slasq3.c

来自「提供矩阵类的函数库」· C语言 代码 · 共 346 行

#include "blaswrap.h"
/*  -- translated by f2c (version 19990503).
   You must link the resulting object file with the libraries:
	-lf2c -lm   (in that order)
*/

#include "f2c.h"

/* Common Block Declarations */

struct {
    real ops, itcnt;
} latime_;

#define latime_1 latime_

/* Subroutine */ int slasq3_(integer *i0, integer *n0, real *z__, integer *pp,
	 real *dmin__, real *sigma, real *desig, real *qmax, integer *nfail, 
	integer *iter, integer *ndiv, logical *ieee)
{
    /* Initialized data */

    static integer ttype = 0;
    static real dmin1 = 0.f;
    static real dmin2 = 0.f;
    static real dn = 0.f;
    static real dn1 = 0.f;
    static real dn2 = 0.f;
    static real tau = 0.f;

    /* System generated locals */
    integer i__1;
    real r__1, r__2;

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

    /* Local variables */
    static real temp, s, t;
    static integer j4;
    extern /* Subroutine */ int slasq4_(integer *, integer *, real *, integer 
	    *, integer *, real *, real *, real *, real *, real *, real *, 
	    real *, integer *), slasq5_(integer *, integer *, real *, integer 
	    *, real *, real *, real *, real *, real *, real *, real *, 
	    logical *), slasq6_(integer *, integer *, real *, integer *, real 
	    *, real *, real *, real *, real *, real *);
    static integer nn;
    extern doublereal slamch_(char *);
    static real safmin, eps, tol;
    static integer n0in, ipn4;
    static real tol2;


/*  -- LAPACK auxiliary routine (instrumented to count ops, version 3.0) --   
       Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,   
       Courant Institute, Argonne National Lab, and Rice University   
       May 17, 2000   


    Purpose   
    =======   

    SLASQ3 checks for deflation, computes a shift (TAU) and calls dqds.   
    In case of failure it changes shifts, and tries again until output   
    is positive.   

    Arguments   
    =========   

    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.   

    DMIN   (output) REAL   
           Minimum value of d.   

    SIGMA  (output) REAL   
           Sum of shifts used in current segment.   

    DESIG  (input/output) REAL   
           Lower order part of SIGMA   

    QMAX   (input) REAL   
           Maximum value of q.   

    NFAIL  (output) INTEGER   
           Number of times shift was too big.   

    ITER   (output) INTEGER   
           Number of iterations.   

    NDIV   (output) INTEGER   
           Number of divisions.   

    TTYPE  (output) INTEGER   
           Shift type.   

    IEEE   (input) LOGICAL   
           Flag for IEEE or non IEEE arithmetic (passed to SLASQ5).   

    =====================================================================   

       Parameter adjustments */
    --z__;

    /* Function Body */

    latime_1.ops += 2.f;
    n0in = *n0;
    eps = slamch_("Precision");
    safmin = slamch_("Safe minimum");
    tol = eps * 100.f;
/* Computing 2nd power */
    r__1 = tol;
    tol2 = r__1 * r__1;

/*     Check for deflation. */

L10:

    if (*n0 < *i0) {
	return 0;
    }
    if (*n0 == *i0) {
	goto L20;
    }
    nn = (*n0 << 2) + *pp;
    if (*n0 == *i0 + 1) {
	goto L40;
    }

/*     Check whether E(N0-1) is negligible, 1 eigenvalue. */

    latime_1.ops += 3.f;
    if (z__[nn - 5] > tol2 * (*sigma + z__[nn - 3]) && z__[nn - (*pp << 1) - 
	    4] > tol2 * z__[nn - 7]) {
	goto L30;
    }

L20:

    latime_1.ops += 1.f;
    z__[(*n0 << 2) - 3] = z__[(*n0 << 2) + *pp - 3] + *sigma;
    --(*n0);
    goto L10;

/*     Check  whether E(N0-2) is negligible, 2 eigenvalues. */

L30:

    latime_1.ops += 2.f;
    if (z__[nn - 9] > tol2 * *sigma && z__[nn - (*pp << 1) - 8] > tol2 * z__[
	    nn - 11]) {
	goto L50;
    }

L40:

    if (z__[nn - 3] > z__[nn - 7]) {
	s = z__[nn - 3];
	z__[nn - 3] = z__[nn - 7];
	z__[nn - 7] = s;
    }
    latime_1.ops += 3.f;
    if (z__[nn - 5] > z__[nn - 3] * tol2) {
	latime_1.ops += 5.f;
	t = (z__[nn - 7] - z__[nn - 3] + z__[nn - 5]) * .5f;
	s = z__[nn - 3] * (z__[nn - 5] / t);
	if (s <= t) {
	    latime_1.ops += 7.f;
	    s = z__[nn - 3] * (z__[nn - 5] / (t * (sqrt(s / t + 1.f) + 1.f)));
	} else {
	    latime_1.ops += 6.f;
	    s = z__[nn - 3] * (z__[nn - 5] / (t + sqrt(t) * sqrt(t + s)));
	}
	latime_1.ops += 4.f;
	t = z__[nn - 7] + (s + z__[nn - 5]);
	z__[nn - 3] *= z__[nn - 7] / t;
	z__[nn - 7] = t;
    }
    z__[(*n0 << 2) - 7] = z__[nn - 7] + *sigma;
    z__[(*n0 << 2) - 3] = z__[nn - 3] + *sigma;
    *n0 += -2;
    goto L10;

L50:

/*     Reverse the qd-array, if warranted. */

    if (*dmin__ <= 0.f || *n0 < n0in) {
	latime_1.ops += 1.f;
	if (z__[(*i0 << 2) + *pp - 3] * 1.5f < z__[(*n0 << 2) + *pp - 3]) {
	    ipn4 = *i0 + *n0 << 2;
	    i__1 = *i0 + *n0 - 1 << 1;
	    for (j4 = *i0 << 2; j4 <= i__1; j4 += 4) {
		temp = z__[j4 - 3];
		z__[j4 - 3] = z__[ipn4 - j4 - 3];
		z__[ipn4 - j4 - 3] = temp;
		temp = z__[j4 - 2];
		z__[j4 - 2] = z__[ipn4 - j4 - 2];
		z__[ipn4 - j4 - 2] = temp;
		temp = z__[j4 - 1];
		z__[j4 - 1] = z__[ipn4 - j4 - 5];
		z__[ipn4 - j4 - 5] = temp;
		temp = z__[j4];
		z__[j4] = z__[ipn4 - j4 - 4];
		z__[ipn4 - j4 - 4] = temp;
/* L60: */
	    }
	    if (*n0 - *i0 <= 4) {
		z__[(*n0 << 2) + *pp - 1] = z__[(*i0 << 2) + *pp - 1];
		z__[(*n0 << 2) - *pp] = z__[(*i0 << 2) - *pp];
	    }
/* Computing MIN */
	    r__1 = dmin2, r__2 = z__[(*n0 << 2) + *pp - 1];
	    dmin2 = dmin(r__1,r__2);
/* Computing MIN */
	    r__1 = z__[(*n0 << 2) + *pp - 1], r__2 = z__[(*i0 << 2) + *pp - 1]
		    , r__1 = min(r__1,r__2), r__2 = z__[(*i0 << 2) + *pp + 3];
	    z__[(*n0 << 2) + *pp - 1] = dmin(r__1,r__2);
/* Computing MIN */
	    r__1 = z__[(*n0 << 2) - *pp], r__2 = z__[(*i0 << 2) - *pp], r__1 =
		     min(r__1,r__2), r__2 = z__[(*i0 << 2) - *pp + 4];
	    z__[(*n0 << 2) - *pp] = dmin(r__1,r__2);
/* Computing MAX */
	    r__1 = *qmax, r__2 = z__[(*i0 << 2) + *pp - 3], r__1 = max(r__1,
		    r__2), r__2 = z__[(*i0 << 2) + *pp + 1];
	    *qmax = dmax(r__1,r__2);
	    *dmin__ = 0.f;
	}
    }

/* L70:   

   Computing MIN */
    r__1 = z__[(*n0 << 2) + *pp - 1], r__2 = z__[(*n0 << 2) + *pp - 9], r__1 =
	     min(r__1,r__2), r__2 = dmin2 + z__[(*n0 << 2) - *pp];
    if (*dmin__ < 0.f || safmin * *qmax < dmin(r__1,r__2)) {

/*        Choose a shift. */

	slasq4_(i0, n0, &z__[1], pp, &n0in, dmin__, &dmin1, &dmin2, &dn, &dn1,
		 &dn2, &tau, &ttype);

/*        Call dqds until DMIN > 0. */

L80:

	slasq5_(i0, n0, &z__[1], pp, &tau, dmin__, &dmin1, &dmin2, &dn, &dn1, 
		&dn2, ieee);

	*ndiv += *n0 - *i0 + 2;
	++(*iter);

/*        Check status. */

	if (*dmin__ >= 0.f && dmin1 > 0.f) {

/*           Success. */

	    goto L100;

	} else if (*dmin__ < 0.f && dmin1 > 0.f && z__[(*n0 - 1 << 2) - *pp] <
		 tol * (*sigma + dn1) && dabs(dn) < tol * *sigma) {

/*           Convergence hidden by negative DN. */

	    latime_1.ops += 2.f;
	    z__[(*n0 - 1 << 2) - *pp + 2] = 0.f;
	    *dmin__ = 0.f;
	    goto L100;
	} else if (*dmin__ < 0.f) {

/*           TAU too big. Select new TAU and try again. */

	    ++(*nfail);
	    if (ttype < -22) {

/*              Failed twice. Play it safe. */

		tau = 0.f;
	    } else if (dmin1 > 0.f) {

/*              Late failure. Gives excellent shift. */

		latime_1.ops += 4.f;
		tau = (tau + *dmin__) * (1.f - eps * 2.f);
		ttype += -11;
	    } else {

/*              Early failure. Divide by 4. */

		latime_1.ops += 1.f;
		tau *= .25f;
		ttype += -12;
	    }
	    goto L80;
	} else if (*dmin__ != *dmin__) {

/*           NaN. */

	    tau = 0.f;
	    goto L80;
	} else {

/*           Possible underflow. Play it safe. */

	    goto L90;
	}
    }

/*     Risk of underflow. */

L90:
    slasq6_(i0, n0, &z__[1], pp, dmin__, &dmin1, &dmin2, &dn, &dn1, &dn2);
    *ndiv += *n0 - *i0 + 2;
    ++(*iter);
    tau = 0.f;

L100:
    latime_1.ops += 4.f;
    if (tau < *sigma) {
	*desig += tau;
	t = *sigma + *desig;
	*desig -= t - *sigma;
    } else {
	t = *sigma + tau;
	*desig = *sigma - (t - tau) + *desig;
    }
    *sigma = t;

    return 0;

/*     End of SLASQ3 */

} /* slasq3_ */