View Javadoc

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   * QR-decomposition of a real matrix.
24   * <p>This interface is based on the class with similar name from the now defunct
25   * <a href="http://math.nist.gov/javanumerics/jama/">JAMA</a> library, with the
26   * following changes:</p>
27   * <ul>
28   *   <li>a {@link #getQT() getQT} method has been added,</li>
29   *   <li>the <code>solve</code> and <code>isFullRank</code> methods have been replaced
30   *   by a {@link #getSolver() getSolver} method and the equivalent methods provided by
31   *   the returned {@link DecompositionSolver}.</li>
32   * </ul>
33   *   
34   * @see <a href="http://mathworld.wolfram.com/QRDecomposition.html">MathWorld</a>
35   * @see <a href="http://en.wikipedia.org/wiki/QR_decomposition">Wikipedia</a>
36   * @version $Revision: 799857 $ $Date: 2009-08-01 09:07:12 -0400 (Sat, 01 Aug 2009) $
37   * @since 1.2
38   */
39  public interface QRDecomposition {
40  
41      /**
42       * Returns the matrix R of the decomposition. 
43       * <p>R is an upper-triangular matrix</p>
44       * @return the R matrix
45       */
46      RealMatrix getR();
47  
48      /**
49       * Returns the matrix Q of the decomposition.
50       * <p>Q is an orthogonal matrix</p>
51       * @return the Q matrix
52       */
53      RealMatrix getQ();
54  
55      /**
56       * Returns the transpose of the matrix Q of the decomposition.
57       * <p>Q is an orthogonal matrix</p>
58       * @return the Q matrix
59       */
60      RealMatrix getQT();
61  
62      /**
63       * Returns the Householder reflector vectors.
64       * <p>H is a lower trapezoidal matrix whose columns represent
65       * each successive Householder reflector vector. This matrix is used
66       * to compute Q.</p>
67       * @return a matrix containing the Householder reflector vectors
68       */
69      RealMatrix getH();
70  
71      /**
72       * Get a solver for finding the A &times; X = B solution in least square sense.
73       * @return a solver
74       */
75      DecompositionSolver getSolver();
76  
77  }