context: // <copyright file="ResidualStopCriterium.cs" company="Math.NET">
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  namespace MathNet.Numerics.LinearAlgebra.Complex.Solvers.StopCriterium
  {
      using System;
      using System.Diagnostics;
      using Generic.Solvers.Status;
      using Generic.Solvers.StopCriterium;
      using Properties;
  
      /// <summary>
      /// Defines an <see cref="IIterationStopCriterium"/> that monitors residuals as stop criterium.
      /// </summary>
      public sealed class ResidualStopCriterium : IIterationStopCriterium
      {
          /// <summary>
          /// The default value for the maximum value of the residual.
          /// </summary>
          public const double DefaultMaximumResidual = 1e-12;
  
          /// <summary>
          /// The default value for the minimum number of iterations.
          /// </summary>
          public const int DefaultMinimumIterationsBelowMaximum = 0;
  
          /// <summary>
          /// Defines the default last iteration number. Set to -1 because iterations normally start at 0.
          /// </summary>
          private const int DefaultLastIterationNumber = -1;
  
          /// <summary>
          /// The default status.
          /// </summary>
          private static readonly ICalculationStatus DefaultStatus = new CalculationIndetermined();
  
          /// <summary>
          /// The maximum value for the residual below which the calculation is considered converged.
          /// </summary>
          private double _maximum;
  
          /// <summary>
          /// The minimum number of iterations for which the residual has to be below the maximum before
          /// the calculation is considered converged.
          /// </summary>
          private int _minimumIterationsBelowMaximum;
  
          /// <summary>
          /// The status of the calculation
          /// </summary>
          private ICalculationStatus _status = DefaultStatus;
  
          /// <summary>
          /// The number of iterations since the residuals got below the maximum.
          /// </summary>
          private int _iterationCount;
  
          /// <summary>
          /// The iteration number of the last iteration.
          /// </summary>
          private int _lastIteration = DefaultLastIterationNumber;
  
          /// <summary>
          /// Initializes a new instance of the <see cref="ResidualStopCriterium"/> class with the default maximum 
          /// residual and the default minimum number of iterations.
          /// </summary>
          public ResidualStopCriterium() : this(DefaultMaximumResidual, DefaultMinimumIterationsBelowMaximum)
          {
          }
  
          /// <summary>
          /// Initializes a new instance of the <see cref="ResidualStopCriterium"/> class with the specified 
          /// maximum residual and the default minimum number of iterations.
          /// </summary>
          /// <param name="maximum">The maximum value for the residual below which the calculation is considered converged.</param>
          public ResidualStopCriterium(double maximum) : this(maximum, DefaultMinimumIterationsBelowMaximum)
          {
          }
  
          /// <summary>
          /// Initializes a new instance of the <see cref="ResidualStopCriterium"/> class with the default maximum residual
          /// and specified minimum number of iterations.
          /// </summary>
          /// <param name="minimumIterationsBelowMaximum">
          /// The minimum number of iterations for which the residual has to be below the maximum before
          /// the calculation is considered converged.
          /// </param>
          public ResidualStopCriterium(int minimumIterationsBelowMaximum) : this(DefaultMaximumResidual, minimumIterationsBelowMaximum)
          {
          }
  
          /// <summary>
          /// Initializes a new instance of the <see cref="ResidualStopCriterium"/> class with the specified 
          /// maximum residual and minimum number of iterations.
          /// </summary>
          /// <param name="maximum">
          /// The maximum value for the residual below which the calculation is considered converged.
          /// </param>
          /// <param name="minimumIterationsBelowMaximum">
          /// The minimum number of iterations for which the residual has to be below the maximum before
          /// the calculation is considered converged.
          /// </param>
          public ResidualStopCriterium(double maximum, int minimumIterationsBelowMaximum)
          {
              if (maximum < 0)
              {
                  throw new ArgumentOutOfRangeException("maximum");
              }
  
              if (minimumIterationsBelowMaximum < 0)
              {
                  throw new ArgumentOutOfRangeException("minimumIterationsBelowMaximum");
              }
  
              _maximum = maximum;
              _minimumIterationsBelowMaximum = minimumIterationsBelowMaximum;
          }
  
          /// <summary>
          /// Gets or sets the maximum value for the residual below which the calculation is considered 
          /// converged.
          /// </summary>
          /// <exception cref="ArgumentOutOfRangeException">Thrown if the <c>Maximum</c> is set to a negative value.</exception>
          public double Maximum
          {
              [DebuggerStepThrough]
              get
              {
                  return _maximum;
              }
  
              [DebuggerStepThrough]
              set
              {
                  if (value < 0)
                  {
                      throw new ArgumentOutOfRangeException("value");
                  }
  
                  _maximum = value;
              }
          }
  
          /// <summary>
          /// Returns the maximum residual to the default.
          /// </summary>
          public void ResetMaximumResidualToDefault()
          {
              _maximum = DefaultMaximumResidual;
          }
  
          /// <summary>
          /// Gets or sets the minimum number of iterations for which the residual has to be
          /// below the maximum before the calculation is considered converged.
          /// </summary>
          /// <exception cref="ArgumentOutOfRangeException">Thrown if the <c>BelowMaximumFor</c> is set to a value less than 1.</exception>
          public int MinimumIterationsBelowMaximum
          {
              [DebuggerStepThrough]
              get
              {
                  return _minimumIterationsBelowMaximum;
              }
  
              [DebuggerStepThrough]
              set
              {
                  if (value < 0)
                  {
                      throw new ArgumentOutOfRangeException("value");
                  }
  
                  _minimumIterationsBelowMaximum = value;
              }
          }
  
          /// <summary>
          /// Returns the minimum number of iterations to the default.
          /// </summary>
          public void ResetMinimumIterationsBelowMaximumToDefault()
          {
              _minimumIterationsBelowMaximum = DefaultMinimumIterationsBelowMaximum;
          }
  
          /// <summary>
          /// Determines the status of the iterative calculation based on the stop criteria stored
          /// by the current <see cref="IIterationStopCriterium"/>. Result is set into <c>Status</c> field.
          /// </summary>
          /// <param name="iterationNumber">The number of iterations that have passed so far.</param>
          /// <param name="solutionVector">The vector containing the current solution values.</param>
          /// <param name="sourceVector">The right hand side vector.</param>
          /// <param name="residualVector">The vector containing the current residual vectors.</param>
          /// <remarks>
          /// The individual stop criteria may internally track the progress of the calculation based
          /// on the invocation of this method. Therefore this method should only be called if the 
          /// calculation has moved forwards at least one step.
          /// </remarks>
          public void DetermineStatus(int iterationNumber, Vector solutionVector, Vector sourceVector, Vector residualVector)
          {
              if (iterationNumber < 0)
              {
                  throw new ArgumentOutOfRangeException("iterationNumber");
              }
  
              if (solutionVector == null)
              {
                  throw new ArgumentNullException("solutionVector");
              }
  
              if (sourceVector == null)
              {
                  throw new ArgumentNullException("sourceVector");
              }
              
              if (residualVector == null)
              {
                  throw new ArgumentNullException("residualVector");
              }
  
              if (solutionVector.Count != sourceVector.Count)
              {
                  throw new ArgumentException(Resources.ArgumentVectorsSameLength, "sourceVector");
              }
  
              if (solutionVector.Count != residualVector.Count)
              {
                  throw new ArgumentException(Resources.ArgumentVectorsSameLength, "residualVector");
              }
  
              // Store the infinity norms of both the solution and residual vectors
              // These values will be used to calculate the relative drop in residuals
              // later on.
              var residualNorm = residualVector.Norm(Double.PositiveInfinity);
              
              // Check the residuals by calculating:
              // ||r_i|| <= stop_tol * ||b||
              var stopCriterium = ComputeStopCriterium(sourceVector.Norm(Double.PositiveInfinity).Real);
  
              // First check that we have real numbers not NaN's.
              // NaN's can occur when the iterative process diverges so we
              // stop if that is the case.
              if (double.IsNaN(stopCriterium) || double.IsNaN(residualNorm.Real))
              {
                  _iterationCount = 0;
                  SetStatusToDiverged();
                  return;
              }
  
              // ||r_i|| <= stop_tol * ||b||
              // Stop the calculation if it's clearly smaller than the tolerance
  
gt:             var decimalMagnitude = Math.Abs(stopCriterium.Magnitude()) + 1;