package swcparts;
import java.util.Random;
public class GammaDist { //from "Algorithm from Numerical Recipes in C", Second Ed.
public double GetGammaAL(double a, double lambda, Random globalRand) {
if (Double.isInfinite(a) || Double.isInfinite(a)) {
System.out.println(
" Infinite input to GammaDist. a = " + a + " lambda = " + lambda);
System.exit( -9);
}
double aa = -1.0, aaa = -1.0, b = 0, c = 0, d = 0, e = 0, r = 0, s = 0, si = 0, ss = 0,
q0 = 0,
q1 = 0.0416666664, q2 = 0.0208333723, q3 = 0.0079849875,
q4 = 0.0015746717, q5 = -0.0003349403, q6 = 0.0003340332,
q7 = 0.0006053049, q8 = -0.0004701849, q9 = 0.0001710320,
a1 = 0.333333333, a2 = -0.249999949, a3 = 0.199999867,
a4 = -0.166677482, a5 = 0.142873973, a6 = -0.124385581,
a7 = 0.110368310, a8 = -0.112750886, a9 = 0.104089866,
e1 = 1.000000000, e2 = 0.499999994, e3 = 0.166666848,
e4 = 0.041664508, e5 = 0.008345522, e6 = 0.001353826,
e7 = 0.000247453;
double gds, p, q, t, sign_u, u, v, w, x;
double v1, v2, v12;
if (a <= 0.0) {
return ( -1.0);
}
if (lambda <= 0.0) {
return ( -1.0);
}
if (a < 1.0) { // CASE A: Acceptance rejection algorithm gs
b = 1.0 + 0.36788794412 * a; // Step 1
for (; ; ) {
p = b * globalRand.nextDouble();
if (p <= 1.0) { // Step 2. Case gds <= 1
gds = Math.exp(Math.log(p) / a);
if (Math.log(globalRand.nextDouble()) <= -gds) {
if (Double.isNaN(gds / lambda)) {
System.out.println(
"Gamma distribution function NaN error at point 1");
System.exit(9);
}
return (gds / lambda);
}
}
else { // Step 3. Case gds > 1
gds = -Math.log( (b - p) / a);
if (Math.log(globalRand.nextDouble()) <= ( (a - 1.0) * Math.log(gds))) {
if (Double.isNaN(gds / lambda)) {
System.out.println(
"Gamma distribution function NaN error at point 2");
System.exit(9);
}
return (gds / lambda);
}
}
}
}
else { // CASE B: Acceptance complement algorithm gd
if (a != aa) { // Step 1. Preparations
aa = a;
ss = a - 0.5;
s = Math.sqrt(ss);
d = 5.656854249 - 12.0 * s;
}
// Step 2. Normal deviate
do {
v1 = 2.0 * globalRand.nextDouble() - 1.0;
v2 = 2.0 * globalRand.nextDouble() - 1.0;
v12 = v1 * v1 + v2 * v2;
}
while (v12 > 1.0);
t = v1 * Math.sqrt( -2.0 * Math.log(v12) / v12);
x = s + 0.5 * t;
gds = x * x;
if (t >= 0.0) {
if (Double.isNaN(gds / lambda)) {
System.out.println("Gamma distribution function NaN error at point 3.");
System.exit(9);
}
return (gds / lambda); // Immediate acceptance
}
u = globalRand.nextDouble(); // Step 3. Uniform random number
if (d * u <= t * t * t) {
if (Double.isNaN(gds / lambda)) {
System.out.println("Gamma distribution function NaN error at point 4");
System.exit(9);
}
return (gds / lambda); // Squeeze acceptance
}
if (a != aaa) { // Step 4. Set-up for hat case
aaa = a;
r = 1.0 / a;
q0 = ( ( ( ( ( ( ( (q9 * r + q8) * r + q7) * r + q6) * r + q5) * r + q4) *
r + q3) * r + q2) * r + q1) * r;
if (a > 3.686) {
if (a > 13.022) {
b = 1.77;
si = 0.75;
c = 0.1515 / s;
}
else {
b = 1.654 + 0.0076 * ss;
si = 1.68 / s + 0.275;
c = 0.062 / s + 0.024;
}
}
else {
b = 0.463 + s - 0.178 * ss;
si = 1.235;
c = 0.195 / s - 0.079 + 0.016 * s;
}
}
if (x > 0.0) { // Step 5. Calculation of q
v = t / (s + s); // Step 6.
if (Math.abs(v) > 0.25) {
q = q0 - s * t + 0.25 * t * t + (ss + ss) * Math.log(1.0 + v);
}
else {
q = q0 + 0.5 * t * t * ( ( ( ( ( ( ( (a9 * v + a8) * v + a7) * v + a6) *
v + a5) * v + a4) * v + a3) * v + a2) * v + a1) * v;
} // Step 7. Quotient acceptance
if (Math.log(1.0 - u) <= q) {
if (Double.isNaN(gds / lambda)) {
System.out.println("Gamma distribution function NaN error at point 5");
System.exit(9);
}
return (gds / lambda);
}
}
for (; ; ) {
// Step 8. Double exponential deviate t
do {
e = -Math.log(globalRand.nextDouble());
u = globalRand.nextDouble();
u = u + u - 1.0;
sign_u = (u > 0) ? 1.0 : -1.0;
t = b + (e * si) * sign_u;
}
while (t <= -0.71874483771719); // Step 9. Rejection of t
v = t / (s + s); // Step 10. New q(t)
if (Math.abs(v) > 0.25) {
q = q0 - s * t + 0.25 * t * t + (ss + ss) * Math.log(1.0 + v);
}
else {
q = q0 + 0.5 * t * t * ( ( ( ( ( ( ( (a9 * v + a8) * v + a7) * v + a6) *
v + a5) * v + a4) * v + a3) * v + a2) * v + a1) * v;
}
if (q <= 0.0) {
continue; // Step 11.
}
if (q > 0.5) {
w = Math.exp(q) - 1.0;
}
else {
w = ( ( ( ( ( (e7 * q + e6) * q + e5) * q + e4) * q + e3) * q + e2) *
q + e1) * q;
} // Step 12. Hat acceptance
if (c * u * sign_u <= w * Math.exp(e - 0.5 * t * t)) {
x = s + 0.5 * t;
if (Double.isNaN(x * x / lambda)) {
System.out.println("Gamma distribution function NaN error at point 6");
System.exit(9);
}
return (x * x / lambda);
}
}
}
}
public double GetGammaAB(double alpha, double beta, Random globalRand) {
double lambda = 1 / beta;
return GetGammaAL(alpha, lambda, globalRand);
}
public double GetGammaMS(double mean, double stdev, Random globalRand) {
if (stdev <= 0) {
return mean;
}
double variance = stdev * stdev;
double lambda = 1 / (variance / mean);
double alpha = mean * mean / variance;
return GetGammaAL(alpha, lambda, globalRand);
}
public static int getCurveType(double[] realData, int length, Random globalRand) {
if (length <= 2) {
// System.out.println(" length less than 2");
return 1;
}
double[] uniformToTest = new double[length];
double[] gaussianToTest = new double[length];
double[] gammaToTest = new double[length];
GammaDist gd = new GammaDist();
double uniformDiff = 0;
double gammaDiff = 0;
double gaussianDiff = 0;
double tempDouble = 0;
double realMin = realData[1];
double realMax = 0;
double realStdev = 0;
double realMean = 0;
double realSymetricMax = 0;
double realSum = 0;
double diffSqSum = 0;
for (int i = length + 1; --i >= 1; ) { //for each array element
realSum += realData[i]; //find sum
if (realMax < realData[i]) { //find max
realMax = realData[i];
}
if (realMin > realData[i]) { //find min
realMin = realData[i];
}
}
//bubble sort real data
// for (int i = length + 1; --i >= 1; ) { //for each array element
//
// for (int j = 1; j < i; j++) {
// if (realData[j] > realData[j + 1]) {
// tempDouble = realData[j];
// realData[j] = realData[j + 1];
// realData[j + 1] = tempDouble;
// }
// }
// }
java.util.Arrays.sort(realData,1,length+1);
if (realMin == realMax) {
// System.out.println(" min = max");
return 1;
}
realMean = realSum / length;
if ( (realMin >= realMean) || (realMax <= realMean)) {
System.out.println(
"mean in function getCurveType is outside range, possible infinite loop. Min, Mean, Max: " +
realMin + " " + realMean + " " + realMax);
System.exit(11);
}
//find stdev of real data
for (int i = 1; i < length; i++) {
diffSqSum += ( (realData[i] - realMean) * (realData[i] - realMean));
}
if ( (diffSqSum == 0) || (length <= 2)) {
realStdev = 0;
}
else {
realStdev = java.lang.Math.sqrt(diffSqSum / (length - 1));
}
if (realStdev <= 0) {
// System.out.println(" stdev less than 0");
return 1;
}
realSymetricMax = ( (realMean * 2) - realMin);
//populate three new double arrays with sampled data, sort them
for (int i = 1; i < length; i++) {
//uniform
uniformToTest[i] = (globalRand.nextDouble() * (realSymetricMax - realMin) + realMin);
//gaussian
gaussianToTest[i] = realMin - 1;
while ( (gaussianToTest[i] < realMin) || (gaussianToTest[i] > realSymetricMax)) {
gaussianToTest[i] = (globalRand.nextGaussian() * realStdev) + realMean;
}
//gamma
gammaToTest[i] = realMin - 1;
while ( (gammaToTest[i] < realMin) || (gammaToTest[i] > realMax)) {
gammaToTest[i] = (gd.GetGammaMS(realMean, realStdev, globalRand));
}
}
//find least mean squares between real and sampled
for (int i = 1; i < length; i++) {
uniformDiff += ( (realData[i] - uniformToTest[i]) * (realData[i] - uniformToTest[i]));
gaussianDiff +=
( (realData[i] - gaussianToTest[i]) * (realData[i] - gaussianToTest[i]));
gammaDiff += ( (realData[i] - gammaToTest[i]) * (realData[i] - gammaToTest[i]));
}
//
//
//
//
//
//debugging
/* System.out.println();
System.out.println("///////// Uniform distribution //////////");
System.out.println();
for (int i = 1; i < length; i++) {
System.out.println(uniformToTest[i]);
}
System.out.println();
System.out.println("///////// Gaussian distribution //////////");
System.out.println();
for (int i = 1; i < length; i++) {
System.out.println(gaussianToTest[i]);
}
System.out.println();
System.out.println("///////// Gamma distribution //////////");
System.out.println();
for (int i = 1; i < length; i++) {
System.out.println(gammaToTest[i]);
}
*/ System.out.println("mean, stdev, min, max, uni diff, gaus diff, gamma diff: "+realMean+" "+realStdev+" "+realMin+" "+realMax+" "+uniformDiff+" "+gaussianDiff+" "+gammaDiff );
//
//
//
//
//
//
if (uniformDiff < gaussianDiff) {
if (uniformDiff < gammaDiff) {
return 1;
}
else {
return 3;
}
}
else if (gammaDiff < gaussianDiff) {
return 3;
}
else {
return 2;
}
}
//takes in the mean, and stdev so they don't have to be computed again
static public int getCurveType(double[] realData, int length, double realMean, double realStdev,
Random globalRand) {
if (length <= 2) {
return 1;
}
if (realStdev <= 0) {
return 1;
}
double[] uniformToTest = new double[length];
double[] gaussianToTest = new double[length];
double[] gammaToTest = new double[length];
GammaDist gd = new GammaDist();
double uniformDiff = 0;
double gammaDiff = 0;
double gaussianDiff = 0;
double tempDouble = 0;
double realMin = realData[1];
double realMax = 0;
// double realStdev = 0;
// double realMean = 0;
double realSymetricMax = 0;
double realSum = 0;
double diffSqSum = 0;
//bubble sort real data
for (int i = length + 1; --i >= 1; ) { //for each array element
// realSum += realData[i]; //find sum
if (realMax < realData[i]) { //find max
realMax = realData[i];
}
if (realMin > realData[i]) { //find min
realMin = realData[i];
}
for (int j = 1; j < i; j++) {
if (realData[j] > realData[j + 1]) {
tempDouble = realData[j];
realData[j] = realData[j + 1];
realData[j + 1] = tempDouble;
}
}
}
if (realMin == realMax) {
return 1;
}
if ( (realMin >= realMean) || (realMax <= realMean)) {
System.out.println(
"mean in function getCurveType is outside range, possible infinite loop. Min, Mean, Max: " +
realMin + " " + realMean + " " + realMax);
System.exit(11);
}
/*
realMean = realSum / length;
//find stdev of real data
for (int i = 1; i < length; i++) {
diffSqSum += ( (realData[i] - realMean) * (realData[i] - realMean));
}
if ( (diffSqSum == 0) || (length <= 2)) {
realStdev = 0;
}
else {
realStdev = java.lang.Math.sqrt(diffSqSum / (length - 1));
}
*/
realSymetricMax = ( (realMean * 2) - realMin);
//populate three new double arrays with sampled data, sort them
for (int i = 1; i < length; i++) {
//uniform
uniformToTest[i] = (globalRand.nextDouble() * (realSymetricMax - realMin) + realMin);
//gaussian
gaussianToTest[i] = realMin - 1;
while ( (gaussianToTest[i] < realMin) || (gaussianToTest[i] > realSymetricMax)) {
gaussianToTest[i] = (globalRand.nextGaussian() * realStdev) + realMean;
}
//gamma
gammaToTest[i] = realMin - 1;
while ( (gammaToTest[i] < realMin) || (gammaToTest[i] > realMax)) {
gammaToTest[i] = (gd.GetGammaMS(realMean, realStdev, globalRand));
}
}
//find least mean squares between real and sampled
for (int i = 1; i < length; i++) {
uniformDiff += ( (realData[i] - uniformToTest[i]) * (realData[i] - uniformToTest[i]));
gaussianDiff +=
( (realData[i] - gaussianToTest[i]) * (realData[i] - gaussianToTest[i]));
gammaDiff += ( (realData[i] - gammaToTest[i]) * (realData[i] - gammaToTest[i]));
}
if (uniformDiff < gaussianDiff) {
if (uniformDiff < gammaDiff) {
return 1;
}
else {
return 3;
}
}
else if (gammaDiff < gaussianDiff) {
return 3;
}
else {
return 2;
}
}
//sort ascending double array
//find mean of double array
//find stdev of double array
//find min of double array
//find max of double array
}