室橋/モンテカルロ法
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開始行:
[[室橋/並列処理輪講2009]]
*モンテカルロ法 [#w84b0ebe]
[[ぐぐってみた:http://www.google.co.jp/search?q=%E3%83%A2%E3%83%B3%E3%83%86%E3%82%AB%E3%83%AB%E3%83%AD%E6%B3%95&lr=lang_ja&ie=utf-8&oe=utf-8&aq=t&rls=org.mozilla:ja:official&client=firefox-a]]
参考~
[[擬似乱数とモンテカルロ法:http://www.sm.rim.or.jp/~shishido/pie.html]]~
[[Yahoo!知恵袋:http://detail.chiebukuro.yahoo.co.jp/qa/question_detail/q1113743691]]
*MEMO [#t66e4af5]
srand((unsigned) time(NULL));
[[参照ページ:http://www9.plala.or.jp/sgwr-t/lib/srand.html]]
[[処理時間を測定する:http://ms-06s.ie.isenshu-u.ac.jp/ucc/parapara/section4/section4-2.htm]]~
同期関数MPI_Barrier,時間測定関数MPI_Wtimeおよび測定時間の精度を返す関数MPI_Wtickの使い方
[[性能を評価する:http://ms-06s.ie.isenshu-u.ac.jp/ucc/parapara/section4/section4-3.htm]]~
性能評価の参考に
-----------------------------------------------------
time
-Sequential
|点の総数/np|実行時間|
|10|0.000144958496093750000000000000|
|100|0.001447916030883789062500000000|
|1000|0.015103816986083984375000000000|
|10000|0.138165950775146484375000000000|
|100000|1.363204002380371093750000000000|
|1000000|13.782168865203857421875000000000|
|10000000|138.284456014633178710937500000000|
-Parallel
--hdw1dc1〜hdw1dc20
|点の総数/np|1|2|3|4|5|6|7|8|9|10|
|10|0.000398|0.000784|0.000826|0.000950|0.000997|0.000963|0.001077|0.001179|0.001230|0.001128|
|100|0.001769|0.001498|0.001176|0.001126|0.001122|0.001110|0.001130|0.001196|0.001327|0.001344|
|1000|0.014122|0.008293|0.005358|0.004260|0.003610|0.003217|0.002941|0.002745|0.002610|0.002525|
|10000|0.138497|0.071566|0.047582|0.036137|0.028908|0.024097|0.021033|0.018534|0.016686|0.014876|
|100000|1.367804|0.696724|0.470713|0.356605|0.298868|0.241540|0.201304|0.173816|0.154612|0.152233|
|1000000|13.706661|7.271650|4.679834|3.546187|4.430716|2.472957|2.104143|1.827114|1.565170|1.411978|
|10000000|139.204318|73.424605|53.184961|40.144732|33.719439|23.984708|20.287690|19.526851|15.875831|14.107626|
|点の総数/np|11|12|13|14|15|16|17|18|19|20|
|10|0.001323|0.001709|0.001583|0.001440|0.001321|0.001296|0.001572|0.013752|0.001571|0.001939|
|100|0.001739|0.001332|0.001397|0.001395|0.001381|0.001707|0.001766|0.001695|0.001912|0.001825|
|1000|0.002346|0.002377|0.002269|0.002287|0.002120|0.002158|0.002117|0.002221|0.002183|0.002297|
|10000|0.014003|0.013170|0.013458|0.011271|0.010525|0.010177|0.009988|0.009215|0.008690|0.009495|
|100000|0.128070|0.118024|0.109333|0.101453|0.094617|0.089227|0.083934|0.079350|0.074317|0.071703|
|1000000|1.320252|1.252005|1.109181|1.104789|0.937800|1.269041|0.834027|0.784736|0.794062|0.771301|
|10000000|13.241760|11.898025|11.354126|10.766786|11.023046|10.989997|9.794955|11.357627|8.610881|7.910759|
~
-hdw2dc1〜hdw2dc20
|点の総数/np|1|2|4|8|12|16|20|
|1000|0.013919|0.007628|0.004399|0.002800|0.002412|0.002211|0.002421|
|100000|1.368106|0.714029|0.344662|0.174139|0.125282|0.088812|0.071319|
|10000000|138.739047|73.334015|34.524816|17.234803|12.330005|8.674981|7.011602|
~
-hdw3dc1〜hdw3dc20
|点の総数/np|1|2|4|8|12|16|20|
|1000|0.014264|0.008115|0.004860|0.003564|0.003535|0.003871|0.004244|
|100000|1.373948|0.752023|0.371113|0.178610|0.119177|0.090676|0.077325|
|10000000|142.758247|71.799747|35.800604|17.798581|12.034355|9.255141|7.282093|
~
-高速化率(Speed up ratio)
|p→|1|2|3|4|5|6|7|8|9|10|
|time|139.204318|73.424605|53.184961|40.144732|33.719439|23.984708|20.287690|19.526851|15.875831|14.107626|
|ideal|139.204318|69.602159|46.401439|34.8010795|27.840863|23.200719|9.886331|17.400539|15.467146|13.920431|
|S(p)|1|1.895881|2.617362|3.467561|4.128310|5.803877|6.861516|7.128866|8.768316|9.867309|
|p→|11|12|13|14|15|16|17|18|19|20|
|time|13.241760|11.898025|11.354126|10.766786|11.023046|10.989997|19.794955|11.357627|8.610881|7.910759|
|ideal|12.654938|11.600359|10.708024|9.943165|9.280287|8.700269|8.188489|7.733573|7.326543|6.960215|
|S(p)|10.512523|11.699783|12.260240|12.929050|12.628480|12.666456|14.211838|12.256461|16.166094|17.596834|
~
-omake
|p→|30|40|50|60|70|80|90|100|110|120|123|
|time|6.492620|5.197024|5.477336|4.899514|4.078449|3.446444|3.119258|3.084653|3.019316|2.932370|2.868360|
終了行:
[[室橋/並列処理輪講2009]]
*モンテカルロ法 [#w84b0ebe]
[[ぐぐってみた:http://www.google.co.jp/search?q=%E3%83%A2%E3%83%B3%E3%83%86%E3%82%AB%E3%83%AB%E3%83%AD%E6%B3%95&lr=lang_ja&ie=utf-8&oe=utf-8&aq=t&rls=org.mozilla:ja:official&client=firefox-a]]
参考~
[[擬似乱数とモンテカルロ法:http://www.sm.rim.or.jp/~shishido/pie.html]]~
[[Yahoo!知恵袋:http://detail.chiebukuro.yahoo.co.jp/qa/question_detail/q1113743691]]
*MEMO [#t66e4af5]
srand((unsigned) time(NULL));
[[参照ページ:http://www9.plala.or.jp/sgwr-t/lib/srand.html]]
[[処理時間を測定する:http://ms-06s.ie.isenshu-u.ac.jp/ucc/parapara/section4/section4-2.htm]]~
同期関数MPI_Barrier,時間測定関数MPI_Wtimeおよび測定時間の精度を返す関数MPI_Wtickの使い方
[[性能を評価する:http://ms-06s.ie.isenshu-u.ac.jp/ucc/parapara/section4/section4-3.htm]]~
性能評価の参考に
-----------------------------------------------------
time
-Sequential
|点の総数/np|実行時間|
|10|0.000144958496093750000000000000|
|100|0.001447916030883789062500000000|
|1000|0.015103816986083984375000000000|
|10000|0.138165950775146484375000000000|
|100000|1.363204002380371093750000000000|
|1000000|13.782168865203857421875000000000|
|10000000|138.284456014633178710937500000000|
-Parallel
--hdw1dc1〜hdw1dc20
|点の総数/np|1|2|3|4|5|6|7|8|9|10|
|10|0.000398|0.000784|0.000826|0.000950|0.000997|0.000963|0.001077|0.001179|0.001230|0.001128|
|100|0.001769|0.001498|0.001176|0.001126|0.001122|0.001110|0.001130|0.001196|0.001327|0.001344|
|1000|0.014122|0.008293|0.005358|0.004260|0.003610|0.003217|0.002941|0.002745|0.002610|0.002525|
|10000|0.138497|0.071566|0.047582|0.036137|0.028908|0.024097|0.021033|0.018534|0.016686|0.014876|
|100000|1.367804|0.696724|0.470713|0.356605|0.298868|0.241540|0.201304|0.173816|0.154612|0.152233|
|1000000|13.706661|7.271650|4.679834|3.546187|4.430716|2.472957|2.104143|1.827114|1.565170|1.411978|
|10000000|139.204318|73.424605|53.184961|40.144732|33.719439|23.984708|20.287690|19.526851|15.875831|14.107626|
|点の総数/np|11|12|13|14|15|16|17|18|19|20|
|10|0.001323|0.001709|0.001583|0.001440|0.001321|0.001296|0.001572|0.013752|0.001571|0.001939|
|100|0.001739|0.001332|0.001397|0.001395|0.001381|0.001707|0.001766|0.001695|0.001912|0.001825|
|1000|0.002346|0.002377|0.002269|0.002287|0.002120|0.002158|0.002117|0.002221|0.002183|0.002297|
|10000|0.014003|0.013170|0.013458|0.011271|0.010525|0.010177|0.009988|0.009215|0.008690|0.009495|
|100000|0.128070|0.118024|0.109333|0.101453|0.094617|0.089227|0.083934|0.079350|0.074317|0.071703|
|1000000|1.320252|1.252005|1.109181|1.104789|0.937800|1.269041|0.834027|0.784736|0.794062|0.771301|
|10000000|13.241760|11.898025|11.354126|10.766786|11.023046|10.989997|9.794955|11.357627|8.610881|7.910759|
~
-hdw2dc1〜hdw2dc20
|点の総数/np|1|2|4|8|12|16|20|
|1000|0.013919|0.007628|0.004399|0.002800|0.002412|0.002211|0.002421|
|100000|1.368106|0.714029|0.344662|0.174139|0.125282|0.088812|0.071319|
|10000000|138.739047|73.334015|34.524816|17.234803|12.330005|8.674981|7.011602|
~
-hdw3dc1〜hdw3dc20
|点の総数/np|1|2|4|8|12|16|20|
|1000|0.014264|0.008115|0.004860|0.003564|0.003535|0.003871|0.004244|
|100000|1.373948|0.752023|0.371113|0.178610|0.119177|0.090676|0.077325|
|10000000|142.758247|71.799747|35.800604|17.798581|12.034355|9.255141|7.282093|
~
-高速化率(Speed up ratio)
|p→|1|2|3|4|5|6|7|8|9|10|
|time|139.204318|73.424605|53.184961|40.144732|33.719439|23.984708|20.287690|19.526851|15.875831|14.107626|
|ideal|139.204318|69.602159|46.401439|34.8010795|27.840863|23.200719|9.886331|17.400539|15.467146|13.920431|
|S(p)|1|1.895881|2.617362|3.467561|4.128310|5.803877|6.861516|7.128866|8.768316|9.867309|
|p→|11|12|13|14|15|16|17|18|19|20|
|time|13.241760|11.898025|11.354126|10.766786|11.023046|10.989997|19.794955|11.357627|8.610881|7.910759|
|ideal|12.654938|11.600359|10.708024|9.943165|9.280287|8.700269|8.188489|7.733573|7.326543|6.960215|
|S(p)|10.512523|11.699783|12.260240|12.929050|12.628480|12.666456|14.211838|12.256461|16.166094|17.596834|
~
-omake
|p→|30|40|50|60|70|80|90|100|110|120|123|
|time|6.492620|5.197024|5.477336|4.899514|4.078449|3.446444|3.119258|3.084653|3.019316|2.932370|2.868360|
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