/*
 * 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 &times; X = B.
 * <p>
 * Decomposition algorithms decompose an A matrix has a product of several
 * specific matrices from which they can solve A &times; X = B in least squares
 * sense: they find X such that ||A &times; 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 &times; 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 $Revision$ $Date$
 * @since 2.0
 */
public interface FieldDecompositionSolver<T extends FieldElement<T>> {

	/**
	 * Solve the linear equation A &times; 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 &times; X = B
	 * @return a vector X that minimizes the two norm of A &times; 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 &times; 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 &times; X = B
	 * @return a vector X that minimizes the two norm of A &times; 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 &times; 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 &times; X = B
	 * @return a matrix X that minimizes the two norm of A &times; 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;

}
