public void Replace(Dictionary <string, FloatingPoint> symbols)
{
foreach (var b in Table.Backend)
{
foreach (var i in b.Value.Backend)
{
Evaluate.Evaluate(symbols, i.Value);
}
}
}
public static Expression Subsitute(this Expression function, string symbol, Expression value)
{
return(Evaluate.Evaluate(
new Dictionary <string, FloatingPoint> {
{
symbol, value.ToReal()
}
},
function).RealValue.ToFraction());
}
public static double ToReal(this Expression expression, int places = 5)
{
var value = double.NaN;
if (expression.IsNumber)
{
var empty = new Dictionary <string, FloatingPoint>();
value = Evaluate.Evaluate(empty, expression).RealValue;
}
return(value.Round(places));
}
public static void CalculateEquation(ref Dictionary <string, FloatingPoint> initialVector, int i)
{
var df1x = Calculus.Differentiate(x, f1);
var df1y = Calculus.Differentiate(y, f1);
var df2x = Calculus.Differentiate(x, f2);
var df2y = Calculus.Differentiate(y, f2);
double j11 = Eval.Evaluate(initialVector, df1x).RealValue;
double j12 = Eval.Evaluate(initialVector, df1y).RealValue;
double j21 = Eval.Evaluate(initialVector, df2x).RealValue;
double j22 = Eval.Evaluate(initialVector, df2y).RealValue;
if (i == 1)
{
Console.WriteLine("Jacobian matrix symbolic:");
Console.WriteLine(Infix.FormatStrict(df1x) + " " + Infix.Format(df1y) + "\n" + Infix.Format(df2x) + " " + Infix.Format(df2y));
}
double[] m = { j11, j21, j12, j22 };
Matrix <double> jacobian = new DenseMatrix(2, 2, m);
Console.WriteLine("Jacobian matrix numeric:\n");
Console.WriteLine(jacobian.ToString());
Matrix <double> initial = new DenseMatrix(2, 1, new double[] { Eval.Evaluate(initialVector, f1).RealValue, Eval.Evaluate(initialVector, f2).RealValue });
jacobian = jacobian.Inverse();
var solution = jacobian * (-initial);
var xn = x0 + solution[0, 0];
var yn = y0 + solution[1, 0];
var outVal = new Dictionary <string, FloatingPoint> {
{ "x", xn }, { "y", yn }
};
Console.WriteLine("Iteration " + i + ":\n");
Console.WriteLine("x" + i.ToString() + " = " + xn + Environment.NewLine + "y" + i.ToString() + " = " + yn);
Console.WriteLine("f1(x" + i + ",y" + i + ")=" + Math.Round(Eval.Evaluate(initialVector, f1).RealValue, 3));
Console.WriteLine("f2(x" + i + ",y" + i + ")=" + Eval.Evaluate(initialVector, f2).RealValue);
Console.WriteLine("\n");
initialVector = outVal;
x0 = xn;
y0 = yn;
}
