iparmq.c

/* iparmq.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"


integer iparmq_(integer *ispec, char *name__, char *opts, integer *n, integer 
	*ilo, integer *ihi, integer *lwork)
{
    /* System generated locals */
    integer ret_val, i__1, i__2;
    real r__1;

    /* Builtin functions */
    double log(doublereal);
    integer i_nint(real *);

    /* Local variables */
    integer nh, ns;


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

/*     .. Scalar Arguments .. */

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

/*       This program sets problem and machine dependent parameters */
/*       useful for xHSEQR and its subroutines. It is called whenever */
/*       ILAENV is called with 12 <= ISPEC <= 16 */

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

/*       ISPEC  (input) integer scalar */
/*              ISPEC specifies which tunable parameter IPARMQ should */
/*              return. */

/*              ISPEC=12: (INMIN)  Matrices of order nmin or less */
/*                        are sent directly to xLAHQR, the implicit */
/*                        double shift QR algorithm.  NMIN must be */
/*                        at least 11. */

/*              ISPEC=13: (INWIN)  Size of the deflation window. */
/*                        This is best set greater than or equal to */
/*                        the number of simultaneous shifts NS. */
/*                        Larger matrices benefit from larger deflation */
/*                        windows. */

/*              ISPEC=14: (INIBL) Determines when to stop nibbling and */
/*                        invest in an (expensive) multi-shift QR sweep. */
/*                        If the aggressive early deflation subroutine */
/*                        finds LD converged eigenvalues from an order */
/*                        NW deflation window and LD.GT.(NW*NIBBLE)/100, */
/*                        then the next QR sweep is skipped and early */
/*                        deflation is applied immediately to the */
/*                        remaining active diagonal block.  Setting */
/*                        IPARMQ(ISPEC=14) = 0 causes TTQRE to skip a */
/*                        multi-shift QR sweep whenever early deflation */
/*                        finds a converged eigenvalue.  Setting */
/*                        IPARMQ(ISPEC=14) greater than or equal to 100 */
/*                        prevents TTQRE from skipping a multi-shift */
/*                        QR sweep. */

/*              ISPEC=15: (NSHFTS) The number of simultaneous shifts in */
/*                        a multi-shift QR iteration. */

/*              ISPEC=16: (IACC22) IPARMQ is set to 0, 1 or 2 with the */
/*                        following meanings. */
/*                        0:  During the multi-shift QR sweep, */
/*                            xLAQR5 does not accumulate reflections and */
/*                            does not use matrix-matrix multiply to */
/*                            update the far-from-diagonal matrix */
/*                            entries. */
/*                        1:  During the multi-shift QR sweep, */
/*                            xLAQR5 and/or xLAQRaccumulates reflections and uses */
/*                            matrix-matrix multiply to update the */
/*                            far-from-diagonal matrix entries. */
/*                        2:  During the multi-shift QR sweep. */
/*                            xLAQR5 accumulates reflections and takes */
/*                            advantage of 2-by-2 block structure during */
/*                            matrix-matrix multiplies. */
/*                        (If xTRMM is slower than xGEMM, then */
/*                        IPARMQ(ISPEC=16)=1 may be more efficient than */
/*                        IPARMQ(ISPEC=16)=2 despite the greater level of */
/*                        arithmetic work implied by the latter choice.) */

/*       NAME    (input) character string */
/*               Name of the calling subroutine */

/*       OPTS    (input) character string */
/*               This is a concatenation of the string arguments to */
/*               TTQRE. */

/*       N       (input) integer scalar */
/*               N is the order of the Hessenberg matrix H. */

/*       ILO     (input) INTEGER */
/*       IHI     (input) INTEGER */
/*               It is assumed that H is already upper triangular */
/*               in rows and columns 1:ILO-1 and IHI+1:N. */

/*       LWORK   (input) integer scalar */
/*               The amount of workspace available. */

/*  Further Details */
/*  =============== */

/*       Little is known about how best to choose these parameters. */
/*       It is possible to use different values of the parameters */
/*       for each of CHSEQR, DHSEQR, SHSEQR and ZHSEQR. */

/*       It is probably best to choose different parameters for */
/*       different matrices and different parameters at different */
/*       times during the iteration, but this has not been */
/*       implemented --- yet. */


/*       The best choices of most of the parameters depend */
/*       in an ill-understood way on the relative execution */
/*       rate of xLAQR3 and xLAQR5 and on the nature of each */
/*       particular eigenvalue problem.  Experiment may be the */
/*       only practical way to determine which choices are most */
/*       effective. */

/*       Following is a list of default values supplied by IPARMQ. */
/*       These defaults may be adjusted in order to attain better */
/*       performance in any particular computational environment. */

/*       IPARMQ(ISPEC=12) The xLAHQR vs xLAQR0 crossover point. */
/*                        Default: 75. (Must be at least 11.) */

/*       IPARMQ(ISPEC=13) Recommended deflation window size. */
/*                        This depends on ILO, IHI and NS, the */
/*                        number of simultaneous shifts returned */
/*                        by IPARMQ(ISPEC=15).  The default for */
/*                        (IHI-ILO+1).LE.500 is NS.  The default */
/*                        for (IHI-ILO+1).GT.500 is 3*NS/2. */

/*       IPARMQ(ISPEC=14) Nibble crossover point.  Default: 14. */

/*       IPARMQ(ISPEC=15) Number of simultaneous shifts, NS. */
/*                        a multi-shift QR iteration. */

/*                        If IHI-ILO+1 is ... */

/*                        greater than      ...but less    ... the */
/*                        or equal to ...      than        default is */

/*                                0               30       NS =   2+ */
/*                               30               60       NS =   4+ */
/*                               60              150       NS =  10 */
/*                              150              590       NS =  ** */
/*                              590             3000       NS =  64 */
/*                             3000             6000       NS = 128 */
/*                             6000             infinity   NS = 256 */

/*                    (+)  By default matrices of this order are */
/*                         passed to the implicit double shift routine */
/*                         xLAHQR.  See IPARMQ(ISPEC=12) above.   These */
/*                         values of NS are used only in case of a rare */
/*                         xLAHQR failure. */

/*                    (**) The asterisks (**) indicate an ad-hoc */
/*                         function increasing from 10 to 64. */

/*       IPARMQ(ISPEC=16) Select structured matrix multiply. */
/*                        (See ISPEC=16 above for details.) */
/*                        Default: 3. */

/*     ================================================================ */
/*     .. Parameters .. */
/*     .. */
/*     .. Local Scalars .. */
/*     .. */
/*     .. Intrinsic Functions .. */
/*     .. */
/*     .. Executable Statements .. */
    if (*ispec == 15 || *ispec == 13 || *ispec == 16) {

/*        ==== Set the number simultaneous shifts ==== */

	nh = *ihi - *ilo + 1;
	ns = 2;
	if (nh >= 30) {
	    ns = 4;
	}
	if (nh >= 60) {
	    ns = 10;
	}
	if (nh >= 150) {
/* Computing MAX */
	    r__1 = log((real) nh) / log(2.f);
	    i__1 = 10, i__2 = nh / i_nint(&r__1);
	    ns = max(i__1,i__2);
	}
	if (nh >= 590) {
	    ns = 64;
	}
	if (nh >= 3000) {
	    ns = 128;
	}
	if (nh >= 6000) {
	    ns = 256;
	}
/* Computing MAX */
	i__1 = 2, i__2 = ns - ns % 2;
	ns = max(i__1,i__2);
    }

    if (*ispec == 12) {


/*        ===== Matrices of order smaller than NMIN get sent */
/*        .     to xLAHQR, the classic double shift algorithm. */
/*        .     This must be at least 11. ==== */

	ret_val = 75;

    } else if (*ispec == 14) {

/*        ==== INIBL: skip a multi-shift qr iteration and */
/*        .    whenever aggressive early deflation finds */
/*        .    at least (NIBBLE*(window size)/100) deflations. ==== */

	ret_val = 14;

    } else if (*ispec == 15) {

/*        ==== NSHFTS: The number of simultaneous shifts ===== */

	ret_val = ns;

    } else if (*ispec == 13) {

/*        ==== NW: deflation window size.  ==== */

	if (nh <= 500) {
	    ret_val = ns;
	} else {
	    ret_val = ns * 3 / 2;
	}

    } else if (*ispec == 16) {

/*        ==== IACC22: Whether to accumulate reflections */
/*        .     before updating the far-from-diagonal elements */
/*        .     and whether to use 2-by-2 block structure while */
/*        .     doing it.  A small amount of work could be saved */
/*        .     by making this choice dependent also upon the */
/*        .     NH=IHI-ILO+1. */

	ret_val = 0;
	if (ns >= 14) {
	    ret_val = 1;
	}
	if (ns >= 14) {
	    ret_val = 2;
	}

    } else {
/*        ===== invalid value of ispec ===== */
	ret_val = -1;

    }

/*     ==== End of IPARMQ ==== */

    return ret_val;
} /* iparmq_ */