protected void AddVariableToEquationSystem(EquationSystem system, Variable vari, string group)
{
vari.ModelName = Name;
vari.ModelClass = Class;
vari.Group = group;
system.AddVariables(vari);
}
public void CanSolveMinProblem()
{
var problem = new EquationSystem();
var x1 = new Variable("x1", 6);
problem.AddVariables(x1);
problem.AddConstraints((Sym.Min(x1, 25)).IsEqualTo(5));
var solver = new Newton();
solver.Solve(problem);
Assert.AreEqual(5, x1.ValueInSI, 1e-5);
Assert.AreEqual(true, solver.IsConverged);
}
public virtual void FillEquationSystem(EquationSystem problem)
{
foreach (var vari in Variables)
{
vari.ModelClass = Class;
vari.ModelName = Name;
if (vari.IsFixed)
{
if (!problem.TreatFixedVariablesAsConstants && !vari.IsConstant)
{
//if (vari.DefiningExpression == null)
//{
// problem.AddVariables(vari);
//}
double scale = 1.0;
if (vari.Dimension == PhysicalDimension.Pressure)
{
scale = 1e5;
}
if (vari.Dimension == PhysicalDimension.Temperature)
{
scale = 1e3;
}
AddEquationToEquationSystem(problem, (vari / scale).IsEqualTo(vari.ValueInSI / scale), "Specification");
// problem.RemoveVariable(vari);
}
else
{
problem.RemoveVariable(vari);
}
}
if (vari.DefiningExpression != null)
{
problem.AddDefinedVariables(vari);
}
else
{
if (!(problem.TreatFixedVariablesAsConstants && vari.IsFixed) && !vari.IsConstant)
{
problem.AddVariables(vari);
}
}
}
}
public void Can_Solve_Nonlinear_System_with_3_Variables()
{
var problem = new EquationSystem();
var x1 = new Variable("x1", 1);
var x2 = new Variable("x2", 1);
var x3 = new Variable("x3", 1);
problem.AddVariables(x1, x2, x3);
problem.AddConstraints(new Equation((3 * x1 - Sym.Cos(x2 * x3) - 3.0 / 2.0)));
problem.AddConstraints(new Equation(4 * Sym.Pow(x1, 2) - 625 * Sym.Pow(x2, 2) + 2 * x2 - 1));
problem.AddConstraints(new Equation(Sym.Exp(-x1 * x2) + 20 * x3 + (10 * Math.PI - 3.0) / 3.0));
var solver = new Newton();
solver.Solve(problem);
Assert.AreEqual(true, solver.IsConverged);
Assert.AreEqual(8, solver.Iterations);
}
static void Test3()
{
Console.WriteLine();
Console.WriteLine("### Test Problem: Well-conditioned at solution");
var problem = new EquationSystem();
var x1 = new Variable("x", 2);
problem.AddVariables(x1);
problem.AddConstraints(new Equation(Sym.Pow(x1, 3) - 1));
//problem.OnLog += Console.WriteLine;
var solver = new Newton();
solver.OnLog += Console.WriteLine;
solver.OnLogDebug += Console.WriteLine;
solver.OnLogError += Console.WriteLine;
solver.OnLogSuccess += Console.WriteLine;
solver.Solve(problem);
}
static void Test4()
{
Console.WriteLine();
Console.WriteLine("### Test Problem: Powell Badly Scaled Function");
var problem = new EquationSystem();
var x1 = new Variable("x1", 2);
var x2 = new Variable("x2", 1);
problem.AddVariables(x1, x2);
problem.AddConstraints(new Equation(10000 * x1 * x2 - 1));
problem.AddConstraints(new Equation(Sym.Exp(-x1) + Sym.Exp(-x2) - 1.0001));
//
var solver = new Newton();
solver.OnLog += Console.WriteLine;
solver.OnLogDebug += Console.WriteLine;
solver.OnLogError += Console.WriteLine;
solver.OnLogSuccess += Console.WriteLine;
solver.Solve(problem);
}
void PrecalculateZP(MaterialStream stream)
{
stream.Mixed.TotalMolarflow.ValueInSI = stream.Mixed.ComponentMolarflow.Sum(v => v.ValueInSI);
var NC = stream.System.Components.Count;
for (int i = 0; i < NC; i++)
{
stream.Mixed.ComponentMolarFraction[i].ValueInSI = stream.Mixed.ComponentMolarflow[i].ValueInSI / stream.Mixed.TotalMolarflow.ValueInSI;
stream.Liquid.ComponentMolarFraction[i].ValueInSI = stream.Mixed.ComponentMolarFraction[i].ValueInSI;
stream.Vapor.ComponentMolarFraction[i].ValueInSI = stream.Mixed.ComponentMolarFraction[i].ValueInSI;
}
var rachfordRice = Sym.Sum(0, NC, i => stream.Mixed.ComponentMolarFraction[i] * (1 - stream.KValues[i]) / (1 + stream.Vfmolar * (stream.KValues[i] - 1)));
var rachfordRiceEq = rachfordRice.IsEqualTo(0);
var problem2 = new EquationSystem()
{
Name = "Rachford-Rice"
};
if (stream.Vfmolar.ValueInSI <= 1e-10)
{
problem2.AddConstraints(Sym.Sum(0, NC, i => stream.Mixed.ComponentMolarFraction[i] * stream.KValues[i]).IsEqualTo(1));
}
else if (stream.Vfmolar.ValueInSI >= 1 - 1e-10)
{
problem2.AddConstraints(Sym.Sum(0, NC, i => stream.Mixed.ComponentMolarFraction[i] / stream.KValues[i]).IsEqualTo(1));
}
else
{
problem2.AddConstraints(rachfordRiceEq);
}
problem2.AddVariables(stream.Mixed.Temperature);
_solver.Solve(problem2);
performMassBalance(stream, stream.KValues);
performDensityUpdate(stream);
performEnthalpyUpdate(stream);
}
/*Jacobian Density = 88,889%
* Hessian Density = 0,000%
* Solving NLP Problem(3 Variables, 3 Equations)
* ITER SCALE D_NORM INF_PR ALG
* 0001 1 1.6 620 ___(NEWTON, LU/MinimumDegreeAtPlusA)
* 0002 1 0.48 153.0758 ___(NEWTON, LU/MinimumDegreeAtPlusA)
* 0003 1 0.12 38.338978 ___(NEWTON, LU/MinimumDegreeAtPlusA)
* 0004 1 0.055 9.1587665 ___(NEWTON, LU/MinimumDegreeAtPlusA)
* 0005 1 0.02 1.9173079 ___(NEWTON, LU/MinimumDegreeAtPlusA)
* 0006 1 0.0035 0.24865722 ___(NEWTON, LU/MinimumDegreeAtPlusA)
* 0007 1 0.00011 0.0076250521 ___(NEWTON, LU/MinimumDegreeAtPlusA)
* 0008 1 1.2E-07 8.137733E-06 ___(NEWTON, LU/MinimumDegreeAtPlusA)
* [NewtonSolver]
* Problem NLP Problem was successfully solved because constraint violation is below tolerance(8 iterations, 0,04 seconds, problem size: 3)
### Printing debugging information NLP Problem
###x1 = 0,833196581863439
###x2 = 0,0549436583091183
###x3 = -0,521361434378159
###
### Generic 0,0000 ( ((4*(x1)^(2) - 625*(x2)^(2)) + 2*x2 - 1) == 0 )
### Generic 0,0000 ( exp(-(x1)*x2) + 20*x3 + 9.471976 == 0 )
### Generic 0,0000 ( ((3*x1 - cos(x2* x3)) - 1.5) == 0 )*/
static void Test1()
{
Console.WriteLine();
Console.WriteLine("### Test Problem: Difficult Function");
var problem = new EquationSystem();
var x1 = new Variable("x1", 1);
var x2 = new Variable("x2", 1);
var x3 = new Variable("x3", 1);
problem.AddVariables(x1, x2, x3);
problem.AddConstraints(new Equation((3 * x1 - Sym.Cos(x2 * x3) - 3.0 / 2.0)));
problem.AddConstraints(new Equation(4 * Sym.Pow(x1, 2) - 625 * Sym.Pow(x2, 2) + 2 * x2 - 1));
problem.AddConstraints(new Equation(Sym.Exp(-x1 * x2) + 20 * x3 + (10 * Math.PI - 3.0) / 3.0));
var solver = new Newton();
solver.OnLog += Console.WriteLine;
solver.OnLogError += Console.WriteLine;
solver.OnLogSuccess += Console.WriteLine;
solver.Solve(problem);
}
void PrecalculateTP(MaterialStream stream)
{
stream.Mixed.TotalMolarflow.ValueInSI = stream.Mixed.ComponentMolarflow.Sum(v => v.ValueInSI);
var NC = stream.System.Components.Count;
for (int i = 0; i < NC; i++)
{
stream.Mixed.ComponentMolarFraction[i].ValueInSI = stream.Mixed.ComponentMolarflow[i].ValueInSI / stream.Mixed.TotalMolarflow.ValueInSI;
stream.Liquid.ComponentMolarFraction[i].ValueInSI = stream.Mixed.ComponentMolarFraction[i].ValueInSI;
stream.Vapor.ComponentMolarFraction[i].ValueInSI = stream.Mixed.ComponentMolarFraction[i].ValueInSI;
}
//Solving Rachford Rice equation to get actual vapour fraction
var x = stream.Mixed.ComponentMolarFraction;
var K = stream.KValues;
var a = stream.Vfmolar;
var rachfordRice = Sym.Sum(0, NC, i => x[i] * (1 - K[i]) / (1 + a * (K[i] - 1)));
//Evaluate Rachford-Rice at the edge cases of the VLE area
stream.Vfmolar.ValueInSI = 0;
var rrAt0 = rachfordRice.Eval(new Evaluator());
stream.Vfmolar.ValueInSI = 1;
var rrAt1 = rachfordRice.Eval(new Evaluator());
stream.Vfmolar.ValueInSI = 0.5;
if (rrAt0 > 0)
{
stream.Vfmolar.ValueInSI = 0;
}
else if (Math.Abs(rrAt0) < 1e-8)
{
stream.Vfmolar.ValueInSI = 0;
}
else if (Math.Abs(rrAt1) < 1e-8)
{
stream.Vfmolar.ValueInSI = 1;
}
else if (rrAt1 < 0)
{
stream.Vfmolar.ValueInSI = 1;
}
if (stream.Vfmolar.ValueInSI == 0.5 || (rrAt0 == 0 && rrAt1 == 0))
{
for (int i = 0; i < NC; i++)
{
stream.Liquid.ComponentMolarFraction[i].ValueInSI = 0.95 * stream.Mixed.ComponentMolarFraction[i].ValueInSI;
stream.Vapor.ComponentMolarFraction[i].ValueInSI = 1.05 * stream.Mixed.ComponentMolarFraction[i].ValueInSI;
}
stream.Vfmolar.ValueInSI = 0.5;
var problem2 = new EquationSystem()
{
Name = "Rachford-Rice"
};
stream.Vfmolar.LowerBound = -5;
stream.Vfmolar.UpperBound = 5;
problem2.AddConstraints(rachfordRice.IsEqualTo(0));
problem2.AddVariables(stream.Vfmolar);
_solver.Solve(problem2);
}
if (Double.IsNaN(stream.Vfmolar.ValueInSI))
{
stream.Vfmolar.ValueInSI = 0;
}
stream.Vfmolar.LowerBound = 0;
stream.Vfmolar.UpperBound = 1;
if (stream.Vfmolar.ValueInSI > 1)
{
stream.Vfmolar.ValueInSI = 1;
}
if (stream.Vfmolar.ValueInSI < 0)
{
stream.Vfmolar.ValueInSI = 0;
}
performMassBalance(stream, stream.KValues);
performDensityUpdate(stream);
performEnthalpyUpdate(stream);
}