public static double findZero(FunctionModel f, double start, double eps) {
double[] bounds = findZeroBrackets(f, start);
double lower = bounds[0], upper = bounds[1];
double ly = f.eval(lower), uy = f.eval(upper);
// System.out.println(String.format("Zero: [%f, %f] (%f, %f)", lower, upper, ly, uy));
boolean lsign = ly < 0.0;
boolean usign = uy <= 0.0;
while (Math.abs(upper - lower) > eps) {
double middle = (upper + lower) / 2.0;
double my = f.eval(middle);
boolean msign = my < 0.0;
if (my == 0.0) {
return middle;
} else if (msign == lsign) {
lower = middle;
ly = my;
lsign = msign;
// System.out.println(String.format("\tU: [%f, %f] (%f, %f)", lower, upper, ly, uy));
} else {
upper = middle;
uy = my;
usign = msign;
// System.out.println(String.format("\tL: [%f, %f] (%f, %f)", lower, upper, ly, uy));
}
}
double v = (lower + upper) / 2.0;
// System.out.println(String.format("\t-> %f", v));
return v;
}
public static double[] findZeroBrackets(FunctionModel f, double start) {
double fstart = f.eval(start);
if (Double.isInfinite(fstart) || Double.isNaN(fstart)) {
throw new IllegalArgumentException(
String.format("Illegal start: %f (%f)", start, f.eval(start)));
}
boolean sign = fstart >= 0.0;
double lowerSpace = 1.0, upperSpace = 1.0;
double upper = start + upperSpace, lower = start - lowerSpace;
double pupper = start, plower = start;
double fupper = f.eval(upper), flower = f.eval(lower);
boolean usign = fupper >= 0.0, lsign = flower >= 0.0;
int iters = 0;
while ((isBad(fupper) || usign == sign) && (isBad(flower) || lsign == sign)) {
iters += 1;
if (isBad(fupper)) {
upperSpace /= 2.0;
upper -= upperSpace;
} else {
upperSpace *= 2.0;
upper += upperSpace;
}
fupper = f.eval(upper);
usign = fupper >= 0.0;
if (isBad(flower)) {
lowerSpace /= 2.0;
lower += lowerSpace;
} else {
lowerSpace *= 2.0;
lower -= lowerSpace;
}
flower = f.eval(lower);
lsign = flower >= 0.0;
}
if (usign != sign) {
// System.out.println(String.format("\n%f -> (%f, %f]", start, start, upper));
return new double[] {start, upper};
}
if (lsign != sign) {
// System.out.println(String.format("\n%f -> [%f, %f)", start, lower, start));
return new double[] {lower, start};
}
throw new IllegalArgumentException("Couldn't find zero brackets!");
}