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
18package org.apache.commons.math.linear;
19
20
21
22/**
23 * Interface handling decomposition algorithms that can solve A × X = B.
24 * <p>Decomposition algorithms decompose an A matrix has a product of several specific
25 * matrices from which they can solve A &times; X = B in least squares sense: they find X
26 * such that ||A &times; X - B|| is minimal.</p>
27 * <p>Some solvers like {@link LUDecomposition} can only find the solution for
28 * square matrices and when the solution is an exact linear solution, i.e. when
29 * ||A &times; X - B|| is exactly 0. Other solvers can also find solutions
30 * with non-square matrix A and with non-null minimal norm. If an exact linear
31 * solution exists it is also the minimal norm solution.</p>
32 *
33 * @version $Revision: 811685 $ $Date: 2009-09-05 19:36:48 +0200 (sam. 05 sept. 2009) $
34 * @since 2.0
35 */
36public interface DecompositionSolver {
37
38    /** Solve the linear equation A &times; X = B for matrices A.
39     * <p>The A matrix is implicit, it is provided by the underlying
40     * decomposition algorithm.</p>
41     * @param b right-hand side of the equation A &times; X = B
42     * @return a vector X that minimizes the two norm of A &times; X - B
43     * @exception IllegalArgumentException if matrices dimensions don't match
44     * @exception InvalidMatrixException if decomposed matrix is singular
45     */
46    double[] solve(final double[] b)
47        throws IllegalArgumentException, InvalidMatrixException;
48
49    /** Solve the linear equation A &times; X = B for matrices A.
50     * <p>The A matrix is implicit, it is provided by the underlying
51     * decomposition algorithm.</p>
52     * @param b right-hand side of the equation A &times; X = B
53     * @return a vector X that minimizes the two norm of A &times; X - B
54     * @exception IllegalArgumentException if matrices dimensions don't match
55     * @exception InvalidMatrixException if decomposed matrix is singular
56     */
57    RealVector solve(final RealVector b)
58        throws IllegalArgumentException, InvalidMatrixException;
59
60    /** Solve the linear equation A &times; X = B for matrices A.
61     * <p>The A matrix is implicit, it is provided by the underlying
62     * decomposition algorithm.</p>
63     * @param b right-hand side of the equation A &times; X = B
64     * @return a matrix X that minimizes the two norm of A &times; X - B
65     * @exception IllegalArgumentException if matrices dimensions don't match
66     * @exception InvalidMatrixException if decomposed matrix is singular
67     */
68    RealMatrix solve(final RealMatrix b)
69        throws IllegalArgumentException, InvalidMatrixException;
70
71    /**
72     * Check if the decomposed matrix is non-singular.
73     * @return true if the decomposed matrix is non-singular
74     */
75    boolean isNonSingular();
76
77    /** Get the inverse (or pseudo-inverse) of the decomposed matrix.
78     * @return inverse matrix
79     * @throws InvalidMatrixException if decomposed matrix is singular
80     */
81    RealMatrix getInverse()
82        throws InvalidMatrixException;
83
84}
85