// <copyright file="QR.cs" company="Math.NET">
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// Math.NET Numerics, part of the Math.NET Project
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// http://numerics.mathdotnet.com
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// http://github.com/mathnet/mathnet-numerics
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//
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// Copyright (c) 2009-2013 Math.NET
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//
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// Permission is hereby granted, free of charge, to any person
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// obtaining a copy of this software and associated documentation
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// files (the "Software"), to deal in the Software without
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// restriction, including without limitation the rights to use,
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// copy, modify, merge, publish, distribute, sublicense, and/or sell
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// copies of the Software, and to permit persons to whom the
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// Software is furnished to do so, subject to the following
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// conditions:
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//
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// The above copyright notice and this permission notice shall be
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// included in all copies or substantial portions of the Software.
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//
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// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
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// EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES
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// OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
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// NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT
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// OTHER DEALINGS IN THE SOFTWARE.
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// </copyright>
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using System;
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using IStation.Numerics.LinearAlgebra.Factorization;
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namespace IStation.Numerics.LinearAlgebra.Complex.Factorization
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{
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using Complex = System.Numerics.Complex;
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/// <summary>
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/// <para>A class which encapsulates the functionality of the QR decomposition.</para>
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/// <para>Any real square matrix A (m x n) may be decomposed as A = QR where Q is an orthogonal matrix
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/// (its columns are orthogonal unit vectors meaning QTQ = I) and R is an upper triangular matrix
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/// (also called right triangular matrix).</para>
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/// </summary>
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/// <remarks>
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/// The computation of the QR decomposition is done at construction time by Householder transformation.
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/// If a <seealso cref="QRMethod.Full"/> factorization is performed, the resulting Q matrix is an m x m matrix
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/// and the R matrix is an m x n matrix. If a <seealso cref="QRMethod.Thin"/> factorization is performed, the
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/// resulting Q matrix is an m x n matrix and the R matrix is an n x n matrix.
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/// </remarks>
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internal abstract class QR : QR<Complex>
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{
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protected QR(Matrix<Complex> q, Matrix<Complex> rFull, QRMethod method)
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: base(q, rFull, method)
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{
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}
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/// <summary>
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/// Gets the absolute determinant value of the matrix for which the QR matrix was computed.
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/// </summary>
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public override Complex Determinant
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{
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get
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{
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if (FullR.RowCount != FullR.ColumnCount)
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{
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throw new ArgumentException("Matrix must be square.");
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}
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var det = Complex.One;
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for (var i = 0; i < FullR.ColumnCount; i++)
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{
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det *= FullR.At(i, i);
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if (FullR.At(i, i).Magnitude.AlmostEqual(0.0))
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{
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return 0;
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}
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}
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return det.Magnitude;
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}
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}
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/// <summary>
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/// Gets a value indicating whether the matrix is full rank or not.
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/// </summary>
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/// <value><c>true</c> if the matrix is full rank; otherwise <c>false</c>.</value>
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public override bool IsFullRank
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{
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get
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{
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for (var i = 0; i < FullR.ColumnCount; i++)
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{
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if (FullR.At(i, i).Magnitude.AlmostEqual(0.0))
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{
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return false;
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}
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}
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return true;
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}
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}
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}
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}
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