slasq4.c

Go to the documentation of this file.

/* slasq4.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"

/* Subroutine */ int slasq4_(integer *i0, integer *n0, real *z__, integer *pp, 
         integer *n0in, real *dmin__, real *dmin1, real *dmin2, real *dn, 
        real *dn1, real *dn2, real *tau, integer *ttype, real *g)
{
    /* System generated locals */
    integer i__1;
    real r__1, r__2;

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

    /* Local variables */
    real s, a2, b1, b2;
    integer i4, nn, np;
    real gam, gap1, gap2;


/*  -- LAPACK routine (version 3.2)                                    -- */

/*  -- Contributed by Osni Marques of the Lawrence Berkeley National   -- */
/*  -- Laboratory and Beresford Parlett of the Univ. of California at  -- */
/*  -- Berkeley                                                        -- */
/*  -- November 2008                                                   -- */

/*  -- 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 .. */
/*     .. */

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

/*  SLASQ4 computes an approximation TAU to the smallest eigenvalue */
/*  using values of d from the previous transform. */

/*  I0    (input) INTEGER */
/*        First index. */

/*  N0    (input) INTEGER */
/*        Last index. */

/*  Z     (input) REAL array, dimension ( 4*N ) */
/*        Z holds the qd array. */

/*  PP    (input) INTEGER */
/*        PP=0 for ping, PP=1 for pong. */

/*  NOIN  (input) INTEGER */
/*        The value of N0 at start of EIGTEST. */

/*  DMIN  (input) REAL */
/*        Minimum value of d. */

/*  DMIN1 (input) REAL */
/*        Minimum value of d, excluding D( N0 ). */

/*  DMIN2 (input) REAL */
/*        Minimum value of d, excluding D( N0 ) and D( N0-1 ). */

/*  DN    (input) REAL */
/*        d(N) */

/*  DN1   (input) REAL */
/*        d(N-1) */

/*  DN2   (input) REAL */
/*        d(N-2) */

/*  TAU   (output) REAL */
/*        This is the shift. */

/*  TTYPE (output) INTEGER */
/*        Shift type. */

/*  G     (input/output) REAL */
/*        G is passed as an argument in order to save its value between */
/*        calls to SLASQ4. */

/*  Further Details */
/*  =============== */
/*  CNST1 = 9/16 */

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

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

/*     A negative DMIN forces the shift to take that absolute value */
/*     TTYPE records the type of shift. */

    /* Parameter adjustments */
    --z__;

    /* Function Body */
    if (*dmin__ <= 0.f) {
        *tau = -(*dmin__);
        *ttype = -1;
        return 0;
    }

    nn = (*n0 << 2) + *pp;
    if (*n0in == *n0) {

/*        No eigenvalues deflated. */

        if (*dmin__ == *dn || *dmin__ == *dn1) {

            b1 = sqrt(z__[nn - 3]) * sqrt(z__[nn - 5]);
            b2 = sqrt(z__[nn - 7]) * sqrt(z__[nn - 9]);
            a2 = z__[nn - 7] + z__[nn - 5];

/*           Cases 2 and 3. */

            if (*dmin__ == *dn && *dmin1 == *dn1) {
                gap2 = *dmin2 - a2 - *dmin2 * .25f;
                if (gap2 > 0.f && gap2 > b2) {
                    gap1 = a2 - *dn - b2 / gap2 * b2;
                } else {
                    gap1 = a2 - *dn - (b1 + b2);
                }
                if (gap1 > 0.f && gap1 > b1) {
/* Computing MAX */
                    r__1 = *dn - b1 / gap1 * b1, r__2 = *dmin__ * .5f;
                    s = dmax(r__1,r__2);
                    *ttype = -2;
                } else {
                    s = 0.f;
                    if (*dn > b1) {
                        s = *dn - b1;
                    }
                    if (a2 > b1 + b2) {
/* Computing MIN */
                        r__1 = s, r__2 = a2 - (b1 + b2);
                        s = dmin(r__1,r__2);
                    }
/* Computing MAX */
                    r__1 = s, r__2 = *dmin__ * .333f;
                    s = dmax(r__1,r__2);
                    *ttype = -3;
                }
            } else {

/*              Case 4. */

                *ttype = -4;
                s = *dmin__ * .25f;
                if (*dmin__ == *dn) {
                    gam = *dn;
                    a2 = 0.f;
                    if (z__[nn - 5] > z__[nn - 7]) {
                        return 0;
                    }
                    b2 = z__[nn - 5] / z__[nn - 7];
                    np = nn - 9;
                } else {
                    np = nn - (*pp << 1);
                    b2 = z__[np - 2];
                    gam = *dn1;
                    if (z__[np - 4] > z__[np - 2]) {
                        return 0;
                    }
                    a2 = z__[np - 4] / z__[np - 2];
                    if (z__[nn - 9] > z__[nn - 11]) {
                        return 0;
                    }
                    b2 = z__[nn - 9] / z__[nn - 11];
                    np = nn - 13;
                }

/*              Approximate contribution to norm squared from I < NN-1. */

                a2 += b2;
                i__1 = (*i0 << 2) - 1 + *pp;
                for (i4 = np; i4 >= i__1; i4 += -4) {
                    if (b2 == 0.f) {
                        goto L20;
                    }
                    b1 = b2;
                    if (z__[i4] > z__[i4 - 2]) {
                        return 0;
                    }
                    b2 *= z__[i4] / z__[i4 - 2];
                    a2 += b2;
                    if (dmax(b2,b1) * 100.f < a2 || .563f < a2) {
                        goto L20;
                    }
/* L10: */
                }
L20:
                a2 *= 1.05f;

/*              Rayleigh quotient residual bound. */

                if (a2 < .563f) {
                    s = gam * (1.f - sqrt(a2)) / (a2 + 1.f);
                }
            }
        } else if (*dmin__ == *dn2) {

/*           Case 5. */

            *ttype = -5;
            s = *dmin__ * .25f;

/*           Compute contribution to norm squared from I > NN-2. */

            np = nn - (*pp << 1);
            b1 = z__[np - 2];
            b2 = z__[np - 6];
            gam = *dn2;
            if (z__[np - 8] > b2 || z__[np - 4] > b1) {
                return 0;
            }
            a2 = z__[np - 8] / b2 * (z__[np - 4] / b1 + 1.f);

/*           Approximate contribution to norm squared from I < NN-2. */

            if (*n0 - *i0 > 2) {
                b2 = z__[nn - 13] / z__[nn - 15];
                a2 += b2;
                i__1 = (*i0 << 2) - 1 + *pp;
                for (i4 = nn - 17; i4 >= i__1; i4 += -4) {
                    if (b2 == 0.f) {
                        goto L40;
                    }
                    b1 = b2;
                    if (z__[i4] > z__[i4 - 2]) {
                        return 0;
                    }
                    b2 *= z__[i4] / z__[i4 - 2];
                    a2 += b2;
                    if (dmax(b2,b1) * 100.f < a2 || .563f < a2) {
                        goto L40;
                    }
/* L30: */
                }
L40:
                a2 *= 1.05f;
            }

            if (a2 < .563f) {
                s = gam * (1.f - sqrt(a2)) / (a2 + 1.f);
            }
        } else {

/*           Case 6, no information to guide us. */

            if (*ttype == -6) {
                *g += (1.f - *g) * .333f;
            } else if (*ttype == -18) {
                *g = .083250000000000005f;
            } else {
                *g = .25f;
            }
            s = *g * *dmin__;
            *ttype = -6;
        }

    } else if (*n0in == *n0 + 1) {

/*        One eigenvalue just deflated. Use DMIN1, DN1 for DMIN and DN. */

        if (*dmin1 == *dn1 && *dmin2 == *dn2) {

/*           Cases 7 and 8. */

            *ttype = -7;
            s = *dmin1 * .333f;
            if (z__[nn - 5] > z__[nn - 7]) {
                return 0;
            }
            b1 = z__[nn - 5] / z__[nn - 7];
            b2 = b1;
            if (b2 == 0.f) {
                goto L60;
            }
            i__1 = (*i0 << 2) - 1 + *pp;
            for (i4 = (*n0 << 2) - 9 + *pp; i4 >= i__1; i4 += -4) {
                a2 = b1;
                if (z__[i4] > z__[i4 - 2]) {
                    return 0;
                }
                b1 *= z__[i4] / z__[i4 - 2];
                b2 += b1;
                if (dmax(b1,a2) * 100.f < b2) {
                    goto L60;
                }
/* L50: */
            }
L60:
            b2 = sqrt(b2 * 1.05f);
/* Computing 2nd power */
            r__1 = b2;
            a2 = *dmin1 / (r__1 * r__1 + 1.f);
            gap2 = *dmin2 * .5f - a2;
            if (gap2 > 0.f && gap2 > b2 * a2) {
/* Computing MAX */
                r__1 = s, r__2 = a2 * (1.f - a2 * 1.01f * (b2 / gap2) * b2);
                s = dmax(r__1,r__2);
            } else {
/* Computing MAX */
                r__1 = s, r__2 = a2 * (1.f - b2 * 1.01f);
                s = dmax(r__1,r__2);
                *ttype = -8;
            }
        } else {

/*           Case 9. */

            s = *dmin1 * .25f;
            if (*dmin1 == *dn1) {
                s = *dmin1 * .5f;
            }
            *ttype = -9;
        }

    } else if (*n0in == *n0 + 2) {

/*        Two eigenvalues deflated. Use DMIN2, DN2 for DMIN and DN. */

/*        Cases 10 and 11. */

        if (*dmin2 == *dn2 && z__[nn - 5] * 2.f < z__[nn - 7]) {
            *ttype = -10;
            s = *dmin2 * .333f;
            if (z__[nn - 5] > z__[nn - 7]) {
                return 0;
            }
            b1 = z__[nn - 5] / z__[nn - 7];
            b2 = b1;
            if (b2 == 0.f) {
                goto L80;
            }
            i__1 = (*i0 << 2) - 1 + *pp;
            for (i4 = (*n0 << 2) - 9 + *pp; i4 >= i__1; i4 += -4) {
                if (z__[i4] > z__[i4 - 2]) {
                    return 0;
                }
                b1 *= z__[i4] / z__[i4 - 2];
                b2 += b1;
                if (b1 * 100.f < b2) {
                    goto L80;
                }
/* L70: */
            }
L80:
            b2 = sqrt(b2 * 1.05f);
/* Computing 2nd power */
            r__1 = b2;
            a2 = *dmin2 / (r__1 * r__1 + 1.f);
            gap2 = z__[nn - 7] + z__[nn - 9] - sqrt(z__[nn - 11]) * sqrt(z__[
                    nn - 9]) - a2;
            if (gap2 > 0.f && gap2 > b2 * a2) {
/* Computing MAX */
                r__1 = s, r__2 = a2 * (1.f - a2 * 1.01f * (b2 / gap2) * b2);
                s = dmax(r__1,r__2);
            } else {
/* Computing MAX */
                r__1 = s, r__2 = a2 * (1.f - b2 * 1.01f);
                s = dmax(r__1,r__2);
            }
        } else {
            s = *dmin2 * .25f;
            *ttype = -11;
        }
    } else if (*n0in > *n0 + 2) {

/*        Case 12, more than two eigenvalues deflated. No information. */

        s = 0.f;
        *ttype = -12;
    }

    *tau = s;
    return 0;

/*     End of SLASQ4 */

} /* slasq4_ */