IPZtest/test.py at master · Ladramhaiola/IPZtest · GitHub

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
# var 52
# y = f(x) для x<=0 : -(cos(x))^2
# y = f(x) для x>=0 : (cos(x))^2 - 2
# x_min : -pi/2
# x_max : +pi/2
# x0 ^ a : x6

from functools import wraps
from matplotlib import pyplot as plt
import numpy as np
from math import cos, pi, sin, sqrt
from scipy import cbrt

# constants
x_min = -pi/2
x_max = pi/2
# plt.style.use('dark_background')
plt.style.use('seaborn')
# plt.style.use('grayscale')

def plot(path):
	def dec(func):
		@wraps(func)
		def savefig(xx, name, *args):
			fig = plt.figure(name)
			sub = plt.subplot()
			sub.set_xlabel('x-axis')
			sub.set_ylabel('y-axis')
			sub.set_title(name)
			if len(args) > 0:
				xx, yy, xmp, ymp = func(xx, name, *args)
				x_negative = list(filter(lambda x: x < 0, xx))
				x_positive = list(filter(lambda x: x > 0, xx))
				sub.plot(x_negative, yy[:len(x_negative)], zorder=1)
				sub.plot(x_positive, yy[-len(x_positive):], zorder=1)
				sub.scatter(xmp, ymp, marker='x', color='crimson', zorder=2)
			else:
				yy = func(xx, name, *args)
				sub.plot(xx, yy, zorder=1)
				e_x, e_y = [xx[0], xx[-1]], [yy[0], yy[-1]] # межі
				sub.scatter(e_x, e_y, marker='o', color='crimson', zorder=2)
			fig.add_subplot(sub)
			# path = './img/' + name + '.svg'
			fpath = './img/' + path + '.png'
			plt.savefig(fpath, format='png', dpi=400)
			return fig
		return savefig
	return dec

@plot('func')
def f(xx, name):
	yy = []
	for x in xx:
		if x < 0:
			yy.append(-(cos(x))**2)
		elif x > 0:
			yy.append((cos(x))**2 - 2)
		else:
			yy.append(-2)
	return yy

xx = np.linspace(x_min, x_max, 2000)

# 2
@plot('second derivative')
def d2y(xx, name, *args):
	"""
	dy2/dx2 (second derivative)
	f''(x) = 2*cos(2x)\n
	f''(x) = -2*cos(2x)\n
	"""
	yy = []
	for x in xx:
		if x < 0:
			yy.append(2*cos(2*x))
		elif x > 0:
			yy.append(-2*cos(2*x))
		else: yy.append(0)
	return xx, yy, 0, 0

#3
@plot('abs second derivative')
def d2y_abs(xx, name):
	return list([abs(2*cos(2*x)) for x in xx])

# f(xx, 'f(x)')
# d2y(xx, 'Графік другої похідної d^2y/dx^2', 'sder')
# d2y_abs(xx, 'Графік модулю другої похідної |d^2y/dx^2|')

# 4
# (-pi/2, -pi/4), (0, pi/4) ф-я опукла (f''(x)<0)
# (-pi/4, 0), (pi/4, pi/2) ф-я вгнута (f''(x)>0)
# -pi/4, pi/4, 0 - точки перегину
# 0 - точка розриву першого роду lim2 = 2, lim-2 = -2 -> 2 != -2, 2 != -1

@plot('ilya f(x)')
def iif(xx, name):
	yy = []
	for x in xx:
		if x > 0:
			try:
				yy.append(sqrt(cos(x)) - 2)
			except ValueError:
				yy.append(3)
		elif x < 0:
			try:
				yy.append(-sqrt(cos(x)))
			except ValueError:
				yy.append(3)
		else:
			yy.append(-1)
	return yy

@plot('ilya sder')
def isder(xx, name, *args):
	yy, xc = [], []
	xmp, ymp = 0, 0
	for x in xx:
		if x > 0:
			try:
				yy.append(-sqrt(cos(x))/2.0 - sin(x)**2/4/cos(x)**(3/2.0))
				xc.append(x)
			except ValueError: pass
		elif x < 0:
			try:
				yy.append((cos(2*x) + 3)/8/cos(x)**(3/2.0))
				xc.append(x)
			except ValueError: pass
		else:
			pass
	return xc, yy, xmp, ymp

@plot('ilya abs sder')
def iabsder(xx, name, *args):
	yy, xc = [], []
	xmp, ymp = 0, 0
	for x in xx:
		if x > 0:
			try:
				yy.append(abs(-sqrt(cos(x))/2.0 - sin(x)**2/4/cos(x)**(3/2.0)))
				xc.append(x)
			except ValueError: pass
		elif x < 0:
			try:
				yy.append(abs((cos(2*x) + 3)/8/cos(x)**(3/2.0)))
				xc.append(x)
			except ValueError: pass
		else:
			pass
	return xc, yy, xmp, ymp

xi = np.linspace(-pi/2, pi/2, 2000)
xid = np.linspace(-1.5, 1.5, 2000)
yy = iif(xi, 'f(x)')
isder(xid, 'd2y/dx2', 'sder')
iabsder(xid, '|d2y/dx2|', 'abs')