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What is an axis in NumPy?

NumPy axes are the directions along the rows and columns. Just like coordinate systems, NumPy arrays also have axes. In a 2-dimensional NumPy array, the axes are the directions along the rows and columns.

Which axis is row in NumPy?

Axes are defined for arrays with more than one dimension. A 2-dimensional array has two corresponding axes: the first running vertically downwards across rows (axis 0), and the second running horizontally across columns (axis 1).

Are NumPy dimensions called axes?

In NumPy dimensions are called axes. For example, the array for the coordinates of a point in 3D space, [1, 2, 1] , has one axis. That axis has 3 elements in it, so we say it has a length of 3.

What is the axis of an array?

An array with two dimensions has rows and columns. The rows and columns are the two axes of the array.

What is an axis in coding?

An axis is an imaginary line that passes through the origin point of a geometric coordinate system. Each dimension of the system has exactly one axis. For every point on an axis, the value of every other dimensional coordinate is zero.

What does axis mean in pandas?

axis=’index’ means you are moving vertically down along the index. axis=’columns’ means you are moving horizontally right along the columns.

Is NumPy row by column?

NumPy arrays provide a fast and efficient way to store and manipulate data in Python. They are particularly useful for representing data as vectors and matrices in machine learning. Data in NumPy arrays can be accessed directly via column and row indexes, and this is reasonably straightforward.

Is NumPy row Major?

NumPy creates arrays in row-major order by default.

How do I find the row and column of a matrix in Python?

In the NumPy with the help of shape() function, we can find the number of rows and columns. In this function, we pass a matrix and it will return row and column number of the matrix. Return: The number of rows and columns.

What does dimension mean in NumPy?

In Mathematics/Physics, dimension or dimensionality is informally defined as the minimum number of coordinates needed to specify any point within a space. But in Numpy, according to the numpy doc, it’s the same as axis/axes: In Numpy dimensions are called axes. The number of axes is rank.

How do you find the dimensions of an array?

You can get the number of dimensions, shape (length of each dimension), and size (number of all elements) of the NumPy array with ndim , shape , and size attributes of numpy. ndarray . The built-in function len() returns the size of the first dimension.

Can arrays have multiple axes?

Arrays can have multiple axes (more than one axis). Each axis is a dimension. Thus a single-dimension array is also known as a list.

How do you extract the diagonal of a matrix in python?

The diag() function is used to extract a diagonal or construct a diagonal array. If v is a 2-D array, return a copy of its k-th diagonal. If v is a 1-D array, return a 2-D array with v on the k-th diagonal.

What is NumPy stack?

stack() function is used to join a sequence of same dimension arrays along a new axis. The axis parameter specifies the index of the new axis in the dimensions of the result. For example, if axis=0 it will be the first dimension and if axis=-1 it will be the last dimension. Syntax : numpy.stack(arrays, axis)

What is Axis parameter in Python?

For instance, it refers to the direction along columns performing operations over rows. For the sum() function. The axis parameter is the axis to be collapsed. Hence in the above example. For instance, the axis is set to 1 in the sum() function collapses the columns and sums down the rows.

What does dimension mean in NumPy?

What is Keepdims?

keepdims = True, is used for matching dimensions of matrix. If we left this False then it will show error of dimension error.

What is NumPy stack?

Axis in Numpy Pandas

Numpy Axes, Explained – Sharp Sight

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Table of Contents:

Numpy axes are hard to understand

Numpy axes are like axes in a coordinate system

Examples of how Numpy axes are used

Warning 1-dimensional arrays work differently

To learn data science in Python learn NumPy

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Numpy axes are hard to understand

Numpy axes are like axes in a coordinate system

Examples of how Numpy axes are used

Warning 1-dimensional arrays work differently

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Table of Contents:

Prerequisites#

The Basics#

Shape Manipulation#

Copies and Views#

Less Basic#

Advanced indexing and index tricks#

Tricks and Tips#

Numpy Axes, Explained

This tutorial will explain NumPy axes.

It will explain what a NumPy axis is. The tutorial will also explain how axes work, and how we use them with NumPy functions.

Although it’s probably best for you to read the full tutorial, if you want to skip ahead, you can do so by clicking on one of the following links:

Before I get into a detailed explanation of NumPy axes, let me just start by explaining why NumPy axes are problematic.

Numpy axes are hard to understand

I’m going to be honest.

NumPy axes are one of the hardest things to understand in the NumPy system. If you’re just getting started with NumPy, this is particularly true. Many beginners struggle to understand how NumPy axes work.

Don’t worry, it’s not you. A lot of Python data science beginners struggle with this.

Having said that, this tutorial will explain all the essentials that you need to know about axes in NumPy arrays.

Let’s start with the basics. I’ll make NumPy axes easier to understand by connecting them to something you already know.

Numpy axes are like axes in a coordinate system

If you’re reading this blog post, chances are you’ve taken more than a couple of math classes.

Think back to early math, when you were first learning about graphs.

You learned about Cartesian coordinates. NumPy axes are very similar to axes in a Cartesian coordinate system.

An analogy: cartesian coordinate systems have axes

You probably remember this, but just so we’re clear, let’s take a look at a simple Cartesian coordinate system.

A simple 2-dimensional Cartesian coordinate system has two axes, the x axis and the y axis.

These axes are essentially just directions in a Cartesian space (orthogonal directions).

Moreover, we can identify the position of a point in Cartesian space by it’s position along each of the axes.

So if we have a point at position (2, 3) , we’re basically saying that it lies 2 units along the x axis and 3 units along the y axis.

If all of this is familiar to you, good. You’re half way there to understanding NumPy axes.

NumPy axes are the directions along the rows and columns

Just like coordinate systems, NumPy arrays also have axes.

In a 2-dimensional NumPy array, the axes are the directions along the rows and columns.

Axis 0 is the direction along the rows

In a NumPy array, axis 0 is the “first” axis.

Assuming that we’re talking about multi-dimensional arrays, axis 0 is the axis that runs downward down the rows.

Keep in mind that this really applies to 2-d arrays and multi dimensional arrays. 1-dimensional arrays are a bit of a special case, and I’ll explain those later in the tutorial.

Axis 1 is the direction along the columns

In a multi-dimensional NumPy array, axis 1 is the second axis.

When we’re talking about 2-d and multi-dimensional arrays, axis 1 is the axis that runs horizontally across the columns.

Once again, keep in mind that 1-d arrays work a little differently. Technically, 1-d arrays don’t have an axis 1. I’ll explain more about this later in the tutorial.

NumPy array axes are numbered starting with ‘0’

It is probably obvious at this point, but I should point out that array axes in NumPy are numbered.

Importantly, they are numbered starting with 0.

This is just like index values for Python sequences. In Python sequences – like lists and tuples – the values in a the sequence have an index associated with them.

So, let’s say that we have a Python list with a few capital letters:

alpha_list = [‘A’,’B’,’C’,’D’]
If we retrieve the index value of the first item (‘ A ‘) …

alpha_list.index(‘A’)

… we find that ‘ A ‘ is at index position 0.

Here, A is the first item in the list, but the index position is 0.

Essentially all Python sequences work like this. In any Python sequence – like a list, tuple, or string – the index starts at 0.

Numbering of NumPy axes essentially works the same way. They are numbered starting with 0. So the “first” axis is actually “axis 0.” The “second” axis is “axis 1,” and so on.

The structure of NumPy array axes is important

In the following section, I’m going to show you examples of how NumPy axes are used in NumPy, but before I show you that, you need to remember that the structure of NumPy arrays matters.

The details that I just explained, about axis numbers, and about which axis is which is going to impact your understanding of the NumPy functions we use.

Having said that, before you move on to the examples, make sure you really understand the details that I explained above about NumPy axes.

And if you have any questions or you’re still confused about NumPy axes, leave a question in the comments at the bottom of the page.

Ok. Now, let’s move on to the examples.

Examples of how Numpy axes are used

Now that we’ve explained how NumPy axes work in general, let’s look at some specific examples of how NumPy axes are used.

These examples are important, because they will help develop your intuition about how NumPy axes work when used with NumPy functions.

Run this code before you start

Before we start working with these examples, you’ll need to run a small bit of code:

import numpy as np

This code will basically import the NumPy package into your environment so you can work with it. Going forward, you’ll be able to reference the NumPy package as np in our syntax.

A word of advice: pay attention to what the axis parameter controls

Before I show you the following examples, I want to give you a piece of advice.

To understand how to use the axis parameter in the NumPy functions, it’s very important to understand what the axis parameter actually controls for each function.

This is not always as simple as it sounds. For example, in the np.sum() function, the axis parameter behaves in a way that many people think is counter intuitive.

I’ll explain exactly how it works in a minute, but I need to stress this point: pay very careful attention to what the axis parameter actually controls for each function.

Numpy sum

Let’s take a look at how NumPy axes work inside of the NumPy sum function.

When trying to understand axes in NumPy sum, you need to know what the axis parameter actually controls.

In np.sum() , the axis parameter controls which axis will be aggregated.

Said differently, the axis parameter controls which axis will be collapsed.

Remember, functions like sum() , mean() , min() , median() , and other statistical functions aggregate your data.

To explain what I mean by “aggregate,” I’ll give you a simple example.

Imagine you have a set of 5 numbers. If sum up those 5 numbers, the result will be a single number. Summation effectively aggregates your data. It collapses a large number of values into a single value.

Similarly, when you use np.sum() on a 2-d array with the axis parameter, it is going to collapse your 2-d array down to a 1-d array. It will collapse the data and reduce the number of dimensions.

But which axis will get collapsed?

When you use the NumPy sum function with the axis parameter, the axis that you specify is the axis that gets collapsed.

Let’s take a look at that.

Numpy sum with axis = 0

Here, we’re going to use the NumPy sum function with axis = 0 .

First, we’re just going to create a simple NumPy array.

np_array_2d = np.arange(0, 6).reshape([2,3])

And let’s quickly print it out, so you can see the contents.

print(np_array_2d)
[[0 1 2] [3 4 5]]
The array, np_array_2d , is a 2-dimensional array that contains the values from 0 to 5 in a 2-by-3 format.

Next, let’s use the NumPy sum function with axis = 0 .

np.sum(np_array_2d, axis = 0)

And here’s the output.

array([3, 5, 7])

When we set axis = 0 , the function actually sums down the columns. The result is a new NumPy array that contains the sum of each column. Why? Doesn’t axis 0 refer to the rows?

This confuses many beginners, so let me explain.

As I mentioned earlier, the axis parameter indicates which axis gets collapsed.

So when we set axis = 0 , we’re not summing across the rows. When we set axis = 0 , we’re aggregating the data such that we collapse the rows … we collapse axis 0.

Numpy sum with axis = 1

Now, let’s use the NumPy sum function on our array with axis = 1 .

In this example, we’re going to reuse the array that we created earlier, np_array_2d .

Remember that it is a simple 2-d array with 6 values arranged in a 2 by 3 form.

print(np_array_2d)
[[0 1 2] [3 4 5]]
Here, we’re going to use the sum function, and we’ll set the axis parameter to axis = 1 .

np.sum(np_array_2d, axis = 1)

And here’s the output:

array([3, 12])

Let me explain.

Again, with the sum() function, the axis parameter sets the axis that gets collapsed during the summation process.

Recall from earlier in this tutorial that axis 1 refers to the horizontal direction across the columns. That means that the code np.sum(np_array_2d, axis = 1) collapses the columns during the summation.

As I mentioned earlier, this confuses many beginners. They expect that by setting axis = 1 , NumPy would sum down the columns, but that’s not how it works.

The code has the effect of summing across the columns. It collapses axis 1.

Numpy concatenate

Now let’s take a look at a different example.

Here, we’re going to work with the axis parameter in the context of using the NumPy concatenate function.

When we use the axis parameter with the np.concatenate() function, the axis parameter defines the axis along which we stack the arrays. If that doesn’t make sense, then work through the examples. It will probably become more clear once you run the code and see the output.

In both of the following examples, we’re going to work with two 2-dimensional NumPy arrays:

np_array_1s = np.array([[1,1,1],[1,1,1]]) np_array_9s = np.array([[9,9,9],[9,9,9]])

Which have the following structure, respectively:

array([[1, 1, 1], [1, 1, 1]])

And:

array([[9, 9, 9], [9, 9, 9]])

Numpy concatenate with axis = 0

First, let’s look at how to use NumPy concatenate with axis = 0.

np.concatenate([np_array_1s, np_array_9s], axis = 0)

Which produces the following output:

array([[1, 1, 1], [1, 1, 1], [9, 9, 9], [9, 9, 9]])

Let’s carefully evaluate what the syntax did here.

Recall what I mentioned a few paragraphs ago. When we use the concatenate function, the axis parameter defines the axis along which we stack the arrays.

So when we set axis = 0 , we’re telling the concatenate function to stack the two arrays along the rows. We’re specifying that we want to concatenate the arrays along axis 0.

Numpy concatenate with axis = 1

Now let’s take a look at an example of using np.concatenate() with axis = 1 .

Here, we’re going to reuse the two 2-dimensional NumPy arrays that we just created, np_array_1s and np_array_9s .

We’re going to use the concatenate function to combine these arrays together horizontally.

np.concatenate([np_array_1s, np_array_9s], axis = 1)

Which produces the following output:

array([[1, 1, 1, 9, 9, 9], [1, 1, 1, 9, 9, 9]])

If you’ve been reading carefully and you’ve understood the other examples in this tutorial, this should make sense.

However, let’s quickly review what’s going on here.

These arrays are 2 dimensional, so they have two axes, axis 0 and axis 1. Axis 1 is the axis that runs horizontally across the columns of the NumPy arrays.

When we use NumPy concatenate with axis = 1 , we are telling the concatenate() function to combine these arrays together along axis 1.

That is, we’re telling concatenate() to combine them together horizontally, since axis 1 is the axis that runs horizontally across the columns.

Warning: 1-dimensional arrays work differently

Hopefully this NumPy axis tutorial helped you understand how NumPy axes work.

But before I end the tutorial, I want to give you a warning: 1-dimensional arrays work differently!

Everything that I’ve said in this post really applies to 2-dimensional arrays (and to some extent, multi-dimensional arrays).

The axes of 1-dimensional NumPy arrays work differently. For beginners, this is likely to cause issues.

Having said all of that, let me quickly explain how axes work in 1-dimensional NumPy arrays.

1-dimensional NumPy arrays only have one axis

The important thing to know is that 1-dimensional NumPy arrays only have one axis.

If 1-d arrays only have one axis, can you guess the name of that axis?

Remember, axes are numbered like Python indexes. They start at 0.

So, in a 1-d NumPy array, the first and only axis is axis 0.

The fact that 1-d arrays have only one axis can cause some results that confuse NumPy beginners.

Example: concatenating 1-d arrays

Let me show you an example of some of these “confusing” results that can occur when working with 1-d arrays.

We’re going to create two simple 1-dimensional arrays.

np_array_1s_1dim = np.array([1,1,1]) np_array_9s_1dim = np.array([9,9,9])

And we can print them out to see the contents:

print(np_array_1s_1dim) print(np_array_9s_1dim)

Output:
[1 1 1] [9 9 9]
As you can see, these are two simple 1-d arrays.

Next, let’s concatenate them together using np.concatenate() with axis = 0 .

np.concatenate([np_array_1s_1dim, np_array_9s_1dim], axis = 0)

Output:

array([1, 1, 1, 9, 9, 9])

This output confuses many beginners. The arrays were concatenated together horizontally.

This is different from how the function works on 2-dimensional arrays. If we use np.concatenate() with axis = 0 on 2 -dimensional arrays, the arrays will be concatenated together vertically.

What’s going on here?

Recall what I just mentioned a few paragraphs ago: 1-dimensional NumPy arrays only have one axis. Axis 0.

The function is working properly in this case. NumPy concatenate is concatenating these arrays along axis 0. The issue is that in 1-d arrays, axis 0 doesn’t point “downward” like it does in a 2-dimensional array.

Example: an error when concatenating 1-d arrays, with axis = 1

Moreover, you’ll also run into problems if you try to concatenate these arrays on axis 1.

Try it:

np.concatenate([np_array_1s_1dim, np_array_9s_1dim], axis = 1)

This code causes an error:

IndexError: axis 1 out of bounds [0, 1)

If you’ve been reading carefully, this error should make sense. np_array_1s_1dim and np_array_9s_1dim are 1-dimensional arrays. Therefore, they don’t have an axis 1. We’re trying to use np.concatenate() on an axis that doesn’t exist in these arrays. Therefore, the code generates an error.

Be careful when using axes with 1-d arrays

All of this is to say that you need to be careful when working with 1-dimensional arrays. When you’re working with 1-d arrays, and you use some NumPy functions with the axis parameter, the code can generate confusing results.

The results make a lot of sense if you really understand how NumPy axes work. But if you don’t understand NumPy array axes, the results will probably be confusing.

So make sure that before you start working with NumPy array axes that you really understand them!

To learn data science in Python, learn NumPy

As you’ve seen in this tutorial, NumPy axes can be a little confusing. They are especially confusing to NumPy beginners.

But, in order to use NumPy correctly, you really need to understand how NumPy axes work.

Moreover, if you want to learn data science in Python, you need to learn how NumPy axes work. That’s because working with axes is critical for using NumPy, and NumPy is a critical part of the Python data science ecosystem.

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Numpy Axes, Explained

This tutorial will explain NumPy axes.

It will explain what a NumPy axis is. The tutorial will also explain how axes work, and how we use them with NumPy functions.

Although it’s probably best for you to read the full tutorial, if you want to skip ahead, you can do so by clicking on one of the following links:

Before I get into a detailed explanation of NumPy axes, let me just start by explaining why NumPy axes are problematic.

Numpy axes are hard to understand

I’m going to be honest.

NumPy axes are one of the hardest things to understand in the NumPy system. If you’re just getting started with NumPy, this is particularly true. Many beginners struggle to understand how NumPy axes work.

Don’t worry, it’s not you. A lot of Python data science beginners struggle with this.

Having said that, this tutorial will explain all the essentials that you need to know about axes in NumPy arrays.

Let’s start with the basics. I’ll make NumPy axes easier to understand by connecting them to something you already know.

Numpy axes are like axes in a coordinate system

If you’re reading this blog post, chances are you’ve taken more than a couple of math classes.

Think back to early math, when you were first learning about graphs.

You learned about Cartesian coordinates. NumPy axes are very similar to axes in a Cartesian coordinate system.

An analogy: cartesian coordinate systems have axes

You probably remember this, but just so we’re clear, let’s take a look at a simple Cartesian coordinate system.

A simple 2-dimensional Cartesian coordinate system has two axes, the x axis and the y axis.

These axes are essentially just directions in a Cartesian space (orthogonal directions).

Moreover, we can identify the position of a point in Cartesian space by it’s position along each of the axes.

So if we have a point at position (2, 3) , we’re basically saying that it lies 2 units along the x axis and 3 units along the y axis.

If all of this is familiar to you, good. You’re half way there to understanding NumPy axes.

NumPy axes are the directions along the rows and columns

Just like coordinate systems, NumPy arrays also have axes.

In a 2-dimensional NumPy array, the axes are the directions along the rows and columns.

Axis 0 is the direction along the rows

In a NumPy array, axis 0 is the “first” axis.

Assuming that we’re talking about multi-dimensional arrays, axis 0 is the axis that runs downward down the rows.

Keep in mind that this really applies to 2-d arrays and multi dimensional arrays. 1-dimensional arrays are a bit of a special case, and I’ll explain those later in the tutorial.

Axis 1 is the direction along the columns

In a multi-dimensional NumPy array, axis 1 is the second axis.

When we’re talking about 2-d and multi-dimensional arrays, axis 1 is the axis that runs horizontally across the columns.

Once again, keep in mind that 1-d arrays work a little differently. Technically, 1-d arrays don’t have an axis 1. I’ll explain more about this later in the tutorial.

NumPy array axes are numbered starting with ‘0’

It is probably obvious at this point, but I should point out that array axes in NumPy are numbered.

Importantly, they are numbered starting with 0.

This is just like index values for Python sequences. In Python sequences – like lists and tuples – the values in a the sequence have an index associated with them.

So, let’s say that we have a Python list with a few capital letters:

alpha_list = [‘A’,’B’,’C’,’D’]
If we retrieve the index value of the first item (‘ A ‘) …

alpha_list.index(‘A’)

… we find that ‘ A ‘ is at index position 0.

Here, A is the first item in the list, but the index position is 0.

Essentially all Python sequences work like this. In any Python sequence – like a list, tuple, or string – the index starts at 0.

Numbering of NumPy axes essentially works the same way. They are numbered starting with 0. So the “first” axis is actually “axis 0.” The “second” axis is “axis 1,” and so on.

The structure of NumPy array axes is important

In the following section, I’m going to show you examples of how NumPy axes are used in NumPy, but before I show you that, you need to remember that the structure of NumPy arrays matters.

The details that I just explained, about axis numbers, and about which axis is which is going to impact your understanding of the NumPy functions we use.

Having said that, before you move on to the examples, make sure you really understand the details that I explained above about NumPy axes.

And if you have any questions or you’re still confused about NumPy axes, leave a question in the comments at the bottom of the page.

Ok. Now, let’s move on to the examples.

Examples of how Numpy axes are used

Now that we’ve explained how NumPy axes work in general, let’s look at some specific examples of how NumPy axes are used.

These examples are important, because they will help develop your intuition about how NumPy axes work when used with NumPy functions.

Run this code before you start

Before we start working with these examples, you’ll need to run a small bit of code:

import numpy as np

This code will basically import the NumPy package into your environment so you can work with it. Going forward, you’ll be able to reference the NumPy package as np in our syntax.

A word of advice: pay attention to what the axis parameter controls

Before I show you the following examples, I want to give you a piece of advice.

To understand how to use the axis parameter in the NumPy functions, it’s very important to understand what the axis parameter actually controls for each function.

This is not always as simple as it sounds. For example, in the np.sum() function, the axis parameter behaves in a way that many people think is counter intuitive.

I’ll explain exactly how it works in a minute, but I need to stress this point: pay very careful attention to what the axis parameter actually controls for each function.

Numpy sum

Let’s take a look at how NumPy axes work inside of the NumPy sum function.

When trying to understand axes in NumPy sum, you need to know what the axis parameter actually controls.

In np.sum() , the axis parameter controls which axis will be aggregated.

Said differently, the axis parameter controls which axis will be collapsed.

Remember, functions like sum() , mean() , min() , median() , and other statistical functions aggregate your data.

To explain what I mean by “aggregate,” I’ll give you a simple example.

Imagine you have a set of 5 numbers. If sum up those 5 numbers, the result will be a single number. Summation effectively aggregates your data. It collapses a large number of values into a single value.

Similarly, when you use np.sum() on a 2-d array with the axis parameter, it is going to collapse your 2-d array down to a 1-d array. It will collapse the data and reduce the number of dimensions.

But which axis will get collapsed?

When you use the NumPy sum function with the axis parameter, the axis that you specify is the axis that gets collapsed.

Let’s take a look at that.

Numpy sum with axis = 0

Here, we’re going to use the NumPy sum function with axis = 0 .

First, we’re just going to create a simple NumPy array.

np_array_2d = np.arange(0, 6).reshape([2,3])

And let’s quickly print it out, so you can see the contents.

print(np_array_2d)
[[0 1 2] [3 4 5]]
The array, np_array_2d , is a 2-dimensional array that contains the values from 0 to 5 in a 2-by-3 format.

Next, let’s use the NumPy sum function with axis = 0 .

np.sum(np_array_2d, axis = 0)

And here’s the output.

array([3, 5, 7])

When we set axis = 0 , the function actually sums down the columns. The result is a new NumPy array that contains the sum of each column. Why? Doesn’t axis 0 refer to the rows?

This confuses many beginners, so let me explain.

As I mentioned earlier, the axis parameter indicates which axis gets collapsed.

So when we set axis = 0 , we’re not summing across the rows. When we set axis = 0 , we’re aggregating the data such that we collapse the rows … we collapse axis 0.

Numpy sum with axis = 1

Now, let’s use the NumPy sum function on our array with axis = 1 .

In this example, we’re going to reuse the array that we created earlier, np_array_2d .

Remember that it is a simple 2-d array with 6 values arranged in a 2 by 3 form.

print(np_array_2d)
[[0 1 2] [3 4 5]]
Here, we’re going to use the sum function, and we’ll set the axis parameter to axis = 1 .

np.sum(np_array_2d, axis = 1)

And here’s the output:

array([3, 12])

Let me explain.

Again, with the sum() function, the axis parameter sets the axis that gets collapsed during the summation process.

Recall from earlier in this tutorial that axis 1 refers to the horizontal direction across the columns. That means that the code np.sum(np_array_2d, axis = 1) collapses the columns during the summation.

As I mentioned earlier, this confuses many beginners. They expect that by setting axis = 1 , NumPy would sum down the columns, but that’s not how it works.

The code has the effect of summing across the columns. It collapses axis 1.

Numpy concatenate

Now let’s take a look at a different example.

Here, we’re going to work with the axis parameter in the context of using the NumPy concatenate function.

When we use the axis parameter with the np.concatenate() function, the axis parameter defines the axis along which we stack the arrays. If that doesn’t make sense, then work through the examples. It will probably become more clear once you run the code and see the output.

In both of the following examples, we’re going to work with two 2-dimensional NumPy arrays:

np_array_1s = np.array([[1,1,1],[1,1,1]]) np_array_9s = np.array([[9,9,9],[9,9,9]])

Which have the following structure, respectively:

array([[1, 1, 1], [1, 1, 1]])

And:

array([[9, 9, 9], [9, 9, 9]])

Numpy concatenate with axis = 0

First, let’s look at how to use NumPy concatenate with axis = 0.

np.concatenate([np_array_1s, np_array_9s], axis = 0)

Which produces the following output:

array([[1, 1, 1], [1, 1, 1], [9, 9, 9], [9, 9, 9]])

Let’s carefully evaluate what the syntax did here.

Recall what I mentioned a few paragraphs ago. When we use the concatenate function, the axis parameter defines the axis along which we stack the arrays.

So when we set axis = 0 , we’re telling the concatenate function to stack the two arrays along the rows. We’re specifying that we want to concatenate the arrays along axis 0.

Numpy concatenate with axis = 1

Now let’s take a look at an example of using np.concatenate() with axis = 1 .

Here, we’re going to reuse the two 2-dimensional NumPy arrays that we just created, np_array_1s and np_array_9s .

We’re going to use the concatenate function to combine these arrays together horizontally.

np.concatenate([np_array_1s, np_array_9s], axis = 1)

Which produces the following output:

array([[1, 1, 1, 9, 9, 9], [1, 1, 1, 9, 9, 9]])

If you’ve been reading carefully and you’ve understood the other examples in this tutorial, this should make sense.

However, let’s quickly review what’s going on here.

These arrays are 2 dimensional, so they have two axes, axis 0 and axis 1. Axis 1 is the axis that runs horizontally across the columns of the NumPy arrays.

When we use NumPy concatenate with axis = 1 , we are telling the concatenate() function to combine these arrays together along axis 1.

That is, we’re telling concatenate() to combine them together horizontally, since axis 1 is the axis that runs horizontally across the columns.

Warning: 1-dimensional arrays work differently

Hopefully this NumPy axis tutorial helped you understand how NumPy axes work.

But before I end the tutorial, I want to give you a warning: 1-dimensional arrays work differently!

Everything that I’ve said in this post really applies to 2-dimensional arrays (and to some extent, multi-dimensional arrays).

The axes of 1-dimensional NumPy arrays work differently. For beginners, this is likely to cause issues.

Having said all of that, let me quickly explain how axes work in 1-dimensional NumPy arrays.

1-dimensional NumPy arrays only have one axis

The important thing to know is that 1-dimensional NumPy arrays only have one axis.

If 1-d arrays only have one axis, can you guess the name of that axis?

Remember, axes are numbered like Python indexes. They start at 0.

So, in a 1-d NumPy array, the first and only axis is axis 0.

The fact that 1-d arrays have only one axis can cause some results that confuse NumPy beginners.

Example: concatenating 1-d arrays

Let me show you an example of some of these “confusing” results that can occur when working with 1-d arrays.

We’re going to create two simple 1-dimensional arrays.

np_array_1s_1dim = np.array([1,1,1]) np_array_9s_1dim = np.array([9,9,9])

And we can print them out to see the contents:

print(np_array_1s_1dim) print(np_array_9s_1dim)

Output:
[1 1 1] [9 9 9]
As you can see, these are two simple 1-d arrays.

Next, let’s concatenate them together using np.concatenate() with axis = 0 .

np.concatenate([np_array_1s_1dim, np_array_9s_1dim], axis = 0)

Output:

array([1, 1, 1, 9, 9, 9])

This output confuses many beginners. The arrays were concatenated together horizontally.

This is different from how the function works on 2-dimensional arrays. If we use np.concatenate() with axis = 0 on 2 -dimensional arrays, the arrays will be concatenated together vertically.

What’s going on here?

Recall what I just mentioned a few paragraphs ago: 1-dimensional NumPy arrays only have one axis. Axis 0.

The function is working properly in this case. NumPy concatenate is concatenating these arrays along axis 0. The issue is that in 1-d arrays, axis 0 doesn’t point “downward” like it does in a 2-dimensional array.

Example: an error when concatenating 1-d arrays, with axis = 1

Moreover, you’ll also run into problems if you try to concatenate these arrays on axis 1.

Try it:

np.concatenate([np_array_1s_1dim, np_array_9s_1dim], axis = 1)

This code causes an error:

IndexError: axis 1 out of bounds [0, 1)

If you’ve been reading carefully, this error should make sense. np_array_1s_1dim and np_array_9s_1dim are 1-dimensional arrays. Therefore, they don’t have an axis 1. We’re trying to use np.concatenate() on an axis that doesn’t exist in these arrays. Therefore, the code generates an error.

Be careful when using axes with 1-d arrays

All of this is to say that you need to be careful when working with 1-dimensional arrays. When you’re working with 1-d arrays, and you use some NumPy functions with the axis parameter, the code can generate confusing results.

The results make a lot of sense if you really understand how NumPy axes work. But if you don’t understand NumPy array axes, the results will probably be confusing.

So make sure that before you start working with NumPy array axes that you really understand them!

To learn data science in Python, learn NumPy

As you’ve seen in this tutorial, NumPy axes can be a little confusing. They are especially confusing to NumPy beginners.

But, in order to use NumPy correctly, you really need to understand how NumPy axes work.

Moreover, if you want to learn data science in Python, you need to learn how NumPy axes work. That’s because working with axes is critical for using NumPy, and NumPy is a critical part of the Python data science ecosystem.

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Glossary — NumPy v1.10 Manual

along an axis

Axes are defined for arrays with more than one dimension. A 2-dimensional array has two corresponding axes: the first running vertically downwards across rows (axis 0), and the second running horizontally across columns (axis 1). Many operation can take place along one of these axes. For example, we can sum each row of an array, in which case we operate along columns, or axis 1: >>> x = np . arange ( 12 ) . reshape (( 3 , 4 )) >>> x array([[ 0, 1, 2, 3], [ 4, 5, 6, 7], [ 8, 9, 10, 11]]) >>> x . sum ( axis = 1 ) array([ 6, 22, 38])

array

A homogeneous container of numerical elements. Each element in the array occupies a fixed amount of memory (hence homogeneous), and can be a numerical element of a single type (such as float, int or complex) or a combination (such as (float, int, float) ). Each array has an associated data-type (or dtype ), which describes the numerical type of its elements: >>> x = np . array ([ 1 , 2 , 3 ], float ) >>> x array([ 1., 2., 3.]) >>> x . dtype # floating point number, 64 bits of memory per element dtype(‘float64’) # More complicated data type: each array element is a combination of # and integer and a floating point number >>> np . array ([( 1 , 2.0 ), ( 3 , 4.0 )], dtype = [( ‘x’ , int ), ( ‘y’ , float )]) array([(1, 2.0), (3, 4.0)], dtype=[(‘x’, ‘>> x = np . array ([ 1 , 2 , 3 ]) >>> x . shape (3,)

BLAS

broadcast

NumPy can do operations on arrays whose shapes are mismatched: >>> x = np . array ([ 1 , 2 ]) >>> y = np . array ([[ 3 ], [ 4 ]]) >>> x array([1, 2]) >>> y array([[3], [4]]) >>> x + y array([[4, 5], [5, 6]]) See `doc.broadcasting`_ for more information.

C order

See row-major

column-major

A way to represent items in a N-dimensional array in the 1-dimensional computer memory. In column-major order, the leftmost index “varies the fastest”: for example the array: [[ 1 , 2 , 3 ], [ 4 , 5 , 6 ]] is represented in the column-major order as: [ 1 , 4 , 2 , 5 , 3 , 6 ] Column-major order is also known as the Fortran order, as the Fortran programming language uses it.

decorator

An operator that transforms a function. For example, a log decorator may be defined to print debugging information upon function execution: >>> def log ( f ): … def new_logging_func ( * args , ** kwargs ): … print “Logging call with parameters:” , args , kwargs … return f ( * args , ** kwargs ) … … return new_logging_func Now, when we define a function, we can “decorate” it using log : >>> @log … def add ( a , b ): … return a + b Calling add then yields: >>> add ( 1 , 2 ) Logging call with parameters: (1, 2) {} 3

dictionary

Resembling a language dictionary, which provides a mapping between words and descriptions thereof, a Python dictionary is a mapping between two objects: >>> x = { 1 : ‘one’ , ‘two’ : [ 1 , 2 ]} Here, x is a dictionary mapping keys to values, in this case the integer 1 to the string “one”, and the string “two” to the list [1, 2] . The values may be accessed using their corresponding keys: >>> x [ 1 ] ‘one’ >>> x [ ‘two’ ] [1, 2] Note that dictionaries are not stored in any specific order. Also, most mutable (see immutable below) objects, such as lists, may not be used as keys. For more information on dictionaries, read the Python tutorial.

Fortran order

See column-major

flattened

Collapsed to a one-dimensional array. See `ndarray.flatten`_ for details.

immutable

An object that cannot be modified after execution is called immutable. Two common examples are strings and tuples.

instance

A class definition gives the blueprint for constructing an object: >>> class House ( object ): … wall_colour = ‘white’ Yet, we have to build a house before it exists: >>> h = House () # build a house Now, h is called a House instance. An instance is therefore a specific realisation of a class.

iterable

A sequence that allows “walking” (iterating) over items, typically using a loop such as: >>> x = [ 1 , 2 , 3 ] >>> [ item ** 2 for item in x ] [1, 4, 9] It is often used in combintion with enumerate :: >>> keys = [ ‘a’ , ‘b’ , ‘c’ ] >>> for n , k in enumerate ( keys ): … print “Key %d : %s ” % ( n , k ) … Key 0: a Key 1: b Key 2: c

list

A Python container that can hold any number of objects or items. The items do not have to be of the same type, and can even be lists themselves: >>> x = [ 2 , 2.0 , “two” , [ 2 , 2.0 ]] The list x contains 4 items, each which can be accessed individually: >>> x [ 2 ] # the string ‘two’ ‘two’ >>> x [ 3 ] # a list, containing an integer 2 and a float 2.0 [2, 2.0] It is also possible to select more than one item at a time, using slicing: >>> x [ 0 : 2 ] # or, equivalently, x[:2] [2, 2.0] In code, arrays are often conveniently expressed as nested lists: >>> np . array ([[ 1 , 2 ], [ 3 , 4 ]]) array([[1, 2], [3, 4]]) For more information, read the section on lists in the Python tutorial. For a mapping type (key-value), see dictionary.

mask

A boolean array, used to select only certain elements for an operation: >>> x = np . arange ( 5 ) >>> x array([0, 1, 2, 3, 4]) >>> mask = ( x > 2 ) >>> mask array([False, False, False, True, True], dtype=bool) >>> x [ mask ] = – 1 >>> x array([ 0, 1, 2, -1, -1])

masked array

Array that suppressed values indicated by a mask: >>> x = np . ma . masked_array ([ np . nan , 2 , np . nan ], [ True , False , True ]) >>> x masked_array(data = [– 2.0 –], mask = [ True False True], fill_value = 1e+20) >>> x + [ 1 , 2 , 3 ] masked_array(data = [– 4.0 –], mask = [ True False True], fill_value = 1e+20) Masked arrays are often used when operating on arrays containing missing or invalid entries.

matrix

A 2-dimensional ndarray that preserves its two-dimensional nature throughout operations. It has certain special operations, such as * (matrix multiplication) and ** (matrix power), defined: >>> x = np . mat ([[ 1 , 2 ], [ 3 , 4 ]]) >>> x matrix([[1, 2], [3, 4]]) >>> x ** 2 matrix([[ 7, 10], [15, 22]])

method

A function associated with an object. For example, each ndarray has a method called repeat : >>> x = np . array ([ 1 , 2 , 3 ]) >>> x . repeat ( 2 ) array([1, 1, 2, 2, 3, 3])

ndarray

See array.

record array

An `ndarray`_ with `structured data type`_ which has been subclassed as np.recarray and whose dtype is of type np.record, making the fields of its data type to be accessible by attribute.

reference

If a is a reference to b , then (a is b) == True . Therefore, a and b are different names for the same Python object.

row-major

A way to represent items in a N-dimensional array in the 1-dimensional computer memory. In row-major order, the rightmost index “varies the fastest”: for example the array: [[ 1 , 2 , 3 ], [ 4 , 5 , 6 ]] is represented in the row-major order as: [ 1 , 2 , 3 , 4 , 5 , 6 ] Row-major order is also known as the C order, as the C programming language uses it. New Numpy arrays are by default in row-major order.

self

Often seen in method signatures, self refers to the instance of the associated class. For example: >>> class Paintbrush ( object ): … color = ‘blue’ … … def paint ( self ): … print “Painting the city %s !” % self . color … >>> p = Paintbrush () >>> p . color = ‘red’ >>> p . paint () # self refers to ‘p’ Painting the city red!

slice

Used to select only certain elements from a sequence: >>> x = range ( 5 ) >>> x [0, 1, 2, 3, 4] >>> x [ 1 : 3 ] # slice from 1 to 3 (excluding 3 itself) [1, 2] >>> x [ 1 : 5 : 2 ] # slice from 1 to 5, but skipping every second element [1, 3] >>> x [:: – 1 ] # slice a sequence in reverse [4, 3, 2, 1, 0] Arrays may have more than one dimension, each which can be sliced individually: >>> x = np . array ([[ 1 , 2 ], [ 3 , 4 ]]) >>> x array([[1, 2], [3, 4]]) >>> x [:, 1 ] array([2, 4])

structured data type

A data type composed of other datatypes

tuple

A sequence that may contain a variable number of types of any kind. A tuple is immutable, i.e., once constructed it cannot be changed. Similar to a list, it can be indexed and sliced: >>> x = ( 1 , ‘one’ , [ 1 , 2 ]) >>> x (1, ‘one’, [1, 2]) >>> x [ 0 ] 1 >>> x [: 2 ] (1, ‘one’) A useful concept is “tuple unpacking”, which allows variables to be assigned to the contents of a tuple: >>> x , y = ( 1 , 2 ) >>> x , y = 1 , 2 This is often used when a function returns multiple values: >>> def return_many (): … return 1 , ‘alpha’ , None >>> a , b , c = return_many () >>> a , b , c (1, ‘alpha’, None) >>> a 1 >>> b ‘alpha’

ufunc

Universal function. A fast element-wise array operation. Examples include add , sin and logical_or .

view

An array that does not own its data, but refers to another array’s data instead. For example, we may create a view that only shows every second element of another array: >>> x = np . arange ( 5 ) >>> x array([0, 1, 2, 3, 4]) >>> y = x [:: 2 ] >>> y array([0, 2, 4]) >>> x [ 0 ] = 3 # changing x changes y as well, since y is a view on x >>> y array([3, 2, 4])

wrapper

So you have finished reading the numpy axis topic article, if you find this article useful, please share it. Thank you very much. See more: Axis 0 and 1 in NumPy, Concatenate axis=1, Axis=1, Check dimension of numpy array, Import numpy, NumPy array 3 dimensions, Create numpy array with shape, Np index

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