public double getValue(DatanVector x) {
double result;
double a = sqrt2pi * x.getElement(1);
if (a < small) f = big;
else f = Math.log(a);
result = (double) y.length * f;
for (int i = 0; i < y.length; i++) {
f = Math.pow((y[i] - x.getElement(0)), 2.) / (2. * x.getElement(1) * x.getElement(1));
result += f;
}
return result;
}
protected void plotScatterDiagram() {
// plot sample as one dimensional scatter plot and Gaussian
double xmax = 5.;
double xmin = -5.;
DatanGraphics.openWorkstation(getClass().getName(), "E3Min_1.ps");
DatanGraphics.setFormat(0., 0.);
DatanGraphics.setWindowInComputingCoordinates(xmin, xmax, 0., .5);
DatanGraphics.setViewportInWorldCoordinates(-.15, .9, .16, .86);
DatanGraphics.setWindowInWorldCoordinates(-.414, 1., 0., 1.);
DatanGraphics.setBigClippingWindow();
DatanGraphics.chooseColor(2);
DatanGraphics.drawFrame();
DatanGraphics.drawScaleX("y");
DatanGraphics.drawScaleY("f(y)");
DatanGraphics.drawBoundary();
double xpl[] = new double[2];
double ypl[] = new double[2];
// plot scatter diagram
DatanGraphics.chooseColor(1);
for (int i = 0; i < y.length; i++) {
xpl[0] = y[i];
xpl[1] = y[i];
ypl[0] = 0.;
ypl[0] = .1;
DatanGraphics.drawPolyline(xpl, ypl);
}
// draw Gaussian corresponding to solution
int npl = 100;
xpl = new double[npl];
ypl = new double[npl];
double fact = 1. / (Math.sqrt(2. * Math.PI) * x.getElement(1));
double dpl = (xmax - xmin) / (double) (npl - 1);
for (int i = 0; i < npl; i++) {
xpl[i] = xmin + (double) i * dpl;
ypl[i] = fact * Math.exp(-.5 * Math.pow((xpl[i] - x.getElement(0)) / x.getElement(1), 2.));
}
DatanGraphics.chooseColor(5);
DatanGraphics.drawPolyline(xpl, ypl);
// draw caption
String sn = "N = " + nny;
numForm.setMaximumFractionDigits(3);
numForm.setMinimumFractionDigits(3);
String sx1 = ", x_1# = " + numForm.format(x.getElement(0));
String sx2 = ", x_2# = " + numForm.format(x.getElement(1));
String sdx1 = ", &D@x_1# = " + numForm.format(Math.sqrt(cx.getElement(0, 0)));
String sdx2 = ", &D@x_2# = " + numForm.format(Math.sqrt(cx.getElement(1, 1)));
caption = sn + sx1 + sx2 + sdx1 + sdx2;
DatanGraphics.setBigClippingWindow();
DatanGraphics.chooseColor(2);
DatanGraphics.drawCaption(1., caption);
DatanGraphics.closeWorkstation();
}
private class MinLogLikeGauss extends DatanUserFunction {
double[] y;
double sqrt2pi = Math.sqrt(2. * Math.PI);
double big = 1.E10, small = 1.E-10;
double f;
MinLogLikeGauss(double[] y) {
this.y = y;
}
public double getValue(DatanVector x) {
double result;
double a = sqrt2pi * x.getElement(1);
if (a < small) f = big;
else f = Math.log(a);
result = (double) y.length * f;
for (int i = 0; i < y.length; i++) {
f = Math.pow((y[i] - x.getElement(0)), 2.) / (2. * x.getElement(1) * x.getElement(1));
result += f;
}
return result;
}
}
protected void plotParameterPlane() {
double x1 = x.getElement(0);
double x2 = x.getElement(1);
double dx1 = Math.sqrt(cx.getElement(0, 0));
double dx2 = Math.sqrt(cx.getElement(1, 1));
double rho = (cx.getElement(1, 0)) / (dx1 * dx2);
// prepare size of plot
double xmin = x1 - 2. * dx1;
double xmax = x1 + 2. * dx1;
double ymin = x2 - 2. * dx2;
double ymax = x2 + 2. * dx2;
DatanGraphics.openWorkstation(getClass().getName(), "E3Min_2.ps");
DatanGraphics.setFormat(0., 0.);
DatanGraphics.setWindowInComputingCoordinates(xmin, xmax, ymin, ymax);
DatanGraphics.setViewportInWorldCoordinates(.2, .9, .16, .86);
DatanGraphics.setWindowInWorldCoordinates(-.414, 1., 0., 1.);
DatanGraphics.setBigClippingWindow();
DatanGraphics.chooseColor(2);
DatanGraphics.drawFrame();
DatanGraphics.drawScaleX("x_1");
DatanGraphics.drawScaleY("x_2");
DatanGraphics.drawBoundary();
DatanGraphics.chooseColor(5);
// draw data point with errors (and correlation)
DatanGraphics.drawDatapoint(1, 1., x1, x2, dx1, dx2, rho);
DatanGraphics.chooseColor(2);
DatanGraphics.drawCaption(1., caption);
// draw confidence contour
double fcont = mllg.getValue(x) + .5;
int nx = 100;
int ny = 100;
double dx = (xmax - xmin) / (int) nx;
double dy = (ymax - ymin) / (int) ny;
MinLogLikeGaussCont mllgc = new MinLogLikeGaussCont();
// System.out.println(" x = " + x.toString() + ", mllgc.getValue(x) = " +
// mllgc.getValue(x.getElement(0), x.getElement(1)));
DatanGraphics.setBigClippingWindow();
DatanGraphics.chooseColor(1);
DatanGraphics.drawContour(xmin, ymin, dx, dy, nx, ny, fcont, mllgc);
// draw asymmetric errors as horiyontal and vertical bars
DatanGraphics.chooseColor(3);
double[] xpl = new double[2];
double[] ypl = new double[2];
for (int i = 0; i < 2; i++) {
if (i == 0) xpl[0] = x1 - dxasy[0][0];
else xpl[0] = x1 + dxasy[0][1];
xpl[1] = xpl[0];
ypl[0] = ymin;
ypl[1] = ymax;
DatanGraphics.drawPolyline(xpl, ypl);
}
for (int i = 0; i < 2; i++) {
if (i == 0) ypl[0] = x2 - dxasy[1][0];
else ypl[0] = x2 + dxasy[1][1];
ypl[1] = ypl[0];
xpl[0] = xmin;
xpl[1] = xmax;
DatanGraphics.drawPolyline(xpl, ypl);
}
DatanGraphics.closeWorkstation();
}
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);
}
public double getValue(DatanVector x, double t) {
return x.getElement(0) * Math.pow(t, x.getElement(1));
}