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/*
* 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.math.linear;
import org.apache.commons.math.FieldElement;
/**
* 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>
* <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.</p>
*
* @param <T> the type of the field elements
* @version $Revision: 781122 $ $Date: 2009-06-02 20:53:23 +0200 (mar. 02 juin 2009) $
* @since 2.0
*/
public interface FieldDecompositionSolver<T extends FieldElement<T>> {
/** Solve the linear equation A × X = B for matrices A.
* <p>The A matrix is implicit, it is provided by the underlying
* decomposition algorithm.</p>
* @param b right-hand side of the equation A × X = B
* @return a vector X that minimizes the two norm of A × X - B
* @exception IllegalArgumentException if matrices dimensions don't match
* @exception InvalidMatrixException if decomposed matrix is singular
*/
T[] solve(final T[] b)
throws IllegalArgumentException, InvalidMatrixException;
/** Solve the linear equation A × X = B for matrices A.
* <p>The A matrix is implicit, it is provided by the underlying
* decomposition algorithm.</p>
* @param b right-hand side of the equation A × X = B
* @return a vector X that minimizes the two norm of A × X - B
* @exception IllegalArgumentException if matrices dimensions don't match
* @exception InvalidMatrixException if decomposed matrix is singular
*/
FieldVector<T> solve(final FieldVector<T> b)
throws IllegalArgumentException, InvalidMatrixException;
/** Solve the linear equation A × X = B for matrices A.
* <p>The A matrix is implicit, it is provided by the underlying
* decomposition algorithm.</p>
* @param b right-hand side of the equation A × X = B
* @return a matrix X that minimizes the two norm of A × X - B
* @exception IllegalArgumentException if matrices dimensions don't match
* @exception InvalidMatrixException if decomposed matrix is singular
*/
FieldMatrix<T> solve(final FieldMatrix<T> b)
throws IllegalArgumentException, InvalidMatrixException;
/**
* 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 InvalidMatrixException if decomposed matrix is singular
*/
FieldMatrix<T> getInverse()
throws InvalidMatrixException;
}
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