Applications Statistics and machine learning StatsBase.jl Weight Vectors Scalar Statistics Robust Statistics Computing Deviations Scatter Matrix and Covariance Counting Functions Rankings and Rank Correlations Sampling from Population Empirical Estimation Correlation Analysis of Signals Multivariate Summary Statistics Miscellaneous Functions Abstraction for Statistical Models Data Transformations Distributions.jl Getting Started Type Hierarchy Univariate Distributions Truncated Distributions Censored Distributions Multivariate Distributions Matrix-variate Distributions Reshaping distributions Cholesky-variate Distributions Mixture Models Order Statistics Convolutions Distribution Fitting Create New Samplers and Distributions Support for DensityInterface GLM.jl Examples API RDatasets.jl Approximation Polynomials.jl Polynomials.jl Reference/API Types of polynomials Polynomial Chebyshev Polynomials Extensions Extending Polynomials Interpolations.jl Convenience notation General usage Control of interpolation algorithm Extrapolation Knot Iteration Developer documentation Public API Other Interpolation Packages ChainRulesCore Integration GLM.jl Examples API LsqFit.jl Getting Started Tutorial API Optimisation JuMP.jl Installation Guide Should you use JuMP? Tutorials Getting started Introduction Getting started with Julia Getting started with JuMP Getting started with sets and indexing Getting started with data and plotting Debugging Design patterns for larger models Performance tips Performance problems with sum-if formulations Transitioning from MATLAB Linear programs Introduction The knapsack problem example The diet problem The cannery problem The factory schedule example The multi-commodity flow problem The network multi-commodity flow problem Tips and tricks Approximating nonlinear functions The facility location problem Financial modeling problems Geographical clustering Network flow problems The transportation problem Multi-objective knapsack Simple multi-objective examples Sudoku N-Queens Constraint programming Callbacks Sensitivity analysis of a linear program Basis matrices Computing the duals of a mixed-integer program Nonlinear programs Introduction Simple examples Portfolio optimization Rocket Control Optimal control for a Space Shuttle reentry trajectory Tips and tricks User-defined Hessians Nested optimization problems Computing Hessians Mixed complementarity problems Classifiers Automatic differentiation of user-defined operators Conic programs Introduction Primal and dual warm-starts Tips and Tricks Simple semidefinite programming examples Dualization Arbitrary precision arithmetic Logistic regression Experiment design Minimal ellipses Ellipsoid approximation Quantum state discrimination Algorithms Benders decomposition Column generation Traveling Salesperson Problem Parallelism Applications Power Systems Optimal power flow Serving web apps Two-stage stochastic programs Manual Models Variables Constraints Expressions Objectives Containers Solutions Solver-independent Callbacks Complex number support Nonlinear Modeling Nonlinear Modeling (Legacy) Algebraic modeling languages Developer Docs How to contribute to JuMP Extensions How to use a custom binary Style guide and design principles Development roadmap Checklists API API Containers Optim.jl Tutorials Unconstrained Optimization Gradients and Hessians Configurable options Line search Algorithm choice Preconditioning Complex optimization Manifold optimization Dealing with constant parameters Nonlinear constrained optimization Maximum Likelihood Estimation: The Normal Linear Model Conditional Maximum Likelihood for the Rasch Model Algorithms Nelder-Mead Simulated Annealing SAMIN Particle Swarm Adam and AdaMax Conjugate Gradient Descent Gradient Descent (L-)BFGS Acceleration methods: N-GMRES and O-ACCEL Newton’s Method Newton’s Method With a Trust Region Interior point Newton method Notes for contributing Ipopt.jl GLPK.jl HiGHS.jl Getting started Terminology Symbolic calculations Symbolics.jl Getting Started with Symbolics.jl Educational Materials Automated Sparse Parallelism of Julia Functions via Tracing Automatic Conversion of Julia Code to C Functions Examples Mixed Symbolic-Numeric Perturbation Theory User’s Manual Variable and Equation Types Expression Manipulation Derivatives and Differentials Groebner bases Symbolic arrays Function Building and Compilation (build_function) Function Registration and Tracing Parsing Julia Expressions to Symbolic Expressions I/O, Saving, and Latex Structure and Sparsity Detection Supported types and dispatch in Symbolics Frequently Asked Questions Comparison of Julia’s Symbolics.jl vs SymPy for Symbolic Computation Neural networks Flux.jl Getting Started A Neural Network in One Minute Flux Overview: Fitting a Straight Line How Flux Works: Gradients and Layers Training a Flux Model Recurrent Models GPU Support Saving and Loading Models Performance Tips The Julia Ecosystem around Flux Reference Built-in Layer Types Activation Functions from NNlib.jl Random Weight Initialisation Loss Functions Training API Reference Optimisation Rules Shape Inference Flat vs. Nested Structures Callback Helpers Automatic Differentiation using Zygote.jl Working with Data, using MLUtils.jl One-Hot Encoding with OneHotArrays.jl Neural Network primitives from NNlib.jl Recursive transformations from Functors.jl Tutorials Tutorial: Linear Regression Logistic Regression Deep Learning with Julia & Flux: A 60 Minute Blitz Tutorial: Simple Multi-layer Perceptron Tutorial: A Simple ConvNet Tutorial: Generative Adversarial Networks Deep Convolutional Generative Adversarial Network (DCGAN) Defining Customised Layers PyCall.jl ONNX.jl API How to contribute Control systems ControlSystems.jl Getting Started Introduction Creating Systems Performance considerations Noteworthy Differences from other Languages Examples Examples Analysis of linear control systems Smith predictor Iterative-Learning Control Properties of delay systems Automatic Differentiation Functions Constructing systems Analysis Synthesis Time and Frequency response analysis Plotting functions Nonlinear functionality Index ControlSystemIdentification.jl Identification data Statespace model estimation Transfer function estimation Impulse-response estimation Transfer-function estimation using spectral techniques Validation Identification of nonlinear models Examples Temperature control Closed-loop identification Identification of unstable systems Delay estimation Ball and beam Flexible robot arm Glass furnace Evaporator Hair dryer Vector Autoregressive with External inputs (VARX) Nonlinear belt drive Exported functions and types FuzzyLogic.jl Inference Systems Logical connectives Aggregation methods Defuzzification methods Membership functions Reading / writing functionalities Learning fuzzy models Contributor’s guide ModelPredictiveControl.jl Manual: Linear Design Manual: Nonlinear Design Functions: Plant Models Functions: State Estimators Functions: Predictive Controllers Functions: Generic Functions Functions: SimModel Internals Functions: StateEstimator Internals Functions: PredictiveController Internals Index ReinforcementLearning.jl Tutorial How to write a customized environment? How to implement a new algorithm How to use hooks? Episodic vs Non-episodic environments Frequently Asked Questions Tips for Developers RLBase RLCore RLEnvs Signal processing Быстрый старт DSP.jl Welcome to DSP.jl’s documentation! Periodograms - periodogram estimation Estimation - parametric estimation functions Windows - window functions Filters - filter design and filtering Util - utility functions Convolutions - similarity methods LPC - Linear Predictive Coding Index FFTW.jl Fourier Transforms FastTransforms.jl Development Documentation Integration on an annulus Automatic differentiation through spherical harmonic transforms Chebyshev transform Holomorphic integration on the unit disk Half-range Chebyshev polynomials Nonlocal diffusion on S^2 Padua transform Spherical harmonic addition theorem Spin-weighted spherical harmonics Subspace angles Calculus on the reference triangle PortAudio.jl Public interface Internals JuliaMusic Basics Basic MIDI structures Notes Note Tools Quantizing & Humanizing Music data extraction Visualization Plotting Notes Printing into a Score using MuseScore Motif sequence Motif sequence generation Music motifs Becoming a better drummer blog Mixing basic drum patterns Garibaldi’s Foot+Hand doubles 32nd note Gaddisms Wavelets.jl Image processing JuliaImages Getting started Tutorials Quickstart Arrays, Numbers, and Colors Conversions vs. views Arrays: more advanced indexing Packages under JuliaImages ImageAxes.jl ImageMetadata.jl ImageSegmentation.jl ImageTransformations.jl ImageFeatures.jl Demonstrations Image features ORB Descriptor Local Binary Patterns FREAK Descriptor BRIEF Descriptor BRISK Descriptor Object Detection using HOG Spatial transformation Image Difference View Cropping, Resizing and Rescaling Layer Compositing Histogram equalisation Histogram Matching Color channels RGB to HSV and thresholding Image Compression using SVD RGB to GrayScale Indexed image in 5 minutes Contours Edge detection using Sujoy Filter Contour Detection and Drawing Canny Edge Detection Detecting Corners Image morphology Morphological Operations Convex Hull, Filling, Thinning, ClearBorder Watershed Segmentation Algorithm Structural Similarity Index, Peak Signal-to-Noise Ratio Summary and function reference Comparison with other image processing frameworks FileIO.jl FileIO.jl Registry table Registering a new format Implementing loaders/savers World age issue Reference ImageBinarization.jl Function References OffsetArrays.jl For developers Reference ImageEdgeDetection.jl Function References ImageFiltering.jl Tutorial Examples Custom median filters Max min filters Template Matching Filtering images Kernels Image gradients Map windows Padding arrays Technical background Filtering functions ImageMorphology.jl Structuring element Morphology Operators closing dilate erode extreme_filter mgradient mlaplacian mreconstruct opening overbuild tophat underbuild bothat Reference CoordinateTransformations.jl API Reference TestImages.jl Image database testimage testimage_dip3e Function reference Contributing Phased Array System Toolbox EngeePhased System objects EngeePhased.BackscatterRadarTarTarget EngeePhased.ConformalArray EngeePhased.CrossedDipoleAntennaElement EngeePhased.CustomAntennaElement EngeePhased.GaussianAntennaElement EngeePhased.IsotropicAntennaElement EngeePhased.LinearFMWaveform EngeePhased.MFSKWaveform EngeePhased.OmnidirectionalMicrophoneElement EngeePhased.PartitionedArray EngeePhased.PhaseCodedWaveform EngeePhase.RangeDopplerResponse EngeePhased.ReplicatedSubarray EngeePhased.ShortDipoleAntennaElement EngeePhased.SincAntennaElement EngeePhased.StretchProcessor EngeePhased.UCA EngeePhased.ULA EngeePhased.URA EngeePhased.WidebandLOSChannel EngeePhased.SteppedFMWaveform Functions albersheim npwgnthresh rangeangle rocpfa rocsnr steervec Communication Systems EngeeComms System objects EngeeComms.BarkerCodeGenerator EngeeComms.ConvolutionalEncoder EngeeComms.OFDMDemodulatorBaseband EngeeComms.OFDMModulatorBaseband EngeeComms.PhaseFrequencyOffset EngeeComms.ConvolutionalInterleaver EngeeComms.ConvolutionalDeinterleaver EngeeComms.BPSKModulator EngeeComms.BPSKDemodulator Radio, Radar DigitalComm.jl Function list Examples Transmission of xQAM with additive white Gaussian noise Compute the theoretical BER for AWGN channel and various constellation size Plotting PSD of several multicarrier waveforms InterProcessCommunication.jl Semaphores Shared Memory Reference EngeeRadar System objects EngeeRadars.TwoRayChannel Working with maps GeoInterface.jl Simple Features History Traits interface Implementing GeoInterface Defaults API Packages NetCDF.jl Quickstart High-level interface Medium-level interface Short note on reading and writing NC_CHAR and NC_STRING variables Geodesy.jl GeoJSON.jl Miscellaneous System MATLAB.jl DuckDB.jl Maths Roots.jl Roots.jl Visualizing a step for various zero-finding algorithms Reference/API An overview of Roots NumericalIntegration.jl Turing.jl Using Turing Getting Started Probabilistic Programming in Thirty Seconds Guide Advanced Usage Automatic Differentiation Performance Tips Using DynamicHMC Sampler Visualization API Bijectors Advanced HMC For developers Overview The sampling interface How Turing implements AbstractMCMC Variational Inference Contributing Contributing Style Guide DynamicalSystems.jl Overarching tutorial for DynamicalSystems.jl Contents Contributor Guide Calculus.jl IterativeSolvers.jl Getting started Preconditioning Linear systems Conjugate Gradients (CG) Chebyshev iteration MINRES BiCGStab(l) IDR(s) Restarted GMRES LSMR LSQR Stationary methods QMR Eigenproblems (Inverse) power method Locally optimal block preconditioned conjugate gradient (LOBPCG) Golub-Kahan-Lanczos (SVDL) Iterative solvers as iterators TaylorSeries.jl Background User guide Examples Library Noise.jl Additive White Gaussian Multiplicative White Gaussian Salt and Pepper Poisson Quantization Function References NLsolve.jl StatsPlots.jl DecisionTree.jl LightGraphs.jl Graph Types LightGraphs Types Accessing Graph Properties Making and Modifying Graphs Reading and writing Graphs Operators Core Functions Plotting Graphs Path and Traversal Coloring Distance Centrality Measures Linear Algebra Matching Community Structures Graph Decomposition Integration with other packages Experimental Graph Algorithms Parallel Graph Algorithms Contributor Guide Developing Alternate Graph Types License Error Handling Measurements.jl Usage Examples Performance Development Appendix: Technical Details Data types LaTeXStrings.jl Tables.jl StaticArrays.jl API Quick Start Unitful.jl Highlighted features Types Defining new units Conversion/promotion Manipulating units How units are displayed Logarithmic scales Temperature scales Interoperability with the Dates standard library Extending Unitful Troubleshooting Useful libraries CategoricalArrays.jl Using CategoricalArrays Implementation details API Index ScikitLearn.jl Introduction Quick start guide Model Api Reading the Scikit-Learn Documentation Models Cross-validation Model Selection Pipelines DataFrames Saving models to disk Getting help Impute.jl Basics Walkthroughs Spatiotemporal Panel Datasets SVD Imputation API Declaring Missings Validation Filtering Imputation Chaining HypothesisTests.jl Methods Parametric tests Nonparametric tests Time series tests Multivariate tests KernelDensity.jl Docstrings StatsAPI.jl Docstrings PowerAnalyses.jl FreqTables.jl Docstrings BeautifulAlgorithms.jl