org.apache.commons.math3.linear.IterativeLinearSolver

org.apache.commons.math3.linear.PreconditionedIterativeLinearSolver

Direct Known Subclasses:: ConjugateGradient, SymmLQ

public abstract class PreconditionedIterativeLinearSolver extends IterativeLinearSolver

This abstract class defines preconditioned iterative solvers. When A is ill-conditioned, instead of solving system A · x = b directly, it is preferable to solve either

(M · A) · x = M · b (left preconditioning), or (A · M) · y = b, followed by M · y = x (right preconditioning), where M approximates in some way A^-1, while matrix-vector products of the type M · y remain comparatively easy to compute. In this library, M (not M^-1!) is called the preconditionner.

Concrete implementations of this abstract class must be provided with the preconditioner M, as a RealLinearOperator.

Since:: 3.0

Constructor Summary

Constructors

Constructor

Description

PreconditionedIterativeLinearSolver(int maxIterations)

Creates a new instance of this class, with default iteration manager.

PreconditionedIterativeLinearSolver(IterationManager manager)

Creates a new instance of this class, with custom iteration manager.
Method Summary

Modifier and Type

Method

Description

protected static void

checkParameters(RealLinearOperator a, RealLinearOperator m, RealVector b, RealVector x0)

Performs all dimension checks on the parameters of solve and solveInPlace, and throws an exception if one of the checks fails.

RealVector

solve(RealLinearOperator a, RealLinearOperator m, RealVector b)

Returns an estimate of the solution to the linear system A · x = b.

RealVector

solve(RealLinearOperator a, RealLinearOperator m, RealVector b, RealVector x0)

Returns an estimate of the solution to the linear system A · x = b.

RealVector

solve(RealLinearOperator a, RealVector b)

Returns an estimate of the solution to the linear system A · x = b.

RealVector

solve(RealLinearOperator a, RealVector b, RealVector x0)

Returns an estimate of the solution to the linear system A · x = b.

abstract RealVector

solveInPlace(RealLinearOperator a, RealLinearOperator m, RealVector b, RealVector x0)

Returns an estimate of the solution to the linear system A · x = b.

RealVector

solveInPlace(RealLinearOperator a, RealVector b, RealVector x0)

Returns an estimate of the solution to the linear system A · x = b.

Methods inherited from class org.apache.commons.math3.linear.IterativeLinearSolver
checkParameters, getIterationManager

Methods inherited from class java.lang.Object
clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Constructor Details
- PreconditionedIterativeLinearSolver
  
  public PreconditionedIterativeLinearSolver(int maxIterations)
  
  Creates a new instance of this class, with default iteration manager.
  
  Parameters:
  
  maxIterations - the maximum number of iterations
- PreconditionedIterativeLinearSolver
  
  public PreconditionedIterativeLinearSolver(IterationManager manager) throws NullArgumentException
  
  Creates a new instance of this class, with custom iteration manager.
  
  Parameters:
  
  manager - the custom iteration manager
  
  Throws:
  
  NullArgumentException - if manager is null
Method Details
- solve
  
  public RealVector solve(RealLinearOperator a, RealLinearOperator m, RealVector b, RealVector x0) throws NullArgumentException, NonSquareOperatorException, DimensionMismatchException, MaxCountExceededException
  
  Returns an estimate of the solution to the linear system A · x = b.
  
  Parameters:
  
  a - the linear operator A of the system
  
  m - the preconditioner, M (can be null)
  
  b - the right-hand side vector
  
  x0 - the initial guess of the solution
  
  Returns:
  
  a new vector containing the solution
  
  Throws:
  
  NullArgumentException - if one of the parameters is null
  
  NonSquareOperatorException - if a or m is not square
  
  DimensionMismatchException - if m, b or x0 have dimensions inconsistent with a
  
  MaxCountExceededException - at exhaustion of the iteration count, unless a custom callback has been set at construction of the IterationManager
- solve
  
  public RealVector solve(RealLinearOperator a, RealVector b) throws NullArgumentException, NonSquareOperatorException, DimensionMismatchException, MaxCountExceededException
  
  Returns an estimate of the solution to the linear system A · x = b.
  
  Overrides:
  
  solve in class IterativeLinearSolver
  
  Parameters:
  
  a - the linear operator A of the system
  
  b - the right-hand side vector
  
  Returns:
  
  a new vector containing the solution
  
  Throws:
  
  NullArgumentException - if one of the parameters is null
  
  NonSquareOperatorException - if a is not square
  
  DimensionMismatchException - if b has dimensions inconsistent with a
  
  MaxCountExceededException - at exhaustion of the iteration count, unless a custom callback has been set at construction of the IterationManager
- solve
  
  public RealVector solve(RealLinearOperator a, RealVector b, RealVector x0) throws NullArgumentException, NonSquareOperatorException, DimensionMismatchException, MaxCountExceededException
  
  Returns an estimate of the solution to the linear system A · x = b.
  
  Overrides:
  
  solve in class IterativeLinearSolver
  
  Parameters:
  
  a - the linear operator A of the system
  
  b - the right-hand side vector
  
  x0 - the initial guess of the solution
  
  Returns:
  
  a new vector containing the solution
  
  Throws:
  
  NullArgumentException - if one of the parameters is null
  
  NonSquareOperatorException - if a is not square
  
  DimensionMismatchException - if b or x0 have dimensions inconsistent with a
  
  MaxCountExceededException - at exhaustion of the iteration count, unless a custom callback has been set at construction of the IterationManager
- checkParameters
  
  protected static void checkParameters(RealLinearOperator a, RealLinearOperator m, RealVector b, RealVector x0) throws NullArgumentException, NonSquareOperatorException, DimensionMismatchException
  
  Performs all dimension checks on the parameters of solve and solveInPlace, and throws an exception if one of the checks fails.
  
  Parameters:
  
  a - the linear operator A of the system
  
  m - the preconditioner, M (can be null)
  
  b - the right-hand side vector
  
  x0 - the initial guess of the solution
  
  Throws:
  
  NullArgumentException - if one of the parameters is null
  
  NonSquareOperatorException - if a or m is not square
  
  DimensionMismatchException - if m, b or x0 have dimensions inconsistent with a
- solve
  
  public RealVector solve(RealLinearOperator a, RealLinearOperator m, RealVector b) throws NullArgumentException, NonSquareOperatorException, DimensionMismatchException, MaxCountExceededException
  
  Returns an estimate of the solution to the linear system A · x = b.
  
  Parameters:
  
  a - the linear operator A of the system
  
  m - the preconditioner, M (can be null)
  
  b - the right-hand side vector
  
  Returns:
  
  a new vector containing the solution
  
  Throws:
  
  NullArgumentException - if one of the parameters is null
  
  NonSquareOperatorException - if a or m is not square
  
  DimensionMismatchException - if m or b have dimensions inconsistent with a
  
  MaxCountExceededException - at exhaustion of the iteration count, unless a custom callback has been set at construction of the IterationManager
- solveInPlace
  
  public abstract RealVector solveInPlace(RealLinearOperator a, RealLinearOperator m, RealVector b, RealVector x0) throws NullArgumentException, NonSquareOperatorException, DimensionMismatchException, MaxCountExceededException
  
  Returns an estimate of the solution to the linear system A · x = b. The solution is computed in-place (initial guess is modified).
  
  Parameters:
  
  a - the linear operator A of the system
  
  m - the preconditioner, M (can be null)
  
  b - the right-hand side vector
  
  x0 - the initial guess of the solution
  
  Returns:
  
  a reference to x0 (shallow copy) updated with the solution
  
  Throws:
  
  NullArgumentException - if one of the parameters is null
  
  NonSquareOperatorException - if a or m is not square
  
  DimensionMismatchException - if m, b or x0 have dimensions inconsistent with a
  
  MaxCountExceededException - at exhaustion of the iteration count, unless a custom callback has been set at construction of the IterationManager
- solveInPlace
  
  public RealVector solveInPlace(RealLinearOperator a, RealVector b, RealVector x0) throws NullArgumentException, NonSquareOperatorException, DimensionMismatchException, MaxCountExceededException
  
  Returns an estimate of the solution to the linear system A · x = b. The solution is computed in-place (initial guess is modified).
  
  Specified by:
  
  solveInPlace in class IterativeLinearSolver
  
  Parameters:
  
  a - the linear operator A of the system
  
  b - the right-hand side vector
  
  x0 - initial guess of the solution
  
  Returns:
  
  a reference to x0 (shallow copy) updated with the solution
  
  Throws:
  
  NullArgumentException - if one of the parameters is null
  
  NonSquareOperatorException - if a is not square
  
  DimensionMismatchException - if b or x0 have dimensions inconsistent with a
  
  MaxCountExceededException - at exhaustion of the iteration count, unless a custom callback has been set at construction of the IterationManager

Class PreconditionedIterativeLinearSolver

Constructor Summary

Method Summary

Methods inherited from class org.apache.commons.math3.linear.IterativeLinearSolver

Methods inherited from class java.lang.Object

Constructor Details

PreconditionedIterativeLinearSolver

PreconditionedIterativeLinearSolver

Method Details

solve

solve

solve

checkParameters

solve

solveInPlace

solveInPlace