21.等值线图（Counter Plot）、Contour Demo、Creating a “meshgrid”、Calculation of the Values、等

你的名字 2022-11-17 13:56 132阅读 0赞

21.等值线图（Counter Plot）  
21.1.Contour Demo  
21.2.Creating a “meshgrid”  
21.3.Calculation of the Values  
21.4.Changing the Colours and the Line Style  
21.5.Filled Contours  
21.6.Individual Colours

# 21.等值线图（Counter Plot） #

两个变量函数的等值线(或等高线)是函数具有常数值的曲线。它是平行于x，y平面的函数f(x,y)的三维图的横截面。

例如在地理和气象学使用登高线。在制图中，等高线连接高于给定水平的相等高度的点，例如平均海平面。

我们还可以更一般地说，具有两个变量的函数的等值线是连接具有相同值的点的曲线。

contour和contourf都是画三维等高线图的，不同点在于contour() 是绘制轮廓线，contourf()会填充轮廓。

## 21.1.Contour Demo ##

举例说明简单的等值线绘图: 图像上的等值线, 以及用于等值线的色条(colorbar)以及标记的等高线。

使用默认颜色创建带有标签的简单等值线图。 clabel的inline参数将控制是否在等值线的线段上绘制标签，从而去除标签下方的线。

fig, ax = plt.subplots()
    CS = ax.contour(X, Y, Z)
    ax.clabel(CS, inline=1, fontsize=10)
    ax.set_title('Simplest default with labels')

即：

![在这里插入图片描述][watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3RvdG8xMjk3NDg4NTA0_size_16_color_FFFFFF_t_70]

通过提供的数据坐标中的位置列表可以手动放置等值线标签。

fig, ax = plt.subplots()
    CS = ax.contour(X, Y, Z)
    manual_locations = [(-1, -1.4), (-0.62, -0.7), (-2, 0.5), (1.7, 1.2), (2.0, 1.4), (2.4, 1.7)]
    ax.clabel(CS, inline=1, fontsize=10, manual=manual_locations)
    ax.set_title('labels at selected locations')

![在这里插入图片描述][watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3RvdG8xMjk3NDg4NTA0_size_16_color_FFFFFF_t_70 1]  
你可以强制所有等值线为相同颜色。

![在这里插入图片描述][watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3RvdG8xMjk3NDg4NTA0_size_16_color_FFFFFF_t_70 2]  
可以将负等值线设置为实线而不是虚线：

![在这里插入图片描述][watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3RvdG8xMjk3NDg4NTA0_size_16_color_FFFFFF_t_70 3]

可以手动指定等值线的颜色：

![在这里插入图片描述][watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3RvdG8xMjk3NDg4NTA0_size_16_color_FFFFFF_t_70 4]

可以使用颜色图(colormap)来指定颜色。 默认的颜色图(colormap)将用于等值线。

import matplotlib
    import numpy as np
    import matplotlib.cm as cm
    import matplotlib.pyplot as plt
    
    delta = 0.025
    x = np.arange(-3.0, 3.0, delta)
    y = np.arange(-2.0, 2.0, delta)
    X, Y = np.meshgrid(x, y)
    Z1 = np.exp(-X**2 - Y**2)
    Z2 = np.exp(-(X - 1)**2 - (Y - 1)**2)
    Z = (Z1 - Z2) * 2
    
    fig, ax = plt.subplots()
    im = ax.imshow(Z, interpolation='bilinear', origin='lower',
                    cmap=cm.gray, extent=(-3, 3, -2, 2))
    levels = np.arange(-1.2, 1.6, 0.2)
    CS = ax.contour(Z, levels, origin='lower', cmap='flag',
                    linewidths=2, extent=(-3, 3, -2, 2))
    
    # Thicken the zero contour.
    zc = CS.collections[6]
    plt.setp(zc, linewidth=4)
    
    ax.clabel(CS, levels[1::2],  # label every second level
              inline=1, fmt='%1.1f', fontsize=14)
    
    # make a colorbar for the contour lines
    CB = fig.colorbar(CS, shrink=0.8, extend='both')
    
    ax.set_title('Lines with colorbar')
    
    # We can still add a colorbar for the image, too.
    CBI = fig.colorbar(im, orientation='horizontal', shrink=0.8)
    
    # This makes the original colorbar look a bit out of place,
    # so let's improve its position.
    
    l, b, w, h = ax.get_position().bounds
    ll, bb, ww, hh = CB.ax.get_position().bounds
    CB.ax.set_position([ll, b + 0.1*h, ww, h*0.8])
    
    
    plt.show()

![在这里插入图片描述][watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3RvdG8xMjk3NDg4NTA0_size_16_color_FFFFFF_t_70 5]

## 21.2.Creating a “meshgrid” ##

import numpy as np
    
    xlist = np.linspace(-3.0, 3.0, 3)
    ylist = np.linspace(-3.0, 3.0, 4)
    X, Y = np.meshgrid(xlist, ylist)
    print(xlist)
    print(ylist)
    print(X)
    print(Y)
    """ 输出结果： [-3. 0. 3.] [-3. -1. 1. 3.] [[-3. 0. 3.] [-3. 0. 3.] [-3. 0. 3.] [-3. 0. 3.]] [[-3. -3. -3.] [-1. -1. -1.] [ 1. 1. 1.] [ 3. 3. 3.]] """

## 21.3.Calculation of the Values ##

import numpy as np
    import matplotlib.pyplot as plt
    
    xlist = np.linspace(-3.0, 3.0, 3)
    ylist = np.linspace(-3.0, 3.0, 4)
    X, Y = np.meshgrid(xlist, ylist)
    Z = np.sqrt(X**2 + Y**2)
    print(Z)
    """ 输出结果： [[4.24264069 3. 4.24264069] [3.16227766 1. 3.16227766] [3.16227766 1. 3.16227766] [4.24264069 3. 4.24264069]] """
    
    plt.figure()
    cp = plt.contour(X, Y, Z)
    plt.clabel(cp, inline=True,
              fontsize=10)
    plt.title('Contour Plot')
    plt.xlabel('x (cm)')
    plt.ylabel('y (cm)')
    plt.show()

![在这里插入图片描述][watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3RvdG8xMjk3NDg4NTA0_size_16_color_FFFFFF_t_70 6]

## 21.4.Changing the Colours and the Line Style ##

import numpy as np
    import matplotlib.pyplot as plt
    
    xlist = np.linspace(-3.0, 3.0, 3)
    ylist = np.linspace(-3.0, 3.0, 4)
    X, Y = np.meshgrid(xlist, ylist)
    Z = np.sqrt(X**2 + Y**2)
    print(Z)
    """ 输出结果： [[4.24264069 3. 4.24264069] [3.16227766 1. 3.16227766] [3.16227766 1. 3.16227766] [4.24264069 3. 4.24264069]] """
    
    plt.figure()
    cp = plt.contour(X, Y, Z, colors='black', linestyles='dashed')
    plt.clabel(cp, inline=True,
              fontsize=10)
    plt.title('Contour Plot')
    plt.xlabel('x (cm)')
    plt.ylabel('y (cm)')
    plt.show()

![在这里插入图片描述][watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3RvdG8xMjk3NDg4NTA0_size_16_color_FFFFFF_t_70 7]

## 21.5.Filled Contours ##

import numpy as np
    import matplotlib.pyplot as plt
    xlist = np.linspace(-3.0, 3.0, 100)
    ylist = np.linspace(-3.0, 3.0, 100)
    X, Y = np.meshgrid(xlist, ylist)
    Z = np.sqrt(X**2 + Y**2)
    plt.figure()
    cp = plt.contourf(X, Y, Z)
    plt.colorbar(cp)
    plt.title('Filled Contours Plot')
    plt.xlabel('x (cm)')
    plt.ylabel('y (cm)')
    plt.show()

![在这里插入图片描述][watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3RvdG8xMjk3NDg4NTA0_size_16_color_FFFFFF_t_70 8]

## 21.6.Individual Colours ##

import numpy as np
    import matplotlib.pyplot as plt
    xlist = np.linspace(-3.0, 3.0, 100)
    ylist = np.linspace(-3.0, 3.0, 100)
    X, Y = np.meshgrid(xlist, ylist)
    Z = np.sqrt(X**2 + Y**2)
    plt.figure()
    contour = plt.contourf(X, Y, Z)
    plt.clabel(contour, colors = 'k', fmt = '%2.1f', fontsize=12)
    c = ('#ff0000', '#ffff00', '#0000FF', '0.6', 'c', 'm')
    contour_filled = plt.contourf(X, Y, Z, colors=c)
    plt.colorbar(contour)
    plt.title('Filled Contours Plot')
    plt.xlabel('x (cm)')
    plt.ylabel('y (cm)')
    plt.show()

![在这里插入图片描述][watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3RvdG8xMjk3NDg4NTA0_size_16_color_FFFFFF_t_70 9]

## 21.7.Levels ##

到目前为止，levels是由contour和contourf自动确定的。 通过提供一个levels列表作为第四个参数，可以手动定义它们。 如果使用等值线，则会为列表中的每个值绘制等值线。 对于contourf，列表中的值之间将填充彩色区域。

import numpy as np
    import matplotlib.pyplot as plt
    xlist = np.linspace(-3.0, 3.0, 100)
    ylist = np.linspace(-3.0, 3.0, 100)
    X, Y = np.meshgrid(xlist, ylist)
    Z = np.sqrt(X ** 2 + Y ** 2 )
    plt.figure()
    levels = [0.0, 0.2, 0.5, 0.9, 1.5, 2.5, 3.5]
    contour = plt.contour(X, Y, Z, levels, colors='k')
    plt.clabel(contour, colors = 'k', fmt = '%2.1f', fontsize=12)
    contour_filled = plt.contourf(X, Y, Z, levels)
    plt.colorbar(contour_filled)
    plt.title('Plot from level list')
    plt.xlabel('x (cm)')
    plt.ylabel('y (cm)')
    plt.show()

![在这里插入图片描述][watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3RvdG8xMjk3NDg4NTA0_size_16_color_FFFFFF_t_70 10]

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