Interpolate along single dimension of multidimensional array

When working with multidimensional arrays in Julia, you may come across the need to interpolate along a single dimension. This can be achieved in different ways, depending on your specific requirements. In this article, we will explore three different options to solve this problem.

Option 1: Using the Interpolations.jl Package

The Interpolations.jl package provides a convenient way to perform interpolation in Julia. To interpolate along a single dimension of a multidimensional array, you can use the `interpolate` function from this package.

using Interpolations

# Create a multidimensional array
arr = [1 2 3; 4 5 6; 7 8 9]

# Define the dimension along which to interpolate
dim = 2

# Create an interpolator object
itp = interpolate(arr, BSpline(Linear()), Gridded())

# Interpolate along the specified dimension
result = interpolate(itp, Val(dim))

In this example, we create a 3×3 multidimensional array `arr`. We then define the dimension `dim` along which we want to interpolate. Next, we create an interpolator object `itp` using the `interpolate` function from the Interpolations.jl package. Finally, we use the `interpolate` function again to perform the interpolation along the specified dimension, resulting in the interpolated array `result`.

Option 2: Using the LinearAlgebra.jl Package

If you prefer to avoid using additional packages, you can achieve interpolation along a single dimension of a multidimensional array using the `LinearAlgebra.jl` package. This package provides various linear algebra functions, including matrix operations.

using LinearAlgebra

# Create a multidimensional array
arr = [1 2 3; 4 5 6; 7 8 9]

# Define the dimension along which to interpolate
dim = 2

# Interpolate along the specified dimension
result = LinearAlgebra.interpolate(arr, dim)

In this example, we create a 3×3 multidimensional array `arr`. We then define the dimension `dim` along which we want to interpolate. Finally, we use the `interpolate` function from the LinearAlgebra.jl package to perform the interpolation along the specified dimension, resulting in the interpolated array `result`.

Option 3: Manual Interpolation

If you prefer a more manual approach, you can perform interpolation along a single dimension of a multidimensional array by implementing the interpolation logic yourself. This gives you more control over the interpolation process, but requires more code.

# Create a multidimensional array
arr = [1 2 3; 4 5 6; 7 8 9]

# Define the dimension along which to interpolate
dim = 2

# Get the size of the array along the specified dimension
size_dim = size(arr, dim)

# Create an empty array to store the interpolated values
result = similar(arr)

# Perform the interpolation
for i in 1:size_dim
    # Get the indices for interpolation
    indices = [1:size(arr, j) for j in 1:ndims(arr)]
    indices[dim] = i
    
    # Perform the interpolation along the specified dimension
    result[indices...] = interpolate(arr[indices...])
end

In this example, we create a 3×3 multidimensional array `arr`. We then define the dimension `dim` along which we want to interpolate. Next, we get the size of the array along the specified dimension using the `size` function. We create an empty array `result` with the same size as `arr` using the `similar` function. Finally, we use a loop to iterate over the indices along the specified dimension and perform the interpolation using the `interpolate` function, storing the interpolated values in the `result` array.

After exploring these three options, it is clear that using the Interpolations.jl package provides the most convenient and efficient solution for interpolating along a single dimension of a multidimensional array in Julia. It offers a simple and intuitive interface, allowing you to easily perform interpolation without the need for manual implementation. Therefore, Option 1 is the recommended approach for solving this problem.