where_2d.Rmd

---
jupyter:
  jupytext:
    notebook_metadata_filter: all,-language_info
    split_at_heading: true
    text_representation:
      extension: .Rmd
      format_name: rmarkdown
      format_version: '1.2'
      jupytext_version: 1.6.0
  kernelspec:
    display_name: Python 3
    language: python
    name: python3
---

# Where in 2D

This follows from [where and argmin](where_and_argmin).

That page covers how `np.where` and `np.argmin` work for one-dimensional
arrays.

This page covers what happens for `np.where` with arrays of two dimensions and
more.

## Arrays can have two dimensions

```{python}
import numpy as np
```

So far we have only seen one-dimensional arrays.

A *vector* is another term for a one-dimensional array.

Here's a one-dimensional array (vector):

```{python}
arr_one_d = np.array([2, 99, -1, 4, 99])
arr_one_d
```

Notice the `shape` of the array:

```{python}
arr_one_d.shape
```

You can also think of this one-dimensional array as a single *row*.

In fact you can have arrays with more than one row, like this:

```{python}
arr_two_d = np.array([[1, 2, 3, -2, -3], [10, 11, 12, -3, -13]])
arr_two_d
```

Notice the `shape`.  This array has 2 rows, each with 5 columns.

```{python}
arr_two_d.shape
```

Remember, we can ask for a single element from a one-dimensional array, using *indexing* with an integer between square brackets. The integer gives the *position* (or offset) of the element we want.

```{python}
arr_one_d[1]
```

With a two-dimensional array, we need to specify the row *and* column of the element we want:

```{python}
arr_two_d[1, 4]
```

The first value between the brackets is the row position, and the second is the column position.


## Revision - using where on one-dimensional arrays

`np.where` gets the indices of the True values in a Boolean array.

```{python}
# A Boolean array.
equal_to_99 = arr_one_d == 99
equal_to_99
```

```{python}
# Indices of the True values.
indices = np.where(equal_to_99)
indices
```

We can use the returned `indices` to index into the array, using square brackets.

```{python}
arr_one_d[indices]
```

## The two-dimensional case

This also works in two or more dimensions.

`np.where` now returns two index arrays, one for the rows, and one for the
columns.

```{python}
indices2d = np.where(arr_two_d == -3)
indices2d
```

Just as for the one-dimensional case, we can use the returned indices to index
into the array, and get the elements.

```{python}
arr_two_d[indices2d]
```