// <copyright file="UserLU.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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namespace IStation.Numerics.LinearAlgebra.Double.Factorization
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{
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/// <summary>
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/// <para>A class which encapsulates the functionality of an LU factorization.</para>
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/// <para>For a matrix A, the LU factorization is a pair of lower triangular matrix L and
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/// upper triangular matrix U so that A = L*U.</para>
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/// </summary>
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/// <remarks>
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/// The computation of the LU factorization is done at construction time.
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/// </remarks>
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internal sealed class UserLU : LU
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{
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/// <summary>
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/// Initializes a new instance of the <see cref="UserLU"/> class. This object will compute the
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/// LU 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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public static UserLU Create(Matrix<double> matrix)
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{
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if (matrix == null)
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{
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throw new ArgumentNullException(nameof(matrix));
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}
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if (matrix.RowCount != matrix.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 an array for the pivot indices.
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var order = matrix.RowCount;
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var factors = matrix.Clone();
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var pivots = new int[order];
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// Initialize the pivot matrix to the identity permutation.
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for (var i = 0; i < order; i++)
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{
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pivots[i] = i;
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}
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var vectorLUcolj = new double[order];
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for (var j = 0; j < order; j++)
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{
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// Make a copy of the j-th column to localize references.
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for (var i = 0; i < order; i++)
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{
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vectorLUcolj[i] = factors.At(i, j);
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}
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// Apply previous transformations.
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for (var i = 0; i < order; i++)
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{
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var kmax = Math.Min(i, j);
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var s = 0.0;
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for (var k = 0; k < kmax; k++)
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{
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s += factors.At(i, k)*vectorLUcolj[k];
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}
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vectorLUcolj[i] -= s;
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factors.At(i, j, vectorLUcolj[i]);
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}
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// Find pivot and exchange if necessary.
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var p = j;
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for (var i = j + 1; i < order; i++)
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{
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if (Math.Abs(vectorLUcolj[i]) > Math.Abs(vectorLUcolj[p]))
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{
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p = i;
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}
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}
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if (p != j)
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{
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for (var k = 0; k < order; k++)
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{
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var temp = factors.At(p, k);
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factors.At(p, k, factors.At(j, k));
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factors.At(j, k, temp);
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}
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pivots[j] = p;
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}
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// Compute multipliers.
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if (j < order & factors.At(j, j) != 0.0)
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{
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for (var i = j + 1; i < order; i++)
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{
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factors.At(i, j, (factors.At(i, j)/factors.At(j, j)));
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}
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}
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}
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return new UserLU(factors, pivots);
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}
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UserLU(Matrix<double> factors, int[] pivots)
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: base(factors, pivots)
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{
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}
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/// <summary>
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/// Solves a system of linear equations, <c>AX = B</c>, with A LU factorized.
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/// </summary>
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/// <param name="input">The right hand side <see cref="Matrix{T}"/>, <c>B</c>.</param>
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/// <param name="result">The left hand side <see cref="Matrix{T}"/>, <c>X</c>.</param>
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public override void Solve(Matrix<double> input, Matrix<double> result)
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{
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// Check for proper arguments.
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if (input == null)
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{
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throw new ArgumentNullException(nameof(input));
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}
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if (result == null)
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{
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throw new ArgumentNullException(nameof(result));
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}
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// Check for proper dimensions.
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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 != Factors.RowCount)
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{
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throw Matrix.DimensionsDontMatch<ArgumentException>(input, Factors);
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}
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// Copy the contents of input to result.
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input.CopyTo(result);
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for (var i = 0; i < Pivots.Length; i++)
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{
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if (Pivots[i] == i)
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{
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continue;
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}
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var p = Pivots[i];
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for (var j = 0; j < result.ColumnCount; j++)
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{
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var temp = result.At(p, j);
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result.At(p, j, result.At(i, j));
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result.At(i, j, temp);
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}
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}
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var order = Factors.RowCount;
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// Solve L*Y = P*B
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for (var k = 0; k < order; k++)
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{
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for (var i = k + 1; i < order; i++)
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{
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for (var j = 0; j < result.ColumnCount; j++)
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{
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var temp = result.At(k, j)*Factors.At(i, k);
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result.At(i, j, result.At(i, j) - temp);
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}
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}
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}
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// Solve U*X = Y;
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for (var k = order - 1; k >= 0; k--)
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{
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for (var j = 0; j < result.ColumnCount; j++)
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{
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result.At(k, j, (result.At(k, j)/Factors.At(k, k)));
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}
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for (var i = 0; i < k; i++)
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{
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for (var j = 0; j < result.ColumnCount; j++)
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{
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var temp = result.At(k, j)*Factors.At(i, k);
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result.At(i, j, result.At(i, j) - temp);
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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, <c>Ax = b</c>, with A LU factorized.
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/// </summary>
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/// <param name="input">The right hand side vector, <c>b</c>.</param>
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/// <param name="result">The left hand side <see cref="Matrix{T}"/>, <c>x</c>.</param>
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public override void Solve(Vector<double> input, Vector<double> result)
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{
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// Check for proper arguments.
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if (input == null)
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{
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throw new ArgumentNullException(nameof(input));
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}
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if (result == null)
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{
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throw new ArgumentNullException(nameof(result));
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}
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// Check for proper dimensions.
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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 != Factors.RowCount)
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{
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throw Matrix.DimensionsDontMatch<ArgumentException>(input, Factors);
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}
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// Copy the contents of input to result.
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input.CopyTo(result);
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for (var i = 0; i < Pivots.Length; i++)
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{
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if (Pivots[i] == i)
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{
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continue;
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}
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var p = Pivots[i];
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var temp = result[p];
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result[p] = result[i];
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result[i] = temp;
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}
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var order = Factors.RowCount;
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// Solve L*Y = P*B
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for (var k = 0; k < order; k++)
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{
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for (var i = k + 1; i < order; i++)
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{
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result[i] -= result[k]*Factors.At(i, k);
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}
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}
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// Solve U*X = Y;
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for (var k = order - 1; k >= 0; k--)
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{
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result[k] /= Factors.At(k, k);
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for (var i = 0; i < k; i++)
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{
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result[i] -= result[k]*Factors.At(i, k);
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}
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}
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}
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/// <summary>
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/// Returns the inverse of this matrix. The inverse is calculated using LU decomposition.
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/// </summary>
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/// <returns>The inverse of this matrix.</returns>
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public override Matrix<double> Inverse()
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{
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var order = Factors.RowCount;
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var inverse = Matrix<double>.Build.SameAs(Factors, order, order);
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for (var i = 0; i < order; i++)
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{
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inverse.At(i, i, 1.0);
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}
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return Solve(inverse);
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}
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}
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}
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