static GnmValue *
gnumeric_randexp (GnmFuncEvalInfo *ei, GnmValue const * const *argv)
{
gnm_float x = value_get_as_float (argv[0]);
return value_new_float (random_exponential (x));
}
static gboolean
tool_random_engine_run_exponential (data_analysis_output_t *dao,
tools_data_random_t *info,
exponential_random_tool_t *param)
{
int i, n;
for (i = 0; i < info->n_vars; i++) {
for (n = 0; n < info->count; n++) {
gnm_float v;
v = random_exponential (param->b);
dao_set_cell_float (dao, i, n, v);
}
}
return FALSE;
}
// This function samples a stable variable of parameters (alpha,beta)
//
// The algorithm is copied verbatim from formulas (2.3) and (2.4) in
// Chambers, J. M.; Mallows, C. L.; Stuck, B. W. (1976).
// "A Method for Simulating Stable Random Variables".
// Journal of the American Statistical Association 71 (354): 340–344.
// doi:10.1080/01621459.1976.10480344.
//
// Observation: the algorithm is numerically imprecise when alpha approaches 1.
// TODO: implement appropriate rearrangements as suggested in the article.
static double random_stable(double alpha, double beta)
{
double U = (random_uniform() - 0.5) * M_PI;
double W = random_exponential();
double z = -beta * tan(M_PI * alpha / 2);
double x = alpha == 1 ? M_PI/2 : atan(-z) / alpha;
//fprintf(stderr, "U=%g W=%g z=%g x=%g\t\t", U, W, z, x);
double r = NAN;
if (alpha == 1) {
double a = (M_PI/2 + beta * U) * tan(U);
double b = log(((M_PI/2) * W * cos(U)) / ((M_PI/2) + beta * U));
//fprintf(stderr, "a=%g b=%g\n", a, b);
r = (a - beta * b) / x;
} else {
double a = pow(1 + z * z, 1 / (2*alpha));
double b = sin(alpha * (U + x)) / pow(cos(U), 1/alpha);
double c = pow(cos(U - alpha*(U + x)) / W, (1 - alpha) / alpha);
//fprintf(stderr, "a=%g b=%g c=%g\n", a, b, c);
r = a * b * c;
}
//fprintf(stderr, "s(%g,%g) = %g\n", alpha, beta, r);
return r;
}
static double random_pareto(void)
{
return exp(random_exponential());
}
StochasticSEATIRDSchedule::StochasticSEATIRDSchedule(const double &now, MTRand &rand, const std::vector<int> &stratificationValues)
{
stratificationValues_ = stratificationValues;
// the individual starts as exposed
state_ = E;
// the schedule can later be canceled, but starts out active
canceled_ = false;
// generate all transitions starting from "exposed"
// time to progress from exposed to asymptomatic
double Ta = now + random_exponential(1. / g_parameters.getTau(), &rand);
// infected period begins at asymptomatic
infectedTMin_ = Ta;
// infected periods ends at recovery / death and is set inline below
eventQueue_.push(StochasticSEATIRDEvent(now, Ta, EtoA, stratificationValues, stratificationValues));
// compute nu (rate) from nu (CFR)
double nu = -1./g_parameters.getGamma() * log(1. - g_parameters.getNu(stratificationValues[0]));
// asymptomatic transition: -> treatable, -> recovered, or -> deceased
double Tt = Ta + random_exponential(1. / g_parameters.getKappa(), &rand); // time to progress from asymptomatic to treatable
double Tr_a = Ta + random_exponential(1. / g_parameters.getGamma(), &rand); // time to recover from asymptomatic
double Td_a = Ta + random_exponential(nu, &rand); // time to death from asymptomatic
if(Tt < Tr_a && Tt < Td_a)
{
// -> treatable
eventQueue_.push(StochasticSEATIRDEvent(Ta, Tt, AtoT, stratificationValues, stratificationValues));
// treatable transitions: -> infectious, -> recovered, or -> deceased
double Ti = Tt + g_parameters.getChi(); // time to progress from treatable to infectious
double Tr_ti = Tt + random_exponential(1. / g_parameters.getGamma(), &rand); // time to recover from treatable/infectious
double Td_ti = Tt + random_exponential(nu, &rand); // time to death from treatable/infectious
if(Ti < Tr_ti && Ti < Td_ti)
{
// -> infectious
eventQueue_.push(StochasticSEATIRDEvent(Tt, Ti, TtoI, stratificationValues, stratificationValues));
// infectious transitions: -> recovered, or -> deceased
if(Tr_ti < Td_ti)
{
// -> recovered
infectedTMax_ = Tr_ti;
eventQueue_.push(StochasticSEATIRDEvent(Ti, Tr_ti, ItoR, stratificationValues, stratificationValues));
}
else // Td_ti < Tr_ti
{
// -> deceased
infectedTMax_ = Td_ti;
eventQueue_.push(StochasticSEATIRDEvent(Ti, Td_ti, ItoD, stratificationValues, stratificationValues));
}
}
else if(Tr_ti < Td_ti)
{
// -> recovered
infectedTMax_ = Tr_ti;
eventQueue_.push(StochasticSEATIRDEvent(Tt, Tr_ti, TtoR, stratificationValues, stratificationValues));
}
else // Td_ti < Tr_ti
{
// -> deceased
infectedTMax_ = Td_ti;
eventQueue_.push(StochasticSEATIRDEvent(Tt, Td_ti, TtoD, stratificationValues, stratificationValues));
}
}
else if(Tr_a < Td_a)
{
// -> recovered
infectedTMax_ = Tr_a;
eventQueue_.push(StochasticSEATIRDEvent(Ta, Tr_a, AtoR, stratificationValues, stratificationValues));
}
else // Td_a < Tr_a
{
// -> deceased
infectedTMax_ = Td_a;
eventQueue_.push(StochasticSEATIRDEvent(Ta, Td_a, AtoD, stratificationValues, stratificationValues));
}
}
