Matplotllib——绘制复杂函数图与三维图

一、绘制二维函数图

1.1 绘制 $f(x) = sin^2(x-2)e^{-x^2}$ 函数图

代码1：
import matplotlib.pyplot as plt
import numpy as np
plt.rcParams["font.sans-serif"]=['SimHei']  # 用于正常显示中文标签
plt.rcParams['axes.unicode_minus']=False    # 用来正常显示负号

x = np.linspace(-2.5,2,256,endpoint=True)   # 绘制X轴（-2.5,2）的图像

f =(np.sin(x-2))**2*(np.e)**(-x**2)         # y值

plt.plot(x,f,"g-",lw=2.5,label="f(x)")
plt.title('f(x) = sin^2(x-2)e^{-x^2}函数图')
plt.legend()
plt.show()

_______________________________________________
代码2（对于复杂函数，我们可以将其拆分成多单一函数）
        分析：sin^2(x-2)e^{-x^2}分解：
             sin(x1)*sin(x1)*e^x2
        其中：x1 = x-2;    x2 = -x^2
import matplotlib.pyplot as plt
import numpy as np
plt.rcParams['font.sans-serif'] = ['SimHei']  # 用来正常显示中文标签 
plt.rcParams['axes.unicode_minus'] = False    # 用来正常显示负号 

x = np.linspace(0, 2,300, endpoint=True) 
x_1 = x-2
S_1 = np.sin(x_1)
S_2 = S_1**2

E_1 = -x**2
E_2 = np.exp(E_1)
f = S_2*E_2    
plt.figure(figsize = ((8,6)))     # 设置画布大小（可省略）

plt.plot(x,f,'b-',lw=2.5,label='f(x)=sin^2(x-2)e^{-x^2}') 

plt.legend()                      # 显示图例 
plt.show()

1.2 、绘制 sigmoid函数图: $f(x) =\frac{1}{1+e^{-x}}$

import matplotlib.pyplot as plt
import numpy as np
plt.rcParams['font.sans-serif'] = ['SimHei']  # 用来正常显示中文标签 
plt.rcParams['axes.unicode_minus'] = False    # 用来正常显示负号 

x = np.linspace(-10, 10,300, endpoint=True) 

E_1 = -x
E_2 = np.exp(E_1)
f = 1/(1+E_2)    
plt.figure(figsize = ((8,6)))     # 设置画布大小（可省略）
ax1 = plt.subplot(111)

plt.plot(x,f,'b-',lw=2.5,label='f(x)=\\frac{1}{1+e^{-x}}') 

plt.legend()                      # 显示图例 
ax1.grid(True)                    # 显示网格 
plt.show()

1.3、绘制正态分布图

其中 s 为 $\sigma$ , m为 $\mu$

import math
import matplotlib.pyplot as plt
import numpy as np
def gd(x,m,s):                       #其中s为sigma ,m为 mu
    left=1/(math.sqrt(2*math.pi)*s)
    right=math.exp(-math.pow(x-m,2)/(2*math.pow(s,2)))
    return left*right
def showfigure():
    plt.figure(figsize = ((8,6)))   #设置画布大小（可省略）
    x=np.arange(-4,5,0.1)           #绘制x（-4,5）
    y=[]
    for i in x:
        y.append(gd(i,0,1))         #m为0，s为1
    plt.plot(x,y) 
    plt.xlim(-4.0,5.0)
    plt.ylim(-0.2,0.5)
    ax = plt.gca()
    ax.spines['right'].set_color('none')
    ax.spines['top'].set_color('none')
    ax.xaxis.set_ticks_position('bottom')
    ax.spines['bottom'].set_position(('data',0))
    ax.yaxis.set_ticks_position('left')
    ax.spines['left'].set_position(('data',0))

    #设置并添加标签
    label_f1 = "$\mu=0,\ \sigma=1$"
    plt.text(2.5,0.3,label_f1,fontsize=15,verticalalignment="top",
            horizontalalignment="left")
    label_f2 = r"$f(x)=\frac{1}{\sqrt{2\pi}\sigma}exp(-\frac{(x-\mu)^2}{2\sigma^2})$"
    plt.text(1.5,0.4,label_f2,fontsize=15,verticalalignment="top"
            ,horizontalalignment="left")
    plt.show()

def main():
    showfigure()
    gd()
main()

二、绘制三维图

2.1 绘制三维螺旋图

from mpl_toolkits.mplot3d import Axes3D
import numpy as np
import matplotlib.pyplot as plt

fig = plt.figure(figsize = ((8,6)))
ax = fig.add_subplot(1,1,1,projection='3d')
theta = np.linspace(-4 * np.pi, 4 * np.pi, 500) # theta旋转角从-4pi到4pi，相当于两圈
z = np.linspace(0, 2, 500)  # z轴从下到上,从-2到2之间画100个点
r = z                       # 半径设置为z大小
x = r * np.sin(theta)       # x和y画圆
y = r * np.cos(theta)       # x和y画圆
ax.plot(x, y, z, label='curve')
ax.legend()                 # 图例

plt.show()

2.2 绘制三维线性点图

from mpl_toolkits.mplot3d import Axes3D
import numpy as np
import matplotlib.pyplot as plt

fig = plt.figure()
ax = fig.add_subplot(1,1,1,projection='3d')
x = np.linspace(0, 5, 10)      # 在0-5之间生成10个点的向量
y = np.linspace(0, 5, 10)      # 在0-5之间生成10个点的向量
z1 = x
z2 = 2*x
z3 = 3*x
ax.scatter(xx, yy, zz1, c='red', marker='o')   # o型符号
ax.scatter(xx, yy, zz2, c='green', marker='^') # 三角型符号
ax.scatter(xx, yy, zz3, c='black', marker='*') # 星型符号
ax.legend()                                    # 显示图例  

plt.show()

2.3 绘制三维柱状图

import random
import matplotlib as mpl
import matplotlib.dates as mdates
from mpl_toolkits.mplot3d import Axes3D
plt.rcParams['font.sans-serif'] = ['SimHei']  # 用来正常显示中文标签 
plt.rcParams['axes.unicode_minus'] = False    # 用来正常显示负号 

mpl.rcParams['font.size'] = 10

fig = plt.figure(figsize=((8,6)))
ax = fig.add_subplot(111, projection='3d')
for z in [2011, 2012, 2013, 2014]:
    xs = range(1,13)
    ys = 1000 * np.random.rand(12)
    color = plt.cm.Set2(random.choice(range(plt.cm.Set2.N)))
    ax.bar(xs, ys, zs=z, zdir='y', color=color, alpha=0.8)

ax.xaxis.set_major_locator(mpl.ticker.FixedLocator(xs))
ax.yaxis.set_major_locator(mpl.ticker.FixedLocator(ys))
ax.set_xlabel('月份')
ax.set_ylabel('年份')
ax.set_zlabel('销售额 ')
plt.show()

2.4 绘制三维 鞍部 曲面图

import numpy as np
import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import Axes3D
from matplotlib import cm

n_angles = 1000                #曲面衔接角度（平滑度）
n_radii = 20                   #鞍部半径（1：锐角，20：平滑角）
fig = plt.figure(figsize=((10,10)))
radii = np.linspace(0.125, 1.0, n_radii)
angles = np.linspace(0, 2 * np.pi, n_angles, endpoint=False)
angles = np.repeat(angles[..., np.newaxis], n_radii, axis=1)

x = np.append(0, (radii * np.cos(angles)).flatten())
y = np.append(0, (radii * np.sin(angles)).flatten())

z = np.sin(-x * y)
fig = plt.figure()
ax = fig.gca(projection='3d')
ax.plot_trisurf(x, y, z,   
                cmap=cm.jet,    #曲面颜色
                linewidth=0.2)

2.5 绘制山区图 $f(x,y) = x e^{-x^2-y^2}$

import numpy as np
import matplotlib.pyplot as plt
import mpl_toolkits.mplot3d

x,y = np.mgrid[-2:2:100j,-2:2:100j] #100j为设置曲面平滑度
z=x*np.exp(-x**2-y**2)
ax = plt.subplot(111, projection='3d')
ax.set_title('山区图');
ax.plot_surface(x,y,z,rstride=2, cstride=1, cmap=cm.jet)

ax.set_xlabel('X')                #设置坐标轴标签
ax.set_ylabel('Y')
ax.set_zlabel('Z')
plt.show()

鸣谢：非常感谢以下博主的帮助；
https://blog.csdn.net/sinat_36772813/article/details/77365296
https://blog.csdn.net/eddy_zheng/article/details/48713449
https://blog.csdn.net/dahunihao/article/details/77833877