scipy.interpolate.RectSphereBivariateSpline.

__call__

RectSphereBivariateSpline.__call__(theta, phi, dtheta=0, dphi=0, grid=True)

Evaluate the spline or its derivatives at given positions.

Parameters:

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.

dphiint

Order of phi-derivative

Added in version 0.14.0.

gridbool

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.

Examples

Try it in your browser!

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)
>>> plt.show()

Go BackOpen In Tab