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&times;A = L&times;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 &times; X = B solution in exact linear sense.
088         * @return a solver
089         */
090        DecompositionSolver getSolver();
091    
092    }