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.math4.legacy.linear;
19
20 import org.apache.commons.math4.legacy.core.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 × X = B in least squares sense: they find X
27 * such that ||A × X - B|| is minimal.</p>
28 * <p>Some solvers like {@link FieldLUDecomposition} can only find the solution for
29 * square matrices and when the solution is an exact linear solution, i.e. when
30 * ||A × 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 * @since 2.0
36 */
37 public interface FieldDecompositionSolver<T extends FieldElement<T>> {
38
39 /** Solve the linear equation A × X = B for matrices A.
40 * <p>The A matrix is implicit, it is provided by the underlying
41 * decomposition algorithm.</p>
42 * @param b right-hand side of the equation A × X = B
43 * @return a vector X that minimizes the two norm of A × X - B
44 * @throws org.apache.commons.math4.legacy.exception.DimensionMismatchException
45 * if the matrices dimensions do not match.
46 * @throws SingularMatrixException
47 * if the decomposed matrix is singular.
48 */
49 FieldVector<T> solve(FieldVector<T> b);
50
51 /** Solve the linear equation A × 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 × X = B
55 * @return a matrix X that minimizes the two norm of A × X - B
56 * @throws org.apache.commons.math4.legacy.exception.DimensionMismatchException
57 * if the matrices dimensions do not match.
58 * @throws SingularMatrixException
59 * if the decomposed matrix is singular.
60 */
61 FieldMatrix<T> solve(FieldMatrix<T> b);
62
63 /**
64 * Check if the decomposed matrix is non-singular.
65 * @return true if the decomposed matrix is non-singular
66 */
67 boolean isNonSingular();
68
69 /** Get the inverse (or pseudo-inverse) of the decomposed matrix.
70 * @return inverse matrix
71 * @throws SingularMatrixException
72 * if the decomposed matrix is singular.
73 */
74 FieldMatrix<T> getInverse();
75 }