Interpolating over 2D-grid.

[JeanKaddour]

Hi Patrick,

first of all, thank you very much for creating this great library.

I've got a very basic question:

I want to interpolate over a 2D-grid. In SciPy, I run the following code:

import numpy as np
from scipy import interpolate
# Data Generation
X = np.linspace(0.0, 1.0, num=12)
Y = np.linspace(0.0, 1.0, num=4)
z_list = [
    [0.8, 1.6, 2.0, 3.0],
    [0.6, 1.4, 2.5, 2.9],
    [0.2, 0.9, 0.6, 2.8],
    [0.5, 1.0, 1.2, 2.7],
    [0.5, 1.5, 1.6, 2.6],
    [0.5, 1.4, 1.5, 2.5],
    [0.3, 1.4, 1.2, 2.4],
    [0.5, 1.2, 1.5, 2.3],
    [0.4, 1.2, 1.5, 2.0],
    [0.35, 0.9, 1.4, 1.5],
    [0.35, 0.9, 1.4, 1.5],
    [0.35, 0.9, 1.4, 1.5],
]
Z = np.array(z_list)
Z = Z.transpose()
interpol_function = interpolate.interp2d(X, Y, Z, kind="cubic")

Then, I can evaluate interpol_function(X, Y) at arbitrary X and Y.

I tried to match the dimensions to your "batch-length-channel" format, resulting in

num_X, num_Y = 12, 4
X = torch.linspace(0.0, 1.0, steps=num_X)
Y = torch.linspace(0.0, 1.0, steps=num_Y)
t = torch.meshgrid([X, Y])
x = torch.Tensor(
    [
        [0.8, 1.6, 2.0, 3.0],
        [0.6, 1.4, 2.5, 2.9],
        [0.2, 0.9, 0.6, 2.8],
        [0.5, 1.0, 1.2, 2.7],
        [0.5, 1.5, 1.6, 2.6],
        [0.5, 1.4, 1.5, 2.5],
        [0.3, 1.4, 1.2, 2.4],
        [0.5, 1.2, 1.5, 2.3],
        [0.4, 1.2, 1.5, 2.0],
        [0.35, 0.9, 1.4, 1.5],
        [0.35, 0.9, 1.4, 1.5],
        [0.35, 0.9, 1.4, 1.5],
    ]
)
x = torch.reshape(x, (num_X, num_Y, 1))
coeffs = natural_cubic_spline_coeffs(t, x)

However, this results in an error due to the time tensor t not containing one-dimensional floating point values. How would you recommend to reshape the dimensions here?

[patrick-kidger]

Unfortunately torchcubicspline isn't designed to handle two dimensions. It's only capable of interpolating problems of the form f(t) = x, where t is a scalar.

[JeanKaddour]

Got it. Thank you very much!