15-1 立方：數字的三次方被稱為其立方。請繪製一個圖形，顯示前5個整數的立方值，在繪製一個圖形，顯示前面5000個整數的立方值。

 前5個整數的立方值：

import matplotlib.pyplot as plt

x_values  = [1,2,3,4,5]
y_values = [1,8,27,64,125]
plt.title("Li Fang ")
plt.plot(x_values,y_values,linewidth = 5)
plt.xlabel("Value",fontsize = 14)
plt.ylabel("Square of Value",fontsize = 14)
plt.tick_params(axis = 'both' , labelsize = 14)
plt.show()
 

結果：

前面5000個整數的立方值：

import matplotlib.pyplot as plt

x_values  = list(range(1,50001))
y_values = [x**3 for x in x_values]
plt.title("Li Fang ")
plt.scatter(x_values,y_values,linewidth = 5,edgecolor = 'none')
plt.xlabel("Value",fontsize = 14)
plt.ylabel("Square of Value",fontsize = 14)
plt.tick_params(axis = 'both' , labelsize = 14)
plt.show()
 

結果：

15-2 彩色立方：給你前面的立方圖指定顏色對映

import matplotlib.pyplot as plt

x_values  = [1,2,3,4,5]
y_values = [1,8,27,64,125]
plt.title("Li Fang ")
plt.plot(x_values,y_values,linewidth = 5,c = 'red')
plt.xlabel("Value",fontsize = 14)
plt.ylabel("Square of Value",fontsize = 14)
plt.tick_params(axis = 'both' , labelsize = 14)
plt.show()
 

結果：

15-3 分子運動：修改rw_visual.py，將其中的plt.scatter()替換為plt.plot()，為模擬花粉在水滴表面的運動路徑，向plt.plot()傳遞rw.x_values和rw.y_values，並指定實參值linewidth。使用5000個點而不是50000個點。

rw_visual.py

import matplotlib.pyplot as plt

from random_walk import RandomWalk
rw = RandomWalk()
rw.fill_walk()
plt.plot(rw.x_values,rw.y_values,linewidth = 2)

plt.show()

random_walk.py

from random import choice
class RandomWalk(object):
	"""docstring for RandomWalk"""
	def __init__(self, num_points = 5000):
		self.num_points = num_points

		self.x_values = [0]
		self.y_values = [0]

	def fill_walk(self):
		while len(self.x_values) < self.num_points: 
			x_direction = choice([1,-1])
			x_distance = choice([0,1,2,3,4])
			x_step = x_direction * x_distance

			y_direction = choice([1,-1])
			y_distance = choice([0,1,2,3,4])
			y_step = y_direction * y_distance

			if x_step == 0  and y_step ==0:
				continue
			else:
				next_x = self.x_values[-1] + x_step
				next_y = self.y_values[-1] + y_step

				self.x_values.append(next_x)
				self.y_values.append(next_y)

結果：

15-4 改進的隨機漫步：在類RandomWalk中，x_step 和 y_step 是根據相同的條件生成的：從列表【1，-1】中隨機地選擇方向，並經列表【0,1,2,3,4】中隨機地選擇距離。請修改這些列表中的值，看看對隨機漫步路徑有何影響。長沙使用更長距離選擇列表，如0~8；或者將-1從x或y方向列表中刪除

15-5 重構：方法fill_walk()很長。請新建一個名為get_step()的方法，用於確定每次漫步的距離和方向，並計算這次漫步將如何移動。然後，在fill_work() 中呼叫get_step()兩次：

x_step = self.get_step()

y_step = self.get_step()

通過這樣的重構，可縮小fill_walk() 的規模，讓這個方法閱讀和理解起來更容易

from random import choice class RandomWalk(object): """docstring for RandomWalk""" def __init__(self, num_points = 5000): self.num_points = num_points self.x_values = [0] self.y_values = [0] def fill_walk(self): while len(self.x_values)< self.num_points: x_step = self.get_step() y_step = self.get_step() if x_step == 0 and y_step ==0: continue else: next_x = self.x_values[-1] + x_step next_y = self.y_values[-1] + y_step self.x_values.add(next_x) self.y_values.add(next_y) def get_step(self): direction = choice([1,-1]) distance = choice([0,1,2,3,4]) step = direction * distance return step
15-6 自動生成標籤：請修改die.py 和 dice_visual.py，將用來設定 hist.x_labels 值的列表替換為位元組自動生成這種列表的迴圈。如果你熟悉列表解析，可嘗試將 die_visual.py 和 dice_visual.py 中的其他 for 迴圈也替換為列表解析。

die_visual.py

from die import Die
import pygal
def num2char(x):
	return str(x)
die1 = Die()
die2 = Die()
results = []

for roll_num in range(1000):
	result = die1.roll() + die2.roll()
	results.append(result)
# print(results)
frequencies = []
max_result = die1.num_sides + die2.num_sides
for value in range(1,max_result+1):
	frequency = results.count(value)
	frequencies.append(frequency)

hist = pygal.Bar()
hist.title = "Result of rolling me D6 1000 times."
hist.x_labels = list(map(num2char,list(range(1,max_result+1))))
print(hist.x_labels)
hist.x_title = "Result"
hist.y_title = "Frequency of Result"

hist.add('D6+D6',frequencies)
hist.render_to_file('dice1_visual.svg')

15-7 兩個D8骰子：請模擬同時透支兩個8面骰子1000次的結果。逐漸增加投擲骰子的次數，知道系統不堪重負為止。

die.py

from random import randint
class Die(object):
	"""docstring for Die"""
	def __init__(self, num_sides = 8):
		self.num_sides = num_sides

	def roll(self):
		return randint(1,self.num_sides)
		

die_visual.py

from die import Die
import pygal

die1 = Die()
die2 = Die()
results = []

for roll_num in range(1000):
	result = die1.roll() + die2.roll()
	results.append(result)
frequencies = []
max_result = die1.num_sides + die2.num_sides
for value in range(2,max_result+1):
	frequency = results.count(value)
	frequencies.append(frequency)

hist = pygal.Bar()
hist.title = "Result of rolling me D8 1000 times."
hist.x_labels = ['2','3','4','5','6','7','8','9','10','11','12','13','14','15','16']
hist.x_title = "Result"
hist.y_title = "Frequency of Result"

hist.add('D8+D8',frequencies)
hist.render_to_file('dice1_visual.svg')

結果：

15-8 同時投擲三個骰子：如果你同時擲三個D6骰子，可能得到的最小點數為3，而最大點數為18,。請通過視覺化展示同時擲三個D6骰子的結果

die_visual.py

from die import Die
import pygal

die1 = Die()
die2 = Die()
die3 = Die()
results = []

for roll_num in range(1000):
	result = die1.roll() + die2.roll() +  die3.roll()
	results.append(result)
frequencies = []
max_result = die1.num_sides + die2.num_sides + die3.num_sides
for value in range(2,max_result+1):
	frequency = results.count(value)
	frequencies.append(frequency)

hist = pygal.Bar()
hist.title = "Result of rolling me D6 1000 times."
hist.x_labels = ['2','3','4','5','6','7','8','9','10','11','12','13','14','15','16','17','18']
hist.x_title = "Result"
hist.y_title = "Frequency of Result"

hist.add('D6+D6+D6',frequencies)
hist.render_to_file('dice1_visual.svg')

結果：

15-9 將點數相乘：同時擲兩個骰子時，通常將它們的點數相加。通過視覺化展示將兩個骰子的點數相乘的結果

from die import Die
import pygal
def num2char(x):
	return str(x)
die1 = Die()
die2 = Die()
results = []

for roll_num in range(1000):
	result = die1.roll() * die2.roll()
	results.append(result)
# print(results)
frequencies = []
max_result = die1.num_sides * die2.num_sides
for value in range(1,max_result+1):
	frequency = results.count(value)
	frequencies.append(frequency)

hist = pygal.Bar()
hist.title = "Result of rolling me D6 1000 times."
hist.x_labels = list(map(num2char,list(range(1,max_result+1))))
print(hist.x_labels)
hist.x_title = "Result"
hist.y_title = "Frequency of Result"

hist.add('D6*D6',frequencies)
hist.render_to_file('dice1_visual.svg')

結果：

15-10 練習使用本章介紹的兩個庫：嘗試使用 matplotlib 通過視覺化來模擬值骰子的情況。
die_scatter.py

import matplotlib.pyplot as plt
from die import Die

die1 = Die()
die2 = Die()
results = []

for roll_num in range(1000):
	result = die1.roll() + die2.roll()
	results.append(result)
# print(results)
frequencies = []
max_result = die1.num_sides + die2.num_sides
for value in range(1,max_result+1):
	frequency = results.count(value)
	frequencies.append(frequency)
print(frequencies)
plt.plot(list(range(1,max_result+1)),frequencies,linewidth = 2)
plt.title("Result of rolling me D6 1000 times.")
plt.xlabel ("Result",fontsize = 14)
plt.ylabel("Square of D6 1000 times")
plt.show()

結果：

random_walk_Pygal.py