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.math3.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 $Id: DecompositionSolver.java 1416643 2012-12-03 19:37:14Z tn $
034 * @since 2.0
035 */
036public 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     * @throws org.apache.commons.math3.exception.DimensionMismatchException
044     * if the matrices dimensions do not match.
045     * @throws SingularMatrixException
046     * if the decomposed matrix is singular.
047     */
048    RealVector solve(final RealVector b);
049
050    /** Solve the linear equation A &times; X = B for matrices A.
051     * <p>The A matrix is implicit, it is provided by the underlying
052     * decomposition algorithm.</p>
053     * @param b right-hand side of the equation A &times; X = B
054     * @return a matrix X that minimizes the two norm of A &times; X - B
055     * @throws org.apache.commons.math3.exception.DimensionMismatchException
056     * if the matrices dimensions do not match.
057     * @throws SingularMatrixException
058     * if the decomposed matrix is singular.
059     */
060    RealMatrix solve(final RealMatrix b);
061
062    /**
063     * Check if the decomposed matrix is non-singular.
064     * @return true if the decomposed matrix is non-singular.
065     */
066    boolean isNonSingular();
067
068    /** Get the inverse (or pseudo-inverse) of the decomposed matrix.
069     * @return inverse matrix
070     * @throws SingularMatrixException
071     * if the decomposed matrix is singular.
072     */
073    RealMatrix getInverse();
074}