jumbo.euclid
Class RealSquareMatrix

java.lang.Object
  |
  +--jumbo.euclid.Status
        |
        +--jumbo.euclid.RealMatrix
              |
              +--jumbo.euclid.RealSquareMatrix

Direct Known Subclasses:

Transform2, Transform3

public class RealSquareMatrix

extends RealMatrix

RealSquareMatrix - square matrix class

RealSquareMatrix represents a square m-x-m matrix. The basic matrix algebra for square matrices is represented here Check out the exciting member functions, which are supported by Exceptions where appropriate. (NB. No attempt has been made to provide numerical robustness and inversion, diagonalisation, etc are as you find them.)

Fields inherited from class jumbo.euclid.RealMatrix

cols, flmat, rows

Constructor Summary

RealSquareMatrix()
This gives a default matrix, with cols = rows = 0.

RealSquareMatrix(double[][] matrix)
form from a Java 2-D array (it holds row and column count)

RealSquareMatrix(int rows)
This gives a null matrix

RealSquareMatrix(int rows, double f)
initalises all elements in the array with a given double[]

RealSquareMatrix(int rows, double[] array)
Formed by feeding in an existing array to a colsXcols matrix.

RealSquareMatrix(RealMatrix m)
assign a RealMatrix - i.e.

RealSquareMatrix(RealMatrix m, int lowrow, int lowcol, int rows)
submatrix of another matrix

RealSquareMatrix(RealSquareMatrix m)

Method Summary

RealSquareMatrix	copyLowerToUpper() copy lower triangle into upper triangle (i.e.
RealSquareMatrix	copyUpperToLower() copy upper triangle into lower triangle (i.e.
double	determinant() determinant - only goes up to order 3 at present :-(
static RealSquareMatrix	diagonal(RealArray f) make diagonal matrix
int	diagonaliseAndReturnRank(RealArray eigenvalues, RealSquareMatrix eigenvectors, IllCondMatrixException illCond) diagonalisation - returns eigenvalues and vectors as MODIFIED arguments; this is NOT affected
boolean	equals(RealSquareMatrix r) are two matrices identical?
RealSquareMatrix	getInverse() inversion of matrix - creates NEW matrix
boolean	isImproperRotation() is matrix an improper rotation?
boolean	isLowerTriangular() is matrix lower triangular (including diagonal)?
boolean	isOrthogonal() is matrix orthogonal? (rowwise calculation)
boolean	isOrthonormal() is matrix unitary (orthonormal)? (synonym for isUnitary())
boolean	isSymmetric() is matrix symmetric?
boolean	isUnit() is it a unit matrix?
boolean	isUnitary()
boolean	isUpperTriangular() is matrix UpperTriangular?
RealArray	lowerTriangle() copy lower triangle into linear array; order: 0,0; 1,0; 1,1; 2,0 ..
static void	main(java.lang.String[] args) tests RealSquareMatrix routines
RealSquareMatrix	multiply(RealSquareMatrix m) matrix multiplication - multiplies conformable matrices; result is this*m
void	orthogonalise() orthogonalise matrix (only works for 3x3 at present); MODIFIES matrix
RealSquareMatrix	orthonormalise() orthonormalise matrix (only works for 3x3 at present)
static RealSquareMatrix	outerProduct(RealArray f) special types of matrix (Outerproduct, Diagonal, etc)
RealSquareMatrix	plus(RealSquareMatrix m) matrix addition - adds conformable matrices
void	shallowCopy(RealSquareMatrix m) shallowCopy an existing object
RealSquareMatrix	subtract(RealSquareMatrix m) matrix subtraction - subtracts conformable matrices
double	trace() trace
void	transpose() transpose - MODIFIES matrix

Methods inherited from class jumbo.euclid.RealMatrix

appendColumnData, appendColumnData, appendRowData, appendRowData, clearMatrix, clone, columnwiseDivide, deleteColumn, deleteColumns, deleteRow, deleteRows, elementAt, elementAt, elementsInRange, equals, euclideanColumnLength, euclideanColumnLengths, euclideanRowLength, euclideanRowLengths, extractColumnData, extractRowData, extractSubMatrixData, getCols, getMatrix, getMatrixAsArray, getRows, getTranspose, indexOfLargestElement, indexOfLargestElementInColumn, indexOfLargestElementInRow, indexOfSmallestElement, indexOfSmallestElementInColumn, indexOfSmallestElementInRow, insertColumnData, insertColumnData, insertColumns, insertRowData, insertRowData, insertRows, isSquare, largestElement, largestElementInColumn, largestElementInRow, multiply, multiply, multiplyBy, negative, normaliseByColumns, normaliseByRows, plus, reorderColumnsBy, reorderRowsBy, replaceColumnData, replaceColumnData, replaceColumnData, replaceRowData, replaceRowData, replaceRowData, replaceSubMatrixData, setAllElements, setElementAt, shallowCopy, smallestElement, smallestElementInColumn, smallestElementInRow, subtract, toString

Methods inherited from class jumbo.euclid.Status

NYI

Methods inherited from class java.lang.Object

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

Constructor Detail

RealSquareMatrix

public RealSquareMatrix()

This gives a default matrix, with cols = rows = 0.

RealSquareMatrix

public RealSquareMatrix(int rows)

This gives a null matrix

RealSquareMatrix

public RealSquareMatrix(int rows,
                        double[] array)
                 throws BadArgumentException

Formed by feeding in an existing array to a colsXcols matrix. THE COLUMN IS THE FASTEST MOVING INDEX, i.e. the matrix is filled as mat(0,0), mat(0,1) ... C-LIKE

Throws:

BadArgumentException - array size must be multiple of rows

RealSquareMatrix

public RealSquareMatrix(int rows,
                        double f)

initalises all elements in the array with a given double[]

RealSquareMatrix

public RealSquareMatrix(RealMatrix m,
                        int lowrow,
                        int lowcol,
                        int rows)
                 throws BadArgumentException

submatrix of another matrix

Throws:

BadArgumentException - lowrow, lowcol or rows are not consistent with size of m

RealSquareMatrix

public RealSquareMatrix(RealSquareMatrix m)

RealSquareMatrix

public RealSquareMatrix(RealMatrix m)
                 throws NonSquareException

assign a RealMatrix - i.e. NOT copied

Throws:

NonSquareException - m must be square (i.e. cols = rows)

RealSquareMatrix

public RealSquareMatrix(double[][] matrix)
                 throws MatrixShapeException

form from a Java 2-D array (it holds row and column count)

Throws:

MatrixShapeException - matrix is not square (might even not be rectangular!)

Method Detail

outerProduct

public static RealSquareMatrix outerProduct(RealArray f)

special types of matrix (Outerproduct, Diagonal, etc)

diagonal

public static RealSquareMatrix diagonal(RealArray f)

make diagonal matrix

shallowCopy

public void shallowCopy(RealSquareMatrix m)
                 throws UnequalMatricesException

shallowCopy an existing object

Throws:

UnequalMatricesException - m must have the same number of rows and cols as this

equals

public boolean equals(RealSquareMatrix r)
               throws UnequalMatricesException

are two matrices identical?

Throws:

UnequalMatricesException - m must have the same number of rows and cols as this

plus

public RealSquareMatrix plus(RealSquareMatrix m)
                      throws MatrixShapeException

matrix addition - adds conformable matrices

Throws:

MatrixShapeException - m must have the same number of rows and cols as this

subtract

public RealSquareMatrix subtract(RealSquareMatrix m)
                          throws MatrixShapeException

matrix subtraction - subtracts conformable matrices

Throws:

MatrixShapeException - m must have the same number of rows and cols as this

multiply

public RealSquareMatrix multiply(RealSquareMatrix m)
                          throws MatrixShapeException

matrix multiplication - multiplies conformable matrices; result is this*m

Throws:

MatrixShapeException - m must have the same number of rows as this has cols

determinant

public double determinant()
                   throws UnimplementedException

determinant - only goes up to order 3 at present :-(

Throws:

UnimplementedException - I have only written this for this.rows up to 3. If anyone can find a determinant routine, this will disappear ... -(

trace

public double trace()

trace

isUnit

public boolean isUnit()

is it a unit matrix?

isSymmetric

public boolean isSymmetric()

is matrix symmetric?

orthonormalise

public RealSquareMatrix orthonormalise()
                                throws UnimplementedException

orthonormalise matrix (only works for 3x3 at present)

Throws:

UnimplementedException - I have only written this for this.rows up to 3. If anyone can find a routine, this will disappear ... -(

isOrthonormal

public boolean isOrthonormal()

is matrix unitary (orthonormal)? (synonym for isUnitary())

isUpperTriangular

public boolean isUpperTriangular()

is matrix UpperTriangular?

isLowerTriangular

public boolean isLowerTriangular()

is matrix lower triangular (including diagonal)?

isOrthogonal

public boolean isOrthogonal()

is matrix orthogonal? (rowwise calculation)

Overrides:

isOrthogonal in class RealMatrix

isImproperRotation

public boolean isImproperRotation()

is matrix an improper rotation?

isUnitary

public boolean isUnitary()

copyUpperToLower

public RealSquareMatrix copyUpperToLower()

copy upper triangle into lower triangle (i.e. make symmetric)

copyLowerToUpper

public RealSquareMatrix copyLowerToUpper()

copy lower triangle into upper triangle (i.e. make symmetric)

lowerTriangle

public RealArray lowerTriangle()

copy lower triangle into linear array; order: 0,0; 1,0; 1,1; 2,0 ..

transpose

public void transpose()

transpose - MODIFIES matrix

diagonaliseAndReturnRank

public int diagonaliseAndReturnRank(RealArray eigenvalues,
                                    RealSquareMatrix eigenvectors,
                                    IllCondMatrixException illCond)
                             throws ArrayTooSmallException

diagonalisation - returns eigenvalues and vectors as MODIFIED arguments; this is NOT affected

Note that IllCondMatrixException is RETURNED and not thrown

Throws:

ArrayTooSmallException - must have at least order 2

orthogonalise

public void orthogonalise()
                   throws UnimplementedException

orthogonalise matrix (only works for 3x3 at present); MODIFIES matrix

Throws:

UnimplementedException - I have only written this for this.rows up to 3. If anyone can find a routine, this will disappear ... -(

getInverse

public RealSquareMatrix getInverse()
                            throws SingMatrixException

inversion of matrix - creates NEW matrix

Throws:

SingMatrixException - singular matrix (or worse!)

main

public static void main(java.lang.String[] args)

tests RealSquareMatrix routines