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.math3.linear;
019    
020    import org.apache.commons.math3.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     * @version $Id: FieldDecompositionSolver.java 1416643 2012-12-03 19:37:14Z tn $
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         * @throws org.apache.commons.math3.exception.DimensionMismatchException
046         * if the matrices dimensions do not match.
047         * @throws SingularMatrixException
048         * if the decomposed matrix is singular.
049         */
050        FieldVector<T> solve(final FieldVector<T> b);
051    
052        /** Solve the linear equation A &times; X = B for matrices A.
053         * <p>The A matrix is implicit, it is provided by the underlying
054         * decomposition algorithm.</p>
055         * @param b right-hand side of the equation A &times; X = B
056         * @return a matrix X that minimizes the two norm of A &times; X - B
057         * @throws org.apache.commons.math3.exception.DimensionMismatchException
058         * if the matrices dimensions do not match.
059         * @throws SingularMatrixException
060         * if the decomposed matrix is singular.
061         */
062        FieldMatrix<T> solve(final FieldMatrix<T> b);
063    
064        /**
065         * Check if the decomposed matrix is non-singular.
066         * @return true if the decomposed matrix is non-singular
067         */
068        boolean isNonSingular();
069    
070        /** Get the inverse (or pseudo-inverse) of the decomposed matrix.
071         * @return inverse matrix
072         * @throws SingularMatrixException
073         * if the decomposed matrix is singular.
074         */
075        FieldMatrix<T> getInverse();
076    }