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