How to Access Multidimensional Arrays with (n-1)-Dimensional Arrays?

Accessing Multidimensional Arrays with (n-1)-Dimensional Arrays: A Comprehensive Guide

In the realm of multidimensional arrays, arises a tantalizing challenge: accessing an n-dimensional array with an (n-1)-dimensional array along a specific dimension. This puzzle has captivated numerous data scientists and programmers alike.

The Problem: Dissecting a Multidimensional Array

Envision a 3-dimensional array, a, brimming with numerical values distributed across its three axes. Now, suppose we hold an unyielding desire to extract the maxima along a given dimension, say the first. How might we accomplish this with an (n-1)-dimensional array, idx, that holds the indices of the maxima along that very dimension?

Solution 1: Unleashing the Power of Advanced Indexing

Harnessing the might of advanced indexing, we can conjure a solution to our dilemma. By leveraging the grid function of numpy, we can deftly generate coordinates that span the shape of each dimension of a, save for the dimension we seek to index. This operation bestows upon us the ability to access the maxima of a as if extracted through a.max(axis=0).

<code class="python">m, n = a.shape[1:]
I, J = np.ogrid[:m, :n]
a_max_values = a[idx, I, J]</code>

Solution 2: A Generic Approach for the Masses

For those seeking a more generalized solution, we introduce argmax_to_max. This ingenious function empowers us to effortlessly replicate the behavior of arr.max(axis) from argmax and arr. Its elegant design simplifies index-crunching tasks with its intricate machinations.

<code class="python">def argmax_to_max(arr, argmax, axis):
    new_shape = list(arr.shape)
    del new_shape[axis]

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

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

Indexing a Multidimensional Array: Unveiling a Subtlety

Beyond extracting maxima, accessing a multidimensional array with an (n-1)-dimensional array presents another intriguing challenge. By decomposing array shape into (n-1)-dimensional grids, all_idx facilitates seamless retrieval of element values specified by the indices.

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

Armed with this arsenal of index-mangling techniques, you now possess the intellectual capital to conquer the challenges of accessing multidimensional arrays with (n-1)-dimensional arrays in your data wrangling adventures. May it bring you triumph and enlightenment!

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