static void VerifyDifferentialEquations()
{
List <string> expressions = new List <string>
{
"2 * y1 - y + time * exp(time)",
"y1"
};
List <DEVariable> leftVariables = new List <DEVariable>
{
new DEVariable("y", 2),
new DEVariable("y1", 1),
};
DEVariable timeVariable = new DEVariable("time", 0);
DifferentialEquationSystem.DifferentialEquationSystem differentialEquationSystem = new DifferentialEquationSystem.DifferentialEquationSystem(expressions, leftVariables, null, timeVariable, 1.5, 0.001);
List <List <DEVariable> > perTime = new List <List <DEVariable> >();
double calcTime = 0;
List <DEVariable> resultEuler;
calcTime = differentialEquationSystem.Calculate(CalculationTypeName.Euler, out resultEuler, perTime);
double calcTimeForecast = 0;
List <List <DEVariable> > perTimeForecast = new List <List <DEVariable> >();
List <DEVariable> resultForecastCorrection;
calcTimeForecast = differentialEquationSystem.Calculate(CalculationTypeName.ForecastCorrection, out resultForecastCorrection, perTimeForecast);
double calcTimeRK2 = 0;
List <List <DEVariable> > perTimeRK2 = new List <List <DEVariable> >();
List <DEVariable> resultRK2;
calcTimeRK2 = differentialEquationSystem.Calculate(CalculationTypeName.RK2, out resultRK2, perTimeRK2);
double calcTimeRK4 = 0;
List <List <DEVariable> > perTimeRK4 = new List <List <DEVariable> >();
List <DEVariable> resultRK4;
calcTimeRK4 = differentialEquationSystem.Calculate(CalculationTypeName.RK4, out resultRK4, perTimeRK4);
double calcTimeAdams1 = 0;
List <List <DEVariable> > perTimeAdams1 = new List <List <DEVariable> >();
List <DEVariable> resultAdams1;
calcTimeAdams1 = differentialEquationSystem.Calculate(CalculationTypeName.AdamsExtrapolationOne, out resultAdams1, perTimeAdams1);
double calcTimeAdams2 = 0;
List <List <DEVariable> > perTimeAdams2 = new List <List <DEVariable> >();
List <DEVariable> resultAdams2;
calcTimeAdams2 = differentialEquationSystem.Calculate(CalculationTypeName.AdamsExtrapolationTwo, out resultAdams2, perTimeAdams2);
double calcTimeAdams3 = 0;
List <List <DEVariable> > perTimeAdams3 = new List <List <DEVariable> >();
List <DEVariable> resultAdams3;
calcTimeAdams3 = differentialEquationSystem.Calculate(CalculationTypeName.AdamsExtrapolationThree, out resultAdams3, perTimeAdams3);
double calcTimeAdams4 = 0;
List <List <DEVariable> > perTimeAdams4 = new List <List <DEVariable> >();
List <DEVariable> resultAdams4;
calcTimeAdams4 = differentialEquationSystem.Calculate(CalculationTypeName.AdamsExtrapolationFour, out resultAdams4, perTimeAdams4);
double calcTimeMiln = 0;
List <List <DEVariable> > perTimeMiln = new List <List <DEVariable> >();
List <DEVariable> resultMiln;
calcTimeMiln = differentialEquationSystem.Calculate(CalculationTypeName.Miln, out resultMiln, perTimeMiln);
#region CalculateWithGroupOfMethodsSync
List <CalculationTypeName> calculationTypes = new List <CalculationTypeName>
{
CalculationTypeName.Euler,
CalculationTypeName.EulerAsyc,
CalculationTypeName.ForecastCorrection,
CalculationTypeName.ForecastCorrectionAsync,
CalculationTypeName.RK2,
CalculationTypeName.RK2Async,
CalculationTypeName.RK4,
CalculationTypeName.RK4Async,
CalculationTypeName.AdamsExtrapolationOne,
CalculationTypeName.AdamsExtrapolationOneAsync,
CalculationTypeName.AdamsExtrapolationTwo,
CalculationTypeName.AdamsExtrapolationTwoAsync,
CalculationTypeName.AdamsExtrapolationThree,
CalculationTypeName.AdamsExtrapolationThreeAsync,
CalculationTypeName.AdamsExtrapolationFour,
CalculationTypeName.AdamsExtrapolationFourAsync,
CalculationTypeName.Miln,
CalculationTypeName.MilnAsync
};
Dictionary <CalculationTypeName, List <DEVariable> > results;
Dictionary <CalculationTypeName, List <List <DEVariable> > > variablesAtAllSteps = new Dictionary <CalculationTypeName, List <List <DEVariable> > >();
Dictionary <CalculationTypeName, double> calcTimes = differentialEquationSystem.CalculateWithGroupOfMethodsSync(calculationTypes, out results, variablesAtAllSteps);
Reporting.GenerateExcelReport(calculationTypes, calcTimes, results, variablesAtAllSteps, "csharp-Excel.xls", differentialEquationSystem);
#endregion
}
/// <summary>
/// Generates the excel report for the results
/// </summary>
/// <param name="calculationTypes">List of calculation types for which it is required to generate a report</param>
/// <param name="times">Calculation times for each calculation method</param>
/// <param name="results">Results for each calculation method</param>
/// <param name="allVariables">All variables results for each step of each calculation type</param>
/// <param name="excelPath">A path, where the report document is supposed to be saved</param>
public static void GenerateExcelReport(List <CalculationTypeName> calculationTypes, Dictionary <CalculationTypeName, double> times, Dictionary <CalculationTypeName, List <DEVariable> > results,
Dictionary <CalculationTypeName, List <List <DEVariable> > > allVariables, string excelPath, DifferentialEquationSystem differentialEquationSystem)
{
Excel.Application xlApp = new Excel.Application();
if (xlApp == null)
{
throw new NullReferenceException("Excel is not properly installed!!");
}
Excel.Workbook xlWorkbook = xlApp.Workbooks.Add();
// Adding variables per each steps
for (int i = calculationTypes.Count - 1; i >= 0; i--)
{
Excel.Worksheet itemWorkSheet = (Excel.Worksheet)xlWorkbook.Worksheets.Add();
SetCalculationResults(itemWorkSheet, calculationTypes[i], differentialEquationSystem.LeftVariables, results[calculationTypes[i]], allVariables[calculationTypes[i]], times[calculationTypes[i]]);
}
// Generate common results when the amount of calculation times more than 1
if (calculationTypes.Count > 1)
{
Excel.Worksheet commonResultsWorksheet = (Excel.Worksheet)xlWorkbook.Worksheets.Add();
SetCommonResults(commonResultsWorksheet, times, results);
}
Excel.Worksheet initialXlWorkSheet = (Excel.Worksheet)xlWorkbook.Worksheets.Add();
SetInitalSheet(initialXlWorkSheet, calculationTypes, differentialEquationSystem.LeftVariables, differentialEquationSystem.TimeVariable,
differentialEquationSystem.Tau, differentialEquationSystem.TEnd, differentialEquationSystem.ExpressionSystem);
xlWorkbook.SaveAs(excelPath, Excel.XlFileFormat.xlWorkbookNormal);
xlWorkbook.Close();
xlApp.Quit();
Marshal.ReleaseComObject(initialXlWorkSheet);
Marshal.ReleaseComObject(xlWorkbook);
Marshal.ReleaseComObject(xlApp);
}
/// <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>
/// Sets the initial parameters of the DifferentialEquationSystem class.
/// </summary>
/// <param name="differentialEquationSystem">Input instance</param>
public DifferentialEquationSystem(DifferentialEquationSystem differentialEquationSystem) :
this(differentialEquationSystem.ExpressionSystem, differentialEquationSystem.LeftVariables, differentialEquationSystem.Constants,
differentialEquationSystem.TimeVariable, differentialEquationSystem.TEnd, differentialEquationSystem.Tau)
{
}
/// <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);
}