RectSphereBivariateSpline.__call__(theta, phi, dtheta=0, dphi=0, grid=True)[source]#

Evaluate the spline or its derivatives at given positions.

theta, phiarray_like

Input coordinates.

If grid is False, evaluate the spline at points (theta[i], phi[i]), i=0, ..., len(x)-1. Standard Numpy broadcasting is obeyed.

If grid is True: evaluate spline at the grid points defined by the coordinate arrays theta, phi. The arrays must be sorted to increasing order. The ordering of axes is consistent with np.meshgrid(..., indexing="ij") and inconsistent with the default ordering np.meshgrid(..., indexing="xy").

dthetaint, optional

Order of theta-derivative

Added in version 0.14.0.


Order of phi-derivative

Added in version 0.14.0.


Whether to evaluate the results on a grid spanned by the input arrays, or at points specified by the input arrays.

Added in version 0.14.0.


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 on a finer grid.

>>> rsbs = RectSphereBivariateSpline(thetaarr, phiarr, zdata)
>>> thetaarr_fine = np.linspace(0, np.pi, 200)
>>> phiarr_fine = np.linspace(0, 2 * np.pi, 200)
>>> zdata_fine = rsbs(thetaarr_fine, phiarr_fine)

Finally we plot the coarsly-sampled input data alongside the finely-sampled interpolated data to check that they agree.

>>> import matplotlib.pyplot as plt
>>> fig = plt.figure()
>>> ax1 = fig.add_subplot(1, 2, 1)
>>> ax2 = fig.add_subplot(1, 2, 2)
>>> ax1.imshow(zdata)
>>> ax2.imshow(zdata_fine)