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# scipy.interpolate.RectBivariateSpline.ev

RectBivariateSpline.ev(xi, yi, dx=0, dy=0)

  Evaluate the spline at points

  Returns the interpolated value at `(xi[i], yi[i]), i=0,...,len(xi)-1`.

  Parameters:
    xi, yi 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")`.

    dx int, optional

      Order of x-derivative

      New in version 0.14.0.

    dy int, optional

      Order of y-derivative

      New in version 0.14.0.

  Examples

  Suppose that we want to bilinearly interpolate an exponentially decaying function in 2 dimensions.

      >>> import numpy as np
      >>> from scipy.interpolate import RectBivariateSpline
      >>> def f(x, y):
      ...     return np.exp(-np.sqrt((x / 2) ** 2 + y**2))

  We sample the function on a coarse grid and set up the interpolator. Note that the default `indexing="xy"` of meshgrid would result in an unexpected (transposed) result after interpolation.

      >>> xarr = np.linspace(-3, 3, 21)
      >>> yarr = np.linspace(-3, 3, 21)
      >>> xgrid, ygrid = np.meshgrid(xarr, yarr, indexing="ij")
      >>> zdata = f(xgrid, ygrid)
      >>> rbs = RectBivariateSpline(xarr, yarr, zdata, kx=1, ky=1)

  Next we sample the function along a diagonal slice through the coordinate space on a finer grid using interpolation.

      >>> xinterp = np.linspace(-3, 3, 201)
      >>> yinterp = np.linspace(3, -3, 201)
      >>> zinterp = rbs.ev(xinterp, yinterp)

  And check that the interpolation passes through the function evaluations as a function of the distance from the origin along the slice.

      >>> import matplotlib.pyplot as plt
      >>> fig = plt.figure()
      >>> ax1 = fig.add_subplot(1, 1, 1)
      >>> ax1.plot(np.sqrt(xarr**2 + yarr**2), np.diag(zdata), "or")
      >>> ax1.plot(np.sqrt(xinterp**2 + yinterp**2), zinterp, "-b")
      >>> plt.show()