org.hipparchus.linear.FieldDecompositionSolver Maven / Gradle / Ivy
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* 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,
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/*
* This is not the original file distributed by the Apache Software Foundation
* It has been modified by the Hipparchus project
*/
package org.hipparchus.linear;
import org.hipparchus.FieldElement;
/**
* 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 FieldLUDecomposition} 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.
*
* @param the type of the field elements
*/
public interface FieldDecompositionSolver> {
/** 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.hipparchus.exception.MathIllegalArgumentException
* if the matrices dimensions do not match or the decomposed matrix
* is singular.
*/
FieldVector solve(FieldVector b);
/** 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.hipparchus.exception.MathIllegalArgumentException
* if the matrices dimensions do not match or the decomposed matrix
* is singular.
*/
FieldMatrix solve(FieldMatrix b);
/**
* Check if the decomposed matrix is non-singular.
* @return true if the decomposed matrix is non-singular
*/
boolean isNonSingular();
/** Get the inverse (or pseudo-inverse) of the decomposed matrix.
* @return inverse matrix
* @throws org.hipparchus.exception.MathIllegalArgumentException
* if the decomposed matrix is singular.
*/
FieldMatrix getInverse();
}