com.dautelle.math
Class LUDecomposition

java.lang.Object
  com.dautelle.realtime.RealtimeObject
      com.dautelle.math.LUDecomposition

All Implemented Interfaces:

Realtime, java.io.Serializable

public final class LUDecomposition

extends RealtimeObject

This class represents the decomposition of a Matrix into a product of lower and upper triangular matrices (L and U, respectively).

This decomposition is typically used to resolve linear systems of equations (Gaussian elimination) or to calculate the determinant of a square Matrix (O(n³)).

Numerical stability is guaranteed through pivoting if the Operable elements of this matrix are derived from java.lang.Number. For others elements types, numerical stability can be ensured by setting the appropriate pivot comparator (see setPivotComparator(java.util.Comparator)).

Instances of this class are created using the Matrix.lu() factory methods.

Version:

6.0, April 28, 2004

Author:

Jean-Marie Dautelle

See Also:

LU Decomposition -- from MathWorld, Serialized Form

Nested Class Summary

Nested classes inherited from class com.dautelle.realtime.RealtimeObject

RealtimeObject.Factory

Field Summary

static java.util.Comparator

NUMBER_COMPARATOR Holds the comparator for pivoting java.lang.Number instances.

Method Summary

Operable	determinant() Returns the determinant of the Matrix having this LUDecomposition.
java.lang.Object	export() Exports this object out of the current pool context.
Matrix	inverse() Returns the solution X of the equation: A * X = Identity with this = A.lu() using back and forward substitutions.
void	setPivotComparator(java.util.Comparator cmp) Sets the local comparator used for pivoting during LU decomposition (default NUMBER_COMPARATOR).
Matrix	solve(Matrix B) Returns the solution X of the equation: A * X = B with this = A.lu() using back and forward substitutions.
java.lang.Object	toHeap() Moves this object to the heap.

Methods inherited from class com.dautelle.realtime.RealtimeObject

clone, isLocalObject, isPoolObject, recycle

Methods inherited from class java.lang.Object

equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Field Detail

NUMBER_COMPARATOR

public static final java.util.Comparator NUMBER_COMPARATOR

Holds the comparator for pivoting java.lang.Number instances.

Method Detail

setPivotComparator

public void setPivotComparator(java.util.Comparator cmp)

Sets the local comparator used for pivoting during LU decomposition (default NUMBER_COMPARATOR).

Parameters:

cmp - the comparator for pivoting.

solve

public Matrix solve(Matrix B)

Returns the solution X of the equation: A * X = B with this = A.lu() using back and forward substitutions.

Parameters:

B - the input vector.

Returns:

the solution X = (1 / A) * B.

Throws:

DimensionException - if A.getRowDimension() != B.getRowDimension().

inverse

public Matrix inverse()

Returns the solution X of the equation: A * X = Identity with this = A.lu() using back and forward substitutions. This method uses PoolContext internally.

Returns:

this.solve(Identity)

determinant

public Operable determinant()

Returns the determinant of the Matrix having this LUDecomposition.

Returns:

the determinant of the matrix source.

export

public java.lang.Object export()

Description copied from interface: Realtime

Exports this object out of the current pool context. Realtime members are exported as well (recursion). This method affects only objects belonging to the current pool context. To avoid pool depletion, a "free" object from the outer pool is moved to replace the object being exported.

Specified by:

export in interface Realtime

Overrides:

export in class RealtimeObject

toHeap

public java.lang.Object toHeap()

Description copied from interface: Realtime

Moves this object to the heap. Realtime members are moved to the heap as well (recursion). This method affects only objects belonging to a pool context (current or not).

Specified by:

toHeap in interface Realtime

Overrides:

toHeap in class RealtimeObject