public static NewtonResult[][] ExecuteChunk([ActivityTrigger] ChunkOptions options, ILogger log)
{
var fractalOptions = options.FractalOptions;
var element = MathElement.Parse(fractalOptions.Expression, fractalOptions.VariableName);
var func = element.ToNewtonFunction(fractalOptions.Multiplicity).ToFunc();
var result = new NewtonResult[options.MaxWidth - options.MinWidth][];
for (var px = options.MinWidth; px < options.MaxWidth; ++px)
{
var x = fractalOptions.DomainSize.MinX + (fractalOptions.DomainSize.MaxX - fractalOptions.DomainSize.MinX) * px / (fractalOptions.PixelSize.Width - 1);
result[px - options.MinWidth] = new NewtonResult[fractalOptions.PixelSize.Height];
for (var py = 0; py < fractalOptions.PixelSize.Height; ++py)
{
var y = fractalOptions.DomainSize.MaxY - (fractalOptions.DomainSize.MaxY - fractalOptions.DomainSize.MinY) * py / (fractalOptions.PixelSize.Height - 1);
var newtonOptions = new NewtonOptions
{
Precision = fractalOptions.Precision,
StartingPoint = new Complex(x, y),
MaxIterations = fractalOptions.MaxIterations,
};
result[px - options.MinWidth][py] = MathUtils.NewtonMethod(func, newtonOptions);
}
}
return(result);
}
private static List <ISolver> DeafaultSolvers()
{
var opts = new NewtonOptions()
{
MaxIterations = 20, DerivativeStep = new double[] { 0.01 }
};
var solver = new NewtonSolver(opts);
return(new List <ISolver>()
{
solver
});
}
/// <summary>
/// Provides the revesed model, according to the specified variables
/// </summary>
public WorkflowReversedModel Reverse(List <Data> inputs, List <Data> outputs)
{
var opts = new NewtonOptions()
{
MaxIterations = 20, DerivativeStep = new double[] { 0.01 }
};
var solver = new NewtonSolver(opts);
string reversedName = GetReversedName(inputs, outputs);
var reversedModel = new WorkflowReversedModel(reversedName, Description, inputs, outputs, this, new List <ISolver>()
{
solver
});
reversedModel.Rename(FullName + new string(reversedName.SkipWhile(c => c != ':').ToArray()));
return(reversedModel);
}
private static List <ISolver> DeafaultSolversSCC()
{
var solver = new FixedPointSolver()
{
MaxEvals = 20
};
var opts = new NewtonOptions()
{
MaxIterations = 20, DerivativeStep = new double[] { 0.01 }
};
var solver2 = new NewtonSolver(opts);
return(new List <ISolver>()
{
solver, solver2
});
}
private NewtonResult[] NewtonBandInternal(int px)
{
var x = Options.DomainSize.MinX + (Options.DomainSize.MaxX - Options.DomainSize.MinX) * px / (Options.PixelSize.Width - 1);
var result = new NewtonResult[Options.PixelSize.Height];
for (var py = 0; py < Options.PixelSize.Height; ++py)
{
var y = Options.DomainSize.MaxY - (Options.DomainSize.MaxY - Options.DomainSize.MinY) * py / (Options.PixelSize.Height - 1);
var newtonOptions = new NewtonOptions
{
Precision = Options.Precision,
StartingPoint = new Complex(x, y),
MaxIterations = Options.MaxIterations,
};
result[py] = MathUtils.NewtonMethod(Function, newtonOptions);
}
return(result);
}
public void NewtonMethodTests(string expression, double multiplicity, double startingPoint, double expected)
{
// Only testing the real part, as it makes it simpler to pass compile-time
// inputs. The outcome should be the same for complex numbers, especially
// given that the Complex library already existed
var element = MathElement.Parse(expression);
var newton = element.ToNewtonFunction(new Complex(multiplicity, 0));
var func = newton.ToFunc();
var options = new NewtonOptions
{
MaxIterations = 50,
Precision = 1e-3,
StartingPoint = new Complex(startingPoint, 0),
};
var result = MathUtils.NewtonMethod(func, options);
Assert.AreEqual(expected, result.Solution.Real, 1e-2);
}
/// <summary>
/// This function identifies the Modified models (from imMatrixi and imMatrif) in the modelObjects, then creates a 'modified model subprocess' for each modified model,
/// and therafter combines it with other models in the modelObjects and return it in a object array
/// </summary>
/// <param name="IMi"></param>
/// <param name="IMf"></param>
/// <param name="components"></param>
/// <param name="data"></param>
/// <param name="clusters"></param>
/// <param name="name"></param>
/// <returns></returns>
private static WorkflowComponent[] CreateReversedModels(IncidenceMatrix IMi, IncidenceMatrix IMf, List <WorkflowComponent> components, List <Data> data, List <Cluster> clusters, string name)
{
var processedComponents = new WorkflowComponent[IMf.RowCount];
for (int r = 0; r < IMi.RowCount; r++)
{
WorkflowComponent component = components[r];
Vector <double> row = IMi.Row(r);
if (!IMf.Row(r).CompareAssigned(row))
{
List <int> inputIndices = row.FindLocations(IN);
List <int> outputIndices = row.FindLocations(OUT);
var inputs = inputIndices.Select(i => data[i]).ToList();
var outputs = outputIndices.Select(i => data[i]).ToList();
if (component is Model model)
{
processedComponents[r] = model.Reverse(inputs, outputs);
}
else if (component is Workflow workflow)
{
var opts = new NewtonOptions()
{
MaxIterations = 20, DerivativeStep = new double[] { 0.01 }
};
var solver = new NewtonSolver(opts);
processedComponents[r] = new WorkflowGlobal($"{name}#GlobalWorkflow#{workflow.Name}", "", inputs, outputs, workflow.Components, workflow.Components, new List <ISolver>()
{
solver
});
}
}
else
{
processedComponents[r] = components[r];
}
}
return(processedComponents);
}
protected virtual Task <NewtonResult[][]> GenerateNewtonArrayAsync()
{
var result = new NewtonResult[Options.PixelSize.Width][];
for (var px = 0; px < Options.PixelSize.Width; ++px)
{
var x = Options.DomainSize.MinX + (Options.DomainSize.MaxX - Options.DomainSize.MinX) * px / (Options.PixelSize.Width - 1);
result[px] = new NewtonResult[Options.PixelSize.Height];
for (var py = 0; py < Options.PixelSize.Height; ++py)
{
var y = Options.DomainSize.MaxY - (Options.DomainSize.MaxY - Options.DomainSize.MinY) * py / (Options.PixelSize.Height - 1);
var newtonOptions = new NewtonOptions
{
Precision = Options.Precision,
StartingPoint = new Complex(x, y),
MaxIterations = Options.MaxIterations,
};
result[px][py] = MathUtils.NewtonMethod(Function, newtonOptions);
}
}
return(Task.FromResult(result));
}