// <copyright file="UserCholesky.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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// HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY,
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// WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
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// FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
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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.Threading;
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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 a Cholesky factorization for user matrices.</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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internal sealed class UserCholesky : Cholesky
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{
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/// <summary>
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/// Computes the Cholesky factorization in-place.
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/// </summary>
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/// <param name="factor">On entry, the matrix to factor. On exit, the Cholesky factor matrix</param>
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/// <exception cref="ArgumentNullException">If <paramref name="factor"/> is <c>null</c>.</exception>
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/// <exception cref="ArgumentException">If <paramref name="factor"/> is not a square matrix.</exception>
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/// <exception cref="ArgumentException">If <paramref name="factor"/> is not positive definite.</exception>
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static void DoCholesky(Matrix<Complex> factor)
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{
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if (factor.RowCount != factor.ColumnCount)
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{
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throw new ArgumentException("Matrix must be square.");
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}
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// Create a new matrix for the Cholesky factor, then perform factorization (while overwriting).
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var tmpColumn = new Complex[factor.RowCount];
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// Main loop - along the diagonal
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for (var ij = 0; ij < factor.RowCount; ij++)
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{
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// "Pivot" element
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var tmpVal = factor.At(ij, ij);
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if (tmpVal.Real > 0.0)
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{
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tmpVal = tmpVal.SquareRoot();
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factor.At(ij, ij, tmpVal);
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tmpColumn[ij] = tmpVal;
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// Calculate multipliers and copy to local column
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// Current column, below the diagonal
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for (var i = ij + 1; i < factor.RowCount; i++)
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{
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factor.At(i, ij, factor.At(i, ij)/tmpVal);
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tmpColumn[i] = factor.At(i, ij);
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}
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// Remaining columns, below the diagonal
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DoCholeskyStep(factor, factor.RowCount, ij + 1, factor.RowCount, tmpColumn, Control.MaxDegreeOfParallelism);
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}
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else
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{
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throw new ArgumentException("Matrix must be positive definite.");
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}
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for (var i = ij + 1; i < factor.RowCount; i++)
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{
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factor.At(ij, i, Complex.Zero);
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}
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}
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}
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/// <summary>
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/// Initializes a new instance of the <see cref="UserCholesky"/> class. This object will compute the
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/// Cholesky factorization when the constructor is called and cache it's factorization.
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/// </summary>
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/// <param name="matrix">The matrix to factor.</param>
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/// <exception cref="ArgumentNullException">If <paramref name="matrix"/> is <c>null</c>.</exception>
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/// <exception cref="ArgumentException">If <paramref name="matrix"/> is not a square matrix.</exception>
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/// <exception cref="ArgumentException">If <paramref name="matrix"/> is not positive definite.</exception>
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public static UserCholesky Create(Matrix<Complex> matrix)
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{
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// Create a new matrix for the Cholesky factor, then perform factorization (while overwriting).
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var factor = matrix.Clone();
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DoCholesky(factor);
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return new UserCholesky(factor);
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}
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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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/// <exception cref="ArgumentNullException">If <paramref name="matrix"/> is <c>null</c>.</exception>
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/// <exception cref="ArgumentException">If <paramref name="matrix"/> is not a square matrix.</exception>
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/// <exception cref="ArgumentException">If <paramref name="matrix"/> is not positive definite.</exception>
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/// <exception cref="ArgumentOutOfRangeException">If <paramref name="matrix"/> does not have the same dimensions as the existing factor.</exception>
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public override void Factorize(Matrix<Complex> matrix)
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{
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if (matrix.RowCount != Factor.RowCount || matrix.ColumnCount != Factor.ColumnCount)
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{
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throw Matrix.DimensionsDontMatch<ArgumentException>(matrix, Factor);
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}
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matrix.CopyTo(Factor);
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DoCholesky(Factor);
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}
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UserCholesky(Matrix<Complex> factor)
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: base(factor)
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{
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}
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/// <summary>
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/// Calculate Cholesky step
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/// </summary>
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/// <param name="data">Factor matrix</param>
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/// <param name="rowDim">Number of rows</param>
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/// <param name="firstCol">Column start</param>
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/// <param name="colLimit">Total columns</param>
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/// <param name="multipliers">Multipliers calculated previously</param>
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/// <param name="availableCores">Number of available processors</param>
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static void DoCholeskyStep(Matrix<Complex> data, int rowDim, int firstCol, int colLimit, Complex[] multipliers, int availableCores)
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{
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var tmpColCount = colLimit - firstCol;
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if ((availableCores > 1) && (tmpColCount > 200))
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{
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var tmpSplit = firstCol + (tmpColCount/3);
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var tmpCores = availableCores/2;
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CommonParallel.Invoke(
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() => DoCholeskyStep(data, rowDim, firstCol, tmpSplit, multipliers, tmpCores),
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() => DoCholeskyStep(data, rowDim, tmpSplit, colLimit, multipliers, tmpCores));
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}
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else
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{
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for (var j = firstCol; j < colLimit; j++)
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{
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var tmpVal = multipliers[j];
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for (var i = j; i < rowDim; i++)
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{
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data.At(i, j, data.At(i, j) - (multipliers[i]*tmpVal.Conjugate()));
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}
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}
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}
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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 override void Solve(Matrix<Complex> input, Matrix<Complex> result)
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{
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if (result.RowCount != input.RowCount)
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{
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throw new ArgumentException("Matrix row dimensions must agree.");
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}
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if (result.ColumnCount != input.ColumnCount)
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{
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throw new ArgumentException("Matrix column dimensions must agree.");
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}
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if (input.RowCount != Factor.RowCount)
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{
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throw Matrix.DimensionsDontMatch<ArgumentException>(input, Factor);
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}
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input.CopyTo(result);
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var order = Factor.RowCount;
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for (var c = 0; c < result.ColumnCount; c++)
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{
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// Solve L*Y = B;
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Complex sum;
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for (var i = 0; i < order; i++)
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{
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sum = result.At(i, c);
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for (var k = i - 1; k >= 0; k--)
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{
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sum -= Factor.At(i, k)*result.At(k, c);
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}
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result.At(i, c, sum/Factor.At(i, i));
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}
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// Solve L'*X = Y;
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for (var i = order - 1; i >= 0; i--)
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{
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sum = result.At(i, c);
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for (var k = i + 1; k < order; k++)
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{
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sum -= Factor.At(k, i).Conjugate()*result.At(k, c);
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}
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result.At(i, c, sum/Factor.At(i, i));
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}
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}
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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 override void Solve(Vector<Complex> input, Vector<Complex> result)
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{
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if (input.Count != result.Count)
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{
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throw new ArgumentException("All vectors must have the same dimensionality.");
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}
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if (input.Count != Factor.RowCount)
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{
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throw Matrix.DimensionsDontMatch<ArgumentException>(input, Factor);
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}
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input.CopyTo(result);
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var order = Factor.RowCount;
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// Solve L*Y = B;
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Complex sum;
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for (var i = 0; i < order; i++)
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{
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sum = result[i];
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for (var k = i - 1; k >= 0; k--)
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{
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sum -= Factor.At(i, k)*result[k];
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}
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result[i] = sum/Factor.At(i, i);
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}
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// Solve L'*X = Y;
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for (var i = order - 1; i >= 0; i--)
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{
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sum = result[i];
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for (var k = i + 1; k < order; k++)
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{
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sum -= Factor.At(k, i).Conjugate()*result[k];
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}
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result[i] = sum/Factor.At(i, i);
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}
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}
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}
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}
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