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asxaqz
V2EX  ›  Python

Python 求超越方程解

  •  
  •   asxaqz ·
    Zardinality · 2016-05-26 19:20:20 +08:00 · 6300 次点击
    这是一个创建于 3121 天前的主题,其中的信息可能已经有所发展或是发生改变。
    现在我有若干带参数的超越方程,比如:

    我希望把每一个超越方程的解表示成参数的函数的形式(不是显式解,因为方程中中有一个比较长的幂级数, sympy 我觉得是做不了的)。我现在的想法是对参数空间进行搜索,把参数空间的每一个点对应的解求出来,然后进行插值。这些用 scipy 都有函数可以做。

    但是我担心最后精度和稳定性的问题,因为我后面的超越方程要用到前面超越方程的解。不知道有没有人做过相关的事情?或者有现成的包推荐吗?谢谢!
    第 1 条附言  ·  2016-05-27 02:23:44 +08:00
    多谢诸位。解单变量的超越方程 scipy 里 fsolve 就可以,我想求的是把多变量超越方程里的一个变量关于其他参数的函数(因为下面的超越方程会用到,涉及到嵌套)。不过现在已经解决了,因为我意识到只要在后面的方程用到前面方程解的时候,再把参数传入前面方程求解,这样嵌套就能避免非得完全解决一个多变量方程解,才能解决下一个方程的问题了。感谢!
    8 条回复    2016-05-26 22:17:51 +08:00
    ayaseangle
        1
    ayaseangle  
       2016-05-26 19:29:55 +08:00
    为什么规定 python
    xiaket
        2
    xiaket  
       2016-05-26 19:50:14 +08:00
    话说, 写 python 去调 Mathematica 网站的 API 算不算违规...
    strider0505
        3
    strider0505  
       2016-05-26 20:08:05 +08:00   ❤️ 1
    #!/usr/bin/python3
    from math import log, exp
    ## ln(f)=ln(p)+q1*f=ln(p)+q1*exp[ln(f)]
    def f(p,q):
    lp=log(p)
    epsilon=1e-5
    ## initial guess
    y0=0
    y1=1
    while (y1-y0)>epsilon or (y0-y1)>epsilon:
    y1=lp+q*exp(y1)
    y0=y1
    return exp(y1)

    if __name__=="__main__":
    for p in range(10):
    for q in range(10):
    print("p=%s, q=%s, f=%s", p/10+0.1, q/10+0.1, f(p/10+0.1,q/10+0.1))



    结果:
    p=%s, q=%s, f=%s 0.1 0.1 0.13123614957214594
    p=%s, q=%s, f=%s 0.1 0.2 0.17222926954522666
    p=%s, q=%s, f=%s 0.1 0.30000000000000004 0.22602706178738802
    p=%s, q=%s, f=%s 0.1 0.4 0.2966292128808233
    p=%s, q=%s, f=%s 0.1 0.5 0.38928475749095637
    p=%s, q=%s, f=%s 0.1 0.6 0.510882326602397
    p=%s, q=%s, f=%s 0.1 0.7 0.6704622942775809
    p=%s, q=%s, f=%s 0.1 0.7999999999999999 0.8798888993429671
    p=%s, q=%s, f=%s 0.1 0.9 1.1547323120104451
    p=%s, q=%s, f=%s 0.1 1.0 1.5154262241479266
    p=%s, q=%s, f=%s 0.2 0.1 0.26247229914429193
    p=%s, q=%s, f=%s 0.2 0.2 0.3444585390904532
    p=%s, q=%s, f=%s 0.2 0.30000000000000004 0.45205412357477603
    p=%s, q=%s, f=%s 0.2 0.4 0.5932584257616464
    p=%s, q=%s, f=%s 0.2 0.5 0.7785695149819126
    p=%s, q=%s, f=%s 0.2 0.6 1.0217646532047937
    p=%s, q=%s, f=%s 0.2 0.7 1.3409245885551615
    p=%s, q=%s, f=%s 0.2 0.7999999999999999 1.759777798685934
    p=%s, q=%s, f=%s 0.2 0.9 2.3094646240208903
    p=%s, q=%s, f=%s 0.2 1.0 3.0308524482958528
    p=%s, q=%s, f=%s 0.30000000000000004 0.1 0.3937084487164379
    p=%s, q=%s, f=%s 0.30000000000000004 0.2 0.5166878086356799
    p=%s, q=%s, f=%s 0.30000000000000004 0.30000000000000004 0.678081185362164
    p=%s, q=%s, f=%s 0.30000000000000004 0.4 0.8898876386424697
    p=%s, q=%s, f=%s 0.30000000000000004 0.5 1.1678542724728689
    p=%s, q=%s, f=%s 0.30000000000000004 0.6 1.5326469798071907
    p=%s, q=%s, f=%s 0.30000000000000004 0.7 2.0113868828327424
    p=%s, q=%s, f=%s 0.30000000000000004 0.7999999999999999 2.639666698028901
    p=%s, q=%s, f=%s 0.30000000000000004 0.9 3.4641969360313354
    p=%s, q=%s, f=%s 0.30000000000000004 1.0 4.546278672443779
    p=%s, q=%s, f=%s 0.4 0.1 0.5249445982885838
    p=%s, q=%s, f=%s 0.4 0.2 0.6889170781809064
    p=%s, q=%s, f=%s 0.4 0.30000000000000004 0.9041082471495521
    p=%s, q=%s, f=%s 0.4 0.4 1.186516851523293
    p=%s, q=%s, f=%s 0.4 0.5 1.557139029963825
    p=%s, q=%s, f=%s 0.4 0.6 2.0435293064095874
    p=%s, q=%s, f=%s 0.4 0.7 2.681849177110323
    p=%s, q=%s, f=%s 0.4 0.7999999999999999 3.5195555973718675
    p=%s, q=%s, f=%s 0.4 0.9 4.61892924804178
    p=%s, q=%s, f=%s 0.4 1.0 6.061704896591705
    p=%s, q=%s, f=%s 0.5 0.1 0.6561807478607297
    p=%s, q=%s, f=%s 0.5 0.2 0.8611463477261331
    p=%s, q=%s, f=%s 0.5 0.30000000000000004 1.13013530893694
    p=%s, q=%s, f=%s 0.5 0.4 1.4831460644041161
    p=%s, q=%s, f=%s 0.5 0.5 1.9464237874547814
    p=%s, q=%s, f=%s 0.5 0.6 2.554411633011984
    p=%s, q=%s, f=%s 0.5 0.7 3.352311471387903
    p=%s, q=%s, f=%s 0.5 0.7999999999999999 4.399444496714834
    p=%s, q=%s, f=%s 0.5 0.9 5.773661560052224
    p=%s, q=%s, f=%s 0.5 1.0 7.57713112073963
    p=%s, q=%s, f=%s 0.6 0.1 0.7874168974328756
    p=%s, q=%s, f=%s 0.6 0.2 1.0333756172713595
    p=%s, q=%s, f=%s 0.6 0.30000000000000004 1.3561623707243278
    p=%s, q=%s, f=%s 0.6 0.4 1.7797752772849391
    p=%s, q=%s, f=%s 0.6 0.5 2.3357085449457373
    p=%s, q=%s, f=%s 0.6 0.6 3.065293959614381
    p=%s, q=%s, f=%s 0.6 0.7 4.022773765665484
    p=%s, q=%s, f=%s 0.6 0.7999999999999999 5.279333396057801
    p=%s, q=%s, f=%s 0.6 0.9 6.92839387206267
    p=%s, q=%s, f=%s 0.6 1.0 9.092557344887554
    p=%s, q=%s, f=%s 0.7 0.1 0.9186530470050215
    p=%s, q=%s, f=%s 0.7 0.2 1.205604886816586
    p=%s, q=%s, f=%s 0.7 0.30000000000000004 1.5821894325117158
    p=%s, q=%s, f=%s 0.7 0.4 2.0764044901657623
    p=%s, q=%s, f=%s 0.7 0.5 2.7249933024366935
    p=%s, q=%s, f=%s 0.7 0.6 3.5761762862167776
    p=%s, q=%s, f=%s 0.7 0.7 4.6932360599430645
    p=%s, q=%s, f=%s 0.7 0.7999999999999999 6.159222295400768
    p=%s, q=%s, f=%s 0.7 0.9 8.083126184073114
    p=%s, q=%s, f=%s 0.7 1.0 10.607983569035483
    p=%s, q=%s, f=%s 0.7999999999999999 0.1 1.0498891965771675
    p=%s, q=%s, f=%s 0.7999999999999999 0.2 1.3778341563618128
    p=%s, q=%s, f=%s 0.7999999999999999 0.30000000000000004 1.8082164942991037
    p=%s, q=%s, f=%s 0.7999999999999999 0.4 2.3730337030465853
    p=%s, q=%s, f=%s 0.7999999999999999 0.5 3.1142780599276496
    p=%s, q=%s, f=%s 0.7999999999999999 0.6 4.087058612819174
    p=%s, q=%s, f=%s 0.7999999999999999 0.7 5.363698354220644
    p=%s, q=%s, f=%s 0.7999999999999999 0.7999999999999999 7.039111194743734
    p=%s, q=%s, f=%s 0.7999999999999999 0.9 9.23785849608356
    p=%s, q=%s, f=%s 0.7999999999999999 1.0 12.123409793183411
    p=%s, q=%s, f=%s 0.9 0.1 1.1811253461493134
    p=%s, q=%s, f=%s 0.9 0.2 1.5500634259070394
    p=%s, q=%s, f=%s 0.9 0.30000000000000004 2.034243556086492
    p=%s, q=%s, f=%s 0.9 0.4 2.669662915927409
    p=%s, q=%s, f=%s 0.9 0.5 3.503562817418606
    p=%s, q=%s, f=%s 0.9 0.6 4.597940939421571
    p=%s, q=%s, f=%s 0.9 0.7 6.034160648498226
    p=%s, q=%s, f=%s 0.9 0.7999999999999999 7.919000094086702
    p=%s, q=%s, f=%s 0.9 0.9 10.392590808094004
    p=%s, q=%s, f=%s 0.9 1.0 13.638836017331336
    p=%s, q=%s, f=%s 1.0 0.1 1.3123614957214593
    p=%s, q=%s, f=%s 1.0 0.2 1.722292695452266
    p=%s, q=%s, f=%s 1.0 0.30000000000000004 2.26027061787388
    p=%s, q=%s, f=%s 1.0 0.4 2.966292128808232
    p=%s, q=%s, f=%s 1.0 0.5 3.8928475749095623
    p=%s, q=%s, f=%s 1.0 0.6 5.108823266023968
    p=%s, q=%s, f=%s 1.0 0.7 6.704622942775806
    p=%s, q=%s, f=%s 1.0 0.7999999999999999 8.798888993429669
    p=%s, q=%s, f=%s 1.0 0.9 11.54732312010445
    p=%s, q=%s, f=%s 1.0 1.0 15.154262241479262
    w466397352
        4
    w466397352  
       2016-05-26 20:18:07 +08:00 via iPhone
    数值分析啊…可惜当初全还给老师了_(:з」∠)_
    debiann
        5
    debiann  
       2016-05-26 20:20:42 +08:00 via iPhone
    用 mathematica 吧
    Mutoo
        6
    Mutoo  
       2016-05-26 20:51:15 +08:00
    @strider0505
    >>> "value=%s"%(1.0)
    'value=1.0'
    thekoc
        7
    thekoc  
       2016-05-26 22:17:07 +08:00
    不知道 sympy 行不行
    thekoc
        8
    thekoc  
       2016-05-26 22:17:51 +08:00
    上面那条画一个删除线,还是 mathematica 吧= =
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