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    
021    
022    /**
023     * Interface handling decomposition algorithms that can solve A × X = B.
024     * <p>Decomposition algorithms decompose an A matrix has a product of several specific
025     * matrices from which they can solve A &times; X = B in least squares sense: they find X
026     * such that ||A &times; X - B|| is minimal.</p>
027     * <p>Some solvers like {@link LUDecomposition} can only find the solution for
028     * square matrices and when the solution is an exact linear solution, i.e. when
029     * ||A &times; X - B|| is exactly 0. Other solvers can also find solutions
030     * with non-square matrix A and with non-null minimal norm. If an exact linear
031     * solution exists it is also the minimal norm solution.</p>
032     *
033     * @version $Revision: 811685 $ $Date: 2009-09-05 19:36:48 +0200 (sam. 05 sept. 2009) $
034     * @since 2.0
035     */
036    public interface DecompositionSolver {
037    
038        /** Solve the linear equation A &times; X = B for matrices A.
039         * <p>The A matrix is implicit, it is provided by the underlying
040         * decomposition algorithm.</p>
041         * @param b right-hand side of the equation A &times; X = B
042         * @return a vector X that minimizes the two norm of A &times; X - B
043         * @exception IllegalArgumentException if matrices dimensions don't match
044         * @exception InvalidMatrixException if decomposed matrix is singular
045         */
046        double[] solve(final double[] b)
047            throws IllegalArgumentException, InvalidMatrixException;
048    
049        /** Solve the linear equation A &times; X = B for matrices A.
050         * <p>The A matrix is implicit, it is provided by the underlying
051         * decomposition algorithm.</p>
052         * @param b right-hand side of the equation A &times; X = B
053         * @return a vector X that minimizes the two norm of A &times; X - B
054         * @exception IllegalArgumentException if matrices dimensions don't match
055         * @exception InvalidMatrixException if decomposed matrix is singular
056         */
057        RealVector solve(final RealVector b)
058            throws IllegalArgumentException, InvalidMatrixException;
059    
060        /** Solve the linear equation A &times; X = B for matrices A.
061         * <p>The A matrix is implicit, it is provided by the underlying
062         * decomposition algorithm.</p>
063         * @param b right-hand side of the equation A &times; X = B
064         * @return a matrix X that minimizes the two norm of A &times; X - B
065         * @exception IllegalArgumentException if matrices dimensions don't match
066         * @exception InvalidMatrixException if decomposed matrix is singular
067         */
068        RealMatrix solve(final RealMatrix b)
069            throws IllegalArgumentException, InvalidMatrixException;
070    
071        /**
072         * Check if the decomposed matrix is non-singular.
073         * @return true if the decomposed matrix is non-singular
074         */
075        boolean isNonSingular();
076    
077        /** Get the inverse (or pseudo-inverse) of the decomposed matrix.
078         * @return inverse matrix
079         * @throws InvalidMatrixException if decomposed matrix is singular
080         */
081        RealMatrix getInverse()
082            throws InvalidMatrixException;
083    
084    }