public static void main(String[] args) throws IOException {
// generate the data (100 data points)
// GaussDataGen gdg = new GaussDataGen(100);
GaussDataGen gdg = new GaussDataGen(DemoGaussSim.class.getResourceAsStream("GaussDataGen.txt"));
double[] pos = gdg.positions();
double[] meas = gdg.measurements();
double[] var = gdg.variances();
// create FCN function
GaussFcn theFCN = new GaussFcn(meas, pos, var);
// create initial starting values for parameters
double x = 0.;
double x2 = 0.;
double norm = 0.;
double dx = pos[1] - pos[0];
double area = 0.;
for (int i = 0; i < meas.length; i++) {
norm += meas[i];
x += (meas[i] * pos[i]);
x2 += (meas[i] * pos[i] * pos[i]);
area += dx * meas[i];
}
double mean = x / norm;
double rms2 = x2 / norm - mean * mean;
double rms = rms2 > 0. ? Math.sqrt(rms2) : 1.;
System.out.printf("%g %g %g\n", mean, rms, area);
{
// demonstrate minimal required interface for minimization
// create Minuit parameters without names
// starting values for parameters
double[] init_par = {mean, rms, area};
// starting values for initial uncertainties
double[] init_err = {0.1, 0.1, 0.1};
// create minimizer (default constructor)
MnMigrad migrad = new MnMigrad(theFCN, init_par, init_err);
// minimize
FunctionMinimum min = migrad.minimize();
// output
System.out.println("minimum: " + min);
}
{
// demonstrate standard minimization using MIGRAD
// create Minuit parameters with names
MnUserParameters upar = new MnUserParameters();
upar.add("mean", mean, 0.1);
upar.add("sigma", rms, 0.1);
upar.add("area", area, 0.1);
// create MIGRAD minimizer
MnMigrad migrad = new MnMigrad(theFCN, upar);
// minimize
FunctionMinimum min = migrad.minimize();
// output
System.out.println("minimum: " + min);
}
{
// demonstrate full interaction with parameters over subsequent
// minimizations
// create Minuit parameters with names
MnUserParameters upar = new MnUserParameters();
upar.add("mean", mean, 0.1);
upar.add("sigma", rms, 0.1);
upar.add("area", area, 0.1);
// access parameter by name to set limits...
upar.setLimits("mean", mean - 0.01, mean + 0.01);
// ... or access parameter by index
upar.setLimits(1, rms - 0.1, rms + 0.1);
// create Migrad minimizer
MnMigrad migrad = new MnMigrad(theFCN, upar);
// fix a parameter...
migrad.fix("mean");
// ... and minimize
FunctionMinimum min = migrad.minimize();
// output
System.out.println("minimum: " + min);
// release a parameter...
migrad.release("mean");
// ... and fix another one
migrad.fix(1);
// and minimize again
FunctionMinimum min1 = migrad.minimize();
// output
System.out.println("minimum: " + min1);
// release the parameter...
migrad.release(1);
// ... and minimize with all three parameters (still with limits!)
FunctionMinimum min2 = migrad.minimize();
// output
System.out.println("minimum: " + min2);
// remove all limits on parameters...
migrad.removeLimits("mean");
migrad.removeLimits("sigma");
// ... and minimize again with all three parameters (now without limits!)
FunctionMinimum min3 = migrad.minimize();
// output
System.out.println("minimum: " + min3);
}
{
// test single sided limits
MnUserParameters upar = new MnUserParameters();
upar.add("mean", mean, 0.1);
upar.add("sigma", rms - 1., 0.1);
upar.add("area", area, 0.1);
// test lower limits
upar.setLowerLimit("mean", mean - 0.01);
// test upper limits
upar.setUpperLimit("sigma", rms - 0.5);
// create MIGRAD minimizer
MnMigrad migrad = new MnMigrad(theFCN, upar);
// ... and minimize
FunctionMinimum min = migrad.minimize();
System.out.println("test lower limit minimim= " + min);
}
{
// demonstrate MINOS error analysis
// create Minuit parameters with names
MnUserParameters upar = new MnUserParameters();
upar.add("mean", mean, 0.1);
upar.add("sigma", rms, 0.1);
upar.add("area", area, 0.1);
// create Migrad minimizer
MnMigrad migrad = new MnMigrad(theFCN, upar);
// minimize
FunctionMinimum min = migrad.minimize();
// create MINOS error factory
MnMinos minos = new MnMinos(theFCN, min);
{
// 1-sigma MINOS errors (minimal interface)
// output
System.out.println("1-sigma minos errors: ");
System.out.printf(
"par0: %g %g %g\n", min.userState().value("mean"), minos.lower(0), minos.upper(0));
System.out.printf(
"par1: %g %g %g\n", min.userState().value(1), minos.lower(1), minos.upper(1));
System.out.printf(
"par2: %g %g %g\n", min.userState().value("area"), minos.lower(2), minos.upper(2));
}
{
// 2-sigma MINOS errors (rich interface)
MinosError e0 = minos.minos(0, 4.);
MinosError e1 = minos.minos(1, 4.);
MinosError e2 = minos.minos(2, 4.);
// output
System.out.println("2-sigma minos errors: ");
System.out.println(e0);
System.out.println(e1);
System.out.println(e2);
}
}
{
// demonstrate how to use the CONTOURs
// create Minuit parameters with names
MnUserParameters upar = new MnUserParameters();
upar.add("mean", mean, 0.1);
upar.add("sigma", rms, 0.1);
upar.add("area", area, 0.1);
// create Migrad minimizer
MnMigrad migrad = new MnMigrad(theFCN, upar);
// minimize
FunctionMinimum min = migrad.minimize();
// create contours factory with FCN and minimum
MnContours contours = new MnContours(theFCN, min);
// 70% confidence level for 2 parameters contour around the minimum
// (minimal interface)
List<Point> cont = contours.points(0, 1, 2.41, 20);
// 95% confidence level for 2 parameters contour
// (rich interface)
ContoursError cont4 = contours.contour(0, 1, 5.99, 20);
// plot the contours
MnPlot plot = new MnPlot();
cont.addAll(cont4.points());
plot.plot(min.userState().value("mean"), min.userState().value("sigma"), cont);
// print out one contour
System.out.println(cont4);
}
}
public void testPaul4Chi2() {
// create Chi2 FCN function
PaulTest4.PowerLawChi2FCN theFCN = new PaulTest4.PowerLawChi2FCN(m, p, v);
MnUserParameters upar = new MnUserParameters();
upar.add("p0", -2.3, 0.2);
upar.add("p1", 1100., 10.);
MnMigrad migrad = new MnMigrad(theFCN, upar);
FunctionMinimum min = migrad.minimize();
if (!min.isValid()) {
migrad = new MnMigrad(theFCN, upar, 2);
min = migrad.minimize();
}
assertTrue(min.isValid());
assertEquals(102, min.nfcn());
assertEquals(95.243, min.fval(), 1e-3);
assertEquals(3.7209e-11, min.edm(), 1e-15);
assertEquals(-2.10019, min.userParameters().value(0), 1e-5);
assertEquals(999.225, min.userParameters().value(1), 1e-3);
assertEquals(0.0001592, min.userParameters().error(0), 1e-7);
assertEquals(0.8073, min.userParameters().error(1), 1e-4);
assertEquals(2.53567e-08, min.userCovariance().get(0, 0), 1e-13);
assertEquals(0.000127332, min.userCovariance().get(1, 0), 1e-9);
assertEquals(0.651708, min.userCovariance().get(1, 1), 1e-6);
}
public void testPaul4LogLike() {
// create LogLikelihood FCN function
PaulTest4.PowerLawLogLikeFCN theFCN = new PaulTest4.PowerLawLogLikeFCN(m, p);
MnUserParameters upar = new MnUserParameters();
upar.add("p0", -2.1, 0.2);
upar.add("p1", 1000., 10.);
MnMigrad migrad = new MnMigrad(theFCN, upar);
migrad.setErrorDef(0.5);
FunctionMinimum min = migrad.minimize();
if (!min.isValid()) {
// try with higher strategy
migrad = new MnMigrad(theFCN, upar, 2);
min = migrad.minimize();
}
assertTrue(min.isValid());
assertEquals(63, min.nfcn());
assertEquals(-1.33678e+09, min.fval(), 1e4);
assertEquals(0.0170964, min.edm(), 1e-4);
assertEquals(-2.10016, min.userParameters().value(0), 1e-5);
assertEquals(999.394, min.userParameters().value(1), 1e-3);
assertEquals(0.0001488, min.userParameters().error(0), 1e-7);
assertEquals(0.7544, min.userParameters().error(1), 1e-4);
assertEquals(2.21365e-08, min.userCovariance().get(0, 0), 1e-13);
assertEquals(0.000111025, min.userCovariance().get(1, 0), 1e-9);
assertEquals(0.569138, min.userCovariance().get(1, 1), 1e-6);
}
public void testPaul4Simplex() {
PaulTest4.PowerLawChi2FCN chi2 = new PaulTest4.PowerLawChi2FCN(m, p, v);
PaulTest4.PowerLawLogLikeFCN mlh = new PaulTest4.PowerLawLogLikeFCN(m, p);
MnUserParameters upar;
double[] par = {-2.3, 1100.};
double[] err = {1., 1.};
MnSimplex simplex = new MnSimplex(chi2, par, err);
FunctionMinimum min = simplex.minimize();
assertTrue(min.isValid());
assertEquals(105, min.nfcn());
assertEquals(95.2506, min.fval(), 1e-4);
assertEquals(0.0286894, min.edm(), 1e-7);
assertEquals(-2.10018, min.userParameters().value(0), 1e-5);
assertEquals(999.286, min.userParameters().value(1), 1e-3);
assertEquals(0.0001122, min.userParameters().error(0), 1e-7);
assertEquals(0.7701, min.userParameters().error(1), 1e-4);
MnSimplex simplex2 = new MnSimplex(mlh, par, err);
simplex2.setErrorDef(0.5);
min = simplex2.minimize();
assertTrue(min.isValid());
assertEquals(84, min.nfcn());
assertEquals(-1.337e+09, min.fval(), 1e6);
assertEquals(0.03377, min.edm(), 1e-5);
assertEquals(-2.10018, min.userParameters().value(0), 1e-5);
assertEquals(999.279, min.userParameters().value(1), 1e-3);
assertEquals(0.0001793, min.userParameters().error(0), 1e-7);
assertEquals(0.7549, min.userParameters().error(1), 1e-4);
}