IQRResult.java

/*
 * 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 mikera.matrixx.decompose;

import mikera.matrixx.AMatrix;

/**
 * <p>
 * QR decompositions decompose a rectangular matrix 'A' such that 'A=QR'. Where
 * A ∈ ℜ <sup>n × m</sup> , n ≥ m, Q ∈ ℜ <sup>n
 * × n</sup> is an orthogonal matrix, and R ∈ ℜ <sup>n ×
 * m</sup> is an upper triangular matrix. Some implementations of QR
 * decomposition require that A has full rank.
 * </p>
 * <p>
 * Some features of QR decompositions:
 * <ul>
 * <li>Can decompose rectangular matrices.</li>
 * <li>Numerically stable solutions to least-squares problem, but not as stable
 * as SVD</li>
 * </ul>
 * </p>
 * <p>
 * Orthogonal matrices have the following properties:
 * <ul>
 * <li>QQ<sup>T</sup>=I</li>
 * <li>Q<sup>T</sup>=Q<sup>-1</sup></li>
 * </ul>
 * </p>
 *
 * @author Peter Abeles
 */
public interface IQRResult {
  /**
   * <p>
   * Returns the Q matrix from the decomposition.
   * </p>
   *
   * @return The Q matrix.
   */
  public AMatrix getQ();

  /**
   * <p>
   * Returns the R matrix from the decomposition.
   * </p>
   *
   * @return The R matrix.
   */
  public AMatrix getR();
}