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Table of Contents
CppAD: A Package for Differentiation of C++ Algorithms
CppAD: A Package for Differentiation of C++ Algorithms
Table of Contents
CppAD Download, Test, and Installation Instructions
CppAD Download, Test, and Installation Instructions
Unix Download, Test and Installation
Unix Download, Test and Installation
Using Subversion To Download Source Code
Windows Download and Test
An Introduction by Example to Algorithmic Differentiation
An Introduction by Example to Algorithmic Differentiation
A Simple Program Using CppAD to Compute Derivatives
Second Order Exponential Approximation
Second Order Exponential Approximation
exp_2: Implementation
exp_2: Test
exp_2: Operation Sequence and Zero Order Forward Mode
exp_2: Operation Sequence and Zero Order Forward Mode
exp_2: Verify Zero Order Forward Sweep
exp_2: First Order Forward Mode
exp_2: First Order Forward Mode
exp_2: Verify First Order Forward Sweep
exp_2: First Order Reverse Mode
exp_2: First Order Reverse Mode
exp_2: Verify First Order Reverse Sweep
exp_2: Second Order Forward Mode
exp_2: Second Order Forward Mode
exp_2: Verify Second Order Forward Sweep
exp_2: Second Order Reverse Mode
exp_2: Second Order Reverse Mode
exp_2: Verify Second Order Reverse Sweep
exp_2: CppAD Forward and Reverse Sweeps
An Epsilon Accurate Exponential Approximation
An Epsilon Accurate Exponential Approximation
exp_eps: Implementation
exp_eps: Test of exp_eps
exp_eps: Operation Sequence and Zero Order Forward Sweep
exp_eps: Operation Sequence and Zero Order Forward Sweep
exp_eps: Verify Zero Order Forward Sweep
exp_eps: First Order Forward Sweep
exp_eps: First Order Forward Sweep
exp_eps: Verify First Order Forward Sweep
exp_eps: First Order Reverse Sweep
exp_eps: First Order Reverse Sweep
exp_eps: Verify First Order Reverse Sweep
exp_eps: Second Order Forward Mode
exp_eps: Second Order Forward Mode
exp_eps: Verify Second Order Forward Sweep
exp_eps: Second Order Reverse Sweep
exp_eps: Second Order Reverse Sweep
exp_eps: Verify Second Order Reverse Sweep
exp_eps: CppAD Forward and Reverse Sweeps
Run the exp_2 and exp_eps Tests
AD Objects
AD Objects
AD Default Constructor
AD Default Constructor
Default AD Constructor: Example and Test
AD Copy Constructor and Assignment Operator
AD Copy Constructor and Assignment Operator
AD Copy Constructor: Example and Test
AD Constructor From Base Type: Example and Test
AD Assignment Operator: Example and Test
Conversion and Printing of AD Objects
Conversion and Printing of AD Objects
Convert From an AD Type to its Base Type
Convert From an AD Type to its Base Type
Convert From AD to its Base Type: Example and Test
Convert From AD to Integer
Convert From AD to Integer
Convert From AD to Integer: Example and Test
AD Output Stream Operator
AD Output Stream Operator
AD Output Operator: Example and Test
Printing AD Values During Forward Mode
Printing AD Values During Forward Mode
Printing During Forward Mode: Example and Test
Convert an AD Variable to a Parameter
Convert an AD Variable to a Parameter
Convert an AD Variable to a Parameter: Example and Test
AD Valued Operations and Functions
AD Valued Operations and Functions
AD Arithmetic Operators and Computed Assignments
AD Arithmetic Operators and Computed Assignments
AD Unary Plus Operator
AD Unary Plus Operator
AD Unary Plus Operator: Example and Test
AD Unary Minus Operator
AD Unary Minus Operator
AD Unary Minus Operator: Example and Test
AD Binary Arithmetic Operators
AD Binary Arithmetic Operators
AD Binary Addition: Example and Test
AD Binary Subtraction: Example and Test
AD Binary Multiplication: Example and Test
AD Binary Division: Example and Test
AD Computed Assignment Operators
AD Computed Assignment Operators
AD Computed Assignment Addition: Example and Test
AD Computed Assignment Subtraction: Example and Test
AD Computed Assignment Multiplication: Example and Test
AD Computed Assignment Division: Example and Test
AD Standard Math Unary Functions
AD Standard Math Unary Functions
The AD acos Function: Example and Test
The AD asin Function: Example and Test
The AD atan Function: Example and Test
The AD cos Function: Example and Test
The AD cosh Function: Example and Test
The AD exp Function: Example and Test
The AD log Function: Example and Test
The AD log10 Function: Example and Test
The AD sin Function: Example and Test
The AD sinh Function: Example and Test
The AD sqrt Function: Example and Test
The AD tan Function: Example and Test
Other AD Math Functions
Other AD Math Functions
AD Absolute Value Function
AD Absolute Value Function
AD Absolute Value Function: Example and Test
AD Two Argument Inverse Tangent Function
AD Two Argument Inverse Tangent Function
The AD atan2 Function: Example and Test
The AD Error Function
The AD Error Function
The AD erf Function: Example and Test
The AD Power Function
The AD Power Function
The AD Power Function: Example and Test
The Pow Integer Exponent: Example and Test
AD Conditional Expressions
AD Conditional Expressions
Conditional Expressions: Example and Test
Discrete AD Functions
Discrete AD Functions
Taping Array Index Operation: Example and Test
Interpolation With Out Retaping: Example and Test
Interpolation With Retaping: Example and Test
Bool Valued Operations and Functions with AD Arguments
Bool Valued Operations and Functions with AD Arguments
AD Binary Comparison Operators
AD Binary Comparison Operators
AD Binary Comparison Operators: Example and Test
Compare AD and Base Objects for Nearly Equal
Compare AD and Base Objects for Nearly Equal
Compare AD with Base Objects: Example and Test
AD Boolean Functions
AD Boolean Functions
AD Boolean Functions: Example and Test
Is an AD Object a Parameter or Variable
Is an AD Object a Parameter or Variable
AD Parameter and Variable Functions: Example and Test
Check if Equal and Correspond to Same Operation Sequence
Check if Equal and Correspond to Same Operation Sequence
EqualOpSeq: Example and Test
AD Vectors that Record Index Operations
AD Vectors that Record Index Operations
AD Vectors that Record Index Operations: Example and Test
AD<Base> Requirements for Base Type
AD<Base> Requirements for Base Type
Enable use of AD<Base> where Base is std::complex<double>
Enable use of AD<Base> where Base is std::complex<double>
Complex Polynomial: Example and Test
Not Complex Differentiable: Example and Test
Enable use of AD<Base> where Base is Adolc's adouble Type
Enable use of AD<Base> where Base is Adolc's adouble Type
Using Adolc with Multiple Levels of Taping: Example and Test
ADFun Objects
ADFun Objects
Declare Independent Variables and Start Recording
Declare Independent Variables and Start Recording
Independent and ADFun Constructor: Example and Test
Construct an ADFun Object and Stop Recording
Stop Recording and Store Operation Sequence
ADFun Sequence Properties
ADFun Sequence Properties
ADFun Sequence Properties: Example and Test
Evaluate ADFun Functions, Derivatives, and Sparsity Patterns
Evaluate ADFun Functions, Derivatives, and Sparsity Patterns
Forward Mode
Forward Mode
Zero Order Forward Mode: Function Values
First Order Forward Mode: Derivative Values
Any Order Forward Mode
Number Taylor Coefficients, Per Variable, Currently Stored
Comparison Changes During Zero Order Forward Mode
Comparison Changes During Zero Order Forward Mode
CompareChange and Re-Tape: Example and Test
Controlling taylor_ Coefficients Memory Allocation
Forward Mode: Example and Test
Reverse Mode
Reverse Mode
First Order Reverse Mode
First Order Reverse Mode
First Order Reverse Mode: Example and Test
Second Order Reverse Mode
Second Order Reverse Mode
Second Order Reverse ModeExample and Test
Hessian Times Direction: Example and Test
Any Order Reverse Mode
Any Order Reverse Mode
Any Order Reverse Mode: Example and Test
Calculating Sparsity Patterns
Calculating Sparsity Patterns
Jacobian Sparsity Pattern: Forward Mode
Jacobian Sparsity Pattern: Forward Mode
Forward Mode Jacobian Sparsity: Example and Test
Jacobian Sparsity Pattern: Reverse Mode
Jacobian Sparsity Pattern: Reverse Mode
Reverse Mode Jacobian Sparsity: Example and Test
Hessian Sparsity Pattern: Reverse Mode
Hessian Sparsity Pattern: Reverse Mode
Reverse Mode Hessian Sparsity: Example and Test
First and Second Derivatives: Easy Drivers
First and Second Derivatives: Easy Drivers
Jacobian: Driver Routine
Jacobian: Driver Routine
Jacobian: Example and Test
First Order Partial Derivative: Driver Routine
First Order Partial Derivative: Driver Routine
First Order Partial Driver: Example and Test
First Order Derivative: Driver Routine
First Order Derivative: Driver Routine
First Order Derivative Driver: Example and Test
Hessian: Easy Driver
Hessian: Easy Driver
Hessian: Example and Test
Hessian of Lagrangian and ADFun Default Constructor: Example and Test
Forward Mode Second Partial Derivative Driver
Forward Mode Second Partial Derivative Driver
Subset of Second Order Partials: Example and Test
Reverse Mode Second Partial Derivative Driver
Reverse Mode Second Partial Derivative Driver
Second Partials Reverse Driver: Example and Test
Sparse Jacobian: Easy Driver
Sparse Jacobian: Easy Driver
Sparse Jacobian: Example and Test
Sparse Hessian: Easy Driver
Sparse Hessian: Easy Driver
Sparse Hessian: Example and Test
Check an ADFun Sequence of Operations
Check an ADFun Sequence of Operations
ADFun Check and Re-Tape: Example and Test
OpenMP Maximum Thread Number
OpenMP Maximum Thread Number
Compile and Run the OpenMP Test
Compile and Run the OpenMP Test
A Simple Parallel Loop
Multi-Threaded Newton's Method Main Program
Multi-Threaded Newton's Method Main Program
Multi-Threaded Newton's Method Routine
OpenMP Multi-Threading Newton's Method Source Code
Sum of 1/i Main Program
ADFun Object Deprecated Member Functions
The CppAD General Purpose Library
The CppAD General Purpose Library
Replacing the CppAD Error Handler
Replacing the CppAD Error Handler
Replacing The CppAD Error Handler: Example and Test
CppAD Assertions During Execution
Determine if Two Values Are Nearly Equal
Determine if Two Values Are Nearly Equal
NearEqual Function: Example and Test
Run One Speed Test and Return Results
Run One Speed Test and Return Results
speed_test: Example and test
Run One Speed Test and Print Results
Run One Speed Test and Print Results
Example Use of SpeedTest
Definition of a Numeric Type
Definition of a Numeric Type
The NumericType: Example and Test
Check NumericType Class Concept
Check NumericType Class Concept
The CheckNumericType Function: Example and Test
Definition of a Simple Vector
Definition of a Simple Vector
Simple Vector Template Class: Example and Test
Check Simple Vector Concept
Check Simple Vector Concept
The CheckSimpleVector Function: Example and Test
Obtain Nan and Determine if a Value is Nan
Obtain Nan and Determine if a Value is Nan
nan: Example and Test
The Integer Power Function
Evaluate a Polynomial or its Derivative
Evaluate a Polynomial or its Derivative
Polynomial Evaluation: Example and Test
Source: Poly
Compute Determinants and Solve Equations by LU Factorization
Compute Determinants and Solve Equations by LU Factorization
Compute Determinant and Solve Linear Equations
Compute Determinant and Solve Linear Equations
LuSolve With Complex Arguments: Example and Test
Source: LuSolve
LU Factorization of A Square Matrix
LU Factorization of A Square Matrix
LuFactor: Example and Test
Source: LuFactor
Invert an LU Factored Equation
Invert an LU Factored Equation
LuInvert: Example and Test
Source: LuInvert
One DimensionalRomberg Integration
One DimensionalRomberg Integration
One Dimensional Romberg Integration: Example and Test
Multi-dimensional Romberg Integration
Multi-dimensional Romberg Integration
One Dimensional Romberg Integration: Example and Test
An Embedded 4th and 5th Order Runge-Kutta ODE Solver
An Embedded 4th and 5th Order Runge-Kutta ODE Solver
Runge45: Example and Test
A 3rd and 4th Order Rosenbrock ODE Solver
A 3rd and 4th Order Rosenbrock ODE Solver
Rosen34: Example and Test
An Error Controller for ODE Solvers
An Error Controller for ODE Solvers
OdeErrControl: Example and Test
OdeErrControl: Example and Test Using Maxabs Argument
An Arbitrary Order Gear Method
An Arbitrary Order Gear Method
OdeGear: Example and Test
An Error Controller for Gear's Ode Solvers
An Error Controller for Gear's Ode Solvers
OdeGearControl: Example and Test
Computing Jacobian and Hessian of Bender's Reduced Objective
Computing Jacobian and Hessian of Bender's Reduced Objective
BenderQuad: Example and Test
LU Factorization of A Square Matrix and Stability Calculation
LU Factorization of A Square Matrix and Stability Calculation
LuRatio: Example and Test
Float and Double Standard Math Unary Functions
The CppAD::vector Template Class
The CppAD::vector Template Class
CppAD::vector Template Class: Example and Test
CppAD::vectorBool Class: Example and Test
Routines That Track Use of New and Delete
Routines That Track Use of New and Delete
Tracking Use of New and Delete: Example and Test
Preprocessor Definitions Used by CppAD
Examples
Examples
General Examples
General Examples
Nonlinear Programming Using Ipopt and CppAD
Nonlinear Programming Using Ipopt and CppAD
Nonlinear Programming Using CppAD and Ipopt: Example and Test
Interfacing to C: Example and Test
Gradient of Determinant Using Expansion by Minors: Example and Test
Gradient of Determinant Using Lu Factorization: Example and Test
Gradient of Determinant Using Expansion by Minors: Example and Test
Gradient of Determinant Using LU Factorization: Example and Test
A Stiff Ode: Example and Test
Taylor's Ode Solver: An Example and Test
Using Adolc with Taylor's Ode Solver: An Example and Test
Example Differentiating a Stack Machine Interpreter
Using Multiple Levels of AD
Using Multiple Levels of AD
Multiple Tapes: Example and Test
Utility Routines used by CppAD Examples
Utility Routines used by CppAD Examples
Program That Runs the CppAD Examples
Program That Runs the Speed Examples
Lu Factor and Solve with Recorded Pivoting
Lu Factor and Solve with Recorded Pivoting
Lu Factor and Solve With Recorded Pivoting: Example and Test
List of All the CppAD Examples
Choosing The Vector Testing Template Class
Appendix
Appendix
Frequently Asked Questions and Answers
Speed Test Routines
Speed Test Routines
Speed Testing Main Program
Speed Testing Main Program
Speed Testing Gradient of Determinant Using Lu Factorization
Speed Testing Gradient of Determinant by Minor Expansion
Speed Testing Second Derivative of a Polynomial
Speed Testing Sparse Hessian
Speed Testing Gradient of Ode Solution
Speed Testing Utilities
Speed Testing Utilities
Simulate a [0,1] Uniform Random Variate
Simulate a [0,1] Uniform Random Variate
Source: uniform_01
Determinant of a Minor
Determinant of a Minor
Determinant of a Minor: Example and Test
Source: det_of_minor
Determinant Using Expansion by Minors
Determinant Using Expansion by Minors
Determinant Using Expansion by Minors: Example and Test
Source: det_by_minor
Determinant Using Expansion by Lu Factorization
Determinant Using Expansion by Lu Factorization
Determinant Using Lu Factorization: Example and Test
Source: det_by_lu
Check Determinant of 3 by 3 matrix
Check Determinant of 3 by 3 matrix
Source: det_33
Check Gradient of Determinant of 3 by 3 matrix
Check Gradient of Determinant of 3 by 3 matrix
Source: det_grad_33
Evaluate a Function Defined in Terms of an ODE
Evaluate a Function Defined in Terms of an ODE
ode_evaluate: Example and test
Source: ode_evaluate
Evaluate a Function That Has a Sparse Hessian
Evaluate a Function That Has a Sparse Hessian
sparse_evaluate: Example and test
Source: sparse_evaluate
Speed Test Functions in Double
Speed Test Functions in Double
Double Speed: Determinant by Minor Expansion
Double Speed: Determinant Using Lu Factorization
Double Speed: Ode Solution
Double Speed: Evaluate a Polynomial
Double Speed: Sparse Hessian
Speed Test Derivatives Using Adolc
Speed Test Derivatives Using Adolc
Adolc Speed: Gradient of Determinant by Minor Expansion
Adolc Speed: Gradient of Determinant Using Lu Factorization
Adolc Speed: Ode
Adolc Speed: Second Derivative of a Polynomial
Adolc Speed: Sparse Hessian
Speed Test Derivatives Using CppAD
Speed Test Derivatives Using CppAD
CppAD Speed: Gradient of Determinant by Minor Expansion
CppAD Speed: Gradient of Determinant Using Lu Factorization
CppAD Speed: Gradient of Ode Solution
CppAD Speed: Second Derivative of a Polynomial
CppAD Speed: Sparse Hessian
Speed Test Derivatives Using Fadbad
Speed Test Derivatives Using Fadbad
Fadbad Speed: Gradient of Determinant by Minor Expansion
Fadbad Speed: Gradient of Determinant Using Lu Factorization
Fadbad Speed: Ode
Fadbad Speed: Second Derivative of a Polynomial
Fadbad Speed: Sparse Hessian
Speed Test Derivatives Using Sacado
Speed Test Derivatives Using Sacado
Sacado Speed: Gradient of Determinant by Minor Expansion
Sacado Speed: Gradient of Determinant Using Lu Factorization
Sacado Speed: Gradient of Ode Solution
Sacado Speed: Second Derivative of a Polynomial
Sacado Speed: Sparse Hessian
The Theory of Derivative Calculations
The Theory of Derivative Calculations
The Theory of Forward Mode
The Theory of Forward Mode
Exponential Function Forward Taylor Polynomial Theory
Logarithm Function Forward Taylor Polynomial Theory
Square Root Function Forward Taylor Polynomial Theory
Trigonometric and Hyperbolic Sine and Cosine Forward Theory
Arctangent Function Forward Taylor Polynomial Theory
Arcsine Function Forward Taylor Polynomial Theory
Arccosine Function Forward Taylor Polynomial Theory
The Theory of Reverse Mode
The Theory of Reverse Mode
Exponential Function Reverse Mode Theory
Logarithm Function Reverse Mode Theory
Square Root Function Reverse Mode Theory
Trigonometric and Hyperbolic Sine and Cosine Reverse Theory
Arctangent Function Reverse Mode Theory
Arcsine Function Reverse Mode Theory
Arccosine Function Reverse Mode Theory
An Important Reverse Mode Identity
Glossary
Bibliography
Know Bugs and Problems Using CppAD
The CppAD Wish List
Changes and Additions to CppAD
Changes and Additions to CppAD
Changes and Additions to CppAD During 2008
Changes and Additions to CppAD During 2007
Changes and Additions to CppAD During 2006
Changes and Additions to CppAD During 2005
Changes and Additions to CppAD During 2004
Changes and Additions to CppAD During 2003
Deprecated Include Files
Your License for the CppAD Software
Alphabetic Listing of Cross Reference Tags
Keyword Index
Search This Web Site
External Internet References