org.openscience.cdk.graph.invariant

Class GIMatrix

java.lang.Object

org.openscience.cdk.graph.invariant.GIMatrix

public class GIMatrix
extends Object

This class is intended to provide the user an efficient way of implementing matrix of double number and using normal operations (linear operations, addition, subtraction, multiplication, inversion, concatenation) on them. The internal representation of a matrix is an array of array of double objects. For the moment, double class is the best way I have developed to perform exact operation on numbers; however, for irdoubles, normal operations on float and doubles have to be performed, with the well-known risks of error this implies. This class also provides a way of representing matrix as arrays of String for output use.

Please note that although in most books matrix elements' indexes take values between [1..n] I chose not to disturb Java language way of calling indexes; so the indexes used here take values between [0..n-1] instead.

Version:

1.0

Author:

Jean-Sebastien Senecal

Source code:

master

Created on:

1999-05-20

Constructor Summary

Constructors

Constructor and Description
GIMatrix(double[][] array) Class constructor.
GIMatrix(GIMatrix matrix) Class constructor.
GIMatrix(GIMatrix[][] table) Class constructor.
GIMatrix(int[][] array) Class constructor.
GIMatrix(int line, int col) Class constructor.

Method Summary

Modifier and Type	Method and Description
GIMatrix	add(GIMatrix b) Addition from two matrices.
GIMatrix	addLine(int i, int j, double c) Returns the resulting matrix of an elementary linear operation that consists of adding one line, multiplied by some constant factor, to another line.
double	determinant() Returns the determinant of this matrix.
GIMatrix	diagonal() Returns a matrix containing all of the diagonal elements of this matrix and zero (0) everywhere else.
boolean	equals(GIMatrix matrix) Verifies if two given matrix are equal or not.
GIMatrix	GaussJordan() Gauss-Jordan algorithm.
double[][]	getArrayValue() Returns the internal representation of the matrix, that is an array of double objects.
GIMatrix	getColumn(int j) Returns the column-matrix at the given line index.
GIMatrix	getLine(int i) Returns the line-matrix at the given line index.
double	getValueAt(int i, int j) Returns the value of the given element.
int	height() Returns the number of lines of the matrix.
static GIMatrix	identity(int n) Returns the identity matrix.
GIMatrix	inverse() Returns the transpose of this matrix.
GIMatrix	invertLine(int i, int j) Returns the resulting matrix of an elementary linear operation that consists of inverting two lines.
boolean	isAntisymmetric() Verifies if the matrix is antisymmetric, that is if the matrix is equal to the opposite of it's transpose.
boolean	isDiagonal() Verifies whether or not the matrix is diagonal.
boolean	isInvertible() Verifies if the matrix is invertible or not by asking for its determinant.
boolean	isSquare() Verifies if the matrix is square, that is if it has an equal number of lines and columns.
boolean	isSymmetric() Verifies if the matrix is symmetric, that is if the matrix is equal to it's transpose.
boolean	isTriangularInferior() Verifies if the matrix is triangular inferior or not.
boolean	isTriangularSuperior() Verifies if the matrix is triangular superior or not.
GIMatrix	multiply(double c) Returns the result of the scalar multiplication of the matrix, that is the multiplication of every of its elements by a given number.
GIMatrix	multiply(GIMatrix matrix) Returns the result of the matrix multiplication of this matrix by another one.
GIMatrix	multiplyLine(int i, double c) Returns the resulting matrix of an elementary linear operation that consists of multiplying a single line of the matrix by a constant.
void	setArrayValue(double[][] array) Resets the value of the matrix to the given array of double numbers.
void	setColumn(int j, GIMatrix column) Sets the column of the matrix at the specified index to a new value.
void	setLine(int i, GIMatrix line) Sets the line of the matrix at the specified index to a new value.
void	setValueAt(int i, int j, double element) Sets the value of the element at the given index.
double	trace() Returns the trace of this matrix, that is the sum of the elements of its diagonal.
GIMatrix	transpose() Returns the transpose of this matrix.
int	width() Returns the number of columns of the matrix.
static GIMatrix	zero(int m, int n) Returns a null matrix (with zeros everywhere) of given dimensions.

Methods inherited from class java.lang.Object

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

Constructor Detail

GIMatrix

public GIMatrix(int[][] array)

Class constructor. Uses an array of integers to create a new Matrix object. Note that integers will be converted to double objects so mathematical operations may be properly performed and provide exact solutions. The given array should be properly instantiated as a matrix i.e. it must contain a fixed number of lines and columns, otherwise an exception will be thrown. Array must be at leat 1x1.

Parameters:

array - an array of integer (first index is the line, second is the column)

GIMatrix

public GIMatrix(double[][] array)
         throws BadMatrixFormatException

Class constructor. Uses an array of doubles to create a new Matrix object. The given array should be properly instantiated as a matrix i.e. it must contain a fixed number of lines and columns, otherwise an exception will be thrown. Array must be at leat 1x1.

Parameters:

array - an array of double objects (first index is the line, second is the column)

Throws:

BadMatrixFormatException - in case the given array is unproper to construct a matrix

GIMatrix

public GIMatrix(int line,
                int col)

Class constructor. Creates a new Matrix object with fixed dimensions. The matrix is initialised to the "zero" matrix.

Parameters:

line - number of lines

col - number of columns

GIMatrix

public GIMatrix(GIMatrix matrix)

Class constructor. Copies an already existing Matrix object in a new Matrix object.

Parameters:

matrix - a Matrix object

GIMatrix

public GIMatrix(GIMatrix[][] table)
         throws BadMatrixFormatException

Class constructor. Creates a new Matrix object using a table of matrices (an array of Matrix objects). The given array should be properly instantiated i.e. it must contain a fixed number of lines and columns, otherwise an exception will be thrown.

Parameters:

table - an array of matrices

Throws:

BadMatrixFormatException - if the table is not properly instantiated

Method Detail

height

public int height()

Returns the number of lines of the matrix.

Returns:

the height of the matrix

width

public int width()

Returns the number of columns of the matrix.

Returns:

the width of the matrix

getArrayValue

public double[][] getArrayValue()

Returns the internal representation of the matrix, that is an array of double objects.

Returns:

an array of double equivalent to the matrix

setArrayValue

public void setArrayValue(double[][] array)
                   throws BadMatrixFormatException

Resets the value of the matrix to the given array of double numbers.

Parameters:

array - an array of double objects (first index is the line, second is the column)

Throws:

BadMatrixFormatException - in case the given array is unproper to construct a matrix

getValueAt

public double getValueAt(int i,
                         int j)
                  throws IndexOutOfBoundsException

Returns the value of the given element.

Parameters:

i - the line number

j - the column number

Returns:

the double at the given index in the Matrix

Throws:

IndexOutOfBoundsException - if the given index is out of the matrix's range

setValueAt

public void setValueAt(int i,
                       int j,
                       double element)
                throws IndexOutOfBoundsException

Sets the value of the element at the given index.

Parameters:

i - the line number

j - the column number

element - the double to place at the given index in the Matrix

Throws:

IndexOutOfBoundsException - if the given index is out of the matrix's range

getLine

public GIMatrix getLine(int i)
                 throws IndexOutOfBoundsException

Returns the line-matrix at the given line index.

Parameters:

i - the line number

Returns:

the specified line as a Matrix object

Throws:

IndexOutOfBoundsException - if the given index is out of the matrix's range

getColumn

public GIMatrix getColumn(int j)
                   throws IndexOutOfBoundsException

Returns the column-matrix at the given line index.

Parameters:

j - the column number

Returns:

the specified column as a Matrix object

Throws:

IndexOutOfBoundsException - if the given index is out of the matrix's range

setLine

public void setLine(int i,
                    GIMatrix line)
             throws IndexOutOfBoundsException,
                    BadMatrixFormatException

Sets the line of the matrix at the specified index to a new value.

Parameters:

i - the line number

line - the line to be placed at the specified index

Throws:

IndexOutOfBoundsException - if the given index is out of the matrix's range

BadMatrixFormatException - in case the given Matrix is unproper to replace a line of this Matrix

setColumn

public void setColumn(int j,
                      GIMatrix column)
               throws IndexOutOfBoundsException,
                      BadMatrixFormatException

Sets the column of the matrix at the specified index to a new value.

Parameters:

j - the column number

column - the column to be placed at the specified index

Throws:

IndexOutOfBoundsException - if the given index is out of the matrix's range

BadMatrixFormatException - in case the given Matrix is unproper to replace a column of this Matrix

identity

public static GIMatrix identity(int n)

Returns the identity matrix.

Parameters:

n - the matrix's dimension (identity matrix is a square matrix)

Returns:

the identity matrix of format nxn

zero

public static GIMatrix zero(int m,
                            int n)

Returns a null matrix (with zeros everywhere) of given dimensions.

Parameters:

m - number of lines

n - number of columns

Returns:

the zero (null) matrix of format mxn

equals

public boolean equals(GIMatrix matrix)
               throws BadMatrixFormatException

Verifies if two given matrix are equal or not. The matrix must be of the same size and dimensions, otherwise an exception will be thrown.

Parameters:

matrix - the Matrix object to be compared to

Returns:

true if both matrix are equal element to element

Throws:

BadMatrixFormatException - if the given matrix doesn't have the same dimensions as this one

isSquare

public boolean isSquare()

Verifies if the matrix is square, that is if it has an equal number of lines and columns.

Returns:

true if this matrix is square

isSymmetric

public boolean isSymmetric()
                    throws BadMatrixFormatException

Verifies if the matrix is symmetric, that is if the matrix is equal to it's transpose.

Returns:

true if the matrix is symmetric

Throws:

BadMatrixFormatException - if the matrix is not square

isAntisymmetric

public boolean isAntisymmetric()
                        throws BadMatrixFormatException

Verifies if the matrix is antisymmetric, that is if the matrix is equal to the opposite of it's transpose.

Returns:

true if the matrix is antisymmetric

Throws:

BadMatrixFormatException - if the matrix is not square

isTriangularSuperior

public boolean isTriangularSuperior()
                             throws BadMatrixFormatException

Verifies if the matrix is triangular superior or not. A triangular superior matrix has zero (0) values everywhere under it's diagonal.

Returns:

true if the matrix is triangular superior

Throws:

BadMatrixFormatException - if the matrix is not square

isTriangularInferior

public boolean isTriangularInferior()
                             throws BadMatrixFormatException

Verifies if the matrix is triangular inferior or not. A triangular inferior matrix has zero (0) values everywhere upper it's diagonal.

Returns:

true if the matrix is triangular inferior

Throws:

BadMatrixFormatException - if the matrix is not square

isDiagonal

public boolean isDiagonal()
                   throws BadMatrixFormatException

Verifies whether or not the matrix is diagonal. A diagonal matrix only has elements on its diagonal and zeros (0) at every other index. The matrix must be square.

Returns:

true if the matrix is diagonal

Throws:

BadMatrixFormatException - if the matrix is not square

isInvertible

public boolean isInvertible()
                     throws BadMatrixFormatException

Verifies if the matrix is invertible or not by asking for its determinant.

Returns:

true if the matrix is invertible

Throws:

BadMatrixFormatException - if the matrix is not square

inverse

public GIMatrix inverse()
                 throws MatrixNotInvertibleException

Returns the transpose of this matrix. The transpose of a matrix A = {a(i,j)} is the matrix B = {b(i,j)} such that b(i,j) = a(j,i) for every i,j i.e. it is the symmetrical reflection of the matrix along its diagonal. The matrix must be square to use this method, otherwise an exception will be thrown.

Returns:

the matrix's transpose as a Matrix object

Throws:

MatrixNotInvertibleException - if the matrix is not square

GaussJordan

public GIMatrix GaussJordan()

Gauss-Jordan algorithm. Returns the reduced-echeloned matrix of this matrix. The algorithm has not yet been optimised but since it is quite simple, it should not be a serious problem.

Returns:

the reduced matrix

transpose

public GIMatrix transpose()
                   throws BadMatrixFormatException

Returns the transpose of this matrix. The transpose of a matrix A = {a(i,j)} is the matrix B = {b(i,j)} such that b(i,j) = a(j,i) for every i,j i.e. it is the symmetrical reflection of the matrix along its diagonal. The matrix must be square to use this method, otherwise an exception will be thrown.

Returns:

the matrix's transpose as a Matrix object

Throws:

BadMatrixFormatException - if the matrix is not square

diagonal

public GIMatrix diagonal()
                  throws BadMatrixFormatException

Returns a matrix containing all of the diagonal elements of this matrix and zero (0) everywhere else. This matrix is called the diagonal of the matrix.

Returns:

the diagonal of the matrix

Throws:

BadMatrixFormatException - if the matrix is not square

multiplyLine

public GIMatrix multiplyLine(int i,
                             double c)
                      throws IndexOutOfBoundsException

Returns the resulting matrix of an elementary linear operation that consists of multiplying a single line of the matrix by a constant.

Parameters:

i - the line number

c - the double constant that multiplies the line

Returns:

the resulting Matrix object of the linear operation

Throws:

IndexOutOfBoundsException - if the given index is out of the matrix's range

invertLine

public GIMatrix invertLine(int i,
                           int j)
                    throws IndexOutOfBoundsException

Returns the resulting matrix of an elementary linear operation that consists of inverting two lines.

Parameters:

i - the first line number

j - the second line number

Returns:

the resulting Matrix object of the linear operation

Throws:

IndexOutOfBoundsException - if the given index is out of the matrix's range

addLine

public GIMatrix addLine(int i,
                        int j,
                        double c)
                 throws IndexOutOfBoundsException

Returns the resulting matrix of an elementary linear operation that consists of adding one line, multiplied by some constant factor, to another line.

Parameters:

i - the first line number

j - the second line number (to be added to the first)

c - the double constant that multiplies the first line

Returns:

the resulting Matrix object of the linear operation

Throws:

IndexOutOfBoundsException - if the given index is out of the matrix's range

add

public GIMatrix add(GIMatrix b)

Addition from two matrices.

multiply

public GIMatrix multiply(double c)

Returns the result of the scalar multiplication of the matrix, that is the multiplication of every of its elements by a given number.

Parameters:

c - the constant by which the matrix is multiplied

Returns:

the resulting matrix of the scalar multiplication

multiply

public GIMatrix multiply(GIMatrix matrix)
                  throws BadMatrixFormatException

Returns the result of the matrix multiplication of this matrix by another one. The matrix passed as parameter follows this matrix in the multiplication, so for an example if the dimension of the actual matrix is mxn, the dimension of the second one should be nxp in order for the multiplication to be performed (otherwise an exception will be thrown) and the resulting matrix will have dimension mxp.

Parameters:

matrix - the matrix following this one in the matrix multiplication

Returns:

the resulting matrix of the matrix multiplication

Throws:

BadMatrixFormatException - if the matrix passed in arguments has wrong dimensions

determinant

public double determinant()
                   throws BadMatrixFormatException

Returns the determinant of this matrix. The matrix must be square in order to use this method, otherwise an exception will be thrown. Warning: this algorithm is very inefficient and takes too much time to compute with large matrices.

Returns:

the determinant of the matrix

Throws:

BadMatrixFormatException - if the matrix is not square

trace

public double trace()
             throws BadMatrixFormatException

Returns the trace of this matrix, that is the sum of the elements of its diagonal. The matrix must be square in order to use this method, otherwise an exception will be thrown.

Returns:

the trace of the matrix

Throws:

BadMatrixFormatException - if the matrix is not square