/**
* @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);
}