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 018package org.apache.commons.math4.field.linalg; 019 020/** 021 * Interface handling decomposition algorithms that can solve {@code A X = B}. 022 * 023 * <p>Decomposition algorithms decompose an A matrix has a product of several specific 024 * matrices from which they can solve the above system of equations in a least-squares 025 * sense: Find X such that {@code ||A X - B||} is minimal.</p> 026 * 027 * <p>Some solvers like {@link FieldLUDecomposition} can only find the solution for 028 * square matrices and when the solution is an exact linear solution, i.e. when 029 * {@code ||A X - B||} is exactly 0. 030 * Other solvers can also find solutions with non-square matrix {@code A} and with 031 * non-zero minimal norm. 032 * If an exact linear solution exists it is also the minimal norm solution.</p> 033 * 034 * @param <T> Type of the field elements. 035 * 036 * @since 4.0 037 */ 038public interface FieldDecompositionSolver<T> { 039 /** 040 * Solves the linear equation {@code A X = B}. 041 * 042 * <p>Matrix {@code A} is implicit: It is provided by the underlying 043 * decomposition algorithm.</p> 044 * 045 * @param b Right-hand side of the equation. 046 * @return the matrix {@code X} that minimizes {@code ||A X - B||}. 047 * @throws IllegalArgumentException if the dimensions do not match. 048 */ 049 FieldDenseMatrix<T> solve(final FieldDenseMatrix<T> b); 050 051 /** 052 * Computes the inverse of a decomposed (square) matrix. 053 * 054 * @return the inverse matrix. 055 */ 056 FieldDenseMatrix<T> getInverse(); 057}