Ubuntu Manpage: iparmq - iparmq: set parameters for hseqr

NAME

       iparmq - iparmq: set parameters for hseqr

SYNOPSIS

   Functions
       integer function iparmq (ispec, name, opts, n, ilo, ihi, lwork)
           IPARMQ

Detailed Description

Function Documentation

integer function iparmq (integer ispec, character, dimension( * ) name, character, dimension( * ) opts,
integer n, integer ilo, integer ihi, integer lwork)
IPARMQ

Purpose:

This program sets problem and machine dependent parameters
useful for xHSEQR and related subroutines for eigenvalue
problems. It is called whenever
IPARMQ is called with 12 <= ISPEC <= 16

Parameters
ISPEC

ISPEC is INTEGER
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 > (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/QZ sweep,
blocked eigenvalue reordering, blocked
Hessenberg-triangular reduction,
reflections and/or rotations are not
accumulated when updating the
far-from-diagonal matrix entries.
1: During the multi-shift QR/QZ sweep,
blocked eigenvalue reordering, blocked
Hessenberg-triangular reduction,
reflections and/or rotations are
accumulated, and matrix-matrix
multiplication is used to update the
far-from-diagonal matrix entries.
2: During the multi-shift QR/QZ sweep,
blocked eigenvalue reordering, blocked
Hessenberg-triangular reduction,
reflections and/or rotations are
accumulated, and 2-by-2 block structure
is exploited 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.)

ISPEC=17: (ICOST) An estimate of the relative cost of flops
within the near-the-diagonal shift chase compared
to flops within the BLAS calls of a QZ sweep.

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 is INTEGER
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
The amount of workspace available.

Author
Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

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) <= 500 is NS. The default
for (IHI-ILO+1) > 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.

IPARMQ(ISPEC=17) Relative cost heuristic for blocksize selection.
Expressed as a percentage.
Default: 10.

Author

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Version 3.12.0                              Sun Jul 20 2025 01:40:05                                   iparmq(3)