

Java example source code file (DecompositionSolver.java)
The DecompositionSolver.java Java example source code/* * Licensed to the Apache Software Foundation (ASF) under one or more * contributor license agreements. See the NOTICE file distributed with * this work for additional information regarding copyright ownership. * The ASF licenses this file to You under the Apache License, Version 2.0 * (the "License"); you may not use this file except in compliance with * the License. You may obtain a copy of the License at * * http://www.apache.org/licenses/LICENSE2.0 * * Unless required by applicable law or agreed to in writing, software * distributed under the License is distributed on an "AS IS" BASIS, * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. * See the License for the specific language governing permissions and * limitations under the License. */ package org.apache.commons.math3.linear; /** * Interface handling decomposition algorithms that can solve A × X = B. * <p> * Decomposition algorithms decompose an A matrix has a product of several specific * matrices from which they can solve A × X = B in least squares sense: they find X * such that A × X  B is minimal. * <p> * Some solvers like {@link LUDecomposition} can only find the solution for * square matrices and when the solution is an exact linear solution, i.e. when * A × X  B is exactly 0. Other solvers can also find solutions * with nonsquare matrix A and with nonnull minimal norm. If an exact linear * solution exists it is also the minimal norm solution. * * @since 2.0 */ public interface DecompositionSolver { /** * Solve the linear equation A × X = B for matrices A. * <p> * The A matrix is implicit, it is provided by the underlying * decomposition algorithm. * * @param b righthand side of the equation A × X = B * @return a vector X that minimizes the two norm of A × X  B * @throws org.apache.commons.math3.exception.DimensionMismatchException * if the matrices dimensions do not match. * @throws SingularMatrixException if the decomposed matrix is singular. */ RealVector solve(final RealVector b) throws SingularMatrixException; /** * Solve the linear equation A × X = B for matrices A. * <p> * The A matrix is implicit, it is provided by the underlying * decomposition algorithm. * * @param b righthand side of the equation A × X = B * @return a matrix X that minimizes the two norm of A × X  B * @throws org.apache.commons.math3.exception.DimensionMismatchException * if the matrices dimensions do not match. * @throws SingularMatrixException if the decomposed matrix is singular. */ RealMatrix solve(final RealMatrix b) throws SingularMatrixException; /** * Check if the decomposed matrix is nonsingular. * @return true if the decomposed matrix is nonsingular. */ boolean isNonSingular(); /** * Get the <a href="http://en.wikipedia.org/wiki/Moore%E2%80%93Penrose_pseudoinverse">pseudoinverse * of the decomposed matrix. * <p> * <em>This is equal to the inverse of the decomposed matrix, if such an inverse exists. * <p> * If no such inverse exists, then the result has properties that resemble that of an inverse. * <p> * In particular, in this case, if the decomposed matrix is A, then the system of equations * \( A x = b \) may have no solutions, or many. If it has no solutions, then the pseudoinverse * \( A^+ \) gives the "closest" solution \( z = A^+ b \), meaning \( \left \ A z  b \right \_2 \) * is minimized. If there are many solutions, then \( z = A^+ b \) is the smallest solution, * meaning \( \left \ z \right \_2 \) is minimized. * <p> * Note however that some decompositions cannot compute a pseudoinverse for all matrices. * For example, the {@link LUDecomposition} is not defined for nonsquare matrices to begin * with. The {@link QRDecomposition} can operate on nonsquare matrices, but will throw * {@link SingularMatrixException} if the decomposed matrix is singular. Refer to the javadoc * of specific decomposition implementations for more details. * * @return pseudoinverse matrix (which is the inverse, if it exists), * if the decomposition can pseudoinvert the decomposed matrix * @throws SingularMatrixException if the decomposed matrix is singular and the decomposition * can not compute a pseudoinverse */ RealMatrix getInverse() throws SingularMatrixException; } Other Java examples (source code examples)Here is a short list of links related to this Java DecompositionSolver.java source code file: 
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