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JSci is a set of open source Java packages. The aim is to encapsulate scientific methods/principles in the most natural way possible. As such they should greatly aid the development of scientific based software. It offers: abstract math interfaces, linear algebra (support for various matrix and vector types), statistics (including probability distributions), wavelets, newtonian mechanics, chart/graph components (AWT and Swing), MathML DOM implementation, ... Note: some packages, like javax.comm, for the astro and instruments package aren't listed as dependencies (not available).

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package JSci.maths.algebras;

import JSci.maths.*;
import JSci.maths.matrices.AbstractComplexMatrix;
import JSci.maths.matrices.AbstractComplexSquareMatrix;
import JSci.maths.matrices.ComplexSquareMatrix;
import JSci.maths.vectors.AbstractDoubleVector;
import JSci.maths.vectors.Double3Vector;
import JSci.maths.vectors.VectorDimensionException;
import JSci.maths.fields.ComplexField;

/**
* The sp2_RDim3 class encapsulates sp(2,R) algebras using
* the 3 dimensional (adjoint) representation.
* Elements are represented by 3-vectors with a matrix basis.
* @version 1.2
* @author Mark Hale
*/
public final class sp2_RDim3 extends LieAlgebra {
        private final static Complex t1[][]={
                {Complex.ZERO,Complex.ZERO,ComplexField.MINUS_HALF},
                {Complex.ZERO,Complex.ZERO,ComplexField.HALF},
                {ComplexField.MINUS_TWO,ComplexField.TWO,Complex.ZERO}
        };
        private final static Complex t2[][]={
                {Complex.ZERO,Complex.ZERO,ComplexField.MINUS_HALF},
                {Complex.ZERO,Complex.ZERO,ComplexField.MINUS_HALF},
                {ComplexField.TWO,ComplexField.TWO,Complex.ZERO}
        };
        private final static Complex t3[][]={
                {Complex.ONE,Complex.ZERO,Complex.ZERO},
                {Complex.ZERO,ComplexField.MINUS_ONE,Complex.ZERO},
                {Complex.ZERO,Complex.ZERO,Complex.ZERO}
        };
        /**
        * Basis.
        */
        private final static AbstractComplexSquareMatrix basisMatrices[]={
                new ComplexSquareMatrix(t1),
                new ComplexSquareMatrix(t2),
                new ComplexSquareMatrix(t3)
        };

        private final static sp2_RDim3 _instance = new sp2_RDim3();
        /**
        * Constructs an sp(2,R) algebra.
        */
        private sp2_RDim3() {
                super("sp(2,R) [3]");
        }
        /**
        * Singleton.
        */
        public static final sp2_RDim3 getInstance() {
                return _instance;
        }
        /**
        * Returns an element as a matrix (vector*basis).
        */
        public AbstractComplexSquareMatrix getElement(final AbstractDoubleVector v) {
                AbstractComplexMatrix m=basisMatrices[0].scalarMultiply(v.getComponent(0));
                m=m.add(basisMatrices[1].scalarMultiply(v.getComponent(1)));
                m=m.add(basisMatrices[2].scalarMultiply(v.getComponent(2)));
                return (AbstractComplexSquareMatrix)m.scalarMultiply(Complex.I);
        }
        /**
        * Returns the Lie bracket (commutator) of two elements.
        * Same as the vector cross product.
        */
        public AbstractDoubleVector multiply(final AbstractDoubleVector a, final AbstractDoubleVector b) {
                if(!(a instanceof Double3Vector) || !(b instanceof Double3Vector))
                        throw new VectorDimensionException("Vectors must be 3-vectors.");
                return new Double3Vector(
                        a.getComponent(2)*b.getComponent(1)-a.getComponent(1)*b.getComponent(2),
                        a.getComponent(2)*b.getComponent(0)-a.getComponent(0)*b.getComponent(2),
                        a.getComponent(1)*b.getComponent(0)-a.getComponent(0)*b.getComponent(1)
                );
        }
        /**
        * Returns the basis used to represent the Lie algebra.
        */
        public AbstractComplexSquareMatrix[] basis() {
                return basisMatrices;
        }
}