/// <summary>
/// Efficiently computes a sorted random set of <tt>count</tt> elements from the interval <tt>[low,low+N-1]</tt>.
/// Since we are talking about a random set, no element will occur more than once.
///
/// <p>Running time is <tt>O(count)</tt>, on average. Space requirements are zero.
///
/// <p>Numbers are filled into the specified array starting at index <tt>fromIndex</tt> to the right.
/// The array is returned sorted ascending in the range filled with numbers.
///
/// <p><b>Random number generation:</b> By default uses <tt>MersenneTwister</tt>, a very strong random number generator, much better than <tt>java.util.Random</tt>.
/// You can also use other strong random number generators of Paul Houle's RngPack package.
/// For example, <tt>Ranecu</tt>, <tt>Ranmar</tt> and <tt>Ranlux</tt> are strong well analyzed research grade pseudo-random number generators with known periods.
/// </summary>
/// <param name="n">the total number of elements to choose (must be <tt>n >= 0</tt> and <tt>n <= N</tt>).</param>
/// <param name="N">the interval to choose random numbers from is <tt>[low,low+N-1]</tt>.</param>
/// <param name="count">the number of elements to be filled into <tt>values</tt> by this call (must be >= 0 and <=<tt>n</tt>). Normally, you will set <tt>count=n</tt>.</param>
/// <param name="low">the interval to choose random numbers from is <tt>[low,low+N-1]</tt>. Hint: If <tt>low==0</tt>, then draws random numbers from the interval <tt>[0,N-1]</tt>.</param>
/// <param name="values">the array into which the random numbers are to be filled; must have a length <tt>>= count+fromIndex</tt>.</param>
/// <param name="fromIndex">the first index within <tt>values</tt> to be filled with numbers (inclusive).</param>
/// <param name="randomGenerator">a random number generator. Set this parameter to <tt>null</tt> to use the default random number generator.</param>
protected static void SampleMethodA(long n, long N, int count, long low, long[] values, int fromIndex, RandomEngine randomGenerator)
{
double V, quot, Nreal, top;
long S;
long chosen = -1 + low;
top = N - n;
Nreal = N;
while (n >= 2 && count > 0)
{
V = randomGenerator.Raw();
S = 0;
quot = top / Nreal;
while (quot > V)
{
S++;
top--;
Nreal--;
quot = (quot * top) / Nreal;
}
chosen += S + 1;
values[fromIndex++] = chosen;
count--;
Nreal--;
n--;
}
if (count > 0)
{
// special case n==1
S = (long)(System.Math.Round(Nreal) * randomGenerator.Raw());
chosen += S + 1;
values[fromIndex] = chosen;
}
}
/// <summary>
/// Returns a random number from the distribution; bypasses the internal state.
/// </summary>
/// <param name="theMean"></param>
/// <returns></returns>
private int NextInt(double theMean)
{
/*
* Adapted from "Numerical Recipes in C".
*/
double xm = theMean;
double g = this.cached_g;
if (xm == -1.0)
{
return(0); // not defined
}
if (xm < SWITCH_MEAN)
{
int poisson = -1;
double product = 1;
do
{
poisson++;
product *= RandomGenerator.Raw();
} while (product >= g);
// bug in CLHEP 1.4.0: was "} while ( product > g );"
return(poisson);
}
else if (xm < MEAN_MAX)
{
double t;
double em;
double sq = this.cached_sq;
double alxm = this.cached_alxm;
RandomEngine rand = this.RandomGenerator;
do
{
double y;
do
{
y = System.Math.Tan(System.Math.PI * rand.Raw());
em = sq * y + xm;
} while (em < 0.0);
em = (double)(int)(em); // faster than em = System.Math.Floor(em); (em>=0.0)
t = 0.9 * (1.0 + y * y) * System.Math.Exp(em * alxm - LogGamma(em + 1.0) - g);
} while (rand.Raw() > t);
return((int)em);
}
else
{ // mean is too large
return((int)xm);
}
}
/// <summary>
/// Returns a random number from the standard Triangular distribution in (-1,1).
/// <p>
/// <b>Implementation:</b> Inversion method.
/// This is a port of <i>tra.c</i> from the <A HREF="http://www.cis.tu-graz.ac.at/stat/stadl/random.html">C-RAND / WIN-RAND</A> library.
/// <p>
/// </summary>
/// <param name="randomGenerator"></param>
/// <returns></returns>
public static double NextTriangular(RandomEngine randomGenerator)
{
/******************************************************************
* *
* Triangular Distribution - Inversion: x = +-(1-sqrt(u)) *
* *
******************************************************************
* *
* FUNCTION : - tra samples a random number from the *
* standard Triangular distribution in (-1,1) *
* SUBPROGRAM : - drand(seed) ..d (0,1)-Uniform generator with *
* unsigned long int *seedd *
* *
******************************************************************/
double u;
u = randomGenerator.Raw();
if (u <= 0.5)
{
return(System.Math.Sqrt(2.0 * u) - 1.0); /* -1 <= x <= 0 */
}
else
{
return(1.0 - System.Math.Sqrt(2.0 * (1.0 - u))); /* 0 <= x <= 1 */
}
}
/// <summary>
/// Returns a discrete geometric distributed random number; <A HREF="http://www.statsoft.com/textbook/glosf.html#Geometric Distribution">Definition</A>.
/// <p>
/// <i>p(k) = p * (1-p)^k</i> for <i> k >= 0</i>.
/// <p>
/// <b>Implementation:</b> Inversion method.
/// This is a port of <i>geo.c</i> from the <A HREF="http://www.cis.tu-graz.ac.at/stat/stadl/random.html">C-RAND / WIN-RAND</A> library.
/// <p>
/// </summary>
/// <param name="p">must satisfy <i>0 < p < 1</i>.</param>
/// <param name="randomGenerator"></param>
/// <returns></returns>
public static int NextGeometric(double p, RandomEngine randomGenerator)
{
/******************************************************************
* *
* Geometric Distribution - Inversion *
* *
******************************************************************
* *
* On generating random numbers of a discrete distribution by *
* Inversion normally sequential search is necessary, but in the *
* case of the Geometric distribution a direct transformation is *
* possible because of the special parallel to the continuous *
* Exponential distribution Exp(t): *
* X - Exp(t): G(x)=1-exp(-tx) *
* Geo(p): pk=G(k+1)-G(k)=exp(-tk)*(1-exp(-t)) *
* p=1-exp(-t) *
* A random number of the Geometric distribution Geo(p) is *
* obtained by k=(long int)x, where x is from Exp(t) with *
* parameter t=-log(1-p)d *
* *
******************************************************************
* *
* FUNCTION: - geo samples a random number from the Geometric *
* distribution with parameter 0<p<1d *
* SUBPROGRAMS: - drand(seed) ..d (0,1)-Uniform generator with *
* unsigned long int *seedd *
* *
******************************************************************/
double u = randomGenerator.Raw();
return((int)(System.Math.Log(u) / System.Math.Log(1.0 - p)));
}
/// <summary>
/// Returns a random number from the Burr III, IV, V, VI, IX, XII distributions.
/// <p>
/// <b>Implementation:</b> Inversion method.
/// This is a port of <i>burr2.c</i> from the <A HREF="http://www.cis.tu-graz.ac.at/stat/stadl/random.html">C-RAND / WIN-RAND</A> library.
/// C-RAND's implementation, in turn, is based upon
/// <p>
/// Ld Devroye (1986): Non-Uniform Random Variate Generation, Springer Verlag, New Yorkd
/// <p>
/// </summary>
/// <param name="r">must be > 0.</param>
/// <param name="k">must be > 0.</param>
/// <param name="nr">the number of the burr distribution (e.gd 3,4,5,6,9,12).</param>
/// <param name="randomGenerator"></param>
/// <returns></returns>
public static double NextBurr2(double r, double k, int nr, RandomEngine randomGenerator)
{
/******************************************************************
* *
* Burr III, IV, V, VI, IX, XII Distribution - Inversion *
* *
******************************************************************
* *
* FUNCTION : - burr2 samples a random number from one of the *
* Burr III, IV, V, VI, IX, XII distributions with *
* parameters r > 0 and k > 0, where the nod of *
* the distribution is indicated by a pointer *
* variabled *
* REFERENCE : - Ld Devroye (1986): Non-Uniform Random Variate *
* Generation, Springer Verlag, New Yorkd *
* SUBPROGRAM : - drand(seed) ..d (0,1)-Uniform generator with *
* unsigned long int *seedd *
* *
******************************************************************/
double y, u;
u = randomGenerator.Raw(); // U(0/1)
y = System.Math.Exp(-System.Math.Log(u) / r) - 1.0; // u^(-1/r) - 1
switch (nr)
{
case 3: // BURR III
return(System.Math.Exp(-System.Math.Log(y) / k)); // y^(-1/k)
case 4: // BURR IV
y = System.Math.Exp(k * System.Math.Log(y)) + 1.0; // y^k + 1
y = k / y;
return(y);
case 5: // BURR V
y = System.Math.Atan(-System.Math.Log(y / k)); // arctan[log(y/k)]
return(y);
case 6: // BURR VI
y = -System.Math.Log(y / k) / r;
y = System.Math.Log(y + System.Math.Sqrt(y * y + 1.0));
return(y);
case 9: // BURR IX
y = 1.0 + 2.0 * u / (k * (1.0 - u));
y = System.Math.Exp(System.Math.Log(y) / r) - 1.0; // y^(1/r) -1
return(System.Math.Log(y));
case 12: // BURR XII
return(System.Math.Exp(System.Math.Log(y) / k)); // y^(1/k)
}
return(0);
}
/// <summary>
/// Returns a Laplace (Double Exponential) distributed random number from the standard Laplace distribution L(0,1)d
/// <p>
/// <b>Implementation:</b> Inversion method.
/// This is a port of <i>lapin.c</i> from the <A HREF="http://www.cis.tu-graz.ac.at/stat/stadl/random.html">C-RAND / WIN-RAND</A> library.
/// <p>
/// </summary>
/// <param name="randomGenerator"></param>
/// <returns>a number in the open unit interval <code>(0.0,1.0)</code> (excluding 0.0 and 1.0).</returns>
public static double NextLaplace(RandomEngine randomGenerator)
{
double u = randomGenerator.Raw();
u = u + u - 1.0;
if (u > 0)
{
return(-System.Math.Log(1.0 - u));
}
else
{
return(System.Math.Log(1.0 + u));
}
}
/// <summary>
/// Returns a zipfian distributed random number with the given skew.
/// <p>
/// Algorithm from page 551 of:
/// Devroye, Luc (1986) `Non-uniform random variate generation',
/// Springer-Verlag: Berlind ISBN 3-540-96305-7 (also 0-387-96305-7)
/// </summary>
/// <param name="z">the skew of the distribution (must be >1.0).</param>
/// <param name="randomGenerator"></param>
/// <returns>a zipfian distributed number in the closed interval <i>[1,int.MaxValue]</i>.</returns>
public static int NextZipfInt(double z, RandomEngine randomGenerator)
{
/* Algorithm from page 551 of:
* Devroye, Luc (1986) `Non-uniform random variate generation',
* Springer-Verlag: Berlind ISBN 3-540-96305-7 (also 0-387-96305-7)
*/
double b = System.Math.Pow(2.0, z - 1.0);
double constant = -1.0 / (z - 1.0);
int result = 0;
for (; ;)
{
double u = randomGenerator.Raw();
double v = randomGenerator.Raw();
result = (int)(System.Math.Floor(System.Math.Pow(u, constant)));
double t = System.Math.Pow(1.0 + 1.0 / result, z - 1.0);
if (v * result * (t - 1.0) / (b - 1.0) <= t / b)
{
break;
}
}
return(result);
}
/// <summary>
/// Returns an erlang distributed random number with the given variance and mean.
/// </summary>
/// <param name="variance"></param>
/// <param name="mean"></param>
/// <param name="randomGenerator"></param>
/// <returns></returns>
public static double NextErlang(double variance, double mean, RandomEngine randomGenerator)
{
int k = (int)((mean * mean) / variance + 0.5);
k = (k > 0) ? k : 1;
double a = k / mean;
double prod = 1.0;
for (int i = 0; i < k; i++)
{
prod *= randomGenerator.Raw();
}
return(-System.Math.Log(prod) / a);
}
/// <summary>
/// Returns a lambda distributed random number with parameters l3 and l4.
/// <p>
/// <b>Implementation:</b> Inversion method.
/// This is a port of <i>lamin.c</i> from the <A HREF="http://www.cis.tu-graz.ac.at/stat/stadl/random.html">C-RAND / WIN-RAND</A> library.
/// C-RAND's implementation, in turn, is based upon
/// <p>
/// J.Sd Ramberg, B:Wd Schmeiser (1974): An approximate method for generating asymmetric variables, Communications ACM 17, 78-82.
/// <p>
/// </summary>
/// <param name="l3"></param>
/// <param name="l4"></param>
/// <param name="randomGenerator"></param>
/// <returns></returns>
public static double NextLambda(double l3, double l4, RandomEngine randomGenerator)
{
double l_sign;
if ((l3 < 0) || (l4 < 0))
{
l_sign = -1.0; // sign(l)
}
else
{
l_sign = 1.0;
}
double u = randomGenerator.Raw(); // U(0/1)
double x = l_sign * (System.Math.Exp(System.Math.Log(u) * l3) - System.Math.Exp(System.Math.Log(1.0 - u) * l4));
return(x);
}
/// <summary>
/// Returns a random number from the Burr II, VII, VIII, X Distributions.
/// <p>
/// <b>Implementation:</b> Inversion method.
/// This is a port of <i>burr1.c</i> from the <A HREF="http://www.cis.tu-graz.ac.at/stat/stadl/random.html">C-RAND / WIN-RAND</A> library.
/// C-RAND's implementation, in turn, is based upon
/// <p>
/// Ld Devroye (1986): Non-Uniform Random Variate Generation, Springer Verlag, New Yorkd
/// <p>
/// </summary>
/// <param name="r">must be > 0.</param>
/// <param name="nr">the number of the burr distribution (e.gd 2,7,8,10).</param>
/// <param name="randomGenerator"></param>
/// <returns></returns>
public static double NextBurr1(double r, int nr, RandomEngine randomGenerator)
{
/******************************************************************
* *
* Burr II, VII, VIII, X Distributions - Inversion *
* *
******************************************************************
* *
* FUNCTION : - burr1 samples a random number from one of the *
* Burr II, VII, VIII, X distributions with *
* parameter r > 0 , where the nod of the *
* distribution is indicated by a pointer *
* variabled *
* REFERENCE : - Ld Devroye (1986): Non-Uniform Random Variate *
* Generation, Springer Verlag, New Yorkd *
* SUBPROGRAM : - drand(seed) ..d (0,1)-uniform generator with *
* unsigned long int *seedd *
* *
******************************************************************/
double y;
y = System.Math.Exp(System.Math.Log(randomGenerator.Raw()) / r); /* y=u^(1/r) */
switch (nr)
{
// BURR II
case 2: return(-System.Math.Log(1 / y - 1));
// BURR VII
case 7: return(System.Math.Log(2 * y / (2 - 2 * y)) / 2);
// BURR VIII
case 8: return(System.Math.Log(System.Math.Tan(y * System.Math.PI / 2.0)));
// BURR X
case 10: return(System.Math.Sqrt(-System.Math.Log(1 - y)));
}
return(0);
}
/// <summary>
/// Returns a power-law distributed random number with the given exponent and lower cutoff.
/// </summary>
/// <param name="alpha">the exponent </param>
/// <param name="cut">the lower cutoff</param>
/// <param name="randomGenerator"></param>
/// <returns></returns>
public static double NextPowLaw(double alpha, double cut, RandomEngine randomGenerator)
{
return(cut * System.Math.Pow(randomGenerator.Raw(), 1.0 / (alpha + 1.0)));
}
/// <summary>
/// Computes a sorted random set of <tt>count</tt> elements from the interval <tt>[low,low+N-1]</tt>.
/// Since we are talking about a random set, no element will occur more than once.
///
/// <p>Running time is <tt>O(N)</tt>, on average. Space requirements are zero.
///
/// <p>Numbers are filled into the specified array starting at index <tt>fromIndex</tt> to the right.
/// The array is returned sorted ascending in the range filled with numbers.
/// </summary>
/// <param name="n">the total number of elements to choose (must be >= 0).</param>
/// <param name="N">the interval to choose random numbers from is <tt>[low,low+N-1]</tt>.</param>
/// <param name="count">the number of elements to be filled into <tt>values</tt> by this call (must be >= 0 and <=<tt>n</tt>). Normally, you will set <tt>count=n</tt>.</param>
/// <param name="low">the interval to choose random numbers from is <tt>[low,low+N-1]</tt>. Hint: If <tt>low==0</tt>, then draws random numbers from the interval <tt>[0,N-1]</tt>.</param>
/// <param name="values">the array into which the random numbers are to be filled; must have a length <tt>>= count+fromIndex</tt>.</param>
/// <param name="fromIndex">the first index within <tt>values</tt> to be filled with numbers (inclusive).</param>
/// <param name="randomGenerator">a random number generator.</param>
protected static void SampleMethodD(long n, long N, int count, long low, long[] values, int fromIndex, RandomEngine randomGenerator)
{
double nreal, Nreal, ninv, nmin1inv, U, X, Vprime, y1, y2, top, bottom, negSreal, qu1real;
long qu1, threshold, t, limit;
long S;
long chosen = -1 + low;
long negalphainv = -13; //tuning paramter, determines when to switch from method D to method Ad Dependent on programming language, platform, etc.
nreal = n; ninv = 1.0 / nreal; Nreal = N;
Vprime = System.Math.Exp(System.Math.Log(randomGenerator.Raw()) * ninv);
qu1 = -n + 1 + N; qu1real = -nreal + 1.0 + Nreal;
threshold = -negalphainv * n;
while (n > 1 && count > 0 && threshold < N)
{
nmin1inv = 1.0 / (-1.0 + nreal);
for (;;)
{
for (;;)
{ // step D2: generate U and X
X = Nreal * (-Vprime + 1.0); S = (long)X;
if (S < qu1)
{
break;
}
Vprime = System.Math.Exp(System.Math.Log(randomGenerator.Raw()) * ninv);
}
U = randomGenerator.Raw(); negSreal = -S;
//step D3: Accept?
y1 = System.Math.Exp(System.Math.Log(U * Nreal / qu1real) * nmin1inv);
Vprime = y1 * (-X / Nreal + 1.0) * (qu1real / (negSreal + qu1real));
if (Vprime <= 1.0)
{
break; //break inner loop
}
//step D4: Accept?
y2 = 1.0; top = -1.0 + Nreal;
if (n - 1 > S)
{
bottom = -nreal + Nreal; limit = -S + N;
}
else
{
bottom = -1.0 + negSreal + Nreal; limit = qu1;
}
for (t = N - 1; t >= limit; t--)
{
y2 = (y2 * top) / bottom;
top--;
bottom--;
}
if (Nreal / (-X + Nreal) >= y1 * System.Math.Exp(System.Math.Log(y2) * nmin1inv))
{
// accept !
Vprime = System.Math.Exp(System.Math.Log(randomGenerator.Raw()) * nmin1inv);
break; //break inner loop
}
Vprime = System.Math.Exp(System.Math.Log(randomGenerator.Raw()) * ninv);
} //end for
//step D5: select the (S+1)st record !
chosen += S + 1;
values[fromIndex++] = chosen;
/*
* // invert
* for (int iter=0; iter<S && count > 0; iter++) {
* values[fromIndex++] = ++chosen;
* count--;
* }
* chosen++;
*/
count--;
N -= S + 1; Nreal = negSreal + (-1.0 + Nreal);
n--; nreal--; ninv = nmin1inv;
qu1 = -S + qu1; qu1real = negSreal + qu1real;
threshold += negalphainv;
} //end while
if (count > 0)
{
if (n > 1)
{ //faster to use method A to finish the sampling
SampleMethodA(n, N, count, chosen + 1, values, fromIndex, randomGenerator);
}
else
{
//special case n==1
S = (long)(N * Vprime);
chosen += S + 1;
values[fromIndex++] = chosen;
}
}
}
/// <summary>
/// Efficiently computes a sorted random set of <tt>count</tt> elements from the interval <tt>[low,low+N-1]</tt>.
/// Since we are talking about a random set, no element will occur more than once.
///
/// <p>Running time is <tt>O(count)</tt>, on average. Space requirements are zero.
///
/// <p>Numbers are filled into the specified array starting at index <tt>fromIndex</tt> to the right.
/// The array is returned sorted ascending in the range filled with numbers.
/// </summary>
/// <param name="n">the total number of elements to choose (must be >= 0).</param>
/// <param name="N">the interval to choose random numbers from is <tt>[low,low+N-1]</tt>.</param>
/// <param name="count">the number of elements to be filled into <tt>values</tt> by this call (must be >= 0 and <=<tt>n</tt>). Normally, you will set <tt>count=n</tt>.</param>
/// <param name="low">the interval to choose random numbers from is <tt>[low,low+N-1]</tt>. Hint: If <tt>low==0</tt>, then draws random numbers from the interval <tt>[0,N-1]</tt>.</param>
/// <param name="values">the array into which the random numbers are to be filled; must have a length <tt>>= count+fromIndex</tt>.</param>
/// <param name="fromIndex">the first index within <tt>values</tt> to be filled with numbers (inclusive).</param>
/// <param name="randomGenerator">a random number generator.</param>
protected static void RejectMethodD(long n, long N, int count, long low, long[] values, int fromIndex, RandomEngine randomGenerator)
{
/* This algorithm is applicable if a large percentage (90%..100%) of N shall be sampled.
* In such cases it is more efficient than sampleMethodA() and sampleMethodD().
* The idea is that it is more efficient to express
* sample(n,N,count) in terms of reject(N-n,N,count)
* and then invert the result.
* For example, sampling 99% turns into sampling 1% plus inversion.
*
* This algorithm is the same as method sampleMethodD(..d) with the exception that sampled elements are rejected, and not sampled elements included in the result set.
*/
n = N - n; // IMPORTANT !!!
double nreal, Nreal, ninv, nmin1inv, U, X, Vprime, y1, y2, top, bottom, negSreal, qu1real;
long qu1, t, limit;
//long threshold;
long S;
long chosen = -1 + low;
//long negalphainv = -13; //tuning paramter, determines when to switch from method D to method Ad Dependent on programming language, platform, etc.
nreal = n; ninv = 1.0 / nreal; Nreal = N;
Vprime = System.Math.Exp(System.Math.Log(randomGenerator.Raw()) * ninv);
qu1 = -n + 1 + N; qu1real = -nreal + 1.0 + Nreal;
//threshold = -negalphainv * n;
while (n > 1 && count > 0)
{ //&& threshold<N) {
nmin1inv = 1.0 / (-1.0 + nreal);
for (;;)
{
for (;;)
{ // step D2: generate U and X
X = Nreal * (-Vprime + 1.0); S = (long)X;
if (S < qu1)
{
break;
}
Vprime = System.Math.Exp(System.Math.Log(randomGenerator.Raw()) * ninv);
}
U = randomGenerator.Raw(); negSreal = -S;
//step D3: Accept?
y1 = System.Math.Exp(System.Math.Log(U * Nreal / qu1real) * nmin1inv);
Vprime = y1 * (-X / Nreal + 1.0) * (qu1real / (negSreal + qu1real));
if (Vprime <= 1.0)
{
break; //break inner loop
}
//step D4: Accept?
y2 = 1.0; top = -1.0 + Nreal;
if (n - 1 > S)
{
bottom = -nreal + Nreal; limit = -S + N;
}
else
{
bottom = -1.0 + negSreal + Nreal; limit = qu1;
}
for (t = N - 1; t >= limit; t--)
{
y2 = (y2 * top) / bottom;
top--;
bottom--;
}
if (Nreal / (-X + Nreal) >= y1 * System.Math.Exp(System.Math.Log(y2) * nmin1inv))
{
// accept !
Vprime = System.Math.Exp(System.Math.Log(randomGenerator.Raw()) * nmin1inv);
break; //break inner loop
}
Vprime = System.Math.Exp(System.Math.Log(randomGenerator.Raw()) * ninv);
} //end for
//step D5: reject the (S+1)st record !
int iter = count; //int iter = (int)(System.Math.Min(S,count));
if (S < iter)
{
iter = (int)S;
}
count -= iter;
for (; --iter >= 0;)
{
values[fromIndex++] = ++chosen;
}
chosen++;
N -= S + 1; Nreal = negSreal + (-1.0 + Nreal);
n--; nreal--; ninv = nmin1inv;
qu1 = -S + qu1; qu1real = negSreal + qu1real;
//threshold += negalphainv;
} //end while
if (count > 0)
{ //special case n==1
//reject the (S+1)st record !
S = (long)(N * Vprime);
int iter = count; //int iter = (int)(System.Math.Min(S,count));
if (S < iter)
{
iter = (int)S;
}
count -= iter;
for (; --iter >= 0;)
{
values[fromIndex++] = ++chosen;
}
chosen++;
// fill the rest
for (; --count >= 0;)
{
values[fromIndex++] = ++chosen;
}
}
}
/// <summary>
/// Returns a weibull distributed random numberd
/// Polar method.
/// See Simulation, Modelling & Analysis by Law & Kelton, pp259
/// </summary>
/// <param name="alpha"></param>
/// <param name="beta"></param>
/// <param name="randomGenerator"></param>
/// <returns></returns>
public static double NextWeibull(double alpha, double beta, RandomEngine randomGenerator)
{
// Polar method.
// See Simulation, Modelling & Analysis by Law & Kelton, pp259
return(System.Math.Pow(beta * (-System.Math.Log(1.0 - randomGenerator.Raw())), 1.0 / alpha));
}
/// <summary>
/// Returns a random number from the distribution.
/// </summary>
/// <param name="N"></param>
/// <param name="M"></param>
/// <param name="n"></param>
/// <param name="randomGenerator"></param>
/// <returns></returns>
protected int Hmdu(int N, int M, int n, RandomEngine randomGenerator)
{
int I, K;
double p, nu, c, d, U;
if (N != N_last || M != M_last || n != n_last)
{ // set-up */
N_last = N;
M_last = M;
n_last = n;
Mp = (double)(M + 1);
np = (double)(n + 1); N_Mn = N - M - n;
p = Mp / (N + 2.0);
nu = np * p; /* mode, real */
if ((m = (int)nu) == nu && p == 0.5)
{ /* mode, int */
mp = m--;
}
else
{
mp = m + 1; /* mp = m + 1 */
}
/* mode probability, using the external function flogfak(k) = ln(k!) */
fm = System.Math.Exp(Arithmetic.LogFactorial(N - M) - Arithmetic.LogFactorial(N_Mn + m) - Arithmetic.LogFactorial(n - m)
+ Arithmetic.LogFactorial(M) - Arithmetic.LogFactorial(M - m) - Arithmetic.LogFactorial(m)
- Arithmetic.LogFactorial(N) + Arithmetic.LogFactorial(N - n) + Arithmetic.LogFactorial(n));
/* safety bound - guarantees at least 17 significant decimal digits */
/* b = min(n, (long int)(nu + k*c')) */
b = (int)(nu + 11.0 * System.Math.Sqrt(nu * (1.0 - p) * (1.0 - n / (double)N) + 1.0));
if (b > n)
{
b = n;
}
}
for (; ;)
{
if ((U = randomGenerator.Raw() - fm) <= 0.0)
{
return(m);
}
c = d = fm;
/* down- and upward search from the mode */
for (I = 1; I <= m; I++)
{
K = mp - I; /* downward search */
c *= (double)K / (np - K) * ((double)(N_Mn + K) / (Mp - K));
if ((U -= c) <= 0.0)
{
return(K - 1);
}
K = m + I; /* upward search */
d *= (np - K) / (double)K * ((Mp - K) / (double)(N_Mn + K));
if ((U -= d) <= 0.0)
{
return(K);
}
}
/* upward search from K = 2m + 1 to K = b */
for (K = mp + m; K <= b; K++)
{
d *= (np - K) / (double)K * ((Mp - K) / (double)(N_Mn + K));
if ((U -= d) <= 0.0)
{
return(K);
}
}
}
}
/// <summary>
/// Returns a zeta distributed random number.
/// </summary>
/// <param name="ro"></param>
/// <param name="pk"></param>
/// <param name="randomGenerator"></param>
/// <returns></returns>
protected long GenerateZeta(double ro, double pk, RandomEngine randomGenerator)
{
/******************************************************************
* *
* Zeta Distribution - Acceptance Rejection *
* *
******************************************************************
* *
* To sample from the Zeta distribution with parameters ro and pk *
* it suffices to sample variates x from the distribution with *
* density function f(x)=B*{[x+0.5]+pk}^(-(1+ro))( x > .5 ) *
* and then deliver k=[x+0.5]d *
* 1/B=Sum[(j+pk)^-(ro+1)] (j=1,2,..d) converges for ro >= .5 d *
* It is not necessary to compute B, because variates x are *
* generated by acceptance rejection using density function *
* g(x)=ro*(c+0.5)^ro*(c+x)^-(ro+1)d *
* * *
* int overflow is possible, when ro is small (ro <= .5) and *
* pk larged In this case a new sample is generatedd If ro and pk *
* satisfy the inequality ro > .14 + pk*1.85e-8 + .02*ln(pk) *
* the percentage of overflow is less than 1%, so that the *
* result is reliabled *
* NOTE: The comment above is likely to be nomore valid since *
* the C-version operated on 32-bit ints, while this Java *
* version operates on 64-bit intsd However, the following is *
* still valid: * *
* * *
* If either ro > 100 or k > 10000 numerical problems in *
* computing the theoretical moments arise, therefore ro<=100 and *
* k<=10000 are recommendedd *
* *
******************************************************************
* *
* FUNCTION: - zeta samples a random number from the *
* Zeta distribution with parameters ro > 0 and *
* pk >= 0d *
* REFERENCE: - Jd Dagpunar (1988): Principles of Random *
* Variate Generation, Clarendon Press, Oxfordd *
* *
******************************************************************/
double u, v, e, x;
long k;
if (ro != ro_prev || pk != pk_prev)
{ // Set-up
ro_prev = ro;
pk_prev = pk;
if (ro < pk)
{
c = pk - 0.5;
d = 0;
}
else
{
c = ro - 0.5;
d = (1.0 + ro) * System.Math.Log((1.0 + pk) / (1.0 + ro));
}
}
do
{
do
{
u = randomGenerator.Raw();
v = randomGenerator.Raw();
x = (c + 0.5) * System.Math.Exp(-System.Math.Log(u) / ro) - c;
} while (x <= 0.5 || x >= maxlongint);
k = (int)(x + 0.5);
e = -System.Math.Log(v);
} while (e < (1.0 + ro) * System.Math.Log((k + pk) / (x + c)) - d);
return(k);
}
/// <summary>
/// Returns a random number from the standard Logistic distribution Log(0,1).
/// <p>
/// <b>Implementation:</b> Inversion method.
/// This is a port of <i>login.c</i> from the <A HREF="http://www.cis.tu-graz.ac.at/stat/stadl/random.html">C-RAND / WIN-RAND</A> library.
/// </summary>
/// <param name="randomGenerator"></param>
/// <returns></returns>
public static double NextLogistic(RandomEngine randomGenerator)
{
double u = randomGenerator.Raw();
return(-System.Math.Log(1.0 / u - 1.0));
}
/// <summary>
/// Returns a cauchy distributed random number from the standard Cauchy distribution C(0,1)d
/// <A HREF="http://www.cern.ch/RD11/rkb/AN16pp/node25.html#SECTION000250000000000000000"> math definition</A>
/// and <A HREF="http://www.statsoft.com/textbook/glosc.html#Cauchy Distribution"> animated definition</A>d
/// <p>
/// <i>p(x) = 1/ (mean*pi * (1+(x/mean)^2))</i>.
/// <p>
/// <b>Implementation:</b>
/// This is a port of <i>cin.c</i> from the <A HREF="http://www.cis.tu-graz.ac.at/stat/stadl/random.html">C-RAND / WIN-RAND</A> library.
/// <p>
/// </summary>
/// <param name="randomGenerator"></param>
/// <returns>a number in the open unit interval <code>(0.0,1.0)</code> (excluding 0.0 and 1.0).</returns>
public static double NextCauchy(RandomEngine randomGenerator)
{
return(System.Math.Tan(System.Math.PI * randomGenerator.Raw()));
}
/// <summary>
/// Returns a random number from the distribution; bypasses the internal state.
/// </summary>
/// <param name="theMean"></param>
/// <returns></returns>
public int NextInt(double theMean)
{
/******************************************************************
* *
* Poisson Distribution - Patchwork Rejection/Inversion *
* *
******************************************************************
* *
* For parameter my < 10 Tabulated Inversion is appliedd *
* For my >= 10 Patchwork Rejection is employed: *
* The area below the histogram function f(x) is rearranged in *
* its body by certain point reflectionsd Within a large center *
* interval variates are sampled efficiently by rejection from *
* uniform hatsd Rectangular immediate acceptance regions speed *
* up the generationd The remaining tails are covered by *
* exponential functionsd *
* *
*****************************************************************/
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 = System.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 = gen.Raw(); // Step Ud Uniform sample
k = 0;
if (u <= p0)
{
return(k);
}
if (llll != 0)
{ // Step Td Table comparison
i = (u > 0.458) ? System.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 Cd Creation of new probd
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 = System.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)System.Math.Ceiling(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 expond tail envelopes
ll = System.Math.Log(r1); // expond tail left
lr = -System.Math.Log(r5); // expond tail right
// Poisson constants, necessary for computing function values f(k)
l_my = System.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 = Function(k2, l_my, c_pm);
f4 = Function(k4, l_my, c_pm);
f1 = Function(k1, l_my, c_pm);
f5 = Function(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); // immedd left
p2 = f2 * dl + p1; // centre left
p3 = f4 * (dr + 1.0) + p2; // immedd right
p4 = f4 * dr + p3; // centre right
p5 = f1 / ll + p4; // expond tail left
p6 = f5 / lr + p5; // expond tail right
} // end set-up
for (; ;)
{
// generate uniform number U -- U(0, p6)
// case distinction corresponding to U
if ((U = gen.Raw() * p6) < p2)
{ // centre left
// immediate acceptance region R2 = [k2, m) *[0, f2), X = k2, ..d m -1
if ((V = U - p1) < 0.0)
{
return(k2 + (int)(U / f2));
}
// immediate acceptance region R1 = [k1, k2)*[0, f1), X = k1, ..d 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 * gen.Raw()) + 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 <= Function(Y, l_my, c_pm))
{
return(Y); // accept of Y
}
}
X = k2 - Dk;
}
else if (U < p4)
{ // centre right
// immediate acceptance region R3 = [m, k4+1)*[0, f4), X = m, ..d 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 * gen.Raw()) + 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 <= Function(Y, l_my, c_pm))
{
return(Y); // accept of Y
}
}
X = k4 + Dk;
}
else
{
W = gen.Raw();
if (U < p5)
{ // expond tail left
Dk = (int)(1.0 - System.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
{ // expond tail right
Dk = (int)(1.0 - System.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 (System.Math.Log(W) <= X * l_my - Arithmetic.LogFactorial(X) - c_pm)
{
return(X);
}
}
}
else
{ // mean is too large
return((int)my);
}
}
/// <summary>
/// Returns a random number from the distribution.
/// Uses the Patchwork Rejection method of Heinz Zechner (HPRS)
/// </summary>
/// <param name="N"></param>
/// <param name="M"></param>
/// <param name="n"></param>
/// <param name="randomGenerator"></param>
/// <returns></returns>
protected int Hprs(int N, int M, int n, RandomEngine randomGenerator)
{
int Dk, X, V;
double Mp, np, p, nu, U, Y, W; /* (X, Y) <-> (V, W) */
if (N != N_last || M != M_last || n != n_last)
{ /* set-up */
N_last = N;
M_last = M;
n_last = n;
Mp = (double)(M + 1);
np = (double)(n + 1); N_Mn = N - M - n;
p = Mp / (N + 2.0); nu = np * p; // main parameters
// approximate deviation of reflection points k2, k4 from nu - 1/2
U = System.Math.Sqrt(nu * (1.0 - p) * (1.0 - (n + 2.0) / (N + 3.0)) + 0.25);
// mode m, reflection points k2 and k4, and points k1 and k5, which
// delimit the centre region of h(x)
// k2 = ceil (nu - 1/2 - U), k1 = 2*k2 - (m - 1 + delta_ml)
// k4 = floor(nu - 1/2 + U), k5 = 2*k4 - (m + 1 - delta_mr)
m = (int)nu;
k2 = (int)System.Math.Ceiling(nu - 0.5 - U); if (k2 >= m)
{
k2 = m - 1;
}
k4 = (int)(nu - 0.5 + U);
k1 = k2 + k2 - m + 1; // delta_ml = 0
k5 = k4 + k4 - m; // delta_mr = 1
// 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 = (np / (double)k1 - 1.0) * (Mp - k1) / (double)(N_Mn + k1);
r2 = (np / (double)k2 - 1.0) * (Mp - k2) / (double)(N_Mn + k2);
r4 = (np / (double)(k4 + 1) - 1.0) * (M - k4) / (double)(N_Mn + k4 + 1);
r5 = (np / (double)(k5 + 1) - 1.0) * (M - k5) / (double)(N_Mn + k5 + 1);
// reciprocal values of the scale parameters of expond tail envelopes
ll = System.Math.Log(r1); // expond tail left //
lr = -System.Math.Log(r5); // expond tail right //
// hypergeomd constant, necessary for computing function values f(k)
c_pm = Fc_lnpk(m, N_Mn, M, n);
// function values f(k) = p(k)/p(m) at k = k2, k4, k1, k5
f2 = System.Math.Exp(c_pm - Fc_lnpk(k2, N_Mn, M, n));
f4 = System.Math.Exp(c_pm - Fc_lnpk(k4, N_Mn, M, n));
f1 = System.Math.Exp(c_pm - Fc_lnpk(k1, N_Mn, M, n));
f5 = System.Math.Exp(c_pm - Fc_lnpk(k5, N_Mn, M, n));
// 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); // immedd left
p2 = f2 * dl + p1; // centre left
p3 = f4 * (dr + 1.0) + p2; // immedd right
p4 = f4 * dr + p3; // centre right
p5 = f1 / ll + p4; // expond tail left
p6 = f5 / lr + p5; // expond tail right
}
for (; ;)
{
// generate uniform number U -- U(0, p6)
// case distinction corresponding to U
if ((U = randomGenerator.Raw() * p6) < p2)
{ // centre left
// immediate acceptance region R2 = [k2, m) *[0, f2), X = k2, ..d m -1
if ((W = U - p1) < 0.0)
{
return(k2 + (int)(U / f2));
}
// immediate acceptance region R1 = [k1, k2)*[0, f1), X = k1, ..d k2-1
if ((Y = W / dl) < f1)
{
return(k1 + (int)(W / f1));
}
// computation of candidate X < k2, and its counterpart V > k2
// either squeeze-acceptance of X or acceptance-rejection of V
Dk = (int)(dl * randomGenerator.Raw()) + 1;
if (Y <= f2 - Dk * (f2 - f2 / r2))
{ // quick accept of
return(k2 - Dk); // X = k2 - Dk
}
if ((W = f2 + f2 - Y) < 1.0)
{ // quick reject of V
V = k2 + Dk;
if (W <= f2 + Dk * (1.0 - f2) / (dl + 1.0))
{ // quick accept of
return(V); // V = k2 + Dk
}
if (System.Math.Log(W) <= c_pm - Fc_lnpk(V, N_Mn, M, n))
{
return(V); // accept of V
}
}
X = k2 - Dk;
}
else if (U < p4)
{ // centre right
// immediate acceptance region R3 = [m, k4+1)*[0, f4), X = m, ..d k4
if ((W = U - p3) < 0.0)
{
return(k4 - (int)((U - p2) / f4));
}
// immediate acceptance region R4 = [k4+1, k5+1)*[0, f5)
if ((Y = W / dr) < f5)
{
return(k5 - (int)(W / f5));
}
// computation of candidate X > k4, and its counterpart V < k4
// either squeeze-acceptance of X or acceptance-rejection of V
Dk = (int)(dr * randomGenerator.Raw()) + 1;
if (Y <= f4 - Dk * (f4 - f4 * r4))
{ // quick accept of
return(k4 + Dk); // X = k4 + Dk
}
if ((W = f4 + f4 - Y) < 1.0)
{ // quick reject of V
V = k4 - Dk;
if (W <= f4 + Dk * (1.0 - f4) / dr)
{ // quick accept of
return(V); // V = k4 - Dk
}
if (System.Math.Log(W) <= c_pm - Fc_lnpk(V, N_Mn, M, n))
{
return(V); // accept of V
}
}
X = k4 + Dk;
}
else
{
Y = randomGenerator.Raw();
if (U < p5)
{ // expond tail left
Dk = (int)(1.0 - System.Math.Log(Y) / ll);
if ((X = k1 - Dk) < 0)
{
continue; // 0 <= X <= k1 - 1
}
Y *= (U - p4) * ll; // Y -- U(0, h(x))
if (Y <= f1 - Dk * (f1 - f1 / r1))
{
return(X); // quick accept of X
}
}
else
{ // expond tail right
Dk = (int)(1.0 - System.Math.Log(Y) / lr);
if ((X = k5 + Dk) > n)
{
continue; // k5 + 1 <= X <= n
}
Y *= (U - p5) * lr; // Y -- U(0, h(x)) /
if (Y <= f5 - Dk * (f5 - f5 * r5))
{
return(X); // quick accept of X
}
}
}
// acceptance-rejection test of candidate X from the original area
// test, whether Y <= f(X), with Y = U*h(x) and U -- U(0, 1)
// log f(X) = log( m! (M - m)! (n - m)! (N - M - n + m)! )
// - log( X! (M - X)! (n - X)! (N - M - n + X)! )
// by using an external function for log k!
if (System.Math.Log(Y) <= c_pm - Fc_lnpk(X, N_Mn, M, n))
{
return(X);
}
}
}
