Interpolate transition guide — SciPy v1.14.0 Manual (2024)

1. How to transition away from using interp2d#

interp2d silently switches between interpolation on a 2D regular grid and interpolating 2D scattered data. The switch is based on the lengths of the (raveled) x, y, and z arrays. In short, for regular grid use scipy.interpolate.RectBivariateSpline; for scattered interpolation, use the bisprep/bisplev combo. Below we give examples of the literal point-for-point transition, which should preserve the interp2d results exactly.

>>> import numpy as np>>> import matplotlib.pyplot as plt>>> from scipy.interpolate import interp2d, RectBivariateSpline>>> x = np.arange(-5.01, 5.01, 0.25)>>> y = np.arange(-5.01, 7.51, 0.25)>>> xx, yy = np.meshgrid(x, y)>>> z = np.sin(xx**2 + 2.*yy**2)>>> f = interp2d(x, y, z, kind='cubic')

>>> z.size == len(x) * len(y)True

>>> x.size, y.size(41, 51)

>>> def plot(f, xnew, ynew):...  fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(8, 4))...  znew = f(xnew, ynew)...  ax1.plot(x, z[0, :], 'ro-', xnew, znew[0, :], 'b-')...  im = ax2.imshow(znew)...  plt.colorbar(im, ax=ax2)...  plt.show()...  return znew...>>> xnew = np.arange(-5.01, 5.01, 1e-2)>>> ynew = np.arange(-5.01, 7.51, 1e-2)>>> znew_i = plot(f, xnew, ynew)

>>> r = RectBivariateSpline(x, y, z.T)>>> rt = lambda xnew, ynew: r(xnew, ynew).T>>> znew_r = plot(rt, xnew, ynew)

>>> from numpy.testing import assert_allclose>>> assert_allclose(znew_i, znew_r, atol=1e-14)

>>> xxr = xx.ravel()>>> yyr = yy.ravel()>>> zzr = z.ravel()>>> f = interp2d(xxr, yyr, zzr, kind='cubic')

>>> len(xxr) == len(yyr) == len(zzr)True

>>> xnew = np.arange(-5.01, 5.01, 1e-2)>>> ynew = np.arange(-5.01, 7.51, 1e-2)>>> znew_i = plot(f, xnew, ynew)

>>> from scipy.interpolate import bisplrep, bisplev>>> tck = bisplrep(xxr, yyr, zzr, kx=3, ky=3, s=0)# convenience: make up a callable from bisplev>>> ff = lambda xnew, ynew: bisplev(xnew, ynew, tck).T # Note the transpose, to mimic what interp2d does>>> znew_b = plot(ff, xnew, ynew)

>>> assert_allclose(znew_i, znew_b, atol=1e-15)

2. Alternative to interp2d: regular grid#

For new code, the recommended alternative is RegularGridInterpolator. It is an independent implementation, not based on FITPACK. Supports nearest, linear interpolation and odd-order tensor product splines.

The spline knots are guaranteed to coincide with the data points.

Note that, here:

1. the tuple argument, is (x, y)

2. z array needs a transpose

3. the keyword name is method, not kind

4. bounds_error argument is True by default.

>>> from scipy.interpolate import RegularGridInterpolator as RGI>>> r = RGI((x, y), z.T, method='linear', bounds_error=False)

Evaluation: create a 2D meshgrid. Use indexing=’ij’ and sparse=True to save some memory:

>>> xxnew, yynew = np.meshgrid(xnew, ynew, indexing='ij', sparse=True)

Evaluate, note the tuple argument:

>>> znew_reggrid = r((xxnew, yynew))

>>> fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(8, 4))# Again, note the transpose to undo the `interp2d` convention>>> znew_reggrid_t = znew_reggrid.T>>> ax1.plot(x, z[0, :], 'ro-', xnew, znew_reggrid_t[0, :], 'b-')>>> im = ax2.imshow(znew_reggrid_t)>>> plt.colorbar(im, ax=ax2)

3. Scattered 2D linear interpolation: prefer LinearNDInterpolator to SmoothBivariateSpline or bisplrep#

For 2D scattered linear interpolation, both SmoothBivariateSpline and biplrep may either emit warnings, or fail to interpolate the data, or produce splines which with knots away from the data points. Instead, prefer LinearNDInterpolator, which is based on triangulating the data via QHull.

# TestSmoothBivariateSpline::test_integral>>> from scipy.interpolate import SmoothBivariateSpline, LinearNDInterpolator>>> x = np.array([1,1,1,2,2,2,4,4,4])>>> y = np.array([1,2,3,1,2,3,1,2,3])>>> z = np.array([0,7,8,3,4,7,1,3,4])

Now, use the linear interpolation over Qhull-based triangulation of data:

>>> xy = np.c_[x, y] # or just list(zip(x, y))>>> lut2 = LinearNDInterpolator(xy, z)>>> X = np.linspace(min(x), max(x))>>> Y = np.linspace(min(y), max(y))>>> X, Y = np.meshgrid(X, Y)

The result is easy to understand and interpret:

>>> fig = plt.figure()>>> ax = fig.add_subplot(projection='3d')>>> ax.plot_wireframe(X, Y, lut2(X, Y))>>> ax.scatter(x, y, z, 'o', color='k', s=48)

Note that bisplrep does something different! It may place spline knots outside of the data.

For illustration, consider the same data from the previous example:

>>> tck = bisplrep(x, y, z, kx=1, ky=1, s=0)>>> fig = plt.figure()>>> ax = fig.add_subplot(projection='3d')>>> xx = np.linspace(min(x), max(x))>>> yy = np.linspace(min(y), max(y))>>> X, Y = np.meshgrid(xx, yy)>>> Z = bisplev(xx, yy, tck)>>> Z = Z.reshape(*X.shape).T>>> ax.plot_wireframe(X, Y, Z, rstride=2, cstride=2)>>> ax.scatter(x, y, z, 'o', color='k', s=48)

Also, SmoothBivariateSpline fails to interpolate the data. Again, use the same data from the previous example.

>>> lut = SmoothBivariateSpline(x, y, z, kx=1, ky=1, s=0)>>> fig = plt.figure()>>> ax = fig.add_subplot(projection='3d')>>> xx = np.linspace(min(x), max(x))>>> yy = np.linspace(min(y), max(y))>>> X, Y = np.meshgrid(xx, yy)>>> ax.plot_wireframe(X, Y, lut(xx, yy).T, rstride=4, cstride=4)>>> ax.scatter(x, y, z, 'o', color='k', s=48)

Note that both SmoothBivariateSpline and bisplrep results have artifacts, unlike the LinearNDInterpolator’s. Issues illustrated here were reported for linear interpolation, however the FITPACK knot-selection mechanism does not guarantee to avoid either of these issues for higher-order (e.g. cubic) spline surfaces.