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 import org.apache.commons.math.FieldElement; 021 022 /** 023 * An interface to classes that implement an algorithm to calculate the 024 * LU-decomposition of a real matrix. 025 * <p>The LU-decomposition of matrix A is a set of three matrices: P, L and U 026 * such that P×A = L×U. P is a rows permutation matrix that is used 027 * to rearrange the rows of A before so that it can be decomposed. L is a lower 028 * triangular matrix with unit diagonal terms and U is an upper triangular matrix.</p> 029 * <p>This interface is based on the class with similar name from the 030 * <a href="http://math.nist.gov/javanumerics/jama/">JAMA</a> library.</p> 031 * <ul> 032 * <li>a {@link #getP() getP} method has been added,</li> 033 * <li>the <code>det</code> method has been renamed as {@link #getDeterminant() 034 * getDeterminant},</li> 035 * <li>the <code>getDoublePivot</code> method has been removed (but the int based 036 * {@link #getPivot() getPivot} method has been kept),</li> 037 * <li>the <code>solve</code> and <code>isNonSingular</code> methods have been replaced 038 * by a {@link #getSolver() getSolver} method and the equivalent methods provided by 039 * the returned {@link DecompositionSolver}.</li> 040 * </ul> 041 * 042 * @param <T> the type of the field elements 043 * @see <a href="http://mathworld.wolfram.com/LUDecomposition.html">MathWorld</a> 044 * @see <a href="http://en.wikipedia.org/wiki/LU_decomposition">Wikipedia</a> 045 * @version $Revision: 826627 $ $Date: 2009-10-19 12:27:47 +0200 (lun. 19 oct. 2009) $ 046 * @since 2.0 047 */ 048 public interface FieldLUDecomposition<T extends FieldElement<T>> { 049 050 /** 051 * Returns the matrix L of the decomposition. 052 * <p>L is an lower-triangular matrix</p> 053 * @return the L matrix (or null if decomposed matrix is singular) 054 */ 055 FieldMatrix<T> getL(); 056 057 /** 058 * Returns the matrix U of the decomposition. 059 * <p>U is an upper-triangular matrix</p> 060 * @return the U matrix (or null if decomposed matrix is singular) 061 */ 062 FieldMatrix<T> getU(); 063 064 /** 065 * Returns the P rows permutation matrix. 066 * <p>P is a sparse matrix with exactly one element set to 1.0 in 067 * each row and each column, all other elements being set to 0.0.</p> 068 * <p>The positions of the 1 elements are given by the {@link #getPivot() 069 * pivot permutation vector}.</p> 070 * @return the P rows permutation matrix (or null if decomposed matrix is singular) 071 * @see #getPivot() 072 */ 073 FieldMatrix<T> getP(); 074 075 /** 076 * Returns the pivot permutation vector. 077 * @return the pivot permutation vector 078 * @see #getP() 079 */ 080 int[] getPivot(); 081 082 /** 083 * Return the determinant of the matrix 084 * @return determinant of the matrix 085 */ 086 T getDeterminant(); 087 088 /** 089 * Get a solver for finding the A × X = B solution in exact linear sense. 090 * @return a solver 091 */ 092 FieldDecompositionSolver<T> getSolver(); 093 094 }