static int Main()
{
Func <double, double>[] lnexp = new Func <double, double> [2];
lnexp[0] = (x) => 1;
lnexp[1] = (x) => - x;
double[] t = { 1, 2, 3, 4, 6, 9, 10, 13 };
double[] yt = { 117, 100, 88, 72, 53, 29.5, 25.2, 15.2 };
vector xs = new vector(t);
vector ys = new vector(yt);
vector lny = new vector(yt.Length);
vector yerr = new vector(yt.Length);
vector lnerr = new vector(yt.Length);
for (int i = 0; i < yt.Length; i++)
{
lny[i] = Log(yt[i]);
yerr[i] = yt[i] / 20;
lnerr[i] = yerr[i] / yt[i];
}
lsfit fit1 = new lsfit(xs, lny, lnerr, lnexp);
vector c = fit1.C;
WriteLine("\n Data:");
xs.print("time in days = ");
ys.print("y = ");
WriteLine("\n Attempting to make fit y=a*Exp(-lambda*t) by using ln(y)=ln(a)-lambda*t");
c.print("c = ln(a) lambda = ");
WriteLine("a = {0:f6}", Exp(c[0]));
WriteLine("half life = {0:f6}\n", Log(2) * 1 / c[1]);
Func <double, double> fit1fun = x => c[0] * lnexp[0](x) + c[1] * lnexp[1](x);
var fitwriter = new System.IO.StreamWriter("out.fit.txt");
for (double x = 0; x < 20; x += 0.1)
{
fitwriter.Write("{0:f16} {1:f16}\n", x, Exp(fit1fun(x)));
}
fitwriter.Close();
var datwriter = new System.IO.StreamWriter("out.data.txt");
for (int i = 0; i < xs.size; i++)
{
datwriter.Write("{0:f16} {1:f16} {2:f16}\n", xs[i], yt[i], yerr[i]);
}
datwriter.Close();
return(0);
}
/*************************************************************************
Subroutine for nonlinear fitting of linear problem
DerAvailable:
* 0 when only function value should be used
* 1 when we can provide gradient/function
* 2 when we can provide Hessian/gradient/function
When something which is not permitted by DerAvailable is requested,
this function sets NLSErrors to True.
*************************************************************************/
private static void fitlinearnonlinear(int m,
int deravailable,
double[,] xy,
lsfit.lsfitstate state,
ref bool nlserrors)
{
int i = 0;
int j = 0;
double v = 0;
int i_ = 0;
while( lsfit.lsfititeration(state) )
{
//
// assume that one and only one of flags is set
// test that we didn't request hessian in hessian-free setting
//
if( deravailable<1 & state.needfg )
{
nlserrors = true;
}
if( deravailable<2 & state.needfgh )
{
nlserrors = true;
}
i = 0;
if( state.needf )
{
i = i+1;
}
if( state.needfg )
{
i = i+1;
}
if( state.needfgh )
{
i = i+1;
}
if( i!=1 )
{
nlserrors = true;
}
//
// test that PointIndex is consistent with actual point passed
//
for(i=0; i<=m-1; i++)
{
nlserrors = nlserrors | (double)(xy[state.pointindex,i])!=(double)(state.x[i]);
}
//
// calculate
//
if( state.needf )
{
v = 0.0;
for(i_=0; i_<=m-1;i_++)
{
v += state.x[i_]*state.c[i_];
}
state.f = v;
continue;
}
if( state.needfg )
{
v = 0.0;
for(i_=0; i_<=m-1;i_++)
{
v += state.x[i_]*state.c[i_];
}
state.f = v;
for(i_=0; i_<=m-1;i_++)
{
state.g[i_] = state.x[i_];
}
continue;
}
if( state.needfgh )
{
v = 0.0;
for(i_=0; i_<=m-1;i_++)
{
v += state.x[i_]*state.c[i_];
}
state.f = v;
for(i_=0; i_<=m-1;i_++)
{
state.g[i_] = state.x[i_];
}
for(i=0; i<=m-1; i++)
{
for(j=0; j<=m-1; j++)
{
state.h[i,j] = 0;
}
}
continue;
}
}
}
static int Main()
{
Func <double, double>[] lnexp = new Func <double, double> [2];
lnexp[0] = (x) => 1;
lnexp[1] = (x) => - x;
double[] t = { 1, 2, 3, 4, 6, 9, 10, 13 };
double[] yt = { 117, 100, 88, 72, 53, 29.5, 25.2, 15.2 };
vector xs = new vector(t);
vector lny = new vector(yt.Length);
vector yerr = new vector(yt.Length);
vector lnerr = new vector(yt.Length);
for (int i = 0; i < yt.Length; i++)
{
lny[i] = Log(yt[i]);
yerr[i] = yt[i] / 20;
lnerr[i] = yerr[i] / yt[i];
}
lsfit fit1 = new lsfit(xs, lny, lnerr, lnexp);
WriteLine("Trying to fit y=a*Exp(-lambda*x) on log form ln(y) = ln(a)-lambda*x \n");
vector c = fit1.C;
vector cerr = fit1.Cerr;
matrix covar = fit1.Covar;
c.print("c = ln(a) lambda = ");
covar.print("covariance matrix = ");
double a = Exp(c[0]);
double aerr = Exp(c[0]) * cerr[0];
double ml = 1 / c[1];
double hlerr = cerr[1] * Log(2) / ((-c[1]) * (-c[1]));
double hl = Log(2) * ml;
WriteLine("a = {0:f6} +- {1:f6}", a, aerr);
WriteLine("lambda = {0:f6} +- {1:f6}\n", c[1], cerr[1]);
WriteLine("Lambda converted to half life, error found by simplified propagation formula");
WriteLine("half life = {0:f6} +- {1:f6}", hl, hlerr);
Func <double, double> expfun = x => a *Exp(-c[1] *x);
Func <double, double> expu = x => (a + aerr) * Exp(-(c[1] - cerr[1]) * x);
Func <double, double> expl = x => (a - aerr) * Exp(-(c[1] + cerr[1]) * x);
vector x_eval = new vector(200);
for (int i = 0; i < x_eval.size; i++)
{
x_eval[i] = (double)i / 10;
}
var fitwriter = new System.IO.StreamWriter("out.fit.txt");
var fitupwriter = new System.IO.StreamWriter("out.fitu.txt");
var fitlowriter = new System.IO.StreamWriter("out.fitl.txt");
for (int i = 0; i < x_eval.size; i++)
{
fitwriter.Write("{0:f16} {1:f16}\n", x_eval[i], expfun(x_eval[i]));
fitupwriter.Write("{0:f16} {1:f16}\n", x_eval[i], expu(x_eval[i]));
fitlowriter.Write("{0:f16} {1:f16}\n", x_eval[i], expl(x_eval[i]));
}
fitwriter.Close();
fitupwriter.Close();
fitlowriter.Close();
var datwriter = new System.IO.StreamWriter("out.data.txt");
for (int i = 0; i < xs.size; i++)
{
datwriter.Write("{0:f16} {1:f16} {2:f16}\n", xs[i], yt[i], yerr[i]);
}
datwriter.Close();
return(0);
}
static void Main()
{
/* A */
var t0 = new vector(new double[] { 1, 2, 3, 4, 6, 9, 10, 13, 15 });
var y0 = new vector(new double[] { 117, 100, 88, 72, 53, 29.5, 25.2, 15.2, 11.1 });
var dy0 = 0.05 * y0;
var f = new Func <double, double>[] { x => 1, x => x };
int n = t0.size;
var t = new vector(n);
var y = new vector(n);
var dy = new vector(n);
for (int i = 0; i < n; i++)
{
t[i] = t0[i];
y[i] = Log(y0[i]);
dy[i] = dy0[i] / y0[i];
}
var fit = new lsfit(t, y, dy, f);
for (int i = 0; i < t.size; i++)
{
WriteLine($"{t0[i]} {y0[i]} {dy0[i]}");
}
int k, N = 100;
double z, step = (t[t.size - 1] - t[0]) / (N - 1);
WriteLine("\n\n");
for (z = t[0], k = 0; k < N; z = t[0] + (++k) * step)
{
WriteLine($"{z} {Exp(fit.eval(z))}");
}
double lambda = fit.c[1];
double dlambda = Sqrt(fit.sigma[1, 1]);
// Error.WriteLine($"lambda={lambda:f5}, dlambda={dlambda:f5}");
double T = -Log(2.0) / lambda; // half-life
double dT = Abs(dlambda / lambda / lambda); // half-life uncertainty
Error.WriteLine("A)");
Error.WriteLine($"ThX half-life from fit = {T:f1} +/- {dT:f1} days");
Error.WriteLine($"The modern value for the half-life of 224-Rn = {3.619} +/- {0.023} days");
Error.WriteLine("The value obtained from the fit agrees with the modern value within the uncertainties of the fit");
Error.WriteLine("(Source: https://en.wikipedia.org/wiki/Isotopes_of_radium)\n");
/* B) */
matrix sigma = fit.sigma;
Error.WriteLine("B)");
Error.WriteLine($"The covariance matrix, Σ: \n {sigma[0,0]:f6} {sigma[0,1]:f6} \n {sigma[1,0]:f6} {sigma[1,1]:f6}");
Error.WriteLine("\nThe fitting parameters with uncertainties are:");
vector unc = new vector(sigma.size1);
for (int i = 0; i < sigma.size1; i++)
{
unc[i] = Sqrt(sigma[i, i]);
Error.WriteLine($"c[{i}]: {fit.c[i]:f6} +/- {unc[i]:f6}");
}
/* C) */
WriteLine("\n\n");
fit.c[0] += Sqrt(fit.sigma[0, 0]);
for (z = t[0], k = 0; k < N; z = t[0] + (++k) * step)
{
WriteLine($"{z} {Exp(fit.eval(z))}");
}
WriteLine("\n\n");
fit.c[0] -= 2 * Sqrt(fit.sigma[0, 0]);
for (z = t[0], k = 0; k < N; z = t[0] + (++k) * step)
{
WriteLine($"{z} {Exp(fit.eval(z))}");
}
fit.c[0] += Sqrt(fit.sigma[0, 0]);
WriteLine("\n\n");
fit.c[1] += Sqrt(fit.sigma[1, 1]);
for (z = t[0], k = 0; k < N; z = t[0] + (++k) * step)
{
WriteLine($"{z} {Exp(fit.eval(z))}");
}
WriteLine("\n\n");
fit.c[1] -= 2 * Sqrt(fit.sigma[1, 1]);
for (z = t[0], k = 0; k < N; z = t[0] + (++k) * step)
{
WriteLine($"{z} {Exp(fit.eval(z))}");
}
}
public lsfitstate(lsfit.lsfitstate obj)
{
_innerobj = obj;
}
public lsfitreport(lsfit.lsfitreport obj)
{
_innerobj = obj;
}
public spline1dfitreport(lsfit.spline1dfitreport obj)
{
_innerobj = obj;
}
public barycentricfitreport(lsfit.barycentricfitreport obj)
{
_innerobj = obj;
}
public polynomialfitreport(lsfit.polynomialfitreport obj)
{
_innerobj = obj;
}
static void Main()
{
//Original coordinates
vector xo = new vector(new double[] { 1, 2, 3, 4, 6, 9, 10, 13, 15 });
vector yo = new vector(new double[] { 117, 100, 88, 72, 53, 29.5, 25.2, 15.2, 11.1 });
vector dyo = yo / 20;
var f = new Func <double, double>[] { t => 1, t => t };
for (int i = 0; i < xo.size; i++)
{
WriteLine($"{xo[i]}\t{yo[i]}\t{dyo[i]}");
}
WriteLine(); WriteLine(); //Linebreak
vector x = xo.copy();
vector y = new vector(x.size);
vector dy = new vector(x.size);
for (int i = 0; i < x.size; i++)
{
y[i] = Log(yo[i]);
dy[i] = dyo[i] / yo[i];
}
var fit = new lsfit(x, y, dy, f);
vector c = fit.c; //Coefficients
vector delta_c = fit.delta_c; //Uncertienties of the coefficients
double lambda = c[1];
double dlambda = delta_c[1];
Error.WriteLine($"lambda={lambda:f5} ± {dlambda:f5} ");
double T = Log(0.5) / lambda;
double dT = Abs(dlambda / lambda / lambda);
Error.WriteLine($"Halvlife= {T:f1} ± {dT:f1} days");
if (T + dT >= 3.6 && (T - dT) <= 3.6)
{
Error.WriteLine("Halvlife matches modern value of 3.6 days");
}
else
{
Error.WriteLine("Halvlife does not match modern value of 3.6 days");
}
int N = 1000;
double x_lnmin = x[0];
double x_lnmax = x[x.size - 1];
vector x_fit = new vector(N + 1);
vector y_lnfit = new vector(N + 1);
vector y_fit = new vector(N + 1);
double xi;
for (int i = 0; i <= N; i++)
{
xi = (x_lnmax - x_lnmin) / 1000 * i + x_lnmin;
x_fit[i] = xi;
y_lnfit[i] = fit.eval(xi);
y_fit[i] = Exp(y_lnfit[i]);
WriteLine($"{x_fit[i]:f5} {y_fit[i]:f5} ");
}
WriteLine(); WriteLine();
fit.c[0] += fit.delta_c[0];
for (int i = 0; i <= N; i++)
{
y_fit[i] = Exp(fit.eval(x_fit[i]));
WriteLine($"{x_fit[i]:f5} {y_fit[i]:f5} ");
}
WriteLine(); WriteLine();
fit.c[0] -= 2 * fit.delta_c[0];
for (int i = 0; i <= N; i++)
{
y_fit[i] = Exp(fit.eval(x_fit[i]));
WriteLine($"{x_fit[i]:f5} {y_fit[i]:f5} ");
}
WriteLine(); WriteLine();
fit.c[0] += fit.delta_c[0];
fit.c[1] += fit.delta_c[1];
for (int i = 0; i <= N; i++)
{
y_fit[i] = Exp(fit.eval(x_fit[i]));
WriteLine($"{x_fit[i]:f5} {y_fit[i]:f5} ");
}
WriteLine(); WriteLine();
fit.c[1] -= 2 * fit.delta_c[1];
for (int i = 0; i <= N; i++)
{
y_fit[i] = Exp(fit.eval(x_fit[i]));
WriteLine($"{x_fit[i]:f5} {y_fit[i]:f5} ");
}
}
static void B1()
{
WriteLine("\n Problem B1: Test Jacobi cycle time \n");
int n = 50;
WriteLine("Symmetric random test matrix A of size {0}", n);
Stopwatch sw = new Stopwatch();
double time_avg = 0;
int k = 15;
vector times = new vector(k);
for (int i = 0; i < k; i++)
{
sw.Reset();
matrix A = rand_sym_mat(n);
matrix B = A.copy();
sw.Start();
jcbi_cycl test = new jcbi_cycl(B);
sw.Stop();
times[i] = sw.Elapsed.TotalMilliseconds;
time_avg += times[i];
}
time_avg = time_avg / times.size;
WriteLine("Average Jacobi diagonalisation time");
WriteLine("time_avg = {0} ms\n", time_avg);
WriteLine("Perform calculation for different matrix sizes");
var timewriter = new System.IO.StreamWriter("out.time.txt");
k = 5; // number of tries for each avg
int l = 30; // upper range of matrix sizes;
vector tavgs = new vector(l - 5);
vector xs = new vector(l - 5);
vector terr = new vector(l - 5);
for (int i = 5; i < l; i++)
{
xs[i - 5] = i * 1.0;
tavgs[i - 5] = 0;
for (int j = 0; j < k; j++)
{
matrix A = rand_sym_mat(i);
sw.Reset();
matrix B = A.copy();
sw.Start();
jcbi_cycl test = new jcbi_cycl(B);
sw.Stop();
tavgs[i - 5] += sw.Elapsed.TotalMilliseconds;
}
tavgs[i - 5] = tavgs[i - 5] / k;
terr[i - 5] = tavgs[i - 5] * 0.025;
timewriter.WriteLine($"{i} {tavgs[i-5]}");
}
timewriter.Close();
Func <double, double>[] tfun = new Func <double, double> [2];
tfun[0] = (x) => 1; tfun[1] = (x) => x * x * x;
//tfun[0] = (x) => 1; tfun[1] = (x) => x; tfun[2] = (x) => x*x; tfun[3] = (x) => x*x*x;
lsfit tfit = new lsfit(xs, tavgs, terr, tfun);
WriteLine("exec time fit params {0} {1}", tfit.C[0], tfit.C[1]);
vector fiteval = tfit.evaluate(xs);
var tfunw = new System.IO.StreamWriter("out.tfun.txt");
for (int i = 0; i < xs.size; i++)
{
tfunw.WriteLine($"{xs[i]} {fiteval[i]}");
}
tfunw.Close();
WriteLine("See PlotB1.svg for execution time calculation and a+b*x^3 fit");
}
static void Main()
{
// Note: Contains problem A, B and C, since they are so interrelated, that splitting
// it up in several files and folders would be quite an unneccesary hassle.
// Arrays with the measured data points
vector x = new vector(new double[] { 1, 2, 3, 4, 6, 9, 10, 13, 15 });
vector y = new vector(new double[] { 117, 100, 88, 72, 53, 29.5, 25.2, 15.2, 11.1 });
// The uncertainty of the data points is 5% of the values
vector dy = y / 20;
int n = x.size;
StreamWriter writeData = new StreamWriter("originalData.txt");
for (int i = 0; i < x.size; i++)
{
writeData.WriteLine("{0}\t{1}\t{2}", x[i], y[i], dy[i]);
}
writeData.Close();
vector yln = new vector(n);
vector dyln = new vector(n);
// Take the logarithm of the data
for (int i = 0; i < n; i++)
{
yln[i] = Log(y[i]);
dyln[i] = dy[i] / y[i];
}
// Fit the data
// We fit with a linear equation with a constant
var f = new Func <double, double>[] { t => 1, t => t };
var fit = new lsfit(x, yln, dyln, f);
// The lambda coefficient is now stored in the c[1] entry of the c-vector
// The uncertainty of lambda can be found from the covariance matrix
double lna = fit.c[0];
double dlna = Sqrt(fit.sigma[0, 0]);
double lambda = fit.c[1];
double dlambda = Sqrt(fit.sigma[1, 1]);
// The half-life is then
double T = -Log(2.0) / lambda;
// Write out the found half-life and lambda+-dlambda
StreamWriter writeFitResult = new StreamWriter("outA-B.txt");
writeFitResult.WriteLine("The least squares fit gave the results:");
writeFitResult.WriteLine("lambda = {0:f5} +/- {1:f5}", lambda, dlambda);
writeFitResult.WriteLine("ln(a) = {0:f5} +/- {1:f5}", lna, dlna);
writeFitResult.WriteLine("The half-life is thus estimated to be {0:f2} days", T);
writeFitResult.WriteLine("The table value half-life is 3.66 days");
// Generate data for the fitted curve
StreamWriter writeFitData = new StreamWriter("fitData.txt");
double delta = 0.02;
for (double i = x[0]; i <= x[n - 1]; i += delta)
{
writeFitData.WriteLine("{0:f2}\t{1}", i, Exp(fit.eval(i)));
}
// Part B
// The uncertainty of the half-life value for ThX is calculated via the usual formula
// for the uncertainty of a function with one variable: dq = dx*|dq/dx|
double dT = Log(2.0) * 1 / (lambda * lambda) * dlambda;
writeFitResult.WriteLine("\nThe uncertainty in the estimated halflife is {0:f2} days",
dT);
writeFitResult.WriteLine("The estimated value does thus not match the modern value" +
" within the estimated uncertainty, but it is close.");
writeFitResult.Close();
// Part C
// We generate data for plots where the fit coefficients are changed by the estimated
// uncertainties. First they are changed one at time, and at last they are changed
// together for the upper and lower boundaries of the uncertainty
writeFitData.WriteLine();
writeFitData.WriteLine();
// ln(a) + dln(a)
fit.c[0] += dlna;
for (double i = x[0]; i <= x[n - 1]; i += delta)
{
writeFitData.WriteLine("{0:f2}\t{1}", i, Exp(fit.eval(i)));
}
writeFitData.WriteLine();
writeFitData.WriteLine();
// ln(a) - dln(a)
fit.c[0] -= 2 * dlna;
for (double i = x[0]; i <= x[n - 1]; i += delta)
{
writeFitData.WriteLine("{0:f2}\t{1}", i, Exp(fit.eval(i)));
}
// Restore ln(a) to the original value from the fit
fit.c[0] += dlna;
writeFitData.WriteLine();
writeFitData.WriteLine();
// lambda + dlambda
fit.c[1] += dlambda;
for (double i = x[0]; i <= x[n - 1]; i += delta)
{
writeFitData.WriteLine("{0:f2}\t{1}", i, Exp(fit.eval(i)));
}
writeFitData.WriteLine();
writeFitData.WriteLine();
// lambda - dlambda
fit.c[1] -= 2 * dlambda;
for (double i = x[0]; i <= x[n - 1]; i += delta)
{
writeFitData.WriteLine("{0:f2}\t{1}", i, Exp(fit.eval(i)));
}
// Restore lambda to original value
fit.c[1] += dlambda;
// Lower boundary - lowest constant with fastest decay
writeFitData.WriteLine();
writeFitData.WriteLine();
fit.c[0] += dlna;
fit.c[1] += dlambda;
for (double i = x[0]; i <= x[n - 1]; i += delta)
{
writeFitData.WriteLine("{0:f2}\t{1}", i, Exp(fit.eval(i)));
}
// Upper boundary - highest constant with slowest decay
writeFitData.WriteLine();
writeFitData.WriteLine();
fit.c[0] -= 2 * dlna;
fit.c[1] -= 2 * dlambda;
for (double i = x[0]; i <= x[n - 1]; i += delta)
{
writeFitData.WriteLine("{0:f2}\t{1}", i, Exp(fit.eval(i)));
}
writeFitData.Close();
}