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.math.linear; 19 20 import org.apache.commons.math.FieldElement; 21 22 23 /** 24 * Interface handling decomposition algorithms that can solve A × X = B. 25 * <p>Decomposition algorithms decompose an A matrix has a product of several specific 26 * matrices from which they can solve A × X = B in least squares sense: they find X 27 * such that ||A × X - B|| is minimal.</p> 28 * <p>Some solvers like {@link LUDecomposition} can only find the solution for 29 * square matrices and when the solution is an exact linear solution, i.e. when 30 * ||A × X - B|| is exactly 0. Other solvers can also find solutions 31 * with non-square matrix A and with non-null minimal norm. If an exact linear 32 * solution exists it is also the minimal norm solution.</p> 33 * 34 * @param <T> the type of the field elements 35 * @version $Revision: 781122 $ $Date: 2009-06-02 20:53:23 +0200 (mar. 02 juin 2009) $ 36 * @since 2.0 37 */ 38 public interface FieldDecompositionSolver<T extends FieldElement<T>> { 39 40 /** Solve the linear equation A × X = B for matrices A. 41 * <p>The A matrix is implicit, it is provided by the underlying 42 * decomposition algorithm.</p> 43 * @param b right-hand side of the equation A × X = B 44 * @return a vector X that minimizes the two norm of A × X - B 45 * @exception IllegalArgumentException if matrices dimensions don't match 46 * @exception InvalidMatrixException if decomposed matrix is singular 47 */ 48 T[] solve(final T[] b) 49 throws IllegalArgumentException, InvalidMatrixException; 50 51 /** Solve the linear equation A × X = B for matrices A. 52 * <p>The A matrix is implicit, it is provided by the underlying 53 * decomposition algorithm.</p> 54 * @param b right-hand side of the equation A × X = B 55 * @return a vector X that minimizes the two norm of A × X - B 56 * @exception IllegalArgumentException if matrices dimensions don't match 57 * @exception InvalidMatrixException if decomposed matrix is singular 58 */ 59 FieldVector<T> solve(final FieldVector<T> b) 60 throws IllegalArgumentException, InvalidMatrixException; 61 62 /** Solve the linear equation A × X = B for matrices A. 63 * <p>The A matrix is implicit, it is provided by the underlying 64 * decomposition algorithm.</p> 65 * @param b right-hand side of the equation A × X = B 66 * @return a matrix X that minimizes the two norm of A × X - B 67 * @exception IllegalArgumentException if matrices dimensions don't match 68 * @exception InvalidMatrixException if decomposed matrix is singular 69 */ 70 FieldMatrix<T> solve(final FieldMatrix<T> b) 71 throws IllegalArgumentException, InvalidMatrixException; 72 73 /** 74 * Check if the decomposed matrix is non-singular. 75 * @return true if the decomposed matrix is non-singular 76 */ 77 boolean isNonSingular(); 78 79 /** Get the inverse (or pseudo-inverse) of the decomposed matrix. 80 * @return inverse matrix 81 * @throws InvalidMatrixException if decomposed matrix is singular 82 */ 83 FieldMatrix<T> getInverse() 84 throws InvalidMatrixException; 85 86 } 87
