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# Java example source code file (DecompositionSolver.java)

This example Java source code file (DecompositionSolver.java) is included in the alvinalexander.com "Java Source Code Warehouse" project. The intent of this project is to help you "Learn Java by Example" TM.

## Java - Java tags/keywords

decompositionsolver, realmatrix, realvector, singularmatrixexception

## 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
* 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
*
*
* Unless required by applicable law or agreed to in writing, software
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
*/

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 non-square matrix A and with non-null 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 right-hand 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 right-hand 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 non-singular.
* @return true if the decomposed matrix is non-singular.
*/
boolean isNonSingular();

/**
* Get the <a href="http://en.wikipedia.org/wiki/Moore%E2%80%93Penrose_pseudoinverse">pseudo-inverse
* 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 pseudo-inverse
* $$A^+$$ 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 pseudo-inverse for all matrices.
* For example, the {@link LUDecomposition} is not defined for non-square matrices to begin
* with. The {@link QRDecomposition} can operate on non-square matrices, but will throw
* {@link SingularMatrixException} if the decomposed matrix is singular. Refer to the javadoc
* of specific decomposition implementations for more details.
*
* @return pseudo-inverse matrix (which is the inverse, if it exists),
* if the decomposition can pseudo-invert the decomposed matrix
* @throws SingularMatrixException if the decomposed matrix is singular and the decomposition
* can not compute a pseudo-inverse
*/
RealMatrix getInverse() throws SingularMatrixException;
}


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