How can `np.ix_` simplify index selection and assignment in multidimensional NumPy arrays?

Indexing Arrays and Boolean Masks for Index Selection or Assignment Using np.ix_

Manipulating selections or assignments in multidimensional NumPy arrays can be simplified using np.ix_. Here's how it works:

1. Using Indexing Arrays

A. Selection

np.ix_ allows you to group indexing arrays into higher-dimensional combinations for indexing multidimensional arrays. To make a selection using two 1D indexing arrays (e.g., row_indices and col_indices), use:

<code class="python">x_indexed = x[np.ix_(row_indices, col_indices)]</code>

This is equivalent to a nested version where the outer indexing array (e.g., row_indices) are broadcast against the inner indexing array (col_indices):

<code class="python">x_indexed = x[np.asarray(row_indices)[:,None], col_indices]</code>

B. Assignment

Similarly, using the indexing arrays tuple created by np.ix_, scalar assignments or broadcasting of a block of data can be done directly:

<code class="python">x[np.ix_(row_indices, col_indices)] = scalar # assign a scalar
x[np.ix_(row_indices, col_indices)] = block  # assign a broadcastable block</code>

2. Using Boolean Masks

np.ix_ also works with Boolean masks:

A. Selection

To select a block of data using Boolean masks (row_mask and col_mask), use:

<code class="python">x[np.ix_(row_mask, col_mask)]</code>

B. Assignment

For assignments with Boolean masks, use:

<code class="python">x[np.ix_(row_mask, col_mask)] = scalar # assign a scalar
x[np.ix_(row_mask, col_mask)] = block  # assign a broadcastable block</code>

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