NumPy in Python. Part 1

Translator's Preface


Good day, Habr. I start a series of articles that are a translation of a little mana by numpy, a reference . Enjoy reading.



Introduction


NumPy is an open-source module for python that provides general mathematical and numerical operations in the form of pre-compiled, fast functions. They are combined in high-level packages. They provide functionality that can be compared with the functionality of MatLab. NumPy (Numeric Python) provides basic methods for manipulating large arrays and matrices. SciPy (Scientific Python) extends the numpy functionality with a huge collection of useful algorithms such as minimization, Fourier transform, regression, and other applied mathematical techniques.

Installation


If you have Python (x, y) ( Translator's note: Python (x, y), this is a distribution of free scientific and engineering software for numerical calculations, analysis and visualization of data based on the Python programming language and a large number of modules (libraries)) on a Windows platform, then you are ready to start. If not, then after installing python, you need to install the packages yourself, first NumPy then SciPy. Installation is available here . Follow the installation on the page, everything is very clear there.

A bit of additional information


The NumPy and SciPy community supports an online guide including guides and tutorials, here: docs.scipy.org/doc.

Importing a numpy module

There are several import paths. The standard method is to use a simple expression:

>>> import numpy

However, for a large number of calls to numpy functions, it becomes tedious to write numpy.X again and again. Instead, it is much easier to do it like this:

>>> import numpy as np

This expression allows us to access numpy objects using np.X instead of numpy.X. You can also import numpy directly into the namespace you use so that you don’t use functions through the dot at all, but call them directly:

>>> from numpy import *

However, this option is not welcomed in python programming, as it removes some of the useful structures that the module provides. Until the end of this tutorial, we will use the second import option (import numpy as np).

Arrays


The main feature of numpy is the array object. Arrays are similar to lists in python, except that the elements of the array must have the same data type, like float and int. Arrays can perform numerical operations with a large amount of information many times faster and, most importantly, much more efficiently than with lists.

Creating an array from a list:

a = np.array([1, 4, 5, 8], float)
>>> a
array([ 1.,  4.,  5.,  8.])
>>> type(a)

Here, the array function takes two arguments: a list to convert to an array and a type for each element. All elements can be accessed and manipulated in the same way as you would with regular lists:

>>> a[:2]
array([ 1.,  4.])
>>> a[3]
8.0
>>> a[0] = 5.
>>> a
array([ 5.,  4.,  5.,  8.])

Arrays can be multidimensional. Unlike lists, you can specify commands in brackets. Here is an example of a two-dimensional array (matrix):

>>> a = np.array([[1, 2, 3], [4, 5, 6]], float)
>>> a
array([[ 1.,  2.,  3.],
[ 4.,  5.,  6.]])
>>> a[0,0]
1.0
>>> a[0,1]
2.0

Array slicing works with multidimensional arrays in the same way as with one-dimensional arrays, applying each slice as a filter for the established measurement. Use ":" in a dimension to indicate the use of all the elements of this dimension:

>>> a = np.array([[1, 2, 3], [4, 5, 6]], float)
>>> a[1,:]
array([ 4.,  5.,  6.])
>>> a[:,2]
array([ 3.,  6.])
>>> a[-1:, -2:]
array([[ 5.,  6.]])

The shape method returns the number of rows and columns in the matrix:

>>> a.shape
(2, 3)

The dtype method returns the type of variables stored in the array:

>>> a.dtype
dtype('float64')

Here float64 is a numpy numeric data type that is used to store double precision real numbers. So what about a float in Python.

The len method returns the length of the first dimension (axis):

a = np.array([[1, 2, 3], [4, 5, 6]], float)
>>> len(a)
2

The in method is used to check for the presence of an element in the array:

>>> a = np.array([[1, 2, 3], [4, 5, 6]], float)
>>> 2 in a
True
>>> 0 in a
False

Arrays can be reorganized using the method that defines a new multidimensional array. Following the following example, we reformat the one-dimensional array of ten elements into a two-dimensional array of five rows and two columns:

>>> a = np.array(range(10), float)
>>> a
array([ 0.,  1.,  2., 3.,  4.,  5.,  6.,  7.,  8.,  9.])
>>> a = a.reshape((5, 2))
>>> a
array([[ 0.,  1.],
[ 2.,  3.],
[ 4.,  5.],
[ 6.,  7.],
[ 8.,  9.]])
>>> a.shape
(5, 2)

Note that the reshape method creates a new array, and does not modify the original.

Keep in mind name binding in python also works with arrays. The copy method is used to create a copy of an existing array in memory:

>>> a = np.array([1, 2, 3], float)
>>> b = a
>>> c =  a.copy()
>>> a[0] = 0
>>> a
array([0., 2., 3.])
>>> b
array([0., 2., 3.])
>>> c
array([1., 2., 3.])

Lists can also be created from arrays:

>>> a = np.array([1, 2, 3], float)
>>> a.tolist()
[1.0, 2.0, 3.0]
>>> list(a)
[1.0, 2.0, 3.0]

You can also convert the array to a binary string (that is, a non-human-readable form). Use the tostring method to do this. The fromstring method works for inverse conversion. These operations are sometimes useful for storing large amounts of data in files that may be read in the future.

>>> a = array([1, 2, 3], float)
>>> s = a.tostring()
>>> s
'\x00\x00\x00\x00\x00\x00\xf0?\x00\x00\x00\x00\x00\x00\x00@\x00\x00\x00\x00\x00\x00\x08@'
>>> np.fromstring(s)
array([ 1.,  2.,  3.])

Filling an array with the same value.

>>> a = array([1, 2, 3], float)
>>> a
array([ 1.,  2.,  3.])
>>> a.fill(0)
>>> a
array([ 0.,  0.,  0.])

Transposing arrays is also possible, creating a new array:

>>> a = np.array(range(6), float).reshape((2, 3))
>>> a
array([[ 0.,  1.,  2.],
[ 3.,  4.,  5.]])
>>> a.transpose()
array([[ 0.,  3.],
[ 1.,  4.],
[ 2.,  5.]])

A multidimensional array can be converted to a one-dimensional array using the flatten method:

>>> a = np.array([[1, 2, 3], [4, 5, 6]], float)
>>> a
array([[ 1.,  2.,  3.],
[ 4.,  5.,  6.]])
>>> a.flatten()
array([ 1.,  2.,  3.,  4.,  5.,  6.])

Two or more arrays can be concatenated using the concatenate method:

>>> a = np.array([1,2], float)
>>> b = np.array([3,4,5,6], float)
>>> c = np.array([7,8,9], float)
>>> np.concatenate((a, b, c))
array([1., 2., 3., 4., 5., 6., 7., 8., 9.])

If the array is not one-dimensional, you can specify the axis along which the connection will occur. By default (without setting the axis value), the connection will occur according to the first measurement:

>>> a = np.array([[1, 2], [3, 4]], float)
>>> b = np.array([[5, 6], [7,8]], float)
>>> np.concatenate((a,b))
array([[ 1.,  2.],
[ 3.,  4.],
[ 5.,  6.],
[ 7.,  8.]])
>>> np.concatenate((a,b), axis=0)
array([[ 1.,  2.],
[ 3.,  4.],
[ 5.,  6.],
[ 7.,  8.]])
>>>
np.concatenate((a,b), axis=1)
array([[ 1.,  2.,  5.,  6.],
[ 3.,  4.,  7.,  8.]])

In conclusion, the dimension of the array can be increased by using the newaxis constant in square brackets:

>>> a = np.array([1, 2, 3], float)
>>> a
array([1., 2., 3.])
>>> a[:,np.newaxis]
array([[ 1.],
[ 2.],
[ 3.]])
>>> a[:,np.newaxis].shape
(3,1)
>>> b[np.newaxis,:]
array([[ 1.,  2.,  3.]])
>>> b[np.newaxis,:].shape
(1,3)

Note that here each array is two-dimensional; created using newaxis has a dimension of one. The newaxis method is suitable for conveniently creating properly dimensional arrays in vector and matrix mathematics.

This is the end of the first part of the translation. Thanks for attention.

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