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);
}
/*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);
}
Expression HandleExpression(DAEProblem problem, ModelicaExpression expr)
{
switch (expr)
{
case BinaryExpression b:
{
switch (b.Operator)
{
case BinaryOperator.Add:
return(HandleExpression(problem, b.Left) + HandleExpression(problem, b.Right));
case BinaryOperator.Subtract:
return(HandleExpression(problem, b.Left) - HandleExpression(problem, b.Right));
case BinaryOperator.Multiply:
return(HandleExpression(problem, b.Left) * HandleExpression(problem, b.Right));
case BinaryOperator.Divide:
return(HandleExpression(problem, b.Left) / HandleExpression(problem, b.Right));
case BinaryOperator.Power:
return(Sym.Pow(HandleExpression(problem, b.Left), HandleExpression(problem, b.Right)));
}
}
break;
case UnaryExpression u:
{
switch (u.Operator)
{
case UnaryOperator.Negate:
return(-HandleExpression(problem, u.Child));
case UnaryOperator.Parentheses:
return(Sym.Par(HandleExpression(problem, u.Child)));
case UnaryOperator.TimeDerivative:
var y = HandleExpression(problem, u.Child) as Variable;
if (y == null)
{
throw new InvalidOperationException("Cannot handle expressions inside der operator yet.");
}
var dery = new Variable("der(" + y.Name + ")", 0);
var existingVar = problem.DifferentialVariables.FirstOrDefault(v => v.Name == dery.Name);
if (existingVar == null)
{
problem.DifferentialVariables.Add(dery);
problem.Mapping.Add(dery, y);
return(dery);
}
else
{
return(existingVar);
}
default:
throw new InvalidOperationException("Unknown unary operator " + u.Operator.ToString());
}
}
case BuiltinFunction u:
{
switch (u.Type)
{
case BuiltinFunctionType.Sin:
return(Sym.Sin(HandleExpression(problem, u.Child)));
case BuiltinFunctionType.Cos:
return(Sym.Cos(HandleExpression(problem, u.Child)));
case BuiltinFunctionType.Tan:
return(Sym.Tan(HandleExpression(problem, u.Child)));
case BuiltinFunctionType.Log:
return(Sym.Ln(HandleExpression(problem, u.Child)));
case BuiltinFunctionType.Exp:
return(Sym.Exp(HandleExpression(problem, u.Child)));
case BuiltinFunctionType.Sqrt:
return(Sym.Sqrt(HandleExpression(problem, u.Child)));
default:
throw new InvalidOperationException("Unknown built-in fucntion " + u.Type.ToString());
}
}
case DoubleLiteral l:
return(new Variable(l.Value.ToString(), l.Value));
case Reference r:
{
var vari = problem.ResolveReference(r.ToString());
if (vari != null)
{
return(vari);
}
else
{
throw new NullReferenceException("Variable " + r.ToString() + " not defined.");
}
}
default:
throw new InvalidOperationException("Unknown expression " + expr.ToString());
}
return(null);
}
