public static void Main()
{
vector time = new vector(new double[] { 1, 2, 3, 4, 6, 9, 10, 13, 15 });
vector A = new vector(new double[] { 117, 100, 88, 72, 53, 29.5, 25.2, 15.2, 11.1 });
vector dA = new vector(A.size);
dA = 0.05 * A;
// Transform y = a*exp(-lambda * t) --> ln(y) = ln(a) - lambda*t
for (int i = 0; i < A.size; i++)
{
dA[i] = dA[i] / A[i];
A[i] = Log(A[i]);
}
Func <double, double>[] funcs = new Func <double, double>[] { x => 1, x => x };
TextWriter dataWriter = Error;
fit fitresult = qrfit.qrfitting(time, A, dA, funcs);
vector cErrors = fitresult.getParamErrors();
double a = Exp(fitresult.c[0]);
double lambda = -fitresult.c[1];
double aErr = cErrors[0];
double lambdaErr = cErrors[1];
WriteLine("----- Problem A -----");
fitresult.c.print("Parameters:");
WriteLine($"Acording to these paramaters, a = {a} and lambda = {lambda}");
WriteLine($"This gives a half life of {Log(2) / lambda} days");
WriteLine($"The half life of Ra224 is actually 3.6319 days");
WriteLine("");
WriteLine("----- Problem B -----");
fitresult.cov.print("The covariance matrix:");
cErrors.print("The errors are for the parameters are:");
WriteLine($"The half life of Ra224 is then estimated to {Log(2) / lambda} +- {-Log(2)/Pow(lambda, 2) * lambdaErr}");
for (double x = 0; x < 22; x += 1.0 / 16)
{
dataWriter.WriteLine($"{x} {Exp(fitresult.eval(x))}");
TextWriter answerWriter = Out;
}
}
