| /* |
| * 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.math4.linear; |
| |
| import org.apache.commons.math4.FieldElement; |
| |
| |
| /** |
| * 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 FieldLUDecomposition} 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> |
| * |
| * @param <T> the type of the field elements |
| * @since 2.0 |
| */ |
| public interface FieldDecompositionSolver<T extends FieldElement<T>> { |
| |
| /** 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.math4.exception.DimensionMismatchException |
| * if the matrices dimensions do not match. |
| * @throws SingularMatrixException |
| * if the decomposed matrix is singular. |
| */ |
| FieldVector<T> solve(final FieldVector<T> 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.math4.exception.DimensionMismatchException |
| * if the matrices dimensions do not match. |
| * @throws SingularMatrixException |
| * if the decomposed matrix is singular. |
| */ |
| FieldMatrix<T> solve(final FieldMatrix<T> 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. |
| */ |
| FieldMatrix<T> getInverse(); |
| } |