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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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/* AUTO-GENERATED */
package JSci.maths.matrices;

import JSci.maths.ArrayMath;
import JSci.maths.Complex;
import JSci.maths.ComplexMapping;
import JSci.maths.LinearMath;
import JSci.maths.DimensionException;
import JSci.maths.MaximumIterationsExceededException;
import JSci.maths.vectors.AbstractComplexVector;
import JSci.maths.vectors.ComplexVector;

/**
* The ComplexTridiagonalMatrix class provides an object for encapsulating tridiagonal matrices containing complex numbers.
* Uses compressed diagonal storage.
* @version 2.2
* @author Mark Hale
*/
public class ComplexTridiagonalMatrix extends AbstractComplexSquareMatrix implements TridiagonalMatrix {
        /**
        * Tridiagonal data.
        */
        protected final double ldiagRe[],ldiagIm[];
        protected final double diagRe[],diagIm[];
        protected final double udiagRe[],udiagIm[];
        /**
        * Constructs an empty matrix.
        * @param size the number of rows/columns
        */
        public ComplexTridiagonalMatrix(final int size) {
                super(size);
                ldiagRe=new double[size];
                ldiagIm=new double[size];
                diagRe=new double[size];
                diagIm=new double[size];
                udiagRe=new double[size];
                udiagIm=new double[size];
        }
        /**
        * Constructs a matrix from an array.
        * Any non-tridiagonal elements in the array are ignored.
        * @param array an assigned value
        * @exception MatrixDimensionException If the array is not square.
        */
        public ComplexTridiagonalMatrix(final Complex array[][]) {
                this(array.length);
                if(!ArrayMath.isSquare(array))
                        throw new MatrixDimensionException("Array is not square.");
                diagRe[0]=array[0][0].real();
                diagIm[0]=array[0][0].imag();
                udiagRe[0]=array[0][1].real();
                udiagIm[0]=array[0][1].imag();
                int i=1;
                for(;i=0 && i=0 && j=0 && i=0 && j=0 && i=0 && j=0 && i=0 && j=0 && i=0 && j-norm.
        * @author Taber Smith
        */
        public double infNorm() {
                double result = Math.sqrt(#modSqrA("diag" "[0]")) + Math.sqrt(#modSqrA("udiag" "[0]"));
                double tmpResult;
                int i=1;
                for(;iresult)
                                result=tmpResult;
                }
                tmpResult = Math.sqrt(#modSqrA("ldiag" "[i]")) + Math.sqrt(#modSqrA("diag" "[i]"));
                if(tmpResult>result)
                        result=tmpResult;
                return result;
        }
        /**
        * Returns the Frobenius (l²) norm.
        * @author Taber Smith
        */
        public double frobeniusNorm() {
                double result=diagRe[0]*diagRe[0]+diagIm[0]*diagIm[0]+
                        udiagRe[0]*udiagRe[0]+udiagIm[0]*udiagIm[0];
                int i=1;
                for(;i3) {
                                arrayRe[1][0]=#multAARe("ldiag" "[1]" "m.diag" "[0]")+#multAARe("diag" "[1]" "m.ldiag" "[1]");
                                arrayIm[1][0]=#multAAIm("ldiag" "[1]" "m.diag" "[0]")+#multAAIm("diag" "[1]" "m.ldiag" "[1]");
                                arrayRe[1][1]=#multAARe("ldiag" "[1]" "m.udiag" "[0]")+#multAARe("diag" "[1]" "m.diag" "[1]")+#multAARe("udiag" "[1]" "m.ldiag" "[2]");
                                arrayIm[1][1]=#multAAIm("ldiag" "[1]" "m.udiag" "[0]")+#multAAIm("diag" "[1]" "m.diag" "[1]")+#multAAIm("udiag" "[1]" "m.ldiag" "[2]");
                                arrayRe[1][2]=#multAARe("diag" "[1]" "m.udiag" "[1]")+#multAARe("udiag" "[1]" "m.diag" "[2]");
                                arrayIm[1][2]=#multAAIm("diag" "[1]" "m.udiag" "[1]")+#multAAIm("udiag" "[1]" "m.diag" "[2]");
                                arrayRe[1][3]=#multAARe("udiag" "[1]" "m.udiag" "[2]");
                                arrayIm[1][3]=#multAAIm("udiag" "[1]" "m.udiag" "[2]");
                        }
                        if(mRow==3) {
                                arrayRe[1][0]=#multAARe("ldiag" "[1]" "m.diag" "[0]")+#multAARe("diag" "[1]" "m.ldiag" "[1]");
                                arrayIm[1][0]=#multAAIm("ldiag" "[1]" "m.diag" "[0]")+#multAAIm("diag" "[1]" "m.ldiag" "[1]");
                                arrayRe[1][1]=#multAARe("ldiag" "[1]" "m.udiag" "[0]")+#multAARe("diag" "[1]" "m.diag" "[1]")+#multAARe("udiag" "[1]" "m.ldiag" "[2]");
                                arrayIm[1][1]=#multAAIm("ldiag" "[1]" "m.udiag" "[0]")+#multAAIm("diag" "[1]" "m.diag" "[1]")+#multAAIm("udiag" "[1]" "m.ldiag" "[2]");
                                arrayRe[1][2]=#multAARe("diag" "[1]" "m.udiag" "[1]")+#multAARe("udiag" "[1]" "m.diag" "[2]");
                                arrayIm[1][2]=#multAAIm("diag" "[1]" "m.udiag" "[1]")+#multAAIm("udiag" "[1]" "m.diag" "[2]");
                        } else if(mRow>4) {
                                for(int i=2;i3) {
                                arrayRe[mRow-2][mRow-4]=#multAARe("ldiag" "[mRow-2]" "m.ldiag" "[mRow-3]");
                                arrayIm[mRow-2][mRow-4]=#multAAIm("ldiag" "[mRow-2]" "m.ldiag" "[mRow-3]");
                                arrayRe[mRow-2][mRow-3]=#multAARe("ldiag" "[mRow-2]" "m.diag" "[mRow-3]")+#multAARe("diag" "[mRow-2]" "m.ldiag" "[mRow-2]");
                                arrayIm[mRow-2][mRow-3]=#multAAIm("ldiag" "[mRow-2]" "m.diag" "[mRow-3]")+#multAAIm("diag" "[mRow-2]" "m.ldiag" "[mRow-2]");
                                arrayRe[mRow-2][mRow-2]=#multAARe("ldiag" "[mRow-2]" "m.udiag" "[mRow-3]")+#multAARe("diag" "[mRow-2]" "m.diag" "[mRow-2]")+#multAARe("udiag" "[mRow-2]" "m.ldiag" "[mRow-1]");
                                arrayIm[mRow-2][mRow-2]=#multAAIm("ldiag" "[mRow-2]" "m.udiag" "[mRow-3]")+#multAAIm("diag" "[mRow-2]" "m.diag" "[mRow-2]")+#multAAIm("udiag" "[mRow-2]" "m.ldiag" "[mRow-1]");
                                arrayRe[mRow-2][mRow-1]=#multAARe("diag" "[mRow-2]" "m.udiag" "[mRow-2]")+#multAARe("udiag" "[mRow-2]" "m.diag" "[mRow-1]");
                                arrayIm[mRow-2][mRow-1]=#multAAIm("diag" "[mRow-2]" "m.udiag" "[mRow-2]")+#multAAIm("udiag" "[mRow-2]" "m.diag" "[mRow-1]");
                        }
                        mRow--;
                        arrayRe[mRow][mRow-2]=#multAARe("ldiag" "[mRow]" "m.ldiag" "[mRow-1]");
                        arrayIm[mRow][mRow-2]=#multAAIm("ldiag" "[mRow]" "m.ldiag" "[mRow-1]");
                        arrayRe[mRow][mRow-1]=#multAARe("ldiag" "[mRow]" "m.diag" "[mRow-1]")+#multAARe("diag" "[mRow]" "m.ldiag" "[mRow]");
                        arrayIm[mRow][mRow-1]=#multAAIm("ldiag" "[mRow]" "m.diag" "[mRow-1]")+#multAAIm("diag" "[mRow]" "m.ldiag" "[mRow]");
                        arrayRe[mRow][mRow]=#multAARe("ldiag" "[mRow]" "m.udiag" "[mRow-1]")+#multAARe("diag" "[mRow]" "m.diag" "[mRow]");
                        arrayIm[mRow][mRow]=#multAAIm("ldiag" "[mRow]" "m.udiag" "[mRow-1]")+#multAAIm("diag" "[mRow]" "m.diag" "[mRow]");
                        return new ComplexSquareMatrix(arrayRe,arrayIm);
                } else
                        throw new MatrixDimensionException("Incompatible matrices.");
        }
        private ComplexSquareMatrix multiplyTridiagonal(final AbstractComplexSquareMatrix m) {
                int mRow=numRows;
                if(numCols==m.rows()) {
                        final double arrayRe[][]=new double[mRow][mRow];
                        final double arrayIm[][]=new double[mRow][mRow];
                        Complex elem1,elem2,elem3;
                        elem1=m.getElement(0,0);elem2=m.getElement(1,0);
                        arrayRe[0][0]=#multAZRe("diag" "[0]" "elem1")+#multAZRe("udiag" "[0]" "elem2");
                        arrayIm[0][0]=#multAZIm("diag" "[0]" "elem1")+#multAZIm("udiag" "[0]" "elem2");
                        elem1=m.getElement(0,1);elem2=m.getElement(1,1);
                        arrayRe[0][1]=#multAZRe("diag" "[0]" "elem1")+#multAZRe("udiag" "[0]" "elem2");
                        arrayIm[0][1]=#multAZIm("diag" "[0]" "elem1")+#multAZIm("udiag" "[0]" "elem2");
                        elem1=m.getElement(1,2);
                        arrayRe[0][2]=#multAZRe("udiag" "[0]" "elem1");
                        arrayIm[0][2]=#multAZIm("udiag" "[0]" "elem1");
                        if(mRow>3) {
                                elem1=m.getElement(0,0);elem2=m.getElement(1,0);
                                arrayRe[1][0]=#multAZRe("ldiag" "[1]" "elem1")+#multAZRe("diag" "[1]" "elem2");
                                arrayIm[1][0]=#multAZIm("ldiag" "[1]" "elem1")+#multAZIm("diag" "[1]" "elem2");
                                elem1=m.getElement(0,1);elem2=m.getElement(1,1);elem3=m.getElement(2,1);
                                arrayRe[1][1]=#multAZRe("ldiag" "[1]" "elem1")+#multAZRe("diag" "[1]" "elem2")+#multAZRe("udiag" "[1]" "elem3");
                                arrayIm[1][1]=#multAZIm("ldiag" "[1]" "elem1")+#multAZIm("diag" "[1]" "elem2")+#multAZIm("udiag" "[1]" "elem3");
                                elem1=m.getElement(1,2);elem2=m.getElement(2,2);
                                arrayRe[1][2]=#multAZRe("diag" "[1]" "elem1")+#multAZRe("udiag" "[1]" "elem2");
                                arrayIm[1][2]=#multAZIm("diag" "[1]" "elem1")+#multAZIm("udiag" "[1]" "elem2");
                                elem1=m.getElement(2,3);
                                arrayRe[1][3]=#multAZRe("udiag" "[1]" "elem1");
                                arrayIm[1][3]=#multAZIm("udiag" "[1]" "elem1");
                        }
                        if(mRow==3) {
                                elem1=m.getElement(0,0);elem2=m.getElement(1,0);
                                arrayRe[1][0]=#multAZRe("ldiag" "[1]" "elem1")+#multAZRe("diag" "[1]" "elem2");
                                arrayIm[1][0]=#multAZIm("ldiag" "[1]" "elem1")+#multAZIm("diag" "[1]" "elem2");
                                elem1=m.getElement(0,1);elem2=m.getElement(1,1);elem3=m.getElement(2,1);
                                arrayRe[1][1]=#multAZRe("ldiag" "[1]" "elem1")+#multAZRe("diag" "[1]" "elem2")+#multAZRe("udiag" "[1]" "elem3");
                                arrayIm[1][1]=#multAZIm("ldiag" "[1]" "elem1")+#multAZIm("diag" "[1]" "elem2")+#multAZIm("udiag" "[1]" "elem3");
                                elem1=m.getElement(1,2);elem2=m.getElement(2,2);
                                arrayRe[1][2]=#multAZRe("diag" "[1]" "elem1")+#multAZRe("udiag" "[1]" "elem2");
                                arrayIm[1][2]=#multAZIm("diag" "[1]" "elem1")+#multAZIm("udiag" "[1]" "elem2");
                        } else if(mRow>4) {
                                for(int i=2;i3) {
                                elem1=m.getElement(mRow-3,mRow-4);
                                arrayRe[mRow-2][mRow-4]=#multAZRe("ldiag" "[mRow-2]" "elem1");
                                arrayIm[mRow-2][mRow-4]=#multAZIm("ldiag" "[mRow-2]" "elem1");
                                elem1=m.getElement(mRow-3,mRow-3);elem2=m.getElement(mRow-2,mRow-3);
                                arrayRe[mRow-2][mRow-3]=#multAZRe("ldiag" "[mRow-2]" "elem1")+#multAZRe("diag" "[mRow-2]" "elem2");
                                arrayIm[mRow-2][mRow-3]=#multAZIm("ldiag" "[mRow-2]" "elem1")+#multAZIm("diag" "[mRow-2]" "elem2");
                                elem1=m.getElement(mRow-3,mRow-2);elem2=m.getElement(mRow-2,mRow-2);elem3=m.getElement(mRow-1,mRow-2);
                                arrayRe[mRow-2][mRow-2]=#multAZRe("ldiag" "[mRow-2]" "elem1")+#multAZRe("diag" "[mRow-2]" "elem2")+#multAZRe("udiag" "[mRow-2]" "elem3");
                                arrayIm[mRow-2][mRow-2]=#multAZIm("ldiag" "[mRow-2]" "elem1")+#multAZIm("diag" "[mRow-2]" "elem2")+#multAZIm("udiag" "[mRow-2]" "elem3");
                                elem1=m.getElement(mRow-2,mRow-1);elem2=m.getElement(mRow-1,mRow-1);
                                arrayRe[mRow-2][mRow-1]=#multAZRe("diag" "[mRow-2]" "elem1")+#multAZRe("udiag" "[mRow-2]" "elem2");
                                arrayIm[mRow-2][mRow-1]=#multAZIm("diag" "[mRow-2]" "elem1")+#multAZIm("udiag" "[mRow-2]" "elem2");
                        }
                        mRow--;
                        elem1=m.getElement(mRow-1,mRow-2);
                        arrayRe[mRow][mRow-2]=#multAZRe("ldiag" "[mRow]" "elem1");
                        arrayIm[mRow][mRow-2]=#multAZIm("ldiag" "[mRow]" "elem1");
                        elem1=m.getElement(mRow-1,mRow-1);elem2=m.getElement(mRow,mRow-1);
                        arrayRe[mRow][mRow-1]=#multAZRe("ldiag" "[mRow]" "elem1")+#multAZRe("diag" "[mRow]" "elem2");
                        arrayIm[mRow][mRow-1]=#multAZIm("ldiag" "[mRow]" "elem1")+#multAZIm("diag" "[mRow]" "elem2");
                        elem1=m.getElement(mRow-1,mRow);elem2=m.getElement(mRow,mRow);
                        arrayRe[mRow][mRow]=#multAZRe("ldiag" "[mRow]" "elem1")+#multAZRe("diag" "[mRow]" "elem2");
                        arrayIm[mRow][mRow]=#multAZIm("ldiag" "[mRow]" "elem1")+#multAZIm("diag" "[mRow]" "elem2");
                        return new ComplexSquareMatrix(arrayRe,arrayIm);
                } else {
                        throw new MatrixDimensionException("Incompatible matrices.");
                }
        }

// HERMITIAN ADJOINT

        /**
        * Returns the hermitian adjoint of this matrix.
        * @return a complex tridiagonal matrix
        */
        public AbstractComplexMatrix hermitianAdjoint() {
                int mRow=numRows;
                final ComplexTridiagonalMatrix ans=new ComplexTridiagonalMatrix(mRow);
                System.arraycopy(ldiagRe,1,ans.udiagRe,0,ldiagRe.length-1);
                System.arraycopy(diagRe,0,ans.diagRe,0,diagRe.length);
                System.arraycopy(udiagRe,0,ans.ldiagRe,1,udiagRe.length-1);
                ans.diagIm[0]=-diagIm[0];
                ans.ldiagIm[1]=-udiagIm[0];
                mRow--;
                for(int i=1;i

    

    

    
            
    
            

    
        
            
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