/*
 * 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 Cholesky
 * decomposition of a real symmetric positive-definite matrix.
 * <p>
 * This interface is based on the class with similar name from the now defunct
 * <a href="http://math.nist.gov/javanumerics/jama/">JAMA</a> library, with the
 * following changes:
 * </p>
 * <ul>
 * <li>a {@link #getLT() getLT} method has been added,</li>
 * <li>the <code>isspd</code> method has been removed, the constructors of
 * implementation classes being expected to throw
 * {@link NotPositiveDefiniteMatrixException} when a matrix cannot be
 * decomposed,</li>
 * <li>a {@link #getDeterminant() getDeterminant} method has been added,</li>
 * <li>the <code>solve</code> method has been replaced by a {@link #getSolver()
 * getSolver} method and the equivalent method provided by the returned
 * {@link DecompositionSolver}.</li>
 * </ul>
 * 
 * @see <a href=
 *      "http://mathworld.wolfram.com/CholeskyDecomposition.html">MathWorld</a>
 * @see <a href=
 *      "http://en.wikipedia.org/wiki/Cholesky_decomposition">Wikipedia</a>
 * @version $Revision$ $Date$
 * @since 2.0
 */
public interface CholeskyDecomposition {

	/**
	 * Returns the matrix L of the decomposition.
	 * <p>
	 * L is an lower-triangular matrix
	 * </p>
	 * 
	 * @return the L matrix
	 */
	RealMatrix getL();

	/**
	 * Returns the transpose of the matrix L of the decomposition.
	 * <p>
	 * L<sup>T</sup> is an upper-triangular matrix
	 * </p>
	 * 
	 * @return the transpose of the matrix L of the decomposition
	 */
	RealMatrix getLT();

	/**
	 * 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 least square
	 * sense.
	 * 
	 * @return a solver
	 */
	DecompositionSolver getSolver();

}
