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 × X = B in least squares sense: they find X
026 * such that ||A × 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 × 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 × 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 × X = B
042 * @return a vector X that minimizes the two norm of A × 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 × 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 × X = B
053 * @return a vector X that minimizes the two norm of A × 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 × 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 × X = B
064 * @return a matrix X that minimizes the two norm of A × 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 }