/* tql1.f -- translated by f2c (version 19961017).
   You must link the resulting object file with the libraries:
	-lf2c -lm   (in that order)
*/

#include "f2c.h"

/* Table of constant values */

static doublereal c_b10 = 1.;

/* 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 */
    static doublereal c__, f, g, h__;
    static integer i__, j, l, m;
    static doublereal p, r__, s, c2, c3;
    static integer l1, l2;
    static doublereal s2;
    static integer ii;
    extern doublereal pythag_(doublereal *, doublereal *);
    static doublereal dl1, el1;
    static integer mml;
    static doublereal tst1, tst2;



/*     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. */

/*     ------------------------------------------------------------------ 
*/

    /* Parameter adjustments */
    --e;
    --d__;

    /* Function Body */
    *ierr = 0;
    if (*n == 1) {
	goto L1001;
    }

    i__1 = *n;
    for (i__ = 2; i__ <= i__1; ++i__) {
/* L100: */
	e[i__ - 1] = e[i__];
    }

    f = 0.;
    tst1 = 0.;
    e[*n] = 0.;

    i__1 = *n;
    for (l = 1; l <= i__1; ++l) {
	j = 0;
	h__ = (d__1 = d__[l], abs(d__1)) + (d__2 = e[l], abs(d__2));
	if (tst1 < h__) {
	    tst1 = h__;
	}
/*     .......... LOOK FOR SMALL SUB-DIAGONAL ELEMENT .......... */
	i__2 = *n;
	for (m = l; m <= i__2; ++m) {
	    tst2 = tst1 + (d__1 = e[m], abs(d__1));
	    if (tst2 == tst1) {
		goto L120;
	    }
/*     .......... E(N) IS ALWAYS ZERO, SO THERE IS NO EXIT */
/*                THROUGH THE BOTTOM OF THE LOOP .......... */
/* L110: */
	}

L120:
	if (m == l) {
	    goto L210;
	}
L130:
	if (j == 30) {
	    goto L1000;
	}
	++j;
/*     .......... FORM SHIFT .......... */
	l1 = l + 1;
	l2 = l1 + 1;
	g = d__[l];
	p = (d__[l1] - g) / (e[l] * 2.);
	r__ = pythag_(&p, &c_b10);
	d__[l] = e[l] / (p + d_sign(&r__, &p));
	d__[l1] = e[l] * (p + d_sign(&r__, &p));
	dl1 = d__[l1];
	h__ = g - d__[l];
	if (l2 > *n) {
	    goto L145;
	}

	i__2 = *n;
	for (i__ = l2; i__ <= i__2; ++i__) {
/* L140: */
	    d__[i__] -= h__;
	}

L145:
	f += h__;
/*     .......... QL TRANSFORMATION .......... */
	p = d__[m];
	c__ = 1.;
	c2 = c__;
	el1 = e[l1];
	s = 0.;
	mml = m - l;
/*     .......... FOR I=M-1 STEP -1 UNTIL L DO -- .......... */
	i__2 = mml;
	for (ii = 1; ii <= i__2; ++ii) {
	    c3 = c2;
	    c2 = c__;
	    s2 = s;
	    i__ = m - ii;
	    g = c__ * e[i__];
	    h__ = c__ * p;
	    r__ = pythag_(&p, &e[i__]);
	    e[i__ + 1] = s * r__;
	    s = e[i__] / r__;
	    c__ = p / r__;
	    p = c__ * d__[i__] - s * g;
	    d__[i__ + 1] = h__ + s * (c__ * g + s * d__[i__]);
/* L200: */
	}

	p = -s * s2 * c3 * el1 * e[l] / dl1;
	e[l] = s * p;
	d__[l] = c__ * p;
	tst2 = tst1 + (d__1 = e[l], abs(d__1));
	if (tst2 > tst1) {
	    goto L130;
	}
L210:
	p = d__[l] + f;
/*     .......... ORDER EIGENVALUES .......... */
	if (l == 1) {
	    goto L250;
	}
/*     .......... FOR I=L STEP -1 UNTIL 2 DO -- .......... */
	i__2 = l;
	for (ii = 2; ii <= i__2; ++ii) {
	    i__ = l + 2 - ii;
	    if (p >= d__[i__ - 1]) {
		goto L270;
	    }
	    d__[i__] = d__[i__ - 1];
/* L230: */
	}

L250:
	i__ = 1;
L270:
	d__[i__] = p;
/* L290: */
    }

    goto L1001;
/*     .......... SET ERROR -- NO CONVERGENCE TO AN */
/*                EIGENVALUE AFTER 30 ITERATIONS .......... */
L1000:
    *ierr = l;
L1001:
    return 0;
} /* tql1_ */