The Cumulative Sum And Cumulative Product Of Arrays

Overview:

  • numpy.ndarray supports cumulative sum and cumulative product of the n dimensional arrays.

 

  • When cumulative sum or cumulative product is performed for a 1 dimensional array, the number of axes is 1. For a 2 dimensional array number of axis is 2 and for a 3 dimensional array number of axes is 3 and so on.

 

  • When cumulative sum or cumulative product is performed for a one-dimensional array the axis parameter of cumsum() or cumprod() will take a value of 0. For a two dimensional array the axis parameter of cumsum() or cumprod() will take the values 0, 1 and for a three dimensional array the axis parameter of cumsum() or cumprod() will take the values 0, 1, 2 and so on.

 

  • The diagram below illustrates how the cumsum() or cumprod() work in numpy on an ndarray object.

Cumulative Sum and Cumulative Product using numpy.ndarray

Example - numpy.ndaray.csum:

# Example Python program demonstrating cumulative sum of a numpy.ndarray

 

# Import numpy module

import numpy as np

 

# Import standard library module random

import random

 

# Create a 3 dimensional ndarray object

array_3d = np.array([[[1,2,3,4],

                    [1,2,3,4],

                    [1,2,3,4]],

                   

                    [[1,2,3,4],

                    [1,2,3,4],

                    [1,2,3,4]],

                   

                    [[1,2,3,4],

                    [1,2,3,4],

                    [1,2,3,4]]])

print("Maximum value allowed for axis object for a 3 dimensional array:%d"%(array_3d.ndim-1))

print("Shape of the array: %d,%d,%d"%(array_3d.shape[0],array_3d.shape[1],array_3d.shape[2]))

 

print("Original Array:")

print(array_3d)                   

 

print("Cumulative Sum along Axis 0:")

csum = array_3d.cumsum(axis=0)

print(csum)

 

print("Cumulative Sum along Axis 1:")

csum = array_3d.cumsum(axis=1)

print(csum)

 

print("Cumulative Sum along Axis 2:")

csum = array_3d.cumsum(axis=2)

print(csum)

 

 

Output:

Maximum value allowed for axis object for a 3 dimensional array:2

Shape of the array: 3,3,4

Original Array:

[[[1 2 3 4]

  [1 2 3 4]

  [1 2 3 4]]

 

 [[1 2 3 4]

  [1 2 3 4]

  [1 2 3 4]]

 

 [[1 2 3 4]

  [1 2 3 4]

  [1 2 3 4]]]

Cumulative Sum along Axis 0:

[[[ 1  2  3  4]

  [ 1  2  3  4]

  [ 1  2  3  4]]

 

 [[ 2  4  6  8]

  [ 2  4  6  8]

  [ 2  4  6  8]]

 

 [[ 3  6  9 12]

  [ 3  6  9 12]

  [ 3  6  9 12]]]

Cumulative Sum along Axis 1:

[[[ 1  2  3  4]

  [ 2  4  6  8]

  [ 3  6  9 12]]

 

 [[ 1  2  3  4]

  [ 2  4  6  8]

  [ 3  6  9 12]]

 

 [[ 1  2  3  4]

  [ 2  4  6  8]

  [ 3  6  9 12]]]

Cumulative Sum along Axis 2:

[[[ 1  3  6 10]

  [ 1  3  6 10]

  [ 1  3  6 10]]

 

 [[ 1  3  6 10]

  [ 1  3  6 10]

  [ 1  3  6 10]]

 

 [[ 1  3  6 10]

  [ 1  3  6 10]

  [ 1  3  6 10]]]

 

 

Example - numpy.ndaray.cumprod:

# Example Python program demonstrating cumulative product of a numpy.ndarray

 

# Import numpy module

import numpy as np

 

# Import standard library module random

import random

 

# Create a 2-dimensional ndarray object

array_2d = np.array([[1,1,1,1],

                    [2,2,2,2],

                    [3,3,3,4]])

                   

print("Maximum value allowed for axis object for a 2 dimensional array:%d"%(array_2d.ndim-1))

print("Shape of the array: %d,%d"%(array_2d.shape[0], array_2d.shape[1]))

 

print("Original Array:")

print(array_2d)                   

 

print("Cumulative Product along Axis 0:")

cproduct = array_2d.cumprod(axis=0)

print(cproduct)

 

print("Cumulative Product along Axis 1:")

cproduct = array_2d.cumprod(axis=1)

print(cproduct)

 

 

Output:

Maximum value allowed for axis object for a 2 dimensional array:1

Shape of the array: 3,4

Original Array:

[[1 1 1 1]

 [2 2 2 2]

 [3 3 3 4]]

Cumulative Product along Axis 0:

[[1 1 1 1]

 [2 2 2 2]

 [6 6 6 8]]

Cumulative Product along Axis 1:

[[  1   1   1   1]

 [  2   4   8  16]

 [  3   9  27 108]]


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