Applied 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 Distributions 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 GLM Examples GLM API RDatasets.jl Approximation Polynomials.jl Sections Polynomials.jl Polynomials Reference/API Types of polynomials Polynomial Chebyshev Polynomials 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 GLM Examples GLM API LsqFit.jl LsqFit Getting Started LsqFit Tutorial LsqFit API Optimisation JuMP.jl Installation Guide Should you use JuMP? JuMP Tutorials JuMP Getting started Introduction in структуру руководств JuMP 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 JuMP Performance tips Performance problems with sum-if formulations Transitioning from MATLAB Linear programs Introduction to linear programs 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 for linear programs 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 in JuMP Sensitivity analysis of a linear program Basis matrices Computing the duals of a mixed-integer program Nonlinear programs Introduction to nonlinear programs Simple examples Portfolio optimization Rocket Control Optimal control for a Space Shuttle reentry trajectory Tips for nonlinear programs User-defined Hessians Nested optimization problems Computing Hessians Mixed complementarity problems Classifiers Automatic differentiation of user-defined operators Conic programs Introduction to conic programs Primal and dual warm-starts Tips for conic programs Simple semidefinite programming examples Dualization Arbitrary precision arithmetic Logistic regression in JuMP Experiment design Minimal ellipses Ellipsoid approximation Quantum state discrimination Algorithms in JuMP Benders decomposition Column generation Traveling Salesperson Problem Parallelism Applications Power Systems Optimal power flow Serving web apps Two-stage stochastic programs JuMP Manual Models in JuMP JuMP Variables Constraints Expressions Objectives Containers Solutions Solver-independent Callbacks Complex number support Nonlinear Modeling 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OptimizationState OptimizationStats Optimization Common Solver Options (Solve Keyword Arguments) Ipopt.jl GLPK.jl HiGHS.jl HiGHS Getting started Terminology Symbolic calculations in Symbolics 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 Symbolics Examples Mixed Symbolic-Numeric Perturbation Theory Symbolics 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 Symbolics Frequently Asked Questions Comparison of Julia’s Symbolics.jl vs SymPy for Symbolic Computation Neural networks Flux.jl Flux 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 Flux Performance Tips The Julia Ecosystem around Flux 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 Flux Tutorials Tutorial: Linear Regression Logistic Regression in Flux 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 ONNX API How to contribute Control systems ControlSystems.jl ControlSystems Getting Started ControlSystems Introduction Creating Systems Performance considerations ControlSystems Noteworthy Differences from other Languages ControlSystems Examples Other ControlSystems Examples Analysis of linear control systems Smith predictor Iterative-Learning Control Properties of delay systems Automatic Differentiation in ControlSystems ControlSystems Functions Constructing systems Analysis Synthesis Time and Frequency response analysis ControlSystems Plotting functions Nonlinear functionality ControlSystems Index EngeeControlSystems Functions Mathematical models of dynamical systems Representations of linear system models Linear stationary systems frd Pid PidStd Properties of models isct isdt Transformations of structural schemes feedback parallel series Transitions between continuous and discrete systems c2d d2c d2d Operating points and linearization trim Synthesis of control systems PID regulation pidtune ControlSystemIdentification.jl Identification data Statespace model estimation Transfer function estimation Impulse-response estimation Transfer-function estimation using spectral techniques ControlSystemIdentification Validation Identification of nonlinear models ControlSystemIdentification 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 FuzzyLogic 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 ModelPredictiveControl Index ReinforcementLearning.jl ReinforcementLearning Tutorial How to write a customized environment? How to implement a new algorithm How to use hooks? Episodic vs Non-episodic environments ReinforcementLearning 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 DSP 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 PortAudio Internals JuliaMusic JuliaMusic Basics Basic MIDI structures Notes Note Tools Quantizing & Humanizing Music data extraction JuliaMusic Visualization Plotting Notes Printing into a Score using MuseScore Motif sequence Motif sequence generation Music motifs Becoming a better drummer blog Combining basic drum rhythms Garibaldi’s Deuces "leg + arm" Gaddisms from the thirty-second notes Wavelets.jl EngeeDSP Functions Signal generation, analysis, and preprocessing chirp demod diric gauspuls gmonopuls medfilt1 modulate pulstran rectpuls sawtooth shiftdata sinc square tripuls unshiftdata Digital and analogue filters bandpass bandstop butter cheby1 cheby2 ctf2zp decimate downsample ellip fillgaps filtfilt fir1 fir2 fircls fircls1 firls firpm firpmord freqz gaussdesign grpdelay highpass impz impzlength interp intfilt isallpass islinphase ismaxphase isminphase isstable lowpass phasedelay rcosdesign resample residuez scaleFilterSections sgolay sos2cell sos2ctf sos2ss sos2tf sos2zp sosfilt ss2sos ss2zp tf2latc tf2sos tf2ss tf2zp tf2zpk upfirdn upsample yulewalk zp2ctf zp2sos zp2ss zp2tf Mathematics abs angle coeffs conv conv2 cos deconv fft fft2 fftshift filter ifft ifft2 ifftshift interp1 pchip randn sin spline ss2tf Matrices and arrays circshift Spectral analysis barthannwin bartlett blackman blackmanharris bohmanwin chebwin dpss flattopwin gausswin hamming hann kaiser nuttallwin parzenwin rectwin taylorwin triang tukeywin Data import and analysis corrcoef cov cummax cummin detrend max mean median min movmad movmean movmedian rms smoothdata std var xcorr xcov Transformations, correlation, and modeling ac2poly ac2rc arburg arcov armcov aryule bitrevorder cceps cconv convmtx corrmtx czt dct dftmtx digitrevorder emd envelope hilbert idct invfreqs invfreqz istft levinson lpc lsf2poly poly2rc prony pspectrum rc2is rc2lar rc2poly rceps spectrogram stft vmd xcorr2 poly2lsf poly2ac rlevinson Filter development and analysis allpass2wdf designHighpassFIR designHighpassIIR designMultirateFIR designNotchPeakIIR Measuring and highlighting features alignsignals bandpower cusum dtw dutycycle edr enbw falltime finddelay findpeaks findsignal instbw instfreq meanfreq medfreq midcross obw overshoot peak2peak peak2rms powerbw pulseperiod pulsesep pulsewidth risetime rssq settlingtime sfdr sinad slewrate snr spectralCrest spectralEntropy spectralFlatness spectralKurtosis spectralSkewness statelevels toi undershoot System objects EngeeDSP.CICDecimator EngeeDSP.CICInterpolator EngeeDSP.FIRFilter EngeeDSP.NotchPeakFilter EngeeDSP.spectrumAnalyzer EngeeDSP.gpsWaveformGenerator EngeeDSP.VariableBandwidthFIRFilter Image processing in JuliaImages JuliaImages Julia Images Getting started Julia Images Tutorials Julia Images 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 Julia Images 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 Introduction Registry table Registering a new format Implementing loaders/savers World age issue FileIO Reference ImageBinarization.jl ImageBinarization Function References OffsetArrays.jl OffsetArrays For developers OffsetArrays Reference ImageEdgeDetection.jl ImageEdgeDetection Function References ImageFiltering.jl ImageFiltering Tutorial ImageFiltering 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 ImageMorphology Reference CoordinateTransformations.jl CoordinateTransformations API Reference TestImages.jl Image database testimage testimage_dip3e TestImages Function reference TestImages Contributing Phased array antennas EngeePhased System objects EngeePhased.BackscatterRadarTarget EngeePhased.ConformalArray EngeePhased.CrossedDipoleAntennaElement EngeePhased.CustomAntennaElement EngeePhased.GaussianAntennaElement EngeePhased.IsotropicAntennaElement EngeePhased.LinearFMWaveform EngeePhased.MFSKWaveform EngeePhased.OmnidirectionalMicrophoneElement EngeePhased.PartitionedArray EngeePhased.PhaseCodedWaveform EngeePhased.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.BPSKModulatorBaseband EngeeComms.BPSKDemodulatorBaseband EngeeComms.AWGN EngeeComms.BernoulliBinaryGenerator EngeeComms.DQPSK_DemodulatorBaseband EngeeComms.DQPSK_ModulatorBaseband EngeeComms.ErrorRateCalculation EngeeComms.EVM EngeeComms.FreeSpacePathLoss EngeeComms.GeneralQAMDemodulatorBaseband EngeeComms.GeneralQAMModulatorBaseband EngeeComms.QPSKBasebandDemodulator EngeeComms.RaisedCosineReceiveFilter EngeeComms.RaisedCosineTransmitFilter EngeeComms.RandomIntegerGenerator EngeeComms.Repeat EngeeComms.RectangularQAMModulatorBaseband Radios, Radars DigitalComm.jl Function list DigitalComm 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 InterProcessCommunication Reference EngeeRF Functions abcd2h abcd2s abcd2y abcd2z abcdparameters add amplifier analyze attenuator capacitor circuit clone g2h gamma2z gparameters groupdelay h2abcd h2g h2s h2y h2z hparameters inductor lcladder mixerIMT modulator noisefigure nport phaseshift resistor rfbudget rfckt.coaxial rfckt.parallelplate rfckt.rlcgline rfckt.twowire rfdata.data rffilter rfinterp1 rfplot richards s2abcd s2h s2s s2t s2y s2z seriesRLC setports setterminals shuntRLC sparameters t2s tparameters txlineCPW txlineElectricalLength txlineLumped txlineMicrostrip txlineStripline txlineTwoWire y2abcd y2h y2s y2z yparameters z2abcd z2gamma z2h z2s z2y zparameters EngeeRadar System objects EngeeRadars.TwoRayChannel Working with maps GeoInterface.jl Simple Features History Traits interface Implementing GeoInterface Defaults GeoInterface API Packages NetCDF.jl NetCDF 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 Sections Roots.jl Visualizing a step for various zero-finding algorithms Roots Reference/API An overview of Roots NumericalIntegration.jl Turing.jl Using Turing Turing Getting Started Probabilistic Programming in Thirty Seconds Turing Guide Turing Advanced Usage Automatic Differentiation in Turing Turing Performance Tips Using DynamicHMC Sampler Visualization Turing API Bijectors Advanced HMC Turing For developers Turing Overview The sampling interface How Turing implements AbstractMCMC Variational Inference Turing Contributing Turing Contributing Guide Turing Style Guide DynamicalSystems.jl Overarching tutorial for DynamicalSystems.jl Contents DynamicalSystems Contributor Guide Calculus.jl IterativeSolvers.jl IterativeSolvers Getting started IterativeSolvers 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 TaylorSeries User guide TaylorSeries Examples Library Noise.jl Additive White Gaussian Multiplicative White Gaussian Salt and Pepper Poisson Quantization Noise 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 LightGraphs Plotting Path and Traversal Coloring Distance Centrality Measures LightGraphs Linear Algebra Matching Community Structures Graph Decomposition Integration with other packages Experimental Graph Algorithms Parallel Graph Algorithms Contributor Guide Developing Alternate Graph Types LightGraphs License Error Handling Measurements.jl Usage Examples Performance Development Appendix: Technical Details Data types LaTeXStrings.jl Tables.jl StaticArrays.jl StaticArrays API StaticArrays 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 to ScikitLearn Quick start guide Model Api Reading the Scikit-Learn Documentation Models in ScikitLearn Cross-validation Model Selection Pipelines DataFrames Saving models to disk Getting help Impute.jl Basics Walkthroughs Spatiotemporal Panel Datasets SVD Imputation Impute API Declaring Missings Impute Validation Filtering Imputation Chaining HypothesisTests.jl Methods Parametric tests Nonparametric tests Time series tests Multivariate tests KernelDensity.jl KernelDensity Docstrings StatsAPI.jl StatsAPI Docstrings PowerAnalyses.jl FreqTables.jl FreqTables Docstrings BeautifulAlgorithms.jl