// <copyright file="DivergenceStopCriterion.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) 2009-2014 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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// 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 System.Diagnostics;
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namespace IStation.Numerics.LinearAlgebra.Solvers
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{
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/// <summary>
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/// Monitors an iterative calculation for signs of divergence.
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/// </summary>
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public sealed class DivergenceStopCriterion<T> : IIterationStopCriterion<T> where T : struct, IEquatable<T>, IFormattable
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{
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/// <summary>
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/// The maximum relative increase the residual may experience without triggering a divergence warning.
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/// </summary>
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double _maximumRelativeIncrease;
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/// <summary>
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/// The number of iterations over which a residual increase should be tracked before issuing a divergence warning.
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/// </summary>
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int _minimumNumberOfIterations;
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/// <summary>
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/// The status of the calculation
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/// </summary>
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IterationStatus _status = IterationStatus.Continue;
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/// <summary>
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/// The array that holds the tracking information.
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/// </summary>
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double[] _residualHistory;
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/// <summary>
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/// The iteration number of the last iteration.
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/// </summary>
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int _lastIteration = -1;
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/// <summary>
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/// Initializes a new instance of the <see cref="DivergenceStopCriterion{T}"/> class with the specified maximum
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/// relative increase and the specified minimum number of tracking iterations.
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/// </summary>
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/// <param name="maximumRelativeIncrease">The maximum relative increase that the residual may experience before a divergence warning is issued. </param>
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/// <param name="minimumIterations">The minimum number of iterations over which the residual must grow before a divergence warning is issued.</param>
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public DivergenceStopCriterion(double maximumRelativeIncrease = 0.08, int minimumIterations = 10)
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{
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if (maximumRelativeIncrease <= 0)
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{
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throw new ArgumentOutOfRangeException(nameof(maximumRelativeIncrease));
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}
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// There must be at least three iterations otherwise we can't calculate the relative increase
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if (minimumIterations < 3)
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{
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throw new ArgumentOutOfRangeException(nameof(minimumIterations));
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}
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_maximumRelativeIncrease = maximumRelativeIncrease;
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_minimumNumberOfIterations = minimumIterations;
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}
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/// <summary>
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/// Gets or sets the maximum relative increase that the residual may experience before a divergence warning is issued.
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/// </summary>
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/// <exception cref="ArgumentOutOfRangeException">Thrown if the <c>Maximum</c> is set to zero or below.</exception>
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public double MaximumRelativeIncrease
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{
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[DebuggerStepThrough]
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get => _maximumRelativeIncrease;
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[DebuggerStepThrough]
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set
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{
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if (value <= 0)
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{
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throw new ArgumentOutOfRangeException(nameof(value));
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}
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_maximumRelativeIncrease = value;
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}
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}
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/// <summary>
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/// Gets or sets the minimum number of iterations over which the residual must grow before
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/// issuing a divergence warning.
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/// </summary>
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/// <exception cref="ArgumentOutOfRangeException">Thrown if the <c>value</c> is set to less than one.</exception>
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public int MinimumNumberOfIterations
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{
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[DebuggerStepThrough]
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get => _minimumNumberOfIterations;
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[DebuggerStepThrough]
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set
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{
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// There must be at least three iterations otherwise we can't calculate
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// the relative increase
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if (value < 3)
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{
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throw new ArgumentOutOfRangeException(nameof(value));
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}
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_minimumNumberOfIterations = value;
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}
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}
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/// <summary>
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/// Determines the status of the iterative calculation based on the stop criteria stored
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/// by the current <see cref="IIterationStopCriterion{T}"/>. Result is set into <c>Status</c> field.
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/// </summary>
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/// <param name="iterationNumber">The number of iterations that have passed so far.</param>
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/// <param name="solutionVector">The vector containing the current solution values.</param>
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/// <param name="sourceVector">The right hand side vector.</param>
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/// <param name="residualVector">The vector containing the current residual vectors.</param>
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/// <remarks>
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/// The individual stop criteria may internally track the progress of the calculation based
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/// on the invocation of this method. Therefore this method should only be called if the
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/// calculation has moved forwards at least one step.
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/// </remarks>
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public IterationStatus DetermineStatus(int iterationNumber, Vector<T> solutionVector, Vector<T> sourceVector, Vector<T> residualVector)
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{
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if (iterationNumber < 0)
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{
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throw new ArgumentOutOfRangeException(nameof(iterationNumber));
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}
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if (_lastIteration >= iterationNumber)
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{
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// We have already stored the actual last iteration number
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// For now do nothing. We only care about the next step.
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return _status;
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}
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if ((_residualHistory == null) || (_residualHistory.Length != RequiredHistoryLength))
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{
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_residualHistory = new double[RequiredHistoryLength];
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}
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// We always track the residual.
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// Move the old versions one element up in the array.
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for (var i = 1; i < _residualHistory.Length; i++)
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{
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_residualHistory[i - 1] = _residualHistory[i];
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}
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// Store the infinity norms of both the solution and residual vectors
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// These values will be used to calculate the relative drop in residuals later on.
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_residualHistory[_residualHistory.Length - 1] = residualVector.InfinityNorm();
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// Check if we have NaN's. If so we've gone way beyond normal divergence.
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// Stop the iteration.
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if (double.IsNaN(_residualHistory[_residualHistory.Length - 1]))
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{
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_status = IterationStatus.Diverged;
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return _status;
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}
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// Check if we are diverging and if so set the status
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_status = IsDiverging() ? IterationStatus.Diverged : IterationStatus.Continue;
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_lastIteration = iterationNumber;
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return _status;
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}
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/// <summary>
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/// Detect if solution is diverging
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/// </summary>
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/// <returns><c>true</c> if diverging, otherwise <c>false</c></returns>
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bool IsDiverging()
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{
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// Run for each variable
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for (var i = 1; i < _residualHistory.Length; i++)
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{
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var difference = _residualHistory[i] - _residualHistory[i - 1];
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// Divergence is occurring if:
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// - the last residual is larger than the previous one
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// - the relative increase of the residual is larger than the setting allows
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if ((difference < 0) || (_residualHistory[i - 1]*(1 + _maximumRelativeIncrease) >= _residualHistory[i]))
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{
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// No divergence taking place within the required number of iterations
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// So reset and stop the iteration. There is no way we can get to the
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// required number of iterations anymore.
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return false;
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}
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}
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return true;
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}
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/// <summary>
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/// Gets required history Length
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/// </summary>
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int RequiredHistoryLength
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{
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[DebuggerStepThrough]
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get => _minimumNumberOfIterations + 1;
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}
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/// <summary>
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/// Gets the current calculation status.
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/// </summary>
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public IterationStatus Status
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{
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[DebuggerStepThrough]
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get => _status;
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}
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/// <summary>
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/// Resets the <see cref="IIterationStopCriterion{T}"/> to the pre-calculation state.
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/// </summary>
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public void Reset()
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{
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_status = IterationStatus.Continue;
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_lastIteration = -1;
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_residualHistory = null;
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}
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/// <summary>
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/// Clones the current <see cref="DivergenceStopCriterion{T}"/> and its settings.
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/// </summary>
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/// <returns>A new instance of the <see cref="DivergenceStopCriterion{T}"/> class.</returns>
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public IIterationStopCriterion<T> Clone()
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{
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return new DivergenceStopCriterion<T>(_maximumRelativeIncrease, _minimumNumberOfIterations);
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}
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}
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}
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