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## Thủ Thuật về Convert 2D list to array Python Mới Nhất

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In this tutorial, I’ll show you how to convert from Numpy array to list. Essentially, we’ll take a Numpy array and convert it to a Python list using the tolist() method.

Nội dung chính

- A quick introduction Numpy tolistThe tolist method converts from Numpy array to Python listThe syntax of the tolist methodThe Output of tolistExamples: How to Convert from a Numpy array to a Python ListEXAMPLE 1: Convert a 1-dimensional array to a listEXAMPLE 2: Convert a 2-dimensional array to a nested listJoin our course to learn more about NumpyVideo liên quan

In the tutorial, I’ll give you a quick introduction, I’ll explain the syntax, and I’ll show you a couple of simple examples of this technique.

If you need something specific, you can click on any of the following links, and the link will take you directly to the appropriate location in the post.

**Table of Contents:**

- Introduction Syntax Examples Frequently Asked Questions

Ok. Let’s get into it.

## A quick introduction Numpy tolist

Let’s start with a quick introduction to the technique.

If you’re reading this post, you’re probably already a little familiar with Numpy arrays and Python lists, but let’s quickly recap.

Lists and Numpy arrays are special data structures that store data in Python programs.

In particular, Numpy arrays are a special structure for storing numeric data and working with Numeric data. They store numeric data in a row-and-column structure that looks something like this:

We typically use Numpy arrays quite a bit for data science, machine learning, and scientific computing. When working with numeric data in Numpy, we commonly keep the data in array form, but there are some instances where we need to convert the array to a Python list.

### The tolist method converts from Numpy array to Python list

To accomplish this, we can use the tolist() method from Numpy.

The tolist() method takes a Numpy array and outputs a Python list.

It’s really very simple.

Having said that, let’s look the syntax.

## The syntax of the tolist method

The syntax of the Numpy tolist() method is extremely simple. It’s arguably one of the simplest Numpy techniques.

You start by typing the name of a Numpy array.

This is important. Since the tolist() technique is a method, you call it by typing the name of an object first.

After you type the name of your Numpy array, you use so-called “dot syntax” to call the method.

So you type a “dot” and then the name of the method, tolist().

That’s really it!

Obviously, this assumes that you already have a Numpy array of some kind.

For more information about how to generate different kinds of Numpy arrays, you might check out our tutorials about:

### The Output of tolist

Once you call the tolist() method, the output will be a Python list.

If the input array is a 1-dimensional Numpy array, then the output will be a simple 1D list.

If the input array is 2-dimensional or multi-dimensional, then the output will be a nested list.

Additionally, the elements of the input will be converted to the closest built-in Python data types.

## Examples: How to Convert from a Numpy array to a Python List

Ok. Now that you’ve seen how the syntax works, let’s look a couple of simple examples.

**Examples:**

Let’s start with example 1.

### EXAMPLE 1: Convert a 1-dimensional array to a list

Here, we’re going to convert a simple 1-dimensional Numpy array to a Python list.

Create 1D Numpy Array

First, we need to create a 1-dimensional Numpy array.

To do this, we’ll use the Numpy arange function to create a 1D array that contains a sequence of values.

my_1d_array = np.arange(start = 1, stop = 6)

And let’s print it out to see the contents:

print(my_1d_array)

OUT:

[1 2 3 4 5]

Having said that, if we check the data type with type(my_1d_array), you’ll notice that my_1d_array is a numpy.ndarray.

Convert Array to List

Now, let’s convert it to a list.

Here, we’ll use the tolist() method and save the output to the name my_1d_list.

my_1d_list = my_1d_array.tolist()

And lets print it out:

print(my_1d_list)

OUT:

[1, 2, 3, 4, 5]

Additionally, if we check the data type with the code type(my_1d_list), you’ll see that my_1d_list is a list.

Explanation

This is really simple.

We typed the name of the Numpy array, and called the tolist() method using “dot syntax.”

The output, my_1d_list, essentially contains the same elements, but it’s a Python list instead of a Numpy array.

### EXAMPLE 2: Convert a 2-dimensional array to a nested list

Next, we’l convert a 2-dimensional Numpy array to a nested Python list.

Create 2D Numpy Array

First, we need to create the 2-dimensional Numpy array.

To do this, we’ll use Numpy arange to create a sequence of values, and we’ll use the Numpy reshape method to re-shape that 1D array into a 2D array.

my_2d_array = np.arange(start = 1, stop = 7).reshape(2,3)

And let’s print it out to see the contents:

print(my_2d_array)

OUT:

[[1 2 3]

[4 5 6]]

And again, if we check the data type with type(my_2d_array), you’ll notice that my_2d_array is a numpy.ndarray.

Convert Array to List

Now, let’s convert the array to a list.

Once again, we’ll use the tolist() method. And we’ll save the output to the name my_2d_list.

my_1d_list = my_1d_array.tolist()

And lets print it out:

print(my_2d_list)

OUT:

[[1, 2, 3], [4, 5, 6]]

If you check the data type with the code type(my_2d_list), you’ll see that my_2d_list is a Python list.

Explanation

Again, this is really simple.

To convert from a Numpy array to list, we simply typed the name of the 2D Numpy array, and then called the Numpy tolist() method which produced a Python list as an output.

Moreover, take a look the output list itself: [[1, 2, 3], [4, 5, 6]]

From the structure, we can see that this is a nested Python list. Two lists of 3 elements each, that exist within a larger list. It’s a list-of-lists.

This is how the Numpy tolist method handles multi-dimensional input arrays. When tolist operates on a multi-dimensional input, it produces a nested array as an output.

Leave your other questions in the comments below

Do you have any other questions about the Numpy tolist method?

If so, leave your questions in the comments section near the bottom of the page.

## Join our course to learn more about Numpy

Are you interested in learning more about Numpy?

This tutorial should have shown you how to use the Numpy tolist() method, but to master numeric data manipulation in Python, there’s a lot more to learn.

If you’re serious about learning Numpy, you should join our premium course, Numpy Mastery.

In this course, you’ll learn everything you need to know about Numpy.

- How to create Numpy arrays How to use the Numpy random functions What Numpy axes are, and how to use them What the “Numpy random seed” function does How to reshape, split, and combine your Numpy arrays and much more …

Additionally, when you join, you’ll get access to our unique practice system.

This practice system will enable you to memorize all of the syntax that you learn. If you take this course and practice like we show you, you’ll be able to write Numpy code fluently, accurately, and 100% from memory.

Find out more here:

Learn More About Numpy Mastery

Welcome to the absolute beginner’s guide to NumPy! If you have comments or

suggestions, please don’t hesitate to reach out!

NumPy (**Numerical Python**) is an open source Python library that’s used in

almost every field of science and engineering. It’s the universal standard for

working with numerical data in Python, and it’s the core of the scientific

Python and PyData ecosystems. NumPy users include everyone from beginning coders

to experienced researchers doing state-of-the-art scientific and industrial

research and development. The NumPy API is used extensively in Pandas, SciPy,

Matplotlib, scikit-learn, scikit-image and most other data science and

scientific Python packages.

The NumPy library contains multidimensional array and matrix data structures

(you’ll find more information about this in later sections). It provides

**ndarray**, a homogeneous n-dimensional array object, with methods to

efficiently operate on it. NumPy can be used to perform a wide variety of

mathematical operations on arrays. It adds powerful data structures to Python

that guarantee efficient calculations with arrays and matrices and it supplies

an enormous library of high-level mathematical functions that operate on these

arrays and matrices.

Learn more about NumPy here!

To install NumPy, we strongly recommend using a scientific Python distribution.

If you’re looking for the full instructions for installing NumPy on your

operating system, see Installing NumPy.

If you already have Python, you can install NumPy with:

or

If you don’t have Python yet, you might want to consider using Anaconda. It’s the easiest way to get started. The good

thing about getting this distribution is the fact that you don’t need to worry

too much about separately installing NumPy or any of the major packages that

you’ll be using for your data analyses, like pandas, Scikit-Learn, etc.

To access NumPy and its functions import it in your Python code like this:

We shorten the imported name to np for better readability of code using

NumPy. This is a widely adopted convention that you should follow so that

anyone working with your code can easily understand it.

If you aren’t already comfortable with reading tutorials that contain a lot of code,

you might not know how to interpret a code block that looks

like this:

>>> a = np.arange(6)

>>> a2 = a[np.newaxis, :]

>>> a2.shape

(1, 6)

If you aren’t familiar with this style, it’s very easy to understand.

If you see >>>, you’re looking **input**, or the code that

you would enter. Everything that doesn’t have >>> in front of it

is **output**, or the results of running your code. This is the style

you see when you run python on the command line, but if you’re using

IPython, you might see a different style. Note that it is not part of the

code and will cause an error if typed or pasted into the Python

shell. It can be safely typed or pasted into the IPython shell; the >>>

is ignored.

NumPy gives you an enormous range of fast and efficient ways of creating arrays

and manipulating numerical data inside them. While a Python list can contain

different data types within a single list, all of the elements in a NumPy array

should be homogeneous. The mathematical operations that are meant to be performed

on arrays would be extremely inefficient if the arrays weren’t homogeneous.

**Why use NumPy?**

NumPy arrays are faster and more compact than Python lists. An array consumes

less memory and is convenient to use. NumPy uses much less memory to store data

and it provides a mechanism of specifying the data types. This allows the code

to be optimized even further.

An array is a central data structure of the NumPy library. An array is a grid of

values and it contains information about the raw data, how to locate an element,

and how to interpret an element. It has a grid of elements that can be indexed

in various ways.

The elements are all of the same type, referred to as the array dtype.

An array can be indexed by a tuple of nonnegative integers, by booleans, by

another array, or by integers. The rank of the array is the number of

dimensions. The shape of the array is a tuple of integers giving the size of

the array along each dimension.

One way we can initialize NumPy arrays is from Python lists, using nested lists

for two- or higher-dimensional data.

For example:

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

or:

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

We can access the elements in the array using square brackets. When you’re

accessing elements, remember that indexing in NumPy starts 0. That means that

if you want to access the first element in your array, you’ll be accessing

element “0”.

>>> print(a[0])

[1 2 3 4]

This section covers 1D array, 2D array, ndarray, vector, matrix

You might occasionally hear an array referred to as a “ndarray,” which is

shorthand for “N-dimensional array.” An N-dimensional array is simply an array

with any number of dimensions. You might also hear **1-D**, or one-dimensional

array, **2-D**, or two-dimensional array, and so on. The NumPy ndarray class

is used to represent both matrices and vectors. A **vector** is an array with a

single dimension (there’s no difference

between row and column vectors), while a **matrix** refers to an

array with two dimensions. For **3-D** or higher dimensional arrays, the term

**tensor** is also commonly used.

**What are the attributes of an array?**

An array is usually a fixed-size container of items of the same type and size.

The number of dimensions and items in an array is defined by its shape. The

shape of an array is a tuple of non-negative integers that specify the sizes of

each dimension.

In NumPy, dimensions are called **axes**. This means that if you have a 2D array

that looks like this:

[[0., 0., 0.], [1., 1., 1.]]

Your array has 2 axes. The first axis has a length of 2 and the second axis has

a length of 3.

Just like in other Python container objects, the contents of an array can be

accessed and modified by indexing or slicing the array. Unlike the typical container

objects, different arrays can share the same data, so changes made on one array might

be visible in another.

Array **attributes** reflect information intrinsic to the array itself. If you

need to get, or even set, properties of an array without creating a new array,

you can often access an array through its attributes.

Read more about array attributes here and learn about

array objects here.

This section covers np.array(), np.zeros(), np.ones(),

np.empty(), np.arange(), np.linspace(), dtype

To create a NumPy array, you can use the function np.array().

All you need to do to create a simple array is pass a list to it. If you choose

to, you can also specify the type of data in your list.

You can find more information about data types here.

>>> import numpy as np

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

You can visualize your array this way:

Be aware that these visualizations are meant to simplify ideas and give you a basic understanding of NumPy concepts and mechanics. Arrays and array operations are much more complicated than are captured here!

Besides creating an array from a sequence of elements, you can easily create an

array 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 initial

content is random and depends on the state of the memory. The reason to use

empty over zeros (or something similar) is speed – just make sure to

fill 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 are

spaced 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 explicitly

specify which data type you want using the dtype keyword.

>>> x = np.ones(2, dtype=np.int64)

>>> x

array([1, 1])

Learn more about creating arrays here

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 select

the elements that you want to keep.

To read more about concatenate, see: concatenate.

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. This

is the product of the elements of the array’s shape.

ndarray.shape will display a tuple of integers that indicate the number of

elements stored along each dimension of the array. If, for example, you have a

2-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:

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

>>> array_example.size

24

And to find the shape of your array, run:

>>> array_example.shape

(3, 2, 4)

This section covers arr.reshape()

**Yes!**

Using arr.reshape() will give a new shape to an array without changing the

data. Just remember that when you use the reshape method, the array you want to

produce needs to have the same number of elements as the original array. If you

start with an array with 12 elements, you’ll need to make sure that your new

array 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 reshape

this 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 of

integers. 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, A

means to read/write the elements in Fortran-like index order if a is Fortran

contiguous in memory, C-like order otherwise. (This is an optional parameter and

doesn’t need to be specified.)

If you want to learn more about C and Fortran order, you can

read more about the internal organization of NumPy arrays here.

Essentially, C and Fortran orders have to do with how indices correspond

to the order the array is stored in memory. In Fortran, when moving through

the elements of a two-dimensional array as it is stored in memory, the **first**

index is the most rapidly varying index. As the first index moves to the next

row as it changes, the matrix is stored one column a time.

This is why Fortran is thought of as a **Column-major language**.

In C on the other hand, the **last** index changes

the most rapidly. The matrix is stored by rows, making it a **Row-major
language**. What you do for C or Fortran depends on whether it’s more important

to preserve the indexing convention or not reorder the data.

Learn more about shape manipulation here.

This section covers np.newaxis, np.expand_dims

You can use np.newaxis and np.expand_dims to increase the dimensions of

your existing array.

Using np.newaxis will increase the dimensions of your array by one dimension

when used once. This means that a **1D** array will become a **2D** array, a

**2D** 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 with either a row vector or a column

vector using np.newaxis. For example, you can convert a 1D array to a row

vector 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 a specified position

with 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 index position 1 with:

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

>>> b.shape

(6, 1)

You can add an axis index position 0 with:

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

>>> c.shape

(1, 6)

Find more information about newaxis here and

expand_dims expand_dims.

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

lists.

>>> 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 use

in 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 >> print(c)

[ 3 4 5 6 7 8 9 10]

You can also make use of the logical operators **&** and **|** in order to

return boolean values that specify whether or not the values in an array fulfill

a certain condition. This can be useful with arrays that contain names or other

categorical 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, for

example, less than 5:

>>> b = np.nonzero(a >> 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. The

first array represents the row indices where these values are found, and the

second array represents the column indices where the values are found.

If you want to generate a list of coordinates where the elements exist, you can

zip the arrays, iterate over the list of coordinates, and print them. For

example:

>>> list_of_coordinates= list(zip(b[0], b[1])) >>> for coord in list_of_coordinates:

… print(coord)

(0, 0)

(0, 1)

(0, 2)

(0, 3)

You can also use np.nonzero() to print the elements in an array that are less

than 5 with:

>>> print(a[b])

[1 2 3 4]

If the element you’re looking for doesn’t exist in the array, then the returned

array 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 here

and here.

Read more about using the nonzero function : nonzero.

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 specifying

where you want to slice your array.

>>> arr1 = a[3:8]

>>> arr1

array([4, 5, 6, 7, 8])

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

position 8.

You can also stack two existing arrays, both vertically and horizontally. Let’s

say 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 can

specify either the number of equally shaped arrays to return or the columns

after which the division should occur.

Let’s say you have this array:

>>> x = np.arange(1, 25).reshape(2, 12)

>>> x

array([[ 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 would

run:

>>> 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 the

same data as the original array (a shallow copy).

Views are an important NumPy concept! NumPy functions, as well as operations

like indexing and slicing, will return views whenever possible. This saves

memory and is faster (no copy of the data has to be made). However it’s

important to be aware of this – modifying data in a view also modifies the

original 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 of

b1. This will modify the corresponding element in a as well!

>>> b1 = a[0, :]

>>> b1

array([1, 2, 3, 4])

>>> b1[0] = 99

>>> b1

array([99, 2, 3, 4])

>>> a

array([[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 (a

deep copy). To use this on your array, you could run:

Learn more about copies and views here.

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 + ones

array([2, 3])

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

>>> data – ones

array([0, 1])

>>> data * data

array([1, 4])

>>> data / data

array([1., 1.])

Basic operations are simple with NumPy. If you want to find the sum of the

elements 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.

There are times when you might want to carry out an operation between an array

and 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 to

convert the information to kilometers. You can perform this operation with:

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

>>> data * 1.6

array([1.6, 3.2])

NumPy understands that the multiplication should happen with each cell. That

concept is called **broadcasting**. Broadcasting is a mechanism that allows

NumPy to perform operations on arrays of different shapes. The dimensions of

your array must be compatible, for example, when the dimensions of both arrays

are equal or when one of them is 1. If the dimensions are not compatible, you

will get a ValueError.

Learn more about broadcasting here.

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

NumPy also performs aggregation functions. In addition to min, max, and

sum, you can easily run mean to get the average, prod to get the

result of multiplying the elements together, std to get the standard

deviation, 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, every

NumPy aggregation function will return the aggregate of the entire array. To

find the sum or the minimum of the elements in your array, run:

Or:

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 specifying

axis=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.

You can pass Python lists of lists to create a 2-D array (or “matrix”) to

represent them in NumPy.

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

>>> data

array([[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 across

columns or rows using the axis parameter. To illustrate this point, let’s

look a slightly modified dataset:

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

>>> data

array([[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 using

arithmetic 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 + ones

array([[2, 3],

[4, 5]])

You can do these arithmetic operations on matrices of different sizes, but only

if one matrix has only one column or one row. In this case, NumPy will use its

broadcast rules for the operation.

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

>>> ones_row = np.array([[1, 1]])

>>> data + ones_row

array([[2, 3],

[4, 5],

[6, 7]])

Be aware that when NumPy prints N-dimensional arrays, the last axis is looped

over 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 an

array. NumPy offers functions like ones() and zeros(), and the

random.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 create

a 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 or

uninitialized, array creation routines.

The use of random number generation is an important part of the configuration

and evaluation of many numerical and machine learning algorithms. Whether you

need to randomly initialize weights in an artificial neural network, split data

into random sets, or randomly shuffle your dataset, being able to generate

random numbers (actually, repeatable pseudo-random numbers) is essential.

With Generator.integers, you can generate random integers from low (remember

that this is inclusive with NumPy) to high (exclusive). You can set

endpoint=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.

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 index

positions of unique values in the array), just pass the return_index

argument 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 your

array 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 axis

argument. To find the unique rows, specify axis=0 and for columns, specify

axis=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.

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

It’s common to need to transpose your matrices. NumPy arrays have the property

T 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 is

different 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 array

according to the values you specify.

If you start with this array:

>>> arr = np.arange(6).reshape((2, 3))

>>> arr

array([[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.T

array([[0, 3],

[1, 4],

[2, 5]])

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

reshape.

This section covers np.flip()

NumPy’s np.flip() function allows you to flip, or reverse, the contents of

an array along an axis. When using np.flip(), specify the array you would like

to reverse and the axis. If you don’t specify the axis, NumPy will reverse the

contents 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, you

can reverse the contents of the row 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 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 flip.

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 using

ravel() is actually a reference to the parent array (i.e., a “view”). This

means 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 parent

array.

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 affect

the 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 ndarray.flatten and ravel ravel.

This section covers help(), ?, ??

When it comes to the data science ecosystem, Python and NumPy are built with the

user in mind. One of the best examples of this is the built-in access to

documentation. Every object contains the reference to a string, which is known

as the **docstring**. In most cases, this docstring contains a quick and concise

summary 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 any

time you need more information, you can use help() to quickly find the

information 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 other

relevant information. IPython is a command shell for interactive computing in

multiple languages.

You can find more information about IPython here.

For example:

In [0]: 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.

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: ndarray

String form: [1 2 3 4 5 6]

Length: 6

File: ~/anaconda3/lib/python3.7/site-packages/numpy/__init__.py

Docstring:

Class docstring:

ndarray(shape, dtype=float, buffer=None, offset=0,

strides=None, order=None) An array object represents a multidimensional, homogeneous array

of fixed-size items. An associated data-type object describes the

format of each element in the array (its byte-order, how many bytes it

occupies in memory, whether it is an integer, a floating point number,

or something else, etc.) Arrays should be constructed using `array`, `zeros` or `empty` (refer

to the See Also section below). The parameters given here refer to

a low-level method (`ndarray(…)`) for instantiating an array. For more information, refer to the `numpy` module and examine the

methods 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. Just

remember 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 * 2

File: ~/Desktop/

Type: function

You can reach another level of information by reading the source code of the

object you’re interested in. Using a double question mark (??) allows you to

access the source code.

For example:

In [3]: double??

Signature: double(a)

Source:

def double(a):

”’Return a * 2”’

return a * 2

File: ~/Desktop/

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 of

built-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 other

than Python.

The ease of implementing mathematical formulas that work on arrays is one of

the 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 in

supervised machine learning models that giảm giá with regression):

Implementing this formula is simple and straightforward in NumPy:

What makes this work so well is that predictions and labels can contain

one 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 values

in the vector are squared. Then NumPy sums the values, and your result is the

error value for that prediction and a score for the quality of the model.

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

np.load, np.loadtxt

You will, some point, want to save your arrays to disk and load them back

without having to re-run the code. Fortunately, there are several ways to save

and load objects with NumPy. The ndarray objects can be saved to and loaded from

the disk files with loadtxt and savetxt functions that handle normal

text files, load and save functions that handle NumPy binary files with

a **.npy** file extension, and a savez function that handles NumPy files

with a **.npz** file extension.

The **.npy** and **.npz** files store data, shape, dtype, and other information

required to reconstruct the ndarray in a way that allows the array to be

correctly retrieved, even when the file is on another machine with different

architecture.

If you want to store a single ndarray object, store it as a .npy file using

np.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 arrays

into 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 to

specify the array you want to save and a file name. For example, if you create

this 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** file

with 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 optional

parameters such as header, footer, and delimiter. While text files can be easier

for sharing, .npy and .npz files are smaller and faster to read. If you need more

sophisticated handling of your text file (for example, if you need to work with

lines that contain missing values), you will want to use the genfromtxt

function.

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

Learn more about input and output routines here.

It’s simple to read in a CSV that contains existing information. The best and

easiest way to do this is to use

Pandas.

>>> 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 new

to NumPy, you may want to create a Pandas dataframe from the values in your

array 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 3

0 -2.582892 0.430148 -1.240820 1.595726

1 0.990278 1.171510 0.941257 -0.146925

2 0.769893 0.812997 -0.950684 0.117696

3 0.204840 0.347845 1.969792 0.519928

You can easily save your dataframe with:

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 a

command such as:

$ cat np.csv

# 1, 2, 3, 4

-2.58,0.43,-1.24,1.60

0.99,1.17,0.94,-0.15

0.77,0.81,-0.95,0.12

0.20,0.35,1.97,0.52

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

If you’re interested in learning more about Pandas, take a look the

official Pandas documentation.

Learn how to install Pandas with the

official Pandas installation information.

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

Matplotlib.

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

the official documentation.

For directions regarding installing Matplotlib, see the official

installation section.

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

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