Created
April 17, 2020 18:09
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See programmilõik käib kaasas minu kodutööga, mille eesmärgiks oli lähendada Taylori valemiga funktsiooni f(x) = ln(x).
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| import matplotlib | |
| import numpy as np | |
| from math import * | |
| import matplotlib.pyplot as plt | |
| '''Funktsioon, mida peame lähendama: f(x) = ln(x)''' | |
| def f(x): | |
| output = [] | |
| for elem in x: | |
| output.append(log(elem)) | |
| return np.asarray(output) | |
| '''See funktsioon loob Taylori polünoomi konstandid. | |
| Konstandid on ümardatud kümne komakoha täpsuseni, et | |
| vältida segadust 64-bitiste arvude aritmeetikaga -- | |
| null olgu võrdne nulliga, mitte nullilähedase väärtusega!''' | |
| def coef(n): | |
| value = 1/n*(-1)**(n+1) | |
| return round(value,10) | |
| def taylor(n): | |
| def P(x): | |
| total = log(4) | |
| for i in range(1, n+1): | |
| total += ((x-4)/4)**i * coef(i) | |
| return total | |
| return P | |
| P = taylor(5) | |
| x = np.linspace(3, 5, num=40) | |
| plt.plot(x, f(x)-P(x), 'bo',label="f(x)-T_5(x)") | |
| plt.legend(loc="best") | |
| plt.show() | |
| x = np.linspace(1, 8, num=40) | |
| plt.plot(x, P(x), 'bo', label="T_5(x)") | |
| plt.plot(x, f(x), 'r-', label="f(x)") | |
| plt.legend(loc="upper left") | |
| plt.show() |
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