/**
* @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;
}
}
}
}
