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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