src/main/java/org/apache/commons/math3/linear/FieldDecompositionSolver.java


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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;

import org.apache.commons.math3.FieldElement;

/**
 * Interface handling decomposition algorithms that can solve A &times; X = B.
 *
 * <p>Decomposition algorithms decompose an A matrix has a product of several specific matrices from
 * which they can solve A &times; X = B in least squares sense: they find X such that ||A &times; X
 * - B|| is minimal.
 *
 * <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 &times; 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.
 *
 * @param <T> the type of the field elements
 * @since 2.0
 */
public interface FieldDecompositionSolver<T extends FieldElement<T>> {

    /**
     * Solve the linear equation A &times; X = B for matrices A.
     *
     * <p>The A matrix is implicit, it is provided by the underlying decomposition algorithm.
     *
     * @param b right-hand side of the equation A &times; X = B
     * @return a vector X that minimizes the two norm of A &times; X - B
     * @throws org.apache.commons.math3.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 &times; X = B for matrices A.
     *
     * <p>The A matrix is implicit, it is provided by the underlying decomposition algorithm.
     *
     * @param b right-hand side of the equation A &times; X = B
     * @return a matrix X that minimizes the two norm of A &times; X - B
     * @throws org.apache.commons.math3.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();
}