jigl.math
Class Matrix

java.lang.Object
  |
  +--jigl.math.Matrix

All Implemented Interfaces:

Cloneable

Direct Known Subclasses:

IdentityMatrix, ProjectionMatrix, RotationMatrix, ScaleMatrix, TranslationMatrix

public class Matrix

extends Object

implements Cloneable

This class allows a programmer to create real matrices with an arbitrary number of rows and columns.

Field Summary

double[][]

mem This member is the reference to the arrays where the entries of the matrix are stored.

Constructor Summary

Matrix()
This is the default constructor.

Matrix(double[][] b)
This constructor builds a matrix from the double array b.

Matrix(int m, int n)
This constructor builds a zero matrix of size m-by-n.

Matrix(Matrix A)
This constructor builds a matrix from the matrix A.

Method Summary

Matrix	add(Matrix A) This method creates a new matrix and stores the sum of this and A in it.
Matrix	assign(double[][] b) This method replaces the contents of the mem array with the data contained in b.
Matrix	assign(Matrix A) This method replaces the members of this with those of A.
Object	clone()
void	eigsrt(double[] lambda) Given the eigenvalues lambda[0..n-1] and eigenvectors contained in the matrix this as output from jacobi, this routine sorts the eigenvalues into descending order, and rearranges the columns the columns of this correspondingly.
boolean	equals(Matrix A) This method compares if two matrices are equal.
Matrix	gaussj(Matrix B) Linear equation solution by Gauss-Jordan elimination.
double	get(int i, int j) This method returns the (i, j) entry of the matrix.
Vector	getColumn(int j) This method returns column j of the matrix.
Vector	getRow(int i) This method returns row i of the matrix.
int	jacobi(double[] lambda, Matrix S) Computes all eigenvalues and eigenvectors of a real symmetric matrix this.
Matrix	mult(double a) This method returns of new matrix with each entry multiplied by a.
Matrix	mult(Matrix A) This method creates a new matrix and stores the product of this and A in it.
Vector	mult(Vector x) This method returns a new vector that is the result of this multplied with x.
int	nColumns() This method returns the number of columns in the matrix.
int	nRows() This method returns the number of rows in the matrix.
static double	pythag(double a, double b) Computes (a² + b²)½ without destructive underflow or overflow.
private void	rotate(int i, int j, int k, int l, double s, double tau) The method performs a Jacobi rotation between entries (i, j) and (k, l).
void	set(int i, int j, double c) This method sets element (i, j) to c.
static double	sign(double a, double b)
Matrix	sub(Matrix A) This method creates a new matrix and stores the difference of this and A in it.
static Vector	svbksb(Matrix U, double[] w, Matrix V, Vector b) Solves A·X = B for a vector X, where is specified by the matrices U and V and the array of singular values w as returned by svdcmp.
void	svdcmp(Matrix U, double[] w, Matrix V) Given a matrix, this routine computes its singular value decomposition, UWVT.
private void	swap(int i, int j, int k, int l) This method exchanges entry (i, j) with entry (k, l).
Matrix	t() This method returns a new matrix containing the transpose of this.
String	toString() This method creates a string from the matrix.

Methods inherited from class java.lang.Object

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

Field Detail

mem

public double[][] mem

This member is the reference to the arrays where the entries of the matrix are stored.

Constructor Detail

Matrix

public Matrix()

This is the default constructor. It does not allocate any memory.

Matrix

public Matrix(int m,
              int n)

This constructor builds a zero matrix of size m-by-n.

Matrix

public Matrix(double[][] b)

This constructor builds a matrix from the double array b.

Matrix

public Matrix(Matrix A)

This constructor builds a matrix from the matrix A.

Method Detail

nRows

public int nRows()

This method returns the number of rows in the matrix.

nColumns

public int nColumns()

This method returns the number of columns in the matrix.

get

public double get(int i,
                  int j)
           throws ArrayIndexOutOfBoundsException,
                  NullPointerException

This method returns the (i, j) entry of the matrix.

ArrayIndexOutOfBoundsException

NullPointerException

getRow

public Vector getRow(int i)
              throws ArrayIndexOutOfBoundsException,
                     NullPointerException

This method returns row i of the matrix.

ArrayIndexOutOfBoundsException

NullPointerException

getColumn

public Vector getColumn(int j)
                 throws ArrayIndexOutOfBoundsException,
                        NullPointerException

This method returns column j of the matrix.

ArrayIndexOutOfBoundsException

NullPointerException

set

public void set(int i,
                int j,
                double c)
         throws ArrayIndexOutOfBoundsException,
                NullPointerException

This method sets element (i, j) to c.

ArrayIndexOutOfBoundsException

NullPointerException

assign

public Matrix assign(double[][] b)
              throws ArrayStoreException

This method replaces the contents of the mem array with the data contained in b. Each sub-array of b must be of the same length.

ArrayStoreException

assign

public Matrix assign(Matrix A)

This method replaces the members of this with those of A.

equals

public boolean equals(Matrix A)
               throws ArithmeticException

This method compares if two matrices are equal. They are equal if and only if every element of this is equal to evey element of A.

ArithmeticException

add

public Matrix add(Matrix A)
           throws ArithmeticException

This method creates a new matrix and stores the sum of this and A in it.

The matrices must be the same size.

ArithmeticException

sub

public Matrix sub(Matrix A)
           throws ArithmeticException

This method creates a new matrix and stores the difference of this and A in it.

The matrices must be the same size.

ArithmeticException

mult

public Matrix mult(Matrix A)
            throws ArithmeticException

This method creates a new matrix and stores the product of this and A in it.

The number of columns in this must equal the number of rows of A.

ArithmeticException

mult

public Matrix mult(double a)

This method returns of new matrix with each entry multiplied by a.

mult

public Vector mult(Vector x)
            throws ArithmeticException

This method returns a new vector that is the result of this multplied with x.

The number of columns of this must be equal to the dimension of x.

ArithmeticException

t

public Matrix t()
         throws ArithmeticException

This method returns a new matrix containing the transpose of this.

The matrix must be a square matrix.

ArithmeticException

swap

private void swap(int i,
                  int j,
                  int k,
                  int l)

This method exchanges entry (i, j) with entry (k, l).

It is called by gaussj.

gaussj

public Matrix gaussj(Matrix B)
              throws ArithmeticException

Linear equation solution by Gauss-Jordan elimination. this references the input matrix. B is an n-by-m matrix containing the m right-hand side vectors. On output, a matrix is returned that is the inverse of this, and the values of B are replaced by the corresponding set of solution vectors.

ArithmeticException

See Also:

Gauss-Jordan elimination Algorithm

rotate

private void rotate(int i,
                    int j,
                    int k,
                    int l,
                    double s,
                    double tau)

The method performs a Jacobi rotation between entries (i, j) and (k, l).

eigsrt

public void eigsrt(double[] lambda)

Given the eigenvalues lambda[0..n-1] and eigenvectors contained in the matrix this as output from jacobi, this routine sorts the eigenvalues into descending order, and rearranges the columns the columns of this correspondingly. The method is straight insertion.

jacobi

public int jacobi(double[] lambda,
                  Matrix S)
           throws ArithmeticException,
                  ArrayStoreException

Computes all eigenvalues and eigenvectors of a real symmetric matrix this. lamdba contains the eigenvalues of this. S is a matrix whose columns contain, on output, the normalized eigenvectors of this.

ArithmeticException

ArrayStoreException

pythag

public static double pythag(double a,
                            double b)

Computes (a² + b²)^½ without destructive underflow or overflow.

sign

public static double sign(double a,
                          double b)

svbksb

public static Vector svbksb(Matrix U,
                            double[] w,
                            Matrix V,
                            Vector b)
                     throws ArithmeticException

Solves A·X = B for a vector X, where is specified by the matrices U and V and the array of singular values w as returned by svdcmp. b is the input right-hand side. No input quantities are destroyed, so the routine may be called sequentially with different b's.

ArithmeticException

svdcmp

public void svdcmp(Matrix U,
                   double[] w,
                   Matrix V)
            throws ArithmeticException,
                   ArrayStoreException

Given a matrix, this routine computes its singular value decomposition, UWV^T. The diagonal matrix of singular values W is output as the array w.

ArithmeticException

ArrayStoreException

toString

public String toString()

This method creates a string from the matrix.

Overrides:

toString in class Object

clone

public Object clone()

Overrides:

clone in class Object