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    1: *> \brief \b IPARMQ
    2: *
    3: *  =========== DOCUMENTATION ===========
    4: *
    5: * Online html documentation available at 
    6: *            http://www.netlib.org/lapack/explore-html/ 
    7: *
    8: *> \htmlonly
    9: *> Download IPARMQ + dependencies 
   10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/iparmq.f"> 
   11: *> [TGZ]</a> 
   12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/iparmq.f"> 
   13: *> [ZIP]</a> 
   14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/iparmq.f"> 
   15: *> [TXT]</a>
   16: *> \endhtmlonly 
   17: *
   18: *  Definition:
   19: *  ===========
   20: *
   21: *       INTEGER FUNCTION IPARMQ( ISPEC, NAME, OPTS, N, ILO, IHI, LWORK )
   22: * 
   23: *       .. Scalar Arguments ..
   24: *       INTEGER            IHI, ILO, ISPEC, LWORK, N
   25: *       CHARACTER          NAME*( * ), OPTS*( * )
   26: *  
   27: *
   28: *> \par Purpose:
   29: *  =============
   30: *>
   31: *> \verbatim
   32: *>
   33: *>      This program sets problem and machine dependent parameters
   34: *>      useful for xHSEQR and its subroutines. It is called whenever 
   35: *>      ILAENV is called with 12 <= ISPEC <= 16
   36: *> \endverbatim
   37: *
   38: *  Arguments:
   39: *  ==========
   40: *
   41: *> \param[in] ISPEC
   42: *> \verbatim
   43: *>          ISPEC is integer scalar
   44: *>              ISPEC specifies which tunable parameter IPARMQ should
   45: *>              return.
   46: *>
   47: *>              ISPEC=12: (INMIN)  Matrices of order nmin or less
   48: *>                        are sent directly to xLAHQR, the implicit
   49: *>                        double shift QR algorithm.  NMIN must be
   50: *>                        at least 11.
   51: *>
   52: *>              ISPEC=13: (INWIN)  Size of the deflation window.
   53: *>                        This is best set greater than or equal to
   54: *>                        the number of simultaneous shifts NS.
   55: *>                        Larger matrices benefit from larger deflation
   56: *>                        windows.
   57: *>
   58: *>              ISPEC=14: (INIBL) Determines when to stop nibbling and
   59: *>                        invest in an (expensive) multi-shift QR sweep.
   60: *>                        If the aggressive early deflation subroutine
   61: *>                        finds LD converged eigenvalues from an order
   62: *>                        NW deflation window and LD.GT.(NW*NIBBLE)/100,
   63: *>                        then the next QR sweep is skipped and early
   64: *>                        deflation is applied immediately to the
   65: *>                        remaining active diagonal block.  Setting
   66: *>                        IPARMQ(ISPEC=14) = 0 causes TTQRE to skip a
   67: *>                        multi-shift QR sweep whenever early deflation
   68: *>                        finds a converged eigenvalue.  Setting
   69: *>                        IPARMQ(ISPEC=14) greater than or equal to 100
   70: *>                        prevents TTQRE from skipping a multi-shift
   71: *>                        QR sweep.
   72: *>
   73: *>              ISPEC=15: (NSHFTS) The number of simultaneous shifts in
   74: *>                        a multi-shift QR iteration.
   75: *>
   76: *>              ISPEC=16: (IACC22) IPARMQ is set to 0, 1 or 2 with the
   77: *>                        following meanings.
   78: *>                        0:  During the multi-shift QR sweep,
   79: *>                            xLAQR5 does not accumulate reflections and
   80: *>                            does not use matrix-matrix multiply to
   81: *>                            update the far-from-diagonal matrix
   82: *>                            entries.
   83: *>                        1:  During the multi-shift QR sweep,
   84: *>                            xLAQR5 and/or xLAQRaccumulates reflections and uses
   85: *>                            matrix-matrix multiply to update the
   86: *>                            far-from-diagonal matrix entries.
   87: *>                        2:  During the multi-shift QR sweep.
   88: *>                            xLAQR5 accumulates reflections and takes
   89: *>                            advantage of 2-by-2 block structure during
   90: *>                            matrix-matrix multiplies.
   91: *>                        (If xTRMM is slower than xGEMM, then
   92: *>                        IPARMQ(ISPEC=16)=1 may be more efficient than
   93: *>                        IPARMQ(ISPEC=16)=2 despite the greater level of
   94: *>                        arithmetic work implied by the latter choice.)
   95: *> \endverbatim
   96: *>
   97: *> \param[in] NAME
   98: *> \verbatim
   99: *>          NAME is character string
  100: *>               Name of the calling subroutine
  101: *> \endverbatim
  102: *>
  103: *> \param[in] OPTS
  104: *> \verbatim
  105: *>          OPTS is character string
  106: *>               This is a concatenation of the string arguments to
  107: *>               TTQRE.
  108: *> \endverbatim
  109: *>
  110: *> \param[in] N
  111: *> \verbatim
  112: *>          N is integer scalar
  113: *>               N is the order of the Hessenberg matrix H.
  114: *> \endverbatim
  115: *>
  116: *> \param[in] ILO
  117: *> \verbatim
  118: *>          ILO is INTEGER
  119: *> \endverbatim
  120: *>
  121: *> \param[in] IHI
  122: *> \verbatim
  123: *>          IHI is INTEGER
  124: *>               It is assumed that H is already upper triangular
  125: *>               in rows and columns 1:ILO-1 and IHI+1:N.
  126: *> \endverbatim
  127: *>
  128: *> \param[in] LWORK
  129: *> \verbatim
  130: *>          LWORK is integer scalar
  131: *>               The amount of workspace available.
  132: *> \endverbatim
  133: *
  134: *  Authors:
  135: *  ========
  136: *
  137: *> \author Univ. of Tennessee 
  138: *> \author Univ. of California Berkeley 
  139: *> \author Univ. of Colorado Denver 
  140: *> \author NAG Ltd. 
  141: *
  142: *> \date November 2011
  143: *
  144: *> \ingroup auxOTHERauxiliary
  145: *
  146: *> \par Further Details:
  147: *  =====================
  148: *>
  149: *> \verbatim
  150: *>
  151: *>       Little is known about how best to choose these parameters.
  152: *>       It is possible to use different values of the parameters
  153: *>       for each of CHSEQR, DHSEQR, SHSEQR and ZHSEQR.
  154: *>
  155: *>       It is probably best to choose different parameters for
  156: *>       different matrices and different parameters at different
  157: *>       times during the iteration, but this has not been
  158: *>       implemented --- yet.
  159: *>
  160: *>
  161: *>       The best choices of most of the parameters depend
  162: *>       in an ill-understood way on the relative execution
  163: *>       rate of xLAQR3 and xLAQR5 and on the nature of each
  164: *>       particular eigenvalue problem.  Experiment may be the
  165: *>       only practical way to determine which choices are most
  166: *>       effective.
  167: *>
  168: *>       Following is a list of default values supplied by IPARMQ.
  169: *>       These defaults may be adjusted in order to attain better
  170: *>       performance in any particular computational environment.
  171: *>
  172: *>       IPARMQ(ISPEC=12) The xLAHQR vs xLAQR0 crossover point.
  173: *>                        Default: 75. (Must be at least 11.)
  174: *>
  175: *>       IPARMQ(ISPEC=13) Recommended deflation window size.
  176: *>                        This depends on ILO, IHI and NS, the
  177: *>                        number of simultaneous shifts returned
  178: *>                        by IPARMQ(ISPEC=15).  The default for
  179: *>                        (IHI-ILO+1).LE.500 is NS.  The default
  180: *>                        for (IHI-ILO+1).GT.500 is 3*NS/2.
  181: *>
  182: *>       IPARMQ(ISPEC=14) Nibble crossover point.  Default: 14.
  183: *>
  184: *>       IPARMQ(ISPEC=15) Number of simultaneous shifts, NS.
  185: *>                        a multi-shift QR iteration.
  186: *>
  187: *>                        If IHI-ILO+1 is ...
  188: *>
  189: *>                        greater than      ...but less    ... the
  190: *>                        or equal to ...      than        default is
  191: *>
  192: *>                                0               30       NS =   2+
  193: *>                               30               60       NS =   4+
  194: *>                               60              150       NS =  10
  195: *>                              150              590       NS =  **
  196: *>                              590             3000       NS =  64
  197: *>                             3000             6000       NS = 128
  198: *>                             6000             infinity   NS = 256
  199: *>
  200: *>                    (+)  By default matrices of this order are
  201: *>                         passed to the implicit double shift routine
  202: *>                         xLAHQR.  See IPARMQ(ISPEC=12) above.   These
  203: *>                         values of NS are used only in case of a rare
  204: *>                         xLAHQR failure.
  205: *>
  206: *>                    (**) The asterisks (**) indicate an ad-hoc
  207: *>                         function increasing from 10 to 64.
  208: *>
  209: *>       IPARMQ(ISPEC=16) Select structured matrix multiply.
  210: *>                        (See ISPEC=16 above for details.)
  211: *>                        Default: 3.
  212: *> \endverbatim
  213: *>
  214: *  =====================================================================
  215:       INTEGER FUNCTION IPARMQ( ISPEC, NAME, OPTS, N, ILO, IHI, LWORK )
  216: *
  217: *  -- LAPACK auxiliary routine (version 3.4.0) --
  218: *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
  219: *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
  220: *     November 2011
  221: *
  222: *     .. Scalar Arguments ..
  223:       INTEGER            IHI, ILO, ISPEC, LWORK, N
  224:       CHARACTER          NAME*( * ), OPTS*( * )
  225: *
  226: *  ================================================================
  227: *     .. Parameters ..
  228:       INTEGER            INMIN, INWIN, INIBL, ISHFTS, IACC22
  229:       PARAMETER          ( INMIN = 12, INWIN = 13, INIBL = 14,
  230:      $                   ISHFTS = 15, IACC22 = 16 )
  231:       INTEGER            NMIN, K22MIN, KACMIN, NIBBLE, KNWSWP
  232:       PARAMETER          ( NMIN = 75, K22MIN = 14, KACMIN = 14,
  233:      $                   NIBBLE = 14, KNWSWP = 500 )
  234:       REAL               TWO
  235:       PARAMETER          ( TWO = 2.0 )
  236: *     ..
  237: *     .. Local Scalars ..
  238:       INTEGER            NH, NS
  239: *     ..
  240: *     .. Intrinsic Functions ..
  241:       INTRINSIC          LOG, MAX, MOD, NINT, REAL
  242: *     ..
  243: *     .. Executable Statements ..
  244:       IF( ( ISPEC.EQ.ISHFTS ) .OR. ( ISPEC.EQ.INWIN ) .OR.
  245:      $    ( ISPEC.EQ.IACC22 ) ) THEN
  246: *
  247: *        ==== Set the number simultaneous shifts ====
  248: *
  249:          NH = IHI - ILO + 1
  250:          NS = 2
  251:          IF( NH.GE.30 )
  252:      $      NS = 4
  253:          IF( NH.GE.60 )
  254:      $      NS = 10
  255:          IF( NH.GE.150 )
  256:      $      NS = MAX( 10, NH / NINT( LOG( REAL( NH ) ) / LOG( TWO ) ) )
  257:          IF( NH.GE.590 )
  258:      $      NS = 64
  259:          IF( NH.GE.3000 )
  260:      $      NS = 128
  261:          IF( NH.GE.6000 )
  262:      $      NS = 256
  263:          NS = MAX( 2, NS-MOD( NS, 2 ) )
  264:       END IF
  265: *
  266:       IF( ISPEC.EQ.INMIN ) THEN
  267: *
  268: *
  269: *        ===== Matrices of order smaller than NMIN get sent
  270: *        .     to xLAHQR, the classic double shift algorithm.
  271: *        .     This must be at least 11. ====
  272: *
  273:          IPARMQ = NMIN
  274: *
  275:       ELSE IF( ISPEC.EQ.INIBL ) THEN
  276: *
  277: *        ==== INIBL: skip a multi-shift qr iteration and
  278: *        .    whenever aggressive early deflation finds
  279: *        .    at least (NIBBLE*(window size)/100) deflations. ====
  280: *
  281:          IPARMQ = NIBBLE
  282: *
  283:       ELSE IF( ISPEC.EQ.ISHFTS ) THEN
  284: *
  285: *        ==== NSHFTS: The number of simultaneous shifts =====
  286: *
  287:          IPARMQ = NS
  288: *
  289:       ELSE IF( ISPEC.EQ.INWIN ) THEN
  290: *
  291: *        ==== NW: deflation window size.  ====
  292: *
  293:          IF( NH.LE.KNWSWP ) THEN
  294:             IPARMQ = NS
  295:          ELSE
  296:             IPARMQ = 3*NS / 2
  297:          END IF
  298: *
  299:       ELSE IF( ISPEC.EQ.IACC22 ) THEN
  300: *
  301: *        ==== IACC22: Whether to accumulate reflections
  302: *        .     before updating the far-from-diagonal elements
  303: *        .     and whether to use 2-by-2 block structure while
  304: *        .     doing it.  A small amount of work could be saved
  305: *        .     by making this choice dependent also upon the
  306: *        .     NH=IHI-ILO+1.
  307: *
  308:          IPARMQ = 0
  309:          IF( NS.GE.KACMIN )
  310:      $      IPARMQ = 1
  311:          IF( NS.GE.K22MIN )
  312:      $      IPARMQ = 2
  313: *
  314:       ELSE
  315: *        ===== invalid value of ispec =====
  316:          IPARMQ = -1
  317: *
  318:       END IF
  319: *
  320: *     ==== End of IPARMQ ====
  321: *
  322:       END