slasq4.c

/* 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 "clapack.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_ */