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/* * Licensed to the Apache Software Foundation (ASF) under one or more * contributor license agreements. See the NOTICE file distributed with * this work for additional information regarding copyright ownership. * The ASF licenses this file to You under the Apache License, Version 2.0 * (the "License"); you may not use this file except in compliance with * the License. You may obtain a copy of the License at * * http://www.apache.org/licenses/LICENSE-2.0 * * Unless required by applicable law or agreed to in writing, software * distributed under the License is distributed on an "AS IS" BASIS, * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. * See the License for the specific language governing permissions and * limitations under the License. */ package org.apache.commons.math3.linear; /** * Interface handling decomposition algorithms that can solve A × X = B. * <p>Decomposition algorithms decompose an A matrix has a product of several specific * matrices from which they can solve A × X = B in least squares sense: they find X * such that ||A × X - B|| is minimal.</p> * <p>Some solvers like {@link LUDecomposition} can only find the solution for * square matrices and when the solution is an exact linear solution, i.e. when * ||A × X - B|| is exactly 0. Other solvers can also find solutions * with non-square matrix A and with non-null minimal norm. If an exact linear * solution exists it is also the minimal norm solution.</p> * * @version $Id: DecompositionSolver.java 1416643 2012-12-03 19:37:14Z tn $ * @since 2.0 */ public interface DecompositionSolver { /** Solve the linear equation A × X = B for matrices A. * <p>The A matrix is implicit, it is provided by the underlying * decomposition algorithm.</p> * @param b right-hand side of the equation A × X = B * @return a vector X that minimizes the two norm of A × X - B * @throws org.apache.commons.math3.exception.DimensionMismatchException * if the matrices dimensions do not match. * @throws SingularMatrixException * if the decomposed matrix is singular. */ RealVector solve(final RealVector b); /** Solve the linear equation A × X = B for matrices A. * <p>The A matrix is implicit, it is provided by the underlying * decomposition algorithm.</p> * @param b right-hand side of the equation A × X = B * @return a matrix X that minimizes the two norm of A × X - B * @throws org.apache.commons.math3.exception.DimensionMismatchException * if the matrices dimensions do not match. * @throws SingularMatrixException * if the decomposed matrix is singular. */ RealMatrix solve(final RealMatrix b); /** * Check if the decomposed matrix is non-singular. * @return true if the decomposed matrix is non-singular. */ boolean isNonSingular(); /** Get the inverse (or pseudo-inverse) of the decomposed matrix. * @return inverse matrix * @throws SingularMatrixException * if the decomposed matrix is singular. */ RealMatrix getInverse(); }