root / src / lapack / util / iparmq.f @ 10
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| 1 | 1 | pfleura2 | INTEGER FUNCTION IPARMQ( ISPEC, NAME, OPTS, N, ILO, IHI, LWORK ) |
|---|---|---|---|
| 2 | 1 | pfleura2 | * |
| 3 | 1 | pfleura2 | * -- LAPACK auxiliary routine (version 3.2) -- |
| 4 | 1 | pfleura2 | * -- LAPACK is a software package provided by Univ. of Tennessee, -- |
| 5 | 1 | pfleura2 | * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- |
| 6 | 1 | pfleura2 | * November 2006 |
| 7 | 1 | pfleura2 | * |
| 8 | 1 | pfleura2 | * .. Scalar Arguments .. |
| 9 | 1 | pfleura2 | INTEGER IHI, ILO, ISPEC, LWORK, N |
| 10 | 1 | pfleura2 | CHARACTER NAME*( * ), OPTS*( * ) |
| 11 | 1 | pfleura2 | * |
| 12 | 1 | pfleura2 | * Purpose |
| 13 | 1 | pfleura2 | * ======= |
| 14 | 1 | pfleura2 | * |
| 15 | 1 | pfleura2 | * This program sets problem and machine dependent parameters |
| 16 | 1 | pfleura2 | * useful for xHSEQR and its subroutines. It is called whenever |
| 17 | 1 | pfleura2 | * ILAENV is called with 12 <= ISPEC <= 16 |
| 18 | 1 | pfleura2 | * |
| 19 | 1 | pfleura2 | * Arguments |
| 20 | 1 | pfleura2 | * ========= |
| 21 | 1 | pfleura2 | * |
| 22 | 1 | pfleura2 | * ISPEC (input) integer scalar |
| 23 | 1 | pfleura2 | * ISPEC specifies which tunable parameter IPARMQ should |
| 24 | 1 | pfleura2 | * return. |
| 25 | 1 | pfleura2 | * |
| 26 | 1 | pfleura2 | * ISPEC=12: (INMIN) Matrices of order nmin or less |
| 27 | 1 | pfleura2 | * are sent directly to xLAHQR, the implicit |
| 28 | 1 | pfleura2 | * double shift QR algorithm. NMIN must be |
| 29 | 1 | pfleura2 | * at least 11. |
| 30 | 1 | pfleura2 | * |
| 31 | 1 | pfleura2 | * ISPEC=13: (INWIN) Size of the deflation window. |
| 32 | 1 | pfleura2 | * This is best set greater than or equal to |
| 33 | 1 | pfleura2 | * the number of simultaneous shifts NS. |
| 34 | 1 | pfleura2 | * Larger matrices benefit from larger deflation |
| 35 | 1 | pfleura2 | * windows. |
| 36 | 1 | pfleura2 | * |
| 37 | 1 | pfleura2 | * ISPEC=14: (INIBL) Determines when to stop nibbling and |
| 38 | 1 | pfleura2 | * invest in an (expensive) multi-shift QR sweep. |
| 39 | 1 | pfleura2 | * If the aggressive early deflation subroutine |
| 40 | 1 | pfleura2 | * finds LD converged eigenvalues from an order |
| 41 | 1 | pfleura2 | * NW deflation window and LD.GT.(NW*NIBBLE)/100, |
| 42 | 1 | pfleura2 | * then the next QR sweep is skipped and early |
| 43 | 1 | pfleura2 | * deflation is applied immediately to the |
| 44 | 1 | pfleura2 | * remaining active diagonal block. Setting |
| 45 | 1 | pfleura2 | * IPARMQ(ISPEC=14) = 0 causes TTQRE to skip a |
| 46 | 1 | pfleura2 | * multi-shift QR sweep whenever early deflation |
| 47 | 1 | pfleura2 | * finds a converged eigenvalue. Setting |
| 48 | 1 | pfleura2 | * IPARMQ(ISPEC=14) greater than or equal to 100 |
| 49 | 1 | pfleura2 | * prevents TTQRE from skipping a multi-shift |
| 50 | 1 | pfleura2 | * QR sweep. |
| 51 | 1 | pfleura2 | * |
| 52 | 1 | pfleura2 | * ISPEC=15: (NSHFTS) The number of simultaneous shifts in |
| 53 | 1 | pfleura2 | * a multi-shift QR iteration. |
| 54 | 1 | pfleura2 | * |
| 55 | 1 | pfleura2 | * ISPEC=16: (IACC22) IPARMQ is set to 0, 1 or 2 with the |
| 56 | 1 | pfleura2 | * following meanings. |
| 57 | 1 | pfleura2 | * 0: During the multi-shift QR sweep, |
| 58 | 1 | pfleura2 | * xLAQR5 does not accumulate reflections and |
| 59 | 1 | pfleura2 | * does not use matrix-matrix multiply to |
| 60 | 1 | pfleura2 | * update the far-from-diagonal matrix |
| 61 | 1 | pfleura2 | * entries. |
| 62 | 1 | pfleura2 | * 1: During the multi-shift QR sweep, |
| 63 | 1 | pfleura2 | * xLAQR5 and/or xLAQRaccumulates reflections and uses |
| 64 | 1 | pfleura2 | * matrix-matrix multiply to update the |
| 65 | 1 | pfleura2 | * far-from-diagonal matrix entries. |
| 66 | 1 | pfleura2 | * 2: During the multi-shift QR sweep. |
| 67 | 1 | pfleura2 | * xLAQR5 accumulates reflections and takes |
| 68 | 1 | pfleura2 | * advantage of 2-by-2 block structure during |
| 69 | 1 | pfleura2 | * matrix-matrix multiplies. |
| 70 | 1 | pfleura2 | * (If xTRMM is slower than xGEMM, then |
| 71 | 1 | pfleura2 | * IPARMQ(ISPEC=16)=1 may be more efficient than |
| 72 | 1 | pfleura2 | * IPARMQ(ISPEC=16)=2 despite the greater level of |
| 73 | 1 | pfleura2 | * arithmetic work implied by the latter choice.) |
| 74 | 1 | pfleura2 | * |
| 75 | 1 | pfleura2 | * NAME (input) character string |
| 76 | 1 | pfleura2 | * Name of the calling subroutine |
| 77 | 1 | pfleura2 | * |
| 78 | 1 | pfleura2 | * OPTS (input) character string |
| 79 | 1 | pfleura2 | * This is a concatenation of the string arguments to |
| 80 | 1 | pfleura2 | * TTQRE. |
| 81 | 1 | pfleura2 | * |
| 82 | 1 | pfleura2 | * N (input) integer scalar |
| 83 | 1 | pfleura2 | * N is the order of the Hessenberg matrix H. |
| 84 | 1 | pfleura2 | * |
| 85 | 1 | pfleura2 | * ILO (input) INTEGER |
| 86 | 1 | pfleura2 | * IHI (input) INTEGER |
| 87 | 1 | pfleura2 | * It is assumed that H is already upper triangular |
| 88 | 1 | pfleura2 | * in rows and columns 1:ILO-1 and IHI+1:N. |
| 89 | 1 | pfleura2 | * |
| 90 | 1 | pfleura2 | * LWORK (input) integer scalar |
| 91 | 1 | pfleura2 | * The amount of workspace available. |
| 92 | 1 | pfleura2 | * |
| 93 | 1 | pfleura2 | * Further Details |
| 94 | 1 | pfleura2 | * =============== |
| 95 | 1 | pfleura2 | * |
| 96 | 1 | pfleura2 | * Little is known about how best to choose these parameters. |
| 97 | 1 | pfleura2 | * It is possible to use different values of the parameters |
| 98 | 1 | pfleura2 | * for each of CHSEQR, DHSEQR, SHSEQR and ZHSEQR. |
| 99 | 1 | pfleura2 | * |
| 100 | 1 | pfleura2 | * It is probably best to choose different parameters for |
| 101 | 1 | pfleura2 | * different matrices and different parameters at different |
| 102 | 1 | pfleura2 | * times during the iteration, but this has not been |
| 103 | 1 | pfleura2 | * implemented --- yet. |
| 104 | 1 | pfleura2 | * |
| 105 | 1 | pfleura2 | * |
| 106 | 1 | pfleura2 | * The best choices of most of the parameters depend |
| 107 | 1 | pfleura2 | * in an ill-understood way on the relative execution |
| 108 | 1 | pfleura2 | * rate of xLAQR3 and xLAQR5 and on the nature of each |
| 109 | 1 | pfleura2 | * particular eigenvalue problem. Experiment may be the |
| 110 | 1 | pfleura2 | * only practical way to determine which choices are most |
| 111 | 1 | pfleura2 | * effective. |
| 112 | 1 | pfleura2 | * |
| 113 | 1 | pfleura2 | * Following is a list of default values supplied by IPARMQ. |
| 114 | 1 | pfleura2 | * These defaults may be adjusted in order to attain better |
| 115 | 1 | pfleura2 | * performance in any particular computational environment. |
| 116 | 1 | pfleura2 | * |
| 117 | 1 | pfleura2 | * IPARMQ(ISPEC=12) The xLAHQR vs xLAQR0 crossover point. |
| 118 | 1 | pfleura2 | * Default: 75. (Must be at least 11.) |
| 119 | 1 | pfleura2 | * |
| 120 | 1 | pfleura2 | * IPARMQ(ISPEC=13) Recommended deflation window size. |
| 121 | 1 | pfleura2 | * This depends on ILO, IHI and NS, the |
| 122 | 1 | pfleura2 | * number of simultaneous shifts returned |
| 123 | 1 | pfleura2 | * by IPARMQ(ISPEC=15). The default for |
| 124 | 1 | pfleura2 | * (IHI-ILO+1).LE.500 is NS. The default |
| 125 | 1 | pfleura2 | * for (IHI-ILO+1).GT.500 is 3*NS/2. |
| 126 | 1 | pfleura2 | * |
| 127 | 1 | pfleura2 | * IPARMQ(ISPEC=14) Nibble crossover point. Default: 14. |
| 128 | 1 | pfleura2 | * |
| 129 | 1 | pfleura2 | * IPARMQ(ISPEC=15) Number of simultaneous shifts, NS. |
| 130 | 1 | pfleura2 | * a multi-shift QR iteration. |
| 131 | 1 | pfleura2 | * |
| 132 | 1 | pfleura2 | * If IHI-ILO+1 is ... |
| 133 | 1 | pfleura2 | * |
| 134 | 1 | pfleura2 | * greater than ...but less ... the |
| 135 | 1 | pfleura2 | * or equal to ... than default is |
| 136 | 1 | pfleura2 | * |
| 137 | 1 | pfleura2 | * 0 30 NS = 2+ |
| 138 | 1 | pfleura2 | * 30 60 NS = 4+ |
| 139 | 1 | pfleura2 | * 60 150 NS = 10 |
| 140 | 1 | pfleura2 | * 150 590 NS = ** |
| 141 | 1 | pfleura2 | * 590 3000 NS = 64 |
| 142 | 1 | pfleura2 | * 3000 6000 NS = 128 |
| 143 | 1 | pfleura2 | * 6000 infinity NS = 256 |
| 144 | 1 | pfleura2 | * |
| 145 | 1 | pfleura2 | * (+) By default matrices of this order are |
| 146 | 1 | pfleura2 | * passed to the implicit double shift routine |
| 147 | 1 | pfleura2 | * xLAHQR. See IPARMQ(ISPEC=12) above. These |
| 148 | 1 | pfleura2 | * values of NS are used only in case of a rare |
| 149 | 1 | pfleura2 | * xLAHQR failure. |
| 150 | 1 | pfleura2 | * |
| 151 | 1 | pfleura2 | * (**) The asterisks (**) indicate an ad-hoc |
| 152 | 1 | pfleura2 | * function increasing from 10 to 64. |
| 153 | 1 | pfleura2 | * |
| 154 | 1 | pfleura2 | * IPARMQ(ISPEC=16) Select structured matrix multiply. |
| 155 | 1 | pfleura2 | * (See ISPEC=16 above for details.) |
| 156 | 1 | pfleura2 | * Default: 3. |
| 157 | 1 | pfleura2 | * |
| 158 | 1 | pfleura2 | * ================================================================ |
| 159 | 1 | pfleura2 | * .. Parameters .. |
| 160 | 1 | pfleura2 | INTEGER INMIN, INWIN, INIBL, ISHFTS, IACC22 |
| 161 | 1 | pfleura2 | PARAMETER ( INMIN = 12, INWIN = 13, INIBL = 14, |
| 162 | 1 | pfleura2 | $ ISHFTS = 15, IACC22 = 16 ) |
| 163 | 1 | pfleura2 | INTEGER NMIN, K22MIN, KACMIN, NIBBLE, KNWSWP |
| 164 | 1 | pfleura2 | PARAMETER ( NMIN = 75, K22MIN = 14, KACMIN = 14, |
| 165 | 1 | pfleura2 | $ NIBBLE = 14, KNWSWP = 500 ) |
| 166 | 1 | pfleura2 | REAL TWO |
| 167 | 1 | pfleura2 | PARAMETER ( TWO = 2.0 ) |
| 168 | 1 | pfleura2 | * .. |
| 169 | 1 | pfleura2 | * .. Local Scalars .. |
| 170 | 1 | pfleura2 | INTEGER NH, NS |
| 171 | 1 | pfleura2 | * .. |
| 172 | 1 | pfleura2 | * .. Intrinsic Functions .. |
| 173 | 1 | pfleura2 | INTRINSIC LOG, MAX, MOD, NINT, REAL |
| 174 | 1 | pfleura2 | * .. |
| 175 | 1 | pfleura2 | * .. Executable Statements .. |
| 176 | 1 | pfleura2 | IF( ( ISPEC.EQ.ISHFTS ) .OR. ( ISPEC.EQ.INWIN ) .OR. |
| 177 | 1 | pfleura2 | $ ( ISPEC.EQ.IACC22 ) ) THEN |
| 178 | 1 | pfleura2 | * |
| 179 | 1 | pfleura2 | * ==== Set the number simultaneous shifts ==== |
| 180 | 1 | pfleura2 | * |
| 181 | 1 | pfleura2 | NH = IHI - ILO + 1 |
| 182 | 1 | pfleura2 | NS = 2 |
| 183 | 1 | pfleura2 | IF( NH.GE.30 ) |
| 184 | 1 | pfleura2 | $ NS = 4 |
| 185 | 1 | pfleura2 | IF( NH.GE.60 ) |
| 186 | 1 | pfleura2 | $ NS = 10 |
| 187 | 1 | pfleura2 | IF( NH.GE.150 ) |
| 188 | 1 | pfleura2 | $ NS = MAX( 10, NH / NINT( LOG( REAL( NH ) ) / LOG( TWO ) ) ) |
| 189 | 1 | pfleura2 | IF( NH.GE.590 ) |
| 190 | 1 | pfleura2 | $ NS = 64 |
| 191 | 1 | pfleura2 | IF( NH.GE.3000 ) |
| 192 | 1 | pfleura2 | $ NS = 128 |
| 193 | 1 | pfleura2 | IF( NH.GE.6000 ) |
| 194 | 1 | pfleura2 | $ NS = 256 |
| 195 | 1 | pfleura2 | NS = MAX( 2, NS-MOD( NS, 2 ) ) |
| 196 | 1 | pfleura2 | END IF |
| 197 | 1 | pfleura2 | * |
| 198 | 1 | pfleura2 | IF( ISPEC.EQ.INMIN ) THEN |
| 199 | 1 | pfleura2 | * |
| 200 | 1 | pfleura2 | * |
| 201 | 1 | pfleura2 | * ===== Matrices of order smaller than NMIN get sent |
| 202 | 1 | pfleura2 | * . to xLAHQR, the classic double shift algorithm. |
| 203 | 1 | pfleura2 | * . This must be at least 11. ==== |
| 204 | 1 | pfleura2 | * |
| 205 | 1 | pfleura2 | IPARMQ = NMIN |
| 206 | 1 | pfleura2 | * |
| 207 | 1 | pfleura2 | ELSE IF( ISPEC.EQ.INIBL ) THEN |
| 208 | 1 | pfleura2 | * |
| 209 | 1 | pfleura2 | * ==== INIBL: skip a multi-shift qr iteration and |
| 210 | 1 | pfleura2 | * . whenever aggressive early deflation finds |
| 211 | 1 | pfleura2 | * . at least (NIBBLE*(window size)/100) deflations. ==== |
| 212 | 1 | pfleura2 | * |
| 213 | 1 | pfleura2 | IPARMQ = NIBBLE |
| 214 | 1 | pfleura2 | * |
| 215 | 1 | pfleura2 | ELSE IF( ISPEC.EQ.ISHFTS ) THEN |
| 216 | 1 | pfleura2 | * |
| 217 | 1 | pfleura2 | * ==== NSHFTS: The number of simultaneous shifts ===== |
| 218 | 1 | pfleura2 | * |
| 219 | 1 | pfleura2 | IPARMQ = NS |
| 220 | 1 | pfleura2 | * |
| 221 | 1 | pfleura2 | ELSE IF( ISPEC.EQ.INWIN ) THEN |
| 222 | 1 | pfleura2 | * |
| 223 | 1 | pfleura2 | * ==== NW: deflation window size. ==== |
| 224 | 1 | pfleura2 | * |
| 225 | 1 | pfleura2 | IF( NH.LE.KNWSWP ) THEN |
| 226 | 1 | pfleura2 | IPARMQ = NS |
| 227 | 1 | pfleura2 | ELSE |
| 228 | 1 | pfleura2 | IPARMQ = 3*NS / 2 |
| 229 | 1 | pfleura2 | END IF |
| 230 | 1 | pfleura2 | * |
| 231 | 1 | pfleura2 | ELSE IF( ISPEC.EQ.IACC22 ) THEN |
| 232 | 1 | pfleura2 | * |
| 233 | 1 | pfleura2 | * ==== IACC22: Whether to accumulate reflections |
| 234 | 1 | pfleura2 | * . before updating the far-from-diagonal elements |
| 235 | 1 | pfleura2 | * . and whether to use 2-by-2 block structure while |
| 236 | 1 | pfleura2 | * . doing it. A small amount of work could be saved |
| 237 | 1 | pfleura2 | * . by making this choice dependent also upon the |
| 238 | 1 | pfleura2 | * . NH=IHI-ILO+1. |
| 239 | 1 | pfleura2 | * |
| 240 | 1 | pfleura2 | IPARMQ = 0 |
| 241 | 1 | pfleura2 | IF( NS.GE.KACMIN ) |
| 242 | 1 | pfleura2 | $ IPARMQ = 1 |
| 243 | 1 | pfleura2 | IF( NS.GE.K22MIN ) |
| 244 | 1 | pfleura2 | $ IPARMQ = 2 |
| 245 | 1 | pfleura2 | * |
| 246 | 1 | pfleura2 | ELSE |
| 247 | 1 | pfleura2 | * ===== invalid value of ispec ===== |
| 248 | 1 | pfleura2 | IPARMQ = -1 |
| 249 | 1 | pfleura2 | * |
| 250 | 1 | pfleura2 | END IF |
| 251 | 1 | pfleura2 | * |
| 252 | 1 | pfleura2 | * ==== End of IPARMQ ==== |
| 253 | 1 | pfleura2 | * |
| 254 | 1 | pfleura2 | END |