Trigradient 演示

使用 matplotlib.tri.CubicTriInterpolator 演示梯度计算。

  1. from matplotlib.tri import (
  2.     Triangulation, UniformTriRefiner, CubicTriInterpolator)
  3. import matplotlib.pyplot as plt
  4. import matplotlib.cm as cm
  5. import numpy as np
  8. #-----------------------------------------------------------------------------
  9. # Electrical potential of a dipole
  10. #-----------------------------------------------------------------------------
  11. def dipole_potential(x, y):
  12.     """ The electric dipole potential V """
  13.     r_sq = x**2 + y**2
  14.     theta = np.arctan2(y, x)
  15.     z = np.cos(theta)/r_sq
  16.     return (np.max(z) - z) / (np.max(z) - np.min(z))
  19. #-----------------------------------------------------------------------------
  20. # Creating a Triangulation
  21. #-----------------------------------------------------------------------------
  22. # First create the x and y coordinates of the points.
  23. n_angles = 30
  24. n_radii = 10
  25. min_radius = 0.2
  26. radii = np.linspace(min_radius, 0.95, n_radii)
  28. angles = np.linspace(0, 2 * np.pi, n_angles, endpoint=False)
  29. angles = np.repeat(angles[..., np.newaxis], n_radii, axis=1)
  30. angles[:, 1::2] += np.pi / n_angles
  32. x = (radii*np.cos(angles)).flatten()
  33. y = (radii*np.sin(angles)).flatten()
  34. V = dipole_potential(x, y)
  36. # Create the Triangulation; no triangles specified so Delaunay triangulation
  37. # created.
  38. triang = Triangulation(x, y)
  40. # Mask off unwanted triangles.
  41. triang.set_mask(np.hypot(x[triang.triangles].mean(axis=1),
  42.                          y[triang.triangles].mean(axis=1))
  43.                 < min_radius)
  45. #-----------------------------------------------------------------------------
  46. # Refine data - interpolates the electrical potential V
  47. #-----------------------------------------------------------------------------
  48. refiner = UniformTriRefiner(triang)
  49. tri_refi, z_test_refi = refiner.refine_field(V, subdiv=3)
  51. #-----------------------------------------------------------------------------
  52. # Computes the electrical field (Ex, Ey) as gradient of electrical potential
  53. #-----------------------------------------------------------------------------
  54. tci = CubicTriInterpolator(triang, -V)
  55. # Gradient requested here at the mesh nodes but could be anywhere else:
  56. (Ex, Ey) = tci.gradient(triang.x, triang.y)
  57. E_norm = np.sqrt(Ex**2 + Ey**2)
  59. #-----------------------------------------------------------------------------
  60. # Plot the triangulation, the potential iso-contours and the vector field
  61. #-----------------------------------------------------------------------------
  62. fig, ax = plt.subplots()
  63. ax.set_aspect('equal')
  64. # Enforce the margins, and enlarge them to give room for the vectors.
  65. ax.use_sticky_edges = False
  66. ax.margins(0.07)
  68. ax.triplot(triang, color='0.8')
  70. levels = np.arange(0., 1., 0.01)
  71. cmap = cm.get_cmap(name='hot', lut=None)
  72. ax.tricontour(tri_refi, z_test_refi, levels=levels, cmap=cmap,
  73.               linewidths=[2.0, 1.0, 1.0, 1.0])
  74. # Plots direction of the electrical vector field
  75. ax.quiver(triang.x, triang.y, Ex/E_norm, Ey/E_norm,
  76.           units='xy', scale=10., zorder=3, color='blue',
  77.           width=0.007, headwidth=3., headlength=4.)
  79. ax.set_title('Gradient plot: an electrical dipole')
  80. plt.show()

Trigradient 演示

参考

此示例中显示了以下函数，方法，类和模块的使用：

  1. import matplotlib
  2. matplotlib.axes.Axes.tricontour
  3. matplotlib.pyplot.tricontour
  4. matplotlib.axes.Axes.triplot
  5. matplotlib.pyplot.triplot
  6. matplotlib.tri
  7. matplotlib.tri.Triangulation
  8. matplotlib.tri.CubicTriInterpolator
  9. matplotlib.tri.CubicTriInterpolator.gradient
  10. matplotlib.tri.UniformTriRefiner
  11. matplotlib.axes.Axes.quiver
  12. matplotlib.pyplot.quiver

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