001 /*
002 * Licensed to the Apache Software Foundation (ASF) under one or more
003 * contributor license agreements. See the NOTICE file distributed with
004 * this work for additional information regarding copyright ownership.
005 * The ASF licenses this file to You under the Apache License, Version 2.0
006 * (the "License"); you may not use this file except in compliance with
007 * the License. You may obtain a copy of the License at
008 *
009 * http://www.apache.org/licenses/LICENSE-2.0
010 *
011 * Unless required by applicable law or agreed to in writing, software
012 * distributed under the License is distributed on an "AS IS" BASIS,
013 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
014 * See the License for the specific language governing permissions and
015 * limitations under the License.
016 */
017
018 package org.apache.commons.math.linear;
019
020
021 /**
022 * An interface to classes that implement an algorithm to calculate the
023 * LU-decomposition of a real matrix.
024 * <p>The LU-decomposition of matrix A is a set of three matrices: P, L and U
025 * such that P×A = L×U. P is a rows permutation matrix that is used
026 * to rearrange the rows of A before so that it can be decomposed. L is a lower
027 * triangular matrix with unit diagonal terms and U is an upper triangular matrix.</p>
028 * <p>This interface is based on the class with similar name from the
029 * <a href="http://math.nist.gov/javanumerics/jama/">JAMA</a> library.</p>
030 * <ul>
031 * <li>a {@link #getP() getP} method has been added,</li>
032 * <li>the <code>det</code> method has been renamed as {@link #getDeterminant()
033 * getDeterminant},</li>
034 * <li>the <code>getDoublePivot</code> method has been removed (but the int based
035 * {@link #getPivot() getPivot} method has been kept),</li>
036 * <li>the <code>solve</code> and <code>isNonSingular</code> methods have been replaced
037 * by a {@link #getSolver() getSolver} method and the equivalent methods provided by
038 * the returned {@link DecompositionSolver}.</li>
039 * </ul>
040 *
041 * @see <a href="http://mathworld.wolfram.com/LUDecomposition.html">MathWorld</a>
042 * @see <a href="http://en.wikipedia.org/wiki/LU_decomposition">Wikipedia</a>
043 * @version $Revision: 826627 $ $Date: 2009-10-19 12:27:47 +0200 (lun. 19 oct. 2009) $
044 * @since 2.0
045 */
046 public interface LUDecomposition {
047
048 /**
049 * Returns the matrix L of the decomposition.
050 * <p>L is an lower-triangular matrix</p>
051 * @return the L matrix (or null if decomposed matrix is singular)
052 */
053 RealMatrix getL();
054
055 /**
056 * Returns the matrix U of the decomposition.
057 * <p>U is an upper-triangular matrix</p>
058 * @return the U matrix (or null if decomposed matrix is singular)
059 */
060 RealMatrix getU();
061
062 /**
063 * Returns the P rows permutation matrix.
064 * <p>P is a sparse matrix with exactly one element set to 1.0 in
065 * each row and each column, all other elements being set to 0.0.</p>
066 * <p>The positions of the 1 elements are given by the {@link #getPivot()
067 * pivot permutation vector}.</p>
068 * @return the P rows permutation matrix (or null if decomposed matrix is singular)
069 * @see #getPivot()
070 */
071 RealMatrix getP();
072
073 /**
074 * Returns the pivot permutation vector.
075 * @return the pivot permutation vector
076 * @see #getP()
077 */
078 int[] getPivot();
079
080 /**
081 * Return the determinant of the matrix
082 * @return determinant of the matrix
083 */
084 double getDeterminant();
085
086 /**
087 * Get a solver for finding the A × X = B solution in exact linear sense.
088 * @return a solver
089 */
090 DecompositionSolver getSolver();
091
092 }