package jsci.maths.groups;

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

/**
* 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