dsterf.c

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/* dsterf.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 "f2c.h"
#include "blaswrap.h"

/* Table of constant values */

static integer c__0 = 0;
static integer c__1 = 1;
static doublereal c_b32 = 1.;

/* 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_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, jtot;
    extern /* Subroutine */ int dlae2_(doublereal *, doublereal *, doublereal 
            *, doublereal *, doublereal *);
    doublereal gamma, alpha, sigma, anorm;
    extern doublereal dlapy2_(doublereal *, doublereal *), dlamch_(char *);
    integer iscale;
    extern /* Subroutine */ int dlascl_(char *, integer *, integer *, 
            doublereal *, doublereal *, integer *, integer *, doublereal *, 
            integer *, integer *);
    doublereal oldgam, safmin;
    extern /* Subroutine */ int xerbla_(char *, integer *);
    doublereal safmax;
    extern doublereal dlanst_(char *, integer *, doublereal *, doublereal *);
    extern /* Subroutine */ int dlasrt_(char *, integer *, doublereal *, 
            integer *);
    integer lendsv;
    doublereal ssfmin;
    integer nmaxit;
    doublereal ssfmax;


/*  -- LAPACK routine (version 3.2) -- */
/*     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/*     November 2006 */

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

/*  Purpose */
/*  ======= */

/*  DSTERF computes all eigenvalues of a symmetric tridiagonal matrix */
/*  using the Pal-Walker-Kahan variant of the QL or QR algorithm. */

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

/*  N       (input) INTEGER */
/*          The order of the matrix.  N >= 0. */

/*  D       (input/output) 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. */

/*  E       (input/output) DOUBLE PRECISION array, dimension (N-1) */
/*          On entry, the (n-1) subdiagonal elements of the tridiagonal */
/*          matrix. */
/*          On exit, E has been destroyed. */

/*  INFO    (output) 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. */

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

/*     .. 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_("DSTERF", &i__1);
        return 0;
    }
    if (*n <= 1) {
        return 0;
    }

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

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

/*     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_("I", &i__1, &d__[l], &e[l]);
    iscale = 0;
    if (anorm > ssfmax) {
        iscale = 1;
        i__1 = lend - l + 1;
        dlascl_("G", &c__0, &c__0, &anorm, &ssfmax, &i__1, &c__1, &d__[l], n, 
                info);
        i__1 = lend - l;
        dlascl_("G", &c__0, &c__0, &anorm, &ssfmax, &i__1, &c__1, &e[l], n, 
                info);
    } else if (anorm < ssfmin) {
        iscale = 2;
        i__1 = lend - l + 1;
        dlascl_("G", &c__0, &c__0, &anorm, &ssfmin, &i__1, &c__1, &d__[l], n, 
                info);
        i__1 = lend - l;
        dlascl_("G", &c__0, &c__0, &anorm, &ssfmin, &i__1, &c__1, &e[l], n, 
                info);
    }

    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_b32);
        sigma = p - rte / (sigma + d_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_b32);
        sigma = p - rte / (sigma + d_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_("G", &c__0, &c__0, &ssfmax, &anorm, &i__1, &c__1, &d__[lsv], 
                n, info);
    }
    if (iscale == 2) {
        i__1 = lendsv - lsv + 1;
        dlascl_("G", &c__0, &c__0, &ssfmin, &anorm, &i__1, &c__1, &d__[lsv], 
                n, info);
    }

/*     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_("I", n, &d__[1], info);

L180:
    return 0;

/*     End of DSTERF */

} /* dsterf_ */