jahuwaldt.js.param

Class Matrix3D<Q extends Quantity>

java.lang.Object

org.jscience.mathematics.vector.Matrix<Parameter<Q>>

jahuwaldt.js.param.Matrix3D<Q>

All Implemented Interfaces:

j2me.io.Serializable, javolution.lang.Immutable, javolution.lang.Realtime, javolution.lang.ValueType, javolution.xml.XMLSerializable, GroupAdditive<Matrix<Parameter<Q>>>, Ring<Matrix<Parameter<Q>>>, Structure<Matrix<Parameter<Q>>>, VectorSpace<Matrix<Parameter<Q>>,Parameter<Q>>

public final class Matrix3D<Q extends Quantity>
extends Matrix<Parameter<Q>>
implements javolution.lang.Realtime, javolution.lang.ValueType, javolution.xml.XMLSerializable

This class represents a 3x3 matrix implementation for parameter elements.

Instances of this class can be created from Vector3D, either as rows or columns if the matrix is transposed. For example:

         Vector3D column0 = Vector3D.valueOf(...);
         Vector3D column1 = Vector3D.valueOf(...);
         Vector3D column2 = Vector3D.valueOf(...);
         Matrix3D M = Matrix3D.valueOf(column0, column1, column2).transpose();
 

Modified by: Joseph A. Huwaldt

Version:

October 23, 2015

Author:

Joseph A. Huwaldt, Date: November 26, 2008

Method Summary

Modifier and Type	Method and Description
Matrix3D	adjoint() Returns the adjoint of this matrix.
<T extends Quantity> Matrix3D<T>	asType(java.lang.Class<T> type) Casts this Matrix3D to a parameterized unit of specified nature or throw a ClassCastException if the specified quantity and this matrix unit dimension do not match.
Parameter	cofactor(int i, int j) Returns the cofactor of an element in this matrix.
Matrix3D<Q>	copy() Returns a copy of this matrix allocated by the calling thread (possibly on the stack).
Parameter	determinant() Returns the determinant of this matrix.
Parameter<Q>	get(int i, int j) Returns a single element from this matrix.
Vector3D<Q>	getColumn(int j) Returns the column identified by the specified index in this matrix.
Vector3D<Q>	getDiagonal() Returns the diagonal vector.
int	getNumberOfColumns() Returns the number of columns n for this matrix.
int	getNumberOfRows() Returns the number of rows m for this matrix.
Vector3D<Q>	getRow(int i) Returns the row identified by the specified index in this matrix.
Unit<Q>	getUnit() Returns the unit in which the values in this vector are stated.
double	getValue(int i, int j) Returns a single element from this matrix as a double.
Matrix3D	inverse() Returns the inverse of this matrix.
boolean	isApproxZero() Compares this Matrix3D for approximate equality to zero (all the values are within the numerical roundoff error of zero).
static void	main(java.lang.String[] args) Tests the methods in this class.
Matrix3D<Q>	minus(Matrix<Parameter<Q>> that) Returns the difference between this matrix and the one specified.
Matrix3D<Q>	opposite() Returns the negation of this matrix.
Matrix3D<Q>	plus(Matrix<Parameter<Q>> that) Returns the sum of this matrix with the one specified.
Matrix	tensor(Matrix that) Returns the linear algebraic matrix tensor product of this matrix and another (Kronecker product).
Matrix3D<Q>	times(double k) Returns the product of this matrix by the specified factor.
Matrix3D	times(Matrix that) Returns the product of this matrix with the one specified.
Matrix3D	times(Parameter k) Returns the product of this matrix by the specified factor.
Vector3D	times(Vector v) Returns the product of this matrix by the specified vector.
<R extends Quantity> Matrix3D<R>	to(Unit<R> unit) Returns the equivalent to this matrix but stated in the specified unit.
Float64Matrix	toFloat64Matrix() Returns a Float64Matrix containing the data in this matrix in the current units of this matrix.
Matrix3D<Q>	transpose() Returns the transpose of this matrix.
static <Q extends Quantity> Matrix3D<Q>	valueOf(double[][] matrix, Unit<Q> unit) Returns a Matrix3D instance containing the specified matrix of double values stated in the specified units.
static <Q extends Quantity> Matrix3D<Q>	valueOf(double a, double b, double c, double d, double e, double f, double g, double h, double i, Unit<Q> unit) Returns 3D matrix from a sequence of 9 double values.
static <Q extends Quantity> Matrix3D<Q>	valueOf(Float64Vector row0, Float64Vector row1, Float64Vector row2, Unit<Q> unit) Returns a 3D matrix holding the specified row vectors in the stated units (column vectors if transposed).
static <Q extends Quantity> Matrix3D<Q>	valueOf(java.util.List<Vector3D<Q>> rows) Returns a 3D matrix holding the row vectors from the specified collection (column vectors if transposed).
static <Q extends Quantity> Matrix3D<Q>	valueOf(Matrix<Float64> matrix, Unit<Q> unit) Returns a Matrix3D instance containing the specified matrix of Float64 values stated in the specified units.
static <Q extends Quantity> Matrix3D<Q>	valueOf(Matrix<Parameter<Q>> that) Returns a 3D matrix equivalent to the specified matrix.
static <Q extends Quantity> Matrix3D<Q>	valueOf(Vector3D<Q> row0, Vector3D<Q> row1, Vector3D<Q> row2) Returns a 3D matrix holding the specified row vectors (column vectors if transposed).
Vector<Parameter<Q>>	vectorization() Returns the vectorization of this matrix.

Methods inherited from class org.jscience.mathematics.vector.Matrix

divide, equals, equals, hashCode, isSquare, pow, pseudoInverse, solve, solve, toString, toText, trace

Methods inherited from class java.lang.Object

getClass, notify, notifyAll, wait, wait, wait

Methods inherited from interface javolution.lang.Realtime

toText

Method Detail

valueOf

public static <Q extends Quantity> Matrix3D<Q> valueOf(double a,
                                                       double b,
                                                       double c,
                                                       double d,
                                                       double e,
                                                       double f,
                                                       double g,
                                                       double h,
                                                       double i,
                                                       Unit<Q> unit)

Returns 3D matrix from a sequence of 9 double values.

Values are ordered as follows:

         | a b c |
         | d e f |
         | g h i |
 

Parameters:

a - matrix element 0,0

b - matrix element 0,1

c - matrix element 0,2

d - matrix element 1,0

e - matrix element 1,1

f - matrix element 1,2

g - matrix element 2,0

h - matrix element 2,1

i - matrix element 2,2

unit - the unit in which the elements are stated.

Returns:

the 3D matrix having the specified elements stated in the specified units.

valueOf

public static <Q extends Quantity> Matrix3D<Q> valueOf(Float64Vector row0,
                                                       Float64Vector row1,
                                                       Float64Vector row2,
                                                       Unit<Q> unit)

Returns a 3D matrix holding the specified row vectors in the stated units (column vectors if transposed).

Parameters:

row0 - the 1st row vector.

row1 - the 2nd row vector.

row2 - the 3rd row vector.

unit - the unit in which the elements are stated.

Returns:

the 3D matrix having the specified elements stated in the specified units.

valueOf

public static <Q extends Quantity> Matrix3D<Q> valueOf(Vector3D<Q> row0,
                                                       Vector3D<Q> row1,
                                                       Vector3D<Q> row2)

Returns a 3D matrix holding the specified row vectors (column vectors if transposed). All the values are converted to the same units as the 1st row (row0).

Parameters:

row0 - the 1st row vector.

row1 - the 2nd row vector.

row2 - the 3rd row vector.

Returns:

the 3D matrix having the specified rows.

valueOf

public static <Q extends Quantity> Matrix3D<Q> valueOf(java.util.List<Vector3D<Q>> rows)

Returns a 3D matrix holding the row vectors from the specified collection (column vectors if transposed). All the values are converted to the same units as the 1st row (row0).

Parameters:

rows - The list of row vectors. If there are more than 3 elements, an exception is thrown.

Returns:

the 3D matrix having the specified rows.

Throws:

DimensionException - if the rows do not have a dimension of 3.

valueOf

public static <Q extends Quantity> Matrix3D<Q> valueOf(Matrix<Float64> matrix,
                                                       Unit<Q> unit)

Returns a Matrix3D instance containing the specified matrix of Float64 values stated in the specified units. The input matrix must have dimensions of 3x3.

Parameters:

matrix - the matrix of Float64 values stated in the specified unit (must have dimension of 3x3).

unit - the unit in which the elements are stated.

Returns:

the matrix having the specified values.

valueOf

public static <Q extends Quantity> Matrix3D<Q> valueOf(double[][] matrix,
                                                       Unit<Q> unit)

Returns a Matrix3D instance containing the specified matrix of double values stated in the specified units. The input matrix must have dimensions of 3x3.

Parameters:

matrix - the matrix of double values stated in the specified unit (must have dimension of 3x3).

unit - the unit in which the elements are stated.

Returns:

the matrix having the specified values.

valueOf

public static <Q extends Quantity> Matrix3D<Q> valueOf(Matrix<Parameter<Q>> that)

Returns a 3D matrix equivalent to the specified matrix. All the values are converted to the same units as the 1st element (row=0,column=0).

Parameters:

that - the matrix to convert.

Returns:

that or a 3D matrix holding the same elements as the specified matrix.

getNumberOfRows

public int getNumberOfRows()

Returns the number of rows m for this matrix. This implementation always returns 3.

Specified by:

getNumberOfRows in class Matrix<Parameter<Q extends Quantity>>

Returns:

m, the number of rows.

getNumberOfColumns

public int getNumberOfColumns()

Returns the number of columns n for this matrix. This implementation always returns 3.

Specified by:

getNumberOfColumns in class Matrix<Parameter<Q extends Quantity>>

Returns:

n, the number of columns.

getUnit

public Unit<Q> getUnit()

Returns the unit in which the values in this vector are stated.

to

public <R extends Quantity> Matrix3D<R> to(Unit<R> unit)

Returns the equivalent to this matrix but stated in the specified unit.

Parameters:

unit - the unit of the matrix to be returned.

Returns:

a matrix equivalent to this vector but stated in the specified unit.

Throws:

ConversionException - if the current model does not allows for conversion to the specified unit.

asType

public <T extends Quantity> Matrix3D<T> asType(java.lang.Class<T> type)
                                        throws java.lang.ClassCastException

Casts this Matrix3D to a parameterized unit of specified nature or throw a ClassCastException if the specified quantity and this matrix unit dimension do not match.

Parameters:

type - the quantity class identifying the nature of the unit.

Returns:

this matrix parameterized with the specified type.

Throws:

java.lang.ClassCastException - if the dimension of this parameter's unit is different from the specified quantity dimension.

java.lang.UnsupportedOperationException - if the specified quantity class does not have a public static field named "UNIT" holding the standard unit for the quantity.

get

public Parameter<Q> get(int i,
                        int j)

Returns a single element from this matrix.

Specified by:

get in class Matrix<Parameter<Q extends Quantity>>

Parameters:

i - the row index (range [0..3[).

j - the column index (range [0..3[).

Returns:

the element read at [i,j].

getValue

public double getValue(int i,
                       int j)

Returns a single element from this matrix as a double.

Parameters:

i - the row index (range [0..3[).

j - the column index (range [0..3[).

Returns:

the element read at [i,j].

getRow

public Vector3D<Q> getRow(int i)

Returns the row identified by the specified index in this matrix.

Specified by:

getRow in class Matrix<Parameter<Q extends Quantity>>

Parameters:

i - the row index (range [0..3[).

Returns:

the vector holding the specified row.

getColumn

public Vector3D<Q> getColumn(int j)

Returns the column identified by the specified index in this matrix.

Specified by:

getColumn in class Matrix<Parameter<Q extends Quantity>>

Parameters:

j - the column index (range [0..3[).

Returns:

the vector holding the specified column.

getDiagonal

public Vector3D<Q> getDiagonal()

Returns the diagonal vector.

Specified by:

getDiagonal in class Matrix<Parameter<Q extends Quantity>>

Returns:

the vector holding the diagonal elements.

opposite

public Matrix3D<Q> opposite()

Returns the negation of this matrix.

Specified by:

opposite in interface GroupAdditive<Matrix<Parameter<Q extends Quantity>>>

Specified by:

opposite in class Matrix<Parameter<Q extends Quantity>>

Returns:

-this

plus

public Matrix3D<Q> plus(Matrix<Parameter<Q>> that)

Returns the sum of this matrix with the one specified.

Specified by:

plus in interface GroupAdditive<Matrix<Parameter<Q extends Quantity>>>

Specified by:

plus in class Matrix<Parameter<Q extends Quantity>>

Parameters:

that - the matrix to be added.

Returns:

this + that

Throws:

DimensionException - if the matrix dimensions are different.

minus

public Matrix3D<Q> minus(Matrix<Parameter<Q>> that)

Returns the difference between this matrix and the one specified.

Overrides:

minus in class Matrix<Parameter<Q extends Quantity>>

Parameters:

that - the matrix to be subtracted from this one.

Returns:

this - that

Throws:

DimensionException - if the matrix dimensions are different.

times

public Matrix3D times(Parameter k)

Returns the product of this matrix by the specified factor.

Specified by:

times in interface VectorSpace<Matrix<Parameter<Q extends Quantity>>,Parameter<Q extends Quantity>>

Specified by:

times in class Matrix<Parameter<Q extends Quantity>>

Parameters:

k - the coefficient multiplier

Returns:

this · k

times

public Matrix3D<Q> times(double k)

Returns the product of this matrix by the specified factor.

Parameters:

k - the coefficient multiplier

Returns:

this · k

times

public Vector3D times(Vector v)

Returns the product of this matrix by the specified vector.

Specified by:

times in class Matrix<Parameter<Q extends Quantity>>

Parameters:

v - the vector.

Returns:

this · v

Throws:

DimensionException - - if v.getDimension() != this.getNumberOfColumns()

times

public Matrix3D times(Matrix that)

Returns the product of this matrix with the one specified.

Specified by:

times in interface Ring<Matrix<Parameter<Q extends Quantity>>>

Specified by:

times in class Matrix<Parameter<Q extends Quantity>>

Parameters:

that - the matrix multiplier.

Returns:

this · that

Throws:

DimensionException - - if this.getNumberOfColumns() != that.getNumberOfRows().

inverse

public Matrix3D inverse()

Returns the inverse of this matrix. If the matrix is singular, the determinant() will be zero (or nearly zero).

Specified by:

inverse in class Matrix<Parameter<Q extends Quantity>>

Returns:

1 / this

determinant

public Parameter determinant()

Returns the determinant of this matrix.

Specified by:

determinant in class Matrix<Parameter<Q extends Quantity>>

Returns:

this matrix determinant.

transpose

public Matrix3D<Q> transpose()

Returns the transpose of this matrix.

Specified by:

transpose in class Matrix<Parameter<Q extends Quantity>>

Returns:

A'

cofactor

public Parameter cofactor(int i,
                          int j)

Returns the cofactor of an element in this matrix. It is the value obtained by evaluating the determinant formed by the elements not in that particular row or column.

Specified by:

cofactor in class Matrix<Parameter<Q extends Quantity>>

Parameters:

i - the row index.

j - the column index.

Returns:

the cofactor of THIS[i,j].

adjoint

public Matrix3D adjoint()

Returns the adjoint of this matrix. It is obtained by replacing each element in this matrix with its cofactor and applying a + or - sign according to (-1)**(i+j), and then finding the transpose of the resulting matrix.

Specified by:

adjoint in class Matrix<Parameter<Q extends Quantity>>

Returns:

the adjoint of this matrix.

tensor

public Matrix tensor(Matrix that)

Returns the linear algebraic matrix tensor product of this matrix and another (Kronecker product).

Specified by:

tensor in class Matrix<Parameter<Q extends Quantity>>

Parameters:

that - the second matrix

Returns:

this times that

See Also:

Wikipedia: Kronecker Product

isApproxZero

public boolean isApproxZero()

Compares this Matrix3D for approximate equality to zero (all the values are within the numerical roundoff error of zero).

Returns:

true if this Matrix3D is approximately equal to zero; false otherwise.

vectorization

public Vector<Parameter<Q>> vectorization()

Returns the vectorization of this matrix. The vectorization of a matrix is the column vector obtained by stacking the columns of the matrix on top of one another. The default implementation returns a DenseVector>.

Specified by:

vectorization in class Matrix<Parameter<Q extends Quantity>>

Returns:

the vectorization of this matrix.

See Also:

Wikipedia: Vectorization.

copy

public Matrix3D<Q> copy()

Returns a copy of this matrix allocated by the calling thread (possibly on the stack).

Specified by:

copy in interface javolution.lang.ValueType

Specified by:

copy in class Matrix<Parameter<Q extends Quantity>>

Returns:

an identical and independent copy of this matrix.

toFloat64Matrix

public Float64Matrix toFloat64Matrix()

Returns a Float64Matrix containing the data in this matrix in the current units of this matrix.

main

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

Tests the methods in this class.