# scipy.interpolate.RectSphereBivariateSpline.ev

RectSphereBivariateSpline.ev(theta, phi, dtheta=0, dphi=0)

  Evaluate the spline at points

  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

      New in version 0.14.0.

    dphi int, optional

      Order of phi-derivative

      New in version 0.14.0.

  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()