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  • from sympy import *from sympy import log,sin,expimport math #定义变量为xx=Symbol("x") #函数为def taylor (f = x**4,n = 10,x0 = 0,t = 2):#n = 100 #泰勒展开项数i = 0F = list()#n阶导while i <...

    from sympy import *

    from sympy import log,sin,exp

    import math #定义变量为x

    x=Symbol("x") #函数为

    def taylor (f = x**4,n = 10,x0 = 0,t = 2):

    #n = 100 #泰勒展开项数

    i = 0

    F = list()

    #n阶导

    while i <= n:

    f1 = diff(f,x,i)

    value = f.evalf(subs={x: x0})

    F.append(value)

    i = i+1

    print (F)

    #求阶乘

    M = list()

    for i in range (n+1):

    if i == 0:

    M.append(1)

    else:

    for j in range(i):

    if j == 0:

    v = 1

    else:

    v = v*(j+1)

    M.append(v)

    print (M)

    #求(x - x0)^i

    J = list()

    for i in range(n+1):

    v = (t - x0)**i

    J.append(v)

    print (J)

    V = list()

    for i in range(n+1):

    value = J[i]/M[i]*F[i]

    V.append(value)

    return sum(V)

    def main():

    f = exp(x)

    n = int(input('请输入泰勒展开项数'))

    x0 = int(input('请输入x0'))

    t = int(input('请输入x'))

    value = f.evalf(subs={x: t})

    predict = taylor(f,n,x0,t)

    print (value)

    print (predict)

    main()

    默认f(x) = exp(x)

    请输入泰勒展开项数10

    请输入x02

    请输入x9

    [7.38905609893065, 7.38905609893065, 7.38905609893065, 7.38905609893065, 7.38905609893065, 7.38905609893065, 7.38905609893065, 7.38905609893065, 7.38905609893065, 7.38905609893065, 7.38905609893065]

    [1, 1, 2, 6, 24, 120, 720, 5040, 40320, 362880, 3628800]

    [1, 7, 49, 343, 2401, 16807, 117649, 823543, 5764801, 40353607, 282475249]

    8103.08392757538

    7304.76166428328

    请输入泰勒展开项数10

    请输入x05

    请输入x9

    [148.413159102577, 148.413159102577, 148.413159102577, 148.413159102577, 148.413159102577, 148.413159102577, 148.413159102577, 148.413159102577, 148.413159102577, 148.413159102577, 148.413159102577]

    [1, 1, 2, 6, 24, 120, 720, 5040, 40320, 362880, 3628800]

    [1, 4, 16, 64, 256, 1024, 4096, 16384, 65536, 262144, 1048576]8103.08392757538

    8080.07306436618

    可见泰勒公式的近似值与x0无关

    /usr/bin/python3.5 /home/rui/ComputerScience/PythonProjects/数值分析/Taylor.py

    请输入泰勒展开项数100

    请输入x05

    请输入x9

    [148.413159102577, 148.413159102577, 148.413159102577, 148.413159102577, 148.413159102577, 148.413159102577, 148.413159102577, 148.413159102577, 148.413159102577, 148.413159102577, 148.413159102577, 148.413159102577, 148.413159102577, 148.413159102577, 148.413159102577, 148.413159102577, 148.413159102577, 148.413159102577, 148.413159102577, 148.413159102577, 148.413159102577, 148.413159102577, 148.413159102577, 148.413159102577, 148.413159102577, 148.413159102577, 148.413159102577, 148.413159102577, 148.413159102577, 148.413159102577, 148.413159102577, 148.413159102577, 148.413159102577, 148.413159102577, 148.413159102577, 148.413159102577, 148.413159102577, 148.413159102577, 148.413159102577, 148.413159102577, 148.413159102577, 148.413159102577, 148.413159102577, 148.413159102577, 148.413159102577, 148.413159102577, 148.413159102577, 148.413159102577, 148.413159102577, 148.413159102577, 148.413159102577, 148.413159102577, 148.413159102577, 148.413159102577, 148.413159102577, 148.413159102577, 148.413159102577, 148.413159102577, 148.413159102577, 148.413159102577, 148.413159102577, 148.413159102577, 148.413159102577, 148.413159102577, 148.413159102577, 148.413159102577, 148.413159102577, 148.413159102577, 148.413159102577, 148.413159102577, 148.413159102577, 148.413159102577, 148.413159102577, 148.413159102577, 148.413159102577, 148.413159102577, 148.413159102577, 148.413159102577, 148.413159102577, 148.413159102577, 148.413159102577, 148.413159102577, 148.413159102577, 148.413159102577, 148.413159102577, 148.413159102577, 148.413159102577, 148.413159102577, 148.413159102577, 148.413159102577, 148.413159102577, 148.413159102577, 148.413159102577, 148.413159102577, 148.413159102577, 148.413159102577, 148.413159102577, 148.413159102577, 148.413159102577, 148.413159102577, 148.413159102577]

    [1, 1, 2, 6, 24, 120, 720, 5040, 40320, 362880, 3628800, 39916800, 479001600, 6227020800, 87178291200, 1307674368000, 20922789888000, 355687428096000, 6402373705728000, 121645100408832000, 2432902008176640000, 51090942171709440000, 1124000727777607680000, 25852016738884976640000, 620448401733239439360000, 15511210043330985984000000, 403291461126605635584000000, 10888869450418352160768000000, 304888344611713860501504000000, 8841761993739701954543616000000, 265252859812191058636308480000000, 8222838654177922817725562880000000, 263130836933693530167218012160000000, 8683317618811886495518194401280000000, 295232799039604140847618609643520000000, 10333147966386144929666651337523200000000, 371993326789901217467999448150835200000000, 13763753091226345046315979581580902400000000, 523022617466601111760007224100074291200000000, 20397882081197443358640281739902897356800000000, 815915283247897734345611269596115894272000000000, 33452526613163807108170062053440751665152000000000, 1405006117752879898543142606244511569936384000000000, 60415263063373835637355132068513997507264512000000000, 2658271574788448768043625811014615890319638528000000000, 119622220865480194561963161495657715064383733760000000000, 5502622159812088949850305428800254892961651752960000000000, 258623241511168180642964355153611979969197632389120000000000, 12413915592536072670862289047373375038521486354677760000000000, 608281864034267560872252163321295376887552831379210240000000000, 30414093201713378043612608166064768844377641568960512000000000000, 1551118753287382280224243016469303211063259720016986112000000000000, 80658175170943878571660636856403766975289505440883277824000000000000, 4274883284060025564298013753389399649690343788366813724672000000000000, 230843697339241380472092742683027581083278564571807941132288000000000000, 12696403353658275925965100847566516959580321051449436762275840000000000000, 710998587804863451854045647463724949736497978881168458687447040000000000000, 40526919504877216755680601905432322134980384796226602145184481280000000000000, 2350561331282878571829474910515074683828862318181142924420699914240000000000000, 138683118545689835737939019720389406345902876772687432540821294940160000000000000, 8320987112741390144276341183223364380754172606361245952449277696409600000000000000, 507580213877224798800856812176625227226004528988036003099405939480985600000000000000, 31469973260387937525653122354950764088012280797258232192163168247821107200000000000000, 1982608315404440064116146708361898137544773690227268628106279599612729753600000000000000, 126886932185884164103433389335161480802865516174545192198801894375214704230400000000000000, 8247650592082470666723170306785496252186258551345437492922123134388955774976000000000000000, 544344939077443064003729240247842752644293064388798874532860126869671081148416000000000000000, 36471110918188685288249859096605464427167635314049524593701628500267962436943872000000000000000, 2480035542436830599600990418569171581047399201355367672371710738018221445712183296000000000000000, 171122452428141311372468338881272839092270544893520369393648040923257279754140647424000000000000000, 11978571669969891796072783721689098736458938142546425857555362864628009582789845319680000000000000000, 850478588567862317521167644239926010288584608120796235886430763388588680378079017697280000000000000000, 61234458376886086861524070385274672740778091784697328983823014963978384987221689274204160000000000000000, 4470115461512684340891257138125051110076800700282905015819080092370422104067183317016903680000000000000000, 330788544151938641225953028221253782145683251820934971170611926835411235700971565459250872320000000000000000, 24809140811395398091946477116594033660926243886570122837795894512655842677572867409443815424000000000000000000, 1885494701666050254987932260861146558230394535379329335672487982961844043495537923117729972224000000000000000000, 145183092028285869634070784086308284983740379224208358846781574688061991349156420080065207861248000000000000000000, 11324281178206297831457521158732046228731749579488251990048962825668835325234200766245086213177344000000000000000000, 894618213078297528685144171539831652069808216779571907213868063227837990693501860533361810841010176000000000000000000, 71569457046263802294811533723186532165584657342365752577109445058227039255480148842668944867280814080000000000000000000, 5797126020747367985879734231578109105412357244731625958745865049716390179693892056256184534249745940480000000000000000000, 475364333701284174842138206989404946643813294067993328617160934076743994734899148613007131808479167119360000000000000000000, 39455239697206586511897471180120610571436503407643446275224357528369751562996629334879591940103770870906880000000000000000000, 3314240134565353266999387579130131288000666286242049487118846032383059131291716864129885722968716753156177920000000000000000000, 281710411438055027694947944226061159480056634330574206405101912752560026159795933451040286452340924018275123200000000000000000000, 24227095383672732381765523203441259715284870552429381750838764496720162249742450276789464634901319465571660595200000000000000000000, 2107757298379527717213600518699389595229783738061356212322972511214654115727593174080683423236414793504734471782400000000000000000000, 185482642257398439114796845645546284380220968949399346684421580986889562184028199319100141244804501828416633516851200000000000000000000, 16507955160908461081216919262453619309839666236496541854913520707833171034378509739399912570787600662729080382999756800000000000000000000, 1485715964481761497309522733620825737885569961284688766942216863704985393094065876545992131370884059645617234469978112000000000000000000000, 135200152767840296255166568759495142147586866476906677791741734597153670771559994765685283954750449427751168336768008192000000000000000000000, 12438414054641307255475324325873553077577991715875414356840239582938137710983519518443046123837041347353107486982656753664000000000000000000000, 1156772507081641574759205162306240436214753229576413535186142281213246807121467315215203289516844845303838996289387078090752000000000000000000000, 108736615665674308027365285256786601004186803580182872307497374434045199869417927630229109214583415458560865651202385340530688000000000000000000000, 10329978488239059262599702099394727095397746340117372869212250571234293987594703124871765375385424468563282236864226607350415360000000000000000000000, 991677934870949689209571401541893801158183648651267795444376054838492222809091499987689476037000748982075094738965754305639874560000000000000000000000, 96192759682482119853328425949563698712343813919172976158104477319333745612481875498805879175589072651261284189679678167647067832320000000000000000000000, 9426890448883247745626185743057242473809693764078951663494238777294707070023223798882976159207729119823605850588608460429412647567360000000000000000000000, 933262154439441526816992388562667004907159682643816214685929638952175999932299156089414639761565182862536979208272237582511852109168640000000000000000000000, 93326215443944152681699238856266700490715968264381621468592963895217599993229915608941463976156518286253697920827223758251185210916864000000000000000000000000]

    [1, 4, 16, 64, 256, 1024, 4096, 16384, 65536, 262144, 1048576, 4194304, 16777216, 67108864, 268435456, 1073741824, 4294967296, 17179869184, 68719476736, 274877906944, 1099511627776, 4398046511104, 17592186044416, 70368744177664, 281474976710656, 1125899906842624, 4503599627370496, 18014398509481984, 72057594037927936, 288230376151711744, 1152921504606846976, 4611686018427387904, 18446744073709551616, 73786976294838206464, 295147905179352825856, 1180591620717411303424, 4722366482869645213696, 18889465931478580854784, 75557863725914323419136, 302231454903657293676544, 1208925819614629174706176, 4835703278458516698824704, 19342813113834066795298816, 77371252455336267181195264, 309485009821345068724781056, 1237940039285380274899124224, 4951760157141521099596496896, 19807040628566084398385987584, 79228162514264337593543950336, 316912650057057350374175801344, 1267650600228229401496703205376, 5070602400912917605986812821504, 20282409603651670423947251286016, 81129638414606681695789005144064, 324518553658426726783156020576256, 1298074214633706907132624082305024, 5192296858534827628530496329220096, 20769187434139310514121985316880384, 83076749736557242056487941267521536, 332306998946228968225951765070086144, 1329227995784915872903807060280344576, 5316911983139663491615228241121378304, 21267647932558653966460912964485513216, 85070591730234615865843651857942052864, 340282366920938463463374607431768211456, 1361129467683753853853498429727072845824, 5444517870735015415413993718908291383296, 21778071482940061661655974875633165533184, 87112285931760246646623899502532662132736, 348449143727040986586495598010130648530944, 1393796574908163946345982392040522594123776, 5575186299632655785383929568162090376495104, 22300745198530623141535718272648361505980416, 89202980794122492566142873090593446023921664, 356811923176489970264571492362373784095686656, 1427247692705959881058285969449495136382746624, 5708990770823839524233143877797980545530986496, 22835963083295358096932575511191922182123945984, 91343852333181432387730302044767688728495783936, 365375409332725729550921208179070754913983135744, 1461501637330902918203684832716283019655932542976, 5846006549323611672814739330865132078623730171904, 23384026197294446691258957323460528314494920687616, 93536104789177786765035829293842113257979682750464, 374144419156711147060143317175368453031918731001856, 1496577676626844588240573268701473812127674924007424, 5986310706507378352962293074805895248510699696029696, 23945242826029513411849172299223580994042798784118784, 95780971304118053647396689196894323976171195136475136, 383123885216472214589586756787577295904684780545900544, 1532495540865888858358347027150309183618739122183602176, 6129982163463555433433388108601236734474956488734408704, 24519928653854221733733552434404946937899825954937634816, 98079714615416886934934209737619787751599303819750539264, 392318858461667547739736838950479151006397215279002157056, 1569275433846670190958947355801916604025588861116008628224, 6277101735386680763835789423207666416102355444464034512896, 25108406941546723055343157692830665664409421777856138051584, 100433627766186892221372630771322662657637687111424552206336, 401734511064747568885490523085290650630550748445698208825344, 1606938044258990275541962092341162602522202993782792835301376]

    8103.08392757538

    8103.08392757538

    当项数达到100时可见已经十分逼近正确值

    展开全文
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    展开全文
  • 这样做是为了解析您希望扩展为泰勒级数的函数的代码,使用Sympy将其转换为符号表示,然后计算泰勒扩展。一个限制是您需要具有显式的函数定义,因此您不能使用lambda表达式。 这可以通过进一步的工作来解决。 否则,...

    以下代码与您正在寻找的代码很接近。 这样做是为了解析您希望扩展为泰勒级数的函数的代码,使用Sympy将其转换为符号表示,然后计算泰勒扩展。

    一个限制是您需要具有显式的函数定义,因此您不能使用lambda表达式。 这可以通过进一步的工作来解决。 否则,代码将满足您的要求。 请注意,定义函数时,该函数必须包含y = ...形式的行,此代码才能工作

    from inspect import *

    import sympy

    def f(x):

    # a very complicated function

    y = sin(x) + cos(x) + log(abs(x)+2)**2/e**2 + sin(cos(x/2)**2) + 1

    return y

    def my_sin(x):

    y = sin(x)

    return y

    def my_exp(x):

    y = e**x

    return y

    x = sympy.Symbol('x')

    def get_polynomial(function, x0, degree):

    # parse function definition code

    lines_list = getsource(function).split("\n")

    for line in lines_list:

    if '=' in line:

    func_def = line

    elements = func_def.split('=')

    line = ' '.join(elements[1:])

    sympy_function = sympy.sympify(line)

    # compute taylor expansion symbolically

    i = 0

    taylor_exp = sympy.Integer(0)

    while i <= degree:

    taylor_exp = taylor_exp + (sympy.diff(sympy_function,x,i).subs(x,x0))/(sympy.factorial(i))*(x-x0)**i

    i += 1

    return taylor_exp

    print (get_polynomial(my_sin,0,5))

    print (get_polynomial(my_exp,0,5))

    print (get_polynomial(f,0,5))

    展开全文
  • 这是为了解析函数的代码,你想把它展开成泰勒级数,用Sympy把它转换成符号表示,然后计算泰勒展开。在一个限制是需要有一个显式函数定义,这样就不能使用lambda表达式。这可以通过进一步的工作来解决。否则代码就...

    下面的代码与您要查找的代码非常接近。这是为了解析函数的代码,你想把它展开成泰勒级数,用Sympy把它转换成符号表示,然后计算泰勒展开。在

    一个限制是需要有一个显式函数定义,这样就不能使用lambda表达式。这可以通过进一步的工作来解决。否则代码就可以满足您的要求。请注意,当您定义一个函数时,它必须包含y = ...形式的一行代码才能工作from inspect import *

    import sympy

    def f(x):

    # a very complicated function

    y = sin(x) + cos(x) + log(abs(x)+2)**2/e**2 + sin(cos(x/2)**2) + 1

    return y

    def my_sin(x):

    y = sin(x)

    return y

    def my_exp(x):

    y = e**x

    return y

    x = sympy.Symbol('x')

    def get_polynomial(function, x0, degree):

    # parse function definition code

    lines_list = getsource(function).split("\n")

    for line in lines_list:

    if '=' in line:

    func_def = line

    elements = func_def.split('=')

    line = ' '.join(elements[1:])

    sympy_function = sympy.sympify(line)

    # compute taylor expansion symbolically

    i = 0

    taylor_exp = sympy.Integer(0)

    while i <= degree:

    taylor_exp = taylor_exp + (sympy.diff(sympy_function,x,i).subs(x,x0))/(sympy.factorial(i))*(x-x0)**i

    i += 1

    return taylor_exp

    print (get_polynomial(my_sin,0,5))

    print (get_polynomial(my_exp,0,5))

    print (get_polynomial(f,0,5))

    展开全文
  • I'm trying to build an approximation for ln(1.9) within ten digits of accuracy (so .641853861).I'm using a simple function I've built from ln[(1 + x)/(1 - x)]Here is my code so far:# function for ln[...
  • 正如@asmurer所描述的,现在这是可能的from sympy import init_printing, symbols, Functioninit_printing()x, h = symbols("x,h")f = Function("f")pprint(f(x).series(x, x0=h, n=3))或者from sympy import ...
  • 题目:c++:用下列泰勒级数求sinx的近似值,x的值从键盘输入,精度要求为10-6.sinx=x-(x3)/3!+(x5)/5!+...+{(-1)n-1*x(2n-1)}/(20-1)!次方的上标不会打请多多见见谅请编写程序解答:首先,我们知道sin(x) = sin(x+k*2pi)...
  • 正弦函数两种泰勒展开式的比较张文华,汲守峰【摘要】摘要:讨论了正弦函数在两种不同情况下的泰勒公式展开式,并利用余项比较两种展开式在近似计算中误差的大小区别,解释了正弦函数展开式中经常展开偶数项而不是...
  • 也许有点过头了,但这里有个不错的解决方法,用辛普森法来计算无穷级数。from sympy.abc import kfrom sympy import Sum, oo as infimport mathx = 0.5result = Sum((x**(2*k-1) /(2*k-1)) - (x**(2*k) / (2*k)),(k,...
  • python泰勒展开

    千次阅读 2019-10-01 18:46:55
    Taylor展开式的应用 ' , fontsize=18 ) plt.xlabel( ' X ' , fontsize=15 ) plt.ylabel( ' exp(X) ' , fontsize=15 ) plt.grid(True) plt.show()   转载于:...
  • 展开全部e的x次方在x0=0的泰勒展开式是1+x+x^2/2!32313133353236313431303231363533e4b893e5b19e31333431373937+x^3/3!+...+x^n/n!+Rn(x) ,求解过程如下:把e^x在x=0处展开得:f(x)=e^x= f(0)+ f′(0)x+ f″(0)x ²...
  • 15楼兄弟 我可能找到了你说的那个dsp算法 但是汇编的 大家帮忙用c语言描述下;***********************************************************************;;* *;;* File Name ...
  • 求解方程的解有两种方法,一种是泰勒展开,一种是二分法。 class Solution: def mySqrt(self, x: int) -> int: x_k = 1 while True: x_k2 = x_k - (x_k**2-x)/(2.0*x_k) if abs(x_k2-x_k)(x_k2) 参考: 计算方法:...
  • Python-用泰勒展开求解COS函数

    千次阅读 2019-03-30 13:55:00
    直接贴代码吧,泰勒展开没什么好说的 #-*-coding:utf8;-*- #qpy:3 #qpy:console import math print("This is console module") def fa(a): b=1 while a!=1: b*=a a-=1 return b def taylor(x,n): a=1 count...
  • 我仿佛已经勉强跟上了一个叫泰勒的人的脚步了 有个不恰当的比喻,扶手电梯的台阶不断下降,但扶手电梯还是扶手电梯,看不出任何变化,其实还是有变化的。 作为一个学渣,能理解到这一步,我很欣慰!!! 有空我会...
  • 我仿佛已经勉强跟上了一个叫泰勒的人的脚步了 有个不恰当的比喻,扶手电梯的台阶不断下降,但扶手电梯还是扶手电梯,看不出任何变化,其实还是有变化的。 作为一个学渣,能理解到这一步,我很欣慰!!! 有空我会...
  • 首先来看一下大名鼎鼎的泰勒展开式: 看到这个公式的时候,也许你马上就会感到崩溃,如此复杂的公式,我怎么可能编辑的出来呢? 不用担心,我们将一步步的为大家分解,完成这样的一个公式编辑,需要掌握的基础知识...
  • 下面我先不加预告地列出函数f(x)在x=0处展开泰勒级数的定义:我们的高中数学知识告诉我们对指数函数无论求多次导,还是其本身:因而依据上面的定义展开有:多项式近似(Polynomial Approximantion)多项式近似的本质...
  • 机器学习之 sklearn 线性回归之泰勒展开导入相关依赖构造数据按照同样的方法生成测试集数据打印数据形状查看训练集数据分布训练普通线性模型绘图基于线性回归的泰勒展开计算该模型的mse评分绘 tlzk 模型的图 ...
  • 二、非线性方程线性化,通过## 标题调用matlab并运用泰勒展开式 解决思路: 1、运用python调用matlab中taylor函数对非线性方程进行线性展开 2、编写matlab .m脚本,并在脚本中调用matlab库taylor函数 3、通过...
  • 下面我先不加预告地列出函数f(x)在x=0处展开泰勒级数的定义:我们的高中数学知识告诉我们对指数函数无论求多次导,还是其本身:因而依据上面的定义展开有:多项式近似(Polynomial Approximantion)多项式近似的本质...
  • 泰勒展开式的理解

    2018-09-30 17:12:00
    2019独角兽企业重金招聘Python工程师标准>>> ...
  • python麦克劳林级数展开

    千次阅读 2019-06-08 15:07:25
    我们利用python的sympy模块能够很方便的进行科学计算,可以利用它对变量表达式进行泰勒展开并绘制图像,下面是我对sin(x)进行麦克劳林展开并绘制图像 from matplotlib import pyplot as plt import numpy as np ...
  • 在上一篇《机器学习1》中提到梯度下降算法并列出了代数表达式,来看一下代数实现下面我们把它放到python 3里面,转变成代码的形式去实现梯度下降。import numpy as np X=2*np.random.rand(100,1)#生成训练函数(特征...
  • 2019独角兽企业重金招聘Python工程师标准>>> ...
  • 在上一篇《机器学习1》中提到梯度下降算法并列出了代数表达式,来看一下代数实现下面我们把它放到python 3里面,转变成代码的形式去实现梯度下降。import numpy as np X=2*np.random.rand(100,1)#生成训练函数(特征...
  • /usr/bin/python# -*- coding:utf-8 -*-import numpy as npimport mathimport matplotlib as mplimport matplotlib.pyplot as plt2注意事项exp(x)的近似求解方案:ln2 = 0.69314718055994530941723212145818(2)...
  • 下面我先不加预告地列出函数f(x)在x=0处展开泰勒级数的定义:我们的高中数学知识告诉我们对指数函数无论求多次导,还是其本身:因而依据上面的定义展开有:多项式近似(Polynomial Approximantion)多项式近似的本质...

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