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Julia と微分方程式でメシを食う

8efe990be3aad3b8c6bac487b8ef7b2b?s=47 horiem
October 20, 2018

Julia と微分方程式でメシを食う

Julia Tokyo #8 on 20th Oct. 2018

8efe990be3aad3b8c6bac487b8ef7b2b?s=128

horiem

October 20, 2018
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  1. Julia ͱඍ෼ํఔࣜͰ ϝγΛ৯͏ JuliaTokyo #8 horiem@yellowshippo

  2. ϝοηʔδ • ඍ෼ํఔࣜ • Julia • ָ͍͠ʂʂʂʂ

  3. ඍ෼ํఔࣜ

  4. ͱ͸

  5. ʢৗʣඍ෼ํఔࣜͱ͸ʁ • Կ͔ͷඍ෼ = ؔ਺ɹͷܗ • ݱࡏͷঢ়ଶ͔Β
 ʮͪΐͬͱະདྷʯΛ༧ଌ • ෺ཧɺ͸΋ͪΖΜɺ


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  6. ඍ෼ํఔࣜΛܭࢉػͰղ͘ • ۃݶ͸ܭࢉͰ͖ͳ͍ͷͰΊͬͪΌখ͍͞஋Ͱ୅༻ dx dt = f(x) <latexit sha1_base64="/dnHsardr9RVVYH+b3AEQBHx1Hs=">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</latexit> <latexit

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  7. ඍ෼ํఔࣜΛܭࢉػͰղ͘ • ۃݶ͸ܭࢉͰ͖ͳ͍ͷͰΊͬͪΌখ͍͞஋Ͱ୅༻ x t = f(x) <latexit sha1_base64="kzQM85skjQFeGNKeiYtjzNcSeBY=">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</latexit> <latexit

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sha1_base64="Ul8Uz847IGSoX26VI3KqUENor4g=">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</latexit> <latexit sha1_base64="Ul8Uz847IGSoX26VI3KqUENor4g=">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</latexit> x(t + t) = x(t) + f(x) t <latexit sha1_base64="NgrfEIsezxMtEjF5if87aXXxPbc=">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</latexit> <latexit sha1_base64="NgrfEIsezxMtEjF5if87aXXxPbc=">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</latexit> <latexit sha1_base64="NgrfEIsezxMtEjF5if87aXXxPbc=">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</latexit> <latexit sha1_base64="NgrfEIsezxMtEjF5if87aXXxPbc=">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</latexit> dx dt = f(x) <latexit sha1_base64="/dnHsardr9RVVYH+b3AEQBHx1Hs=">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</latexit> <latexit sha1_base64="/dnHsardr9RVVYH+b3AEQBHx1Hs=">AAAEqHicjVNdb9MwFPW2AKN8deORF4uq0kDQJRUSPACaQJN4LBJth5qochynteo4wXZYKy/8FF7hL/FvsJNA2xSkWUp0fe8951yfxGHGqFSu+2tv/8C5cfPW4e3Wnbv37j9oHx2PZJoLTIY4Zam4CJEkjHIyVFQxcpEJgpKQkXG4eG/r469ESJryT2qVkSBBM05jipEyqWn72I9oHOtloVUB38D4ZPlk2u64PbdccDfw6qAD6jWYHh1886MU5wnhCjMk5cRzMxVoJBTFjBQtP5ckQ3iBZmRiQo4SIgNdDl/ArslEME6FebiCZXYToVEi5SoJTWeC1Fw2azb5z1qYNJRV/CrQlGe5IhxXwnHOoEqhdQZGVBCs2MoECAtqZod4jgTCyvjX8jm5xGmSIB7p0rNi0g+0H5u6jmDHK+y7XxQQdlMRUY6EJYpjIowrFLFtgqzB4GfWLMRKovXG8G3jKP8LtKLwFJaqRpTy5/YfgNcQNxas5dfChmxTeYPzT/b/lDmnqph4hg/69kuIRE86XlDaYWvwkqo5lF9yJAgMzYkXRDU8RaoaiJFY9ew4vqCzubqa6l0bIsKM343k0DgXJnrYbB5V+ZHJd+FWhVQVsutyJtL1NK/NNM+MJfVEb5v8SFRHrw9u9yXO1+tj+E2N8y3M+TUQKJQVxnZebThUmBvrNe/nbjDq9zy353180Tl7V9/dQ/AIPAYnwAMvwRn4AAZgCDBYgu/gB/jpPHUGztj5XLXu79WYh2BrOeFvBm2QrA==</latexit> <latexit sha1_base64="/dnHsardr9RVVYH+b3AEQBHx1Hs=">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</latexit> <latexit sha1_base64="/dnHsardr9RVVYH+b3AEQBHx1Hs=">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</latexit> • x ΍ f ΛϕΫτϧͩͱࢥͬͯ΋͍͍ ୅༻ ʢΦΠϥʔ๏ʣ
  8. Julia

  9. ͳͥʁ

  10. ͳͥ Julia ͔ʁ • C++ɺFortran ͳͲʹൺ΂ͯॻ͖΍͍͢ • Python ͳͲʹൺ΂ͯ଎͍

  11. ଎͍

  12. ຊ౰ʁ

  13. @bicycle1885 ࢯʮJuliaͷQAʯΑΓҾ༻ https://qiita.com/bicycle1885/items/ab8fff19a4ff0cdea287

  14. ߦྻੵ଎౓ൺֱ

  15. ߦྻੵ଎౓ൺֱ

  16. ͔֬ʹ

  17. ඍ෼ํఔࣜ଎౓ൺֱ

  18. ඍ෼ํఔࣜ଎౓ൺֱ

  19. ඍ෼ํఔࣜ଎౓ൺֱ

  20. ଎͍ʂ

  21. ָ͍͠ྫ

  22. Van der Pol ৼಈࢠ d2x dt2 µ(1 x2) dx dt

    + x = 0 <latexit sha1_base64="bO8WEZcrgQSPW7Jgq/c56qbUsw4=">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</latexit> <latexit sha1_base64="bO8WEZcrgQSPW7Jgq/c56qbUsw4=">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</latexit> <latexit sha1_base64="bO8WEZcrgQSPW7Jgq/c56qbUsw4=">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</latexit> <latexit sha1_base64="bO8WEZcrgQSPW7Jgq/c56qbUsw4=">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</latexit>
  23. d dt ✓ x v ◆ = ✓ v µ(1

    x2)v x ◆ <latexit sha1_base64="qdmQIk3vBlAWRMoUQwTKxb2l5Zk=">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</latexit> <latexit sha1_base64="qdmQIk3vBlAWRMoUQwTKxb2l5Zk=">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</latexit> <latexit sha1_base64="qdmQIk3vBlAWRMoUQwTKxb2l5Zk=">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</latexit> <latexit sha1_base64="qdmQIk3vBlAWRMoUQwTKxb2l5Zk=">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</latexit> d2x dt2 µ(1 x2) dx dt + x = 0 <latexit sha1_base64="bO8WEZcrgQSPW7Jgq/c56qbUsw4=">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</latexit> <latexit sha1_base64="bO8WEZcrgQSPW7Jgq/c56qbUsw4=">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</latexit> <latexit sha1_base64="bO8WEZcrgQSPW7Jgq/c56qbUsw4=">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</latexit> <latexit sha1_base64="bO8WEZcrgQSPW7Jgq/c56qbUsw4=">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</latexit> d dt x = f(x) <latexit sha1_base64="usCGqu4cHSeukE6XD9H0B04qKP0=">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</latexit> <latexit sha1_base64="usCGqu4cHSeukE6XD9H0B04qKP0=">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</latexit> <latexit sha1_base64="usCGqu4cHSeukE6XD9H0B04qKP0=">AAAEuHicjVNdb9MwFPW2AKN8rINHXqxVk4YEJamQQAjQBJrE45BoN6mJiuM4rVXbCbbDqLzwzK/hFf4K/wY7CbRNQZqlRNfn+p5z70kc54wq7fu/trZ3vGvXb+ze7Ny6fefuXnf/3khlhcRkiDOWyfMYKcKoIENNNSPnuSSIx4ycxfO3Ln/2mUhFM/FBL3IScTQVNKUYaQtNugdhQtPUlEaXMIy5+VLCV1WQlkf1/uGk2/P7frXgZhA0QQ8063Syv/M1TDJccCI0ZkipceDnOjJIaooZKTthoUiO8BxNydiGAnGiIlMNU8JDiyQwzaR9hIYVulphEFdqwWN7kiM9U+2cA/+Zi3lLWafPI0NFXmgicC2cFgzqDDqnYEIlwZotbICwpLZ3iGdIIqytn51QkAuccY5EYioPy/EgMmFq8yaBvaB070FZQniYyYQKJB1RmhJpXaGIrRPkLYYwd2YhVhEtN5ZvvY6Kv4VOFD6BlaoVpeKx+yfgFcStBUv5pbAlW1Ve4fyD/p+yEFSX48DywdB9CcnNuBdElR0uBy+onkH1qUCSwNhOPCe65SnSdUOMpLrv2gklnc705cRs2pAQZv1ugUPrnP2Dh+3DoxofWfwQrmVInSGbLucyW3bz0nbzyFrSdPS6zY9kPXozuNtXdaFZjhG2NU7Wak6uUIFiVde4k5crDpX2xgbt+7kZjAb9wO8H75/2jt80d3cXPAAH4AgE4Bk4Bu/AKRgCDL6B7+AH+Om98D56U4/WR7e3mpr7YG158jeI4JfV</latexit> <latexit sha1_base64="usCGqu4cHSeukE6XD9H0B04qKP0=">AAAEuHicjVNdb9MwFPW2AKN8rINHXqxVk4YEJamQQAjQBJrE45BoN6mJiuM4rVXbCbbDqLzwzK/hFf4K/wY7CbRNQZqlRNfn+p5z70kc54wq7fu/trZ3vGvXb+ze7Ny6fefuXnf/3khlhcRkiDOWyfMYKcKoIENNNSPnuSSIx4ycxfO3Ln/2mUhFM/FBL3IScTQVNKUYaQtNugdhQtPUlEaXMIy5+VLCV1WQlkf1/uGk2/P7frXgZhA0QQ8063Syv/M1TDJccCI0ZkipceDnOjJIaooZKTthoUiO8BxNydiGAnGiIlMNU8JDiyQwzaR9hIYVulphEFdqwWN7kiM9U+2cA/+Zi3lLWafPI0NFXmgicC2cFgzqDDqnYEIlwZotbICwpLZ3iGdIIqytn51QkAuccY5EYioPy/EgMmFq8yaBvaB070FZQniYyYQKJB1RmhJpXaGIrRPkLYYwd2YhVhEtN5ZvvY6Kv4VOFD6BlaoVpeKx+yfgFcStBUv5pbAlW1Ve4fyD/p+yEFSX48DywdB9CcnNuBdElR0uBy+onkH1qUCSwNhOPCe65SnSdUOMpLrv2gklnc705cRs2pAQZv1ugUPrnP2Dh+3DoxofWfwQrmVInSGbLucyW3bz0nbzyFrSdPS6zY9kPXozuNtXdaFZjhG2NU7Wak6uUIFiVde4k5crDpX2xgbt+7kZjAb9wO8H75/2jt80d3cXPAAH4AgE4Bk4Bu/AKRgCDL6B7+AH+Om98D56U4/WR7e3mpr7YG158jeI4JfV</latexit> Van der Pol ৼಈࢠ
  24. None
  25. None
  26. ͭͳ͛ͯΈΔ d dt ✓ x v ◆ = ✓ v

    µ(1 x2)v x ◆ <latexit sha1_base64="qdmQIk3vBlAWRMoUQwTKxb2l5Zk=">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</latexit> <latexit sha1_base64="qdmQIk3vBlAWRMoUQwTKxb2l5Zk=">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</latexit> <latexit sha1_base64="qdmQIk3vBlAWRMoUQwTKxb2l5Zk=">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</latexit> <latexit sha1_base64="qdmQIk3vBlAWRMoUQwTKxb2l5Zk=">AAAFGnicjVPdbtMwGE23AiP8dXAF3FhUlTqJlaZCggtAE2gSl0Oi3aS6VI7jtFZjJ9hOt8oLVzwGT8Md4pYbXoGnwE4CbdNNmqVEn7/P55zPx7afRFSqbvd3bWu7fu36jZ2b7q3bd+7ea+zeH8g4FZj0cRzF4sRHkkSUk76iKiIniSCI+RE59mfvbP14ToSkMf+oFgkZMTThNKQYKZMaN77CgIahzrTKXBiRULVd6JMJ5RoJgRaZxpl75kLozl1IeFBmXSjoZKr23NeXguYWBFkK2h7YB2efentgboOLaMaNZrfTzQfYDLwyaDrlOBrvbn+BQYxTRrjCEZJy6HUTNTK0iuKIGOJUkgThGZqQoQk5YkSOdG5XBlomE4AwFubjCuTZVYRGTMoF881KhtRUVms2eWHNZxVlFb4cacqTVBGOC+EwjYCKgT0LEFBBsIoWJkBYUNM7wFMkEFbmxFzIySmOGUPGr/yUsmFvpGFo6joATS+z/16WAdCKRUA5EpYoDIkwrlAUrRMkFQaYWLNQlBMtJ4ZvHUf5f6AVBc9ArmpEKd+3tw5cQdxYsJRfChuyVeUVzn/ZyylTTlU29AwfgPYkBNPDpjfK7bA1cErVFMjPKRIE+GbHM6IqniJVNGRvcMe2U1zH87HetCEgkfG7kuwb53ym+9XFgyI/MPkWWKuQokI2XU5EvOzmlenmqbGk7OhNlR+JYuvlxu08x0G93AasahyuYQ6vgEC+LDB25fmKQ5l5sV71fW4Gg17H63a8D8+bB2/Lt7vjPHaeOG3Hc144B85758jpO9j5U2vUHtYe1b/Vv9d/1H8WS7dqJeaBszbqv/4CgAe5FA==</latexit>
  27. ͭͳ͛ͯΈΔ d dt ✓ xi vi ◆ = ✓ vi

    µ(1 x2 i )vi xi + c P j6=i (vj vi) ◆ <latexit sha1_base64="d36BRMXFN4g+VLqdjn3b1J6nv2Q=">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</latexit> <latexit sha1_base64="d36BRMXFN4g+VLqdjn3b1J6nv2Q=">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</latexit> <latexit sha1_base64="d36BRMXFN4g+VLqdjn3b1J6nv2Q=">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</latexit> <latexit sha1_base64="d36BRMXFN4g+VLqdjn3b1J6nv2Q=">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</latexit> d dt ✓ x v ◆ = ✓ v µ(1 x2)v x ◆ <latexit sha1_base64="qdmQIk3vBlAWRMoUQwTKxb2l5Zk=">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</latexit> <latexit sha1_base64="qdmQIk3vBlAWRMoUQwTKxb2l5Zk=">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</latexit> <latexit sha1_base64="qdmQIk3vBlAWRMoUQwTKxb2l5Zk=">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</latexit> <latexit sha1_base64="qdmQIk3vBlAWRMoUQwTKxb2l5Zk=">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</latexit>
  28. None
  29. ָ͍͠ʂʂ

  30. ·ͱΊ • Julia Ͱඍ෼ํఔࣜΛղ͘ͱ଎͍ʂ • ඍ෼ํఔࣜΛղ͘ͷ͸ָ͍͠ʂ • Julia ΍ͬͯΔͷΛΞϐʔϧ͍͚ͯ͠͹
 ϝγ͕৯͑ΔΑ͏ʹͳΔ͔΋ɾɾɾʁ