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/*
* Licensed to the Hipparchus project under one or more
* contributor license agreements. See the NOTICE file distributed with
* this work for additional information regarding copyright ownership.
* The Hipparchus project licenses this file to You under the Apache License, Version 2.0
* (the "License"); you may not use this file except in compliance with
* the License. You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*/
package org.hipparchus.linear;
import java.util.TreeSet;
import org.hipparchus.complex.Complex;
import org.hipparchus.complex.ComplexComparator;
/**
* Given a matrix A, it computes an eigen decomposition A = VDV^{T}.
*
* It also ensures that eigen values in the diagonal of D are in ascending
* order.
*
*/
public class OrderedEigenDecomposition extends EigenDecomposition {
/**
* Constructor using the EigenDecomposition as starting point for ordering.
*
* @param matrix matrix to decompose
*/
public OrderedEigenDecomposition(final RealMatrix matrix) {
super(matrix);
final RealMatrix D = this.getD();
final RealMatrix V = this.getV();
// getting eigen values
TreeSet eigenValues = new TreeSet(
new ComplexComparator());
for (int ij = 0; ij < matrix.getRowDimension(); ij++) {
eigenValues.add(new Complex(getRealEigenvalue(ij),
getImagEigenvalue(ij)));
}
// ordering
for (int ij = 0; ij < matrix.getRowDimension() - 1; ij++) {
final Complex eigValue = eigenValues.pollFirst();
int currentIndex = -1;
// searching the current index
for (currentIndex = ij; currentIndex < matrix.getRowDimension(); currentIndex++) {
Complex compCurrent = null;
if (currentIndex == 0) {
compCurrent = new Complex(D.getEntry(currentIndex,
currentIndex), D.getEntry(currentIndex + 1,
currentIndex));
} else if (currentIndex + 1 == matrix.getRowDimension()) {
compCurrent = new Complex(D.getEntry(currentIndex,
currentIndex), D.getEntry(currentIndex - 1,
currentIndex));
} else {
if (D.getEntry(currentIndex - 1, currentIndex) != 0) {
compCurrent = new Complex(D.getEntry(currentIndex,
currentIndex), D.getEntry(currentIndex - 1,
currentIndex));
} else {
compCurrent = new Complex(D.getEntry(currentIndex,
currentIndex), D.getEntry(currentIndex + 1,
currentIndex));
}
}
if (eigValue.equals(compCurrent)) {
break;
}
}
if (ij == currentIndex) {
continue;
}
// exchanging D
Complex previousValue = null;
if (ij == 0) {
previousValue = new Complex(D.getEntry(ij, ij), D.getEntry(ij + 1, ij));
} else if (ij + 1 == matrix.getRowDimension()) {
previousValue = new Complex(D.getEntry(ij, ij), D.getEntry(ij - 1, ij));
} else {
if (D.getEntry(ij - 1, ij) != 0) {
previousValue = new Complex(D.getEntry(ij, ij), D.getEntry(ij - 1, ij));
} else {
previousValue = new Complex(D.getEntry(ij, ij), D.getEntry(ij + 1, ij));
}
}
// moved eigenvalue
D.setEntry(ij, ij, eigValue.getReal());
if (ij == 0) {
D.setEntry(ij + 1, ij, eigValue.getImaginary());
} else if ((ij + 1) == matrix.getRowDimension()) {
D.setEntry(ij - 1, ij, eigValue.getImaginary());
} else {
if (eigValue.getImaginary() > 0) {
D.setEntry(ij - 1, ij, eigValue.getImaginary());
D.setEntry(ij + 1, ij, 0);
} else {
D.setEntry(ij + 1, ij, eigValue.getImaginary());
D.setEntry(ij - 1, ij, 0);
}
}
// previous eigen value
D.setEntry(currentIndex, currentIndex, previousValue.getReal());
if (currentIndex == 0) {
D.setEntry(currentIndex + 1, currentIndex,
previousValue.getImaginary());
} else if ((currentIndex + 1) == matrix.getRowDimension()) {
D.setEntry(currentIndex - 1, currentIndex,
previousValue.getImaginary());
} else {
if (previousValue.getImaginary() > 0) {
D.setEntry(currentIndex - 1, currentIndex,
previousValue.getImaginary());
D.setEntry(currentIndex + 1, currentIndex, 0);
} else {
D.setEntry(currentIndex + 1, currentIndex,
previousValue.getImaginary());
D.setEntry(currentIndex - 1, currentIndex, 0);
}
}
// exchanging V
final double[] previousColumnV = V.getColumn(ij);
V.setColumn(ij, V.getColumn(currentIndex));
V.setColumn(currentIndex, previousColumnV);
}
}
/** {@inheritDoc} */
@Override
public RealMatrix getVT() {
return getV().transpose();
}
}
