org.apache.commons.math3.linear.DecompositionSolver Maven / Gradle / Ivy
Show all versions of commons-math3 Show documentation
/*
* 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/LICENSE-2.0
*
* 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.
*
* 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.
*
* 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.
*
* 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.
*
* 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 pseudo-inverse
* of the decomposed matrix.
*
* This is equal to the inverse of the decomposed matrix, if such an inverse exists.
*
* If no such inverse exists, then the result has properties that resemble that of an inverse.
*
* 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.
*
* 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;
}