// <copyright file="LU.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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// </copyright>
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using IStation.Numerics.LinearAlgebra.Factorization;
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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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/// <para>In the Math.Net implementation we also store a set of pivot elements for increased
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/// numerical stability. The pivot elements encode a permutation matrix P such that P*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 abstract class LU : LU<double>
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{
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protected LU(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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/// Gets the determinant of the matrix for which the LU factorization was computed.
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/// </summary>
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public override double Determinant
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{
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get
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{
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var det = 1.0;
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for (var j = 0; j < Factors.RowCount; j++)
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{
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if (Pivots[j] != j)
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{
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det *= -Factors.At(j, j);
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}
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else
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{
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det *= Factors.At(j, j);
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}
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}
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return det;
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}
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}
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}
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}
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