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
20import org.apache.commons.math.FieldElement;
21
22
23/**
24 * Interface handling decomposition algorithms that can solve A × X = B.
25 * <p>Decomposition algorithms decompose an A matrix has a product of several specific
26 * matrices from which they can solve A &times; X = B in least squares sense: they find X
27 * such that ||A &times; X - B|| is minimal.</p>
28 * <p>Some solvers like {@link LUDecomposition} can only find the solution for
29 * square matrices and when the solution is an exact linear solution, i.e. when
30 * ||A &times; X - B|| is exactly 0. Other solvers can also find solutions
31 * with non-square matrix A and with non-null minimal norm. If an exact linear
32 * solution exists it is also the minimal norm solution.</p>
33 *
34 * @param <T> the type of the field elements
35 * @version $Revision: 781122 $ $Date: 2009-06-02 20:53:23 +0200 (mar. 02 juin 2009) $
36 * @since 2.0
37 */
38public interface FieldDecompositionSolver<T extends FieldElement<T>> {
39
40    /** Solve the linear equation A &times; X = B for matrices A.
41     * <p>The A matrix is implicit, it is provided by the underlying
42     * decomposition algorithm.</p>
43     * @param b right-hand side of the equation A &times; X = B
44     * @return a vector X that minimizes the two norm of A &times; X - B
45     * @exception IllegalArgumentException if matrices dimensions don't match
46     * @exception InvalidMatrixException if decomposed matrix is singular
47     */
48    T[] solve(final T[] b)
49        throws IllegalArgumentException, InvalidMatrixException;
50
51    /** Solve the linear equation A &times; X = B for matrices A.
52     * <p>The A matrix is implicit, it is provided by the underlying
53     * decomposition algorithm.</p>
54     * @param b right-hand side of the equation A &times; X = B
55     * @return a vector X that minimizes the two norm of A &times; X - B
56     * @exception IllegalArgumentException if matrices dimensions don't match
57     * @exception InvalidMatrixException if decomposed matrix is singular
58     */
59    FieldVector<T> solve(final FieldVector<T> b)
60        throws IllegalArgumentException, InvalidMatrixException;
61
62    /** Solve the linear equation A &times; X = B for matrices A.
63     * <p>The A matrix is implicit, it is provided by the underlying
64     * decomposition algorithm.</p>
65     * @param b right-hand side of the equation A &times; X = B
66     * @return a matrix X that minimizes the two norm of A &times; X - B
67     * @exception IllegalArgumentException if matrices dimensions don't match
68     * @exception InvalidMatrixException if decomposed matrix is singular
69     */
70    FieldMatrix<T> solve(final FieldMatrix<T> b)
71        throws IllegalArgumentException, InvalidMatrixException;
72
73    /**
74     * Check if the decomposed matrix is non-singular.
75     * @return true if the decomposed matrix is non-singular
76     */
77    boolean isNonSingular();
78
79    /** Get the inverse (or pseudo-inverse) of the decomposed matrix.
80     * @return inverse matrix
81     * @throws InvalidMatrixException if decomposed matrix is singular
82     */
83    FieldMatrix<T> getInverse()
84        throws InvalidMatrixException;
85
86}
87