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version 1.8, 2011/07/22 07:40:26 version 1.9, 2011/11/21 22:18:50
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   *> \brief \b IPARMQ
   *
   *  =========== DOCUMENTATION ===========
   *
   * Online html documentation available at 
   *            http://www.netlib.org/lapack/explore-html/ 
   *
   *> \htmlonly
   *> Download IPARMQ + dependencies 
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/iparmq.f"> 
   *> [TGZ]</a> 
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/iparmq.f"> 
   *> [ZIP]</a> 
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/iparmq.f"> 
   *> [TXT]</a>
   *> \endhtmlonly 
   *
   *  Definition:
   *  ===========
   *
   *       INTEGER FUNCTION IPARMQ( ISPEC, NAME, OPTS, N, ILO, IHI, LWORK )
   * 
   *       .. Scalar Arguments ..
   *       INTEGER            IHI, ILO, ISPEC, LWORK, N
   *       CHARACTER          NAME*( * ), OPTS*( * )
   *  
   *
   *> \par Purpose:
   *  =============
   *>
   *> \verbatim
   *>
   *>      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
   *> \endverbatim
   *
   *  Arguments:
   *  ==========
   *
   *> \param[in] ISPEC
   *> \verbatim
   *>          ISPEC is 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.)
   *> \endverbatim
   *>
   *> \param[in] NAME
   *> \verbatim
   *>          NAME is character string
   *>               Name of the calling subroutine
   *> \endverbatim
   *>
   *> \param[in] OPTS
   *> \verbatim
   *>          OPTS is character string
   *>               This is a concatenation of the string arguments to
   *>               TTQRE.
   *> \endverbatim
   *>
   *> \param[in] N
   *> \verbatim
   *>          N is integer scalar
   *>               N is the order of the Hessenberg matrix H.
   *> \endverbatim
   *>
   *> \param[in] ILO
   *> \verbatim
   *>          ILO is INTEGER
   *> \endverbatim
   *>
   *> \param[in] IHI
   *> \verbatim
   *>          IHI is INTEGER
   *>               It is assumed that H is already upper triangular
   *>               in rows and columns 1:ILO-1 and IHI+1:N.
   *> \endverbatim
   *>
   *> \param[in] LWORK
   *> \verbatim
   *>          LWORK is integer scalar
   *>               The amount of workspace available.
   *> \endverbatim
   *
   *  Authors:
   *  ========
   *
   *> \author Univ. of Tennessee 
   *> \author Univ. of California Berkeley 
   *> \author Univ. of Colorado Denver 
   *> \author NAG Ltd. 
   *
   *> \date November 2011
   *
   *> \ingroup auxOTHERauxiliary
   *
   *> \par Further Details:
   *  =====================
   *>
   *> \verbatim
   *>
   *>       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.
   *> \endverbatim
   *>
   *  =====================================================================
       INTEGER FUNCTION IPARMQ( ISPEC, NAME, OPTS, N, ILO, IHI, LWORK )        INTEGER FUNCTION IPARMQ( ISPEC, NAME, OPTS, N, ILO, IHI, LWORK )
 *  *
 *  -- LAPACK auxiliary routine (version 3.2) --  *  -- LAPACK auxiliary routine (version 3.4.0) --
 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --  *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--  *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
 *     November 2006  *     November 2011
 *       *
 *     .. Scalar Arguments ..  *     .. Scalar Arguments ..
       INTEGER            IHI, ILO, ISPEC, LWORK, N        INTEGER            IHI, ILO, ISPEC, LWORK, N
       CHARACTER          NAME*( * ), OPTS*( * )        CHARACTER          NAME*( * ), OPTS*( * )
 *  *
 *  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 ..  *     .. Parameters ..
       INTEGER            INMIN, INWIN, INIBL, ISHFTS, IACC22        INTEGER            INMIN, INWIN, INIBL, ISHFTS, IACC22
       PARAMETER          ( INMIN = 12, INWIN = 13, INIBL = 14,        PARAMETER          ( INMIN = 12, INWIN = 13, INIBL = 14,
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  Added in v.1.9

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