How to Access Values in Multidimensional Arrays Using Lower- Dimensional Arrays Effectively?

Accessing Multidimensional Arrays with Lower-Dimensional Arrays

In multidimensional arrays, retrieving values along a specific dimension using an array of lower dimensionality can be challenging. Consider the example below:

<code class="python">a = np.random.random_sample((3,4,4))
b = np.random.random_sample((3,4,4))
idx = np.argmax(a, axis=0)</code>

How can we access the maxima in a using idx as if we had used a.max(axis=0)? How do we retrieve the corresponding values from b?

Elegant Solution Using Advanced Indexing

Advanced indexing provides a flexible way to achieve this:

<code class="python">m, n = a.shape[1:]  # Extract dimensions excluding axis 0
I, J = np.ogrid[:m, :n]
a_max_values = a[idx, I, J]  # Index using the grid
b_max_values = b[idx, I, J]</code>

This solution exploits the fact that the grid [idx, I, J] spans all possible combinations of indices for the remaining dimensions.

Generalization for Arbitrary Dimensionality

For a general n-dimensional array, a function can be defined to generalize the above solution:

<code class="python">def argmax_to_max(arr, argmax, axis):
    """
    Apply argmax() operation along one axis to retrieve maxima.

    Args:
        arr: Array to apply argmax to
        argmax: Resulting argmax array
        axis: Axis to apply argmax (0-based)
    Returns:
        Maximum values along specified axis
    """
    new_shape = list(arr.shape)
    del new_shape[axis]

    grid = np.ogrid[tuple(map(slice, new_shape))]  # Create grid of indices
    grid.insert(axis, argmax)

    return arr[tuple(grid)]</code>

Alternative Indexing Method

Alternatively, a function can be created to generate a grid of indices for all axes:

<code class="python">def all_idx(idx, axis):
    grid = np.ogrid[tuple(map(slice, idx.shape))]
    grid.insert(axis, idx)
    return tuple(grid)</code>

This grid can then be used to access a multidimensional array with a lower-dimensional array:

<code class="python">a_max_values = a[all_idx(idx, axis=axis)]
b_max_values = b[all_idx(idx, axis=axis)]</code>

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