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LAPACK 3.3.1
Linear Algebra PACKage
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LAPACK 3.3.1
Linear Algebra PACKage
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00001 INTEGER FUNCTION IPARMQ( ISPEC, NAME, OPTS, N, ILO, IHI, LWORK ) 00002 * 00003 * -- LAPACK auxiliary routine (version 3.2) -- 00004 * -- LAPACK is a software package provided by Univ. of Tennessee, -- 00005 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- 00006 * November 2006 00007 * 00008 * .. Scalar Arguments .. 00009 INTEGER IHI, ILO, ISPEC, LWORK, N 00010 CHARACTER NAME*( * ), OPTS*( * ) 00011 * 00012 * Purpose 00013 * ======= 00014 * 00015 * This program sets problem and machine dependent parameters 00016 * useful for xHSEQR and its subroutines. It is called whenever 00017 * ILAENV is called with 12 <= ISPEC <= 16 00018 * 00019 * Arguments 00020 * ========= 00021 * 00022 * ISPEC (input) integer scalar 00023 * ISPEC specifies which tunable parameter IPARMQ should 00024 * return. 00025 * 00026 * ISPEC=12: (INMIN) Matrices of order nmin or less 00027 * are sent directly to xLAHQR, the implicit 00028 * double shift QR algorithm. NMIN must be 00029 * at least 11. 00030 * 00031 * ISPEC=13: (INWIN) Size of the deflation window. 00032 * This is best set greater than or equal to 00033 * the number of simultaneous shifts NS. 00034 * Larger matrices benefit from larger deflation 00035 * windows. 00036 * 00037 * ISPEC=14: (INIBL) Determines when to stop nibbling and 00038 * invest in an (expensive) multi-shift QR sweep. 00039 * If the aggressive early deflation subroutine 00040 * finds LD converged eigenvalues from an order 00041 * NW deflation window and LD.GT.(NW*NIBBLE)/100, 00042 * then the next QR sweep is skipped and early 00043 * deflation is applied immediately to the 00044 * remaining active diagonal block. Setting 00045 * IPARMQ(ISPEC=14) = 0 causes TTQRE to skip a 00046 * multi-shift QR sweep whenever early deflation 00047 * finds a converged eigenvalue. Setting 00048 * IPARMQ(ISPEC=14) greater than or equal to 100 00049 * prevents TTQRE from skipping a multi-shift 00050 * QR sweep. 00051 * 00052 * ISPEC=15: (NSHFTS) The number of simultaneous shifts in 00053 * a multi-shift QR iteration. 00054 * 00055 * ISPEC=16: (IACC22) IPARMQ is set to 0, 1 or 2 with the 00056 * following meanings. 00057 * 0: During the multi-shift QR sweep, 00058 * xLAQR5 does not accumulate reflections and 00059 * does not use matrix-matrix multiply to 00060 * update the far-from-diagonal matrix 00061 * entries. 00062 * 1: During the multi-shift QR sweep, 00063 * xLAQR5 and/or xLAQRaccumulates reflections and uses 00064 * matrix-matrix multiply to update the 00065 * far-from-diagonal matrix entries. 00066 * 2: During the multi-shift QR sweep. 00067 * xLAQR5 accumulates reflections and takes 00068 * advantage of 2-by-2 block structure during 00069 * matrix-matrix multiplies. 00070 * (If xTRMM is slower than xGEMM, then 00071 * IPARMQ(ISPEC=16)=1 may be more efficient than 00072 * IPARMQ(ISPEC=16)=2 despite the greater level of 00073 * arithmetic work implied by the latter choice.) 00074 * 00075 * NAME (input) character string 00076 * Name of the calling subroutine 00077 * 00078 * OPTS (input) character string 00079 * This is a concatenation of the string arguments to 00080 * TTQRE. 00081 * 00082 * N (input) integer scalar 00083 * N is the order of the Hessenberg matrix H. 00084 * 00085 * ILO (input) INTEGER 00086 * IHI (input) INTEGER 00087 * It is assumed that H is already upper triangular 00088 * in rows and columns 1:ILO-1 and IHI+1:N. 00089 * 00090 * LWORK (input) integer scalar 00091 * The amount of workspace available. 00092 * 00093 * Further Details 00094 * =============== 00095 * 00096 * Little is known about how best to choose these parameters. 00097 * It is possible to use different values of the parameters 00098 * for each of CHSEQR, DHSEQR, SHSEQR and ZHSEQR. 00099 * 00100 * It is probably best to choose different parameters for 00101 * different matrices and different parameters at different 00102 * times during the iteration, but this has not been 00103 * implemented --- yet. 00104 * 00105 * 00106 * The best choices of most of the parameters depend 00107 * in an ill-understood way on the relative execution 00108 * rate of xLAQR3 and xLAQR5 and on the nature of each 00109 * particular eigenvalue problem. Experiment may be the 00110 * only practical way to determine which choices are most 00111 * effective. 00112 * 00113 * Following is a list of default values supplied by IPARMQ. 00114 * These defaults may be adjusted in order to attain better 00115 * performance in any particular computational environment. 00116 * 00117 * IPARMQ(ISPEC=12) The xLAHQR vs xLAQR0 crossover point. 00118 * Default: 75. (Must be at least 11.) 00119 * 00120 * IPARMQ(ISPEC=13) Recommended deflation window size. 00121 * This depends on ILO, IHI and NS, the 00122 * number of simultaneous shifts returned 00123 * by IPARMQ(ISPEC=15). The default for 00124 * (IHI-ILO+1).LE.500 is NS. The default 00125 * for (IHI-ILO+1).GT.500 is 3*NS/2. 00126 * 00127 * IPARMQ(ISPEC=14) Nibble crossover point. Default: 14. 00128 * 00129 * IPARMQ(ISPEC=15) Number of simultaneous shifts, NS. 00130 * a multi-shift QR iteration. 00131 * 00132 * If IHI-ILO+1 is ... 00133 * 00134 * greater than ...but less ... the 00135 * or equal to ... than default is 00136 * 00137 * 0 30 NS = 2+ 00138 * 30 60 NS = 4+ 00139 * 60 150 NS = 10 00140 * 150 590 NS = ** 00141 * 590 3000 NS = 64 00142 * 3000 6000 NS = 128 00143 * 6000 infinity NS = 256 00144 * 00145 * (+) By default matrices of this order are 00146 * passed to the implicit double shift routine 00147 * xLAHQR. See IPARMQ(ISPEC=12) above. These 00148 * values of NS are used only in case of a rare 00149 * xLAHQR failure. 00150 * 00151 * (**) The asterisks (**) indicate an ad-hoc 00152 * function increasing from 10 to 64. 00153 * 00154 * IPARMQ(ISPEC=16) Select structured matrix multiply. 00155 * (See ISPEC=16 above for details.) 00156 * Default: 3. 00157 * 00158 * ================================================================ 00159 * .. Parameters .. 00160 INTEGER INMIN, INWIN, INIBL, ISHFTS, IACC22 00161 PARAMETER ( INMIN = 12, INWIN = 13, INIBL = 14, 00162 $ ISHFTS = 15, IACC22 = 16 ) 00163 INTEGER NMIN, K22MIN, KACMIN, NIBBLE, KNWSWP 00164 PARAMETER ( NMIN = 75, K22MIN = 14, KACMIN = 14, 00165 $ NIBBLE = 14, KNWSWP = 500 ) 00166 REAL TWO 00167 PARAMETER ( TWO = 2.0 ) 00168 * .. 00169 * .. Local Scalars .. 00170 INTEGER NH, NS 00171 * .. 00172 * .. Intrinsic Functions .. 00173 INTRINSIC LOG, MAX, MOD, NINT, REAL 00174 * .. 00175 * .. Executable Statements .. 00176 IF( ( ISPEC.EQ.ISHFTS ) .OR. ( ISPEC.EQ.INWIN ) .OR. 00177 $ ( ISPEC.EQ.IACC22 ) ) THEN 00178 * 00179 * ==== Set the number simultaneous shifts ==== 00180 * 00181 NH = IHI - ILO + 1 00182 NS = 2 00183 IF( NH.GE.30 ) 00184 $ NS = 4 00185 IF( NH.GE.60 ) 00186 $ NS = 10 00187 IF( NH.GE.150 ) 00188 $ NS = MAX( 10, NH / NINT( LOG( REAL( NH ) ) / LOG( TWO ) ) ) 00189 IF( NH.GE.590 ) 00190 $ NS = 64 00191 IF( NH.GE.3000 ) 00192 $ NS = 128 00193 IF( NH.GE.6000 ) 00194 $ NS = 256 00195 NS = MAX( 2, NS-MOD( NS, 2 ) ) 00196 END IF 00197 * 00198 IF( ISPEC.EQ.INMIN ) THEN 00199 * 00200 * 00201 * ===== Matrices of order smaller than NMIN get sent 00202 * . to xLAHQR, the classic double shift algorithm. 00203 * . This must be at least 11. ==== 00204 * 00205 IPARMQ = NMIN 00206 * 00207 ELSE IF( ISPEC.EQ.INIBL ) THEN 00208 * 00209 * ==== INIBL: skip a multi-shift qr iteration and 00210 * . whenever aggressive early deflation finds 00211 * . at least (NIBBLE*(window size)/100) deflations. ==== 00212 * 00213 IPARMQ = NIBBLE 00214 * 00215 ELSE IF( ISPEC.EQ.ISHFTS ) THEN 00216 * 00217 * ==== NSHFTS: The number of simultaneous shifts ===== 00218 * 00219 IPARMQ = NS 00220 * 00221 ELSE IF( ISPEC.EQ.INWIN ) THEN 00222 * 00223 * ==== NW: deflation window size. ==== 00224 * 00225 IF( NH.LE.KNWSWP ) THEN 00226 IPARMQ = NS 00227 ELSE 00228 IPARMQ = 3*NS / 2 00229 END IF 00230 * 00231 ELSE IF( ISPEC.EQ.IACC22 ) THEN 00232 * 00233 * ==== IACC22: Whether to accumulate reflections 00234 * . before updating the far-from-diagonal elements 00235 * . and whether to use 2-by-2 block structure while 00236 * . doing it. A small amount of work could be saved 00237 * . by making this choice dependent also upon the 00238 * . NH=IHI-ILO+1. 00239 * 00240 IPARMQ = 0 00241 IF( NS.GE.KACMIN ) 00242 $ IPARMQ = 1 00243 IF( NS.GE.K22MIN ) 00244 $ IPARMQ = 2 00245 * 00246 ELSE 00247 * ===== invalid value of ispec ===== 00248 IPARMQ = -1 00249 * 00250 END IF 00251 * 00252 * ==== End of IPARMQ ==== 00253 * 00254 END
1.7.3 
