2,231 → 2,63 |
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public class FormulaProbe { |
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protected static double round(double value, int decimalPlace) { |
if (value < 0) { |
// positive value only. |
return -round(-value, decimalPlace); |
} |
private static final double PRECIOUS = 1000; |
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double power_of_ten = 1; |
// floating point arithmetic can be very tricky. |
// that's why I introduce a "fudge factor" |
double fudge_factor = 0.05; |
while (decimalPlace-- > 0) { |
power_of_ten *= 10.0d; |
fudge_factor /= 10.0d; |
/** |
* Kollissionsradius für 2D-Raum |
* |
* @param b |
* Korridorverkleinerungsfaktor |
* @param g |
* Raumverkleinerungsfaktor |
* @param w |
* Verhältnis des initialen Korridors mit dem Ursprungsraum |
* @return =0 für Berührung, <0 für Abstand, > für Kollission |
*/ |
private static double calc_2d(double b, double g, double w) { |
return (3 - g) / (1 - g) - g + Math.pow(g, 2) - 4 + 2 * w |
* (b / (1 - b) - b - Math.pow(b, 2) - 1); |
} |
return Math.round((value + fudge_factor) * power_of_ten) / power_of_ten; |
} |
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protected static String roundu(double value) { |
if (Math.abs(value) < 0.000000000000001) { |
// return "<0.000000000000001"; |
return "0"; |
/** |
* Kollissionsradius für 3D-Raum |
* |
* @param b |
* Korridorverkleinerungsfaktor |
* @param g |
* Raumverkleinerungsfaktor |
* @param w |
* Verhältnis des initialen Korridors mit dem Ursprungsraum |
* @return =0 für Berührung, <0 für Abstand, > für Kollission |
*/ |
private static double calc_3d(double b, double g, double w) { |
return w * b * (1 / (1 - b) - 1 - b - Math.pow(b, 2)) + 1 / (1 - g) - 1 |
- g - Math.pow(g, 2) - w; |
} |
return "" + round(value, 17); |
} |
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protected static boolean nearlyEqual(double a, double b) { |
return Math.abs(Math.abs(a) - Math.abs(b)) < 0.0000000000001; |
} |
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protected static double pow(double x, double y) { |
return Math.pow(x, y); |
} |
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protected static double sqrt(double x) { |
return Math.pow(x, 1.0 / 2.0); |
} |
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protected static double sqrt3(double x) { |
if (x >= 0) |
return Math.pow(x, 1.0 / 3.0); |
else |
return -Math.pow(-x, 1.0 / 3.0); |
} |
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// Seite 1 |
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public static double g_star() { |
return (double) (3 - sqrt(5)) / 2; |
} |
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public static double b_star() { |
return sqrt3(0.5 + sqrt(31.0 / 108.0)) |
+ sqrt3(0.5 - sqrt(31.0 / 108.0)); |
} |
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public static double w2(double b, double g) { |
if (nearlyEqual(b, b_star())) { |
System.out.println("FATAL: w2(b*) is Lambda!"); |
return Double.NaN; |
} |
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if (!((g <= g_star()) && (b > b_star()) || (g >= g_star()) |
&& (b < b_star()))) { |
System.out.println("w ist nicht definiert für b=" + b + "; g=" + g); |
return Double.NaN; |
} |
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return (double) ((1 - b) * (g + 1) * (pow(g, 2) - 3 * g + 1)) |
/ (2 * (1 - g) * (pow(b, 3) + b - 1)); |
} |
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public static double K2(double b, double g, double w) { |
// Vor Umstellung |
double res = (double) (3 - g) / (1 - g) - g + pow(g, 2) - 4 + 2 * w |
* (b / (1 - b) - b - pow(b, 2) - 1); |
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// Nach Umstellen |
double res2 = (double) (-(1 - b) * (g + 1) * (pow(g, 2) - 3 * g + 1) + 2 |
* w * (1 - g) * (pow(b, 3) + b - 1)) |
/ ((1 - b) * (1 - g)); |
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if (!nearlyEqual(res, res2)) { |
System.out.println("Fatal in K2"); |
System.out.println(res); |
System.out.println(res2); |
System.exit(1); |
} |
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return res; |
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} |
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// Seite 2 |
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public static double X(double b, double g) { |
if (nearlyEqual(b, b_star())) { |
System.out.println("FATAL: X(b,g) may not have b*"); |
return Double.NaN; |
} |
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return (g + 1) * (pow(g, 2) - 3 * g + 1) * (1 - b + pow(b, 4)) - 2 |
* pow(g, 3) * (pow(b, 3) + b - 1); |
} |
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public static double X_star(double b, double g) { |
return (g + 1) * (pow(g, 2) - 3 * g + 1) * (1 - b + pow(b, 4)) |
* (pow(b, 3) + b - 1) - 2 * pow(g, 3) |
* pow((pow(b, 3) + b - 1), 2); |
} |
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public static double w23(double b, double g) { |
if (nearlyEqual(b, b_star())) |
return w3(b, g); |
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boolean dec1 = nearlyEqual(X(b, g), 0.0); |
boolean dec2 = nearlyEqual(w3(b, g), w2(b, g)); |
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if (dec1 != dec2) { |
System.out.println("FATAL: X(b,g) ist falsch"); |
System.exit(1); |
return Double.NaN; |
} |
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if (!dec1) { |
System.out.println("w23 ist nicht definiert für b=" + b + "; g=" |
+ g); |
return Double.NaN; |
} else { |
return w3(b, g); // == w2(b,g) |
} |
} |
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public static double w3(double b, double g) { |
return (double) (pow(g, 3) * (1 - b)) / ((1 - g) * (1 - b + pow(b, 4))); |
} |
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public static double K3(double b, double g, double w) { |
// Vor Umstellung |
double res = (1.0 / (1 - g)) - g - pow(g, 2) - 1 - w + b * w |
* ((1.0 / (1 - b)) - b - pow(b, 2) - 1); |
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// Nach Umstellen |
double res2 = (double) ((1 - b) * (pow(g, 3)) - w * (1 - b) * (1 - g) + pow( |
b, 4) |
* w * (1 - g)) |
/ ((1 - b) * (1 - g)); |
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if (!nearlyEqual(res, res2)) { |
System.out.println("Fatal in K3"); |
System.out.println(res); |
System.out.println(res2); |
System.exit(1); |
} |
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return res; |
} |
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public static double w_star() { |
double res = (double) (pow(3 - sqrt(5), 3) * (1 - sqrt3(0.5 + sqrt(31.0 / 108.0)) - sqrt3(0.5 - sqrt(31.0 / 108.0)))) |
/ (8 * (1 - (double) (3 - sqrt(5)) / 2) * (1 |
- sqrt3(0.5 + sqrt(31.0 / 108.0)) |
- sqrt3(0.5 - sqrt(31.0 / 108.0)) + pow( |
sqrt3(0.5 + sqrt(31.0 / 108.0)) |
+ sqrt3(0.5 - sqrt(31.0 / 108.0)), 4))); |
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if (!nearlyEqual(res, w3(b_star(), g_star()))) { |
System.out.println("Self test for w_star() failed!"); |
System.exit(1); |
return Double.NaN; |
} |
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return res; |
} |
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/** |
* Findet 2D=0 Punkte |
* |
* @param args |
*/ |
public static void main(String[] args) { |
// vereinfachte K2 prüfen |
// vereinfachte K3 prüfen (???) |
// Die Formel w2 prüfen |
// Die Formel w3 prüfen |
// Die Formeln w2,3 numerisch prüfen: Ist 2D=3D=0? |
// für b=b* |
// für b!=b* |
// b* g* lambda prüfen: Ist 2D=3D=0 |
// b* g* [irgendwas] prüfen: ist 2D=0 und 3D!=0? |
for (int bi = 0; bi < PRECIOUS; bi++) { |
for (int gi = 0; gi < PRECIOUS; gi++) { |
for (int wi = 0; wi < PRECIOUS; wi++) { |
double b = (double) bi / PRECIOUS; |
double g = (double) gi / PRECIOUS; |
double w = (double) wi / PRECIOUS; |
double r2d = calc_2d(b, g, w); |
double r3d = calc_3d(b, g, w); |
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System.out.println("b* = " + roundu(b_star())); |
System.out.println("g* = " + roundu(g_star())); |
System.out.println("w* = " + roundu(w_star())); |
System.out.println("w23(b*, g*) = " + roundu(w23(b_star(), g_star()))); |
System.out.println("w3(b*, g*) = " + roundu(w3(b_star(), g_star()))); |
System.out.println("K2(.5 .5 .5) = " + roundu(K2(0.5, 0.5, 0.5))); |
System.out.println("K3(.5 .5 .5) = " + roundu(K3(0.5, 0.5, 0.5))); |
System.out.println("K2(0 .5 .375) = " + roundu(K2(0.0, 0.5, 0.375))); |
System.out.println("K3(0 .5 .375) = " + roundu(K3(0.0, 0.5, 0.375))); |
System.out.println("K2(b*, g*, 0.0) = " |
+ roundu(K2(b_star(), g_star(), 0.0))); |
System.out.println("K2(b*, g*, 0.1) = " |
+ roundu(K2(b_star(), g_star(), 0.1))); |
System.out.println("K2(b*, g*, 0.3) = " |
+ roundu(K2(b_star(), g_star(), 0.3))); |
System.out.println("K2(b*, g*, 0.5) = " |
+ roundu(K2(b_star(), g_star(), 0.5))); |
System.out.println("K2(b*, g*, 0.7) = " |
+ roundu(K2(b_star(), g_star(), 0.7))); |
System.out.println("K2(b*, g*, 0.99) = " |
+ roundu(K2(b_star(), g_star(), 0.99))); |
System.out.println("K2(b*, g*, w*) = " |
+ roundu(K2(b_star(), g_star(), w_star()))); |
System.out.println("K3(b*, g*, w*) = " |
+ roundu(K3(b_star(), g_star(), w_star()))); |
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// w23test(0.2, 0.7); |
w23test(b_star(), g_star()); |
if ((Math.abs(r2d) == 0) /* || (Math.abs(r3d) == 0) */) { |
System.out.println("(b=" + b + ", g=" + g + ", w=" + w |
+ ") = " + r2d + " (2D), " + r3d + " (3D)"); |
} |
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protected static void w23test(double b, double g) { |
double w = w23(b, g); |
System.out.println("w23(" + b + " " + g + ") = " + roundu(w)); |
System.out.println("K2(" + b + " " + g + " " + w + ") = " |
+ roundu(K2(b, g, w))); |
System.out.println("K3(" + b + " " + g + " " + w + ") = " |
+ roundu(K3(b, g, w))); |
} |
} |
} |
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System.out.println("Beendet"); |
} |
} |