org.ejml.alg.dense.linsol.gj
Class GaussJordan

java.lang.Object
  org.ejml.alg.dense.linsol.LinearSolverAbstract
      org.ejml.alg.dense.linsol.gj.GaussJordan

All Implemented Interfaces:

LinearSolver<DenseMatrix64F>

public class GaussJordan
extends LinearSolverAbstract

Gauss-Jordan elimination is an algorithm that can solve linear equations and invert matrices. This implementation includes full pivoting to improve numerical stability. In almost all situations this should be used instead of GaussJordanNoPivot.

Finding the solutions for the 'x' variables is less prone to numerical errors when done at the same time as solving for the inverse of 'A'.

Numerical Recipes The Art of Scientific Computing
Third Edition
Pages 44-45

Author:

Peter Abeles

Field Summary

Fields inherited from class org.ejml.alg.dense.linsol.LinearSolverAbstract

A, numCols, numRows

Constructor Summary

GaussJordan(int dimen)

Method Summary

static void	checkArgumentSquare(RowD1Matrix64F mat, String name)
void	invert(DenseMatrix64F A) Computes the inverse of of the 'A' matrix passed into LinearSolver.setA(org.ejml.data.Matrix64F) and writes the results to the provided matrix.
boolean	modifiesA() Returns true if the passed in matrix to LinearSolver.setA(org.ejml.data.Matrix64F) is modified.
boolean	modifiesB() Returns true if the passed in 'B' matrix to LinearSolver.solve(org.ejml.data.Matrix64F, org.ejml.data.Matrix64F) is modified.
double	quality() Returns a very quick to compute measure of how singular the system is.
boolean	setA(DenseMatrix64F A) Specifies the A matrix in the linear equation.
void	solve(DenseMatrix64F B, DenseMatrix64F X) Computes the inverse of matrix A and solves for X for each column in B.

Methods inherited from class org.ejml.alg.dense.linsol.LinearSolverAbstract

_setA, getA

Methods inherited from class java.lang.Object

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

Constructor Detail

GaussJordan

public GaussJordan(int dimen)

Method Detail

setA

public boolean setA(DenseMatrix64F A)

Description copied from interface: LinearSolver

Specifies the A matrix in the linear equation. A reference might be saved and it might also be modified depending on the implementation. If it is modified then LinearSolver.modifiesA() will return true.

If this value returns true that does not guarantee a valid solution was generated. This is because some decompositions don't detect singular matrices.

Parameters:

A - The 'A' matrix in the linear equation. Might be modified or save the reference.

Returns:

true if it can be processed.

quality

public double quality()

Description copied from interface: LinearSolver

Returns a very quick to compute measure of how singular the system is. This measure will be invariant to the scale of the matrix and always be positive, with larger values indicating it is less singular. If not supported by the solver then the runtime exception IllegalArgumentException is thrown. This is NOT the matrix's condition.

How this function is implemented is not specified. One possible implementation is the following: In many decompositions a triangular matrix is extracted. The determinant of a triangular matrix is easily computed and once normalized to be scale invariant and its absolute value taken it will provide functionality described above.

Returns:

The quality of the linear system.

checkArgumentSquare

public static void checkArgumentSquare(RowD1Matrix64F mat,
                                       String name)

invert

public void invert(DenseMatrix64F A)

Description copied from interface: LinearSolver

Computes the inverse of of the 'A' matrix passed into LinearSolver.setA(org.ejml.data.Matrix64F) and writes the results to the provided matrix. If 'A_inv' needs to be different from 'A' is implementation dependent.

Specified by:

invert in interface LinearSolver<DenseMatrix64F>

Overrides:

invert in class LinearSolverAbstract

Parameters:

A - Where the inverted matrix saved. Modified.

solve

public void solve(DenseMatrix64F B,
                  DenseMatrix64F X)

Computes the inverse of matrix A and solves for X for each column in B. Both matrices are modified.

Parameters:

B - A matrix ℜ ^{m × p}. Might be modified.

X - A matrix ℜ ^{n × p}, where the solution is written to. Modified.

modifiesA

public boolean modifiesA()

Description copied from interface: LinearSolver

Returns true if the passed in matrix to LinearSolver.setA(org.ejml.data.Matrix64F) is modified.

Returns:

true if A is modified in setA().

modifiesB

public boolean modifiesB()

Description copied from interface: LinearSolver

Returns true if the passed in 'B' matrix to LinearSolver.solve(org.ejml.data.Matrix64F, org.ejml.data.Matrix64F) is modified.

Returns:

true if B is modified in solve(B,X).