# -*- coding: utf-8 -*-

from adipy import ad, sin, adn

#ad object creation
x = ad(1.5)

#Substitute x squared for y
y = x**2
print y
# ad(2.25, array([ 3.]))
# array([ 3.])"3" is the value obtained by differentiating y once and substituting x.

# dy(1)/dx
print y.d(1)
# 3.0

z = x*sin(x**2)
print z
# ad(1.1671097953318819, array([-2.04870811]))

# dy(1)/dx
print z.d(1)
# -2.04870810536

#adn object creation
#The second argument 4 is calculated up to the fourth derivative
x = adn(1.5, 4)

y = x**2
print y
# ad(2.25, array([ 3.,  2.,  0., -0.]))

# dy(２)/dx
print y.d(2)
# 2.0

z = x*sin(x**2)
print z
# ad(1.1671097953318819, array([  -2.04870811,  -16.15755076,  -20.34396265,  194.11618384]))

# dy(４)/dx
print z.d(4)
# 194.116183837

# -*- coding: utf-8 -*-

from adipy import adn, sin, taylorfunc
import matplotlib.pyplot as plt
import numpy as np

#adn object creation
xAD = [adn(1.5, i) for i in xrange(1, 7)]

def z(x):
    return x*sin(x**2)

#Set the x-axis range of the graph
x = np.linspace(0.75, 2.25)
#Label and draw the original function as an Actual Function
plt.plot(x, z(x), label='Actual Function')


for i in xrange(len(xAD)):
    #Use Taylor polynomial
    fz = taylorfunc(z(xAD[i]), at=xAD[i].nom)
    plt.plot(x, fz(x), label='Order %d Taylor'%(i+1))

#Set the position of the function label
plt.legend(loc=0)
plt.show()

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