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Fast double-precision vector and matrix maths library for Java, supporting N-dimensional numeric arrays.

There is a newer version: 0.67.0

/*
 * Copyright (c) 2009-2013, 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 mikera.matrixx.decompose.impl.qr;

import mikera.matrixx.AMatrix;
import mikera.matrixx.decompose.IQRResult;

/**
 * 
 * QR decompositions decompose a rectangular matrix 'A' such that 'A=QR'.  Where
 * A ∈ ℜ ^{n × m} , n ≥ m, Q ∈ ℜ ^{n × n} is an orthogonal matrix,
 * and R ∈ ℜ ^{n × m} is an upper triangular matrix.  Some implementations
 * of QR decomposition require that A has full rank.
 * 
 * 
 * Some features of QR decompositions:
 * 

 *  Can decompose rectangular matrices. 
 *  Numerically stable solutions to least-squares problem, but not as stable as SVD 
 *  Can incrementally add and remove columns from the decomposed matrix.  See {@link org.ejml.alg.dense.linsol.qr.AdjLinearSolverQr} 
 * 
 * 
 * 
 * Orthogonal matrices have the following properties:
 * 

 * QQ^T=I
 * Q^T=Q^-1
 * 
 * 
 *
 * @author Peter Abeles
 */
public interface QRDecomposition {
    public IQRResult decompose( AMatrix A );
}