1 /* 2 * Licensed to the Apache Software Foundation (ASF) under one or more 3 * contributor license agreements. See the NOTICE file distributed with 4 * this work for additional information regarding copyright ownership. 5 * The ASF licenses this file to You under the Apache License, Version 2.0 6 * (the "License"); you may not use this file except in compliance with 7 * the License. You may obtain a copy of the License at 8 * 9 * http://www.apache.org/licenses/LICENSE-2.0 10 * 11 * Unless required by applicable law or agreed to in writing, software 12 * distributed under the License is distributed on an "AS IS" BASIS, 13 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. 14 * See the License for the specific language governing permissions and 15 * limitations under the License. 16 */ 17 18 package org.apache.commons.math.linear; 19 20 21 /** 22 * An interface to classes that implement an algorithm to calculate the 23 * LU-decomposition of a real matrix. 24 * <p>The LU-decomposition of matrix A is a set of three matrices: P, L and U 25 * such that P×A = L×U. P is a rows permutation matrix that is used 26 * to rearrange the rows of A before so that it can be decomposed. L is a lower 27 * triangular matrix with unit diagonal terms and U is an upper triangular matrix.</p> 28 * <p>This interface is based on the class with similar name from the 29 * <a href="http://math.nist.gov/javanumerics/jama/">JAMA</a> library.</p> 30 * <ul> 31 * <li>a {@link #getP() getP} method has been added,</li> 32 * <li>the <code>det</code> method has been renamed as {@link #getDeterminant() 33 * getDeterminant},</li> 34 * <li>the <code>getDoublePivot</code> method has been removed (but the int based 35 * {@link #getPivot() getPivot} method has been kept),</li> 36 * <li>the <code>solve</code> and <code>isNonSingular</code> methods have been replaced 37 * by a {@link #getSolver() getSolver} method and the equivalent methods provided by 38 * the returned {@link DecompositionSolver}.</li> 39 * </ul> 40 * 41 * @see <a href="http://mathworld.wolfram.com/LUDecomposition.html">MathWorld</a> 42 * @see <a href="http://en.wikipedia.org/wiki/LU_decomposition">Wikipedia</a> 43 * @version $Revision: 826627 $ $Date: 2009-10-19 12:27:47 +0200 (lun. 19 oct. 2009) $ 44 * @since 2.0 45 */ 46 public interface LUDecomposition { 47 48 /** 49 * Returns the matrix L of the decomposition. 50 * <p>L is an lower-triangular matrix</p> 51 * @return the L matrix (or null if decomposed matrix is singular) 52 */ 53 RealMatrix getL(); 54 55 /** 56 * Returns the matrix U of the decomposition. 57 * <p>U is an upper-triangular matrix</p> 58 * @return the U matrix (or null if decomposed matrix is singular) 59 */ 60 RealMatrix getU(); 61 62 /** 63 * Returns the P rows permutation matrix. 64 * <p>P is a sparse matrix with exactly one element set to 1.0 in 65 * each row and each column, all other elements being set to 0.0.</p> 66 * <p>The positions of the 1 elements are given by the {@link #getPivot() 67 * pivot permutation vector}.</p> 68 * @return the P rows permutation matrix (or null if decomposed matrix is singular) 69 * @see #getPivot() 70 */ 71 RealMatrix getP(); 72 73 /** 74 * Returns the pivot permutation vector. 75 * @return the pivot permutation vector 76 * @see #getP() 77 */ 78 int[] getPivot(); 79 80 /** 81 * Return the determinant of the matrix 82 * @return determinant of the matrix 83 */ 84 double getDeterminant(); 85 86 /** 87 * Get a solver for finding the A × X = B solution in exact linear sense. 88 * @return a solver 89 */ 90 DecompositionSolver getSolver(); 91 92 } 93
