From dee0849a9704d532af0b550146cbafbaa6ee1d19 Mon Sep 17 00:00:00 2001 From: Raymond Date: Thu, 2 Apr 2015 10:43:13 -0700 Subject: third party library: apache-commons-math Change-Id: I52a325624a7f0dd652b362a9840626d6d9f3c42b --- .../commons/math/linear/EigenDecomposition.java | 137 +++++++++++++++++++++ 1 file changed, 137 insertions(+) create mode 100644 src/main/java/org/apache/commons/math/linear/EigenDecomposition.java (limited to 'src/main/java/org/apache/commons/math/linear/EigenDecomposition.java') 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. + *

The eigen decomposition of matrix A is a set of two matrices: + * V and D such that A = V × D × VT. + * A, V and D are all m × m matrices.

+ *

This interface is similar in spirit to the EigenvalueDecomposition + * class from the JAMA + * library, with the following changes:

+ * + * @see MathWorld + * @see Wikipedia + * @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. + *

V is an orthogonal matrix, i.e. its transpose is also its inverse.

+ *

The columns of V are the eigenvectors of the original matrix.

+ *

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).

+ * @return the V matrix + */ + RealMatrix getV(); + + /** + * Returns the block diagonal matrix D of the decomposition. + *

D is a block diagonal matrix.

+ *

Real eigenvalues are on the diagonal while complex values are on + * 2x2 blocks { {real +imaginary}, {-imaginary, real} }.

+ * @return the D matrix + * @see #getRealEigenvalues() + * @see #getImagEigenvalues() + */ + RealMatrix getD(); + + /** + * Returns the transpose of the matrix V of the decomposition. + *

V is an orthogonal matrix, i.e. its transpose is also its inverse.

+ *

The columns of V are the eigenvectors of the original matrix.

+ *

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).

+ * @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 ith eigenvalue of the original matrix. + * @param i index of the eigenvalue (counting from 0) + * @return real part of the ith 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 ith eigenvalue of the original matrix. + * @param i index of the eigenvalue (counting from 0) + * @return imaginary part of the ith eigenvalue of the original matrix + * @see #getD() + * @see #getImagEigenvalues() + * @see #getRealEigenvalue(int) + */ + double getImagEigenvalue(int i); + + /** + * Returns a copy of the ith eigenvector of the original matrix. + * @param i index of the eigenvector (counting from 0) + * @return copy of the ith 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(); + +} -- cgit v1.2.3