/* -- translated by f2c (version 20100827). You must link the resulting object file with libf2c: on Microsoft Windows system, link with libf2c.lib; on Linux or Unix systems, link with .../path/to/libf2c.a -lm or, if you install libf2c.a in a standard place, with -lf2c -lm -- in that order, at the end of the command line, as in cc *.o -lf2c -lm Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., http://www.netlib.org/f2c/libf2c.zip */ #include "f2c.h" integer splicingiparmq_(integer *ispec, char *name__, char *opts, integer *n, integer *ilo, integer *ihi, integer *lwork) { /* System generated locals */ integer ret_val, i__1, i__2; real r__1; /* Builtin functions */ double log(doublereal); integer i_nint(real *); /* Local variables */ static integer nh, ns; /* -- LAPACK auxiliary routine (version 3.2) -- -- LAPACK is a software package provided by Univ. of Tennessee, -- -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- November 2006 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 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 (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. ================================================================ */ if (*ispec == 15 || *ispec == 13 || *ispec == 16) { /* ==== Set the number simultaneous shifts ==== */ nh = *ihi - *ilo + 1; ns = 2; if (nh >= 30) { ns = 4; } if (nh >= 60) { ns = 10; } if (nh >= 150) { /* Computing MAX */ r__1 = log((real) nh) / log(2.f); i__1 = 10, i__2 = nh / i_nint(&r__1); ns = max(i__1,i__2); } if (nh >= 590) { ns = 64; } if (nh >= 3000) { ns = 128; } if (nh >= 6000) { ns = 256; } /* Computing MAX */ i__1 = 2, i__2 = ns - ns % 2; ns = max(i__1,i__2); } if (*ispec == 12) { /* ===== Matrices of order smaller than NMIN get sent . to xLAHQR, the classic double shift algorithm. . This must be at least 11. ==== */ ret_val = 75; } else if (*ispec == 14) { /* ==== INIBL: skip a multi-shift qr iteration and . whenever aggressive early deflation finds . at least (NIBBLE*(window size)/100) deflations. ==== */ ret_val = 14; } else if (*ispec == 15) { /* ==== NSHFTS: The number of simultaneous shifts ===== */ ret_val = ns; } else if (*ispec == 13) { /* ==== NW: deflation window size. ==== */ if (nh <= 500) { ret_val = ns; } else { ret_val = ns * 3 / 2; } } else if (*ispec == 16) { /* ==== IACC22: Whether to accumulate reflections . before updating the far-from-diagonal elements . and whether to use 2-by-2 block structure while . doing it. A small amount of work could be saved . by making this choice dependent also upon the . NH=IHI-ILO+1. */ ret_val = 0; if (ns >= 14) { ret_val = 1; } if (ns >= 14) { ret_val = 2; } } else { /* ===== invalid value of ispec ===== */ ret_val = -1; } /* ==== End of IPARMQ ==== */ return ret_val; } /* splicingiparmq_ */