public void setXY(double x, double y) {
// not validated
// x and y between -1 and 1
double sigmoidSteepness, sigmoidZero, baseLength;
double sensitivity =
1.1; // evaluated with set to 1.1: a sensitivity of 1 means the complete space of the button
// is used. 2 means only the middle part is used, making it more sensitive and more
// easy to get to extreme arousal (from a CHI perspective).
if (!down) {
p = x * sensitivity;
d = y * sensitivity;
baseLength = Math.max(Math.abs(p), Math.abs(d)); // MAX (P, D) base
// baseLength=Math.sqrt(Math.pow(p,2)+Math.pow(d,2))/Math.sqrt(2.0); //euclid P,D base
// now do the mapping to arousal.
// Arousal is controlled simple by using a Sigmoid function based on length of PD vector
sigmoidSteepness = 11;
sigmoidZero = 8;
a = 2 / (1 + Math.exp(-(sigmoidSteepness * baseLength - sigmoidZero))) - 1;
a_base = a;
// Arousal is controlled simply by using a quadratic function that has 0,0,0 as middle point,
// then drops to -1, then to 1 based MIN (P,D) length (mimics better original linear)
// sigmoidSteepness=6;
// sigmoidZero=0.35;
// a=sigmoidSteepness*Math.pow(Math.max(Math.abs(p),Math.abs(d))-sigmoidZero, 2)-1;
p = (p > 1 ? 1 : (p < -1 ? -1 : p));
d = (d > 1 ? 1 : (d < -1 ? -1 : d));
a = (a > 1 ? 1 : (a < -1 ? -1 : a));
} else {
double tmp_p, tmp_d;
tmp_p = x * sensitivity;
tmp_d = y * sensitivity;
baseLength = Math.max(Math.abs(tmp_p), Math.abs(tmp_d)); // MAX (P, D) base
// baseLength=Math.sqrt(Math.pow(p,2)+Math.pow(d,2))/Math.sqrt(2.0); //euclid P,D base
// now do the mapping to arousal.
// Arousal is controlled simple by using a Sigmoid function based on length of PD vector
sigmoidSteepness = 11;
sigmoidZero = 8;
// a=a_base-(d-tmp_d)+2/(1+Math.exp(-(sigmoidSteepness*baseLength-sigmoidZero)))-1;
a = tmp_d;
// Arousal is controlled simply by using a quadratic function that has 0,0,0 as middle point,
// then drops to -1, then to 1 based MIN (P,D) length (mimics better original linear)
// sigmoidSteepness=6;
// sigmoidZero=0.35;
// a=sigmoidSteepness*Math.pow(Math.max(Math.abs(p),Math.abs(d))-sigmoidZero, 2)-1;
// p=(p>1?1:(p<-1?-1:p));
// d=(d>1?1:(d<-1?-1:d));
a = (a > 1 ? 1 : (a < -1 ? -1 : a));
}
}
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();
}
public double evaluate_1(double x) {
return (2 * x / x * x + 1)
- 0.4 * Math.exp(0.4 * x) * Math.cos(Math.PI * x)
+ Math.PI * Math.exp(0.4 * x) * Math.sin(Math.PI * x);
}
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 evaluate(double x) {
return Math.log(x * x + 1) - Math.exp(0.4 * x) * Math.cos(Math.PI * x);
}