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ConjugateGradient Class |
Inheritance HierarchyAccord.Math.OptimizationBaseOptimizationMethod
Accord.Math.OptimizationBaseGradientOptimizationMethod
Accord.Math.OptimizationConjugateGradient
Namespace: Accord.Math.Optimization
Assembly: Accord.Math (in Accord.Math.dll) Version: 3.8.0
Syntaxpublic class ConjugateGradient : BaseGradientOptimizationMethod, IGradientOptimizationMethod, IOptimizationMethod, IOptimizationMethod<double[], double>, IGradientOptimizationMethod<double[], double>, IFunctionOptimizationMethod<double[], double>, IOptimizationMethod<ConjugateGradientCode>, IOptimizationMethod<double[], double, ConjugateGradientCode>, ISupportsCancellation
The ConjugateGradient type exposes the following members.
Constructors| Name | Description | |
|---|---|---|
 | ConjugateGradient |
Creates a new instance of the CG optimization algorithm.
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| ConjugateGradient(Int32) |
Creates a new instance of the CG optimization algorithm.
|
| ConjugateGradient(Int32, FuncDouble, Double, FuncDouble, Double) |
Creates a new instance of the CG optimization algorithm.
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Properties| Name | Description | |
|---|---|---|
 | Evaluations |
Gets the number of function evaluations performed
in the last call to Minimize.
|
| Function |
Gets or sets the function to be optimized.
(Inherited from BaseOptimizationMethod.) |
| Gradient |
Gets or sets a function returning the gradient
vector of the function to be optimized for a
given value of its free parameters.
(Inherited from BaseGradientOptimizationMethod.) |
| Iterations |
Gets the number of iterations performed
in the last call to Minimize.
|
| MaxIterations |
Gets or sets the maximum number of iterations
to be performed during optimization. Default
is 0 (iterate until convergence).
|
| Method |
Gets or sets the conjugate gradient update
method to be used during optimization.
|
| NumberOfVariables |
Gets the number of variables (free parameters)
in the optimization problem.
(Inherited from BaseOptimizationMethod.) |
| Searches |
Gets the number of linear searches performed
in the last call to Minimize.
|
| Solution |
Gets the current solution found, the values of
the parameters which optimizes the function.
(Inherited from BaseOptimizationMethod.) |
| Status | |
| Token |
Gets or sets a cancellation token that can be used to
stop the learning algorithm while it is running.
(Inherited from BaseOptimizationMethod.) |
| Tolerance |
Gets or sets the relative difference threshold
to be used as stopping criteria between two
iterations. Default is 0 (iterate until convergence).
|
| Value |
Gets the output of the function at the current Solution.
(Inherited from BaseOptimizationMethod.) |
Methods| Name | Description | |
|---|---|---|
| Equals | Determines whether the specified object is equal to the current object. (Inherited from Object.) |
 | Finalize | Allows an object to try to free resources and perform other cleanup operations before it is reclaimed by garbage collection. (Inherited from Object.) |
| GetHashCode | Serves as the default hash function. (Inherited from Object.) |
| GetType | Gets the Type of the current instance. (Inherited from Object.) |
| Maximize |
Finds the maximum value of a function. The solution vector
will be made available at the Solution property.
(Inherited from BaseGradientOptimizationMethod.) |
| Maximize(Double) |
Finds the maximum value of a function. The solution vector
will be made available at the Solution property.
(Inherited from BaseOptimizationMethod.) |
| MemberwiseClone | Creates a shallow copy of the current Object. (Inherited from Object.) |
| Minimize |
Finds the minimum value of a function. The solution vector
will be made available at the Solution property.
(Inherited from BaseGradientOptimizationMethod.) |
| Minimize(Double) |
Finds the minimum value of a function. The solution vector
will be made available at the Solution property.
(Inherited from BaseOptimizationMethod.) |
| OnNumberOfVariablesChanged |
Called when the NumberOfVariables property has changed.
(Overrides BaseOptimizationMethodOnNumberOfVariablesChanged(Int32).) |
| Optimize |
Implements the actual optimization algorithm. This
method should try to minimize the objective function.
(Overrides BaseOptimizationMethodOptimize.) |
| ToString | Returns a string that represents the current object. (Inherited from Object.) |
Events
Extension Methods| Name | Description | |
|---|---|---|
 | HasMethod |
Checks whether an object implements a method with the given name.
(Defined by ExtensionMethods.) |
| IsEqual |
Compares two objects for equality, performing an elementwise
comparison if the elements are vectors or matrices.
(Defined by Matrix.) |
| To(Type) | Overloaded.
Converts an object into another type, irrespective of whether
the conversion can be done at compile time or not. This can be
used to convert generic types to numeric types during runtime.
(Defined by ExtensionMethods.) |
| ToT | Overloaded.
Converts an object into another type, irrespective of whether
the conversion can be done at compile time or not. This can be
used to convert generic types to numeric types during runtime.
(Defined by ExtensionMethods.) |
RemarksIn mathematics, the conjugate gradient method is an algorithm for the numerical solution of particular systems of linear equations, namely those whose matrix is symmetric and positive- definite. The conjugate gradient method is an iterative method, so it can be applied to sparse systems that are too large to be handled by direct methods. Such systems often arise when numerically solving partial differential equations. The nonlinear conjugate gradient method generalizes the conjugate gradient method to nonlinear optimization (Wikipedia, 2011).
T
The framework implementation of this method is based on the original FORTRAN source code by Jorge Nocedal (see references below). The original FORTRAN source code of CG+ (for large scale unconstrained problems) is available at http://users.eecs.northwestern.edu/~nocedal/CG+.html and had been made freely available for educational or commercial use. The original authors expect that all publications describing work using this software quote the (Gilbert and Nocedal, 1992) reference given below.
References:
- J. C. Gilbert and J. Nocedal. Global Convergence Properties of Conjugate Gradient Methods for Optimization, (1992) SIAM J. on Optimization, 2, 1.
- Wikipedia contributors, "Nonlinear conjugate gradient method," Wikipedia, The Free Encyclopedia, http://en.wikipedia.org/w/index.php?title=Nonlinear_conjugate_gradient_method (accessed December 22, 2011).
- Wikipedia contributors, "Conjugate gradient method," Wikipedia, The Free Encyclopedia, http://en.wikipedia.org/w/index.php?title=Conjugate_gradient_method (accessed December 22, 2011).
See Also