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 06:27:47 -0400 (Mon, 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 }