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Class pmr.euclid.RealSquareMatrix

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

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.)

Author:

(C) P. Murray-Rust, 1996

RealSquareMatrix()

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

RealSquareMatrix(double[][])

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

RealSquareMatrix(int)

This gives a null matrix

RealSquareMatrix(int, double)

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

RealSquareMatrix(int, double[])

Formed by feeding in an existing array to a colsXcols matrix.

RealSquareMatrix(RealMatrix)

assign a RealMatrix - i.e.

RealSquareMatrix(RealMatrix, int, int, int)

submatrix of another matrix

RealSquareMatrix(RealSquareMatrix)

copyLowerToUpper()

copy lower triangle into upper triangle (i.e.

copyUpperToLower()

copy upper triangle into lower triangle (i.e.

determinant()

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

diagonal(RealArray)

make diagonal matrix

diagonaliseAndReturnRank(RealArray, RealSquareMatrix, IllConditionedMatrixException)

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

Note that IllConditionedMatrixException is RETURNED and not thrown

equals(RealSquareMatrix)

are two matrices identical?

getInverse()

inversion of matrix - creates NEW matrix

isImproperRotation()

is matrix an improper rotation?

isLowerTriangular()

is matrix lower triangular (including diagonal)?

isOrthogonal()

is matrix orthogonal? (rowwise calculation)

isOrthonormal()

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

isSymmetric()

is matrix symmetric?

isUnit()

is it a unit matrix?

isUnitary()

isUpperTriangular()

is matrix UpperTriangular?

lowerTriangle()

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

main(String[])

tests RealSquareMatrix routines

multiply(RealSquareMatrix)

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

orthogonalise()

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

orthonormalise()

orthonormalise matrix (only works for 3x3 at present)

outerProduct(RealArray)

special types of matrix (Outerproduct, Diagonal, etc)

plus(RealSquareMatrix)

matrix addition - adds conformable matrices

shallowCopy(RealSquareMatrix)

shallowCopy an existing object

subtract(RealSquareMatrix)

matrix subtraction - subtracts conformable matrices

trace()

trace

transpose()

transpose - MODIFIES matrix

  public RealSquareMatrix()

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

  public RealSquareMatrix(int rows)

This gives a null matrix

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

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: InvalidArgumentException

array size must be multiple of rows

  public RealSquareMatrix(int rows,
                          double f)

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

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

submatrix of another matrix

Throws: InvalidArgumentException

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

  public RealSquareMatrix(RealSquareMatrix m)

  public RealSquareMatrix(RealMatrix m) throws NonSquareMatrixException

assign a RealMatrix - i.e. NOT copied

Throws: NonSquareMatrixException

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

  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!)

  public static RealSquareMatrix outerProduct(RealArray f)

special types of matrix (Outerproduct, Diagonal, etc)

  public static RealSquareMatrix diagonal(RealArray f)

make diagonal matrix

  public void shallowCopy(RealSquareMatrix m) throws UnconformableMatricesException

shallowCopy an existing object

Throws: UnconformableMatricesException

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

  public boolean equals(RealSquareMatrix r) throws UnconformableMatricesException

are two matrices identical?

Throws: UnconformableMatricesException

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

  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

  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

  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

  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 ... -(

  public double trace()

trace

  public boolean isUnit()

is it a unit matrix?

  public boolean isSymmetric()

is matrix symmetric?

  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 ... -(

  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 ... -(

  public boolean isOrthonormal()

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

  public boolean isUnitary()

  public boolean isImproperRotation()

is matrix an improper rotation?

  public boolean isUpperTriangular()

is matrix UpperTriangular?

  public boolean isLowerTriangular()

is matrix lower triangular (including diagonal)?

  public boolean isOrthogonal()

is matrix orthogonal? (rowwise calculation)

Overrides:

isOrthogonal in class RealMatrix

  public RealSquareMatrix copyUpperToLower()

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

  public RealSquareMatrix copyLowerToUpper()

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

  public RealArray lowerTriangle()

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

  public void transpose()

transpose - MODIFIES matrix

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

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

Note that IllConditionedMatrixException is RETURNED and not thrown

Throws: ArrayTooSmallException

must have at least order 2

  public RealSquareMatrix getInverse() throws SingularMatrixException

inversion of matrix - creates NEW matrix

Throws: SingularMatrixException

singular matrix (or worse!)

  public static void main(String args[])

tests RealSquareMatrix routines

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