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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&times;A = L&times;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 now defunct
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: 799857 $ $Date: 2009-08-01 09:07:12 -0400 (Sat, 01 Aug 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 &times; X = B solution in exact linear sense.
88       * @return a solver
89       */
90      DecompositionSolver getSolver();
91  
92  }