JSci.maths.groups.LieGroup Maven / Gradle / Ivy

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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.groups;

import JSci.maths.*;
import JSci.maths.vectors.AbstractDoubleVector;
import JSci.maths.matrices.AbstractComplexMatrix;
import JSci.maths.matrices.AbstractComplexSquareMatrix;
import JSci.maths.matrices.ComplexDiagonalMatrix;

/**
* The LieGroup class provides an encapsulation for Lie groups.
* Elements are represented by complex matrices, and are limited
* to being near the identity.
* @jsci.planetmath LieGroup
* @version 1.3
* @author Mark Hale
*/
public class LieGroup extends Object {
        private AbstractComplexSquareMatrix generators[];
        private AbstractComplexSquareMatrix identityMatrix;
        /**
        * Constructs a Lie group from a Lie algebra.
        * @param gens the group generators
        */
        public LieGroup(AbstractComplexSquareMatrix gens[]) {
                generators=gens;
                identityMatrix=ComplexDiagonalMatrix.identity(generators[0].rows());
        }
        /**
        * Returns the dimension of the group.
        */
        public final int dimension() {
                return generators.length;
        }
        /**
        * Returns an element near the identity.
        * @param v a small element from the Lie algebra
        */
        public AbstractComplexSquareMatrix getElement(AbstractDoubleVector v) {
                if(generators.length!=v.dimension())
                        throw new IllegalArgumentException("The vector should match the generators.");
                AbstractComplexMatrix phase=generators[0].scalarMultiply(v.getComponent(0));
                for(int i=1;i