GNU Octave

• Preface
  • Acknowledgements
  • Citing Octave in Publications
  • How You Can Contribute to Octave
  • Distribution
• 1 A Brief Introduction to Octave
  • 1.1 Running Octave
  • 1.2 Simple Examples
    • 1.2.1 Elementary Calculations
    • 1.2.2 Creating a Matrix
    • 1.2.3 Matrix Arithmetic
    • 1.2.4 Solving Systems of Linear Equations
    • 1.2.5 Integrating Differential Equations
    • 1.2.6 Producing Graphical Output
    • 1.2.7 Help and Documentation
    • 1.2.8 Editing What You Have Typed
  • 1.3 Conventions
    • 1.3.1 Fonts
    • 1.3.2 Evaluation Notation
    • 1.3.3 Printing Notation
    • 1.3.4 Error Messages
    • 1.3.5 Format of Descriptions
      • 1.3.5.1 A Sample Function Description
      • 1.3.5.2 A Sample Command Description
• 2 Getting Started
  • 2.1 Invoking Octave from the Command Line
    • 2.1.1 Command Line Options
    • 2.1.2 Startup Files
  • 2.2 Quitting Octave
  • 2.3 Commands for Getting Help
  • 2.4 Command Line Editing
    • 2.4.1 Cursor Motion
    • 2.4.2 Killing and Yanking
    • 2.4.3 Commands for Changing Text
    • 2.4.4 Letting Readline Type for You
    • 2.4.5 Commands for Manipulating the History
    • 2.4.6 Customizing readline
    • 2.4.7 Customizing the Prompt
    • 2.4.8 Diary and Echo Commands
  • 2.5 How Octave Reports Errors
  • 2.6 Executable Octave Programs
    • 2.6.1 Passing Arguments to Executable Scripts
    • 2.6.2 Dual-Purpose Executable Scripts and Octave Functions
  • 2.7 Comments in Octave Programs
    • 2.7.1 Single Line Comments
    • 2.7.2 Block Comments
    • 2.7.3 Comments and the Help System
• 3 Data Types
  • 3.1 Built-in Data Types
    • 3.1.1 Numeric Objects
    • 3.1.2 Missing Data
    • 3.1.3 String Objects
    • 3.1.4 Data Structure Objects
    • 3.1.5 Cell Array Objects
  • 3.2 User-defined Data Types
  • 3.3 Object Sizes
• 4 Numeric Data Types
  • 4.1 Matrices
    • 4.1.1 Empty Matrices
  • 4.2 Ranges
  • 4.3 Single Precision Data Types
  • 4.4 Integer Data Types
    • 4.4.1 Integer Arithmetic
  • 4.5 Bit Manipulations
  • 4.6 Logical Values
  • 4.7 Promotion and Demotion of Data Types
  • 4.8 Predicates for Numeric Objects
• 5 Strings
  • 5.1 Escape Sequences in String Constants
  • 5.2 Character Arrays
  • 5.3 Creating Strings
    • 5.3.1 Concatenating Strings
    • 5.3.2 Converting Numerical Data to Strings
  • 5.4 Comparing Strings
  • 5.5 Manipulating Strings
  • 5.6 String Conversions
  • 5.7 Character Class Functions
• 6 Data Containers
  • 6.1 Structures
    • 6.1.1 Basic Usage and Examples
    • 6.1.2 Structure Arrays
    • 6.1.3 Creating Structures
    • 6.1.4 Manipulating Structures
    • 6.1.5 Processing Data in Structures
  • 6.2 containers.Map
  • 6.3 Cell Arrays
    • 6.3.1 Basic Usage of Cell Arrays
    • 6.3.2 Creating Cell Arrays
    • 6.3.3 Indexing Cell Arrays
    • 6.3.4 Cell Arrays of Strings
    • 6.3.5 Processing Data in Cell Arrays
  • 6.4 Comma Separated Lists
    • 6.4.1 Comma Separated Lists Generated from Cell Arrays
    • 6.4.2 Comma Separated Lists Generated from Structure Arrays
• 7 Variables
  • 7.1 Global Variables
  • 7.2 Persistent Variables
  • 7.3 Status of Variables
• 8 Expressions
  • 8.1 Index Expressions
    • 8.1.1 Advanced Indexing
  • 8.2 Calling Functions
    • 8.2.1 Call by Value
    • 8.2.2 Recursion
    • 8.2.3 Access via Handle
  • 8.3 Arithmetic Operators
  • 8.4 Comparison Operators
  • 8.5 Boolean Expressions
    • 8.5.1 Element-by-element Boolean Operators
    • 8.5.2 Short-circuit Boolean Operators
  • 8.6 Assignment Expressions
  • 8.7 Increment Operators
  • 8.8 Operator Precedence
• 9 Evaluation
  • 9.1 Calling a Function by its Name
  • 9.2 Evaluation in a Different Context
• 10 Statements
  • 10.1 The if Statement
  • 10.2 The switch Statement
    • 10.2.1 Notes for the C Programmer
  • 10.3 The while Statement
  • 10.4 The do-until Statement
  • 10.5 The for Statement
    • 10.5.1 Looping Over Structure Elements
  • 10.6 The break Statement
  • 10.7 The continue Statement
  • 10.8 The unwind_protect Statement
  • 10.9 The try Statement
  • 10.10 Continuation Lines
• 11 Functions and Scripts
  • 11.1 Introduction to Function and Script Files
  • 11.2 Defining Functions
  • 11.3 Returning from a Function
  • 11.4 Multiple Return Values
  • 11.5 Variable-length Return Lists
  • 11.6 Variable-length Argument Lists
  • 11.7 Ignoring Arguments
  • 11.8 Default Arguments
  • 11.9 Validating Arguments
    • 11.9.1 Validating the number of Arguments
    • 11.9.2 Validating the type of Arguments
    • 11.9.3 Parsing Arguments
  • 11.10 Function Files
    • 11.10.1 Manipulating the Load Path
    • 11.10.2 Subfunctions
    • 11.10.3 Private Functions
    • 11.10.4 Nested Functions
    • 11.10.5 Overloading and Autoloading
    • 11.10.6 Function Locking
    • 11.10.7 Function Precedence
  • 11.11 Script Files
    • 11.11.1 Publish Octave Script Files
    • 11.11.2 Publishing Markup
      • 11.11.2.1 Using Publishing Markup in Script Files
      • 11.11.2.2 Text Formatting
      • 11.11.2.3 Sections
      • 11.11.2.4 Preformatted Code
      • 11.11.2.5 Preformatted Text
      • 11.11.2.6 Bulleted Lists
      • 11.11.2.7 Numbered Lists
      • 11.11.2.8 Including File Content
      • 11.11.2.9 Including Graphics
      • 11.11.2.10 Including URLs
      • 11.11.2.11 Mathematical Equations
      • 11.11.2.12 HTML Markup
      • 11.11.2.13 LaTeX Markup
  • 11.12 Function Handles and Anonymous Functions
    • 11.12.1 Function Handles
    • 11.12.2 Anonymous Functions
  • 11.13 Command Syntax and Function Syntax
  • 11.14 Organization of Functions Distributed with Octave
• 12 Errors and Warnings
  • 12.1 Handling Errors
    • 12.1.1 Raising Errors
    • 12.1.2 Catching Errors
    • 12.1.3 Recovering From Errors
  • 12.2 Handling Warnings
    • 12.2.1 Issuing Warnings
    • 12.2.2 Enabling and Disabling Warnings
• 13 Debugging
  • 13.1 Entering Debug Mode
  • 13.2 Leaving Debug Mode
  • 13.3 Breakpoints
  • 13.4 Debug Mode
  • 13.5 Call Stack
  • 13.6 Profiling
  • 13.7 Profiler Example
• 14 Input and Output
  • 14.1 Basic Input and Output
    • 14.1.1 Terminal Output
      • 14.1.1.1 Paging Screen Output
    • 14.1.2 Terminal Input
    • 14.1.3 Simple File I/O
      • 14.1.3.1 Saving Data on Unexpected Exits
  • 14.2 C-Style I/O Functions
    • 14.2.1 Opening and Closing Files
    • 14.2.2 Simple Output
    • 14.2.3 Line-Oriented Input
    • 14.2.4 Formatted Output
    • 14.2.5 Output Conversion for Matrices
    • 14.2.6 Output Conversion Syntax
    • 14.2.7 Table of Output Conversions
    • 14.2.8 Integer Conversions
    • 14.2.9 Floating-Point Conversions
    • 14.2.10 Other Output Conversions
    • 14.2.11 Formatted Input
    • 14.2.12 Input Conversion Syntax
    • 14.2.13 Table of Input Conversions
    • 14.2.14 Numeric Input Conversions
    • 14.2.15 String Input Conversions
    • 14.2.16 Binary I/O
    • 14.2.17 Temporary Files
    • 14.2.18 End of File and Errors
    • 14.2.19 File Positioning
• 15 Plotting
  • 15.1 Introduction to Plotting
  • 15.2 High-Level Plotting
    • 15.2.1 Two-Dimensional Plots
      • 15.2.1.1 Axis Configuration
      • 15.2.1.2 Two-dimensional Function Plotting
      • 15.2.1.3 Two-dimensional Geometric Shapes
    • 15.2.2 Three-Dimensional Plots
      • 15.2.2.1 Aspect Ratio
      • 15.2.2.2 Three-dimensional Function Plotting
      • 15.2.2.3 Three-dimensional Geometric Shapes
    • 15.2.3 Plot Annotations
    • 15.2.4 Multiple Plots on One Page
    • 15.2.5 Multiple Plot Windows
    • 15.2.6 Manipulation of Plot Objects
    • 15.2.7 Manipulation of Plot Windows
    • 15.2.8 Use of the interpreter Property
      • 15.2.8.1 Degree Symbol
    • 15.2.9 Printing and Saving Plots
    • 15.2.10 Interacting with Plots
    • 15.2.11 Test Plotting Functions
  • 15.3 Graphics Data Structures
    • 15.3.1 Introduction to Graphics Structures
    • 15.3.2 Graphics Objects
      • 15.3.2.1 Creating Graphics Objects
      • 15.3.2.2 Handle Functions
    • 15.3.3 Graphics Object Properties
      • 15.3.3.1 Root Properties
      • 15.3.3.2 Figure Properties
      • 15.3.3.3 Axes Properties
      • 15.3.3.4 Legend Properties
      • 15.3.3.5 Line Properties
      • 15.3.3.6 Text Properties
      • 15.3.3.7 Image Properties
      • 15.3.3.8 Patch Properties
      • 15.3.3.9 Surface Properties
      • 15.3.3.10 Light Properties
      • 15.3.3.11 Uimenu Properties
      • 15.3.3.12 Uibuttongroup Properties
      • 15.3.3.13 Uicontextmenu Properties
      • 15.3.3.14 Uipanel Properties
      • 15.3.3.15 Uicontrol Properties
      • 15.3.3.16 Uitable Properties
      • 15.3.3.17 Uitoolbar Properties
      • 15.3.3.18 Uipushtool Properties
      • 15.3.3.19 Uitoggletool Properties
    • 15.3.4 Searching Properties
    • 15.3.5 Managing Default Properties
  • 15.4 Advanced Plotting
    • 15.4.1 Colors
    • 15.4.2 Line Styles
    • 15.4.3 Marker Styles
    • 15.4.4 Callbacks
    • 15.4.5 Application-defined Data
    • 15.4.6 Object Groups
      • 15.4.6.1 Data Sources in Object Groups
      • 15.4.6.2 Area Series
      • 15.4.6.3 Bar Series
      • 15.4.6.4 Contour Groups
      • 15.4.6.5 Error Bar Series
      • 15.4.6.6 Line Series
      • 15.4.6.7 Quiver Group
      • 15.4.6.8 Scatter Group
      • 15.4.6.9 Stair Group
      • 15.4.6.10 Stem Series
      • 15.4.6.11 Surface Group
    • 15.4.7 Transform Groups
    • 15.4.8 Graphics Toolkits
      • 15.4.8.1 Customizing Toolkit Behavior
      • 15.4.8.2 Hardware vs. Software Rendering
      • 15.4.8.3 Precision issues
• 16 Matrix Manipulation
  • 16.1 Finding Elements and Checking Conditions
  • 16.2 Rearranging Matrices
  • 16.3 Special Utility Matrices
  • 16.4 Famous Matrices
• 17 Arithmetic
  • 17.1 Exponents and Logarithms
  • 17.2 Complex Arithmetic
  • 17.3 Trigonometry
  • 17.4 Sums and Products
  • 17.5 Utility Functions
  • 17.6 Special Functions
  • 17.7 Rational Approximations
  • 17.8 Coordinate Transformations
  • 17.9 Mathematical Constants
• 18 Linear Algebra
  • 18.1 Techniques Used for Linear Algebra
  • 18.2 Basic Matrix Functions
  • 18.3 Matrix Factorizations
  • 18.4 Functions of a Matrix
  • 18.5 Specialized Solvers
• 19 Vectorization and Faster Code Execution
  • 19.1 Basic Vectorization
  • 19.2 Broadcasting
    • 19.2.1 Broadcasting and Legacy Code
  • 19.3 Function Application
  • 19.4 Accumulation
  • 19.5 JIT Compiler
  • 19.6 Miscellaneous Techniques
  • 19.7 Examples
• 20 Nonlinear Equations
  • 20.1 Solvers
  • 20.2 Minimizers
• 21 Diagonal and Permutation Matrices
  • 21.1 Creating and Manipulating Diagonal/Permutation Matrices
    • 21.1.1 Creating Diagonal Matrices
    • 21.1.2 Creating Permutation Matrices
    • 21.1.3 Explicit and Implicit Conversions
  • 21.2 Linear Algebra with Diagonal/Permutation Matrices
    • 21.2.1 Expressions Involving Diagonal Matrices
    • 21.2.2 Expressions Involving Permutation Matrices
  • 21.3 Functions That Are Aware of These Matrices
    • 21.3.1 Diagonal Matrix Functions
    • 21.3.2 Permutation Matrix Functions
  • 21.4 Examples of Usage
  • 21.5 Differences in Treatment of Zero Elements
• 22 Sparse Matrices
  • 22.1 Creation and Manipulation of Sparse Matrices
    • 22.1.1 Storage of Sparse Matrices
    • 22.1.2 Creating Sparse Matrices
    • 22.1.3 Finding Information about Sparse Matrices
    • 22.1.4 Basic Operators and Functions on Sparse Matrices
      • 22.1.4.1 Sparse Functions
      • 22.1.4.2 Return Types of Operators and Functions
      • 22.1.4.3 Mathematical Considerations
  • 22.2 Linear Algebra on Sparse Matrices
  • 22.3 Iterative Techniques Applied to Sparse Matrices
  • 22.4 Real Life Example using Sparse Matrices
• 23 Numerical Integration
  • 23.1 Functions of One Variable
  • 23.2 Orthogonal Collocation
  • 23.3 Functions of Multiple Variables
• 24 Differential Equations
  • 24.1 Ordinary Differential Equations
  • 24.2 Differential-Algebraic Equations
  • 24.3 Matlab-compatible solvers
• 25 Optimization
  • 25.1 Linear Programming
  • 25.2 Quadratic Programming
  • 25.3 Nonlinear Programming
  • 25.4 Linear Least Squares
• 26 Statistics
  • 26.1 Descriptive Statistics
  • 26.2 Statistics on Sliding Windows of Data
  • 26.3 Basic Statistical Functions
  • 26.4 Correlation and Regression Analysis
  • 26.5 Distributions
  • 26.6 Random Number Generation
• 27 Sets
  • 27.1 Set Operations
• 28 Polynomial Manipulations
  • 28.1 Evaluating Polynomials
  • 28.2 Finding Roots
  • 28.3 Products of Polynomials
  • 28.4 Derivatives / Integrals / Transforms
  • 28.5 Polynomial Interpolation
  • 28.6 Miscellaneous Functions
• 29 Interpolation
  • 29.1 One-dimensional Interpolation
  • 29.2 Multi-dimensional Interpolation
• 30 Geometry
  • 30.1 Delaunay Triangulation
    • 30.1.1 Plotting the Triangulation
    • 30.1.2 Identifying Points in Triangulation
  • 30.2 Voronoi Diagrams
  • 30.3 Convex Hull
  • 30.4 Interpolation on Scattered Data
  • 30.5 Vector Rotation Matrices
• 31 Signal Processing
• 32 Image Processing
  • 32.1 Loading and Saving Images
  • 32.2 Displaying Images
  • 32.3 Representing Images
  • 32.4 Plotting on top of Images
  • 32.5 Color Conversion
• 33 Audio Processing
  • 33.1 Audio File Utilities
  • 33.2 Audio Device Information
  • 33.3 Audio Player
    • 33.3.1 Playback
    • 33.3.2 Properties
  • 33.4 Audio Recorder
    • 33.4.1 Recording
    • 33.4.2 Data Retrieval
    • 33.4.3 Properties
  • 33.5 Audio Data Processing
• 34 Object Oriented Programming
  • 34.1 Creating a Class
  • 34.2 Class Methods
  • 34.3 Indexing Objects
    • 34.3.1 Defining Indexing And Indexed Assignment
    • 34.3.2 Indexed Assignment Optimization
  • 34.4 Overloading Objects
    • 34.4.1 Function Overloading
    • 34.4.2 Operator Overloading
    • 34.4.3 Precedence of Objects
  • 34.5 Inheritance and Aggregation
  • 34.6 classdef Classes
    • 34.6.1 Creating a classdef Class
    • 34.6.2 Properties
    • 34.6.3 Methods
    • 34.6.4 Inheritance
    • 34.6.5 Value Classes vs. Handle Classes
• 35 GUI Development
  • 35.1 I/O Dialogs
  • 35.2 Progress Bar
  • 35.3 UI Elements
  • 35.4 GUI Utility Functions
  • 35.5 User-Defined Preferences
  • 35.6 Octave Workspace Windows
• 36 System Utilities
  • 36.1 Timing Utilities
  • 36.2 Filesystem Utilities
  • 36.3 File Archiving Utilities
  • 36.4 Networking Utilities
    • 36.4.1 FTP Objects
    • 36.4.2 WWW Access
    • 36.4.3 Base64 and Binary Data Transmission
  • 36.5 Controlling Subprocesses
  • 36.6 Process, Group, and User IDs
  • 36.7 Environment Variables
  • 36.8 Current Working Directory
  • 36.9 Password Database Functions
  • 36.10 Group Database Functions
  • 36.11 System Information
  • 36.12 Hashing Functions
• 37 Packages
  • 37.1 Installing and Removing Packages
  • 37.2 Using Packages
  • 37.3 Administrating Packages
  • 37.4 Creating Packages
    • 37.4.1 The DESCRIPTION File
    • 37.4.2 The INDEX File
    • 37.4.3 PKG_ADD and PKG_DEL Directives
    • 37.4.4 Missing Components
• Appendix A External Code Interface
  • A.1 Oct-Files
    • A.1.1 Getting Started with Oct-Files
    • A.1.2 Matrices and Arrays in Oct-Files
    • A.1.3 Character Strings in Oct-Files
    • A.1.4 Cell Arrays in Oct-Files
    • A.1.5 Structures in Oct-Files
    • A.1.6 Sparse Matrices in Oct-Files
      • A.1.6.1 Array and Sparse Class Differences
      • A.1.6.2 Creating Sparse Matrices in Oct-Files
      • A.1.6.3 Using Sparse Matrices in Oct-Files
    • A.1.7 Accessing Global Variables in Oct-Files
    • A.1.8 Calling Octave Functions from Oct-Files
    • A.1.9 Calling External Code from Oct-Files
    • A.1.10 Allocating Local Memory in Oct-Files
    • A.1.11 Input Parameter Checking in Oct-Files
    • A.1.12 Exception and Error Handling in Oct-Files
    • A.1.13 Documentation and Testing of Oct-Files
  • A.2 Mex-Files
    • A.2.1 Getting Started with Mex-Files
    • A.2.2 Working with Matrices and Arrays in Mex-Files
    • A.2.3 Character Strings in Mex-Files
    • A.2.4 Cell Arrays with Mex-Files
    • A.2.5 Structures with Mex-Files
    • A.2.6 Sparse Matrices with Mex-Files
    • A.2.7 Calling Other Functions in Mex-Files
  • A.3 Standalone Programs
  • A.4 Java Interface
    • A.4.1 Making Java Classes Available
    • A.4.2 How to use Java from within Octave
    • A.4.3 Set up the JVM
    • A.4.4 Java Interface Functions
• Appendix B Test and Demo Functions
  • B.1 Test Functions
  • B.2 Demonstration Functions
• Appendix C Obsolete Functions
• Appendix D Known Causes of Trouble
  • D.1 Actual Bugs We Haven’t Fixed Yet
  • D.2 Reporting Bugs
    • D.2.1 Have You Found a Bug?
    • D.2.2 Where to Report Bugs
    • D.2.3 How to Report Bugs
    • D.2.4 Sending Patches for Octave
  • D.3 How To Get Help with Octave
  • D.4 How to Distinguish Between Octave and Matlab
• Appendix E Installing Octave
  • E.1 Build Dependencies
    • E.1.1 Obtaining the Dependencies Automatically
    • E.1.2 Build Tools
    • E.1.3 External Packages
  • E.2 Running Configure and Make
  • E.3 Compiling Octave with 64-bit Indexing
  • E.4 Installation Problems
• Appendix F Grammar and Parser
  • F.1 Keywords
  • F.2 Parser
• Appendix G GNU GENERAL PUBLIC LICENSE
• Concept Index
• Function Index
• Operator Index
• Graphics Properties Index