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 }