org.drip.quant.linearalgebra

Class LinearSystemSolver

java.lang.Object

org.drip.quant.linearalgebra.LinearSystemSolver

public class LinearSystemSolver
extends java.lang.Object

LinearSystemSolver implements the solver for a system of linear equations given by A * x = B, where A is the matrix, x the set of variables, and B is the result to be solved for. It exports the following functions: - Row Regularization and Diagonal Pivoting - Check for Diagonal Dominance - Solving the linear system using any one of the following: Gaussian Elimination, Gauss Seidel reduction, or matrix inversion.

Author:

Lakshmi Krishnamurthy

Constructor Summary

Constructors

Constructor and Description
LinearSystemSolver()

Method Summary

Modifier and Type	Method and Description
static boolean	IsDiagonallyDominant(double[][] aadblA, boolean bCheckForStrongDominance) Check to see if the matrix is diagonally dominant.
static double[]	Pivot(double[][] aadblA, double[] adblB) Pivots the matrix A (Refer to wikipedia to find out what "pivot a matrix" means ;))
static boolean	RegulariseRow(double[][] aadblA, double[] adblSolution, int iInnerRow, int iOuter) Regularize (i.e., convert the diagonal entries of the given cell to non-zero using suitable linear transformations)
static LinearizationOutput	SolveUsingGaussianElimination(double[][] aadblAIn, double[] adblB) Solve the Linear System using Gaussian Elimination from the Set of Values in the Array
static LinearizationOutput	SolveUsingGaussSeidel(double[][] aadblAIn, double[] adblB) Solve the Linear System using the Gauss-Seidel algorithm from the Set of Values in the Array
static LinearizationOutput	SolveUsingMatrixInversion(double[][] aadblAIn, double[] adblB) Solve the Linear System using Matrix Inversion from the Set of Values in the Array

Methods inherited from class java.lang.Object

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

Constructor Detail

LinearSystemSolver

public LinearSystemSolver()

Method Detail

RegulariseRow

public static final boolean RegulariseRow(double[][] aadblA,
                                          double[] adblSolution,
                                          int iInnerRow,
                                          int iOuter)

Regularize (i.e., convert the diagonal entries of the given cell to non-zero using suitable linear transformations)

Parameters:

aadblA - In/Out Matrix to be regularized

adblSolution - In/out RHS

iInnerRow - Matrix Cell Row that needs to be regularized

iOuter - Matrix Cell Column that needs to be regularized

Returns:

TRUE - Matrix has been successfully regularized

IsDiagonallyDominant

public static final boolean IsDiagonallyDominant(double[][] aadblA,
                                                 boolean bCheckForStrongDominance)

Check to see if the matrix is diagonally dominant.

Parameters:

aadblA - Input Matrix

bCheckForStrongDominance - TRUE - Fail if the matrix is not strongly diagonally dominant.

Returns:

TRUE - Strongly or weakly Diagonally Dominant

Pivot

public static final double[] Pivot(double[][] aadblA,
                                   double[] adblB)

Pivots the matrix A (Refer to wikipedia to find out what "pivot a matrix" means ;))

Parameters:

aadblA - Input Matrix

adblB - Input RHS

Returns:

The pivoted input matrix and the re-jigged input RHS

SolveUsingMatrixInversion

public static final LinearizationOutput SolveUsingMatrixInversion(double[][] aadblAIn,
                                                                  double[] adblB)

Solve the Linear System using Matrix Inversion from the Set of Values in the Array

Parameters:

aadblAIn - Input Matrix

adblB - The Array of Values to be calibrated to

Returns:

The Linear System Solution for the Coefficients

SolveUsingGaussianElimination

public static final LinearizationOutput SolveUsingGaussianElimination(double[][] aadblAIn,
                                                                      double[] adblB)

Solve the Linear System using Gaussian Elimination from the Set of Values in the Array

Parameters:

aadblAIn - Input Matrix

adblB - The Array of Values to be calibrated to

Returns:

The Linear System Solution for the Coefficients

SolveUsingGaussSeidel

public static final LinearizationOutput SolveUsingGaussSeidel(double[][] aadblAIn,
                                                              double[] adblB)

Solve the Linear System using the Gauss-Seidel algorithm from the Set of Values in the Array

Parameters:

aadblAIn - Input Matrix

adblB - The Array of Values to be calibrated to

Returns:

The Linear System Solution for the Coefficients