/** Returns a random number from the distribution; bypasses the internal state. */
public int nextInt(double theMean) {
/**
* **************************************************************** * Poisson Distribution -
* Patchwork Rejection/Inversion * *
* ***************************************************************** * For parameter my < 10
* Tabulated Inversion is applied. * For my >= 10 Patchwork Rejection is employed: * The area
* below the histogram function f(x) is rearranged in * its body by certain point reflections.
* Within a large center * interval variates are sampled efficiently by rejection from * uniform
* hats. Rectangular immediate acceptance regions speed * up the generation. The remaining tails
* are covered by * exponential functions. * *
* ***************************************************************
*/
// RandomEngine gen =this.randomGenerator;
double my = theMean;
double t, g, my_k;
double gx, gy, px, py, e, x, xx, delta, v;
int sign;
// static double p,q,p0,pp[36];
// static long ll,m;
double u;
int k, i;
if (my < SWITCH_MEAN) { // CASE B: Inversion- start new table and calculate p0
if (my != my_old) {
my_old = my;
llll = 0;
p = Math.exp(-my);
q = p;
p0 = p;
// for (k=pp.length; --k >=0; ) pp[k] = 0;
}
m = (my > 1.0) ? (int) my : 1;
for (; ; ) {
u = random.nextDouble(); // gen.raw(); // Step U. Uniform sample
k = 0;
if (u <= p0) return (k);
if (llll != 0) { // Step T. Table comparison
i = (u > 0.458) ? Math.min(llll, m) : 1;
for (k = i; k <= llll; k++) if (u <= pp[k]) return (k);
if (llll == 35) continue;
}
for (k = llll + 1; k <= 35; k++) { // Step C. Creation of new prob.
p *= my / (double) k;
q += p;
pp[k] = q;
if (u <= q) {
llll = k;
return (k);
}
}
llll = 35;
}
} // end my < SWITCH_MEAN
else if (my < MEAN_MAX) { // CASE A: acceptance complement
// static double my_last = -1.0;
// static long int m, k2, k4, k1, k5;
// static double dl, dr, r1, r2, r4, r5, ll, lr, l_my, c_pm,
// f1, f2, f4, f5, p1, p2, p3, p4, p5, p6;
int Dk, X, Y;
double Ds, U, V, W;
m = (int) my;
if (my != my_last) { // set-up
my_last = my;
// approximate deviation of reflection points k2, k4 from my - 1/2
Ds = Math.sqrt(my + 0.25);
// mode m, reflection points k2 and k4, and points k1 and k5, which
// delimit the centre region of h(x)
k2 = (int) Math.ceil(my - 0.5 - Ds);
k4 = (int) (my - 0.5 + Ds);
k1 = k2 + k2 - m + 1;
k5 = k4 + k4 - m;
// range width of the critical left and right centre region
dl = (double) (k2 - k1);
dr = (double) (k5 - k4);
// recurrence constants r(k) = p(k)/p(k-1) at k = k1, k2, k4+1, k5+1
r1 = my / (double) k1;
r2 = my / (double) k2;
r4 = my / (double) (k4 + 1);
r5 = my / (double) (k5 + 1);
// reciprocal values of the scale parameters of expon. tail envelopes
ll = Math.log(r1); // expon. tail left
lr = -Math.log(r5); // expon. tail right
// Poisson constants, necessary for computing function values f(k)
l_my = Math.log(my);
c_pm = m * l_my - Arithmetic.logFactorial(m);
// function values f(k) = p(k)/p(m) at k = k2, k4, k1, k5
f2 = f(k2, l_my, c_pm);
f4 = f(k4, l_my, c_pm);
f1 = f(k1, l_my, c_pm);
f5 = f(k5, l_my, c_pm);
// area of the two centre and the two exponential tail regions
// area of the two immediate acceptance regions between k2, k4
p1 = f2 * (dl + 1.0); // immed. left
p2 = f2 * dl + p1; // centre left
p3 = f4 * (dr + 1.0) + p2; // immed. right
p4 = f4 * dr + p3; // centre right
p5 = f1 / ll + p4; // expon. tail left
p6 = f5 / lr + p5; // expon. tail right
} // end set-up
for (; ; ) {
// generate uniform number U -- U(0, p6)
// case distinction corresponding to U
if ((U = random.nextDouble() * p6) < p2) { // centre left
// immediate acceptance region R2 = [k2, m) *[0, f2), X = k2, ... m -1
if ((V = U - p1) < 0.0) return (k2 + (int) (U / f2));
// immediate acceptance region R1 = [k1, k2)*[0, f1), X = k1, ... k2-1
if ((W = V / dl) < f1) return (k1 + (int) (V / f1));
// computation of candidate X < k2, and its counterpart Y > k2
// either squeeze-acceptance of X or acceptance-rejection of Y
Dk = (int) (dl * random.nextDouble()) + 1;
if (W <= f2 - Dk * (f2 - f2 / r2)) { // quick accept of
return (k2 - Dk); // X = k2 - Dk
}
if ((V = f2 + f2 - W) < 1.0) { // quick reject of Y
Y = k2 + Dk;
if (V <= f2 + Dk * (1.0 - f2) / (dl + 1.0)) { // quick accept of
return (Y); // Y = k2 + Dk
}
if (V <= f(Y, l_my, c_pm)) return (Y); // final accept of Y
}
X = k2 - Dk;
} else if (U < p4) { // centre right
// immediate acceptance region R3 = [m, k4+1)*[0, f4), X = m, ... k4
if ((V = U - p3) < 0.0) return (k4 - (int) ((U - p2) / f4));
// immediate acceptance region R4 = [k4+1, k5+1)*[0, f5)
if ((W = V / dr) < f5) return (k5 - (int) (V / f5));
// computation of candidate X > k4, and its counterpart Y < k4
// either squeeze-acceptance of X or acceptance-rejection of Y
Dk = (int) (dr * random.nextDouble()) + 1;
if (W <= f4 - Dk * (f4 - f4 * r4)) { // quick accept of
return (k4 + Dk); // X = k4 + Dk
}
if ((V = f4 + f4 - W) < 1.0) { // quick reject of Y
Y = k4 - Dk;
if (V <= f4 + Dk * (1.0 - f4) / dr) { // quick accept of
return (Y); // Y = k4 - Dk
}
if (V <= f(Y, l_my, c_pm)) return (Y); // final accept of Y
}
X = k4 + Dk;
} else {
W = random.nextDouble();
if (U < p5) { // expon. tail left
Dk = (int) (1.0 - Math.log(W) / ll);
if ((X = k1 - Dk) < 0) continue; // 0 <= X <= k1 - 1
W *= (U - p4) * ll; // W -- U(0, h(x))
if (W <= f1 - Dk * (f1 - f1 / r1)) return (X); // quick accept of X
} else { // expon. tail right
Dk = (int) (1.0 - Math.log(W) / lr);
X = k5 + Dk; // X >= k5 + 1
W *= (U - p5) * lr; // W -- U(0, h(x))
if (W <= f5 - Dk * (f5 - f5 * r5)) return (X); // quick accept of X
}
}
// acceptance-rejection test of candidate X from the original area
// test, whether W <= f(k), with W = U*h(x) and U -- U(0, 1)
// log f(X) = (X - m)*log(my) - log X! + log m!
if (Math.log(W) <= X * l_my - Arithmetic.logFactorial(X) - c_pm) return (X);
}
} else { // mean is too large
return (int) my;
}
}
private static double f(int k, double l_nu, double c_pm) {
return Math.exp(k * l_nu - Arithmetic.logFactorial(k) - c_pm);
}