001 /*
002 * Licensed to the Apache Software Foundation (ASF) under one or more
003 * contributor license agreements. See the NOTICE file distributed with
004 * this work for additional information regarding copyright ownership.
005 * The ASF licenses this file to You under the Apache License, Version 2.0
006 * (the "License"); you may not use this file except in compliance with
007 * the License. You may obtain a copy of the License at
008 *
009 * http://www.apache.org/licenses/LICENSE-2.0
010 *
011 * Unless required by applicable law or agreed to in writing, software
012 * distributed under the License is distributed on an "AS IS" BASIS,
013 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
014 * See the License for the specific language governing permissions and
015 * limitations under the License.
016 */
017
018 package org.apache.commons.math3.linear;
019
020
021
022 /**
023 * Interface handling decomposition algorithms that can solve A × X = B.
024 * <p>Decomposition algorithms decompose an A matrix has a product of several specific
025 * matrices from which they can solve A × X = B in least squares sense: they find X
026 * such that ||A × X - B|| is minimal.</p>
027 * <p>Some solvers like {@link LUDecomposition} can only find the solution for
028 * square matrices and when the solution is an exact linear solution, i.e. when
029 * ||A × X - B|| is exactly 0. Other solvers can also find solutions
030 * with non-square matrix A and with non-null minimal norm. If an exact linear
031 * solution exists it is also the minimal norm solution.</p>
032 *
033 * @version $Id: DecompositionSolver.java 1416643 2012-12-03 19:37:14Z tn $
034 * @since 2.0
035 */
036 public interface DecompositionSolver {
037
038 /** Solve the linear equation A × X = B for matrices A.
039 * <p>The A matrix is implicit, it is provided by the underlying
040 * decomposition algorithm.</p>
041 * @param b right-hand side of the equation A × X = B
042 * @return a vector X that minimizes the two norm of A × X - B
043 * @throws org.apache.commons.math3.exception.DimensionMismatchException
044 * if the matrices dimensions do not match.
045 * @throws SingularMatrixException
046 * if the decomposed matrix is singular.
047 */
048 RealVector solve(final RealVector b);
049
050 /** Solve the linear equation A × X = B for matrices A.
051 * <p>The A matrix is implicit, it is provided by the underlying
052 * decomposition algorithm.</p>
053 * @param b right-hand side of the equation A × X = B
054 * @return a matrix X that minimizes the two norm of A × X - B
055 * @throws org.apache.commons.math3.exception.DimensionMismatchException
056 * if the matrices dimensions do not match.
057 * @throws SingularMatrixException
058 * if the decomposed matrix is singular.
059 */
060 RealMatrix solve(final RealMatrix b);
061
062 /**
063 * Check if the decomposed matrix is non-singular.
064 * @return true if the decomposed matrix is non-singular.
065 */
066 boolean isNonSingular();
067
068 /** Get the inverse (or pseudo-inverse) of the decomposed matrix.
069 * @return inverse matrix
070 * @throws SingularMatrixException
071 * if the decomposed matrix is singular.
072 */
073 RealMatrix getInverse();
074 }