1IPARMQ(1) LAPACK auxiliary routine (version 3.2) IPARMQ(1)
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6 IPARMQ - This program sets problem and machine dependent parameters
7 useful for xHSEQR and its subroutines
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10 INTEGER FUNCTION IPARMQ( ISPEC, NAME, OPTS, N, ILO, IHI, LWORK )
11 INTEGER IHI, ILO, ISPEC, LWORK, N
13 CHARACTER NAME*( * ), OPTS*( * )
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17 This program sets problem and machine dependent parameters
18 useful for xHSEQR and its subroutines. It is called whenever
19 ILAENV is called with 12 <= ISPEC <= 16
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22 ISPEC (input) integer scalar
23 ISPEC specifies which tunable parameter IPARMQ should return.
24 ISPEC=12: (INMIN) Matrices of order nmin or less are sent
25 directly to xLAHQR, the implicit double shift QR algorithm.
26 NMIN must be at least 11. ISPEC=13: (INWIN) Size of the defla‐
27 tion window. This is best set greater than or equal to the num‐
28 ber of simultaneous shifts NS. Larger matrices benefit from
29 larger deflation windows. ISPEC=14: (INIBL) Determines when to
30 stop nibbling and invest in an (expensive) multi-shift QR sweep.
31 If the aggressive early deflation subroutine finds LD converged
32 eigenvalues from an order NW deflation window and LD.GT.(NW*NIB‐
33 BLE)/100, then the next QR sweep is skipped and early deflation
34 is applied immediately to the remaining active diagonal block.
35 Setting IPARMQ(ISPEC=14) = 0 causes TTQRE to skip a multi-shift
36 QR sweep whenever early deflation finds a converged eigenvalue.
37 Setting IPARMQ(ISPEC=14) greater than or equal to 100 prevents
38 TTQRE from skipping a multi-shift QR sweep. ISPEC=15: (NSHFTS)
39 The number of simultaneous shifts in a multi-shift QR iteration.
40 ISPEC=16: (IACC22) IPARMQ is set to 0, 1 or 2 with the following
41 meanings. 0: During the multi-shift QR sweep, xLAQR5 does not
42 accumulate reflections and does not use matrix-matrix multiply
43 to update the far-from-diagonal matrix entries. 1: During the
44 multi-shift QR sweep, xLAQR5 and/or xLAQRaccumulates reflections
45 and uses matrix-matrix multiply to update the far-from-diagonal
46 matrix entries. 2: During the multi-shift QR sweep. xLAQR5
47 accumulates reflections and takes advantage of 2-by-2 block
48 structure during matrix-matrix multiplies. (If xTRMM is slower
49 than xGEMM, then IPARMQ(ISPEC=16)=1 may be more efficient than
50 IPARMQ(ISPEC=16)=2 despite the greater level of arithmetic work
51 implied by the latter choice.)
52 NAME (input) character string
54 Name of the calling subroutine
55 OPTS (input) character string
57 This is a concatenation of the string arguments to TTQRE.
58 N (input) integer scalar
60 N is the order of the Hessenberg matrix H.
61 ILO (input) INTEGER
63 IHI (input) INTEGER It is assumed that H is already upper
64 triangular in rows and columns 1:ILO-1 and IHI+1:N.
65 LWORK (input) integer scalar
67 The amount of workspace available.
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70 Little is known about how best to choose these parameters.
71 It is possible to use different values of the parameters
72 for each of CHSEQR, DHSEQR, SHSEQR and ZHSEQR.
73 It is probably best to choose different parameters for
74 different matrices and different parameters at different
75 times during the iteration, but this has not been
76 implemented --- yet.
77 The best choices of most of the parameters depend
78 in an ill-understood way on the relative execution
79 rate of xLAQR3 and xLAQR5 and on the nature of each
80 particular eigenvalue problem. Experiment may be the
81 only practical way to determine which choices are most
82 effective.
83 Following is a list of default values supplied by IPARMQ.
84 These defaults may be adjusted in order to attain better
85 performance in any particular computational environment.
86 IPARMQ(ISPEC=12) The xLAHQR vs xLAQR0 crossover point.
87 Default: 75. (Must be at least 11.)
88 IPARMQ(ISPEC=13) Recommended deflation window size.
89 This depends on ILO, IHI and NS, the
90 number of simultaneous shifts returned
91 by IPARMQ(ISPEC=15). The default for
92 (IHI-ILO+1).LE.500 is NS. The default
93 for (IHI-ILO+1).GT.500 is 3*NS/2.
94 IPARMQ(ISPEC=14) Nibble crossover point. Default: 14.
95 IPARMQ(ISPEC=15) Number of simultaneous shifts, NS.
96 a multi-shift QR iteration.
97 If IHI-ILO+1 is ...
98 greater than ...but less ... the
99 or equal to ... than default is
100 0 30 NS = 2+
101 30 60 NS = 4+
102 60 150 NS = 10
103 150 590 NS = **
104 590 3000 NS = 64
105 3000 6000 NS = 128
106 6000 infinity NS = 256
107 (+) By default matrices of this order are
108 passed to the implicit double shift routine
109 xLAHQR. See IPARMQ(ISPEC=12) above. These
110 values of NS are used only in case of a rare
111 xLAHQR failure.
112 (**) The asterisks (**) indicate an ad-hoc
113 function increasing from 10 to 64.
114 IPARMQ(ISPEC=16) Select structured matrix multiply.
115 (See ISPEC=16 above for details.)
116 Default: 3.
117 LAPACK auxiliary routine (versionNo3v.e2m)ber 2008 IPARMQ(1)