iparmq.f man page

iparmq.f —

Synopsis

Functions/Subroutines

INTEGER function iparmq (ISPEC, NAME, OPTS, N, ILO, IHI, LWORK)
IPARMQ

Function/Subroutine Documentation

INTEGER function iparmq (integerISPEC, character, dimension( * )NAME, character, dimension( * )OPTS, integerN, integerILO, integerIHI, integerLWORK)

IPARMQ

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

Parameters:

ISPEC

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.)

NAME

NAME is character string
     Name of the calling subroutine

OPTS

OPTS is character string
     This is a concatenation of the string arguments to
     TTQRE.

N

N is integer scalar
     N is the order of the Hessenberg matrix H.

ILO

ILO is INTEGER

IHI

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

LWORK

LWORK is integer scalar
     The amount of workspace available.

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

November 2011

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.

Definition at line 215 of file iparmq.f.

Author

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Referenced By

iparmq(3) is an alias of iparmq.f(3).

Sat Nov 16 2013 Version 3.4.2 LAPACK