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.math3.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 × X = B in least squares sense: they find X
26 * such that ||A × 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 × 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 $Id: DecompositionSolver.java 1416643 2012-12-03 19:37:14Z tn $
34 * @since 2.0
35 */
36 public interface DecompositionSolver {
37
38 /** Solve the linear equation A × 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 × X = B
42 * @return a vector X that minimizes the two norm of A × X - B
43 * @throws org.apache.commons.math3.exception.DimensionMismatchException
44 * if the matrices dimensions do not match.
45 * @throws SingularMatrixException
46 * if the decomposed matrix is singular.
47 */
48 RealVector solve(final RealVector b);
49
50 /** Solve the linear equation A × X = B for matrices A.
51 * <p>The A matrix is implicit, it is provided by the underlying
52 * decomposition algorithm.</p>
53 * @param b right-hand side of the equation A × X = B
54 * @return a matrix X that minimizes the two norm of A × X - B
55 * @throws org.apache.commons.math3.exception.DimensionMismatchException
56 * if the matrices dimensions do not match.
57 * @throws SingularMatrixException
58 * if the decomposed matrix is singular.
59 */
60 RealMatrix solve(final RealMatrix b);
61
62 /**
63 * Check if the decomposed matrix is non-singular.
64 * @return true if the decomposed matrix is non-singular.
65 */
66 boolean isNonSingular();
67
68 /** Get the inverse (or pseudo-inverse) of the decomposed matrix.
69 * @return inverse matrix
70 * @throws SingularMatrixException
71 * if the decomposed matrix is singular.
72 */
73 RealMatrix getInverse();
74 }