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bundles / scipy latest / scipy / interpolate / _fitpack2 / SphereBivariateSpline / ev

function

scipy.interpolate._fitpack2:SphereBivariateSpline.ev

source: /scipy/interpolate/_fitpack2.py :1781

Signature

def   ev ( self ,  theta ,  phi ,  dtheta = 0 ,  dphi = 0 )

Summary

Evaluate the spline at points

Extended Summary

Returns the interpolated value at (theta[i], phi[i]), i=0,...,len(theta)-1.

Parameters

theta, phi : array_like

Input coordinates. Standard Numpy broadcasting is obeyed. The ordering of axes is consistent with np.meshgrid(..., indexing="ij") and inconsistent with the default ordering np.meshgrid(..., indexing="xy").

dtheta : int, optional

Order of theta-derivative

dphi : int, optional

Order of phi-derivative

Examples

Suppose that we want to use splines to interpolate a bivariate function on a sphere. The value of the function is known on a grid of longitudes and colatitudes. 
import numpy as np
from scipy.interpolate import RectSphereBivariateSpline
def f(theta, phi):
    return np.sin(theta) * np.cos(phi)
✓
We evaluate the function on the grid. Note that the default indexing="xy" of meshgrid would result in an unexpected (transposed) result after interpolation. 
thetaarr = np.linspace(0, np.pi, 22)[1:-1]
phiarr = np.linspace(0, 2 * np.pi, 21)[:-1]
thetagrid, phigrid = np.meshgrid(thetaarr, phiarr, indexing="ij")
zdata = f(thetagrid, phigrid)
✓
We next set up the interpolator and use it to evaluate the function at points not on the original grid. 
rsbs = RectSphereBivariateSpline(thetaarr, phiarr, zdata)
thetainterp = np.linspace(thetaarr[0], thetaarr[-1], 200)
phiinterp = np.linspace(phiarr[0], phiarr[-1], 200)
zinterp = rsbs.ev(thetainterp, phiinterp)
✓
Finally we plot the original data for a diagonal slice through the initial grid, and the spline approximation along the same slice. 
import matplotlib.pyplot as plt
fig = plt.figure()
ax1 = fig.add_subplot(1, 1, 1)
✓
ax1.plot(np.sin(thetaarr) * np.sin(phiarr), np.diag(zdata), "or")
ax1.plot(np.sin(thetainterp) * np.sin(phiinterp), zinterp, "-b")
✗
plt.show()
✓
fig-2c7e5e5416c08d00.png

Aliases

  • scipy.interpolate._fitpack2.SphereBivariateSpline.ev