/*
 * 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 now defunct
 * <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 $Revision$ $Date$
 * @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>
	 * 
	 * @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>
	 * 
	 * @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();

}
