PIPARMQ(3) ScaLAPACK routine of NEC Numeric Library Collection PIPARMQ(3)
NAME
PIPARMQ - sets problem and machine dependent parameters useful for PxH-
SEQR and its subroutines
SYNOPSIS
INTEGER FUNCTION PIPARMQ(
ICTXT, ISPEC, NAME, OPTS, N, ILO, IHI, LWORKNB )
INTEGER ICTXT, IHI, ILO, ISPEC, LWORKNB, N
CHARACTER NAME*( * ), OPTS*( * )
PURPOSE
This program sets problem and machine dependent parameters useful for
PxHSEQR and its subroutines. It is called whenever PILAENVX is called
with 12 <= ISPEC <= 16
ARGUMENTS
ICTXT (local input) INTEGER
On entry, ICTXT specifies the BLACS context handle, indicat-
ing the global context of the operation. The context itself is
global, but the value of ICTXT is local.
ISPEC (global input) INTEGER
ISPEC specifies which tunable parameter PIPARMQ should return.
ISPEC=12: (INMIN) Matrices of order nmin or less
are sent directly to PxLAHQR, 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
PIPARMQ(ISPEC=14) = 0 causes PxLAQR0 to skip a
multi-shift QR sweep whenever early deflation
finds a converged eigenvalue. Setting
PIPARMQ(ISPEC=14) greater than or equal to 100
prevents PxLAQR0 from skipping a multi-shift
QR sweep.
ISPEC=15: (NSHFTS) The number of simultaneous shifts in
a multi-shift QR iteration.
ISPEC=16: (IACC22) PIPARMQ is set to 1 or 2 with the
following meanings.
1: During the multi-shift QR sweep,
PxLAQR5 and/or xLAQR6 accumulates reflections
and uses matrix-matrix multiply to update
the far-from-diagonal matrix entries.
2: During the multi-shift QR sweep.
PxLAQR5 accumulates reflections and takes
advantage of 2-by-2 block structure during
matrix-matrix multiplies.
( IACC22=0 is valid in LAPACK but not here.
Householder reflections are always accumulated
for the performance consideration.
If xTRMM is slower than xGEMM or NB is small,
PIPARMQ(ISPEC=16)=1 may be more efficient than
PIPARMQ(ISPEC=16)=2 despite the greater level of
arithmetic work implied by the latter choice. )
NAME (global input) character string
Name of the calling subroutine
OPTS (global input) character string
This is a concatenation of the string arguments to TTQRE.
N (global input) integer scalar
N is the order of the Hessenberg matrix H.
ILO (global input) INTEGER
IHI (global input) INTEGER
It is assumed that H is already upper triangular in rows and
columns 1:ILO-1 and IHI+1:N.
LWORKNB (global input) INTEGER
The amount of workspace available or the blockfactor.
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
PCHSEQR, PDHSEQR, PSHSEQR and PZHSEQR.
It is probably best to choose different parameters for different matri-
ces and different parameters at different times during the iteration,
but this has not been fully implemented --- yet.
The best choices of most of the parameters depend in an ill-understood
way on the relative execution rate of PxLAQR3 and PxLAQR5 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 PIPARMQ.
These defaults may be adjusted in order to attain better performance in
any particular computational environment.
PIPARMQ(ISPEC=12) The PxLAQR1 vs PxLAQR0 crossover point.
Default: 220. (Must be at least 11.)
PIPARMQ(ISPEC=13) Recommended deflation window size.
This depends on ILO, IHI and NS, the
number of simultaneous shifts returned
by PIPARMQ(ISPEC=15). The default for
(IHI-ILO+1).LE.500 is NS. The default
for (IHI-ILO+1).GT.500 is 3*NS/2.
PIPARMQ(ISPEC=14) Nibble crossover point.
The default for the serial case is 14.
The default for the parallel case is
335 * N**(-0.44) * NPROCS.
PIPARMQ(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 12000 NS = 256
12000 24000 NS = 512
24000 48000 NS = 1024
48000 96000 NS = 2048
96000 INFINITY NS = 4096
(+) By default matrices of this order are
passed to the implicit double shift routine
PxLAQR1. See PIPARMQ(ISPEC=12) above. These
values of NS are used only in case of a rare
PxLAQR1 failure.
(**) The asterisks (**) indicate an ad-hoc
function increasing from 10 to 64.
PIPARMQ(ISPEC=16) Select structured matrix multiply.
(See ISPEC=16 above for details.)
Default: 3.
ScaLAPACK routine 31 October 2017 PIPARMQ(3)