예제 #1
0
 /**
  * @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;
       }
     }
   }
 }
예제 #2
0
 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);
 }