Anbei der Haskell Code.
kompiliert wird das mit
Code:
ghc --make haskell.hs
Bei Debian ist der Compiler enthalten und heisst ghc6.
Code:
aptitude install ghc6
Ich habe da nichts optimiert. Die Funktion printf in haskell ist elendiglich langsam.
Wenn ich das durch ein putStrLn ersetze gewinne ich etwas an Laufzeit.
Der Flaschenhals dürfte das "String" concat sein. Da werd ich noch mal recherchieren.
Tests durchgeführt auf Debian squeeze , Intel i5
mit printf:
real 0m14.606s
user 0m14.573s
sys 0m0.024s
mit putStrLn
real 0m12.318s
user 0m12.281s
sys 0m0.028s
Code:
import System( getArgs)
import Text.Printf
main = do argv <- getArgs
if (length argv) >= 4
then let dt = read (head argv) ::Float
tMax = read (head (tail argv))::Float
(x,y) = (read (head (tail (tail argv))) ::Float ,read (head (tail(tail(tail argv))))::Float)
result = (oneStep dt (x,y) tMax 0.001)
in mapM_ toString result
else print "fehler - usage haskell dt tMax phi time"
g = 9.81
r = 10.0
toString:: (Float,Float,Float) -> IO()
-- |toString (x,y,z) = putStrLn ((show x) ++ "\t " ++ (show y) ++ "\t " ++ (show z))
toString (x,y,z) = printf "%.3f\t %f\t %f\n" x y z
oneStep :: Float -> (Float,Float) -> Float ->Float -> [(Float,Float,Float)]
oneStep dt phi max index
| index >= max = []
| otherwise = (index,x,y):oneStep dt (x,y) max (index + dt)
where (x,y) = rk4 dt phi
(<+>) :: (Float,Float) -> (Float,Float) ->(Float,Float)
(x,y) <+> (x1,y1) = (x+x1,y+y1)
(<*>) :: Float -> (Float,Float) -> (Float,Float)
scalar <*> (x,y) = (scalar * x,scalar * y)
f:: (Float,Float) -> (Float,Float)
f (x,y) = (y,-(g/r)*(sin(x)))
rk4:: Float -> (Float,Float) -> (Float,Float)
rk4 dt phi =
let
k1 = dt <*> f phi
k2 = dt <*> f (phi <+> (0.5 <*> k1))
k3 = dt <*> f (phi <+> (0.5 <*> k2))
k4 = dt <*> f (phi <+> k3);
in
phi <+> ((1.0/6.0) <*> (k1 <+> (2.0 <*> k2) <+> (2.0 <*> k3) <+> k4))
Auszug Ergebnisse
Code:
0.001 0.0022149999 2.2149987
0.002 0.004429997 2.2149954
0.003 0.0066449903 2.21499
0.004 0.008859977 2.2149823
0.005 0.011074955 2.2149725
0.006 0.013289921 2.2149606
0.007 0.015504874 2.2149465
0.008 0.017719813 2.2149303
0.009 0.019934734 2.214912
0.010 0.022149637 2.2148912
0.011 0.024364518 2.2148683
0.012 0.026579374 2.2148433
0.013 0.028794205 2.214816
0.014 0.031009007 2.2147868
0.015 0.033223778 2.2147553
0.016 0.035438515 2.2147217
0.017 0.03765322 2.214686
0.018 0.039867885 2.214648
0.019 0.042082515 2.2146077
0.020 0.044297103 2.2145653
0.021 0.046511646 2.2145207
0.022 0.048726145 2.214474
0.023 0.050940596 2.214425
0.024 0.053154994 2.214374
0.025 0.05536934 2.214321
0.026 0.057583634 2.2142656
0.027 0.05979787 2.2142081
0.028 0.06201205 2.2141485
0.029 0.064226165 2.2140865
0.030 0.06644022 2.2140224
0.031 0.06865421 2.213956
0.032 0.070868134 2.2138877
0.033 0.073081985 2.2138171
0.034 0.07529577 2.2137444
0.035 0.07750948 2.2136695
0.036 0.07972311 2.2135925
0.037 0.081936665 2.2135134
0.038 0.084150136 2.213432
0.039 0.086363524 2.2133486
0.040 0.08857683 2.213263
0.041 0.09079005 2.213175
0.042 0.093003176 2.213085
0.043 0.095216215 2.2129927
0.044 0.097429164 2.2128983
0.045 0.099642016 2.2128017
0.046 0.10185477 2.212703
0.047 0.10406742 2.2126021
0.048 0.10627998 2.2124991
0.049 0.10849243 2.212394
0.050 0.110704765 2.2122867
0.051 0.112917 2.2121773
0.052 0.11512912 2.2120657
0.053 0.11734113 2.211952
0.054 0.11955302 2.211836
0.055 0.1217648 2.211718
0.056 0.12397646 2.211598
0.057 0.126188 2.2114756
0.058 0.1283994 2.2113512
0.059 0.13061069 2.2112246
0.060 0.13282184 2.2110958
0.061 0.13503288 2.210965
0.062 0.13724378 2.2108319
0.063 0.13945454 2.2106967
0.064 0.14166518 2.2105594
0.065 0.14387566 2.21042
0.066 0.146086 2.2102783
0.067 0.1482962 2.2101345
0.068 0.15050627 2.2099886
0.069 0.15271619 2.2098405
0.070 0.15492596 2.2096903
0.071 0.15713558 2.209538
0.072 0.15934503 2.2093835
0.073 0.16155434 2.2092268
0.074 0.16376348 2.209068
0.075 0.16597247 2.2089071
0.076 0.1681813 2.208744
0.077 0.17038997 2.2085788
0.078 0.17259847 2.2084115
0.079 0.17480679 2.208242
0.080 0.17701495 2.2080703
0.081 0.17922293 2.2078965
0.082 0.18143074 2.2077205
0.083 0.18363838 2.2075424
0.084 0.18584584 2.2073622
0.085 0.1880531 2.2071798
0.086 0.19026019 2.2069952
0.087 0.1924671 2.2068086
0.088 0.1946738 2.2066197
0.089 0.19688033 2.206429
0.090 0.19908667 2.2062361
0.091 0.2012928 2.206041
0.092 0.20349874 2.205844
0.093 0.20570448 2.2056446
0.094 0.20791003 2.2054431
0.095 0.21011537 2.2052395
0.096 0.2123205 2.2050338
0.097 0.21452543 2.2048259
0.098 0.21673015 2.204616
0.099 0.21893466 2.204404
0.100 0.22113895 2.20419
0.101 0.22334303 2.2039738
0.102 0.2255469 2.2037554
0.103 0.22775054 2.2035348
0.104 0.22995396 2.2033124
0.105 0.23215716 2.2030878
0.106 0.23436013 2.202861
0.107 0.23656288 2.2026322
0.108 0.23876539 2.2024012
0.109 0.24096768 2.202168
0.110 0.24316972 2.201933
0.111 0.24537154 2.2016957
0.112 0.24757311 2.2014563
0.113 0.24977444 2.2012148
0.114 0.25197554 2.2009714
0.115 0.25417638 2.2007258
0.116 0.25637698 2.200478
0.117 0.25857735 2.2002282
0.118 0.26077744 2.1999762
0.119 0.2629773 2.1997223
0.120 0.2651769 2.1994662
0.121 0.26737624 2.199208
0.122 0.26957533 2.198948
0.123 0.27177414 2.1986856
0.124 0.2739727 2.1984212
0.125 0.27617097 2.1981547
0.126 0.27836898 2.1978862
0.127 0.28056672 2.1976156
0.128 0.2827642 2.1973429
0.129 0.2849614 2.1970682
0.130 0.28715834 2.1967914
0.131 0.28935498 2.1965125
0.132 0.29155135 2.1962316
0.133 0.29374745 2.1959486
0.134 0.29594326 2.1956635
0.135 0.29813877 2.1953764
0.136 0.300334 2.1950872
0.137 0.30252895 2.1947958
0.138 0.3047236 2.1945026
0.139 0.30691794 2.1942072
0.140 0.30911198 2.19391
0.141 0.31130573 2.1936104
0.142 0.31349918 2.1933088
0.143 0.31569234 2.1930053
0.144 0.3178852 2.1926997
0.145 0.32007775 2.192392
0.146 0.32226998 2.1920824
0.147 0.3244619 2.1917708
0.148 0.3266535 2.191457
0.149 0.32884482 2.1911411
0.150 0.3310358 2.1908233
0.151 0.33322644 2.1905034
0.152 0.3354168 2.1901815
0.153 0.33760682 2.1898575
0.154 0.3397965 2.1895316
0.155 0.34198588 2.1892035
0.156 0.34417492 2.1888735
0.157 0.34636363 2.1885414
0.158 0.34855202 2.1882074
0.159 0.35074005 2.1878712
0.160 0.35292774 2.1875331
0.161 0.35511512 2.1871932
0.162 0.35730213 2.186851
0.163 0.35948882 2.186507
0.164 0.36167514 2.1861608
0.165 0.36386114 2.1858127
0.166 0.3660468 2.1854625
0.167 0.36823207 2.1851103
0.168 0.370417 2.1847563
0.169 0.37260157 2.1844
0.170 0.37478578 2.184042
0.171 0.37696964 2.183682
0.172 0.37915313 2.1833198
0.173 0.38133627 2.1829557
0.174 0.38351905 2.1825898
0.175 0.38570145 2.1822217
0.176 0.38788348 2.1818516
0.177 0.39006516 2.1814797
0.178 0.39224645 2.1811056
0.179 0.39442736 2.1807296
0.180 0.3966079 2.1803517
0.181 0.39878806 2.1799717
0.182 0.40096784 2.1795897
0.183 0.40314722 2.179206
0.184 0.40532625 2.1788201
0.185 0.4075049 2.1784322
0.186 0.40968314 2.1780424
0.187 0.41186097 2.1776507
0.188 0.41403842 2.177257
0.189 0.41621548 2.1768615
0.190 0.41839215 2.1764638
0.191 0.4205684 2.1760643
0.192 0.42274427 2.1756628
0.193 0.42491972 2.1752594
0.194 0.4270948 2.174854
0.195 0.42926943 2.1744468
0.196 0.43144366 2.1740375
0.197 0.4336175 2.1736262
0.198 0.43579093 2.173213
0.199 0.43796393 2.172798
0.200 0.44013652 2.172381
0.201 0.4423087 2.171962
0.202 0.44448045 2.1715412
0.203 0.4466518 2.1711185
0.204 0.4488227 2.1706939
0.205 0.45099318 2.1702673
0.206 0.45316324 2.169839
0.207 0.45533288 2.1694086
0.208 0.45750207 2.1689763
0.209 0.4596708 2.1685421
0.210 0.46183914 2.168106
0.211 0.46400702 2.167668
0.212 0.46617448 2.1672282
0.213 0.4683415 2.1667864
0.214 0.47050807 2.1663427
0.215 0.4726742 2.1658971
0.216 0.47483987 2.1654496
0.217 0.4770051 2.1650002
0.218 0.47916988 2.1645489
0.219 0.4813342 2.1640956
0.220 0.48349807 2.1636405
0.221 0.48566148 2.1631835
0.222 0.48782444 2.1627245
0.223 0.48998693 2.1622639
0.224 0.49214897 2.1618013
0.225 0.49431053 2.161337
0.226 0.49647164 2.1608706
0.227 0.49863228 2.1604023
0.228 0.50079244 2.1599321
0.229 0.50295216 2.1594603
0.230 0.5051114 2.1589866
0.231 0.50727016 2.158511
0.232 0.50942844 2.1580334
0.233 0.51158625 2.1575541
0.234 0.5137436 2.157073
0.235 0.51590043 2.15659
0.236 0.5180568 2.156105
0.237 0.52021265 2.1556184
0.238 0.522368 2.15513
0.239 0.5245229 2.1546395
0.240 0.5266773 2.1541474
0.241 0.5288312 2.1536534
0.242 0.5309846 2.1531575
0.243 0.5331375 2.15266
0.244 0.5352899 2.1521604
0.245 0.5374418 2.151659
0.246 0.5395932 2.151156
0.247 0.5417441 2.150651
0.248 0.5438945 2.1501443
0.249 0.5460444 2.1496358
0.250 0.5481938 2.1491253
0.251 0.5503427 2.1486132
0.252 0.552491 2.1480992
0.253 0.55463886 2.1475835
0.254 0.5567862 2.1470659
0.255 0.55893296 2.1465466
0.256 0.56107926 2.1460254
0.257 0.56322503 2.1455026
0.258 0.56537026 2.1449778
0.259 0.56751496 2.1444514
0.260 0.5696591 2.1439233
0.261 0.5718028 2.1433933
0.262 0.57394594 2.1428616
0.263 0.57608855 2.142328
0.264 0.5782306 2.1417928
0.265 0.58037215 2.1412556
0.266 0.58251315 2.1407168
0.267 0.5846536 2.1401763
0.268 0.58679354 2.139634
0.269 0.58893293 2.1390898
0.270 0.5910717 2.138544
0.271 0.59321 2.1379964
0.272 0.5953477 2.137447
0.273 0.5974849 2.1368961
0.274 0.59962153 2.1363435
0.275 0.6017576 2.135789
0.276 0.6038931 2.1352327
0.277 0.6060281 2.1346748
0.278 0.60816246 2.1341152
0.279 0.6102963 2.1335537
0.280 0.61242956 2.1329906
0.281 0.6145623 2.1324258
0.282 0.6166944 2.1318593
0.283 0.618826 2.1312912
0.284 0.62095696 2.1307213
0.285 0.6230874 2.1301496
0.286 0.62521726 2.1295762
0.287 0.6273466 2.1290011
0.288 0.6294753 2.1284244
0.289 0.6316034 2.127846
0.290 0.63373095 2.127266
0.291 0.63585794 2.1266842
0.292 0.63798434 2.1261008
0.293 0.64011014 2.1255157
0.294 0.64223534 2.124929
0.295 0.64435995 2.1243405
0.296 0.646484 2.1237504
0.297 0.6486075 2.1231587
0.298 0.6507304 2.1225653
0.299 0.65285265 2.1219702
0.300 0.65497434 2.1213734
0.301 0.65709543 2.120775
0.302 0.6592159 2.120175
0.303 0.6613358 2.119573
0.304 0.66345507 2.1189697
0.305 0.6655737 2.1183648
0.306 0.66769177 2.1177583
0.307 0.6698092 2.11715
0.308 0.6719261 2.1165402
0.309 0.67404234 2.1159286
0.310 0.67615795 2.1153154
0.311 0.67827296 2.1147008
0.312 0.6803874 2.1140845
0.313 0.68250114 2.1134665
0.314 0.6846143 2.1128469
0.315 0.6867268 2.1122258
0.316 0.6888387 2.111603
0.317 0.69095004 2.1109786
0.318 0.6930607 2.1103528
0.319 0.69517076 2.1097252
0.320 0.69728017 2.109096
0.321 0.6993889 2.1084654
0.322 0.7014971 2.1078331
0.323 0.7036046 2.1071992
0.324 0.7057115 2.1065638
0.325 0.70781773 2.1059268
0.326 0.7099233 2.105288
0.327 0.7120283 2.1046479
0.328 0.71413267 2.104006
0.329 0.71623635 2.1033628
0.330 0.7183394 2.1027179
0.331 0.72044176 2.1020715
0.332 0.7225435 2.1014235
0.333 0.7246446 2.100774
0.334 0.72674507 2.100123
0.335 0.7288449 2.0994704
0.336 0.73094404 2.0988162
0.337 0.73304254 2.0981605
0.338 0.7351404 2.0975034
0.339 0.7372376 2.0968447
0.340 0.7393341 2.0961845
0.341 0.74143 2.0955226
0.342 0.74352515 2.0948594
0.343 0.74561965 2.0941947
0.344 0.7477135 2.0935283
0.345 0.7498067 2.0928605
0.346 0.75189924 2.0921912
0.347 0.7539911 2.0915203
0.348 0.7560823 2.090848
0.349 0.7581728 2.0901742
0.350 0.76026267 2.089499
0.351 0.7623518 2.0888221
0.352 0.7644403 2.0881438
0.353 0.7665281 2.087464
0.354 0.76861525 2.086783
0.355 0.7707017 2.0861003
0.356 0.77278745 2.0854163
0.357 0.77487254 2.0847306
0.358 0.7769569 2.0840435
0.359 0.77904063 2.083355
0.360 0.78112364 2.082665
0.361 0.783206 2.0819736
0.362 0.7852876 2.0812807
0.363 0.78736854 2.0805864
0.364 0.7894488 2.0798907
0.365 0.79152834 2.0791936
0.366 0.7936072 2.078495
0.367 0.7956853 2.077795
0.368 0.79776275 2.0770936
0.369 0.7998395 2.0763907
0.370 0.8019155 2.0756865
0.371 0.80399084 2.0749807
0.372 0.80606544 2.0742736
0.373 0.8081394 2.073565
0.374 0.8102126 2.072855
0.375 0.8122851 2.0721436
0.376 0.8143569 2.0714307
0.377 0.816428 2.0707166
0.378 0.8184984 2.0700011
0.379 0.820568 2.0692842
0.380 0.82263696 2.0685658
0.381 0.8247052 2.067846
0.382 0.8267727 2.067125
0.383 0.8288395 2.0664027
0.384 0.8309055 2.0656788
0.385 0.8329708 2.0649536
0.386 0.8350354 2.064227
0.387 0.83709925 2.0634992
0.388 0.8391624 2.06277
0.389 0.8412248 2.0620394
0.390 0.84328645 2.0613074
0.391 0.8453474 2.060574
0.392 0.84740764 2.0598395
0.393 0.8494671 2.0591035
0.394 0.85152584 2.058366
0.395 0.8535838 2.0576274
0.396 0.85564107 2.0568874
0.397 0.8576976 2.0561461
0.398 0.8597534 2.0554035
0.399 0.8618084 2.0546596
0.400 0.8638627 2.0539143
0.401 0.86591625 2.0531678
0.402 0.86796904 2.05242
0.403 0.8700211 2.0516708
0.404 0.8720724 2.0509202
0.405 0.8741229 2.0501685
0.406 0.8761727 2.0494153
0.407 0.87822175 2.048661
0.408 0.88027 2.0479054
0.409 0.88231754 2.0471485
0.410 0.8843643 2.0463903
0.411 0.8864103 2.045631
0.412 0.88845557 2.0448701
0.413 0.89050007 2.0441082
0.414 0.8925438 2.043345
0.415 0.89458674 2.0425804
0.416 0.8966289 2.0418146
0.417 0.8986704 2.0410476
0.418 0.90071106 2.0402794
0.419 0.90275097 2.0395098
0.420 0.9047901 2.038739
0.421 0.90682846 2.037967
0.422 0.90886605 2.0371938
0.423 0.91090286 2.0364194
0.424 0.9129389 2.0356438
0.425 0.91497415 2.034867
0.426 0.91700864 2.0340889
0.427 0.91904235 2.0333095
0.428 0.9210753 2.0325289
0.429 0.92310745 2.031747
0.430 0.9251388 2.0309641
0.431 0.9271693 2.03018
0.432 0.9291991 2.0293946
0.433 0.9312281 2.028608
0.434 0.9332563 2.0278203
0.435 0.9352838 2.0270314
0.436 0.9373104 2.0262413
0.437 0.93933624 2.02545
0.438 0.9413613 2.0246575
0.439 0.94338554 2.0238638
0.440 0.945409 2.0230691
0.441 0.9474317 2.0222733
0.442 0.94945353 2.0214763
0.443 0.9514746 2.020678
0.444 0.9534949 2.0198786
0.445 0.9555144 2.019078
0.446 0.95753306 2.0182765
0.447 0.9595509 2.0174737
0.448 0.961568 2.0166698
0.449 0.96358424 2.0158646
0.450 0.9655997 2.0150585
0.451 0.96761435 2.0142512
0.452 0.9696282 2.0134428
0.453 0.97164124 2.012633
0.454 0.9736535 2.0118225
0.455 0.9756649 2.0110106
0.456 0.9776755 2.0101976
0.457 0.9796853 2.0093837
0.458 0.9816943 2.0085685
0.459 0.9837024 2.0077524
0.460 0.9857098 2.0069351
0.461 0.9877163 2.0061169
0.462 0.989722 2.0052974
0.463 0.9917269 2.0044768
0.464 0.99373096 2.0036552
0.465 0.9957342 2.0028324
0.466 0.99773663 2.0020087
0.467 0.9997382 2.0011837
0.468 1.001739 2.0003579
0.469 1.003739 1.9995309
0.470 1.0057381 1.9987029
0.471 1.0077364 1.9978739
0.472 1.0097339 1.9970438
0.473 1.0117306 1.9962127
0.474 1.0137264 1.9953805
0.475 1.0157213 1.9945474
0.476 1.0177155 1.9937131
0.477 1.0197088 1.9928778
0.478 1.0217012 1.9920416
0.479 1.0236928 1.9912043
0.480 1.0256836 1.990366
0.481 1.0276736 1.9895266
0.482 1.0296627 1.9886863
0.483 1.031651 1.987845
0.484 1.0336385 1.9870026
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