Package org.drip.numerical.linearalgebra

Class Matrix

java.lang.Object

org.drip.numerical.linearalgebra.Matrix

public class Matrix
extends java.lang.Object

Matrix implements Matrix manipulation routines. It exports the following functionality:

• Matrix Inversion using Closed form solutions (for low-dimension matrices), or using Gaussian elimination
• Matrix Product
• Matrix Diagonalization and Diagonal Pivoting
• Matrix Regularization through Row Addition/Row Swap

• Module = Computational Core Module
• Library = Numerical Analysis Library
• Project = Numerical Quadrature, Differentiation, Eigenization, Linear Algebra, and Utilities
• Package = Linear Algebra Matrix Transform Library

Author:

Lakshmi Krishnamurthy

Field Summary

Fields

Modifier and Type	Field	Description
static int	LOWER_AND_UPPER_TRIANGULAR	Lower+Upper Triangular Matrix
static int	LOWER_TRIANGULAR	Lower Triangular Matrix
static int	NON_TRIANGULAR	Non Triangular Matrix
static int	UPPER_TRIANGULAR	Upper Triangular Matrix

Constructor Summary

Constructors

Constructor	Description
Matrix()

Method Summary

Modifier and Type	Method	Description
static double[][]	CholeskyBanachiewiczFactorization(double[][] aadblA)	Compute the Cholesky-Banachiewicz Factorization of the specified Matrix.
static double[][]	CrossProduct(double[] vector1, double[] vector2)	Compute the Cross Product between the Specified Vectors
static boolean	DiagonalizeRow(int iQ, double[][] aadblZ2XJack, double[][] aadblZ2YJack)	Diagonalize the specified row in the source matrix, and apply comparable operations to the target
static double	DotProduct(double[] adblA, double[] adblE)	Dot Product of Vectors A and E
static double[][]	GrahamSchmidtOrthogonalization(double[][] aadblV)	Orthogonalize the Specified Matrix Using the Graham-Schmidt Method
static double[][]	GrahamSchmidtOrthonormalization(double[][] aadblV)	Orthonormalize the Specified Matrix Using the Graham-Schmidt Method
static double[][]	Invert(double[][] aadblA, java.lang.String strMethod)	Invert the input matrix using the specified Method
static double[][]	Invert2DMatrixUsingCramerRule(double[][] aadblA)	Invert a 2D Matrix using Cramer's Rule
static double[][]	InvertUsingGaussianElimination(double[][] aadblSource)	Invert the Source Matrix using Gaussian Elimination
static boolean	IsDiagonal(double[][] matrix)	Indicate if the Specified Matrix is Diagonal
static double[][]	MakeSquareDiagonal(double[] adblA)	Make a Square Diagonal Matrix from a Row
static double	Modulus(double[] adbl)	Compute the Modulus of the Input Vector
static boolean	NegativeOrZero(double[] adbl)	Indicate if the Array Entries are Negative or Zero
static double[]	Normalize(double[] adbl)	Normalize the Input Vector
static MatrixComplementTransform	PivotDiagonal(double[][] aadblA)	Pivot the Diagonal of the Input Matrix
static boolean	PositiveLinearlyIndependent(double[] adbl)	Indicate if the Array Entries are Positive Linearly Independent
static boolean	PositiveOrZero(double[] adbl)	Indicate if the Array Entries are Positive or Zero
static double[]	Product(double[][] aadblA, double[] adblB)	Compute the Product of an Input Matrix and a Column
static double[][]	Product(double[][] aadblA, double[][] aadblB)	Compute the Product of the input matrices
static double[][]	Product(double[] adblA, double[][] aadblB)	Compute the Product of an input column and a matrix
static double[]	Project(double[] adblA, double[] adblE)	Project the Vector A along the Vector E
static QR	QRDecomposition(double[][] aadblA)	Perform a QR Decomposition on the Input Matrix
static int	Rank(double[][] aadblSource)	Compute the Rank of the Matrix
static double	RayleighQuotient(double[][] matrix, double[] eigenvector)	Compute the Rayleigh Quotient given the Matrix and one of its Eigenvector
static boolean	RegularizeUsingRowAddition(MatrixComplementTransform mct)	Regularize the specified diagonal entry of the input matrix using Row Addition
static boolean	RegularizeUsingRowSwap(MatrixComplementTransform mct)	Regularize the specified diagonal entry of the input matrix using Row Swapping
static double[]	Scale1D(double[] vector, double scaleFactor)	Scale the Entries of the Input Vector by the Factor
static double[][]	Scale2D(double[][] matrix, double scaleFactor)	Scale the Entries of the Input Matrix by the Factor
static double	Sum(double[] adbl)	Compute the Sum of the Input Vector
static double[][]	Transpose(double[][] aadblA)	Transpose the specified Square Matrix
static int	TriangularType(double[][] aadblA, double dblFloor)	Retrieve the Triangular Type of the Matrix

Methods inherited from class java.lang.Object

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

Field Details

LOWER_TRIANGULAR

public static int LOWER_TRIANGULAR

Lower Triangular Matrix

UPPER_TRIANGULAR

public static int UPPER_TRIANGULAR

Upper Triangular Matrix

LOWER_AND_UPPER_TRIANGULAR

public static int LOWER_AND_UPPER_TRIANGULAR

Lower+Upper Triangular Matrix

NON_TRIANGULAR

public static int NON_TRIANGULAR

Non Triangular Matrix

Constructor Details

Matrix

public Matrix()

Method Details

DiagonalizeRow

public static final boolean DiagonalizeRow(int iQ,
double[][] aadblZ2XJack,
double[][] aadblZ2YJack)

Diagonalize the specified row in the source matrix, and apply comparable operations to the target

Parameters:

iQ - Row in the Source Matrix

aadblZ2XJack - Source Matrix

aadblZ2YJack - Target Matrix

Returns:

TRUE - Diagonalization was successful

Product

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

Compute the Product of an Input Matrix and a Column

Parameters:

aadblA - Matrix A

adblB - Array B

Returns:

The Product

Product

public static final double[][] Product(double[] adblA,
double[][] aadblB)

Compute the Product of an input column and a matrix

Parameters:

adblA - Column A

aadblB - Matrix B

Returns:

The Product

Product

public static final double[][] Product(double[][] aadblA,
double[][] aadblB)

Compute the Product of the input matrices

Parameters:

aadblA - Matrix A

aadblB - Matrix B

Returns:

The Product

MakeSquareDiagonal

public static final double[][] MakeSquareDiagonal(double[] adblA)

Make a Square Diagonal Matrix from a Row

Parameters:

adblA - The Row Array

Returns:

The corresponding Square Diagonal Matrix

Invert2DMatrixUsingCramerRule

public static final double[][] Invert2DMatrixUsingCramerRule(double[][] aadblA)

Invert a 2D Matrix using Cramer's Rule

Parameters:

aadblA - Input 2D Matrix

Returns:

The Inverted Matrix

RegularizeUsingRowSwap

public static final boolean RegularizeUsingRowSwap(MatrixComplementTransform mct)

Regularize the specified diagonal entry of the input matrix using Row Swapping

Parameters:

mct - The Input Matrix Complement Transform

Returns:

The Regularization was successful

RegularizeUsingRowAddition

public static final boolean RegularizeUsingRowAddition(MatrixComplementTransform mct)

Regularize the specified diagonal entry of the input matrix using Row Addition

Parameters:

mct - The Input Matrix Complement Transform

Returns:

The Regularization was successful

PivotDiagonal

public static final MatrixComplementTransform PivotDiagonal(double[][] aadblA)

Pivot the Diagonal of the Input Matrix

Parameters:

aadblA - The Input Matrix

Returns:

The Matrix Complement Transform Instance

InvertUsingGaussianElimination

public static final double[][] InvertUsingGaussianElimination(double[][] aadblSource)

Invert the Source Matrix using Gaussian Elimination

Parameters:

aadblSource - Source Matrix

Returns:

The Inverted Matrix

Invert

public static final double[][] Invert(double[][] aadblA,
java.lang.String strMethod)

Invert the input matrix using the specified Method

Parameters:

aadblA - Input Matrix

strMethod - The Inversion Method

Returns:

The Inverted Matrix

Rank

public static final int Rank(double[][] aadblSource)
                      throws java.lang.Exception

Compute the Rank of the Matrix

Parameters:

aadblSource - Source Matrix

Returns:

The Rank of the Matrix

Throws:

java.lang.Exception - Thrown if the Rank Cannot be computed

Transpose

public static final double[][] Transpose(double[][] aadblA)

Transpose the specified Square Matrix

Parameters:

aadblA - The Input Square Matrix

Returns:

The Transpose of the Square Matrix

CholeskyBanachiewiczFactorization

public static final double[][] CholeskyBanachiewiczFactorization(double[][] aadblA)

Compute the Cholesky-Banachiewicz Factorization of the specified Matrix.

Parameters:

aadblA - The Input Matrix

Returns:

The Factorized Matrix

DotProduct

public static final double DotProduct(double[] adblA,
double[] adblE)
                               throws java.lang.Exception

Dot Product of Vectors A and E

Parameters:

adblA - Vector A

adblE - Vector E

Returns:

The Dot Product

Throws:

java.lang.Exception - Thrown if the Dot-Product cannot be computed

CrossProduct

public static final double[][] CrossProduct(double[] vector1,
double[] vector2)

Compute the Cross Product between the Specified Vectors

Parameters:

vector1 - Vector #1

vector2 - Vector #2

Returns:

The Cross Product

Project

public static final double[] Project(double[] adblA,
double[] adblE)

Project the Vector A along the Vector E

Parameters:

adblA - Vector A

adblE - Vector E

Returns:

The Vector of Projection of A along E

Sum

public static final double Sum(double[] adbl)
                        throws java.lang.Exception

Compute the Sum of the Input Vector

Parameters:

adbl - The Input Vector

Returns:

TRUE - The Sum of the Input Vector

Throws:

java.lang.Exception - Thrown if the Inputs are Invalid

Modulus

public static final double Modulus(double[] adbl)
                            throws java.lang.Exception

Compute the Modulus of the Input Vector

Parameters:

adbl - The Input Vector

Returns:

TRUE - The Modulus of the Input Vector

Throws:

java.lang.Exception - Thrown if the Inputs are Invalid

PositiveOrZero

public static final boolean PositiveOrZero(double[] adbl)
                                    throws java.lang.Exception

Indicate if the Array Entries are Positive or Zero

Parameters:

adbl - The Array

Returns:

TRUE - The Array Entries are Positive or Zero

Throws:

java.lang.Exception - Thrown if the Inputs are Invalid

NegativeOrZero

public static final boolean NegativeOrZero(double[] adbl)
                                    throws java.lang.Exception

Indicate if the Array Entries are Negative or Zero

Parameters:

adbl - The Array

Returns:

The Array Entries are Negative or Zero

Throws:

java.lang.Exception - Thrown if the Inputs are Invalid

PositiveLinearlyIndependent

public static final boolean PositiveLinearlyIndependent(double[] adbl)
                                                 throws java.lang.Exception

Indicate if the Array Entries are Positive Linearly Independent

Parameters:

adbl - The Array

Returns:

TRUE - The Array Entries are Positive Linearly Independent

Throws:

java.lang.Exception - Thrown if the Inputs are Invalid

Normalize

public static final double[] Normalize(double[] adbl)

Normalize the Input Vector

Parameters:

adbl - The Input Vector

Returns:

The Normalized Vector

GrahamSchmidtOrthogonalization

public static final double[][] GrahamSchmidtOrthogonalization(double[][] aadblV)

Orthogonalize the Specified Matrix Using the Graham-Schmidt Method

Parameters:

aadblV - The Input Matrix

Returns:

The Orthogonalized Matrix

GrahamSchmidtOrthonormalization

public static final double[][] GrahamSchmidtOrthonormalization(double[][] aadblV)

Orthonormalize the Specified Matrix Using the Graham-Schmidt Method

Parameters:

aadblV - The Input Matrix

Returns:

The Orthonormalized Matrix

QRDecomposition

public static final QR QRDecomposition(double[][] aadblA)

Perform a QR Decomposition on the Input Matrix

Parameters:

aadblA - The Input Matrix

Returns:

The Output of QR Decomposition

TriangularType

public static final int TriangularType(double[][] aadblA,
double dblFloor)

Retrieve the Triangular Type of the Matrix

Parameters:

aadblA - The Input Matrix

dblFloor - The Floor Level that means "Zero"

Returns:

The Triangular Type

RayleighQuotient

public static final double RayleighQuotient(double[][] matrix,
double[] eigenvector)
                                     throws java.lang.Exception

Compute the Rayleigh Quotient given the Matrix and one of its Eigenvector

Parameters:

matrix - The Given Matrix

eigenvector - The corresponding Eigenvector

Returns:

The Computed Rayleigh Quotient

Throws:

java.lang.Exception - Thrown if the Inputs are Invalid

Scale1D

public static final double[] Scale1D(double[] vector,
double scaleFactor)

Scale the Entries of the Input Vector by the Factor

Parameters:

vector - The Input Vector

scaleFactor - The Scale Factor

Returns:

The Scaled Matrix

Scale2D

public static final double[][] Scale2D(double[][] matrix,
double scaleFactor)

Scale the Entries of the Input Matrix by the Factor

Parameters:

matrix - The Input Matrix

scaleFactor - The Scale Factor

Returns:

The Scaled Matrix

IsDiagonal

public static final boolean IsDiagonal(double[][] matrix)

Indicate if the Specified Matrix is Diagonal

Parameters:

matrix - The Matrix

Returns:

TRUE - The Specified Matrix is Diagonal