def test_interp(z, f, z_fine, title):
interp = PISM.ColumnInterpolation(z, z_fine)
f_fine = interp.coarse_to_fine(f, interp.Mz_fine())
f_fine_numpy = np.interp(z_fine, z, f)
f_roundtrip = interp.fine_to_coarse(f_fine)
if plot:
plt.figure()
plt.plot(z, f, 'o-', label="original coarse-grid data")
plt.plot(z_fine, f_fine, 'o-', label="interpolated onto the fine grid")
plt.plot(z, f_roundtrip, 'o-', label="interpolated back onto the coarse grid")
plt.plot(z, f_roundtrip - f, 'o-', label="difference after the roundtrip")
plt.legend(loc="best")
plt.title(title)
plt.grid(True)
delta = np.linalg.norm(f - f_roundtrip, ord=1)
delta_numpy = np.linalg.norm(f_fine - f_fine_numpy, ord=1)
print("norm1(fine_to_coarse(coarse_to_fine(f)) - f) = %f" % delta)
print("norm1(PISM - NumPy) = %f" % delta_numpy)
return delta, delta_numpy
