fHAND – a fuzzy approach to computing height above nearest drainage
via TopoToolbox (author: wschwanghart)
via TopoToolbox (author: wschwanghart)
TopoToolbox
fHAND – a fuzzy approach to computing height above nearest drainage
The previous blog post was about slope position (or fractional relief), a metric that quantifies the position of each pixel between the river and the ridge. The approach uses multiple flow directio…
📡 MATLAB Central - File Exchange - rating:5.0 | MATLAB AI Agent SDK
# MATLAB AI Agent SDKhttps://www.mathworks.com/images/responsive/global/open-in-matlab-online.svg">MATLAB® AI Agent SDK lets you build and run AI agents in MATLAB.- Create agents based on OpenAI® Chat Completions, Ollama™, or OpenAI-compatible APIs.- Integrate LLMs and agentic workflows into your workflows in a targeted manner, retaining deterministic workflows when those are more suitable.- Create agentic tools that use: - large amounts of data - any MATLAB data type## Research PreviewThis SDK is a Research Preview under active development and APIs may change.Please leave feedback, report bugs and feature requests via Issues. We review all contributions, but we do not merge external pull requests. See CONTRIBUTING.md for details.Help us improve the MATLAB AI Agent SDK by completing our short feedback survey.## SetupUsing this add\-on requires MATLAB R2023a or newer.You can use the add\-on in MATLAB Online™ by clicking this link: https://www.mathworks.com/images/responsive/global/open-in-matlab-online.svg">To use the add\-on on an installed version of MATLAB, you can clone the GitHub repository. In the MATLAB Command Window, run this command:``>> !git clone https://github.com/matlab/matlab-ai-agent-sdk.git`To run code from the add\-on outside of the installation directory, add the path to the installation directory.`>> addpath("path/to/matlab-ai-agent-sdk")`### OpenAIUsing the OpenAI Chat Completions API requires an OpenAI API key. For information on how to obtain one, as well as pricing, terms and conditions of use, and available models, see the https://platform.openai.com/docs/overview">OpenAI documentation.Set your key as an environment variable in a .env file:`OPENAI_API_KEY=`Then load it in MATLAB.`matlabloadenv(".env")`### OpenAI-Compatible APIsTo connect to APIs that are compatible with the OpenAI Chat Completions API, set your key as an environment variable in a .env file:`OPENAI_API_KEY=`If your API does not need an API key, set the environment variable OPENAI_API_KEY to "EMPTY".Then, when creating an LLM client, set the api argument of the aisdk.LLMClient function to "openai" and set the BaseURL name-value argument to the base URL of the API. For example, for OpenAI, BaseURL is "https://api.openai.com/v1".### OllamaTo connect to local or remote Ollama models, first install Ollama.After you have installed Ollama, you can install models from the MATLAB Command Window:`matlab!ollama pull `## Get StartedCreate an LLM client by using the aisdk.LLMClient function and using the API and the model name as input arguments, for example:`matlabclientOpenAI = aisdk.LLMClient("openai", "gpt-4.1-mini");clientOllama = aisdk.LLMClient("ollama", "");`Then, generate text by using the generate function.`matlabtext = generate(client, "This is an example prompt.")````text = "This is an example reponse."`### Create Chat With LLMThis example shows how to create a conversation with an LLM and automatically keep track of the message history.Create the agent from an LLM client client by using the aisdk.AIAgent function. Provide a system prompt.`matlabsystemPrompt = "Reply as if you are writing telegrams.";agent = aisdk.AIAgent(client,SystemPrompt=systemPrompt);`Run the agent by using the run function. Provide a prompt.`matlabprompt = "TOMATO FRUIT OR VEGETABLE STOP";run(agent,prompt)````ans = "TOMATO TECHNICALLY A FRUIT STOP COMMONLY USED AS VEGETABLE IN CULINARY CONTEXT STOP END OF TRANSMISSION."`Ask a follow up question by using the run function.`matlabrun(agent,"HOW ABOUT AVOCADO STOP")````ans = "AVOCADO ALSO A FRUIT STOP KNOWN AS ALLIGATOR PEAR STOP HIGH IN HEALTHY FATS AND NUTRIENTS STOP END OF TRANSMISSION."`Inspect the chat history by using the Messages property of the
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# MATLAB AI Agent SDKhttps://www.mathworks.com/images/responsive/global/open-in-matlab-online.svg">MATLAB® AI Agent SDK lets you build and run AI agents in MATLAB.- Create agents based on OpenAI® Chat Completions, Ollama™, or OpenAI-compatible APIs.- Integrate LLMs and agentic workflows into your workflows in a targeted manner, retaining deterministic workflows when those are more suitable.- Create agentic tools that use: - large amounts of data - any MATLAB data type## Research PreviewThis SDK is a Research Preview under active development and APIs may change.Please leave feedback, report bugs and feature requests via Issues. We review all contributions, but we do not merge external pull requests. See CONTRIBUTING.md for details.Help us improve the MATLAB AI Agent SDK by completing our short feedback survey.## SetupUsing this add\-on requires MATLAB R2023a or newer.You can use the add\-on in MATLAB Online™ by clicking this link: https://www.mathworks.com/images/responsive/global/open-in-matlab-online.svg">To use the add\-on on an installed version of MATLAB, you can clone the GitHub repository. In the MATLAB Command Window, run this command:``>> !git clone https://github.com/matlab/matlab-ai-agent-sdk.git`To run code from the add\-on outside of the installation directory, add the path to the installation directory.`>> addpath("path/to/matlab-ai-agent-sdk")`### OpenAIUsing the OpenAI Chat Completions API requires an OpenAI API key. For information on how to obtain one, as well as pricing, terms and conditions of use, and available models, see the https://platform.openai.com/docs/overview">OpenAI documentation.Set your key as an environment variable in a .env file:`OPENAI_API_KEY=`Then load it in MATLAB.`matlabloadenv(".env")`### OpenAI-Compatible APIsTo connect to APIs that are compatible with the OpenAI Chat Completions API, set your key as an environment variable in a .env file:`OPENAI_API_KEY=`If your API does not need an API key, set the environment variable OPENAI_API_KEY to "EMPTY".Then, when creating an LLM client, set the api argument of the aisdk.LLMClient function to "openai" and set the BaseURL name-value argument to the base URL of the API. For example, for OpenAI, BaseURL is "https://api.openai.com/v1".### OllamaTo connect to local or remote Ollama models, first install Ollama.After you have installed Ollama, you can install models from the MATLAB Command Window:`matlab!ollama pull `## Get StartedCreate an LLM client by using the aisdk.LLMClient function and using the API and the model name as input arguments, for example:`matlabclientOpenAI = aisdk.LLMClient("openai", "gpt-4.1-mini");clientOllama = aisdk.LLMClient("ollama", "");`Then, generate text by using the generate function.`matlabtext = generate(client, "This is an example prompt.")````text = "This is an example reponse."`### Create Chat With LLMThis example shows how to create a conversation with an LLM and automatically keep track of the message history.Create the agent from an LLM client client by using the aisdk.AIAgent function. Provide a system prompt.`matlabsystemPrompt = "Reply as if you are writing telegrams.";agent = aisdk.AIAgent(client,SystemPrompt=systemPrompt);`Run the agent by using the run function. Provide a prompt.`matlabprompt = "TOMATO FRUIT OR VEGETABLE STOP";run(agent,prompt)````ans = "TOMATO TECHNICALLY A FRUIT STOP COMMONLY USED AS VEGETABLE IN CULINARY CONTEXT STOP END OF TRANSMISSION."`Ask a follow up question by using the run function.`matlabrun(agent,"HOW ABOUT AVOCADO STOP")````ans = "AVOCADO ALSO A FRUIT STOP KNOWN AS ALLIGATOR PEAR STOP HIGH IN HEALTHY FATS AND NUTRIENTS STOP END OF TRANSMISSION."`Inspect the chat history by using the Messages property of the
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NEXTNAME returns a filename, incrementing a numbered suffix such that the returned name is not currently used by any file or folder.On occasion it may be required to save files without knowing or requiring a particular number sequence, for example when saving interim results or backups during large calculations. Using an internal counter is one option, but this does not work when there are already existing files with the same names, or when the code is stopped-and-started unpredictably (e.g throws errors while calculating and is restarted). This function offers one simple solution: NEXTNAME will search for existing files/folders that match the provided inputs, increment an integer until the value is unused by any current filename, and then return the next unused filename.Note that unlike some other submissions on FEX, this function compares the number values, not the literal filenames! This means you will not get "x001" if e.g. "x1" or "x01" or "x00000001" already exist in the specified location.Syntax 1One text input is required: the folder/filename (including file extension, if required). The folder/filename must include one integer within angle brackets (aka less/greater than characters), e.g.: 'test.txt'. The integer will be incremented as required to define an unused filename. The angle brackets are not returned in the output.Syntax 2Three text inputs are required:The basic folder/filename, without any file extension.The suffix, which must contain one integer. Some examples of suffixes are: '0', '_1', '(5)', '-0001-backup', '_temp1', etc. This suffix will be appended to the folder/filename, before the file extension, after incrementing the integer as required to define an unused filename.The file extension, if required. For folders (or files without extensions) use '' or "".Note the path, name, and extension inputs can generally be obtained from a filename using FILEPARTS.IntegerThe integer specifies: the value to start incrementing from (this can be zero or any positive integer, i.e. 0, 1, 2, 3, etc.), the minimum width of the output number by using leading zeros as required. For example, "001" specifies the integer in the output has (minimum) width of three characters. The output integer will be automatically zero padded (if required) to this length.Examples% Current directory contains files 'A1.txt', 'A2.txt', and 'A4.txt':>> nextname("A.txt") % syntax 1ans = "A3.txt">> nextname("A","1",".txt") % syntax 2ans = "A3.txt">> nextname("A.txt") % syntax 1ans = "A003.txt">> nextname("A","001",".txt") % syntax 2ans = "A003.txt"% Directory 'test' contains subdirectories 'B(1)', 'B(2)', and 'B(4)':>> nextname('test/B()') % syntax 1ans = 'B(3)'>> nextname('test/B','(1)','') % syntax 2ans = 'B(3)'>> nextname('test','B()') % syntax 1ans = 'B(3)'>> nextname('test','B','(1)','') % syntax 2ans = 'B(3)'>> nextname('test','B()',true) % syntax 1ans = 'test/B(3)'>> nextname('test','B','(1)','',true) % syntax 2ans = 'test/B(3)'
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📡 MATLAB Central - File Exchange - rating:4.7 | Introduction to Kalman Filter and Its Applications
# Kalman_Filter## OverviewMATLAB tutorial examples of the Kalman filter (KF) and extended Kalman filter (EKF) for INS/GNSS navigation, target tracking, and terrain-referenced navigation (TRN, also called terrain-aided navigation).These are the authors' implementations accompanying the **peer-reviewed tutorial chapter** Introduction to Kalman Filter and Its Applications, with source and terrain data available directly in this repository. See the chapter citation, implementation map, and provenance.The accompanying tutorial chapter has received **over 500 citations** on https://scholar.google.com/citations?view_op=view_citation&hl=en&user=8b6KtGYAAAAJ&citation_for_view=8b6KtGYAAAAJ:hC7cP41nSMkC">Google Scholar.For implementations in Python, C++, or other languages, follow the KF equations, EKF update procedure, and terrain measurement model.## MethodPredict the state and covariance with a motion model, then correct them using measurements. The linear KF uses position/velocity observations; the EKFs linearize angle/range or terrain-height observations around the current estimate.### Algorithms and source| Method and application | Chapter | Implementation and runnable example | Technical reference ||---|---|---|---|| Linear KF: inertial/GNSS position and velocity | Sections 2.2-2.3, Eqs. (3)-(18) | KF.m | Kalman filter || EKF: angle/range target tracking | Sections 3.2-3.3.1, Eqs. (23)-(32) | EKF_1.m | Extended Kalman filter || EKF: terrain-referenced navigation | Sections 3.2, 3.3.2, Eqs. (33)-(40) | EKF_2.m | Terrain navigation |## ExamplesRun commands from the repository root with MATLAB and Statistics and Machine Learning Toolbox (normrnd). The shell commands use matlab -batch (R2019a or later); the terrain example uses the included DEM.mat.Generate current-code versions of all seven simulation figures as PNG and PDF files:``bashmatlab -batch "generate_figures"`Generate one figure, such as Figure 5:`bashmatlab -batch "generate_figures(5)"`See the figure map and export options for Figures 1-5, 8, and 9, seeds, and output metadata. The exporter uses the current equations and simulation settings.Run the seeded introductory INS/GNSS example without opening figure windows:`bashmatlab -batch "set(groot,'defaultFigureVisible','off'); main; disp(x_RMSE(:,end))"`In an interactive MATLAB session, select the repository root as the current folder and enter main to see the plots. The scripts clear their calling workspace and close existing figures; save work before running them.See Examples for the two EKF commands, outputs, seeds, and terrain-data conventions.## Implementation scopeEach script contains its model, simulation, filter updates, and plotting code. Current source includes covariance and measurement corrections, with settings and numerical assumptions documented for adaptation.### ChecksRun the focused example and figure checks:`bashmatlab -batch "addpath('tests/integration/examples'); verify_examples; verify_figures"``These check example outputs, deterministic reruns, terrain loading, and figure export.## CitationFor academic attribution, please acknowledge this repository when adapting its code or examples.If you use or adapt these methods or examples, please cite:> Youngjoo Kim and Hyochoong Bang. “Introduction to Kalman Filter and Its Applications.” In Introduction and Implementations of the Kalman Filter. IntechOpen, 2018. https://doi.org/10.5772/intechopen.80600">doi:10.5772/intechopen.80600.Machine-readable software and chapter metadata are in CITATION.cff.## License and provenanceThe license specifies the copyright and redistribution conditions. Citation requests are separate from those license conditions.See provenance for source-distribution and dataset details, and implementation notes for model and numerical choices.
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# Kalman_Filter## OverviewMATLAB tutorial examples of the Kalman filter (KF) and extended Kalman filter (EKF) for INS/GNSS navigation, target tracking, and terrain-referenced navigation (TRN, also called terrain-aided navigation).These are the authors' implementations accompanying the **peer-reviewed tutorial chapter** Introduction to Kalman Filter and Its Applications, with source and terrain data available directly in this repository. See the chapter citation, implementation map, and provenance.The accompanying tutorial chapter has received **over 500 citations** on https://scholar.google.com/citations?view_op=view_citation&hl=en&user=8b6KtGYAAAAJ&citation_for_view=8b6KtGYAAAAJ:hC7cP41nSMkC">Google Scholar.For implementations in Python, C++, or other languages, follow the KF equations, EKF update procedure, and terrain measurement model.## MethodPredict the state and covariance with a motion model, then correct them using measurements. The linear KF uses position/velocity observations; the EKFs linearize angle/range or terrain-height observations around the current estimate.### Algorithms and source| Method and application | Chapter | Implementation and runnable example | Technical reference ||---|---|---|---|| Linear KF: inertial/GNSS position and velocity | Sections 2.2-2.3, Eqs. (3)-(18) | KF.m | Kalman filter || EKF: angle/range target tracking | Sections 3.2-3.3.1, Eqs. (23)-(32) | EKF_1.m | Extended Kalman filter || EKF: terrain-referenced navigation | Sections 3.2, 3.3.2, Eqs. (33)-(40) | EKF_2.m | Terrain navigation |## ExamplesRun commands from the repository root with MATLAB and Statistics and Machine Learning Toolbox (normrnd). The shell commands use matlab -batch (R2019a or later); the terrain example uses the included DEM.mat.Generate current-code versions of all seven simulation figures as PNG and PDF files:``bashmatlab -batch "generate_figures"`Generate one figure, such as Figure 5:`bashmatlab -batch "generate_figures(5)"`See the figure map and export options for Figures 1-5, 8, and 9, seeds, and output metadata. The exporter uses the current equations and simulation settings.Run the seeded introductory INS/GNSS example without opening figure windows:`bashmatlab -batch "set(groot,'defaultFigureVisible','off'); main; disp(x_RMSE(:,end))"`In an interactive MATLAB session, select the repository root as the current folder and enter main to see the plots. The scripts clear their calling workspace and close existing figures; save work before running them.See Examples for the two EKF commands, outputs, seeds, and terrain-data conventions.## Implementation scopeEach script contains its model, simulation, filter updates, and plotting code. Current source includes covariance and measurement corrections, with settings and numerical assumptions documented for adaptation.### ChecksRun the focused example and figure checks:`bashmatlab -batch "addpath('tests/integration/examples'); verify_examples; verify_figures"``These check example outputs, deterministic reruns, terrain loading, and figure export.## CitationFor academic attribution, please acknowledge this repository when adapting its code or examples.If you use or adapt these methods or examples, please cite:> Youngjoo Kim and Hyochoong Bang. “Introduction to Kalman Filter and Its Applications.” In Introduction and Implementations of the Kalman Filter. IntechOpen, 2018. https://doi.org/10.5772/intechopen.80600">doi:10.5772/intechopen.80600.Machine-readable software and chapter metadata are in CITATION.cff.## License and provenanceThe license specifies the copyright and redistribution conditions. Citation requests are separate from those license conditions.See provenance for source-distribution and dataset details, and implementation notes for model and numerical choices.
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PHX is an object-oriented physics engine for MATLAB. Scenes are built from objects such as bodies, shapes, joints, springs, force fields and can be drawn directly into MATLAB axes. Toolbox includes MATLAB API, Simulink block, documentation and examples. MATLAB R2025a or newer is required.
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📡 MATLAB Central - File Exchange - rating:5.0 | Laplacian in 1D, 2D, or 3D
This MATLAB/Octave-compatible code computes analytically **exact eigenpairs of the negative Laplacian operator** in 1D, 2D, or 3D on a rectangular finite-difference grid. It supports a wide range of boundary condition combinations: **Dirichlet (D)**, **Neumann (N)**, and **Periodic (P)**. The first mandatory output is the **sparse Laplacian matrix itself** via Kronecker sums of 1D discrete Laplacians. The actual numerical entries of the matrix fit int8 format, but only double data class is yet supported for sparse matrices in MATLAB.References- https://en.wikipedia.org/wiki/Eigenvalues_and_eigenvectors_of_the_second_derivative">Eigenvalues and eigenvectors of the second derivative- https://en.wikipedia.org/wiki/Kronecker_sum_of_discrete_Laplacians">Kronecker sum of discrete LaplaciansExamplesCompute both matrix and eigenpairs for a 3D Laplacian with mixed boundary conditions:[A, lambda, V] = laplacian([100, 45, 55], {'DD', 'NN', 'P'}, 20); Compute only the matrix:A = laplacian([100, 45, 55], {'DD', 'NN', 'P'}); Features- Supports **Dirichlet** , **Neumann** , and **Periodic** BCs (including mixed combinations)- Computes eigenvalues and eigenvectors analytically using Kronecker structure- Builds the Laplacian matrix directly- Compatible with **GNU Octave**Related Projects. This code is a part of the **BLOPEX eigensolver package:**- https://en.wikipedia.org/wiki/BLOPEX">Wikipedia: BLOPEX- GitHub BLOPEX Repository that also includes tests and solversNotesThe Python multidimensional code in SciPy https://docs.scipy.org/doc/scipy/reference/generated/scipy.sparse.linalg.LaplacianNd.html">LaplacianNd — SciPy Manualsupports arbitrary dimensions, but it does **not yet support mixed boundary conditions**.Being superseded by MATLAB Sparse nD Laplacian with analytic eigenpairs. that supports arbitrary dimensions and mixed boundary conditions on opposite faces.Authors- Bryan C. Smith- Andrew V. Knyazev
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This MATLAB/Octave-compatible code computes analytically **exact eigenpairs of the negative Laplacian operator** in 1D, 2D, or 3D on a rectangular finite-difference grid. It supports a wide range of boundary condition combinations: **Dirichlet (D)**, **Neumann (N)**, and **Periodic (P)**. The first mandatory output is the **sparse Laplacian matrix itself** via Kronecker sums of 1D discrete Laplacians. The actual numerical entries of the matrix fit int8 format, but only double data class is yet supported for sparse matrices in MATLAB.References- https://en.wikipedia.org/wiki/Eigenvalues_and_eigenvectors_of_the_second_derivative">Eigenvalues and eigenvectors of the second derivative- https://en.wikipedia.org/wiki/Kronecker_sum_of_discrete_Laplacians">Kronecker sum of discrete LaplaciansExamplesCompute both matrix and eigenpairs for a 3D Laplacian with mixed boundary conditions:[A, lambda, V] = laplacian([100, 45, 55], {'DD', 'NN', 'P'}, 20); Compute only the matrix:A = laplacian([100, 45, 55], {'DD', 'NN', 'P'}); Features- Supports **Dirichlet** , **Neumann** , and **Periodic** BCs (including mixed combinations)- Computes eigenvalues and eigenvectors analytically using Kronecker structure- Builds the Laplacian matrix directly- Compatible with **GNU Octave**Related Projects. This code is a part of the **BLOPEX eigensolver package:**- https://en.wikipedia.org/wiki/BLOPEX">Wikipedia: BLOPEX- GitHub BLOPEX Repository that also includes tests and solversNotesThe Python multidimensional code in SciPy https://docs.scipy.org/doc/scipy/reference/generated/scipy.sparse.linalg.LaplacianNd.html">LaplacianNd — SciPy Manualsupports arbitrary dimensions, but it does **not yet support mixed boundary conditions**.Being superseded by MATLAB Sparse nD Laplacian with analytic eigenpairs. that supports arbitrary dimensions and mixed boundary conditions on opposite faces.Authors- Bryan C. Smith- Andrew V. Knyazev
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This MATLAB library provides a set of functions for working with involute gears. It allows you to:- Calculate involute gear geometry- Plot a single gear- Plot multiple gears in mesh- Animate gears in meshThe functions support both involute spur gears and helical involute gears.**Graphics dependency**For graphical output, the library uses the
draw19 package, which is available on MATLAB File Exchange:https://www.mathworks.com/matlabcentral/fileexchange/71745-draw19Please install draw19 and add it to your MATLAB path before using the visualization and animation functions.**User guide**A quick user guide describing the workflow and main functions is available here:https://www.researchgate.net/publication/334065197\_MATLAB\_program\_for\_calculating\_the\_geometry\_of\_involute\_gearsThis toolbox can be useful for education, demonstration of gear meshing, and preliminary analysis of gear geometry.Please open Telegram to view this post
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DATAHASH - Hash for Matlab array, struct, cell or file Hash = DataHash(Data, Opts, ...) Data: Array of built-in types (U)INT8/16/32/64, SINGLE, DOUBLE (real or complex) CHAR, LOGICAL, CELL, STRUCT (scalar or array, nested), function\_handle. Options: List of char vectors: Hashing method: 'SHA-1', 'SHA-256', 'SHA-384', 'SHA-512', 'MD2', 'MD5'. Output format: 'hex', 'HEX', 'double', 'uint8', 'base64' Input type: 'array': The contents, type and size of the input [Data] are considered for the creation of the hash. Nested CELLs and STRUCT arrays are parsed recursively. Empty arrays of different type reply different hashs. 'file': [Data] is treated as file name and the hash is calculated for the files contents. 'bin': [Data] is a numerical, LOGICAL or CHAR array. Only the binary contents of the array is considered, such that e.g. empty arrays of different type reply the same hash. 'ascii': Same as 'bin', but only the 8-bit ASCII part of the 16-bit Matlab CHARs is considered. Hash: String or numeric vector. EXAMPLES: Default: MD5, hex: DataHash([]) % 7de5637fd217d0e44e0082f4d79b3e73SHA-1, Base64: S.a = uint8([]); S.b = {{1:10}, struct('q', uint64(415))}; DataHash(S, 'base64', 'SHA-1') % ZMe4eUAp0G9TDrvSW0/Qc0gQ9/AComparison with standard hash programs using ASCII strings: DataHash('abc', 'SHA-256', 'ascii')Michael Kleder's "Compute Hash" works similar, but does not accept structs, cells or files: http://www.mathworks.com/matlabcentral/fileexchange/8944"GetMD5" is 2 to 100 times faster, but it replies only MD5 hashes and a C-compiler is required: http://www.mathworks.com/matlabcentral/fileexchange/25921Tested: Matlab 7.7, 7.8, 7.13, 8.6, 9.1, 9.5, Win7&10/64, Java: 1.3, 1.6, 1.7Bugreports and enhancement requests are welcome. Feel free to ask me about a version for Matlab 6.5.PS. MD5 and SHA1 hash values are "broken": You can construct a data set, which has a specific hash. But to check the integrity of files or to to recognize a set of variables, both methods are reliable.See also Stefano Pradella's expanded version at: https://github.com/stefanopradella/DataHash
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### Title
lobpcg — Locally Optimal Block Preconditioned Conjugate Gradient eigensolver### Short Summarylobpcg computes a few extreme eigenpairs of large Hermitian standard and generalized eigenproblems using a block preconditioned conjugate gradient method. It supports matrix and function-handle operators, optional constraints, optional preconditioning, and iteration histories for convergence analysis. Tested in GNU Octave Version: 11.3.0 and MATLAB with Parallel Computing Toolbox 26.2 (R2026b), but is expected to work on any post 2008 MATLAB and Octave.### Descriptionlobpcg is an iterative eigensolver for large-scale Hermitian problems where forming a full factorization is impractical. It is designed to compute partial spectra efficiently, especially for sparse matrices and operators supplied as functions or function handles.The solver accepts:- a full or sparse initial block of vectors,- a Hermitian operator A,- optional generalized operator B,- optional preconditioner T,- optional constraint vectors Y,- tolerance, iteration limit, and verbosity settings.It returns orthonormalized eigenvectors, the corresponding eigenvalues, a convergence flag, and optional histories of eigenvalue estimates and residual norms.### Features- Standard and generalized Hermitian eigenproblems- Block iterations for clustered and repeated eigenvalues- Optional preconditioning- Optional orthogonality constraints- Supports matrix, function-name, and function-handle operators- Works with sparse and full inputs- Residual and eigenvalue history output for diagnostics- Pure MATLAB (GNU Octave compatible) code- Support for MATLAB distributed or codistributed arrays- Support for double. single, and complex data types - Suitable for MATLAB and GNU Octave workflows### Typical Use CasesThis solver is useful for:- structural mechanics and vibration modes,- graph and network spectral problems,- repeated or clustered eigenvalue problems,- efficient preconditioning available,- large problems where MATLAB's built-in eig is too expensive and eigs is not the desired workflow.### Notes- A does not need to be positive definite- The code computes the algebraically smallest eigenvalues but can trivially be used for the largest simply applied to -A.- B and T should be positive definite when used. There is no check, and the code may break otherwise.- The code is intended for partial eigensolutions, not high-precision full diagonalization.- Performance and convergence depend on block size, preconditioner quality, and the spectral distribution.### Other implementations- A simplified C-version of this code is a part of thehttps://github.com/lobpcg/blopexpackage and is directly available, e.g., in SLEPc and HYPRE.- A Python version LOBPCG is inhttps://docs.scipy.org/doc/scipy/reference/generated/scipy.sparse.linalg.lobpcg.html- LOBPCG is implemented in many open-source packages in various languages for a great variety of applications; see https://en.wikipedia.org/wiki/LOBPCG- https://mfem.org/examples/ Maxwell Eigenproblem LOBPCG run generates the image used to identify this package.### ReferenceA. V. Knyazev, “Toward the Optimal Preconditioned Eigensolver: Locally Optimal Block Preconditioned Conjugate Gradient Method,” SIAM Journal on Scientific Computing, 23(2), 517–541, 2001.### Docstring%LOBPCG solves Hermitian partial eigenproblems using preconditioning%% [blockVectorX,lambda]=lobpcg(blockVectorX,operatorA)%% outputs the array of algebraic smallest eigenvalues lambda and% corresponding matrix of ortho-normalized eigenvectors blockVectorX of the% Hermitian (full or sparse) operator operatorA using input matrix% blockVectorX as an initial guess, without preconditioning, somewhat% similar to%% opts.issym=1;opts.isreal=1;K=size(blockVectorX,2);% [blockVectorX,lambda]=eigs(operatorA,K,'SR',opts);%% for real symmetric operator operatorA, or%% K=size(blockVectorX,2);[blockVectorX,lambda]=eigs(operatorA,K,'SR');% for---------
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Download files from the web and upload files to the web while showing live progress, using MATLAB's HTTP interface. Progress is shown in a waitbar, in a progress dialog attached to an app figure, or in the Command Window. It includes the transferred size, the percentage and an estimate of the remaining time.
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# Fluorescence Tracker App https://www.mathworks.com/images/responsive/global/open-in-matlab-online.svg">This app uses computer vision point tracking to quantify near infrared signals emitted by (ICG) Indocyanine Green during fluorescence angiography. Short overview videos of how to use this app can be found in the https://www.mathworks.com/videos/series/how-to-video-series-for-biomedical-and-pharmaceutical-applications.html">"How To" Video Series for Biomedical and Pharmaceutical Applications.!Fluorescence Tracker AppThe following research in colorectal cancer was carried out using this software: "Digital dynamic discrimination of primary colorectal cancer using systemic indocyanine green with near-infrared endoscopy" by J. Dalli et al., Scientific Reports 11, Article 11349
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This is a simple robotics toolbox designed to study and understand the forward kinematics of robot manipulators. Unlike Peter Corke's toolbox, the representation is not done automatically through the Denavit Hartenberg representation, but the homogeneous transformations are at the user's discretion and therefore the representation is built by the user. This feature enables to represent the kinematic diagram of parallel robots, such as the paralelogram configuration in the Fanuc Robots.All the elements of any kinematic diagram can be represented with solid parts (3D frames, joints and links). The solid links need STL files. If you don't need the representation of solid links, these can be represented with simple lines.The toolbox needs the next included complementary toolboxes/functions:\* FreezeColors toolbox by John Iversen (2005)\* Stlread and patchslim functions by Francis Esmonde-White (2010).A
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