/* fortran/dsterf.f -- translated by f2c (version 20200916).
   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 "lmp_f2c.h"

/* Table of constant values */

static integer c__0 = 0;
static integer c__1 = 1;
static doublereal c_b33 = 1.;

/* > \brief \b DSTERF */

/*  =========== DOCUMENTATION =========== */

/* Online html documentation available at */
/*            http://www.netlib.org/lapack/explore-html/ */

/* > \htmlonly */
/* > Download DSTERF + dependencies */
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dsterf.
f"> */
/* > [TGZ]</a> */
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dsterf.
f"> */
/* > [ZIP]</a> */
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dsterf.
f"> */
/* > [TXT]</a> */
/* > \endhtmlonly */

/*  Definition: */
/*  =========== */

/*       SUBROUTINE DSTERF( N, D, E, INFO ) */

/*       .. Scalar Arguments .. */
/*       INTEGER            INFO, N */
/*       .. */
/*       .. Array Arguments .. */
/*       DOUBLE PRECISION   D( * ), E( * ) */
/*       .. */


/* > \par Purpose: */
/*  ============= */
/* > */
/* > \verbatim */
/* > */
/* > DSTERF computes all eigenvalues of a symmetric tridiagonal matrix */
/* > using the Pal-Walker-Kahan variant of the QL or QR algorithm. */
/* > \endverbatim */

/*  Arguments: */
/*  ========== */

/* > \param[in] N */
/* > \verbatim */
/* >          N is INTEGER */
/* >          The order of the matrix.  N >= 0. */
/* > \endverbatim */
/* > */
/* > \param[in,out] D */
/* > \verbatim */
/* >          D is DOUBLE PRECISION array, dimension (N) */
/* >          On entry, the n diagonal elements of the tridiagonal matrix. */
/* >          On exit, if INFO = 0, the eigenvalues in ascending order. */
/* > \endverbatim */
/* > */
/* > \param[in,out] E */
/* > \verbatim */
/* >          E is DOUBLE PRECISION array, dimension (N-1) */
/* >          On entry, the (n-1) subdiagonal elements of the tridiagonal */
/* >          matrix. */
/* >          On exit, E has been destroyed. */
/* > \endverbatim */
/* > */
/* > \param[out] INFO */
/* > \verbatim */
/* >          INFO is INTEGER */
/* >          = 0:  successful exit */
/* >          < 0:  if INFO = -i, the i-th argument had an illegal value */
/* >          > 0:  the algorithm failed to find all of the eigenvalues in */
/* >                a total of 30*N iterations; if INFO = i, then i */
/* >                elements of E have not converged to zero. */
/* > \endverbatim */

/*  Authors: */
/*  ======== */

/* > \author Univ. of Tennessee */
/* > \author Univ. of California Berkeley */
/* > \author Univ. of Colorado Denver */
/* > \author NAG Ltd. */

/* > \ingroup auxOTHERcomputational */

/*  ===================================================================== */
/* Subroutine */ int dsterf_(integer *n, doublereal *d__, doublereal *e,
        integer *info)
{
    /* System generated locals */
    integer i__1;
    doublereal d__1, d__2, d__3;

    /* Builtin functions */
    double sqrt(doublereal), d_lmp_sign(doublereal *, doublereal *);

    /* Local variables */
    doublereal c__;
    integer i__, l, m;
    doublereal p, r__, s;
    integer l1;
    doublereal bb, rt1, rt2, eps, rte;
    integer lsv;
    doublereal eps2, oldc;
    integer lend;
    doublereal rmax;
    integer jtot;
    extern /* Subroutine */ int dlae2_(doublereal *, doublereal *, doublereal
            *, doublereal *, doublereal *);
    doublereal gamma, alpha, sigma, anorm;
    extern doublereal dlapy2_(doublereal *, doublereal *), dlamch_(char *,
            ftnlen);
    integer iscale;
    extern /* Subroutine */ int dlascl_(char *, integer *, integer *,
            doublereal *, doublereal *, integer *, integer *, doublereal *,
            integer *, integer *, ftnlen);
    doublereal oldgam, safmin;
    extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen);
    doublereal safmax;
    extern doublereal dlanst_(char *, integer *, doublereal *, doublereal *,
            ftnlen);
    extern /* Subroutine */ int dlasrt_(char *, integer *, doublereal *,
            integer *, ftnlen);
    integer lendsv;
    doublereal ssfmin;
    integer nmaxit;
    doublereal ssfmax;


/*  -- LAPACK computational routine -- */
/*  -- LAPACK is a software package provided by Univ. of Tennessee,    -- */
/*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */

/*     .. Scalar Arguments .. */
/*     .. */
/*     .. Array Arguments .. */
/*     .. */

/*  ===================================================================== */

/*     .. Parameters .. */
/*     .. */
/*     .. Local Scalars .. */
/*     .. */
/*     .. External Functions .. */
/*     .. */
/*     .. External Subroutines .. */
/*     .. */
/*     .. Intrinsic Functions .. */
/*     .. */
/*     .. Executable Statements .. */

/*     Test the input parameters. */

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

    /* Function Body */
    *info = 0;

/*     Quick return if possible */

    if (*n < 0) {
        *info = -1;
        i__1 = -(*info);
        xerbla_((char *)"DSTERF", &i__1, (ftnlen)6);
        return 0;
    }
    if (*n <= 1) {
        return 0;
    }

/*     Determine the unit roundoff for this environment. */

    eps = dlamch_((char *)"E", (ftnlen)1);
/* Computing 2nd power */
    d__1 = eps;
    eps2 = d__1 * d__1;
    safmin = dlamch_((char *)"S", (ftnlen)1);
    safmax = 1. / safmin;
    ssfmax = sqrt(safmax) / 3.;
    ssfmin = sqrt(safmin) / eps2;
    rmax = dlamch_((char *)"O", (ftnlen)1);

/*     Compute the eigenvalues of the tridiagonal matrix. */

    nmaxit = *n * 30;
    sigma = 0.;
    jtot = 0;

/*     Determine where the matrix splits and choose QL or QR iteration */
/*     for each block, according to whether top or bottom diagonal */
/*     element is smaller. */

    l1 = 1;

L10:
    if (l1 > *n) {
        goto L170;
    }
    if (l1 > 1) {
        e[l1 - 1] = 0.;
    }
    i__1 = *n - 1;
    for (m = l1; m <= i__1; ++m) {
        if ((d__3 = e[m], abs(d__3)) <= sqrt((d__1 = d__[m], abs(d__1))) *
                sqrt((d__2 = d__[m + 1], abs(d__2))) * eps) {
            e[m] = 0.;
            goto L30;
        }
/* L20: */
    }
    m = *n;

L30:
    l = l1;
    lsv = l;
    lend = m;
    lendsv = lend;
    l1 = m + 1;
    if (lend == l) {
        goto L10;
    }

/*     Scale submatrix in rows and columns L to LEND */

    i__1 = lend - l + 1;
    anorm = dlanst_((char *)"M", &i__1, &d__[l], &e[l], (ftnlen)1);
    iscale = 0;
    if (anorm == 0.) {
        goto L10;
    }
    if (anorm > ssfmax) {
        iscale = 1;
        i__1 = lend - l + 1;
        dlascl_((char *)"G", &c__0, &c__0, &anorm, &ssfmax, &i__1, &c__1, &d__[l], n,
                info, (ftnlen)1);
        i__1 = lend - l;
        dlascl_((char *)"G", &c__0, &c__0, &anorm, &ssfmax, &i__1, &c__1, &e[l], n,
                info, (ftnlen)1);
    } else if (anorm < ssfmin) {
        iscale = 2;
        i__1 = lend - l + 1;
        dlascl_((char *)"G", &c__0, &c__0, &anorm, &ssfmin, &i__1, &c__1, &d__[l], n,
                info, (ftnlen)1);
        i__1 = lend - l;
        dlascl_((char *)"G", &c__0, &c__0, &anorm, &ssfmin, &i__1, &c__1, &e[l], n,
                info, (ftnlen)1);
    }

    i__1 = lend - 1;
    for (i__ = l; i__ <= i__1; ++i__) {
/* Computing 2nd power */
        d__1 = e[i__];
        e[i__] = d__1 * d__1;
/* L40: */
    }

/*     Choose between QL and QR iteration */

    if ((d__1 = d__[lend], abs(d__1)) < (d__2 = d__[l], abs(d__2))) {
        lend = lsv;
        l = lendsv;
    }

    if (lend >= l) {

/*        QL Iteration */

/*        Look for small subdiagonal element. */

L50:
        if (l != lend) {
            i__1 = lend - 1;
            for (m = l; m <= i__1; ++m) {
                if ((d__2 = e[m], abs(d__2)) <= eps2 * (d__1 = d__[m] * d__[m
                        + 1], abs(d__1))) {
                    goto L70;
                }
/* L60: */
            }
        }
        m = lend;

L70:
        if (m < lend) {
            e[m] = 0.;
        }
        p = d__[l];
        if (m == l) {
            goto L90;
        }

/*        If remaining matrix is 2 by 2, use DLAE2 to compute its */
/*        eigenvalues. */

        if (m == l + 1) {
            rte = sqrt(e[l]);
            dlae2_(&d__[l], &rte, &d__[l + 1], &rt1, &rt2);
            d__[l] = rt1;
            d__[l + 1] = rt2;
            e[l] = 0.;
            l += 2;
            if (l <= lend) {
                goto L50;
            }
            goto L150;
        }

        if (jtot == nmaxit) {
            goto L150;
        }
        ++jtot;

/*        Form shift. */

        rte = sqrt(e[l]);
        sigma = (d__[l + 1] - p) / (rte * 2.);
        r__ = dlapy2_(&sigma, &c_b33);
        sigma = p - rte / (sigma + d_lmp_sign(&r__, &sigma));

        c__ = 1.;
        s = 0.;
        gamma = d__[m] - sigma;
        p = gamma * gamma;

/*        Inner loop */

        i__1 = l;
        for (i__ = m - 1; i__ >= i__1; --i__) {
            bb = e[i__];
            r__ = p + bb;
            if (i__ != m - 1) {
                e[i__ + 1] = s * r__;
            }
            oldc = c__;
            c__ = p / r__;
            s = bb / r__;
            oldgam = gamma;
            alpha = d__[i__];
            gamma = c__ * (alpha - sigma) - s * oldgam;
            d__[i__ + 1] = oldgam + (alpha - gamma);
            if (c__ != 0.) {
                p = gamma * gamma / c__;
            } else {
                p = oldc * bb;
            }
/* L80: */
        }

        e[l] = s * p;
        d__[l] = sigma + gamma;
        goto L50;

/*        Eigenvalue found. */

L90:
        d__[l] = p;

        ++l;
        if (l <= lend) {
            goto L50;
        }
        goto L150;

    } else {

/*        QR Iteration */

/*        Look for small superdiagonal element. */

L100:
        i__1 = lend + 1;
        for (m = l; m >= i__1; --m) {
            if ((d__2 = e[m - 1], abs(d__2)) <= eps2 * (d__1 = d__[m] * d__[m
                    - 1], abs(d__1))) {
                goto L120;
            }
/* L110: */
        }
        m = lend;

L120:
        if (m > lend) {
            e[m - 1] = 0.;
        }
        p = d__[l];
        if (m == l) {
            goto L140;
        }

/*        If remaining matrix is 2 by 2, use DLAE2 to compute its */
/*        eigenvalues. */

        if (m == l - 1) {
            rte = sqrt(e[l - 1]);
            dlae2_(&d__[l], &rte, &d__[l - 1], &rt1, &rt2);
            d__[l] = rt1;
            d__[l - 1] = rt2;
            e[l - 1] = 0.;
            l += -2;
            if (l >= lend) {
                goto L100;
            }
            goto L150;
        }

        if (jtot == nmaxit) {
            goto L150;
        }
        ++jtot;

/*        Form shift. */

        rte = sqrt(e[l - 1]);
        sigma = (d__[l - 1] - p) / (rte * 2.);
        r__ = dlapy2_(&sigma, &c_b33);
        sigma = p - rte / (sigma + d_lmp_sign(&r__, &sigma));

        c__ = 1.;
        s = 0.;
        gamma = d__[m] - sigma;
        p = gamma * gamma;

/*        Inner loop */

        i__1 = l - 1;
        for (i__ = m; i__ <= i__1; ++i__) {
            bb = e[i__];
            r__ = p + bb;
            if (i__ != m) {
                e[i__ - 1] = s * r__;
            }
            oldc = c__;
            c__ = p / r__;
            s = bb / r__;
            oldgam = gamma;
            alpha = d__[i__ + 1];
            gamma = c__ * (alpha - sigma) - s * oldgam;
            d__[i__] = oldgam + (alpha - gamma);
            if (c__ != 0.) {
                p = gamma * gamma / c__;
            } else {
                p = oldc * bb;
            }
/* L130: */
        }

        e[l - 1] = s * p;
        d__[l] = sigma + gamma;
        goto L100;

/*        Eigenvalue found. */

L140:
        d__[l] = p;

        --l;
        if (l >= lend) {
            goto L100;
        }
        goto L150;

    }

/*     Undo scaling if necessary */

L150:
    if (iscale == 1) {
        i__1 = lendsv - lsv + 1;
        dlascl_((char *)"G", &c__0, &c__0, &ssfmax, &anorm, &i__1, &c__1, &d__[lsv],
                n, info, (ftnlen)1);
    }
    if (iscale == 2) {
        i__1 = lendsv - lsv + 1;
        dlascl_((char *)"G", &c__0, &c__0, &ssfmin, &anorm, &i__1, &c__1, &d__[lsv],
                n, info, (ftnlen)1);
    }

/*     Check for no convergence to an eigenvalue after a total */
/*     of N*MAXIT iterations. */

    if (jtot < nmaxit) {
        goto L10;
    }
    i__1 = *n - 1;
    for (i__ = 1; i__ <= i__1; ++i__) {
        if (e[i__] != 0.) {
            ++(*info);
        }
/* L160: */
    }
    goto L180;

/*     Sort eigenvalues in increasing order. */

L170:
    dlasrt_((char *)"I", n, &d__[1], info, (ftnlen)1);

L180:
    return 0;

/*     End of DSTERF */

} /* dsterf_ */

#ifdef __cplusplus
        }
#endif