IPARMQ(1) LAPACK auxiliary routine (version 3.2) IPARMQ(1)NAME
IPARMQ - This program sets problem and machine dependent parameters
useful for xHSEQR and its subroutines
SYNOPSIS
INTEGER FUNCTION IPARMQ( ISPEC, NAME, OPTS, N, ILO, IHI, LWORK )
INTEGER IHI, ILO, ISPEC, LWORK, N
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 defla‐
tion window. This is best set greater than or equal to the num‐
ber 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*NIB‐
BLE)/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.
LAPACK auxiliary routine (versioNovember 2008 IPARMQ(1)
