// <copyright file="ResidualStopCriterion.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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// 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 System.Diagnostics;
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namespace IStation.Numerics.LinearAlgebra.Solvers
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{
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/// <summary>
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/// Defines an <see cref="IIterationStopCriterion{T}"/> that monitors residuals as stop criterion.
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/// </summary>
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public sealed class ResidualStopCriterion<T> : IIterationStopCriterion<T> where T : struct, IEquatable<T>, IFormattable
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{
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/// <summary>
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/// The maximum value for the residual below which the calculation is considered converged.
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/// </summary>
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double _maximum;
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/// <summary>
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/// The minimum number of iterations for which the residual has to be below the maximum before
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/// the calculation is considered converged.
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/// </summary>
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int _minimumIterationsBelowMaximum;
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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 number of iterations since the residuals got below the maximum.
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/// </summary>
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int _iterationCount;
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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="ResidualStopCriterion{T}"/> class with the specified
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/// maximum residual and minimum number of iterations.
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/// </summary>
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/// <param name="maximum">
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/// The maximum value for the residual below which the calculation is considered converged.
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/// </param>
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/// <param name="minimumIterationsBelowMaximum">
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/// The minimum number of iterations for which the residual has to be below the maximum before
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/// the calculation is considered converged.
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/// </param>
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public ResidualStopCriterion(double maximum, int minimumIterationsBelowMaximum = 0)
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{
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if (maximum < 0)
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{
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throw new ArgumentOutOfRangeException(nameof(maximum));
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}
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if (minimumIterationsBelowMaximum < 0)
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{
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throw new ArgumentOutOfRangeException(nameof(minimumIterationsBelowMaximum));
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}
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_maximum = maximum;
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_minimumIterationsBelowMaximum = minimumIterationsBelowMaximum;
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}
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/// <summary>
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/// Gets or sets the maximum value for the residual below which the calculation is considered
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/// converged.
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/// </summary>
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/// <exception cref="ArgumentOutOfRangeException">Thrown if the <c>Maximum</c> is set to a negative value.</exception>
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public double Maximum
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{
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[DebuggerStepThrough]
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get => _maximum;
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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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_maximum = 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 for which the residual has to be
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/// below the maximum before the calculation is considered converged.
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/// </summary>
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/// <exception cref="ArgumentOutOfRangeException">Thrown if the <c>BelowMaximumFor</c> is set to a value less than 1.</exception>
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public int MinimumIterationsBelowMaximum
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{
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[DebuggerStepThrough]
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get => _minimumIterationsBelowMaximum;
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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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_minimumIterationsBelowMaximum = 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 (solutionVector.Count != sourceVector.Count)
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{
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throw new ArgumentException("All vectors must have the same dimensionality.", nameof(sourceVector));
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}
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if (solutionVector.Count != residualVector.Count)
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{
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throw new ArgumentException("All vectors must have the same dimensionality.", nameof(residualVector));
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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
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// later on.
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var residualNorm = residualVector.InfinityNorm();
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// This is criterion 1 from Templates for the solution of linear systems.
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// The problem with this criterion is that it's not limiting enough. For now
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// we won't use it. Later on we might get back to it.
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// return mMaximumResidual * (System.Math.Abs(mMatrixNorm) * System.Math.Abs(solutionNorm) + System.Math.Abs(mVectorNorm));
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// For now use criterion 2 from Templates for the solution of linear systems. See page 60.
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// Check the residuals by calculating:
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// ||r_i|| <= stop_tol * ||b||
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var stopCriterion = _maximum*sourceVector.InfinityNorm();
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// First check that we have real numbers not NaN's.
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// NaN's can occur when the iterative process diverges so we
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// stop if that is the case.
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if (double.IsNaN(stopCriterion) || double.IsNaN(residualNorm))
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{
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_iterationCount = 0;
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_status = IterationStatus.Diverged;
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return _status;
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}
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// ||r_i|| <= stop_tol * ||b||
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// Stop the calculation if it's clearly smaller than the tolerance
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if (residualNorm < stopCriterion)
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{
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if (_lastIteration <= iterationNumber)
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{
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_iterationCount = iterationNumber - _lastIteration;
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_status = _iterationCount >= _minimumIterationsBelowMaximum ? IterationStatus.Converged : IterationStatus.Continue;
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}
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}
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else
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{
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_iterationCount = 0;
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_status = IterationStatus.Continue;
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}
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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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/// 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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_iterationCount = 0;
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_lastIteration = -1;
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}
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/// <summary>
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/// Clones the current <see cref="ResidualStopCriterion{T}"/> and its settings.
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/// </summary>
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/// <returns>A new instance of the <see cref="ResidualStopCriterion{T}"/> class.</returns>
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public IIterationStopCriterion<T> Clone()
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{
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return new ResidualStopCriterion<T>(_maximum, _minimumIterationsBelowMaximum);
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}
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}
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}
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