33 skills found · Page 1 of 2
destructurama / AttributedUse attributes to control how complex types are logged to Serilog.
benedekrozemberczki / MUSAEThe reference implementation of "Multi-scale Attributed Node Embedding". (Journal of Complex Networks 2021)
allenai / AlexafsmWith alexafsm, developers can model dialog agents with first-class concepts such as states, attributes, transition, and actions. alexafsm also provides visualization and other tools to help understand, test, debug, and maintain complex FSM conversations.
themsaid / Laravel Model TransformerEasy transformation layer for complex model attributes.
yii2tech / EmbeddedSupport embedded models usage for complex ActiveRecord like MongoDB or ElasticSearch
sanusanth / C Basic ProgramsWhat is C#? C# is pronounced "C-Sharp". It is an object-oriented programming language created by Microsoft that runs on the .NET Framework. C# has roots from the C family, and the language is close to other popular languages like C++ and Java. The first version was released in year 2002. The latest version, C# 8, was released in September 2019. C# is a modern object-oriented programming language developed in 2000 by Anders Hejlsberg, the principal designer and lead architect at Microsoft. It is pronounced as "C-Sharp," inspired by the musical notation “♯” which stands for a note with a slightly higher pitch. As it’s considered an incremental compilation of the C++ language, the name C “sharp” seemed most appropriate. The sharp symbol, however, has been replaced by the keyboard friendly “#” as a suffix to “C” for purposes of programming. Although the code is very similar to C++, C# is newer and has grown fast with extensive support from Microsoft. The fact that it’s so similar to Java syntactically helps explain why it has emerged as one of the most popular programming languages today. C# is pronounced "C-Sharp". It is an object-oriented programming language created by Microsoft that runs on the .NET Framework. C# has roots from the C family, and the language is close to other popular languages like C++ and Java. The first version was released in year 2002. The latest version, C# 8, was released in September 2019. C# is used for: Mobile applications Desktop applications Web applications Web services Web sites Games VR Database applications And much, much more! An Introduction to C# Programming C# is a general-purpose, object-oriented programming language that is structured and easy to learn. It runs on Microsoft’s .Net Framework and can be compiled on a variety of computer platforms. As the syntax is simple and easy to learn, developers familiar with C, C++, or Java have found a comfort zone within C#. C# is a boon for developers who want to build a wide range of applications on the .NET Framework—Windows applications, Web applications, and Web services—in addition to building mobile apps, Windows Store apps, and enterprise software. It is thus considered a powerful programming language and features in every developer’s cache of tools. Although first released in 2002, when it was introduced with .NET Framework 1.0, the C# language has evolved a great deal since then. The most recent version is C# 8.0, available in preview as part of Visual Studio. To get access to all of the new language features, you would need to install the latest preview version of .NET Core 3.0. C# is used for: Mobile applications Desktop applications Web applications Web services Web sites Games VR Database applications And much, much more! Why Use C#? It is one of the most popular programming language in the world It is easy to learn and simple to use It has a huge community support C# is an object oriented language which gives a clear structure to programs and allows code to be reused, lowering development costs. As C# is close to C, C++ and Java, it makes it easy for programmers to switch to C# or vice versa. The C# Environment You need the .NET Framework and an IDE (integrated development environment) to work with the C# language. The .NET Framework The .NET Framework platform of the Windows OS is required to write web and desktop-based applications using not only C# but also Visual Basic and Jscript, as the platform provides language interoperability. Besides, the .Net Framework allows C# to communicate with any of the other common languages, such as C++, Jscript, COBOL, and so on. IDEs Microsoft provides various IDEs for C# programming: Visual Studio 2010 (VS) Visual Studio Express Visual Web Developer Visual Studio Code (VSC) The C# source code files can be written using a basic text editor, like Notepad, and compiled using the command-line compiler of the .NET Framework. Alternative open-source versions of the .Net Framework can work on other operating systems as well. For instance, the Mono has a C# compiler and runs on several operating systems, including Linux, Mac, Android, BSD, iOS, Windows, Solaris, and UNIX. This brings enhanced development tools to the developer. As C# is part of the .Net Framework platform, it has access to its enormous library of codes and components, such as Common Language Runtime (CLR), the .Net Framework Class Library, Common Language Specification, Common Type System, Metadata and Assemblies, Windows Forms, ASP.Net and ASP.Net AJAX, Windows Workflow Foundation (WF), Windows Communication Foundation (WCF), and LINQ. C# and Java C# and Java are high-level programming languages that share several similarities (as well as many differences). They are both object-oriented languages much influenced by C++. But while C# is suitable for application development in the Microsoft ecosystem from the front, Java is considered best for client-side web applications. Also, while C# has many tools for programming, Java has a larger arsenal of tools to choose from in IDEs and Text Editors. C# is used for virtual reality projects like games, mobile, and web applications. It is built specifically for Microsoft platforms and several non-Microsoft-based operating systems, like the Mono Project that works with Linux and OS X. Java is used for creating messaging applications and developing web-based and enterprise-based applications in open-source ecosystems. Both C# and Java support arrays. However, each language uses them differently. In C#, arrays are a specialization of the system; in Java, they are a direct specialization of the object. The C# programming language executes on the CLR. The source code is interpreted into bytecode, which is further compiled by the CLR. Java runs on any platform with the assistance of JRE (Java Runtime Environment). The written source code is first compiled into bytecode and then converted into machine code to be executed on a JRE. C# and C++ Although C# and C++ are both C-based languages with similar code, there are some differences. For one, C# is considered a component-oriented programming language, while C++ is a partial object-oriented language. Also, while both languages are compiled languages, C# compiles to CLR and is interpreted by.NET, but C++ compiles to machine code. The size of binaries in C# is much larger than in C++. Other differences between the two include the following: C# gives compiler errors and warnings, but C++ doesn’t support warnings, which may cause damage to the OS. C# runs in a virtual machine for automatic memory management. C++ requires you to manage memory manually. C# can create Windows, .NET, web, desktop, and mobile applications, but not stand-alone apps. C++ can create server-side, stand-alone, and console applications as it can work directly with the hardware. C++ can be used on any platform, while C# is targeted toward Windows OS. Generally, C++ being faster than C#, the former is preferred for applications where performance is essential. Features of C# The C# programming language has many features that make it more useful and unique when compared to other languages, including: Object-oriented language Being object-oriented, C# allows the creation of modular applications and reusable codes, an advantage over C++. As an object-oriented language, C# makes development and maintenance easier when project size grows. It supports all three object-oriented features: data encapsulation, inheritance, interfaces, and polymorphism. Simplicity C# is a simple language with a structured approach to problem-solving. Unsafe operations, like direct memory manipulation, are not allowed. Speed The compilation and execution time in C# is very powerful and fast. A Modern programming language C# programming is used for building scalable and interoperable applications with support for modern features like automatic garbage collection, error handling, debugging, and robust security. It has built-in support for a web service to be invoked from any app running on any platform. Type-safe Arrays and objects are zero base indexed and bound checked. There is an automatic checking of the overflow of types. The C# type safety instances support robust programming. Interoperability Language interoperability of C# maximizes code reuse for the efficiency of the development process. C# programs can work upon almost anything as a program can call out any native API. Consistency Its unified type system enables developers to extend the type system simply and easily for consistent behavior. Updateable C# is automatically updateable. Its versioning support enables complex frameworks to be developed and evolved. Component oriented C# supports component-oriented programming through the concepts of properties, methods, events, and attributes for self-contained and self-describing components of functionality for robust and scalable applications. Structured Programming Language The structured design and modularization in C# break a problem into parts, using functions for easy implementation to solve significant problems. Rich Library C# has a standard library with many inbuilt functions for easy and fast development. Prerequisites for Learning C# Basic knowledge of C or C++ or any programming language or programming fundamentals. Additionally, the OOP concept makes for a short learning curve of C#. Advantages of C# There are many advantages to the C# language that makes it a useful programming language compared to other languages like Java, C, or C++. These include: Being an object-oriented language, C# allows you to create modular, maintainable applications and reusable codes Familiar syntax Easy to develop as it has a rich class of libraries for smooth implementation of functions Enhanced integration as an application written in .NET will integrate and interpret better when compared to other NET technologies As C# runs on CLR, it makes it easy to integrate with components written in other languages It’s safe, with no data loss as there is no type-conversion so that you can write secure codes The automatic garbage collection keeps the system clean and doesn’t hang it during execution As your machine has to install the .NET Framework to run C#, it supports cross-platform Strong memory backup prevents memory leakage Programming support of the Microsoft ecosystem makes development easy and seamless Low maintenance cost, as C# can develop iOS, Android, and Windows Phone native apps The syntax is similar to C, C++, and Java, which makes it easier to learn and work with C# Useful as it can develop iOS, Android, and Windows Phone native apps with the Xamarin Framework C# is the most powerful programming language for the .NET Framework Fast development as C# is open source steered by Microsoft with access to open source projects and tools on Github, and many active communities contributing to the improvement What Can C Sharp Do for You? C# can be used to develop a wide range of: Windows client applications Windows libraries and components Windows services Web applications Native iOS and Android mobile apps Azure cloud applications and services Gaming consoles and gaming systems Video and virtual reality games Interoperability software like SharePoint Enterprise software Backend services and database programs AI and ML applications Distributed applications Hardware-level programming Virus and malware software GUI-based applications IoT devices Blockchain and distributed ledger technology C# Programming for Beginners: Introduction, Features and Applications By Simplilearn Last updated on Jan 20, 2020674 C# Programming for Beginners As a programmer, you’re motivated to master the most popular languages that will give you an edge in your career. There’s a vast number of programming languages that you can learn, but how do you know which is the most useful? If you know C and C++, do you need to learn C# as well? How similar is C# to Java? Does it become more comfortable for you to learn C# if you already know Java? Every developer and wannabe programmer asks these types of questions. So let us explore C# programming: how it evolved as an extension of C and why you need to learn it as a part of the Master’s Program in integrated DevOps for server-side execution. Are you a web developer or someone interested to build a website? Enroll for the Javascript Certification Training. Check out the course preview now! What is C#? C# is a modern object-oriented programming language developed in 2000 by Anders Hejlsberg, the principal designer and lead architect at Microsoft. It is pronounced as "C-Sharp," inspired by the musical notation “♯” which stands for a note with a slightly higher pitch. As it’s considered an incremental compilation of the C++ language, the name C “sharp” seemed most appropriate. The sharp symbol, however, has been replaced by the keyboard friendly “#” as a suffix to “C” for purposes of programming. Although the code is very similar to C++, C# is newer and has grown fast with extensive support from Microsoft. The fact that it’s so similar to Java syntactically helps explain why it has emerged as one of the most popular programming languages today. An Introduction to C# Programming C# is a general-purpose, object-oriented programming language that is structured and easy to learn. It runs on Microsoft’s .Net Framework and can be compiled on a variety of computer platforms. As the syntax is simple and easy to learn, developers familiar with C, C++, or Java have found a comfort zone within C#. C# is a boon for developers who want to build a wide range of applications on the .NET Framework—Windows applications, Web applications, and Web services—in addition to building mobile apps, Windows Store apps, and enterprise software. It is thus considered a powerful programming language and features in every developer’s cache of tools. Although first released in 2002, when it was introduced with .NET Framework 1.0, the C# language has evolved a great deal since then. The most recent version is C# 8.0, available in preview as part of Visual Studio. To get access to all of the new language features, you would need to install the latest preview version of .NET Core 3.0. The C# Environment You need the .NET Framework and an IDE (integrated development environment) to work with the C# language. The .NET Framework The .NET Framework platform of the Windows OS is required to write web and desktop-based applications using not only C# but also Visual Basic and Jscript, as the platform provides language interoperability. Besides, the .Net Framework allows C# to communicate with any of the other common languages, such as C++, Jscript, COBOL, and so on. IDEs Microsoft provides various IDEs for C# programming: Visual Studio 2010 (VS) Visual Studio Express Visual Web Developer Visual Studio Code (VSC) The C# source code files can be written using a basic text editor, like Notepad, and compiled using the command-line compiler of the .NET Framework. Alternative open-source versions of the .Net Framework can work on other operating systems as well. For instance, the Mono has a C# compiler and runs on several operating systems, including Linux, Mac, Android, BSD, iOS, Windows, Solaris, and UNIX. This brings enhanced development tools to the developer. As C# is part of the .Net Framework platform, it has access to its enormous library of codes and components, such as Common Language Runtime (CLR), the .Net Framework Class Library, Common Language Specification, Common Type System, Metadata and Assemblies, Windows Forms, ASP.Net and ASP.Net AJAX, Windows Workflow Foundation (WF), Windows Communication Foundation (WCF), and LINQ. C# and Java C# and Java are high-level programming languages that share several similarities (as well as many differences). They are both object-oriented languages much influenced by C++. But while C# is suitable for application development in the Microsoft ecosystem from the front, Java is considered best for client-side web applications. Also, while C# has many tools for programming, Java has a larger arsenal of tools to choose from in IDEs and Text Editors. C# is used for virtual reality projects like games, mobile, and web applications. It is built specifically for Microsoft platforms and several non-Microsoft-based operating systems, like the Mono Project that works with Linux and OS X. Java is used for creating messaging applications and developing web-based and enterprise-based applications in open-source ecosystems. Both C# and Java support arrays. However, each language uses them differently. In C#, arrays are a specialization of the system; in Java, they are a direct specialization of the object. The C# programming language executes on the CLR. The source code is interpreted into bytecode, which is further compiled by the CLR. Java runs on any platform with the assistance of JRE (Java Runtime Environment). The written source code is first compiled into bytecode and then converted into machine code to be executed on a JRE. C# and C++ Although C# and C++ are both C-based languages with similar code, there are some differences. For one, C# is considered a component-oriented programming language, while C++ is a partial object-oriented language. Also, while both languages are compiled languages, C# compiles to CLR and is interpreted by.NET, but C++ compiles to machine code. The size of binaries in C# is much larger than in C++. Other differences between the two include the following: C# gives compiler errors and warnings, but C++ doesn’t support warnings, which may cause damage to the OS. C# runs in a virtual machine for automatic memory management. C++ requires you to manage memory manually. C# can create Windows, .NET, web, desktop, and mobile applications, but not stand-alone apps. C++ can create server-side, stand-alone, and console applications as it can work directly with the hardware. C++ can be used on any platform, while C# is targeted toward Windows OS. Generally, C++ being faster than C#, the former is preferred for applications where performance is essential. Features of C# The C# programming language has many features that make it more useful and unique when compared to other languages, including: Object-oriented language Being object-oriented, C# allows the creation of modular applications and reusable codes, an advantage over C++. As an object-oriented language, C# makes development and maintenance easier when project size grows. It supports all three object-oriented features: data encapsulation, inheritance, interfaces, and polymorphism. Simplicity C# is a simple language with a structured approach to problem-solving. Unsafe operations, like direct memory manipulation, are not allowed. Speed The compilation and execution time in C# is very powerful and fast. A Modern programming language C# programming is used for building scalable and interoperable applications with support for modern features like automatic garbage collection, error handling, debugging, and robust security. It has built-in support for a web service to be invoked from any app running on any platform. Type-safe Arrays and objects are zero base indexed and bound checked. There is an automatic checking of the overflow of types. The C# type safety instances support robust programming. Interoperability Language interoperability of C# maximizes code reuse for the efficiency of the development process. C# programs can work upon almost anything as a program can call out any native API. Consistency Its unified type system enables developers to extend the type system simply and easily for consistent behavior. Updateable C# is automatically updateable. Its versioning support enables complex frameworks to be developed and evolved. Component oriented C# supports component-oriented programming through the concepts of properties, methods, events, and attributes for self-contained and self-describing components of functionality for robust and scalable applications. Structured Programming Language The structured design and modularization in C# break a problem into parts, using functions for easy implementation to solve significant problems. Rich Library C# has a standard library with many inbuilt functions for easy and fast development. Full Stack Java Developer Course The Gateway to Master Web DevelopmentEXPLORE COURSEFull Stack Java Developer Course Prerequisites for Learning C# Basic knowledge of C or C++ or any programming language or programming fundamentals. Additionally, the OOP concept makes for a short learning curve of C#. Advantages of C# There are many advantages to the C# language that makes it a useful programming language compared to other languages like Java, C, or C++. These include: Being an object-oriented language, C# allows you to create modular, maintainable applications and reusable codes Familiar syntax Easy to develop as it has a rich class of libraries for smooth implementation of functions Enhanced integration as an application written in .NET will integrate and interpret better when compared to other NET technologies As C# runs on CLR, it makes it easy to integrate with components written in other languages It’s safe, with no data loss as there is no type-conversion so that you can write secure codes The automatic garbage collection keeps the system clean and doesn’t hang it during execution As your machine has to install the .NET Framework to run C#, it supports cross-platform Strong memory backup prevents memory leakage Programming support of the Microsoft ecosystem makes development easy and seamless Low maintenance cost, as C# can develop iOS, Android, and Windows Phone native apps The syntax is similar to C, C++, and Java, which makes it easier to learn and work with C# Useful as it can develop iOS, Android, and Windows Phone native apps with the Xamarin Framework C# is the most powerful programming language for the .NET Framework Fast development as C# is open source steered by Microsoft with access to open source projects and tools on Github, and many active communities contributing to the improvement What Can C Sharp Do for You? C# can be used to develop a wide range of: Windows client applications Windows libraries and components Windows services Web applications Native iOS and Android mobile apps Azure cloud applications and services Gaming consoles and gaming systems Video and virtual reality games Interoperability software like SharePoint Enterprise software Backend services and database programs AI and ML applications Distributed applications Hardware-level programming Virus and malware software GUI-based applications IoT devices Blockchain and distributed ledger technology Who Should Learn the C# Programming Language and Why? C# is one of the most popular programming languages as it can be used for a variety of applications: mobile apps, game development, and enterprise software. What’s more, the C# 8.0 version is packed with several new features and enhancements to the C# language that can change the way developers write their C# code. The most important new features available are ‘null reference types,’ enhanced ‘pattern matching,’ and ‘async streams’ that help you to write more reliable and readable code. As you’re exposed to the fundamental programming concepts of C# in this course, you can work on projects that open the doors for you as a Full Stack Java Developer. So, upskill and master the C# language for a faster career trajectory and salary scope.
Wakals / GASCOLOfficial implementary of HCoG: Apply Hierarchical-Chain-of-Generation to Complex Attributes Text-to-3D Generation [CVPR 2025]
radrumond / TimehetnetLearning complex time series forecasting models usually requires a large amount of data, as each model is trained from scratch for each task/data set. Leveraging learning experience with similar datasets is a well-established technique for classification problems called few-shot classification. However, existing approaches cannot be applied to time-series forecasting because i) multivariate time-series datasets have different channels and ii) forecasting is principally different from classification. In this paper we formalize the problem of few-shot forecasting of time-series with heterogeneous channels for the first time. Extending recent work on heterogeneous attributes in vector data, we develop a model composed of permutation-invariant deep set-blocks which incorporate a temporal embedding. We assemble the first meta-dataset of 40 multivariate time-series datasets and show through experiments that our model provides a good generalization, outperforming baselines carried over from simpler scenarios that either fail to learn across tasks or miss temporal information.
brejoc / Django IntercoolerjsDjango wrapper for intercooler.js - AJAX With Attributes: There is no need to be complex.
byerlikaya / SmartWhere🚀 SmartWhere - Intelligent .NET filtering library that transforms complex filtering logic into simple, declarative code using attributes and interfaces. Perfect for Entity Framework and IQueryable<T> collections.
ZavenArra / LatticeLattice is a graph database CMS system for building Kohana websites with simple to complex content graphs, allowing for a wide variety dynamic associations between objects without the need for building out a complex database structure behind the scenes. Lattice allows you to specify your content graph in a configuration file, edit the content trees and attributes via the cms, and provide this data to the view layer without intervention at the database level.
francnuec / Neo4jClient.DataAnnotationsUse POCO classes in the Neo4jClient library ORM style. Annotate with System.ComponentModel.DataAnnotations.Schema attributes. Supports Complex Types too.
sirisacademic / AffilgoodAffilGood provides annotated datasets and tools to improve the accuracy of attributing scientific works to research organizations, especially in multilingual and complex contexts.
SpongeBed81 / Attribute AnalyzerParse complex attributes on the server with ease
Aryia-Behroziuan / NumpyQuickstart tutorial Prerequisites Before reading this tutorial you should know a bit of Python. If you would like to refresh your memory, take a look at the Python tutorial. If you wish to work the examples in this tutorial, you must also have some software installed on your computer. Please see https://scipy.org/install.html for instructions. Learner profile This tutorial is intended as a quick overview of algebra and arrays in NumPy and want to understand how n-dimensional (n>=2) arrays are represented and can be manipulated. In particular, if you don’t know how to apply common functions to n-dimensional arrays (without using for-loops), or if you want to understand axis and shape properties for n-dimensional arrays, this tutorial might be of help. Learning Objectives After this tutorial, you should be able to: Understand the difference between one-, two- and n-dimensional arrays in NumPy; Understand how to apply some linear algebra operations to n-dimensional arrays without using for-loops; Understand axis and shape properties for n-dimensional arrays. The Basics NumPy’s main object is the homogeneous multidimensional array. It is a table of elements (usually numbers), all of the same type, indexed by a tuple of non-negative integers. In NumPy dimensions are called axes. For example, 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. In the example pictured below, the array has 2 axes. The first axis has a length of 2, the second axis has a length of 3. [[ 1., 0., 0.], [ 0., 1., 2.]] NumPy’s array class is called ndarray. It is also known by the alias array. Note that numpy.array is not the same as the Standard Python Library class array.array, which only handles one-dimensional arrays and offers less functionality. The more important attributes of an ndarray object are: ndarray.ndim the number of axes (dimensions) of the array. ndarray.shape the dimensions of the array. This is a tuple of integers indicating the size of the array in each dimension. For a matrix with n rows and m columns, shape will be (n,m). The length of the shape tuple is therefore the number of axes, ndim. ndarray.size the total number of elements of the array. This is equal to the product of the elements of shape. ndarray.dtype an object describing the type of the elements in the array. One can create or specify dtype’s using standard Python types. Additionally NumPy provides types of its own. numpy.int32, numpy.int16, and numpy.float64 are some examples. ndarray.itemsize the size in bytes of each element of the array. For example, an array of elements of type float64 has itemsize 8 (=64/8), while one of type complex32 has itemsize 4 (=32/8). It is equivalent to ndarray.dtype.itemsize. ndarray.data the buffer containing the actual elements of the array. Normally, we won’t need to use this attribute because we will access the elements in an array using indexing facilities. An example >>> import numpy as np a = np.arange(15).reshape(3, 5) a array([[ 0, 1, 2, 3, 4], [ 5, 6, 7, 8, 9], [10, 11, 12, 13, 14]]) a.shape (3, 5) a.ndim 2 a.dtype.name 'int64' a.itemsize 8 a.size 15 type(a) <class 'numpy.ndarray'> b = np.array([6, 7, 8]) b array([6, 7, 8]) type(b) <class 'numpy.ndarray'> Array Creation There are several ways to create arrays. For example, you can create an array from a regular Python list or tuple using the array function. The type of the resulting array is deduced from the type of the elements in the sequences. >>> >>> import numpy as np >>> a = np.array([2,3,4]) >>> a array([2, 3, 4]) >>> a.dtype dtype('int64') >>> b = np.array([1.2, 3.5, 5.1]) >>> b.dtype dtype('float64') A frequent error consists in calling array with multiple arguments, rather than providing a single sequence as an argument. >>> >>> a = np.array(1,2,3,4) # WRONG Traceback (most recent call last): ... TypeError: array() takes from 1 to 2 positional arguments but 4 were given >>> a = np.array([1,2,3,4]) # RIGHT array transforms sequences of sequences into two-dimensional arrays, sequences of sequences of sequences into three-dimensional arrays, and so on. >>> >>> b = np.array([(1.5,2,3), (4,5,6)]) >>> b array([[1.5, 2. , 3. ], [4. , 5. , 6. ]]) The type of the array can also be explicitly specified at creation time: >>> >>> c = np.array( [ [1,2], [3,4] ], dtype=complex ) >>> c array([[1.+0.j, 2.+0.j], [3.+0.j, 4.+0.j]]) Often, the elements of an array are originally unknown, but its size is known. Hence, NumPy offers several functions to create arrays with initial placeholder content. These minimize the necessity of growing arrays, an expensive operation. The function zeros creates an array full of zeros, the function ones creates an array full of ones, and the function empty creates an array whose initial content is random and depends on the state of the memory. By default, the dtype of the created array is float64. >>> >>> np.zeros((3, 4)) array([[0., 0., 0., 0.], [0., 0., 0., 0.], [0., 0., 0., 0.]]) >>> np.ones( (2,3,4), dtype=np.int16 ) # dtype can also be specified 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]]], dtype=int16) >>> np.empty( (2,3) ) # uninitialized array([[ 3.73603959e-262, 6.02658058e-154, 6.55490914e-260], # may vary [ 5.30498948e-313, 3.14673309e-307, 1.00000000e+000]]) To create sequences of numbers, NumPy provides the arange function which is analogous to the Python built-in range, but returns an array. >>> >>> np.arange( 10, 30, 5 ) array([10, 15, 20, 25]) >>> np.arange( 0, 2, 0.3 ) # it accepts float arguments array([0. , 0.3, 0.6, 0.9, 1.2, 1.5, 1.8]) When arange is used with floating point arguments, it is generally not possible to predict the number of elements obtained, due to the finite floating point precision. For this reason, it is usually better to use the function linspace that receives as an argument the number of elements that we want, instead of the step: >>> >>> from numpy import pi >>> np.linspace( 0, 2, 9 ) # 9 numbers from 0 to 2 array([0. , 0.25, 0.5 , 0.75, 1. , 1.25, 1.5 , 1.75, 2. ]) >>> x = np.linspace( 0, 2*pi, 100 ) # useful to evaluate function at lots of points >>> f = np.sin(x) See also array, zeros, zeros_like, ones, ones_like, empty, empty_like, arange, linspace, numpy.random.Generator.rand, numpy.random.Generator.randn, fromfunction, fromfile Printing Arrays When you print an array, NumPy displays it in a similar way to nested lists, but with the following layout: the last axis is printed from left to right, the second-to-last is printed from top to bottom, the rest are also printed from top to bottom, with each slice separated from the next by an empty line. One-dimensional arrays are then printed as rows, bidimensionals as matrices and tridimensionals as lists of matrices. >>> >>> a = np.arange(6) # 1d array >>> print(a) [0 1 2 3 4 5] >>> >>> b = np.arange(12).reshape(4,3) # 2d array >>> print(b) [[ 0 1 2] [ 3 4 5] [ 6 7 8] [ 9 10 11]] >>> >>> c = np.arange(24).reshape(2,3,4) # 3d array >>> print(c) [[[ 0 1 2 3] [ 4 5 6 7] [ 8 9 10 11]] [[12 13 14 15] [16 17 18 19] [20 21 22 23]]] See below to get more details on reshape. If an array is too large to be printed, NumPy automatically skips the central part of the array and only prints the corners: >>> >>> print(np.arange(10000)) [ 0 1 2 ... 9997 9998 9999] >>> >>> print(np.arange(10000).reshape(100,100)) [[ 0 1 2 ... 97 98 99] [ 100 101 102 ... 197 198 199] [ 200 201 202 ... 297 298 299] ... [9700 9701 9702 ... 9797 9798 9799] [9800 9801 9802 ... 9897 9898 9899] [9900 9901 9902 ... 9997 9998 9999]] To disable this behaviour and force NumPy to print the entire array, you can change the printing options using set_printoptions. >>> >>> np.set_printoptions(threshold=sys.maxsize) # sys module should be imported Basic Operations Arithmetic operators on arrays apply elementwise. A new array is created and filled with the result. >>> >>> a = np.array( [20,30,40,50] ) >>> b = np.arange( 4 ) >>> b array([0, 1, 2, 3]) >>> c = a-b >>> c array([20, 29, 38, 47]) >>> b**2 array([0, 1, 4, 9]) >>> 10*np.sin(a) array([ 9.12945251, -9.88031624, 7.4511316 , -2.62374854]) >>> a<35 array([ True, True, False, False]) Unlike in many matrix languages, the product operator * operates elementwise in NumPy arrays. The matrix product can be performed using the @ operator (in python >=3.5) or the dot function or method: >>> >>> A = np.array( [[1,1], ... [0,1]] ) >>> B = np.array( [[2,0], ... [3,4]] ) >>> A * B # elementwise product array([[2, 0], [0, 4]]) >>> A @ B # matrix product array([[5, 4], [3, 4]]) >>> A.dot(B) # another matrix product array([[5, 4], [3, 4]]) Some operations, such as += and *=, act in place to modify an existing array rather than create a new one. >>> >>> rg = np.random.default_rng(1) # create instance of default random number generator >>> a = np.ones((2,3), dtype=int) >>> b = rg.random((2,3)) >>> a *= 3 >>> a array([[3, 3, 3], [3, 3, 3]]) >>> b += a >>> b array([[3.51182162, 3.9504637 , 3.14415961], [3.94864945, 3.31183145, 3.42332645]]) >>> a += b # b is not automatically converted to integer type Traceback (most recent call last): ... numpy.core._exceptions.UFuncTypeError: Cannot cast ufunc 'add' output from dtype('float64') to dtype('int64') with casting rule 'same_kind' When operating with arrays of different types, the type of the resulting array corresponds to the more general or precise one (a behavior known as upcasting). >>> >>> a = np.ones(3, dtype=np.int32) >>> b = np.linspace(0,pi,3) >>> b.dtype.name 'float64' >>> c = a+b >>> c array([1. , 2.57079633, 4.14159265]) >>> c.dtype.name 'float64' >>> d = np.exp(c*1j) >>> d array([ 0.54030231+0.84147098j, -0.84147098+0.54030231j, -0.54030231-0.84147098j]) >>> d.dtype.name 'complex128' Many unary operations, such as computing the sum of all the elements in the array, are implemented as methods of the ndarray class. >>> >>> a = rg.random((2,3)) >>> a array([[0.82770259, 0.40919914, 0.54959369], [0.02755911, 0.75351311, 0.53814331]]) >>> a.sum() 3.1057109529998157 >>> a.min() 0.027559113243068367 >>> a.max() 0.8277025938204418 By default, these operations apply to the array as though it were a list of numbers, regardless of its shape. However, by specifying the axis parameter you can apply an operation along the specified axis of an array: >>> >>> b = np.arange(12).reshape(3,4) >>> b array([[ 0, 1, 2, 3], [ 4, 5, 6, 7], [ 8, 9, 10, 11]]) >>> >>> b.sum(axis=0) # sum of each column array([12, 15, 18, 21]) >>> >>> b.min(axis=1) # min of each row array([0, 4, 8]) >>> >>> b.cumsum(axis=1) # cumulative sum along each row array([[ 0, 1, 3, 6], [ 4, 9, 15, 22], [ 8, 17, 27, 38]]) Universal Functions NumPy provides familiar mathematical functions such as sin, cos, and exp. In NumPy, these are called “universal functions”(ufunc). Within NumPy, these functions operate elementwise on an array, producing an array as output. >>> >>> B = np.arange(3) >>> B array([0, 1, 2]) >>> np.exp(B) array([1. , 2.71828183, 7.3890561 ]) >>> np.sqrt(B) array([0. , 1. , 1.41421356]) >>> C = np.array([2., -1., 4.]) >>> np.add(B, C) array([2., 0., 6.]) See also all, any, apply_along_axis, argmax, argmin, argsort, average, bincount, ceil, clip, conj, corrcoef, cov, cross, cumprod, cumsum, diff, dot, floor, inner, invert, lexsort, max, maximum, mean, median, min, minimum, nonzero, outer, prod, re, round, sort, std, sum, trace, transpose, var, vdot, vectorize, where Indexing, Slicing and Iterating One-dimensional arrays can be indexed, sliced and iterated over, much like lists and other Python sequences. >>> >>> a = np.arange(10)**3 >>> a array([ 0, 1, 8, 27, 64, 125, 216, 343, 512, 729]) >>> a[2] 8 >>> a[2:5] array([ 8, 27, 64]) # equivalent to a[0:6:2] = 1000; # from start to position 6, exclusive, set every 2nd element to 1000 >>> a[:6:2] = 1000 >>> a array([1000, 1, 1000, 27, 1000, 125, 216, 343, 512, 729]) >>> a[ : :-1] # reversed a array([ 729, 512, 343, 216, 125, 1000, 27, 1000, 1, 1000]) >>> for i in a: ... print(i**(1/3.)) ... 9.999999999999998 1.0 9.999999999999998 3.0 9.999999999999998 4.999999999999999 5.999999999999999 6.999999999999999 7.999999999999999 8.999999999999998 Multidimensional arrays can have one index per axis. These indices are given in a tuple separated by commas: >>> >>> def f(x,y): ... return 10*x+y ... >>> b = np.fromfunction(f,(5,4),dtype=int) >>> b array([[ 0, 1, 2, 3], [10, 11, 12, 13], [20, 21, 22, 23], [30, 31, 32, 33], [40, 41, 42, 43]]) >>> b[2,3] 23 >>> b[0:5, 1] # each row in the second column of b array([ 1, 11, 21, 31, 41]) >>> b[ : ,1] # equivalent to the previous example array([ 1, 11, 21, 31, 41]) >>> b[1:3, : ] # each column in the second and third row of b array([[10, 11, 12, 13], [20, 21, 22, 23]]) When fewer indices are provided than the number of axes, the missing indices are considered complete slices: >>> >>> b[-1] # the last row. Equivalent to b[-1,:] array([40, 41, 42, 43]) The expression within brackets in b[i] is treated as an i followed by as many instances of : as needed to represent the remaining axes. NumPy also allows you to write this using dots as b[i,...]. The dots (...) represent as many colons as needed to produce a complete indexing tuple. For example, if x is an array with 5 axes, then x[1,2,...] is equivalent to x[1,2,:,:,:], x[...,3] to x[:,:,:,:,3] and x[4,...,5,:] to x[4,:,:,5,:]. >>> >>> c = np.array( [[[ 0, 1, 2], # a 3D array (two stacked 2D arrays) ... [ 10, 12, 13]], ... [[100,101,102], ... [110,112,113]]]) >>> c.shape (2, 2, 3) >>> c[1,...] # same as c[1,:,:] or c[1] array([[100, 101, 102], [110, 112, 113]]) >>> c[...,2] # same as c[:,:,2] array([[ 2, 13], [102, 113]]) Iterating over multidimensional arrays is done with respect to the first axis: >>> >>> for row in b: ... print(row) ... [0 1 2 3] [10 11 12 13] [20 21 22 23] [30 31 32 33] [40 41 42 43] However, if one wants to perform an operation on each element in the array, one can use the flat attribute which is an iterator over all the elements of the array: >>> >>> for element in b.flat: ... print(element) ... 0 1 2 3 10 11 12 13 20 21 22 23 30 31 32 33 40 41 42 43 See also Indexing, Indexing (reference), newaxis, ndenumerate, indices Shape Manipulation Changing the shape of an array An array has a shape given by the number of elements along each axis: >>> >>> a = np.floor(10*rg.random((3,4))) >>> a array([[3., 7., 3., 4.], [1., 4., 2., 2.], [7., 2., 4., 9.]]) >>> a.shape (3, 4) The shape of an array can be changed with various commands. Note that the following three commands all return a modified array, but do not change the original array: >>> >>> a.ravel() # returns the array, flattened array([3., 7., 3., 4., 1., 4., 2., 2., 7., 2., 4., 9.]) >>> a.reshape(6,2) # returns the array with a modified shape array([[3., 7.], [3., 4.], [1., 4.], [2., 2.], [7., 2.], [4., 9.]]) >>> a.T # returns the array, transposed array([[3., 1., 7.], [7., 4., 2.], [3., 2., 4.], [4., 2., 9.]]) >>> a.T.shape (4, 3) >>> a.shape (3, 4) The order of the elements in the array resulting from ravel() is normally “C-style”, that is, the rightmost index “changes the fastest”, so the element after a[0,0] is a[0,1]. If the array is reshaped to some other shape, again the array is treated as “C-style”. NumPy normally creates arrays stored in this order, so ravel() will usually not need to copy its argument, but if the array was made by taking slices of another array or created with unusual options, it may need to be copied. The functions ravel() and reshape() can also be instructed, using an optional argument, to use FORTRAN-style arrays, in which the leftmost index changes the fastest. The reshape function returns its argument with a modified shape, whereas the ndarray.resize method modifies the array itself: >>> >>> a array([[3., 7., 3., 4.], [1., 4., 2., 2.], [7., 2., 4., 9.]]) >>> a.resize((2,6)) >>> a array([[3., 7., 3., 4., 1., 4.], [2., 2., 7., 2., 4., 9.]]) If a dimension is given as -1 in a reshaping operation, the other dimensions are automatically calculated: >>> >>> a.reshape(3,-1) array([[3., 7., 3., 4.], [1., 4., 2., 2.], [7., 2., 4., 9.]]) See also ndarray.shape, reshape, resize, ravel Stacking together different arrays Several arrays can be stacked together along different axes: >>> >>> a = np.floor(10*rg.random((2,2))) >>> a array([[9., 7.], [5., 2.]]) >>> b = np.floor(10*rg.random((2,2))) >>> b array([[1., 9.], [5., 1.]]) >>> np.vstack((a,b)) array([[9., 7.], [5., 2.], [1., 9.], [5., 1.]]) >>> np.hstack((a,b)) array([[9., 7., 1., 9.], [5., 2., 5., 1.]]) The function column_stack stacks 1D arrays as columns into a 2D array. It is equivalent to hstack only for 2D arrays: >>> >>> from numpy import newaxis >>> np.column_stack((a,b)) # with 2D arrays array([[9., 7., 1., 9.], [5., 2., 5., 1.]]) >>> a = np.array([4.,2.]) >>> b = np.array([3.,8.]) >>> np.column_stack((a,b)) # returns a 2D array array([[4., 3.], [2., 8.]]) >>> np.hstack((a,b)) # the result is different array([4., 2., 3., 8.]) >>> a[:,newaxis] # view `a` as a 2D column vector array([[4.], [2.]]) >>> np.column_stack((a[:,newaxis],b[:,newaxis])) array([[4., 3.], [2., 8.]]) >>> np.hstack((a[:,newaxis],b[:,newaxis])) # the result is the same array([[4., 3.], [2., 8.]]) On the other hand, the function row_stack is equivalent to vstack for any input arrays. In fact, row_stack is an alias for vstack: >>> >>> np.column_stack is np.hstack False >>> np.row_stack is np.vstack True In general, for arrays with more than two dimensions, hstack stacks along their second axes, vstack stacks along their first axes, and concatenate allows for an optional arguments giving the number of the axis along which the concatenation should happen. Note In complex cases, r_ and c_ are useful for creating arrays by stacking numbers along one axis. They allow the use of range literals (“:”) >>> >>> np.r_[1:4,0,4] array([1, 2, 3, 0, 4]) When used with arrays as arguments, r_ and c_ are similar to vstack and hstack in their default behavior, but allow for an optional argument giving the number of the axis along which to concatenate. See also hstack, vstack, column_stack, concatenate, c_, r_ Splitting one array into several smaller ones Using hsplit, you can split an array along its horizontal axis, either by specifying the number of equally shaped arrays to return, or by specifying the columns after which the division should occur: >>> >>> a = np.floor(10*rg.random((2,12))) >>> a array([[6., 7., 6., 9., 0., 5., 4., 0., 6., 8., 5., 2.], [8., 5., 5., 7., 1., 8., 6., 7., 1., 8., 1., 0.]]) # Split a into 3 >>> np.hsplit(a,3) [array([[6., 7., 6., 9.], [8., 5., 5., 7.]]), array([[0., 5., 4., 0.], [1., 8., 6., 7.]]), array([[6., 8., 5., 2.], [1., 8., 1., 0.]])] # Split a after the third and the fourth column >>> np.hsplit(a,(3,4)) [array([[6., 7., 6.], [8., 5., 5.]]), array([[9.], [7.]]), array([[0., 5., 4., 0., 6., 8., 5., 2.], [1., 8., 6., 7., 1., 8., 1., 0.]])] vsplit splits along the vertical axis, and array_split allows one to specify along which axis to split. Copies and Views When operating and manipulating arrays, their data is sometimes copied into a new array and sometimes not. This is often a source of confusion for beginners. There are three cases: No Copy at All Simple assignments make no copy of objects or their data. >>> >>> a = np.array([[ 0, 1, 2, 3], ... [ 4, 5, 6, 7], ... [ 8, 9, 10, 11]]) >>> b = a # no new object is created >>> b is a # a and b are two names for the same ndarray object True Python passes mutable objects as references, so function calls make no copy. >>> >>> def f(x): ... print(id(x)) ... >>> id(a) # id is a unique identifier of an object 148293216 # may vary >>> f(a) 148293216 # may vary View or Shallow Copy Different array objects can share the same data. The view method creates a new array object that looks at the same data. >>> >>> c = a.view() >>> c is a False >>> c.base is a # c is a view of the data owned by a True >>> c.flags.owndata False >>> >>> c = c.reshape((2, 6)) # a's shape doesn't change >>> a.shape (3, 4) >>> c[0, 4] = 1234 # a's data changes >>> a array([[ 0, 1, 2, 3], [1234, 5, 6, 7], [ 8, 9, 10, 11]]) Slicing an array returns a view of it: >>> >>> s = a[ : , 1:3] # spaces added for clarity; could also be written "s = a[:, 1:3]" >>> s[:] = 10 # s[:] is a view of s. Note the difference between s = 10 and s[:] = 10 >>> a array([[ 0, 10, 10, 3], [1234, 10, 10, 7], [ 8, 10, 10, 11]]) Deep Copy The copy method makes a complete copy of the array and its data. >>> >>> d = a.copy() # a new array object with new data is created >>> d is a False >>> d.base is a # d doesn't share anything with a False >>> d[0,0] = 9999 >>> a array([[ 0, 10, 10, 3], [1234, 10, 10, 7], [ 8, 10, 10, 11]]) Sometimes copy should be called after slicing if the original array is not required anymore. For example, suppose a is a huge intermediate result and the final result b only contains a small fraction of a, a deep copy should be made when constructing b with slicing: >>> >>> a = np.arange(int(1e8)) >>> b = a[:100].copy() >>> del a # the memory of ``a`` can be released. If b = a[:100] is used instead, a is referenced by b and will persist in memory even if del a is executed. Functions and Methods Overview Here is a list of some useful NumPy functions and methods names ordered in categories. See Routines for the full list. Array Creation arange, array, copy, empty, empty_like, eye, fromfile, fromfunction, identity, linspace, logspace, mgrid, ogrid, ones, ones_like, r_, zeros, zeros_like Conversions ndarray.astype, atleast_1d, atleast_2d, atleast_3d, mat Manipulations array_split, column_stack, concatenate, diagonal, dsplit, dstack, hsplit, hstack, ndarray.item, newaxis, ravel, repeat, reshape, resize, squeeze, swapaxes, take, transpose, vsplit, vstack Questions all, any, nonzero, where Ordering argmax, argmin, argsort, max, min, ptp, searchsorted, sort Operations choose, compress, cumprod, cumsum, inner, ndarray.fill, imag, prod, put, putmask, real, sum Basic Statistics cov, mean, std, var Basic Linear Algebra cross, dot, outer, linalg.svd, vdot Less Basic Broadcasting rules Broadcasting allows universal functions to deal in a meaningful way with inputs that do not have exactly the same shape. The first rule of broadcasting is that if all input arrays do not have the same number of dimensions, a “1” will be repeatedly prepended to the shapes of the smaller arrays until all the arrays have the same number of dimensions. The second rule of broadcasting ensures that arrays with a size of 1 along a particular dimension act as if they had the size of the array with the largest shape along that dimension. The value of the array element is assumed to be the same along that dimension for the “broadcast” array. After application of the broadcasting rules, the sizes of all arrays must match. More details can be found in Broadcasting. Advanced indexing and index tricks NumPy offers more indexing facilities than regular Python sequences. In addition to indexing by integers and slices, as we saw before, arrays can be indexed by arrays of integers and arrays of booleans. Indexing with Arrays of Indices >>> >>> a = np.arange(12)**2 # the first 12 square numbers >>> i = np.array([1, 1, 3, 8, 5]) # an array of indices >>> a[i] # the elements of a at the positions i array([ 1, 1, 9, 64, 25]) >>> >>> j = np.array([[3, 4], [9, 7]]) # a bidimensional array of indices >>> a[j] # the same shape as j array([[ 9, 16], [81, 49]]) When the indexed array a is multidimensional, a single array of indices refers to the first dimension of a. The following example shows this behavior by converting an image of labels into a color image using a palette. >>> >>> palette = np.array([[0, 0, 0], # black ... [255, 0, 0], # red ... [0, 255, 0], # green ... [0, 0, 255], # blue ... [255, 255, 255]]) # white >>> image = np.array([[0, 1, 2, 0], # each value corresponds to a color in the palette ... [0, 3, 4, 0]]) >>> palette[image] # the (2, 4, 3) color image array([[[ 0, 0, 0], [255, 0, 0], [ 0, 255, 0], [ 0, 0, 0]], [[ 0, 0, 0], [ 0, 0, 255], [255, 255, 255], [ 0, 0, 0]]]) We can also give indexes for more than one dimension. The arrays of indices for each dimension must have the same shape. >>> >>> a = np.arange(12).reshape(3,4) >>> a array([[ 0, 1, 2, 3], [ 4, 5, 6, 7], [ 8, 9, 10, 11]]) >>> i = np.array([[0, 1], # indices for the first dim of a ... [1, 2]]) >>> j = np.array([[2, 1], # indices for the second dim ... [3, 3]]) >>> >>> a[i, j] # i and j must have equal shape array([[ 2, 5], [ 7, 11]]) >>> >>> a[i, 2] array([[ 2, 6], [ 6, 10]]) >>> >>> a[:, j] # i.e., a[ : , j] array([[[ 2, 1], [ 3, 3]], [[ 6, 5], [ 7, 7]], [[10, 9], [11, 11]]]) In Python, arr[i, j] is exactly the same as arr[(i, j)]—so we can put i and j in a tuple and then do the indexing with that. >>> >>> l = (i, j) # equivalent to a[i, j] >>> a[l] array([[ 2, 5], [ 7, 11]]) However, we can not do this by putting i and j into an array, because this array will be interpreted as indexing the first dimension of a. >>> >>> s = np.array([i, j]) # not what we want >>> a[s] Traceback (most recent call last): File "<stdin>", line 1, in <module> IndexError: index 3 is out of bounds for axis 0 with size 3 # same as a[i, j] >>> a[tuple(s)] array([[ 2, 5], [ 7, 11]]) Another common use of indexing with arrays is the search of the maximum value of time-dependent series: >>> >>> time = np.linspace(20, 145, 5) # time scale >>> data = np.sin(np.arange(20)).reshape(5,4) # 4 time-dependent series >>> time array([ 20. , 51.25, 82.5 , 113.75, 145. ]) >>> data array([[ 0. , 0.84147098, 0.90929743, 0.14112001], [-0.7568025 , -0.95892427, -0.2794155 , 0.6569866 ], [ 0.98935825, 0.41211849, -0.54402111, -0.99999021], [-0.53657292, 0.42016704, 0.99060736, 0.65028784], [-0.28790332, -0.96139749, -0.75098725, 0.14987721]]) # index of the maxima for each series >>> ind = data.argmax(axis=0) >>> ind array([2, 0, 3, 1]) # times corresponding to the maxima >>> time_max = time[ind] >>> >>> data_max = data[ind, range(data.shape[1])] # => data[ind[0],0], data[ind[1],1]... >>> time_max array([ 82.5 , 20. , 113.75, 51.25]) >>> data_max array([0.98935825, 0.84147098, 0.99060736, 0.6569866 ]) >>> np.all(data_max == data.max(axis=0)) True You can also use indexing with arrays as a target to assign to: >>> >>> a = np.arange(5) >>> a array([0, 1, 2, 3, 4]) >>> a[[1,3,4]] = 0 >>> a array([0, 0, 2, 0, 0]) However, when the list of indices contains repetitions, the assignment is done several times, leaving behind the last value: >>> >>> a = np.arange(5) >>> a[[0,0,2]]=[1,2,3] >>> a array([2, 1, 3, 3, 4]) This is reasonable enough, but watch out if you want to use Python’s += construct, as it may not do what you expect: >>> >>> a = np.arange(5) >>> a[[0,0,2]]+=1 >>> a array([1, 1, 3, 3, 4]) Even though 0 occurs twice in the list of indices, the 0th element is only incremented once. This is because Python requires “a+=1” to be equivalent to “a = a + 1”. Indexing with Boolean Arrays When we index arrays with arrays of (integer) indices we are providing the list of indices to pick. With boolean indices the approach is different; we explicitly choose which items in the array we want and which ones we don’t. The most natural way one can think of for boolean indexing is to use boolean arrays that have the same shape as the original array: >>> >>> a = np.arange(12).reshape(3,4) >>> b = a > 4 >>> b # b is a boolean with a's shape array([[False, False, False, False], [False, True, True, True], [ True, True, True, True]]) >>> a[b] # 1d array with the selected elements array([ 5, 6, 7, 8, 9, 10, 11]) This property can be very useful in assignments: >>> >>> a[b] = 0 # All elements of 'a' higher than 4 become 0 >>> a array([[0, 1, 2, 3], [4, 0, 0, 0], [0, 0, 0, 0]]) You can look at the following example to see how to use boolean indexing to generate an image of the Mandelbrot set: >>> import numpy as np import matplotlib.pyplot as plt def mandelbrot( h,w, maxit=20 ): """Returns an image of the Mandelbrot fractal of size (h,w).""" y,x = np.ogrid[ -1.4:1.4:h*1j, -2:0.8:w*1j ] c = x+y*1j z = c divtime = maxit + np.zeros(z.shape, dtype=int) for i in range(maxit): z = z**2 + c diverge = z*np.conj(z) > 2**2 # who is diverging div_now = diverge & (divtime==maxit) # who is diverging now divtime[div_now] = i # note when z[diverge] = 2 # avoid diverging too much return divtime plt.imshow(mandelbrot(400,400)) ../_images/quickstart-1.png The second way of indexing with booleans is more similar to integer indexing; for each dimension of the array we give a 1D boolean array selecting the slices we want: >>> >>> a = np.arange(12).reshape(3,4) >>> b1 = np.array([False,True,True]) # first dim selection >>> b2 = np.array([True,False,True,False]) # second dim selection >>> >>> a[b1,:] # selecting rows array([[ 4, 5, 6, 7], [ 8, 9, 10, 11]]) >>> >>> a[b1] # same thing array([[ 4, 5, 6, 7], [ 8, 9, 10, 11]]) >>> >>> a[:,b2] # selecting columns array([[ 0, 2], [ 4, 6], [ 8, 10]]) >>> >>> a[b1,b2] # a weird thing to do array([ 4, 10]) Note that the length of the 1D boolean array must coincide with the length of the dimension (or axis) you want to slice. In the previous example, b1 has length 3 (the number of rows in a), and b2 (of length 4) is suitable to index the 2nd axis (columns) of a. The ix_() function The ix_ function can be used to combine different vectors so as to obtain the result for each n-uplet. For example, if you want to compute all the a+b*c for all the triplets taken from each of the vectors a, b and c: >>> >>> a = np.array([2,3,4,5]) >>> b = np.array([8,5,4]) >>> c = np.array([5,4,6,8,3]) >>> ax,bx,cx = np.ix_(a,b,c) >>> ax array([[[2]], [[3]], [[4]], [[5]]]) >>> bx array([[[8], [5], [4]]]) >>> cx array([[[5, 4, 6, 8, 3]]]) >>> ax.shape, bx.shape, cx.shape ((4, 1, 1), (1, 3, 1), (1, 1, 5)) >>> result = ax+bx*cx >>> result array([[[42, 34, 50, 66, 26], [27, 22, 32, 42, 17], [22, 18, 26, 34, 14]], [[43, 35, 51, 67, 27], [28, 23, 33, 43, 18], [23, 19, 27, 35, 15]], [[44, 36, 52, 68, 28], [29, 24, 34, 44, 19], [24, 20, 28, 36, 16]], [[45, 37, 53, 69, 29], [30, 25, 35, 45, 20], [25, 21, 29, 37, 17]]]) >>> result[3,2,4] 17 >>> a[3]+b[2]*c[4] 17 You could also implement the reduce as follows: >>> >>> def ufunc_reduce(ufct, *vectors): ... vs = np.ix_(*vectors) ... r = ufct.identity ... for v in vs: ... r = ufct(r,v) ... return r and then use it as: >>> >>> ufunc_reduce(np.add,a,b,c) array([[[15, 14, 16, 18, 13], [12, 11, 13, 15, 10], [11, 10, 12, 14, 9]], [[16, 15, 17, 19, 14], [13, 12, 14, 16, 11], [12, 11, 13, 15, 10]], [[17, 16, 18, 20, 15], [14, 13, 15, 17, 12], [13, 12, 14, 16, 11]], [[18, 17, 19, 21, 16], [15, 14, 16, 18, 13], [14, 13, 15, 17, 12]]]) The advantage of this version of reduce compared to the normal ufunc.reduce is that it makes use of the Broadcasting Rules in order to avoid creating an argument array the size of the output times the number of vectors. Indexing with strings See Structured arrays. Linear Algebra Work in progress. Basic linear algebra to be included here. Simple Array Operations See linalg.py in numpy folder for more. >>> >>> import numpy as np >>> a = np.array([[1.0, 2.0], [3.0, 4.0]]) >>> print(a) [[1. 2.] [3. 4.]] >>> a.transpose() array([[1., 3.], [2., 4.]]) >>> np.linalg.inv(a) array([[-2. , 1. ], [ 1.5, -0.5]]) >>> u = np.eye(2) # unit 2x2 matrix; "eye" represents "I" >>> u array([[1., 0.], [0., 1.]]) >>> j = np.array([[0.0, -1.0], [1.0, 0.0]]) >>> j @ j # matrix product array([[-1., 0.], [ 0., -1.]]) >>> np.trace(u) # trace 2.0 >>> y = np.array([[5.], [7.]]) >>> np.linalg.solve(a, y) array([[-3.], [ 4.]]) >>> np.linalg.eig(j) (array([0.+1.j, 0.-1.j]), array([[0.70710678+0.j , 0.70710678-0.j ], [0. -0.70710678j, 0. +0.70710678j]])) Parameters: square matrix Returns The eigenvalues, each repeated according to its multiplicity. The normalized (unit "length") eigenvectors, such that the column ``v[:,i]`` is the eigenvector corresponding to the eigenvalue ``w[i]`` . Tricks and Tips Here we give a list of short and useful tips. “Automatic” Reshaping To change the dimensions of an array, you can omit one of the sizes which will then be deduced automatically: >>> >>> a = np.arange(30) >>> b = a.reshape((2, -1, 3)) # -1 means "whatever is needed" >>> b.shape (2, 5, 3) >>> b array([[[ 0, 1, 2], [ 3, 4, 5], [ 6, 7, 8], [ 9, 10, 11], [12, 13, 14]], [[15, 16, 17], [18, 19, 20], [21, 22, 23], [24, 25, 26], [27, 28, 29]]]) Vector Stacking How do we construct a 2D array from a list of equally-sized row vectors? In MATLAB this is quite easy: if x and y are two vectors of the same length you only need do m=[x;y]. In NumPy this works via the functions column_stack, dstack, hstack and vstack, depending on the dimension in which the stacking is to be done. For example: >>> >>> x = np.arange(0,10,2) >>> y = np.arange(5) >>> m = np.vstack([x,y]) >>> m array([[0, 2, 4, 6, 8], [0, 1, 2, 3, 4]]) >>> xy = np.hstack([x,y]) >>> xy array([0, 2, 4, 6, 8, 0, 1, 2, 3, 4]) The logic behind those functions in more than two dimensions can be strange. See also NumPy for Matlab users Histograms The NumPy histogram function applied to an array returns a pair of vectors: the histogram of the array and a vector of the bin edges. Beware: matplotlib also has a function to build histograms (called hist, as in Matlab) that differs from the one in NumPy. The main difference is that pylab.hist plots the histogram automatically, while numpy.histogram only generates the data. >>> import numpy as np rg = np.random.default_rng(1) import matplotlib.pyplot as plt # Build a vector of 10000 normal deviates with variance 0.5^2 and mean 2 mu, sigma = 2, 0.5 v = rg.normal(mu,sigma,10000) # Plot a normalized histogram with 50 bins plt.hist(v, bins=50, density=1) # matplotlib version (plot) # Compute the histogram with numpy and then plot it (n, bins) = np.histogram(v, bins=50, density=True) # NumPy version (no plot) plt.plot(.5*(bins[1:]+bins[:-1]), n) ../_images/quickstart-2.png Further reading The Python tutorial NumPy Reference SciPy Tutorial SciPy Lecture Notes A matlab, R, IDL, NumPy/SciPy dictionary © Copyright 2008-2020, The SciPy community. Last updated on Jun 29, 2020. Created using Sphinx 2.4.4.
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