// <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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// 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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// </copyright>
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using System;
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namespace IStation.Numerics.LinearAlgebra.Factorization
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{
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/// <summary>
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/// The type of QR factorization go perform.
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/// </summary>
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public enum QRMethod
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{
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/// <summary>
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/// Compute the full QR factorization of a matrix.
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/// </summary>
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Full = 0,
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/// <summary>
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/// Compute the thin QR factorization of a matrix.
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/// </summary>
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Thin = 1
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}
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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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/// <typeparam name="T">Supported data types are double, single, <see cref="Complex"/>, and <see cref="Complex32"/>.</typeparam>
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public abstract class QR<T> : ISolver<T>
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where T : struct, IEquatable<T>, IFormattable
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{
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readonly Lazy<Matrix<T>> _lazyR;
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protected readonly Matrix<T> FullR;
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protected readonly QRMethod Method;
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protected QR(Matrix<T> q, Matrix<T> rFull, QRMethod method)
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{
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Q = q;
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FullR = rFull;
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Method = method;
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_lazyR = new Lazy<Matrix<T>>(FullR.UpperTriangle);
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}
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/// <summary>
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/// Gets or sets orthogonal Q matrix
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/// </summary>
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public Matrix<T> Q { get; }
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/// <summary>
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/// Gets the upper triangular factor R.
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/// </summary>
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public Matrix<T> R => _lazyR.Value;
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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 abstract T Determinant { get; }
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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 abstract bool IsFullRank { get; }
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/// <summary>
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/// Solves a system of linear equations, <b>AX = B</b>, with A QR factorized.
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/// </summary>
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/// <param name="input">The right hand side <see cref="Matrix{T}"/>, <b>B</b>.</param>
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/// <returns>The left hand side <see cref="Matrix{T}"/>, <b>X</b>.</returns>
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public virtual Matrix<T> Solve(Matrix<T> input)
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{
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var x = Matrix<T>.Build.SameAs(input, FullR.ColumnCount, input.ColumnCount, fullyMutable: true);
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Solve(input, x);
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return x;
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}
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/// <summary>
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/// Solves a system of linear equations, <b>AX = B</b>, with A QR factorized.
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/// </summary>
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/// <param name="input">The right hand side <see cref="Matrix{T}"/>, <b>B</b>.</param>
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/// <param name="result">The left hand side <see cref="Matrix{T}"/>, <b>X</b>.</param>
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public abstract void Solve(Matrix<T> input, Matrix<T> result);
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/// <summary>
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/// Solves a system of linear equations, <b>Ax = b</b>, with A QR factorized.
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/// </summary>
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/// <param name="input">The right hand side vector, <b>b</b>.</param>
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/// <returns>The left hand side <see cref="Vector{T}"/>, <b>x</b>.</returns>
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public virtual Vector<T> Solve(Vector<T> input)
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{
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var x = Vector<T>.Build.SameAs(input, FullR.ColumnCount);
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Solve(input, x);
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return x;
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}
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/// <summary>
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/// Solves a system of linear equations, <b>Ax = b</b>, with A QR factorized.
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/// </summary>
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/// <param name="input">The right hand side vector, <b>b</b>.</param>
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/// <param name="result">The left hand side <see cref="Matrix{T}"/>, <b>x</b>.</param>
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public abstract void Solve(Vector<T> input, Vector<T> result);
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}
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}
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