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 import org.apache.commons.math.FieldElement; 21 22 /** 23 * An interface to classes that implement an algorithm to calculate the 24 * LU-decomposition of a real matrix. 25 * <p>The LU-decomposition of matrix A is a set of three matrices: P, L and U 26 * such that P×A = L×U. P is a rows permutation matrix that is used 27 * to rearrange the rows of A before so that it can be decomposed. L is a lower 28 * triangular matrix with unit diagonal terms and U is an upper triangular matrix.</p> 29 * <p>This interface is based on the class with similar name from the 30 * <a href="http://math.nist.gov/javanumerics/jama/">JAMA</a> library.</p> 31 * <ul> 32 * <li>a {@link #getP() getP} method has been added,</li> 33 * <li>the <code>det</code> method has been renamed as {@link #getDeterminant() 34 * getDeterminant},</li> 35 * <li>the <code>getDoublePivot</code> method has been removed (but the int based 36 * {@link #getPivot() getPivot} method has been kept),</li> 37 * <li>the <code>solve</code> and <code>isNonSingular</code> methods have been replaced 38 * by a {@link #getSolver() getSolver} method and the equivalent methods provided by 39 * the returned {@link DecompositionSolver}.</li> 40 * </ul> 41 * 42 * @param <T> the type of the field elements 43 * @see <a href="http://mathworld.wolfram.com/LUDecomposition.html">MathWorld</a> 44 * @see <a href="http://en.wikipedia.org/wiki/LU_decomposition">Wikipedia</a> 45 * @version $Revision: 826627 $ $Date: 2009-10-19 12:27:47 +0200 (lun. 19 oct. 2009) $ 46 * @since 2.0 47 */ 48 public interface FieldLUDecomposition<T extends FieldElement<T>> { 49 50 /** 51 * Returns the matrix L of the decomposition. 52 * <p>L is an lower-triangular matrix</p> 53 * @return the L matrix (or null if decomposed matrix is singular) 54 */ 55 FieldMatrix<T> getL(); 56 57 /** 58 * Returns the matrix U of the decomposition. 59 * <p>U is an upper-triangular matrix</p> 60 * @return the U matrix (or null if decomposed matrix is singular) 61 */ 62 FieldMatrix<T> getU(); 63 64 /** 65 * Returns the P rows permutation matrix. 66 * <p>P is a sparse matrix with exactly one element set to 1.0 in 67 * each row and each column, all other elements being set to 0.0.</p> 68 * <p>The positions of the 1 elements are given by the {@link #getPivot() 69 * pivot permutation vector}.</p> 70 * @return the P rows permutation matrix (or null if decomposed matrix is singular) 71 * @see #getPivot() 72 */ 73 FieldMatrix<T> getP(); 74 75 /** 76 * Returns the pivot permutation vector. 77 * @return the pivot permutation vector 78 * @see #getP() 79 */ 80 int[] getPivot(); 81 82 /** 83 * Return the determinant of the matrix 84 * @return determinant of the matrix 85 */ 86 T getDeterminant(); 87 88 /** 89 * Get a solver for finding the A × X = B solution in exact linear sense. 90 * @return a solver 91 */ 92 FieldDecompositionSolver<T> getSolver(); 93 94 } 95
