BiConjugateGradientStabilizedSolver<T> Class

Constructs a new sparse linear solver that uses the bi-conjugate gradient algorithm.

Definition

Namespace: Extreme.Mathematics.LinearAlgebra.IterativeSolvers
Assembly: Extreme.Numerics (in Extreme.Numerics.dll) Version: 8.1.23
C#
public class BiConjugateGradientStabilizedSolver<T> : IterativeSparseSolver<T>
Inheritance
Object  →  ManagedIterativeAlgorithm<DenseVector<T>, T, SolutionReport<DenseVector<T>, T>>  →  IterativeSparseSolver<T>  →  BiConjugateGradientStabilizedSolver<T>

Type Parameters

T

Remarks

Use the BiConjugateGradientStabilizedSolver<T> class to solve large, non-symmetric sparse systems of equations using the Stabilized Bi-Conjugate Gradient method (BiCGStab). Convergence is more stable than the Conjugate Gradient Squared (CGS) method.

To solve a system of equations using this class, construct a new instance, passing the matrix of the system to the constructor. You can optionally set a preconditioner by setting the Preconditioner property. By default, a JacobiPreconditioner<T> is used. Finally, the Solve() method solves the system.

Once the algorithm finished, the Status property indicates whether the algorithm completed successfully.

Constructors

BiConjugateGradientStabilizedSolver<T> Constructs a new iterative sparse solver object.

Properties

ConvergenceTests Gets the collection of convergence tests for the algorithm.
(Inherited from ManagedIterativeAlgorithm<T, TError, TReport>)
EstimatedError Gets a value indicating the size of the absolute error of the result.
(Inherited from ManagedIterativeAlgorithm<T, TError, TReport>)
EvaluationsNeeded Gets the number of evaluations needed to execute the algorithm.
(Inherited from ManagedIterativeAlgorithm<T, TError, TReport>)
EvaluationsRemaining Gets the number of evaluations still available.
(Inherited from ManagedIterativeAlgorithm<T, TError, TReport>)
HasSharedDegreeOfParallelism Indicates whether the degree of parallelism is a property that is shared across instances.
(Inherited from ManagedIterativeAlgorithm<T, TError, TReport>)
InitialGuess Gets or sets the solution of the system of equations.
(Inherited from IterativeSparseSolver<T>)
IterationsNeeded Gets the number of iterations needed by the algorithm to reach the desired accuracy.
(Inherited from ManagedIterativeAlgorithm<T, TError, TReport>)
IterationsRemaining Gets the number of iterations remaining.
(Inherited from ManagedIterativeAlgorithm<T, TError, TReport>)
LastCorrection Gets the vector containing the residuals of the solution.
(Inherited from IterativeSparseSolver<T>)
LeftPreconditioner Gets or sets the Preconditioner<T>.
(Inherited from IterativeSparseSolver<T>)
LinearOperator Gets the sparse matrix of the system of equations.
(Inherited from IterativeSparseSolver<T>)
MaxDegreeOfParallelism Gets or sets the maximum degree of parallelism enabled by this instance.
(Inherited from ManagedIterativeAlgorithm<T, TError, TReport>)
MaxEvaluations Gets or sets the maximum number of evaluations during the calculation.
(Inherited from ManagedIterativeAlgorithm<T, TError, TReport>)
MaxIterationsGets or sets the maximum number of iterations to use when approximating the roots of the target function.
(Inherited from ManagedIterativeAlgorithm<T, TError, TReport>)
MinIterations Gets or sets the minimum iterations that have to be performed.
(Inherited from ManagedIterativeAlgorithm<T, TError, TReport>)
ParallelOptions Gets or sets the configuration for the parallel behavior of the algorithm.
(Inherited from ManagedIterativeAlgorithm<T, TError, TReport>)
Preconditioner Gets or sets the Preconditioner<T>.
(Inherited from IterativeSparseSolver<T>)
Residuals Gets the vector containing the residuals of the solution.
(Inherited from IterativeSparseSolver<T>)
ResidualTest Gets the convergence test based on the size of the residuals.
(Inherited from IterativeSparseSolver<T>)
Result Gets or sets the solution of the system of equations.
(Inherited from IterativeSparseSolver<T>)
RightHandSide Gets or sets the right hand side of the system of equations.
(Inherited from IterativeSparseSolver<T>)
SolutionReport Gets the result of an algorithm after it has executed.
(Inherited from ManagedIterativeAlgorithm<T, TError, TReport>)
SolutionTest Gets the convergence test based on the size of the residuals.
(Inherited from IterativeSparseSolver<T>)
Status Gets the AlgorithmStatus following an execution of the algorithm.
(Inherited from ManagedIterativeAlgorithm<T, TError, TReport>)
ThrowExceptionOnFailure Gets or sets a value indicating whether to throw an exception when the algorithm fails to converge.
(Inherited from ManagedIterativeAlgorithm<T, TError, TReport>)

Methods

EqualsDetermines whether the specified object is equal to the current object.
(Inherited from Object)
FinalizeAllows an object to try to free resources and perform other cleanup operations before it is reclaimed by garbage collection.
(Inherited from Object)
GetHashCodeServes as the default hash function.
(Inherited from Object)
GetTypeGets the Type of the current instance.
(Inherited from Object)
IncrementEvaluations() Increments the number of evaluations by one.
(Inherited from ManagedIterativeAlgorithm<T, TError, TReport>)
IncrementEvaluations(Int32) Increments the number of evaluations by the specified amount.
(Inherited from ManagedIterativeAlgorithm<T, TError, TReport>)
Iterate Performs one iteration of the algorithm.
(Overrides ManagedIterativeAlgorithm<T, TError, TReport>.Iterate())
Iterated Performs operations after the iteration stage of the algorithm is complete.
(Inherited from IterativeSparseSolver<T>)
MemberwiseCloneCreates a shallow copy of the current Object.
(Inherited from Object)
OnConvergence Performs any tasks after the main algorithm has converged.
(Inherited from ManagedIterativeAlgorithm<T, TError, TReport>)
OnFailure Performs any tasks after the main algorithm has failed to converge.
(Inherited from ManagedIterativeAlgorithm<T, TError, TReport>)
OnInit Performs initialization tasks when the algorithm is first run.
(Overrides IterativeSparseSolver<T>.OnInit())
ReportFailure Records the results of an algorithm in case it fails.
(Inherited from ManagedIterativeAlgorithm<T, TError, TReport>)
ReportResult Records the results of an algorithm.
(Inherited from ManagedIterativeAlgorithm<T, TError, TReport>)
ReportSuccess Records the results of a algorithm that converged successfully.
(Inherited from ManagedIterativeAlgorithm<T, TError, TReport>)
ResetEvaluations Resets the number of evaluations to zero.
(Inherited from ManagedIterativeAlgorithm<T, TError, TReport>)
Restart Prepares the algorithm to be run again with possibly different inputs.
(Inherited from ManagedIterativeAlgorithm<T, TError, TReport>)
Run() Runs the algorithm.
(Inherited from ManagedIterativeAlgorithm<T, TError, TReport>)
Run(ParallelOptions) Runs the algorithm using the specified parallelization options.
(Inherited from ManagedIterativeAlgorithm<T, TError, TReport>)
SetResult Sets the results of an algorithm's execution.
(Inherited from ManagedIterativeAlgorithm<T, TError, TReport>)
Solve() Solves the system of equations and returns the solution.
(Inherited from IterativeSparseSolver<T>)
Solve(Vector<T>) Solves the system of equations for the specified right-hand side and returns the result.
(Inherited from IterativeSparseSolver<T>)
Solve(Vector<T>, Vector<T>) Solves the system of equations for the specified right-hand side and returns the result.
(Inherited from IterativeSparseSolver<T>)
TestConvergence Checks whether the algorithm has converged.
(Inherited from ManagedIterativeAlgorithm<T, TError, TReport>)
ThreadSafeIncrementEvaluations() Increments the number of evaluations by one.
(Inherited from ManagedIterativeAlgorithm<T, TError, TReport>)
ThreadSafeIncrementEvaluations(Int32) Increments the number of evaluations by the specified amount.
(Inherited from ManagedIterativeAlgorithm<T, TError, TReport>)
ThrowConvergenceException Interprets the AlgorithmStatus and throws the appropriate exception.
(Inherited from ManagedIterativeAlgorithm<T, TError, TReport>)
ToStringReturns a string that represents the current object.
(Inherited from Object)

See Also