### Navigation

- index
- modules |
- home|
- examples|
- tutorials|
- pyplot|
- docs »

# Trigradient Demo

Demonstrates computation of gradient with matplotlib.tri.CubicTriInterpolator.

    from matplotlib.tri import Triangulation, UniformTriRefiner,\
        CubicTriInterpolator
    import matplotlib.pyplot as plt
    import matplotlib.cm as cm
    import numpy as np
    import math

    #-----------------------------------------------------------------------------
    # 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*math.pi, n_angles, endpoint=False)
    angles = np.repeat(angles[..., np.newaxis], n_radii, axis=1)
    angles[:, 1::2] += math.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.
    xmid = x[triang.triangles].mean(axis=1)
    ymid = y[triang.triangles].mean(axis=1)
    mask = np.where(xmid*xmid + ymid*ymid < min_radius*min_radius, 1, 0)
    triang.set_mask(mask)

    #-----------------------------------------------------------------------------
    # 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()

Total running time of the script: ( 0 minutes 0.466 seconds)

Generated by Sphinx-Gallery