// <copyright file="Cholesky.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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// obtaining a copy of this software and associated documentation
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// Software is furnished to do so, subject to the following
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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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/// <para>A class which encapsulates the functionality of a Cholesky factorization.</para>
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/// <para>For a symmetric, positive definite matrix A, the Cholesky factorization
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/// is an lower triangular matrix L so that A = L*L'.</para>
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/// </summary>
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/// <remarks>
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/// The computation of the Cholesky factorization is done at construction time. If the matrix is not symmetric
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/// or positive definite, the constructor will throw an exception.
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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 Cholesky<T> : ISolver<T>
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where T : struct, IEquatable<T>, IFormattable
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{
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protected Cholesky(Matrix<T> factor)
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{
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Factor = factor;
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}
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/// <summary>
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/// Gets the lower triangular form of the Cholesky matrix.
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/// </summary>
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public Matrix<T> Factor { get; private set; }
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/// <summary>
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/// Gets the determinant of the matrix for which the Cholesky 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 the log determinant of the matrix for which the Cholesky matrix was computed.
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/// </summary>
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public abstract T DeterminantLn { get; }
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/// <summary>
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/// Calculates the Cholesky factorization of the input matrix.
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/// </summary>
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/// <param name="matrix">The matrix to be factorized<see cref="Matrix{T}"/>.</param>
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public abstract void Factorize(Matrix<T> matrix);
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/// <summary>
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/// Solves a system of linear equations, <b>AX = B</b>, with A Cholesky 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, input.RowCount, 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 Cholesky 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 Cholesky 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, input.Count);
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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 Cholesky 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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