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();
}
private void computeMatrixOfDerivatives() {
double del, der, fp, fm, arg, sav;
int i2, iy;
fp = 0.;
fm = 0.;
for (int im = 0; im < m; im++) {
i2 = -1;
for (int il = 0; il < n + r; il++) {
if (il < r) {
if (list[il] != 0) {
i2++;
sav = x.getElement(il);
arg = Math.abs(sav);
if (arg < CUT) arg = CUT;
del = DELTA * arg;
x.setElement(il, sav + del);
fp = uf.getValue(y, x, im);
x.setElement(il, sav - del);
fm = uf.getValue(y, x, im);
der = (fp - fm) / (del + del);
e.setElement(im, i2, der);
x.setElement(il, sav);
}
} else {
i2++;
iy = il - r;
sav = y.getElement(iy);
arg = Math.abs(sav);
if (arg < CUT) arg = CUT;
del = DELTA * arg;
y.setElement(iy, sav + del);
fp = uf.getValue(y, x, im);
y.setElement(iy, sav - del);
fm = uf.getValue(y, x, im);
der = (fp - fm) / (del + del);
e.setElement(im, i2, der);
y.setElement(iy, sav);
}
}
}
}
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();
}
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();
}
/**
* @param y vector of measurements.
* @param cy covaariance matrix of measurements.
* @param x vector of first approximations of unknowns.
* @param list array containing the elements of a list specifying which of the n variables are
* fixed (list element = 0) and which are adjustable (list element = 1). m number of constaint
* equations
* @param uf user function which must be an extension of the abstract class DatanUserFunction.
*/
public LsqGen(
DatanVector y, DatanMatrix cy, DatanVector x, int[] list, int m, DatanUserFunction uf) {
this.y = y;
this.cy = cy;
this.x = x;
this.list = list;
this.m = m;
this.uf = uf;
n = y.getNumberOfElements();
r = list.length;
nred = 0;
for (int i = 0; i < r; i++) {
if (list[i] == 1) nred++;
}
l = n + nred;
t = new DatanVector(l);
f = new DatanMatrix(cy);
f.choleskyInversion();
fy = f.choleskyDecomposition();
mfvec = new DatanVector(1);
ok = new boolean[1];
mf = 0.;
nstep = 100;
d = new DatanVector(m);
loop:
for (int istep = 0; istep < nstep; istep++) {
mflast = mf;
f = new DatanMatrix(l, l);
f.putSubmatrix(nred, nred, fy);
e = new DatanMatrix(m, l);
computeMatrixOfDerivatives();
for (int k = 0; k < m; k++) {
d.setElement(k, -uf.getValue(y, x, k));
}
b = f.choleskyMultiply(t);
b = b.multiply(-1.);
u = f.leastSquaresWithConstraints(b, e, d, mfvec, 0., ok);
converged = ok[0];
if (!converged) break loop;
mf = mfvec.getElement(0);
if (nred > 0) {
// update x
int ired = -1;
for (int i = 0; i < r; i++) {
if (list[i] != 0) {
ired++;
x.setElement(i, x.getElement(i) + u.getElement(ired));
}
}
}
// update y and t
for (int i = 0; i < n; i++) {
y.setElement(i, y.getElement(i) + u.getElement(i + nred));
t.setElement(i + nred, t.getElement(i + nred) + u.getElement(i + nred));
}
// test for convergence
if (istep > 0 && Math.abs(mf - mflast) < mf * EPSILON + T) break loop;
}
if (converged) {
computeMatrixOfDerivatives();
a = e.getSubmatrix(m, n, 0, nred);
help = cy.multiplyWithTransposed(a);
gb = a.multiply(help);
gb.choleskyInversion();
if (nred > 0) {
help2 = e.getSubmatrix(m, nred, 0, 0);
help3 = help2.multiplyTransposedWith(gb);
cx = help3.multiply(help2);
cx.choleskyInversion();
// cx contains covariance matrx of unknowns
} else {
cx = new DatanMatrix(1, 1);
// for nred ==0 the matrix cx is set to be the (1 x 1) zero matrix
}
a = e.getSubmatrix(m, n, 0, nred);
help = a.multiply(cy);
help2 = gb.multiply(a.multiply(cy));
help3 = help.multiplyTransposedWith(help2);
cyimproved = cy.sub(help3);
// cyimproved contains covariance matrix of "improved" measurements
}
}
/**
* @param y data
* @param k parameter giving the length 2 * k + 1 of the averaging interval
* @param l oder of the averaging polynomial
* @param p probability defining confidence limits
*/
public TimeSeries(double[] y, int k, int l, double p) {
this.y = y;
this.k = k;
this.l = l;
this.p = p;
n = y.length;
eta = new double[n + 2 * k];
coneta = new double[n + 2 * k];
// quantile of Student's distribution
pprime = 0.5 * (p + 1.);
nf = 2 * k - l;
talpha = StatFunct.quantileStudent(pprime, nf);
// compute matrices depending on k and l
k21 = 2 * k + 1;
l1 = l + 1;
a = new DatanMatrix(k21, l1);
for (int i = 0; i < k21; i++) {
for (int j = 0; j < l1; j++) {
if (j == 0) a.setElement(i, j, -1.);
else a.setElement(i, j, a.getElement(i, j - 1) * (double) (i - k));
}
}
ata1 = a.multiplyTransposedWith(a);
ata1.choleskyInversion();
ata1at = ata1.multiplyWithTransposed(a);
ata1at = ata1at.multiply(-1.);
// moving averages and confidence limits for inner part
ymat = new DatanMatrix(y);
for (int i = 2 * k; i < n; i++) {
ytmp = ymat.getSubmatrix(k21, 1, i - 2 * k, 0);
x = ata1at.multiply(ytmp);
eta[i] = x.getElement(0, 0);
etatmp = a.multiply(x);
etatmp = etatmp.add(ytmp);
sy2 = etatmp.multiplyTransposedWith(etatmp);
double s = sy2.getElement(0, 0) / (double) nf;
double a0 = Math.sqrt(Math.abs(ata1.getElement(0, 0)));
coneta[i] = a0 * Math.sqrt(s) * talpha;
// moving averages and confidence limits for end sections
if (i == 2 * k || i == n - 1) {
tt = new double[l + 1];
if (i == 2 * k) {
iadd = 2 * k;
is = -1;
} else {
iadd = n - 1;
is = 1;
}
for (int i1 = 1; i1 <= 2 * k; i1++) {
j = is * i1;
for (int i2 = 0; i2 < l + 1; i2++) {
for (int i3 = 0; i3 <= i2; i3++) {
if (i3 == 0) tt[i2] = 1.;
else tt[i2] = tt[i2] * (double) j;
}
}
tmat = new DatanMatrix(tt);
seta2 = tmat.multiplyTransposedWith(ata1.multiply(tmat));
double se2 = s * seta2.getElement(0, 0);
etai = tmat.multiplyTransposedWith(x);
eta[iadd + j] = etai.getElement(0, 0);
coneta[iadd + j] = Math.sqrt(Math.abs(se2)) * talpha;
}
}
}
}
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);
}
