the absolute basics for beginners — NumPy v2.0 Manual (2024)

How to import NumPy#

After installing NumPy, it may be importedinto Python code like:

import numpy as np

This widespread convention allows access to NumPy features with a short,recognizable prefix (np.) while distinguishing NumPy features from othersthat have the same name.

Reading the example code#

Throughout the NumPy documentation, you will find blocks that look like:

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

Text preceded by >>> or ... is input, the code that you wouldenter in a script or at a Python prompt. Everything else is output, theresults of running your code. Note that >>> and ... are not part of thecode and may cause an error if entered at a Python prompt.

Why use NumPy?#

Python lists are excellent, general-purpose containers. They can be“heterogeneous”, meaning that they can contain elements of a variety of types,and they are quite fast when used to perform individual operations on a handfulof elements.

Depending on the characteristics of the data and the types of operations thatneed to be performed, other containers may be more appropriate; by exploitingthese characteristics, we can improve speed, reduce memory consumption, andoffer a high-level syntax for performing a variety of common processing tasks.NumPy shines when there are large quantities of “hom*ogeneous” (same-type) datato be processed on the CPU.

What is an “array”?#

In computer programming, an array is a structure for storing and retrievingdata. We often talk about an array as if it were a grid in space, with eachcell storing one element of the data. For instance, if each element of thedata were a number, we might visualize a “one-dimensional” array like alist:

\[\begin{split}\begin{array}{|c||c|c|c|}\hline1 & 5 & 2 & 0 \\\hline\end{array}\end{split}\]

A two-dimensional array would be like a table:

\[\begin{split}\begin{array}{|c||c|c|c|}\hline1 & 5 & 2 & 0 \\\hline8 & 3 & 6 & 1 \\\hline1 & 7 & 2 & 9 \\\hline\end{array}\end{split}\]

A three-dimensional array would be like a set of tables, perhaps stackedas though they were printed on separate pages. In NumPy, this idea isgeneralized to an arbitrary number of dimensions, and so the fundamentalarray class is called ndarray: it represents an “N-dimensionalarray”.

Most NumPy arrays have some restrictions. For instance:

• All elements of the array must be of the same type of data.

• Once created, the total size of the the array can’t change.

• The shape must be “rectangular”, not “jagged”; e.g., each row ofa two-dimensional array must have the same number of columns.

When these conditions are met, NumPy exploits these characteristics tomake the array faster, more memory efficient, and more convenient to use thanless restrictive data structures.

For the remainder of this document, we will use the word “array” to refer toan instance of ndarray.

Array fundamentals#

One way to initialize an array is using a Python sequence, such as a list.For example:

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

Elements of an array can be accessed in various ways. For instance, we can access anindividual element of this array as we would access an element in the originallist: using the integer index of the element within square brackets.

>>> a[0]1

Like the original list, the array is mutable.

>>> a[0] = 10>>> aarray([10, 2, 3, 4, 5, 6])

Also like the original list, Python slice notation can be used for indexing.

>>> a[:3]array([10, 2, 3])

One major difference is that slice indexing of a list copies the elements intoa new list, but slicing an array returns a view: an object that refers to thedata in the original array. The original array can be mutated using the view.

>>> b = a[3:]>>> barray([4, 5, 6])>>> b[0] = 40>>> aarray([ 10, 2, 3, 40, 5, 6])

See Copies and views for a more comprehensive explanation of whenarray operations return views rather than copies.

Two- and higher-dimensional arrays can be initialized from nested Pythonsequences:

>>> a = np.array([[1, 2, 3, 4], [5, 6, 7, 8], [9, 10, 11, 12]])>>> aarray([[ 1, 2, 3, 4], [ 5, 6, 7, 8], [ 9, 10, 11, 12]])

In NumPy, a dimension of an array is sometimes referred to as an “axis”. Thisterminology may be useful to disambiguate between the dimensionality of anarray and the dimensionality of the data represented by the array. Forinstance, the array a could represent three points, each lying within afour-dimensional space, but a has only two “axes”.

Another difference between an array and a list of lists is that anelement of the array can be accessed by specifying the index along eachaxis within a single set of square brackets, separated by commas.For instance, the element 8 is in row 1 and column 3:

>>> a[1, 3]8

Array attributes#

This section covers the ndim, shape, size, and dtypeattributes of an array.

The number of dimensions of an array is contained in the ndim attribute.

>>> a.ndim2

The shape of an array is a tuple of non-negative integers that specify thenumber of elements along each dimension.

>>> a.shape(3, 4)>>> len(a.shape) == a.ndimTrue

The fixed, total number of elements in array is contained in the sizeattribute.

>>> a.size12>>> import math>>> a.size == math.prod(a.shape)True

Arrays are typically “hom*ogeneous”, meaning that they contain elements ofonly one “data type”. The data type is recorded in the dtype attribute.

>>> a.dtypedtype('int64') # "int" for integer, "64" for 64-bit

Read more about array attributes here and learn aboutarray objects here.

How to create a basic array#

This section covers np.zeros(), np.ones(),np.empty(), np.arange(), np.linspace()

Besides creating an array from a sequence of elements, you can easily create anarray filled with 0’s:

>>> np.zeros(2)array([0., 0.])

Or an array filled with 1’s:

>>> np.ones(2)array([1., 1.])

Or even an empty array! The function empty creates an array whose initialcontent is random and depends on the state of the memory. The reason to useempty over zeros (or something similar) is speed - just make sure tofill every element afterwards!

>>> # Create an empty array with 2 elements>>> np.empty(2) array([3.14, 42. ]) # may vary

You can create an array with a range of elements:

>>> np.arange(4)array([0, 1, 2, 3])

And even an array that contains a range of evenly spaced intervals. To do this,you will specify the first number, last number, and the step size.

>>> np.arange(2, 9, 2)array([2, 4, 6, 8])

You can also use np.linspace() to create an array with values that arespaced linearly in a specified interval:

>>> np.linspace(0, 10, num=5)array([ 0. , 2.5, 5. , 7.5, 10. ])

Specifying your data type

While the default data type is floating point (np.float64), you can explicitlyspecify which data type you want using the dtype keyword.

>>> x = np.ones(2, dtype=np.int64)>>> xarray([1, 1])

Learn more about creating arrays here

Adding, removing, and sorting elements#

This section covers np.sort(), np.concatenate()

Sorting an element is simple with np.sort(). You can specify the axis, kind,and order when you call the function.

If you start with this array:

>>> arr = np.array([2, 1, 5, 3, 7, 4, 6, 8])

You can quickly sort the numbers in ascending order with:

>>> np.sort(arr)array([1, 2, 3, 4, 5, 6, 7, 8])

In addition to sort, which returns a sorted copy of an array, you can use:

• argsort, which is an indirect sort along a specified axis,

• lexsort, which is an indirect stable sort on multiple keys,

• searchsorted, which will find elements in a sorted array, and

• partition, which is a partial sort.

To read more about sorting an array, see: sort.

If you start with these arrays:

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

You can concatenate them with np.concatenate().

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

Or, if you start with these arrays:

>>> x = np.array([[1, 2], [3, 4]])>>> y = np.array([[5, 6]])

You can concatenate them with:

>>> np.concatenate((x, y), axis=0)array([[1, 2], [3, 4], [5, 6]])

In order to remove elements from an array, it’s simple to use indexing to selectthe elements that you want to keep.

To read more about concatenate, see: concatenate.

How do you know the shape and size of an array?#

This section covers ndarray.ndim, ndarray.size, ndarray.shape

ndarray.ndim will tell you the number of axes, or dimensions, of the array.

ndarray.size will tell you the total number of elements of the array. Thisis the product of the elements of the array’s shape.

ndarray.shape will display a tuple of integers that indicate the number ofelements stored along each dimension of the array. If, for example, you have a2-D array with 2 rows and 3 columns, the shape of your array is (2, 3).

For example, if you create this array:

>>> array_example = np.array([[[0, 1, 2, 3],...  [4, 5, 6, 7]],......  [[0, 1, 2, 3],...  [4, 5, 6, 7]],......  [[0 ,1 ,2, 3],...  [4, 5, 6, 7]]])

To find the number of dimensions of the array, run:

>>> array_example.ndim3

To find the total number of elements in the array, run:

>>> array_example.size24

And to find the shape of your array, run:

>>> array_example.shape(3, 2, 4)

Can you reshape an array?#

This section covers arr.reshape()

Yes!

Using arr.reshape() will give a new shape to an array without changing thedata. Just remember that when you use the reshape method, the array you want toproduce needs to have the same number of elements as the original array. If youstart with an array with 12 elements, you’ll need to make sure that your newarray also has a total of 12 elements.

If you start with this array:

>>> a = np.arange(6)>>> print(a)[0 1 2 3 4 5]

You can use reshape() to reshape your array. For example, you can reshapethis array to an array with three rows and two columns:

>>> b = a.reshape(3, 2)>>> print(b)[[0 1] [2 3] [4 5]]

With np.reshape, you can specify a few optional parameters:

>>> np.reshape(a, newshape=(1, 6), order='C')array([[0, 1, 2, 3, 4, 5]])

a is the array to be reshaped.

newshape is the new shape you want. You can specify an integer or a tuple ofintegers. If you specify an integer, the result will be an array of that length.The shape should be compatible with the original shape.

order: C means to read/write the elements using C-like index order,F means to read/write the elements using Fortran-like index order, Ameans to read/write the elements in Fortran-like index order if a is Fortrancontiguous in memory, C-like order otherwise. (This is an optional parameter anddoesn’t need to be specified.)

If you want to learn more about C and Fortran order, you canread more about the internal organization of NumPy arrays here.Essentially, C and Fortran orders have to do with how indices correspondto the order the array is stored in memory. In Fortran, when moving throughthe elements of a two-dimensional array as it is stored in memory, the firstindex is the most rapidly varying index. As the first index moves to the nextrow as it changes, the matrix is stored one column at a time.This is why Fortran is thought of as a Column-major language.In C on the other hand, the last index changesthe most rapidly. The matrix is stored by rows, making it a Row-majorlanguage. What you do for C or Fortran depends on whether it’s more importantto preserve the indexing convention or not reorder the data.

Learn more about shape manipulation here.

How to convert a 1D array into a 2D array (how to add a new axis to an array)#

This section covers np.newaxis, np.expand_dims

You can use np.newaxis and np.expand_dims to increase the dimensions ofyour existing array.

Using np.newaxis will increase the dimensions of your array by one dimensionwhen used once. This means that a 1D array will become a 2D array, a2D array will become a 3D array, and so on.

For example, if you start with this array:

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

You can use np.newaxis to add a new axis:

>>> a2 = a[np.newaxis, :]>>> a2.shape(1, 6)

You can explicitly convert a 1D array to either a row vector or a columnvector using np.newaxis. For example, you can convert a 1D array to a rowvector by inserting an axis along the first dimension:

>>> row_vector = a[np.newaxis, :]>>> row_vector.shape(1, 6)

Or, for a column vector, you can insert an axis along the second dimension:

>>> col_vector = a[:, np.newaxis]>>> col_vector.shape(6, 1)

You can also expand an array by inserting a new axis at a specified positionwith np.expand_dims.

For example, if you start with this array:

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

You can use np.expand_dims to add an axis at index position 1 with:

>>> b = np.expand_dims(a, axis=1)>>> b.shape(6, 1)

You can add an axis at index position 0 with:

>>> c = np.expand_dims(a, axis=0)>>> c.shape(1, 6)

Find more information about newaxis here andexpand_dims at expand_dims.

Indexing and slicing#

You can index and slice NumPy arrays in the same ways you can slice Pythonlists.

>>> data = np.array([1, 2, 3])>>> data[1]2>>> data[0:2]array([1, 2])>>> data[1:]array([2, 3])>>> data[-2:]array([2, 3])

You can visualize it this way:

You may want to take a section of your array or specific array elements to usein further analysis or additional operations. To do that, you’ll need to subset,slice, and/or index your arrays.

If you want to select values from your array that fulfill certain conditions,it’s straightforward with NumPy.

For example, if you start with this array:

>>> a = np.array([[1 , 2, 3, 4], [5, 6, 7, 8], [9, 10, 11, 12]])

You can easily print all of the values in the array that are less than 5.

>>> print(a[a < 5])[1 2 3 4]

You can also select, for example, numbers that are equal to or greater than 5,and use that condition to index an array.

>>> five_up = (a >= 5)>>> print(a[five_up])[ 5 6 7 8 9 10 11 12]

You can select elements that are divisible by 2:

>>> divisible_by_2 = a[a%2==0]>>> print(divisible_by_2)[ 2 4 6 8 10 12]

Or you can select elements that satisfy two conditions using the & and |operators:

>>> c = a[(a > 2) & (a < 11)]>>> print(c)[ 3 4 5 6 7 8 9 10]

You can also make use of the logical operators & and | in order toreturn boolean values that specify whether or not the values in an array fulfilla certain condition. This can be useful with arrays that contain names or othercategorical values.

>>> five_up = (a > 5) | (a == 5)>>> print(five_up)[[False False False False] [ True True True True] [ True True True True]]

You can also use np.nonzero() to select elements or indices from an array.

Starting with this array:

>>> a = np.array([[1, 2, 3, 4], [5, 6, 7, 8], [9, 10, 11, 12]])

You can use np.nonzero() to print the indices of elements that are, forexample, less than 5:

>>> b = np.nonzero(a < 5)>>> print(b)(array([0, 0, 0, 0]), array([0, 1, 2, 3]))

In this example, a tuple of arrays was returned: one for each dimension. Thefirst array represents the row indices where these values are found, and thesecond array represents the column indices where the values are found.

If you want to generate a list of coordinates where the elements exist, you canzip the arrays, iterate over the list of coordinates, and print them. Forexample:

>>> list_of_coordinates= list(zip(b[0], b[1]))>>> for coord in list_of_coordinates:...  print(coord)(np.int64(0), np.int64(0))(np.int64(0), np.int64(1))(np.int64(0), np.int64(2))(np.int64(0), np.int64(3))

You can also use np.nonzero() to print the elements in an array that are lessthan 5 with:

>>> print(a[b])[1 2 3 4]

If the element you’re looking for doesn’t exist in the array, then the returnedarray of indices will be empty. For example:

>>> not_there = np.nonzero(a == 42)>>> print(not_there)(array([], dtype=int64), array([], dtype=int64))

Learn more about indexing and slicing hereand here.

Read more about using the nonzero function at: nonzero.

How to create an array from existing data#

This section covers slicing and indexing, np.vstack(), np.hstack(),np.hsplit(), .view(), copy()

You can easily create a new array from a section of an existing array.

Let’s say you have this array:

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

You can create a new array from a section of your array any time by specifyingwhere you want to slice your array.

>>> arr1 = a[3:8]>>> arr1array([4, 5, 6, 7, 8])

Here, you grabbed a section of your array from index position 3 through indexposition 8.

You can also stack two existing arrays, both vertically and horizontally. Let’ssay you have two arrays, a1 and a2:

>>> a1 = np.array([[1, 1],...  [2, 2]])>>> a2 = np.array([[3, 3],...  [4, 4]])

You can stack them vertically with vstack:

>>> np.vstack((a1, a2))array([[1, 1], [2, 2], [3, 3], [4, 4]])

Or stack them horizontally with hstack:

>>> np.hstack((a1, a2))array([[1, 1, 3, 3], [2, 2, 4, 4]])

You can split an array into several smaller arrays using hsplit. You canspecify either the number of equally shaped arrays to return or the columnsafter which the division should occur.

Let’s say you have this array:

>>> x = np.arange(1, 25).reshape(2, 12)>>> xarray([[ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12], [13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24]])

If you wanted to split this array into three equally shaped arrays, you wouldrun:

>>> np.hsplit(x, 3) [array([[ 1, 2, 3, 4], [13, 14, 15, 16]]), array([[ 5, 6, 7, 8], [17, 18, 19, 20]]), array([[ 9, 10, 11, 12], [21, 22, 23, 24]])]

If you wanted to split your array after the third and fourth column, you’d run:

>>> np.hsplit(x, (3, 4)) [array([[ 1, 2, 3], [13, 14, 15]]), array([[ 4], [16]]), array([[ 5, 6, 7, 8, 9, 10, 11, 12], [17, 18, 19, 20, 21, 22, 23, 24]])]

Learn more about stacking and splitting arrays here.

You can use the view method to create a new array object that looks at thesame data as the original array (a shallow copy).

Views are an important NumPy concept! NumPy functions, as well as operationslike indexing and slicing, will return views whenever possible. This savesmemory and is faster (no copy of the data has to be made). However it’simportant to be aware of this - modifying data in a view also modifies theoriginal array!

Let’s say you create this array:

>>> a = np.array([[1, 2, 3, 4], [5, 6, 7, 8], [9, 10, 11, 12]])

Now we create an array b1 by slicing a and modify the first element ofb1. This will modify the corresponding element in a as well!

>>> b1 = a[0, :]>>> b1array([1, 2, 3, 4])>>> b1[0] = 99>>> b1array([99, 2, 3, 4])>>> aarray([[99, 2, 3, 4], [ 5, 6, 7, 8], [ 9, 10, 11, 12]])

Using the copy method will make a complete copy of the array and its data (adeep copy). To use this on your array, you could run:

>>> b2 = a.copy()

Learn more about copies and views here.

Basic array operations#

This section covers addition, subtraction, multiplication, division, and more

Once you’ve created your arrays, you can start to work with them. Let’s say,for example, that you’ve created two arrays, one called “data” and one called“ones”

You can add the arrays together with the plus sign.

>>> data = np.array([1, 2])>>> ones = np.ones(2, dtype=int)>>> data + onesarray([2, 3])

You can, of course, do more than just addition!

>>> data - onesarray([0, 1])>>> data * dataarray([1, 4])>>> data / dataarray([1., 1.])

Basic operations are simple with NumPy. If you want to find the sum of theelements in an array, you’d use sum(). This works for 1D arrays, 2D arrays,and arrays in higher dimensions.

>>> a = np.array([1, 2, 3, 4])>>> a.sum()10

To add the rows or the columns in a 2D array, you would specify the axis.

If you start with this array:

>>> b = np.array([[1, 1], [2, 2]])

You can sum over the axis of rows with:

>>> b.sum(axis=0)array([3, 3])

You can sum over the axis of columns with:

>>> b.sum(axis=1)array([2, 4])

Learn more about basic operations here.

Broadcasting#

There are times when you might want to carry out an operation between an arrayand a single number (also called an operation between a vector and a scalar)or between arrays of two different sizes. For example, your array (we’ll call it“data”) might contain information about distance in miles but you want toconvert the information to kilometers. You can perform this operation with:

>>> data = np.array([1.0, 2.0])>>> data * 1.6array([1.6, 3.2])

NumPy understands that the multiplication should happen with each cell. Thatconcept is called broadcasting. Broadcasting is a mechanism that allowsNumPy to perform operations on arrays of different shapes. The dimensions ofyour array must be compatible, for example, when the dimensions of both arraysare equal or when one of them is 1. If the dimensions are not compatible, youwill get a ValueError.

Learn more about broadcasting here.

More useful array operations#

This section covers maximum, minimum, sum, mean, product, standard deviation, and more

NumPy also performs aggregation functions. In addition to min, max, andsum, you can easily run mean to get the average, prod to get theresult of multiplying the elements together, std to get the standarddeviation, and more.

>>> data.max()2.0>>> data.min()1.0>>> data.sum()3.0

Let’s start with this array, called “a”

>>> a = np.array([[0.45053314, 0.17296777, 0.34376245, 0.5510652],...  [0.54627315, 0.05093587, 0.40067661, 0.55645993],...  [0.12697628, 0.82485143, 0.26590556, 0.56917101]])

It’s very common to want to aggregate along a row or column. By default, everyNumPy aggregation function will return the aggregate of the entire array. Tofind the sum or the minimum of the elements in your array, run:

>>> a.sum()4.8595784

Or:

>>> a.min()0.05093587

You can specify on which axis you want the aggregation function to be computed.For example, you can find the minimum value within each column by specifyingaxis=0.

>>> a.min(axis=0)array([0.12697628, 0.05093587, 0.26590556, 0.5510652 ])

The four values listed above correspond to the number of columns in your array.With a four-column array, you will get four values as your result.

Read more about array methods here.

Creating matrices#

You can pass Python lists of lists to create a 2-D array (or “matrix”) torepresent them in NumPy.

>>> data = np.array([[1, 2], [3, 4], [5, 6]])>>> dataarray([[1, 2], [3, 4], [5, 6]])

Indexing and slicing operations are useful when you’re manipulating matrices:

>>> data[0, 1]2>>> data[1:3]array([[3, 4], [5, 6]])>>> data[0:2, 0]array([1, 3])

You can aggregate matrices the same way you aggregated vectors:

>>> data.max()6>>> data.min()1>>> data.sum()21

You can aggregate all the values in a matrix and you can aggregate them acrosscolumns or rows using the axis parameter. To illustrate this point, let’slook at a slightly modified dataset:

>>> data = np.array([[1, 2], [5, 3], [4, 6]])>>> dataarray([[1, 2], [5, 3], [4, 6]])>>> data.max(axis=0)array([5, 6])>>> data.max(axis=1)array([2, 5, 6])

Once you’ve created your matrices, you can add and multiply them usingarithmetic operators if you have two matrices that are the same size.

>>> data = np.array([[1, 2], [3, 4]])>>> ones = np.array([[1, 1], [1, 1]])>>> data + onesarray([[2, 3], [4, 5]])

You can do these arithmetic operations on matrices of different sizes, but onlyif one matrix has only one column or one row. In this case, NumPy will use itsbroadcast rules for the operation.

>>> data = np.array([[1, 2], [3, 4], [5, 6]])>>> ones_row = np.array([[1, 1]])>>> data + ones_rowarray([[2, 3], [4, 5], [6, 7]])

Be aware that when NumPy prints N-dimensional arrays, the last axis is loopedover the fastest while the first axis is the slowest. For instance:

>>> np.ones((4, 3, 2))array([[[1., 1.], [1., 1.], [1., 1.]], [[1., 1.], [1., 1.], [1., 1.]], [[1., 1.], [1., 1.], [1., 1.]], [[1., 1.], [1., 1.], [1., 1.]]])

There are often instances where we want NumPy to initialize the values of anarray. NumPy offers functions like ones() and zeros(), and therandom.Generator class for random number generation for that.All you need to do is pass in the number of elements you want it to generate:

>>> np.ones(3)array([1., 1., 1.])>>> np.zeros(3)array([0., 0., 0.])>>> rng = np.random.default_rng() # the simplest way to generate random numbers>>> rng.random(3) array([0.63696169, 0.26978671, 0.04097352])

You can also use ones(), zeros(), and random() to createa 2D array if you give them a tuple describing the dimensions of the matrix:

>>> np.ones((3, 2))array([[1., 1.], [1., 1.], [1., 1.]])>>> np.zeros((3, 2))array([[0., 0.], [0., 0.], [0., 0.]])>>> rng.random((3, 2)) array([[0.01652764, 0.81327024], [0.91275558, 0.60663578], [0.72949656, 0.54362499]]) # may vary

Read more about creating arrays, filled with 0’s, 1’s, other values oruninitialized, at array creation routines.

Generating random numbers#

The use of random number generation is an important part of the configurationand evaluation of many numerical and machine learning algorithms. Whether youneed to randomly initialize weights in an artificial neural network, split datainto random sets, or randomly shuffle your dataset, being able to generaterandom numbers (actually, repeatable pseudo-random numbers) is essential.

With Generator.integers, you can generate random integers from low (rememberthat this is inclusive with NumPy) to high (exclusive). You can setendpoint=True to make the high number inclusive.

You can generate a 2 x 4 array of random integers between 0 and 4 with:

>>> rng.integers(5, size=(2, 4)) array([[2, 1, 1, 0], [0, 0, 0, 4]]) # may vary

Read more about random number generation here.

How to get unique items and counts#

This section covers np.unique()

You can find the unique elements in an array easily with np.unique.

For example, if you start with this array:

>>> a = np.array([11, 11, 12, 13, 14, 15, 16, 17, 12, 13, 11, 14, 18, 19, 20])

you can use np.unique to print the unique values in your array:

>>> unique_values = np.unique(a)>>> print(unique_values)[11 12 13 14 15 16 17 18 19 20]

To get the indices of unique values in a NumPy array (an array of first indexpositions of unique values in the array), just pass the return_indexargument in np.unique() as well as your array.

>>> unique_values, indices_list = np.unique(a, return_index=True)>>> print(indices_list)[ 0 2 3 4 5 6 7 12 13 14]

You can pass the return_counts argument in np.unique() along with yourarray to get the frequency count of unique values in a NumPy array.

>>> unique_values, occurrence_count = np.unique(a, return_counts=True)>>> print(occurrence_count)[3 2 2 2 1 1 1 1 1 1]

This also works with 2D arrays!If you start with this array:

>>> a_2d = np.array([[1, 2, 3, 4], [5, 6, 7, 8], [9, 10, 11, 12], [1, 2, 3, 4]])

You can find unique values with:

>>> unique_values = np.unique(a_2d)>>> print(unique_values)[ 1 2 3 4 5 6 7 8 9 10 11 12]

If the axis argument isn’t passed, your 2D array will be flattened.

If you want to get the unique rows or columns, make sure to pass the axisargument. To find the unique rows, specify axis=0 and for columns, specifyaxis=1.

>>> unique_rows = np.unique(a_2d, axis=0)>>> print(unique_rows)[[ 1 2 3 4] [ 5 6 7 8] [ 9 10 11 12]]

To get the unique rows, index position, and occurrence count, you can use:

>>> unique_rows, indices, occurrence_count = np.unique(...  a_2d, axis=0, return_counts=True, return_index=True)>>> print(unique_rows)[[ 1 2 3 4] [ 5 6 7 8] [ 9 10 11 12]]>>> print(indices)[0 1 2]>>> print(occurrence_count)[2 1 1]

To learn more about finding the unique elements in an array, see unique.

Transposing and reshaping a matrix#

This section covers arr.reshape(), arr.transpose(), arr.T

It’s common to need to transpose your matrices. NumPy arrays have the propertyT that allows you to transpose a matrix.

You may also need to switch the dimensions of a matrix. This can happen when,for example, you have a model that expects a certain input shape that isdifferent from your dataset. This is where the reshape method can be useful.You simply need to pass in the new dimensions that you want for the matrix.

>>> data.reshape(2, 3)array([[1, 2, 3], [4, 5, 6]])>>> data.reshape(3, 2)array([[1, 2], [3, 4], [5, 6]])

You can also use .transpose() to reverse or change the axes of an arrayaccording to the values you specify.

If you start with this array:

>>> arr = np.arange(6).reshape((2, 3))>>> arrarray([[0, 1, 2], [3, 4, 5]])

You can transpose your array with arr.transpose().

>>> arr.transpose()array([[0, 3], [1, 4], [2, 5]])

You can also use arr.T:

>>> arr.Tarray([[0, 3], [1, 4], [2, 5]])

To learn more about transposing and reshaping arrays, see transpose andreshape.

How to reverse an array#

This section covers np.flip()

NumPy’s np.flip() function allows you to flip, or reverse, the contents ofan array along an axis. When using np.flip(), specify the array you would liketo reverse and the axis. If you don’t specify the axis, NumPy will reverse thecontents along all of the axes of your input array.

Reversing a 1D array

If you begin with a 1D array like this one:

>>> arr = np.array([1, 2, 3, 4, 5, 6, 7, 8])

You can reverse it with:

>>> reversed_arr = np.flip(arr)

If you want to print your reversed array, you can run:

>>> print('Reversed Array: ', reversed_arr)Reversed Array: [8 7 6 5 4 3 2 1]

Reversing a 2D array

A 2D array works much the same way.

If you start with this array:

>>> arr_2d = np.array([[1, 2, 3, 4], [5, 6, 7, 8], [9, 10, 11, 12]])

You can reverse the content in all of the rows and all of the columns with:

>>> reversed_arr = np.flip(arr_2d)>>> print(reversed_arr)[[12 11 10 9] [ 8 7 6 5] [ 4 3 2 1]]

You can easily reverse only the rows with:

>>> reversed_arr_rows = np.flip(arr_2d, axis=0)>>> print(reversed_arr_rows)[[ 9 10 11 12] [ 5 6 7 8] [ 1 2 3 4]]

Or reverse only the columns with:

>>> reversed_arr_columns = np.flip(arr_2d, axis=1)>>> print(reversed_arr_columns)[[ 4 3 2 1] [ 8 7 6 5] [12 11 10 9]]

You can also reverse the contents of only one column or row. For example, youcan reverse the contents of the row at index position 1 (the second row):

>>> arr_2d[1] = np.flip(arr_2d[1])>>> print(arr_2d)[[ 1 2 3 4] [ 8 7 6 5] [ 9 10 11 12]]

You can also reverse the column at index position 1 (the second column):

>>> arr_2d[:,1] = np.flip(arr_2d[:,1])>>> print(arr_2d)[[ 1 10 3 4] [ 8 7 6 5] [ 9 2 11 12]]

Read more about reversing arrays at flip.

Reshaping and flattening multidimensional arrays#

This section covers .flatten(), ravel()

There are two popular ways to flatten an array: .flatten() and .ravel().The primary difference between the two is that the new array created usingravel() is actually a reference to the parent array (i.e., a “view”). Thismeans that any changes to the new array will affect the parent array as well.Since ravel does not create a copy, it’s memory efficient.

If you start with this array:

>>> x = np.array([[1 , 2, 3, 4], [5, 6, 7, 8], [9, 10, 11, 12]])

You can use flatten to flatten your array into a 1D array.

>>> x.flatten()array([ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12])

When you use flatten, changes to your new array won’t change the parentarray.

For example:

>>> a1 = x.flatten()>>> a1[0] = 99>>> print(x) # Original array[[ 1 2 3 4] [ 5 6 7 8] [ 9 10 11 12]]>>> print(a1) # New array[99 2 3 4 5 6 7 8 9 10 11 12]

But when you use ravel, the changes you make to the new array will affectthe parent array.

For example:

>>> a2 = x.ravel()>>> a2[0] = 98>>> print(x) # Original array[[98 2 3 4] [ 5 6 7 8] [ 9 10 11 12]]>>> print(a2) # New array[98 2 3 4 5 6 7 8 9 10 11 12]

Read more about flatten at ndarray.flatten and ravel at ravel.

How to access the docstring for more information#

This section covers help(), ?, ??

When it comes to the data science ecosystem, Python and NumPy are built with theuser in mind. One of the best examples of this is the built-in access todocumentation. Every object contains the reference to a string, which is knownas the docstring. In most cases, this docstring contains a quick and concisesummary of the object and how to use it. Python has a built-in help()function that can help you access this information. This means that nearly anytime you need more information, you can use help() to quickly find theinformation that you need.

For example:

>>> help(max)Help on built-in function max in module builtins:max(...) max(iterable, *[, default=obj, key=func]) -> value max(arg1, arg2, *args, *[, key=func]) -> value With a single iterable argument, return its biggest item. The default keyword-only argument specifies an object to return if the provided iterable is empty. With two or more arguments, return the largest argument.

Because access to additional information is so useful, IPython uses the ?character as a shorthand for accessing this documentation along with otherrelevant information. IPython is a command shell for interactive computing inmultiple languages.You can find more information about IPython here.

For example:

In [0]: max?max(iterable, *[, default=obj, key=func]) -> valuemax(arg1, arg2, *args, *[, key=func]) -> valueWith a single iterable argument, return its biggest item. Thedefault keyword-only argument specifies an object to return ifthe provided iterable is empty.With two or more arguments, return the largest argument.Type: builtin_function_or_method

You can even use this notation for object methods and objects themselves.

Let’s say you create this array:

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

Then you can obtain a lot of useful information (first details about a itself,followed by the docstring of ndarray of which a is an instance):

In [1]: a?Type: ndarrayString form: [1 2 3 4 5 6]Length: 6File: ~/anaconda3/lib/python3.9/site-packages/numpy/__init__.pyDocstring: <no docstring>Class docstring:ndarray(shape, dtype=float, buffer=None, offset=0, strides=None, order=None)An array object represents a multidimensional, hom*ogeneous arrayof fixed-size items. An associated data-type object describes theformat of each element in the array (its byte-order, how many bytes itoccupies in memory, whether it is an integer, a floating point number,or something else, etc.)Arrays should be constructed using `array`, `zeros` or `empty` (referto the See Also section below). The parameters given here refer toa low-level method (`ndarray(...)`) for instantiating an array.For more information, refer to the `numpy` module and examine themethods and attributes of an array.Parameters----------(for the __new__ method; see Notes below)shape : tuple of ints Shape of created array....

This also works for functions and other objects that you create. Justremember to include a docstring with your function using a string literal(""" """ or ''' ''' around your documentation).

For example, if you create this function:

>>> def double(a):...  '''Return a * 2'''...  return a * 2

You can obtain information about the function:

In [2]: double?Signature: double(a)Docstring: Return a * 2File: ~/Desktop/<ipython-input-23-b5adf20be596>Type: function

You can reach another level of information by reading the source code of theobject you’re interested in. Using a double question mark (??) allows you toaccess the source code.

For example:

In [3]: double??Signature: double(a)Source:def double(a): '''Return a * 2''' return a * 2File: ~/Desktop/<ipython-input-23-b5adf20be596>Type: function

If the object in question is compiled in a language other than Python, using?? will return the same information as ?. You’ll find this with a lot ofbuilt-in objects and types, for example:

In [4]: len?Signature: len(obj, /)Docstring: Return the number of items in a container.Type: builtin_function_or_method

and :

In [5]: len??Signature: len(obj, /)Docstring: Return the number of items in a container.Type: builtin_function_or_method

have the same output because they were compiled in a programming language otherthan Python.

Working with mathematical formulas#

The ease of implementing mathematical formulas that work on arrays is one ofthe things that make NumPy so widely used in the scientific Python community.

For example, this is the mean square error formula (a central formula used insupervised machine learning models that deal with regression):

Implementing this formula is simple and straightforward in NumPy:

What makes this work so well is that predictions and labels can containone or a thousand values. They only need to be the same size.

You can visualize it this way:

In this example, both the predictions and labels vectors contain three values,meaning n has a value of three. After we carry out subtractions the valuesin the vector are squared. Then NumPy sums the values, and your result is theerror value for that prediction and a score for the quality of the model.

How to save and load NumPy objects#

This section covers np.save, np.savez, np.savetxt,np.load, np.loadtxt

You will, at some point, want to save your arrays to disk and load them backwithout having to re-run the code. Fortunately, there are several ways to saveand load objects with NumPy. The ndarray objects can be saved to and loaded fromthe disk files with loadtxt and savetxt functions that handle normaltext files, load and save functions that handle NumPy binary files witha .npy file extension, and a savez function that handles NumPy fileswith a .npz file extension.

The .npy and .npz files store data, shape, dtype, and other informationrequired to reconstruct the ndarray in a way that allows the array to becorrectly retrieved, even when the file is on another machine with differentarchitecture.

If you want to store a single ndarray object, store it as a .npy file usingnp.save. If you want to store more than one ndarray object in a single file,save it as a .npz file using np.savez. You can also save several arraysinto a single file in compressed npz format with savez_compressed.

It’s easy to save and load and array with np.save(). Just make sure tospecify the array you want to save and a file name. For example, if you createthis array:

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

You can save it as “filename.npy” with:

>>> np.save('filename', a)

You can use np.load() to reconstruct your array.

>>> b = np.load('filename.npy')

If you want to check your array, you can run:

>>> print(b)[1 2 3 4 5 6]

You can save a NumPy array as a plain text file like a .csv or .txt filewith np.savetxt.

For example, if you create this array:

>>> csv_arr = np.array([1, 2, 3, 4, 5, 6, 7, 8])

You can easily save it as a .csv file with the name “new_file.csv” like this:

>>> np.savetxt('new_file.csv', csv_arr)

You can quickly and easily load your saved text file using loadtxt():

>>> np.loadtxt('new_file.csv')array([1., 2., 3., 4., 5., 6., 7., 8.])

The savetxt() and loadtxt() functions accept additional optionalparameters such as header, footer, and delimiter. While text files can be easierfor sharing, .npy and .npz files are smaller and faster to read. If you need moresophisticated handling of your text file (for example, if you need to work withlines that contain missing values), you will want to use the genfromtxtfunction.

With savetxt, you can specify headers, footers, comments, and more.

Learn more about input and output routines here.

Importing and exporting a CSV#

It’s simple to read in a CSV that contains existing information. The best andeasiest way to do this is to usePandas.

>>> import pandas as pd>>> # If all of your columns are the same type:>>> x = pd.read_csv('music.csv', header=0).values>>> print(x)[['Billie Holiday' 'Jazz' 1300000 27000000] ['Jimmie Hendrix' 'Rock' 2700000 70000000] ['Miles Davis' 'Jazz' 1500000 48000000] ['SIA' 'Pop' 2000000 74000000]]>>> # You can also simply select the columns you need:>>> x = pd.read_csv('music.csv', usecols=['Artist', 'Plays']).values>>> print(x)[['Billie Holiday' 27000000] ['Jimmie Hendrix' 70000000] ['Miles Davis' 48000000] ['SIA' 74000000]]

It’s simple to use Pandas in order to export your array as well. If you are newto NumPy, you may want to create a Pandas dataframe from the values in yourarray and then write the data frame to a CSV file with Pandas.

If you created this array “a”

>>> a = np.array([[-2.58289208, 0.43014843, -1.24082018, 1.59572603],...  [ 0.99027828, 1.17150989, 0.94125714, -0.14692469],...  [ 0.76989341, 0.81299683, -0.95068423, 0.11769564],...  [ 0.20484034, 0.34784527, 1.96979195, 0.51992837]])

You could create a Pandas dataframe

>>> df = pd.DataFrame(a)>>> print(df) 0 1 2 30 -2.582892 0.430148 -1.240820 1.5957261 0.990278 1.171510 0.941257 -0.1469252 0.769893 0.812997 -0.950684 0.1176963 0.204840 0.347845 1.969792 0.519928

You can easily save your dataframe with:

>>> df.to_csv('pd.csv')

And read your CSV with:

>>> data = pd.read_csv('pd.csv')

You can also save your array with the NumPy savetxt method.

>>> np.savetxt('np.csv', a, fmt='%.2f', delimiter=',', header='1, 2, 3, 4')

If you’re using the command line, you can read your saved CSV any time with acommand such as:

$ cat np.csv# 1, 2, 3, 4-2.58,0.43,-1.24,1.600.99,1.17,0.94,-0.150.77,0.81,-0.95,0.120.20,0.35,1.97,0.52

Or you can open the file any time with a text editor!

If you’re interested in learning more about Pandas, take a look at theofficial Pandas documentation.Learn how to install Pandas with theofficial Pandas installation information.

Plotting arrays with Matplotlib#

If you need to generate a plot for your values, it’s very simple withMatplotlib.

For example, you may have an array like this one:

>>> a = np.array([2, 1, 5, 7, 4, 6, 8, 14, 10, 9, 18, 20, 22])

If you already have Matplotlib installed, you can import it with:

>>> import matplotlib.pyplot as plt# If you're using Jupyter Notebook, you may also want to run the following# line of code to display your code in the notebook:%matplotlib inline

All you need to do to plot your values is run:

>>> plt.plot(a)# If you are running from a command line, you may need to do this:# >>> plt.show()

For example, you can plot a 1D array like this:

>>> x = np.linspace(0, 5, 20)>>> y = np.linspace(0, 10, 20)>>> plt.plot(x, y, 'purple') # line>>> plt.plot(x, y, 'o') # dots

With Matplotlib, you have access to an enormous number of visualization options.

>>> fig = plt.figure()>>> ax = fig.add_subplot(projection='3d')>>> X = np.arange(-5, 5, 0.15)>>> Y = np.arange(-5, 5, 0.15)>>> X, Y = np.meshgrid(X, Y)>>> R = np.sqrt(X**2 + Y**2)>>> Z = np.sin(R)>>> ax.plot_surface(X, Y, Z, rstride=1, cstride=1, cmap='viridis')

To read more about Matplotlib and what it can do, take a look atthe official documentation.For directions regarding installing Matplotlib, see the officialinstallation section.

Image credits: Jay Alammar https://jalammar.github.io/