import numpy as np
import holoviews as hv
from holoviews import dim, opts

hv.extension('matplotlib')

x,y  = np.mgrid[-10:10,-10:10] * 0.25
sine_rings  = np.sin(x**2+y**2)*np.pi+np.pi
exp_falloff = 1/np.exp((x**2+y**2)/8)

vector_data = (x, y, sine_rings, exp_falloff)
hv.VectorField(vector_data).opts(magnitude='Magnitude')

anglecolor = hv.VectorField(vector_data).opts(
    opts.VectorField(title='A', magnitude='Magnitude', color='Angle'))
magcolor = hv.VectorField(vector_data).opts(
    opts.VectorField(title='M', magnitude='Magnitude', color='Magnitude'))
anglecolor + magcolor

hmap = hv.HoloMap({phase: hv.VectorField((x, y,(vector_data[2]+phase)%np.pi*2, vector_data[3]+np.abs(phase)))
                   for phase in np.linspace(-np.pi,np.pi,5)}, kdims='Phase')

hmap.opts(opts.VectorField(color='Angle', magnitude=dim('Magnitude').norm()*0.2, rescale_lengths=False))

xs, ys = np.arange(0, 2 * np.pi, .2), np.arange(0, 2 * np.pi, .2)
X, Y = np.meshgrid(xs, ys)
U = np.cos(X)
V = np.sin(Y)

# Convert U, V to magnitude and angle
mag = np.sqrt(U**2 + V**2)
angle = (np.pi/2.) - np.arctan2(U/mag, V/mag)

vectors = hv.VectorField((xs, ys, angle, mag))
points = hv.Points((X.flat, Y.flat))

(vectors * points).opts(
    opts.Points(color='black', s=1),
    opts.VectorField(aspect=2, color='Magnitude', cmap='fire', fig_size=300, magnitude='Magnitude', pivot='tip', scale=0.8))