# Reducing and accumulating numpy arrays

Martin McBride, 2021-02-27
Tags arrays data types vectorisation
Categories numpy

A reducing function takes a collection of values and calculates a single representative value. Standard Pythion has a number of built-in reducing functions that work with lists and other sequences:

• `sum` calculates the sum of all the elements (ie adds them all together).
• `max` gives the largest element.
• `all` is true if every element is true, false if one or more are false.

NumPy allows to reduce using any binary ufunc.

## Reducing

To explain how reduce works, we will take the example of calculating the sum of all elements in an array. To calculate this, you would add the first two numbers, then add the third number to the total, then the fourth number and so on.

Here is how we do this in NumPy:

```a = np.array([1, 2, 3, 4])
```

In this case, `reduce` is actually a method of the `np.add` function. That might seem odd at first, but remember that in Python, functions are objects, and a function object can have methods of its own.

The `reduce` method of the `add` function start with the value 0 and adds each element of the array, one by one. This calculates `0 + 1 + 2 + 3 + 4`, the sum of all elements.

You can use `reduce` with many other ufuncs. For example, this code calculates the product of all the elements:

```a = np.array([1, 2, 3, 4])
b = np.mul.reduce(a)
```

`mul.reduce` start with 1 and multiples the elements one by one, giving `1 * 1 * 2 * 3 * 4`.

Some reductions are so commonly used that NumPy provides short names that you can use instead:

• `sum` for `add.reduce`.
• `product` for `mul.reduce`.
• `alltrue` for `and.reduce`.
• `sometrue` for `or.reduce`.

### 5.4.2 Accumulation

Accumulation is a bit like reduction, but the result is a running total array, rather than a single value. For example:

```a = np.array([1, 2, 3, 4])
```

Gives:

```b = [ 1  3  6 10]
```

The values in the array are 1, 1+2, 1+2+3, 1+2+3+4.

You can use the short name `cumsum` for `add.accumulate`, and `cumproduct` for `product.accumulate`.

Visit the PythonInformer Discussion Forum for numeric Python.

If you found this article useful, you might be interested in the book NumPy Recipes or other books by the same author.

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