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 06:27:47 -0400 (Mon, 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 }