions */
double d_sign(doublereal *, doublereal *);
/* Local variables */
doublereal c__, f, g, h__;
integer i__, j, l, m;
doublereal p, r__, s, c2, c3=0;
integer l1, l2;
doublereal s2=0;
integer ii;
doublereal dl1, el1;
integer mml;
doublereal tst1, tst2;
extern doublereal pythag_(doublereal *, doublereal *);
/*< integer i,j,l,m,n,ii,l1,l2,mml,ierr >*/
/*< double precision d(n),e(n) >*/
/*< double precision c,c2,c3,dl1,el1,f,g,h,p,r,s,s2,tst1,tst2,pythag >*/
/* this subroutine is a translation of the algol procedure tql1, */
/* num. math. 11, 293-306(1968) by bowdler, martin, reinsch, and */
/* wilkinson. */
/* handbook for auto. comp., vol.ii-linear algebra, 227-240(1971). */
/* this subroutine finds the eigenvalues of a symmetric */
/* tridiagonal matrix by the ql method. */
/* on input */
/* n is the order of the matrix. */
/* d contains the diagonal elements of the input matrix. */
/* e contains the subdiagonal elements of the input matrix */
/* in its last n-1 positions. e(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. */
/* e 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 */
--e;
--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 e(i-1) = e(i) >*/
/* L100: */
e[i__ - 1] = e[i__];
}
/*< f = 0.0d0 >*/
f = 0.;
/*< tst1 = 0.0d0 >*/
tst1 = 0.;
/*< e(n) = 0.0d0 >*/
e[*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)) + dabs(e(l)) >*/
h__ = (d__1 = d__[l], abs(d__1)) + (d__2 = e[l], abs(d__2));
/*< if (tst1 .lt. h) tst1 = h >*/
if (tst1 < h__) {
tst1 = h__;
}
/* .......... look for small sub-diagonal element .......... */
/*< do 110 m = l, n >*/
i__2 = *n;
for (m = l; m <= i__2; ++m) {
/*< tst2 = tst1 + dabs(e(m)) >*/
tst2 = tst1 + (d__1 = e[m], abs(d__1));
/*< if (tst2 .eq. tst1) go to 120 >*/
if (tst2 == tst1) {
goto L120;
}
/* .......... e(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;
/*< l2 = l1 + 1 >*/
l2 = l1 + 1;
/*< g = d(l) >*/
g = d__[l];
/*< p = (d(l1) - g) / (2.0d0 * e(l)) >*/
p = (d__[l1] - g) / (e[l] * 2.);
/*< r = pythag(p,1.0d0) >*/
r__ = pythag_(&p, &c_b10);
/*< d(l) = e(l) / (p + dsign(r,p)) >*/
d__[l] = e[l] / (p + d_sign(&r__, &p));
/*< d(l1) = e(l) * (p + dsign(r,p)) >*/
d__[l1] = e[l] * (p + d_sign(&r__, &p));
/*< dl1 = d(l1) >*/
dl1 = d__[l1];
/*< h = g - d(l) >*/
h__ = g - d__[l];
/*< if (l2 .gt. n) go to 145 >*/
if (l2 > *n) {
goto L145;
}
/*< do 140 i = l2, n >*/
i__2 = *n;
for (i__ = l2; i__ <= i__2; ++i__) {
/*< 140 d(i) = d(i) - h >*/
/* L140: */
d__[i__] -= h__;
}
/*< 145 f = f + h >*/
L145:
f += h__;
/* .......... ql transformation .......... */
/*< p = d(m) >*/
p = d__[m];
/*< c = 1.0d0 >*/
c__ = 1.;
/*< c2 = c >*/
c2 = c__;
/*< el1 = e(l1) >*/
el1 = e[l1];
/*< 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) {
/*< c3 = c2 >*/
c3 = c2;
/*< c2 = c >*/
c2 = c__;
/*< s2 = s >*/
s2 = s;
/*< i = m - ii >*/
i__ = m - ii;
/*< g = c * e(i) >*/
g = c__ * e[i__];
/*< h = c * p >*/
h__ = c__ * p;
/*< r = pythag(p,e(i)) >*/
r__ = pythag_(&p, &e[i__]);
/*< e(i+1) = s * r >*/
e[i__ + 1] = s * r__;
/*< s = e(i) / r >*/
s = e[i__] / r__;
/*< c = p / r >*/
c__ = p / r__;
/*< p = c * d(i) - s * g >*/
p = c__ * d__[i__] - s * g;
/*< d(i+1) = h + s * (c * g + s * d(i)) >*/
d__[i__ + 1] = h__ + s * (c__ * g + s * d__[i__]);
/*< 200 continue >*/
/* L200: */
}
/*< p = -s * s2 * c3 * el1 * e(l) / dl1 >*/
p = -s * s2 * c3 * el1 * e[l] / dl1;
/*< e(l) = s * p >*/
e[l] = s * p;
/*< d(l) = c * p >*/
d__[l] = c__ * p;
/*< tst2 = tst1 + dabs(e(l)) >*/
tst2 = tst1 + (d__1 = e[l], abs(d__1));
/*< if (tst2 .gt. tst1) go to 130 >*/
if (tst2 > tst1) {
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 >*/
} /* tql1_ */
#ifdef __cplusplus
}
#endif
|
