protected void out(double[] y) {
String s, blanks, blanksp, blanksm;
blanksp = " ";
blanksm = " ";
int ny = y.length;
int nlines = ny / 5;
int nrest = ny % 5;
for (int i = 0; i < nlines; i++) {
s = "";
for (int j = 0; j < 5; j++) {
int k = i * 5 + j;
if (y[k] >= 0.) blanks = blanksp;
else blanks = blanksm;
s = s + blanks + numForm.format(y[k]);
}
df.writeLine(s);
}
if (nrest > 0) {
s = "";
for (int j = 0; j < nrest; j++) {
int k = nlines * 5 + j;
if (y[k] >= 0.) blanks = blanksp;
else blanks = blanksm;
s = s + blanks + numForm.format(y[k]);
}
df.writeLine(s);
}
}
protected void compute() {
nny = (int) ni[0].parseInput();
df.writeLine("Number of events is: n = " + nny);
y = DatanRandom.standardNormal(nny);
out(y);
mllg = new MinLogLikeGauss(y);
x0 = new DatanVector(2);
x0.setElement(0, 1.);
x0.setElement(1, 2.);
MinSim ms = new MinSim(x0, mllg);
x = ms.getMinPosition();
fcont = ms.getMinimum();
df.writeLine("Minimization with MinSim yields x = ");
df.writeLine(x.toString());
// covariance matrix
MinCov mc = new MinCov(x, mllg);
cx = mc.getCovarianceMatrix(1.);
df.writeLine("Covariance Matrix cx = ");
df.writeLine(cx.toString());
// asymmetric errors
fcont = fcont + 0.5;
MinAsy ma = new MinAsy(x, cx, mllg);
dxasy = ma.getAsymmetricErrors(fcont);
DatanMatrix as = new DatanMatrix(dxasy);
df.writeLine("Asymmetic errors:");
df.writeLine(as.toString());
df.writeLine("ma.hasConverged() = " + ma.hasConverged());
plotScatterDiagram();
plotParameterPlane();
}
public S3Lsq() {
String s = "Data fitted to power law (nonlinear case)";
df = new DatanFrame(getClass().getName(), s);
// parameter input
AuxJInputGroup ig = new AuxJInputGroup("Parameter input", "");
JLabel errorLabel = new JLabel();
ni[0] = new AuxJNumberInput("n", "number of data points (>=3)", errorLabel);
ni[0].setProperties("n", true, 3);
ni[0].setNumberInTextField(20);
ig.add(ni[0]);
ni[1] = new AuxJNumberInput("t_0", "first value of controlled variable (>=0)", errorLabel);
ni[1].setProperties("t_0", false, 0.);
ni[1].setNumberInTextField(0);
ig.add(ni[1]);
ni[2] = new AuxJNumberInput("delta_t", "step width of controlled variable (>=0)", errorLabel);
ni[2].setProperties("delta_t", false, 0.);
ni[2].setNumberInTextField(.1);
ig.add(ni[2]);
ni[3] = new AuxJNumberInput("x_1", "coefficient in front of exponential term (>0)", errorLabel);
ni[3].setProperties("x_1", false, .000001);
ni[3].setNumberInTextField(1.);
ig.add(ni[3]);
ni[4] = new AuxJNumberInput("x_2", "exponent (>=0)", errorLabel);
ni[4].setProperties("x_2", false, 0.);
ni[4].setNumberInTextField(2.);
ig.add(ni[4]);
ni[5] = new AuxJNumberInput("sigma", "size of measurement errors (>0)", errorLabel);
ni[5].setProperties("sigma", false, 0.00001);
ni[5].setNumberInTextField(.2);
ig.add(ni[5]);
df.add(ig);
df.add(errorLabel);
JButton goButton = new JButton("Go");
GoButtonListener gl = new GoButtonListener();
goButton.addActionListener(gl);
df.add(goButton);
df.pack();
df.toFront();
}
public E3Min() {
numForm = NumberFormat.getNumberInstance(Locale.US);
numForm.setMaximumFractionDigits(12);
numForm.setMinimumFractionDigits(12);
String s =
"Example demonstrating the use of class MinAsy by fitting a Gaussian to small sample"
+ " and determining the asymmetric errors of parameters by MinAsy";
df = new DatanFrame(getClass().getName(), s);
AuxJInputGroup ig = new AuxJInputGroup("Enter number N of events (>= 2, <= 10000)", "");
JLabel errorLabel = new JLabel();
ni[0] = new AuxJNumberInput("N", "number of events", errorLabel);
ig.add(ni[0]);
ni[0].setProperties("N", true);
ni[0].setMinimum(2);
ni[0].setMaximum(10000);
ni[0].setNumberInTextField(10);
df.add(ig);
df.add(errorLabel);
JButton goButton = new JButton("Go");
GoButtonListener gl = new GoButtonListener();
goButton.addActionListener(gl);
df.add(goButton);
df.repaint();
}
protected void compute() {
n = (int) ni[0].parseInput();
t0 = ni[1].parseInput();
deltat = ni[2].parseInput();
x1 = ni[3].parseInput();
x2 = ni[4].parseInput();
sigma = ni[5].parseInput();
// generate data points
t = new DatanVector(n);
y = new DatanVector(n);
dy = new DatanVector(n);
rand = DatanRandom.standardNormal(n);
for (int i = 0; i < n; i++) {
t.setElement(i, t0 + (double) i * deltat);
y.setElement(i, x1 * Math.pow(t.getElement(i), x2) + sigma * rand[i]);
dy.setElement(i, sigma);
}
// find 1st approximation of unknowns by method of log-log plot
tlog = new double[n];
ylog = new double[n];
dellog = new double[n];
int npos = 0;
for (int i = 0; i < n; i++) {
if (t.getElement(i) > 0. && y.getElement(i) > 0.) {
tlog[npos] = Math.log(t.getElement(i));
ylog[npos] = Math.log(y.getElement(i));
dellog[npos] = 1.;
npos++;
}
}
DatanVector vtlog = new DatanVector(npos);
DatanVector vylog = new DatanVector(npos);
DatanVector vdellog = new DatanVector(npos);
for (int j = 0; j < npos; j++) {
vtlog.setElement(j, tlog[j]);
vylog.setElement(j, ylog[j]);
vdellog.setElement(j, dellog[j]);
}
LsqPol lp = new LsqPol(vtlog, vylog, vdellog, 2);
x = lp.getResult();
x.setElement(0, Math.exp(x.getElement(0)));
df.writeLine(" x = " + x.toString());
// perform fit
int[] list = {1, 1};
powerlaw = new Powerlaw();
LsqNon ln = new LsqNon(t, y, dy, x, list, powerlaw);
x = ln.getResult();
x1 = x.getElement(0);
x2 = x.getElement(1);
cov = ln.getCovarianceMatrix();
delx1 = Math.sqrt(cov.getElement(0, 0));
delx2 = Math.sqrt(cov.getElement(1, 1));
rho = cov.getElement(1, 0) / (delx1 * delx2);
m = ln.getChiSquare();
p = 1. - StatFunct.cumulativeChiSquared(m, n - 1);
// curve of fitted exponential
xpl = new double[1001];
ypl = new double[1001];
dpl = (double) (n - 1) * deltat / 1000.;
for (int i = 0; i < 1001; i++) {
xpl[i] = t0 + (double) i * dpl;
ypl[i] = x1 * Math.pow(xpl[i], x2);
}
// prepare data points for plotting
datx = new double[n];
daty = new double[n];
datsx = new double[n];
datsy = new double[n];
datrho = new double[n];
for (int i = 0; i < n; i++) {
datx[i] = t.getElement(i);
daty[i] = y.getElement(i);
datsx[i] = 0.;
datsy[i] = dy.getElement(i);
datrho[i] = 0.;
}
// display data and fitted curve
caption =
"x_1#="
+ String.format(Locale.US, "%5.2f", x1)
+ ", x_2#="
+ String.format(Locale.US, "%5.2f", x2)
+ ", &D@x_1#="
+ String.format(Locale.US, "%5.2f", delx1)
+ ", &D@x_2#="
+ String.format(Locale.US, "%5.2f", delx2)
+ ", &r@="
+ String.format(Locale.US, "%5.2f", rho)
+ ", M="
+ String.format(Locale.US, "%5.2f", m)
+ ", P="
+ String.format(Locale.US, "%6.4f", p);
new GraphicsWithDataPointsAndPolyline(
getClass().getName(),
"",
xpl,
ypl,
1,
.3,
datx,
daty,
datsx,
datsy,
datrho,
"t",
"y",
caption);
}