# Reducing and accumulating numpy arrays

By 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.