NumPy stands for Numerical Python and is a Python library for working with arrays. With the help of these arrays, elements from linear algebra, such as vectors and matrices, can be represented in Python. Since a large part of the library is written in C, it can perform particularly efficient and fast calculations even with large matrices.

### What is NumPy?

Python offers a variety of data structures that can be used to store data without additional libraries. However, these structures, such as Python lists, are only very poorly suited for mathematical operations. Adding two lists of numbers element by element can quickly be detrimental to performance when dealing with large amounts of data.

For this reason, NumPy was developed, as it offers the possibility to perform numerical operations quickly and efficiently. Especially important are calculations from the field of linear algebra, such as matrix multiplications.

### How to install NumPy?

NumPy, like many other libraries, can be installed directly from a notebook using pip. To do this, use the command “pip install” together with the module name. This line must be preceded by an exclamation mark so that the notebook recognizes that it is a terminal command:

If the installation was successful, the module can simply be imported and used in the notebook. The abbreviation “np” is often used here to save a little time in the course of programming and not to have to enter NumPy every time:

### What mathematical functions can be implemented?

NumPy offers an extensive collection of mathematical functions and linear algebra functions that are essential for scientific calculations and data analysis. Mathematical functions include trigonometric functions, exponential and logarithmic functions, hyperbolic functions, and many others. These functions can be applied to NumPy arrays to perform element-wise operations, making it easier to perform complex calculations with large data sets.

NumPy’s linear algebra capabilities are also essential for scientific calculations and data analysis. NumPy provides a set of functions for solving systems of linear equations, calculating eigenvalues and eigenvectors, and performing matrix operations such as multiplication, addition, and inversion. These capabilities make it easier to perform sophisticated mathematical calculations on large data sets, such as those involved in machine learning and data analysis.

In addition to its built-in mathematical and linear algebra capabilities, NumPy also provides access to many external libraries for scientific computing and data analysis. For example, NumPy can be used in conjunction with SciPy, a library that provides advanced scientific computing functions such as optimization, interpolation, and signal processing. NumPy can also be used with scikit-learn, a popular Machine Learning library that provides a wide range of algorithms for classification, regression, and clustering.

Overall, the mathematical functions and linear algebra capabilities are critical for scientific computing and data analysis, making it a versatile tool for researchers and data scientists working in a wide range of fields.

### What are NumPy Arrays?

NumPy arrays are a valid alternative to conventional Python lists. They offer the possibility to store multidimensional collections of data. In most cases, numbers are stored and the arrays are used as vectors or matrices. For example, a one-dimensional vector could look like this:

Besides the different functions of NumPy arrays, which we will cover in a separate post, the possible dimensionalities are still important for differentiation:

The following dimensionalities are distinguished:

**0D – Array**: This is simply a scalar, i.e. a single number or value.**1D – Array**: This is a vector, as a string of numbers or values in one dimension.**2D – Array**: This type of array is a matrix, that is, a collection of several 1D – arrays.**3D – Array**: Several matrices form a so-called tensor. We have explained these in more detail in our article on TensorFlow.

### What are the differences between NumPy arrays and Python lists?

Depending on the source, there are several, fundamental differences between NumPy arrays and Python lists. Among the most commonly mentioned are:

**Memory Consumption**: Arrays are programmed in such a way that they occupy a certain part of the memory. All the elements of the array are then located there. The elements of a list, on the other hand, can be far apart in memory. As a result, a list consumes more memory than an identical array.**Speed**: Arrays can also be processed much faster than lists due to their lower memory consumption. This can make a significant difference for objects with several million elements.**Functionality**: Arrays offer significantly more functionalities, for example, they allow element-by-element operations, whereas lists do not.

### What are Numpy ufuncs?

The so-called “Universal Functions” (short: ufuncs) are used to not have to execute certain operations element by element, but directly for the entire array. In computer programming, one speaks of so-called vectorization when commands are executed directly for the entire vector.

This is not only much faster in programming, but also leads to faster calculations. In NumPy, several of these Universal Functions are offered, which can be used for a variety of operations. Among the best-known are:

- With “add()” you can sum up several arrays element by element.
- “subtract()” is the exact opposite and subtracts the array element by element.
- “multiply()” multiplies two arrays element by element.
- “matmul()” forms the matrix product of two arrays. Note that in most cases this will not give the same result as “multiply()”.

### What applications use NumPy?

NumPy has a wide range of practical applications in scientific computing, data analysis, and machine learning. Here are some examples:

**Scientific Computing**: NumPy is widely used for numerical simulations in physics, chemistry, and biology. For example, it can be used to simulate fluid dynamics, quantum mechanics, and molecular dynamics.**Data analysis**: The library is an indispensable tool for data analysis in fields such as finance, engineering, and economics. It can be used for data cleaning, pre-processing, and feature engineering.**Image Processing**: Numerical Python can be used to process and analyze images, such as in medical imaging or computer vision applications. It can be used to perform operations such as filtering, segmentation, and feature extraction.**Machine Learning**: The Python library is a key component of many machine learning libraries, such as scikit-learn and TensorFlow. It is used for data preprocessing, feature engineering, and model training and evaluation.**Natural Language Processing**: NumPy can be used for natural language processing, such as text classification, sentiment analysis, and language modeling.**Financial Modeling**: NumPy can be used for financial modeling and analysis, such as option pricing, portfolio optimization, and risk management.

Overall, NumPy is a versatile tool that offers numerous real-world applications in a wide range of fields, making it an indispensable tool for researchers and data scientists.

### What should you keep in mind when working with large data sets?

When working with large data sets in NumPy, performance and memory considerations are essential. Here are some key factors to keep in mind:

**Vectorization**: One of NumPy’s biggest advantages is its ability to vectorize operations on arrays. Vectorization reduces the need for explicit loops and can greatly improve performance.**Broadcasting**: The broadcasting capability enables efficient operations between arrays of different shapes and sizes. Broadcasting eliminates unnecessary copying of data and can improve performance.**Memory allocation**: NumPy’s default data type is the 64-bit floating point number, which can be very memory intensive. Choosing an appropriate data type such as 32-bit floating point or integer can significantly reduce memory usage.**Out-of-Memory Errors**: When working with large data sets, it is important to carefully monitor memory usage. If the amount of data exceeds the available memory, this can lead to out-of-memory errors. Using chunking techniques or parallel processing can help avoid this problem.**Algorithm complexity**: The performance of NumPy operations can be affected by the complexity of the algorithm. It is important to choose algorithms that are optimized for the problem at hand.**Parallelization**: the library provides tools for parallel processing, such as parallel computing with Dask and NumPy arrays. Parallel processing can significantly improve performance for complex computations on large data sets.

Overall, optimizing performance and managing memory usage are essential when working with large data sets in NumPy. Selecting appropriate data types, vectorizing operations, and using parallel processing can help improve performance and avoid out-of-memory errors.

### This is what you should take with you

- NumPy stands for Numerical Python and is a Python library for working with arrays.
- With the help of these arrays, elements from linear algebra, such as vectors and matrices, can be represented in Python.
- Since much of the library is written in C, it can perform particularly efficient and fast calculations even with large matrices.
- NumPy arrays are comparable to Python lists but are significantly superior to them in memory requirements and processing speed.

Thanks to Deepnote for sponsoring this article! Deepnote offers me the possibility to embed Python code easily and quickly on this website and also to host the related notebooks in the cloud.

### Other Articles on the Topic of NumPy

- Here you can find the documentation of NumPy.
- For the section about ufuncs this article served as a source.