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.linear;
019
020import org.apache.commons.math4.FieldElement;
021
022
023/**
024 * Interface handling decomposition algorithms that can solve A × X = B.
025 * <p>Decomposition algorithms decompose an A matrix has a product of several specific
026 * matrices from which they can solve A &times; X = B in least squares sense: they find X
027 * such that ||A &times; X - B|| is minimal.</p>
028 * <p>Some solvers like {@link FieldLUDecomposition} can only find the solution for
029 * square matrices and when the solution is an exact linear solution, i.e. when
030 * ||A &times; X - B|| is exactly 0. Other solvers can also find solutions
031 * with non-square matrix A and with non-null minimal norm. If an exact linear
032 * solution exists it is also the minimal norm solution.</p>
033 *
034 * @param <T> the type of the field elements
035 * @since 2.0
036 */
037public interface FieldDecompositionSolver<T extends FieldElement<T>> {
038
039    /** Solve the linear equation A &times; X = B for matrices A.
040     * <p>The A matrix is implicit, it is provided by the underlying
041     * decomposition algorithm.</p>
042     * @param b right-hand side of the equation A &times; X = B
043     * @return a vector X that minimizes the two norm of A &times; X - B
044     * @throws org.apache.commons.math4.exception.DimensionMismatchException
045     * if the matrices dimensions do not match.
046     * @throws SingularMatrixException
047     * if the decomposed matrix is singular.
048     */
049    FieldVector<T> solve(final FieldVector<T> b);
050
051    /** Solve the linear equation A &times; X = B for matrices A.
052     * <p>The A matrix is implicit, it is provided by the underlying
053     * decomposition algorithm.</p>
054     * @param b right-hand side of the equation A &times; X = B
055     * @return a matrix X that minimizes the two norm of A &times; X - B
056     * @throws org.apache.commons.math4.exception.DimensionMismatchException
057     * if the matrices dimensions do not match.
058     * @throws SingularMatrixException
059     * if the decomposed matrix is singular.
060     */
061    FieldMatrix<T> solve(final FieldMatrix<T> b);
062
063    /**
064     * Check if the decomposed matrix is non-singular.
065     * @return true if the decomposed matrix is non-singular
066     */
067    boolean isNonSingular();
068
069    /** Get the inverse (or pseudo-inverse) of the decomposed matrix.
070     * @return inverse matrix
071     * @throws SingularMatrixException
072     * if the decomposed matrix is singular.
073     */
074    FieldMatrix<T> getInverse();
075}