    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
    018    package org.apache.commons.math.linear;
    019
    020    import org.apache.commons.math.FieldElement;
    021
    022
    023    /**
    024     * Interface handling decomposition algorithms that can solve A &times; 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 LUDecomposition} 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     * @version $Revision: 781122 $ $Date: 2009-06-02 20:53:23 +0200 (mar. 02 juin 2009) $
    036     * @since 2.0
    037     */
    038    public interface FieldDecompositionSolver<T extends FieldElement<T>> {
    039
    040        /** Solve the linear equation A &times; X = B for matrices A.
    041         * <p>The A matrix is implicit, it is provided by the underlying
    042         * decomposition algorithm.</p>
    043         * @param b right-hand side of the equation A &times; X = B
    044         * @return a vector X that minimizes the two norm of A &times; X - B
    045         * @exception IllegalArgumentException if matrices dimensions don't match
    046         * @exception InvalidMatrixException if decomposed matrix is singular
    047         */
    048        T[] solve(final T[] b)
    049            throws IllegalArgumentException, InvalidMatrixException;
    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 vector X that minimizes the two norm of A &times; X - B
    056         * @exception IllegalArgumentException if matrices dimensions don't match
    057         * @exception InvalidMatrixException if decomposed matrix is singular
    058         */
    059        FieldVector<T> solve(final FieldVector<T> b)
    060            throws IllegalArgumentException, InvalidMatrixException;
    061
    062        /** Solve the linear equation A &times; X = B for matrices A.
    063         * <p>The A matrix is implicit, it is provided by the underlying
    064         * decomposition algorithm.</p>
    065         * @param b right-hand side of the equation A &times; X = B
    066         * @return a matrix X that minimizes the two norm of A &times; X - B
    067         * @exception IllegalArgumentException if matrices dimensions don't match
    068         * @exception InvalidMatrixException if decomposed matrix is singular
    069         */
    070        FieldMatrix<T> solve(final FieldMatrix<T> b)
    071            throws IllegalArgumentException, InvalidMatrixException;
    072
    073        /**
    074         * Check if the decomposed matrix is non-singular.
    075         * @return true if the decomposed matrix is non-singular
    076         */
    077        boolean isNonSingular();
    078
    079        /** Get the inverse (or pseudo-inverse) of the decomposed matrix.
    080         * @return inverse matrix
    081         * @throws InvalidMatrixException if decomposed matrix is singular
    082         */
    083        FieldMatrix<T> getInverse()
    084            throws InvalidMatrixException;
    085
    086    }