NumPy

The Python programming language was not originally designed for numerical computing, but attracted the attention of the scientific and engineering community early on. In 1995 the special interest group (SIG) matrix-sig was founded with the aim of defining an array computing package; among its members was Python designer and maintainer Guido van Rossum, who extended Python's syntax (in particular the indexing syntax) to make array computing easier.[6]

An implementation of a matrix package was completed by Jim Fulton, then generalized by Jim Hugunin and called Numeric[6] (also variously known as the "Numerical Python extensions" or "NumPy").[7][8] Hugunin, a graduate student at the Massachusetts Institute of Technology (MIT),[8]^:10 joined the Corporation for National Research Initiatives (CNRI) in 1997 to work on JPython,[6] leaving Paul Dubois of Lawrence Livermore National Laboratory (LLNL) to take over as maintainer.[8]^:10 Other early contributors include David Ascher, Konrad Hinsen and Travis Oliphant.[8]^:10

A new package called Numarray was written as a more flexible replacement for Numeric.[9] Like Numeric, it too is now deprecated.[10][11] Numarray had faster operations for large arrays, but was slower than Numeric on small ones,[12] so for a time both packages were used in parallel for different use cases. The last version of Numeric (v24.2) was released on 11 November 2005, while the last version of numarray (v1.5.2) was released on 24 August 2006.[13]

There was a desire to get Numeric into the Python standard library, but Guido van Rossum decided that the code was not maintainable in its state then.[14]

In early 2005, NumPy developer Travis Oliphant wanted to unify the community around a single array package and ported Numarray's features to Numeric, releasing the result as NumPy 1.0 in 2006.[9] This new project was part of SciPy. To avoid installing the large SciPy package just to get an array object, this new package was separated and called NumPy. Support for Python 3 was added in 2011 with NumPy version 1.5.0.[15]

In 2011, PyPy started development on an implementation of the NumPy API for PyPy.[16] It is not yet fully compatible with NumPy.[17]

NumPy targets the CPython reference implementation of Python, which is a non-optimizing bytecode interpreter. Mathematical algorithms written for this version of Python often run much slower than compiled equivalents. NumPy addresses the slowness problem partly by providing multidimensional arrays and functions and operators that operate efficiently on arrays, requiring rewriting some code, mostly inner loops, using NumPy.

Using NumPy in Python gives functionality comparable to MATLAB since they are both interpreted,[18] and they both allow the user to write fast programs as long as most operations work on arrays or matrices instead of scalars. In comparison, MATLAB boasts a large number of additional toolboxes, notably Simulink, whereas NumPy is intrinsically integrated with Python, a more modern and complete programming language. Moreover, complementary Python packages are available; SciPy is a library that adds more MATLAB-like functionality and Matplotlib is a plotting package that provides MATLAB-like plotting functionality. Internally, both MATLAB and NumPy rely on BLAS and LAPACK for efficient linear algebra computations.

Python bindings of the widely used computer vision library OpenCV utilize NumPy arrays to store and operate on data. Since images with multiple channels are simply represented as three-dimensional arrays, indexing, slicing or masking with other arrays are very efficient ways to access specific pixels of an image. The NumPy array as universal data structure in OpenCV for images, extracted feature points, filter kernels and many more vastly simplifies the programming workflow and debugging.

Array creation

>>> import numpy as np
>>> x = np.array([1, 2, 3])
>>> x
array([1, 2, 3])
>>> y = np.arange(10)  # like Python's list(range(10)), but returns an array
>>> y
array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])

Basic operations

>>> a = np.array([1, 2, 3, 6])
>>> b = np.linspace(0, 2, 4)  # create an array with four equally spaced points starting with 0 and ending with 2.
>>> c = a - b
>>> c
array([ 1.        ,  1.33333333,  1.66666667,  4.        ])
>>> a**2
array([ 1,  4,  9, 36])

Universal functions

>>> a = np.linspace(-np.pi, np.pi, 100) 
>>> b = np.sin(a)
>>> c = np.cos(a)

Linear algebra

>>> from numpy.random import rand
>>> from numpy.linalg import solve, inv
>>> a = np.array([[1, 2, 3], [3, 4, 6.7], [5, 9.0, 5]])
>>> a.transpose()
array([[ 1. ,  3. ,  5. ],
       [ 2. ,  4. ,  9. ],
       [ 3. ,  6.7,  5. ]])
>>> inv(a)
array([[-2.27683616,  0.96045198,  0.07909605],
       [ 1.04519774, -0.56497175,  0.1299435 ],
       [ 0.39548023,  0.05649718, -0.11299435]])
>>> b =  np.array([3, 2, 1])
>>> solve(a, b)  # solve the equation ax = b
array([-4.83050847,  2.13559322,  1.18644068])
>>> c = rand(3, 3) * 20  # create a 3x3 random matrix of values within [0,1] scaled by 20
>>> c
array([[  3.98732789,   2.47702609,   4.71167924],
       [  9.24410671,   5.5240412 ,  10.6468792 ],
       [ 10.38136661,   8.44968437,  15.17639591]])
>>> np.dot(a, c)  # matrix multiplication
array([[  53.61964114,   38.8741616 ,   71.53462537],
       [ 118.4935668 ,   86.14012835,  158.40440712],
       [ 155.04043289,  104.3499231 ,  195.26228855]])
>>> a @ c # Starting with Python 3.5 and NumPy 1.10
array([[  53.61964114,   38.8741616 ,   71.53462537],
       [ 118.4935668 ,   86.14012835,  158.40440712],
       [ 155.04043289,  104.3499231 ,  195.26228855]])

Tensors

>>> M = np.zeros(shape=(2, 3, 5, 7, 11))
>>> T = np.transpose(M, (4, 2, 1, 3, 0))
>>> T.shape
(11, 5, 3, 7, 2)

Incorporation with OpenCV

>>> import numpy as np
>>> import cv2
>>> r = np.reshape(np.arange(256*256)%256,(256,256))  # 256x256 pixel array with a horizontal gradient from 0 to 255 for the red color channel
>>> g = np.zeros_like(r)  # array of same size and type as r but filled with 0s for the green color channel
>>> b = r.T # transposed r will give a vertical gradient for the blue color channel
>>> cv2.imwrite('gradients.png', np.dstack([b,g,r]))  # OpenCV images are interpreted as BGR, the depth-stacked array will be written to an 8bit RGB PNG-file called 'gradients.png'
True

Nearest Neighbor Search - Iterative Python algorithm and vectorized NumPy version

>>> # # # Pure iterative Python # # #
>>> points = [[9,2,8],[4,7,2],[3,4,4],[5,6,9],[5,0,7],[8,2,7],[0,3,2],[7,3,0],[6,1,1],[2,9,6]]
>>> qPoint = [4,5,3]
>>> minIdx = -1
>>> minDist = -1
>>> for idx, point in enumerate(points):  # iterate over all points
...     dist = sum([(dp-dq)**2 for dp,dq in zip(point,qPoint)])**0.5  # compute the euclidean distance for each point to q
...     if dist < minDist or minDist < 0:  # if necessary, update minimum distance and index of the corresponding point
...         minDist = dist
...         minIdx = idx

>>> print('Nearest point to q: {0}'.format(points[minIdx]))
Nearest point to q: [3, 4, 4]

>>> # # # Equivalent NumPy vectorization # # #
>>> import numpy as np
>>> points = np.array([[9,2,8],[4,7,2],[3,4,4],[5,6,9],[5,0,7],[8,2,7],[0,3,2],[7,3,0],[6,1,1],[2,9,6]])
>>> qPoint = np.array([4,5,3])
>>> minIdx = np.argmin(np.linalg.norm(points-qPoint,axis=1))  # compute all euclidean distances at once and return the index of the smallest one
>>> print('Nearest point to q: {0}'.format(points[minIdx]))
Nearest point to q: [3 4 4]

• Array programming
• List of numerical-analysis software

• Bressert, Eli (2012). Scipy and Numpy: An Overview for Developers. O'Reilly. ISBN 978-1-4493-0546-8.
• McKinney, Wes (2017). Python for Data Analysis : Data Wrangling with Pandas, NumPy, and IPython (2nd ed.). Sebastopol: O'Reilly. ISBN 978-1-4919-5766-0.
• VanderPlas, Jake (2016). "Introduction to NumPy". Python Data Science Handbook: Essential Tools for Working with Data. O'Reilly. pp. 33–96. ISBN 978-1-4919-1205-8.

• Official website
• History of NumPy