/*
 * Copyright (c) 2009-2014, Peter Abeles. All Rights Reserved.
 *
 * This file is part of Efficient Java Matrix Library (EJML).
 *
 * Licensed 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.ejml.interfaces.linsol;

import org.ejml.data.RealMatrix64F;

/**
 * 

 * An augmented system matrix is said to be in reduced row echelon form (RREF) if the following are true:
 * 
 *
 * 

 *     
If a row has non-zero entries, then the first non-zero entry is 1.  This is known as the leading one.
 *     
If a column contains a leading one then all other entries in that column are zero.
 *     
If a row contains a leading 1, then each row above contains a leading 1 further to the left.
 * 
 *
 * 

 * [1] Page 19 in, Otter Bretscherm "Linear Algebra with Applications" Prentice-Hall Inc, 1997
 * 
 *
 * @author Peter Abeles
 */
public interface ReducedRowEchelonForm {

    /**
     * Puts the augmented matrix into RREF.  The coefficient matrix is stored in
     * columns less than coefficientColumns.
     *
     *
     * @param A Input: Augmented matrix.  Output: RREF.  Modified.
     * @param coefficientColumns Number of coefficients in the system matrix.
     */
    public void reduce( T A , int coefficientColumns );

    /**
     * Specifies tolerance for determining if the system is singular and it should stop processing.
     * A reasonable value is: tol = EPS/max(||tol||).
     *
     * @param tol Tolerance for singular matrix. A reasonable value is: tol = EPS/max(||tol||). Or just set to zero.
     */
    public void setTolerance(double tol);
}