PreconditionedIterativeLinearSolver (Apache Commons Math 3.6.1 API)

java.lang.Object
- 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 and 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

Methods
Modifier and Type	Method and 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 Detail
  - 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 Detail
  - 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 Detail

PreconditionedIterativeLinearSolver

PreconditionedIterativeLinearSolver

Method Detail

solve

solve

solve

checkParameters

solve

solveInPlace

solveInPlace