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Change-Id: I52a325624a7f0dd652b362a9840626d6d9f3c42b

1 files changed, 137 insertions, 0 deletions

diff --git a/src/main/java/org/apache/commons/math/linear/EigenDecomposition.java b/src/main/java/org/apache/commons/math/linear/EigenDecomposition.java
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+/*
+ * 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 &times; D &times; V<sup>T</sup>.
+ * A, V and D are all m &times; 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 &times; X = B solution in exact linear sense.
+     * @return a solver
+     */
+    DecompositionSolver getSolver();
+
+}