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# NumPy Summations

## Summations

What is the difference between summation and addition?

Addition is done between two arguments whereas summation happens over n elements.

### Example

Add the values in arr1 to the values in arr2:

import numpy as np

arr1 = np.array([1, 2, 3])
arr2 = np.array([1, 2, 3])

print(newarr)
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Returns: `[2 4 6]`

### Example

Sum the values in arr1 and the values in arr2:

import numpy as np

arr1 = np.array([1, 2, 3])
arr2 = np.array([1, 2, 3])

newarr = np.sum([arr1, arr2])

print(newarr)
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Returns: `12`

## Summation Over an Axis

If you specify `axis=1`, NumPy will sum the numbers in each array.

### Example

Perform summation in the following array over 1st axis:

import numpy as np

arr1 = np.array([1, 2, 3])
arr2 = np.array([1, 2, 3])

newarr = np.sum([arr1, arr2], axis=1)

print(newarr)
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Returns: `[6 6]`

## Cummulative Sum

Cummulative sum means partially adding the elements in array.

E.g. The partial sum of [1, 2, 3, 4] would be [1, 1+2, 1+2+3, 1+2+3+4] = [1, 3, 6, 10].

Perfom partial sum with the `cumsum()` function.

### Example

Perform cummulative summation in the following array:

import numpy as np

arr = np.array([1, 2, 3])

newarr = np.cumsum(arr)

print(newarr)
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Returns: `[1 3 6]`