public TaylorApproximation(ParseTree pt) {
super(pt);
SymbolTable st = new SymbolTable();
ValueTable vt = new ValueTable();
try {
f = FunctionFactory.getFunction(getArg(0));
x0 = FunctionFactory.getFunction(getArg(1)).evaluate(st, vt);
order = (int) FunctionFactory.getFunction(getArg(2)).evaluate();
} catch (ArrayIndexOutOfBoundsException e) {
e.printStackTrace(System.out);
return;
}
Function D = f;
taylorCoeff = new double[order + 1];
// TODO this is a problem! Make the taylor approximation not always over x.
vt.setValue(VariableToken.X_VAR, x0);
for (int i = 0; i <= order; i++) {
taylorCoeff[i] = D.evaluate(st, vt);
for (int j = 2; j <= i; j++) taylorCoeff[i] = taylorCoeff[i] / j;
D = D.derivative(VariableToken.X_VAR);
}
}
public double evaluate(SymbolTable st, ValueTable vt) {
// So called Horner's Rule which evaluates a polynomial of degree n
// in n multiplies and n adds.
double x = vt.getValue(VariableToken.X_VAR);
double val = 0;
for (int i = taylorCoeff.length - 1; i >= 0; i--) {
val = val * (x - x0) + taylorCoeff[i];
}
return val;
}