// <copyright file="DenseLU.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) 2009-2015 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.Providers.LinearAlgebra;
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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 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 DenseLU : LU
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{
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/// <summary>
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/// Initializes a new instance of the <see cref="DenseLU"/> 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 DenseLU Create(DenseMatrix 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 pivots = new int[matrix.RowCount];
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// Create a new matrix for the LU factors, then perform factorization (while overwriting).
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var factors = (DenseMatrix) matrix.Clone();
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LinearAlgebraControl.Provider.LUFactor(factors.Values, factors.RowCount, pivots);
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return new DenseLU(factors, pivots);
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}
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DenseLU(Matrix<Complex> 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<Complex> input, Matrix<Complex> 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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if (input is DenseMatrix dinput && result is DenseMatrix dresult)
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{
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// Copy the contents of input to result.
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Array.Copy(dinput.Values, 0, dresult.Values, 0, dinput.Values.Length);
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// LU solve by overwriting result.
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var dfactors = (DenseMatrix) Factors;
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LinearAlgebraControl.Provider.LUSolveFactored(input.ColumnCount, dfactors.Values, dfactors.RowCount, Pivots, dresult.Values);
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}
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else
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{
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throw new NotSupportedException("Can only do LU factorization for dense matrices at the moment.");
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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<Complex> input, Vector<Complex> 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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if (input is DenseVector dinput && result is DenseVector dresult)
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{
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// Copy the contents of input to result.
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Array.Copy(dinput.Values, 0, dresult.Values, 0, dinput.Values.Length);
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// LU solve by overwriting result.
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var dfactors = (DenseMatrix) Factors;
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LinearAlgebraControl.Provider.LUSolveFactored(1, dfactors.Values, dfactors.RowCount, Pivots, dresult.Values);
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}
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else
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{
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throw new NotSupportedException("Can only do LU factorization for dense vectors at the moment.");
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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<Complex> Inverse()
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{
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var result = (DenseMatrix) Factors.Clone();
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LinearAlgebraControl.Provider.LUInverseFactored(result.Values, result.RowCount, Pivots);
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return result;
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}
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}
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}
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