python+matplotlib演示电偶极子实例代码-6ren

python+matplotlib演示电偶极子实例代码

转载作者：qq735679552 更新时间：2022-09-28 22:32:09

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使用matplotlib.tri.CubicTriInterpolator.演示变化率计算:

python+matplotlib演示电偶极子实例代码

完整实例:

 
    ? 
   
         from 
         matplotlib.tri  
         import 
         ( 
        
         Triangulation, UniformTriRefiner, CubicTriInterpolator) 
        
         import 
         matplotlib.pyplot as plt 
        
         import 
         matplotlib.cm as cm 
        
         import 
         numpy as np 
        
         #----------------------------------------------------------------------------- 
        
         # Electrical potential of a dipole 
        
         #----------------------------------------------------------------------------- 
        
         def 
         dipole_potential(x, y): 
        
         """ The electric dipole potential V """ 
        
         r_sq  
         = 
         x 
         * 
         * 
         2 
         + 
         y 
         * 
         * 
         2 
        
         theta  
         = 
         np.arctan2(y, x) 
        
         z  
         = 
         np.cos(theta) 
         / 
         r_sq 
        
         return 
         (np. 
         max 
         (z)  
         - 
         z)  
         / 
         (np. 
         max 
         (z)  
         - 
         np. 
         min 
         (z)) 
        
         #----------------------------------------------------------------------------- 
        
         # Creating a Triangulation 
        
         #----------------------------------------------------------------------------- 
        
         # First create the x and y coordinates of the points. 
        
         n_angles  
         = 
         30 
        
         n_radii  
         = 
         10 
        
         min_radius  
         = 
         0.2 
        
         radii  
         = 
         np.linspace(min_radius,  
         0.95 
         , n_radii) 
        
         angles  
         = 
         np.linspace( 
         0 
         ,  
         2 
         * 
         np.pi, n_angles, endpoint 
         = 
         False 
         ) 
        
         angles  
         = 
         np.repeat(angles[..., np.newaxis], n_radii, axis 
         = 
         1 
         ) 
        
         angles[:,  
         1 
         :: 
         2 
         ]  
         + 
         = 
         np.pi  
         / 
         n_angles 
        
         x  
         = 
         (radii 
         * 
         np.cos(angles)).flatten() 
        
         y  
         = 
         (radii 
         * 
         np.sin(angles)).flatten() 
        
         V  
         = 
         dipole_potential(x, y) 
        
         # Create the Triangulation; no triangles specified so Delaunay triangulation 
        
         # created. 
        
         triang  
         = 
         Triangulation(x, y) 
        
         # Mask off unwanted triangles. 
        
         triang.set_mask(np.hypot(x[triang.triangles].mean(axis 
         = 
         1 
         ), 
        
         y[triang.triangles].mean(axis 
         = 
         1 
         )) 
        
         < min_radius) 
        
         #----------------------------------------------------------------------------- 
        
         # Refine data - interpolates the electrical potential V 
        
         #----------------------------------------------------------------------------- 
        
         refiner  
         = 
         UniformTriRefiner(triang) 
        
         tri_refi, z_test_refi  
         = 
         refiner.refine_field(V, subdiv 
         = 
         3 
         ) 
        
         #----------------------------------------------------------------------------- 
        
         # Computes the electrical field (Ex, Ey) as gradient of electrical potential 
        
         #----------------------------------------------------------------------------- 
        
         tci  
         = 
         CubicTriInterpolator(triang,  
         - 
         V) 
        
         # Gradient requested here at the mesh nodes but could be anywhere else: 
        
         (Ex, Ey)  
         = 
         tci.gradient(triang.x, triang.y) 
        
         E_norm  
         = 
         np.sqrt(Ex 
         * 
         * 
         2 
         + 
         Ey 
         * 
         * 
         2 
         ) 
        
         #----------------------------------------------------------------------------- 
        
         # Plot the triangulation, the potential iso-contours and the vector field 
        
         #----------------------------------------------------------------------------- 
        
         fig, ax  
         = 
         plt.subplots() 
        
         ax.set_aspect( 
         'equal' 
         ) 
        
         # Enforce the margins, and enlarge them to give room for the vectors. 
        
         ax.use_sticky_edges  
         = 
         False 
        
         ax.margins( 
         0.07 
         ) 
        
         ax.triplot(triang, color 
         = 
         '0.8' 
         ) 
        
         levels  
         = 
         np.arange( 
         0. 
         ,  
         1. 
         ,  
         0.01 
         ) 
        
         cmap  
         = 
         cm.get_cmap(name 
         = 
         'hot' 
         , lut 
         = 
         None 
         ) 
        
         ax.tricontour(tri_refi, z_test_refi, levels 
         = 
         levels, cmap 
         = 
         cmap, 
        
         linewidths 
         = 
         [ 
         2.0 
         ,  
         1.0 
         ,  
         1.0 
         ,  
         1.0 
         ]) 
        
         # Plots direction of the electrical vector field 
        
         ax.quiver(triang.x, triang.y, Ex 
         / 
         E_norm, Ey 
         / 
         E_norm, 
        
         units 
         = 
         'xy' 
         , scale 
         = 
         10. 
         , zorder 
         = 
         3 
         , color 
         = 
         'blue' 
         , 
        
         width 
         = 
         0.007 
         , headwidth 
         = 
         3. 
         , headlength 
         = 
         4. 
         ) 
        
         ax.set_title( 
         'Gradient plot: an electrical dipole' 
         ) 
        
         plt.show()