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Diffstat (limited to 'src/main/java/org/apache/commons/math/linear/EigenDecomposition.java')
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diff --git a/src/main/java/org/apache/commons/math/linear/EigenDecomposition.java b/src/main/java/org/apache/commons/math/linear/EigenDecomposition.java new file mode 100644 index 0000000..f991e8b --- /dev/null +++ b/src/main/java/org/apache/commons/math/linear/EigenDecomposition.java @@ -0,0 +1,137 @@ +/* + * Licensed to the Apache Software Foundation (ASF) under one or more + * contributor license agreements. See the NOTICE file distributed with + * this work for additional information regarding copyright ownership. + * The ASF 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.apache.commons.math.linear; + + +/** + * An interface to classes that implement an algorithm to calculate the + * eigen decomposition of a real matrix. + * <p>The eigen decomposition of matrix A is a set of two matrices: + * V and D such that A = V × D × V<sup>T</sup>. + * A, V and D are all m × m matrices.</p> + * <p>This interface is similar in spirit to the <code>EigenvalueDecomposition</code> + * class from the <a href="http://math.nist.gov/javanumerics/jama/">JAMA</a> + * library, with the following changes:</p> + * <ul> + * <li>a {@link #getVT() getVt} method has been added,</li> + * <li>two {@link #getRealEigenvalue(int) getRealEigenvalue} and {@link #getImagEigenvalue(int) + * getImagEigenvalue} methods to pick up a single eigenvalue have been added,</li> + * <li>a {@link #getEigenvector(int) getEigenvector} method to pick up a single + * eigenvector has been added,</li> + * <li>a {@link #getDeterminant() getDeterminant} method has been added.</li> + * <li>a {@link #getSolver() getSolver} method has been added.</li> + * </ul> + * @see <a href="http://mathworld.wolfram.com/EigenDecomposition.html">MathWorld</a> + * @see <a href="http://en.wikipedia.org/wiki/Eigendecomposition_of_a_matrix">Wikipedia</a> + * @version $Revision: 997726 $ $Date: 2010-09-16 14:39:51 +0200 (jeu. 16 sept. 2010) $ + * @since 2.0 + */ +public interface EigenDecomposition { + + /** + * Returns the matrix V of the decomposition. + * <p>V is an orthogonal matrix, i.e. its transpose is also its inverse.</p> + * <p>The columns of V are the eigenvectors of the original matrix.</p> + * <p>No assumption is made about the orientation of the system axes formed + * by the columns of V (e.g. in a 3-dimension space, V can form a left- + * or right-handed system).</p> + * @return the V matrix + */ + RealMatrix getV(); + + /** + * Returns the block diagonal matrix D of the decomposition. + * <p>D is a block diagonal matrix.</p> + * <p>Real eigenvalues are on the diagonal while complex values are on + * 2x2 blocks { {real +imaginary}, {-imaginary, real} }.</p> + * @return the D matrix + * @see #getRealEigenvalues() + * @see #getImagEigenvalues() + */ + RealMatrix getD(); + + /** + * Returns the transpose of the matrix V of the decomposition. + * <p>V is an orthogonal matrix, i.e. its transpose is also its inverse.</p> + * <p>The columns of V are the eigenvectors of the original matrix.</p> + * <p>No assumption is made about the orientation of the system axes formed + * by the columns of V (e.g. in a 3-dimension space, V can form a left- + * or right-handed system).</p> + * @return the transpose of the V matrix + */ + RealMatrix getVT(); + + /** + * Returns a copy of the real parts of the eigenvalues of the original matrix. + * @return a copy of the real parts of the eigenvalues of the original matrix + * @see #getD() + * @see #getRealEigenvalue(int) + * @see #getImagEigenvalues() + */ + double[] getRealEigenvalues(); + + /** + * Returns the real part of the i<sup>th</sup> eigenvalue of the original matrix. + * @param i index of the eigenvalue (counting from 0) + * @return real part of the i<sup>th</sup> eigenvalue of the original matrix + * @see #getD() + * @see #getRealEigenvalues() + * @see #getImagEigenvalue(int) + */ + double getRealEigenvalue(int i); + + /** + * Returns a copy of the imaginary parts of the eigenvalues of the original matrix. + * @return a copy of the imaginary parts of the eigenvalues of the original matrix + * @see #getD() + * @see #getImagEigenvalue(int) + * @see #getRealEigenvalues() + */ + double[] getImagEigenvalues(); + + /** + * Returns the imaginary part of the i<sup>th</sup> eigenvalue of the original matrix. + * @param i index of the eigenvalue (counting from 0) + * @return imaginary part of the i<sup>th</sup> eigenvalue of the original matrix + * @see #getD() + * @see #getImagEigenvalues() + * @see #getRealEigenvalue(int) + */ + double getImagEigenvalue(int i); + + /** + * Returns a copy of the i<sup>th</sup> eigenvector of the original matrix. + * @param i index of the eigenvector (counting from 0) + * @return copy of the i<sup>th</sup> eigenvector of the original matrix + * @see #getD() + */ + RealVector getEigenvector(int i); + + /** + * Return the determinant of the matrix + * @return determinant of the matrix + */ + double getDeterminant(); + + /** + * Get a solver for finding the A × X = B solution in exact linear sense. + * @return a solver + */ + DecompositionSolver getSolver(); + +} |