2-Dimensional Interpolation of Tidy Data

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Out:

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 import numpy as np
 import matplotlib.pyplot as plt
 from scipy import interpolate
 from scipy.stats import norm
 from mpl_toolkits.mplot3d import Axes3D

 import pandas as pd

 import itertools

 import ndsplines

 def gaussian(x_in):
     z = norm.ppf(.995)
     x = z*(2*x_in-1)
     return norm.pdf(x)

 def sin(x_in):
     x = np.pi*(x_in-0.5)
     return np.sin(x)

 def tanh(x_in):
     x = 2*np.pi*(x_in-0.5)
     return np.tanh(x)

 def dist(x_in, y_in):
     return np.sqrt((x_in-0.25)**2 + (y_in-0.25)**2)

 funcs = [gaussian, sin, tanh]

 def wrap2d(funcx, funcy):
     def func2d(x_in, y_in):
         return funcx(x_in)*funcy(y_in)
     func2d.__name__ = '_'.join([funcx.__name__, funcy.__name__])
     return func2d

 funcs = [ wrap2d(*funcs_to_wrap) for funcs_to_wrap in itertools.combinations_with_replacement(funcs, r=2)]
 funcs.append(dist)

 x = np.linspace(0, 1, 7)
 y = np.linspace(0, 1, 7)

 xx = np.linspace(0,1,64)
 yy = np.linspace(0,1,64)

 xx = np.linspace(-.25, 1.25, 64)
 yy = np.linspace(-.25, 1.25, 64)
 k = 3


 meshx, meshy = np.meshgrid(x, y, indexing='ij')
 gridxy = np.r_['0,3', meshx, meshy]
 gridxy = np.stack((meshx, meshy), axis=-1)
 tidyxy = gridxy.reshape((-1,2))


 meshxx, meshyy = np.meshgrid(xx, yy, indexing='ij')
 gridxxyy = np.stack((meshxx, meshyy), axis=-1)

 for func in funcs:
     fvals = func(meshx, meshy)
     truef = func(meshxx, meshyy)

     tidy_array = np.concatenate((fvals.reshape((-1,1)), tidyxy,), axis=1)

     tidy_df = pd.DataFrame(tidy_array, columns=['z', 'x', 'y',])
     test_NDBspline3 = ndsplines.make_interp_spline(gridxy, fvals[:, :, None])
     test_NDBspline = ndsplines.make_interp_spline_from_tidy(tidy_df, ['x', 'y'], ['z'])
     test_RectSpline = interpolate.RectBivariateSpline(x, y, fvals)
     test_NDBspline2 = ndsplines.make_interp_spline_from_tidy(tidy_array, [1,2], [0])

     print(np.allclose(test_NDBspline2(gridxxyy),test_NDBspline(gridxxyy)))

     fig = plt.figure()
     ax = fig.add_subplot(111, projection='3d')

     ax.plot_wireframe(meshxx, meshyy, truef, alpha=0.25, color='C0')
     ax.plot_wireframe(meshxx, meshyy, test_NDBspline(gridxxyy)[...,0], color='C1')
     ax.plot_wireframe(meshxx, meshyy, test_RectSpline(meshxx, meshyy, grid=False), color='C2')
     plt.show()