/// <summary>
/// Sets the initial parameters of the DifferentialEquationSystem class.
/// </summary>
/// <param name="expressions">List of expressions</param>
/// <param name="leftVariables">List of left variables</param>
/// <param name="constants">List of constants</param>
/// <param name="timeVariable">Start time (presents in the expressions)</param>
/// <param name="tEnd">End time</param>
/// <param name="tau">Calculation step</param>
public DifferentialEquationSystem(List <string> expressions, List <DEVariable> leftVariables,
List <DEVariable> constants, DEVariable timeVariable, double tEnd, double tau)
{
// Setting up of variables and constants
if (leftVariables != null)
{
this.LeftVariables = DifferentialEquationSystemHelpers.ConvertDEVariablesToVariables(leftVariables);
}
if (constants != null)
{
this.Constants = DifferentialEquationSystemHelpers.ConvertDEVariablesToVariables(constants);
}
if (timeVariable != null)
{
this.TimeVariable = timeVariable;
}
// Setting up of all variables
List <Variable> allVariables = new List <Variable>();
if (this.LeftVariables != null)
{
allVariables.AddRange(this.LeftVariables);
}
if (this.Constants != null && this.Constants.Count > 0)
{
allVariables.AddRange(this.Constants);
}
if (this.TimeVariable != null)
{
allVariables.Add(this.TimeVariable);
}
// Setting up of all expressions
if (expressions == null || expressions.Count == 0)
{
throw new ArgumentException("Container 'expressions' of the constructor cannot be null or empty! Nothing in the differential equation system.");
}
else
{
this.Expressions = expressions;
List <Expression> expressionSystem = new List <Expression>();
foreach (string expression in expressions)
{
expressionSystem.Add(new Expression(expression, allVariables));
}
this.ExpressionSystem = expressionSystem;
}
this.TEnd = tEnd;
this.Tau = tau;
DifferentialEquationSystemHelpers.CheckVariables(this.ExpressionSystem, this.LeftVariables, this.TimeVariable, this.Tau, this.TEnd);
}
/// <summary>
/// Method calculates a differential equation system with Extrapolation Adams One method
/// </summary>
/// <param name="variablesAtAllStep">Container where the intermediate parameters are supposed to be saved</param>
/// <returns>List of result variables</returns>
private List <DEVariable> AdamsExtrapolationOneSync(List <List <DEVariable> > variablesAtAllStep = null)
{
#region Calculation preparation
List <Variable> allVars;
List <Variable> currentLeftVariables = new List <Variable>();
List <Variable> nextLeftVariables = new List <Variable>();
// Copy this.LeftVariables to the current one and to the nex one
// To leave this.LeftVariables member unchanged (for further calculations)
DifferentialEquationSystemHelpers.CopyVariables(this.LeftVariables, currentLeftVariables);
DifferentialEquationSystemHelpers.CopyVariables(this.LeftVariables, nextLeftVariables);
// Setting of current time (to leave this.TimeVariable unchanged)
Variable currentTime = new Variable(this.TimeVariable);
// If it is required to save intermediate calculations - save the start values
if (variablesAtAllStep != null)
{
// This is the first record for intermediate calculations containier
// It has to be clear
variablesAtAllStep.Clear();
DifferentialEquationSystemHelpers.SaveLeftVariableToStatistics(variablesAtAllStep, this.LeftVariables, currentTime);
}
#endregion
#region First variables
// Varables at "timestart + tau" is supposed to be calculated with other method
// It was chosen to use Euler method
// Generated a new instance for its calculation
DifferentialEquationSystem differentialEquationSystem = new DifferentialEquationSystem(this.ExpressionSystem, this.LeftVariables, this.Constants,
this.TimeVariable, this.TimeVariable.Value + this.Tau, this.Tau);
// Calculation
List <Variable> firstLeftVariables;
differentialEquationSystem.Calculate(CalculationTypeName.Euler, out List <DEVariable> bufer);
firstLeftVariables = DifferentialEquationSystemHelpers.ConvertDEVariablesToVariables(bufer);
// Save the second variables calculated with Euler method
if (variablesAtAllStep != null)
{
DifferentialEquationSystemHelpers.SaveLeftVariableToStatistics(variablesAtAllStep, firstLeftVariables, new Variable(currentTime.Name, currentTime.Value + this.Tau));
}
#endregion
allVars = DifferentialEquationSystemHelpers.CollectVariables(currentLeftVariables, this.Constants, currentTime);
double[,] Q = new double[2, this.ExpressionSystem.Count];
for (int i = 0; i < this.ExpressionSystem.Count; i++)
{
Q[0, i] = this.Tau * this.ExpressionSystem[i].GetResultValue(allVars);
}
currentTime.Value += this.Tau;
allVars = DifferentialEquationSystemHelpers.CollectVariables(firstLeftVariables, this.Constants, currentTime);
for (int i = 0; i < this.ExpressionSystem.Count; i++)
{
Q[1, i] = this.Tau * this.ExpressionSystem[i].GetResultValue(allVars);
}
do
{
for (int i = 0; i < nextLeftVariables.Count; i++)
{
nextLeftVariables[i].Value = currentLeftVariables[i].Value + 0.5 * (3 * Q[1, i] - Q[0, i]);
}
allVars = DifferentialEquationSystemHelpers.CollectVariables(nextLeftVariables, this.Constants, new Variable(currentTime.Name, currentTime.Value + this.Tau));
for (int i = 0; i < nextLeftVariables.Count; i++)
{
Q[0, i] = Q[1, i];
Q[1, i] = this.Tau * this.ExpressionSystem[i].GetResultValue(allVars);
}
if (variablesAtAllStep != null)
{
DifferentialEquationSystemHelpers.SaveLeftVariableToStatistics(variablesAtAllStep, nextLeftVariables, new Variable(currentTime.Name, currentTime.Value + this.Tau));
}
DifferentialEquationSystemHelpers.CopyVariables(nextLeftVariables, currentLeftVariables);
// calculation time incrimentation
currentTime.Value += this.Tau;
} while (currentTime.Value < this.TEnd);
List <DEVariable> result = new List <DEVariable>();
DifferentialEquationSystemHelpers.CopyVariables(currentLeftVariables, result);
return(result);
}
/// <summary>
/// Method calculates a differential equation system with Extrapolation Adams Three method
/// </summary>
/// <param name="variablesAtAllStep">Container where the intermediate parameters are supposed to be saved</param>
/// <returns>List of result variables</returns>
private List <DEVariable> AdamsExtrapolationThreeAsync(List <List <DEVariable> > variablesAtAllStep = null)
{
#region Calculation preparation
List <Variable> allVars;
List <Variable> currentLeftVariables = new List <Variable>();
List <Variable> nextLeftVariables = new List <Variable>();
// Copy this.LeftVariables to the current one and to the nex one
// To leave this.LeftVariables member unchanged (for further calculations)
DifferentialEquationSystemHelpers.CopyVariables(this.LeftVariables, currentLeftVariables);
DifferentialEquationSystemHelpers.CopyVariables(this.LeftVariables, nextLeftVariables);
// Setting of current time (to leave this.TimeVariable unchanged)
Variable currentTime = new Variable(this.TimeVariable);
// If it is required to save intermediate calculations - save the start values
if (variablesAtAllStep != null)
{
// This is the first record for intermediate calculations containier
// It has to be clear
variablesAtAllStep.Clear();
DifferentialEquationSystemHelpers.SaveLeftVariableToStatistics(variablesAtAllStep, this.LeftVariables, currentTime);
}
#endregion
#region First variables
DifferentialEquationSystem differentialEquationSystem = new DifferentialEquationSystem(this.ExpressionSystem, this.LeftVariables, this.Constants,
this.TimeVariable, this.TimeVariable.Value + 3 * this.Tau, this.Tau);
List <List <DEVariable> > firstVariables = new List <List <DEVariable> >();
differentialEquationSystem.Calculate(CalculationTypeName.Euler, out List <DEVariable> bufer, firstVariables);
List <Variable> firstLeftVariables;
List <Variable> secondLeftVariables;
List <Variable> thirdLeftVariables;
firstLeftVariables = DifferentialEquationSystemHelpers.ConvertDEVariablesToVariables(firstVariables[1]);
secondLeftVariables = DifferentialEquationSystemHelpers.ConvertDEVariablesToVariables(firstVariables[2]);
thirdLeftVariables = DifferentialEquationSystemHelpers.ConvertDEVariablesToVariables(firstVariables[3]);
firstLeftVariables.RemoveAt(firstLeftVariables.Count - 1);
secondLeftVariables.RemoveAt(secondLeftVariables.Count - 1);
thirdLeftVariables.RemoveAt(thirdLeftVariables.Count - 1);
if (variablesAtAllStep != null)
{
DifferentialEquationSystemHelpers.SaveLeftVariableToStatistics(variablesAtAllStep, firstLeftVariables, new Variable(currentTime.Name, currentTime.Value + this.Tau));
DifferentialEquationSystemHelpers.SaveLeftVariableToStatistics(variablesAtAllStep, secondLeftVariables, new Variable(currentTime.Name, currentTime.Value + 2 * this.Tau));
DifferentialEquationSystemHelpers.SaveLeftVariableToStatistics(variablesAtAllStep, thirdLeftVariables, new Variable(currentTime.Name, currentTime.Value + 3 * this.Tau));
}
#endregion
double[,] Q = new double[4, this.ExpressionSystem.Count];
allVars = DifferentialEquationSystemHelpers.CollectVariables(currentLeftVariables, this.Constants, currentTime);
Parallel.For(0, this.ExpressionSystem.Count, (i) =>
{
Q[0, i] = this.Tau * this.ExpressionSystem[i].GetResultValue(allVars);
});
currentTime.Value += this.Tau;
allVars = DifferentialEquationSystemHelpers.CollectVariables(firstLeftVariables, this.Constants, currentTime);
Parallel.For(0, this.ExpressionSystem.Count, (i) =>
{
Q[1, i] = this.Tau * this.ExpressionSystem[i].GetResultValue(allVars);
});
currentTime.Value += this.Tau;
allVars = DifferentialEquationSystemHelpers.CollectVariables(secondLeftVariables, this.Constants, currentTime);
Parallel.For(0, this.ExpressionSystem.Count, (i) =>
{
Q[2, i] = this.Tau * this.ExpressionSystem[i].GetResultValue(allVars);
});
currentTime.Value += this.Tau;
allVars = DifferentialEquationSystemHelpers.CollectVariables(thirdLeftVariables, this.Constants, currentTime);
Parallel.For(0, this.ExpressionSystem.Count, (i) =>
{
Q[3, i] = this.Tau * this.ExpressionSystem[i].GetResultValue(allVars);
});
DifferentialEquationSystemHelpers.CopyVariables(thirdLeftVariables, currentLeftVariables);
do
{
Parallel.For(0, nextLeftVariables.Count, (i) =>
{
nextLeftVariables[i].Value = currentLeftVariables[i].Value + 1.0 / 24 * (55 * Q[3, i] - 59 * Q[2, i] + 37 * Q[1, i] - 9 * Q[0, i]);
});
allVars = DifferentialEquationSystemHelpers.CollectVariables(nextLeftVariables, this.Constants, new Variable(currentTime.Name, currentTime.Value + this.Tau));
Parallel.For(0, nextLeftVariables.Count, (i) =>
{
Q[0, i] = Q[1, i];
Q[1, i] = Q[2, i];
Q[2, i] = Q[3, i];
Q[3, i] = this.Tau * this.ExpressionSystem[i].GetResultValue(allVars);
});
if (variablesAtAllStep != null)
{
DifferentialEquationSystemHelpers.SaveLeftVariableToStatistics(variablesAtAllStep, nextLeftVariables,
new Variable(currentTime.Name, currentTime.Value + this.Tau));
}
DifferentialEquationSystemHelpers.CopyVariables(nextLeftVariables, currentLeftVariables);
currentTime.Value += this.Tau;
} while (currentTime.Value < this.TEnd);
List <DEVariable> result = new List <DEVariable>();
DifferentialEquationSystemHelpers.CopyVariables(currentLeftVariables, result);
return(result);
}
/// <summary>
/// Method calculates a differential equation system with Miln method
/// </summary>
/// <param name="variablesAtAllStep">Container where the intermediate parameters are supposed to be saved</param>
/// <returns>List of result variables</returns>
private List <DEVariable> MilnSync(List <List <DEVariable> > variablesAtAllStep = null)
{
#region Calculation preparation
List <Variable> allVars;
List <Variable> currentLeftVariables = new List <Variable>();
List <Variable> milnPredicted = new List <Variable>();
List <Variable> nextLeftVariables = new List <Variable>();
// Copy this.LeftVariables to the current one and to the nex one
// To leave this.LeftVariables member unchanged (for further calculations)
DifferentialEquationSystemHelpers.CopyVariables(this.LeftVariables, currentLeftVariables);
DifferentialEquationSystemHelpers.CopyVariables(this.LeftVariables, milnPredicted);
DifferentialEquationSystemHelpers.CopyVariables(this.LeftVariables, nextLeftVariables);
// Setting of current time (to leave this.TimeVariable unchanged)
Variable currentTime = new Variable(this.TimeVariable);
// If it is required to save intermediate calculations - save the start values
if (variablesAtAllStep != null)
{
// This is the first record for intermediate calculations containier
// It has to be clear
variablesAtAllStep.Clear();
DifferentialEquationSystemHelpers.SaveLeftVariableToStatistics(variablesAtAllStep, this.LeftVariables, currentTime);
}
#endregion
#region First variables
DifferentialEquationSystem differentialEquationSystem = new DifferentialEquationSystem(this.ExpressionSystem, this.LeftVariables, this.Constants,
this.TimeVariable, this.TimeVariable.Value + 3 * this.Tau, this.Tau);
List <List <DEVariable> > firstVariables = new List <List <DEVariable> >();
List <DEVariable> bufer;
differentialEquationSystem.Calculate(CalculationTypeName.Euler, out bufer, firstVariables);
List <Variable> firstLeftVariables;
List <Variable> secondLeftVariables;
List <Variable> thirdLeftVariables;
firstLeftVariables = DifferentialEquationSystemHelpers.ConvertDEVariablesToVariables(firstVariables[1]);
secondLeftVariables = DifferentialEquationSystemHelpers.ConvertDEVariablesToVariables(firstVariables[2]);
thirdLeftVariables = DifferentialEquationSystemHelpers.ConvertDEVariablesToVariables(firstVariables[3]);
firstLeftVariables.RemoveAt(firstLeftVariables.Count - 1);
secondLeftVariables.RemoveAt(secondLeftVariables.Count - 1);
thirdLeftVariables.RemoveAt(thirdLeftVariables.Count - 1);
if (variablesAtAllStep != null)
{
DifferentialEquationSystemHelpers.SaveLeftVariableToStatistics(variablesAtAllStep, firstLeftVariables, new Variable(currentTime.Name, currentTime.Value + this.Tau));
DifferentialEquationSystemHelpers.SaveLeftVariableToStatistics(variablesAtAllStep, secondLeftVariables, new Variable(currentTime.Name, currentTime.Value + 2 * this.Tau));
DifferentialEquationSystemHelpers.SaveLeftVariableToStatistics(variablesAtAllStep, thirdLeftVariables, new Variable(currentTime.Name, currentTime.Value + 3 * this.Tau));
}
#endregion
double[,] Q = new double[4, this.ExpressionSystem.Count];
double[,] prevValues = new double[4, this.ExpressionSystem.Count];
allVars = DifferentialEquationSystemHelpers.CollectVariables(currentLeftVariables, this.Constants, currentTime);
for (int i = 0; i < this.ExpressionSystem.Count; i++)
{
Q[0, i] = this.ExpressionSystem[i].GetResultValue(allVars);
prevValues[0, i] = currentLeftVariables[i].Value;
}
currentTime.Value += this.Tau;
allVars = DifferentialEquationSystemHelpers.CollectVariables(firstLeftVariables, this.Constants, currentTime);
for (int i = 0; i < this.ExpressionSystem.Count; i++)
{
Q[1, i] = this.ExpressionSystem[i].GetResultValue(allVars);
prevValues[1, i] = firstLeftVariables[i].Value;
}
currentTime.Value += this.Tau;
allVars = DifferentialEquationSystemHelpers.CollectVariables(secondLeftVariables, this.Constants, currentTime);
for (int i = 0; i < this.ExpressionSystem.Count; i++)
{
Q[2, i] = this.ExpressionSystem[i].GetResultValue(allVars);
prevValues[2, i] = secondLeftVariables[i].Value;
}
currentTime.Value += this.Tau;
allVars = DifferentialEquationSystemHelpers.CollectVariables(thirdLeftVariables, this.Constants, currentTime);
for (int i = 0; i < this.ExpressionSystem.Count; i++)
{
Q[3, i] = this.ExpressionSystem[i].GetResultValue(allVars);
prevValues[3, i] = thirdLeftVariables[i].Value;
}
DifferentialEquationSystemHelpers.CopyVariables(thirdLeftVariables, currentLeftVariables);
do
{
for (int i = 0; i < milnPredicted.Count; i++)
{
milnPredicted[i].Value = prevValues[0, i] + 4 * this.Tau / 3 * (2 * Q[1, i] - Q[2, i] + 2 * Q[3, i]);
}
double[] predictedValues = new double[milnPredicted.Count];
allVars = DifferentialEquationSystemHelpers.CollectVariables(milnPredicted, this.Constants, new Variable(currentTime.Name, currentTime.Value + this.Tau));
for (int i = 0; i < predictedValues.Length; i++)
{
predictedValues[i] = this.ExpressionSystem[i].GetResultValue(allVars);
}
for (int i = 0; i < nextLeftVariables.Count; i++)
{
nextLeftVariables[i].Value = prevValues[2, i] + this.Tau / 3 * (Q[2, i] + 4 * this.ExpressionSystem[i].GetResultValue(DifferentialEquationSystemHelpers.CollectVariables(currentLeftVariables, this.Constants, currentTime)) + predictedValues[i]);
}
allVars = DifferentialEquationSystemHelpers.CollectVariables(nextLeftVariables, this.Constants, new Variable(currentTime.Name, currentTime.Value + this.Tau));
for (int i = 0; i < nextLeftVariables.Count; i++)
{
Q[0, i] = Q[1, i];
Q[1, i] = Q[2, i];
Q[2, i] = Q[3, i];
Q[3, i] = this.ExpressionSystem[i].GetResultValue(allVars);
prevValues[0, i] = prevValues[1, i];
prevValues[1, i] = prevValues[2, i];
prevValues[2, i] = prevValues[3, i];
prevValues[3, i] = nextLeftVariables[i].Value;
}
if (variablesAtAllStep != null)
{
DifferentialEquationSystemHelpers.SaveLeftVariableToStatistics(variablesAtAllStep, nextLeftVariables,
new Variable(currentTime.Name, currentTime.Value + this.Tau));
}
DifferentialEquationSystemHelpers.CopyVariables(nextLeftVariables, currentLeftVariables);
currentTime.Value += this.Tau;
} while (currentTime.Value < this.TEnd);
List <DEVariable> result = new List <DEVariable>();
DifferentialEquationSystemHelpers.CopyVariables(currentLeftVariables, result);
return(result);
}
