MATLAB is a commercial mathematics software produced by MathWorks, USA. It is a high-level technical computing language and interactive environment for algorithm development, data visualization, data analysis and numerical calculation. It mainly includes MATLAB and Simulink.
MATLAB is a combination of the word matrix&laboratory, meaning matrix factory (matrix lab). It is a high-tech computing environment mainly published by mathworks of the United States that faces scientific computing, visualization, and interactive programming. It integrates numerical analysis, matrix calculations, scientific data visualization, and modeling and simulation of nonlinear dynamic systems into one easy-to-use window environment for scientific research, engineering design, and many sciences that must perform effective numerical calculations. The field provides a comprehensive Solution and largely rids the editing mode of traditional non-interactive programming languages ​​(such as C, Fortran), representing the advanced level of today's international scientific computing software.
MATLAB and MathemaTIca, Maple are also called the three major mathematical software. It is second to none in numerical computing in mathematics applications. MATLAB can perform matrix operations, draw functions and data, implement algorithms, create user interfaces, and connect programs in other programming languages. It is mainly used in engineering calculation, control design, signal processing and communication, image processing, signal detection, and financial modeling design. And other areas such as analysis.
The basic data unit of MATLAB is matrix. Its instruction expression is very similar to the form commonly used in mathematics and engineering. Therefore, using MATLAB to solve the problem is much simpler than using C, FORTRAN and other languages ​​to complete the same thing, and MATLAB also It absorbs the advantages of software like Maple and makes MATLAB a powerful mathematical software. Support for C, FORTRAN, C++, and JAVA has also been added to the new version.
1) Efficient numerical calculation and symbolic calculation function can free users from the complicated mathematical operation analysis;
2) Complete graphic processing function to realize the visualization of calculation results and programming;
3) Friendly user interface and natural language close to mathematical expressions, making it easy for scholars to learn and master;
4) A feature-rich application toolbox (such as signal processing toolbox, communication toolbox, etc.) provides users with a large number of convenient and practical processing tools.
Programming environment
MATLAB consists of a series of tools. These tools make it easy for users to use MATLAB functions and files, many of which use a graphical user interface. Includes MATLAB desktop and command windows, history command windows, editors and debuggers, path search and browsers for user browsing help, workspaces, files. With the commercialization of MATLAB and the continuous upgrading of the software itself, MATLAB's user interface has become more and more refined, closer to the standard interface of Windows, with more human-computer interaction and simpler operation. And the new version of MATLAB provides a complete online query and help system, which greatly facilitates the user's use. The simple programming environment provides a relatively complete debugging system. The program can run directly without compiling, and can report errors and analyze the causes of errors in a timely manner.
Easy to use
Matlab is an advanced matrix/array language that contains control statements, functions, data structures, input and output, and object-oriented programming features. The user can synchronize the input statement with the execution command in the command window, or write a large complex application (M file) and run it together. The new version of the MATLAB language is based on the most popular C++ language, so the grammatical features are very similar to the C++ language, and are much simpler and more in line with the writing format of scientific expressions by scientific personnel. Make it more conducive to the use of non-computer professionals. Moreover, this language has good portability and scalability, which is also an important reason why MATLAB can penetrate into various fields of scientific research and engineering calculation.
Powerful processing
MATLAB is a collection of computational algorithms. It has more than 600 mathematical operations functions to be used in the project, which can easily realize various calculation functions required by users. The algorithms used in the functions are the latest research in scientific research and engineering calculations, and have undergone various optimization and fault-tolerant processing. Under normal circumstances, you can use it instead of the underlying programming languages, such as C and C++. With the same computational requirements, the amount of programming effort using MATLAB is greatly reduced. These sets of functions in MATLAB range from the simplest and most basic functions to complex functions such as matrices, eigenvectors, and fast Fourier transforms. The problems that the function can solve include roughly matrix operations and solutions of linear equations, solutions of differential equations and partial differential equations, symbolic operations, Fourier transforms and statistical analysis of data, optimization problems in engineering, sparse matrix operations, Complex operations, trigonometric functions, and other elementary mathematical operations, multidimensional array operations, and modeling dynamic simulation.
Graphics processing
MATLAB has a convenient data visualization function since its inception to graphically represent vectors and matrices, and to mark and print graphics. High-level mapping includes 2D and 3D visualization, image processing, animation, and expression mapping. Can be used for scientific calculations and engineering drawings. The new version of MATLAB has greatly improved and improved the entire graphics processing function, making it not only perfect in the functions of general data visualization software, such as the drawing and processing of 2D curves and 3D surfaces, but also for Some features not available in other software (such as graphics lighting, chroma processing, and the performance of four-dimensional data), MATLAB also shows excellent processing power. At the same time, for some special visualization requirements, such as graphical dialogue, MATLAB also has corresponding function functions to ensure the different levels of user requirements. In addition, the new version of MATLAB also focuses on the improvement of the graphical user interface (GUI), and users with special requirements in this area can also be satisfied.
Module tool
MATLAB has developed powerful module sets and toolboxes for many specialized areas. In general, they are developed by experts in specific fields, and users can directly learn, apply, and evaluate different methods using the toolbox without having to write their own code. Domains such as data acquisition, database interface, probability statistics, spline fitting, optimization algorithms, partial differential equation solving, neural networks, wavelet analysis, signal processing, image processing, system identification, control system design, LMI control, robust control Model prediction, fuzzy logic, financial analysis, map tools, nonlinear control design, real-time rapid prototyping and semi-physical simulation, embedded system development, fixed-point simulation, DSP and communication, power system simulation, etc., all in Toolbox The family has its own place.
Program interface
The new version of MATLAB can automatically convert your own MATLAB programs into C and C++ code that runs independently of MATLAB using the MATLAB compiler and the C/C++ math library and graphics library. Allows users to write C or C++ language programs that can interact with MATLAB. In addition, the MATLAB web service program allows the use of its own MATLAB math and graphics programs in web applications. An important feature of MATLAB is that it has a program extension system and a set of special application subroutines called toolboxes. The toolbox is a subroutine library of MATLAB functions. Each toolbox is customized for a certain class of disciplines and applications, including signal processing, control systems, neural networks, fuzzy logic, wavelet analysis, and system simulation. application.
Software development
In the development environment, it makes it easier for users to control multiple files and graphics windows; in terms of programming, it supports function nesting, conditional interrupts, etc.; in terms of graphics, there are more powerful graphic annotation and processing functions, including Sexual pair connection notes, etc.; in terms of input and output, you can directly connect to Excel and HDF5.
The encoding of the Hamming code is how to obtain a supervised matrix H that corrects an error according to the number of bits of information k, and then obtain the codeword corresponding to the information bit according to H.
1. Calculate the check digit m=nk from the Hamming inequality according to the known information bit number k;
2. In each codeword C: (C1, C2, ⋯, C2m -1), use c02, c12, cn-12 as the supervised bits, and the remaining bits as the information bits;
3, using a binary number to represent 2m-1 column, get 2m-1 column and m row supervision matrix H;
4. Form HCT =0 with 3 steps of H, thus obtaining m supervised equations;
5. Substitute the known information into the equations, and then find the supervised bits c (i = 0, 1, ⋯, m - 1) that satisfy the above equations. For example, using the above method, it is easy to find the supervised matrix of the [7, 4, 3] Hamming code:
And the code word corresponding to the code is C=011001.
operation result:
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