# pomp C API

#### 26 July 2019

This document was produced using pomp version 2.2.1.0 and R version 3.6.1.

## Overview

pomp provides C entry points to a number of facilities for model specification. Below, we describe these, providing the prototypical function calls and descriptions of their arguments.

The final section describes the prototypes for the basic model components. Users wishing to write libraries to hold basic model components must furnish functions of these prototypes that perform the basic model component computations.

## Random variables

### Beta-binomial distribution

double rbetabinom(double size, double prob, double theta);
double dbetabinom(double x, double size, double prob,
double theta, int give_log);

$$X$$ is said to be Beta-binomially distributed with size $$n$$, mean probability $$p$$, and dispersion parameter $$\theta$$ if $P \sim \mathrm{Beta}\left(\theta\,p,\theta\,(1-p)\right)$ and $X|P \sim \mathrm{Binomial}\left(n,P\right).$ If $$X\sim\mathrm{BetaBinomial}\left(n,p,\theta\right)$$, then $\mathbb{E}\left[X\right]=n\,p\qquad\text{and}\qquad\mathrm{Var}\left[X\right]=n\,p\,(1-p)\,\frac{\theta+n}{\theta+1}.$

### Multinomial distribution

double dmultinom(int m, const double *prob, double *x, int give_log);

The R C API provides a simulator for the multinomial distribution, rmultinom. See the “Rmath.h” header file for information on this facility. pomp provides an evaluator for the probability mass function (dmultinom) for this distribution.

Input:

• m is a positive integer, is the dimension of the random variable.
• prob is a pointer to an m-vector of probabilities.
• x is a pointer to an m-vector containing the data.
• give_log is an integer:
• give_log=1 if the log probability is desired.
• give_log=0 if probability is desired.

The return value is the probability or log probability (as requested).

### Euler-multinomial distribution

#### Simulate Euler-multinomial transitions

void reulermultinom(int m, double size, const double *rate,
double dt, double *trans);

Input:

• m, a positive integer, is number of potential transitions (“deaths”).
• size, a positive integer, is the number of individuals at risk.
• rate is a pointer to the vector of transition (“death”) rates.
• dt, a positive real number, is the duration of time interval.
• trans is a pointer to the vector that will hold the random deviate.

On return, trans, …, trans[m-1] will be the numbers of individuals making each of the respective transitions.

See ?reulermultinom, FAQ 3.6, and the package vignettes for more on the Euler-multinomial distributions.

NB: reulermultinom does not call GetRNGstate() or PutRNGstate() internally. This must be done by the calling program. But note that when reulermultinom is called inside a pomp rprocess, there is no need to call either GetRNGState() or PutRNGState(); this is handled by pomp.

#### Compute probabilities of Euler-multinomial transitions

double deulermultinom(int m, double size, const double *rate,
double dt, double *trans, int give_log);

Input:

• m, a positive integer, is the number of potential transitions (“deaths”).
• size, a positive integer, is the number of individuals at risk.
• rate is a pointer to vector of transition (“death”) rates.
• dt, a positive real number, is the duration of time interval.
• trans is pointer to vector containing the data, which are numbers of individuals making the respective transitions.
• give_log is an integer:
• give_log=1 if log probability is desired;
• give_log=0 if probability is desired.

The value returned is the probability or log probability (as requested).

See ?deulermultinom, FAQ 3.6, and the package vignettes for more on the Euler-multinomial distributions.

### Gamma white noise

double rgammawn(double sigma, double dt);

Corresponding to the R function rgammawn, this C function draws a single random increment of a gamma white-noise process. This will have expectation equal to dt and variance sigma^2*dt.

In particular, when dW = rgammawn(sigma,dt); is executed, mu*dW/dt is a candidate for a random rate process within an Euler-multinomial context, i.e., mu*dW will have expectation mu*dt and variance mu*sigma^2*dt.

## Splines

void periodic_bspline_basis_eval(double x, double period, int degree,
int nbasis, double *y);
void periodic_bspline_basis_eval_deriv(double x, double period,
int degree, int nbasis, int deriv, double *y);

These functions work with periodic B-spline basis functions. The period and smoothness of the functions are given by period and degree, respectively. The first function evaluates nbasis periodic B-spline basis functions at x. The second evaluates the order-deriv derivative of each basis function.

## Transformations

### Logit transformation

double logit(double p);
double expit(double x);

The logit transformation is defined by $x = \log\frac{p}{1-p}.$ Its inverse is therefore $p = \frac{1}{1+e^{-x}}.$

### Log-barycentric transformation

void to_log_barycentric(double *xt, const double *x, int n);
void from_log_barycentric(double *xt, const double *x, int n);

The log-barycentric transformation takes a vector $$X_i\in\mathbb{R}^n_+$$, $$i=1,\dots,n$$, to a vector $$Y_i\in\mathbb{R}^n$$, where $Y_i = \log\frac{X_i}{\sum_j\!X_j}.$ The log-barycentric transformation takes every simplex defined by $$\sum_i\!X_i = c$$, $$c$$ constant, to $$n$$-dimensional Euclidean space $$\mathbb{R}^n$$.

The pseudo-inverse transformation takes $$\mathbb{R}^n$$ to the unit simplex $$S=\{X\in\mathbb{R}^n_+\;\vert\;\sum_i\!X_i=1\}$$. Specifically, $X_i = \frac{e^{Y_i}}{\sum_j\!e^{Y_j}}.$

Note that if $$T:\mathbb{R}^n_+\to\mathbb{R}^n$$ is the log-barycentric transformation so defined, $$U$$ is the pseudo-inverse, and $$Id$$ denotes the identity map, then $$T\circ U=Id:\mathbb{R}^n\to\mathbb{R}^n$$ but $$U\circ T\ne Id$$. However, if $$T$$ is restricted to the unit simplex, then $$U\circ T=Id:S\to S$$.

Input:

• x is a pointer to vector of parameters to be tranformed either to or from to log barycentric coordinates.
• n is the length of this vector.
• xt is a pointer to the vector that will hold the results.

On return, xt, …, xt[n-1] will contain the transformed coordinates.

## Convenience functions

### Vector dot product

double dot_product(int n, const double *x, const double *y);

The return value is the dot (inner) product of the n-vectors x and y. By definition, $x{\cdot}y = \sum_i\!x_i\,y_i.$

### Exponential/geometric rate conversion

double exp2geom_rate_correction(double R, double dt);

This function computes $$r$$ such that if $N \sim \mathrm{Geometric}\left(p=1-e^{-r\,{\Delta}t}\right)$ and $T \sim \mathrm{Exponential}\left(\mathrm{rate}=R\right),$ then $$\mathbb{E}\left[N\,{\Delta}t\right] = \mathbb{E}\left[T\right]$$. That is, $$r$$ is the rate for an Euler process that gives the same expected waiting time as the exponential process it approximates. In particular $$r \to R$$ as $${\Delta}t \to 0$$.

const int *get_userdata_int(const char *name);
const double *get_userdata_double(const char *name);
const SEXP get_userdata(const char *name);

The first function returns a pointer to the integer element of the userdata with the given name. The second retrieves a pointer to a double-precision element of userdata by name. The third form returns a general S expression (SEXP). See ?userdata for more information.

## Prototypes for basic model components

pomp provides a facility whereby model codes can be compiled into a dynamically linked library for use in pomp objects. Specifically, basic model components are coded as C functions with the following prototypes.

NB: These functions should not be used within C snippets!

Indices: Each of the following functions is supplied one or more of the stateindex, parindex, covindex, obsindex arguments. Each of these is an integer vector: the integers within are indices giving the positions of specific model variables, according to the user’s specification, the latter being given by means of the statenames, paramnames, covarnames, and obsnames arguments. See ?pomp for more explanation. Thus, for example, within the body of a function of prototype pomp_rinit (see below),

 x[stateindex];
x[stateindex];
p[parindex];
covars[covindex];

refer to the first state variable, the fourth state variable, the third parameter, and the second covariate, respectively.

### rinit

void pomp_rinit(double *x, const double *p, double t,
const int *stateindex, const int *parindex, const int *covindex,
const double *covars);

Description:

• p is a pointer to parameter vector.
• t is the current time.
• stateindex, parindex, covindex: see Indices, above.
• covars is a pointer to a vector containing the (possibly interpolated) values of the covariates at the current time.
• x is a vector that will, on return, contain a draw from the initial-state distribution.

NB: There is no need to call GetRNGstate() or PutRNGstate() in the body of the user-defined function. The RNG is initialized before any call to this function, and the RNG state is written afterward. Inclusion of these calls in the user-defined function may result in significant slowdown.

### rprocess

#### step.fun as used by euler and onestep

void pomp_onestep_sim(double *x, const double *p,
const int *stateindex, const int *parindex, const int *covindex,
const double *covars, double t, double dt);

Description:

• p is the parameter vector.
• stateindex, parindex, covindex: see Indices, above.
• covars is the vector of covariates.
• t is the time at the beginning of the step.
• dt is the step size (duration of the interval).
• x is the vector, that will, on return, contain a draw from the state process at time t+dt.

NB: There is no need to call GetRNGstate() or PutRNGstate() in the body of the user-defined function. The RNG is initialized before any call to this function, and the RNG state is written afterward. Inclusion of these calls in the user-defined function may result in significant slowdown.

#### rate.fun as used by gillespie

double pomp_ssa_rate_fn(int event,
double t, const double *x, const double *p,
const int *stateindex, const int *parindex, const int *covindex,
const double *covars);

Description:

• event is an integer specifying the number of the reaction whose rate is desired (the first is event is 1, not 0).
• t is the current time.
• x is the vector of state variables.
• p is the vector of parameters.
• stateindex, parindex, covindex: see Indices, above.
• covars is the vector of (possibly interpolated) covariates at time t.

The function returns the rate of the requested reaction.

### dprocess

void pomp_onestep_pdf(double *loglik,
const double *x1, const double *x2, double t1, double t2, const double *p,
const int *stateindex, const int *parindex, const int *covindex,
const double *covars);

Description:

• t1, t2 are the times at the beginning and end of the interval, respectively.
• x1, x2 are the state vectors at time t1 and t2, respectively.
• p is the parameter vector.
• stateindex, parindex, covindex: see Indices, above.
• covars is the vector of (possibly interpolated) covariates at time t.
• loglik is a pointer to the scalar that will, on return, contain the log probability density.

### skeleton

void pomp_skeleton(double *f, const double *x, const double *p,
const int *stateindex, const int *parindex, const int *covindex,
const double *covars, double t);

Description:

• t is the time.
• x is the state vector at time t.
• p is the parameter parameter vector.
• stateindex, parindex, covindex: see Indices, above.
• covars is the vector of (possibly interpolated) covariates at time t.
• f is a vector, of the same length as x, that will, on return, contain the value of the map or vectorfield.

### rmeasure

void pomp_measure_model_simulator(double *y,
const double *x, const double *p,
const int *obsindex, const int *stateindex, const int *parindex, const int *covindex,
const double *covars, double t);

Description:

• t is the time at the beginning of the Euler step.
• x is the state vector at time t.
• p is the parameter vector.
• obsindex, stateindex, parindex, covindex: see Indices, above.
• covars is the vector of (possibly interpolated) covariates at time t.
• y is a vector that will, on return, contain the simulated observations.

NB: There is no need to call GetRNGstate() or PutRNGstate() in the body of the user-defined function. The RNG is initialized before any call to this function, and the RNG state is written afterward. Inclusion of these calls in the user-defined function may result in significant slowdown.

### dmeasure

void pomp_measure_model_density(double *lik,
const double *y, const double *x, const double *p, int give_log,
const int *obsindex, const int *stateindex, const int *parindex, const int *covindex,
const double *covars, double t);

Description:

• y is the vector of observables at time t.
• x is the state vector at time t.
• p is the parameter vector.
• give_log is an integer:
• give_log=1 if log probability is desired;
• give_log=0 if probability is desired.
• obsindex, stateindex, parindex, covindex: see Indices, above.
• covars is the vector of (possibly interpolated) covariates at time t.
• lik is a pointer to a scalar that will, on return, contain the requested likelihood or log likelihood.

### rprior

void pomp_rprior(double *p, const int *parindex);

Description:

• p is the parameter vector.
• parindex: see Indices, above.

On return, p will contain a new random draw from the prior distribution.

NB: There is no need to call GetRNGstate() or PutRNGstate() in the body of the user-defined function. The RNG is initialized before any call to this function, and the RNG state is written afterward. Inclusion of these calls in the user-defined function may result in significant slowdown.

### dprior

void pomp_dprior(double *lik, const double *p, int give_log, const int *parindex);

Description:

• p is the parameter vector.
• give_log is an integer:
• give_log=1 if log probability is desired;
• give_log=0 if probability is desired.
• parindex: see Indices, above.
• lik is a pointer to a scalar that will, on return, contain the requested probability density or log probability density.

### partrans

void pomp_transform_fn(double *pt, const double *p, const int *parindex);

Description:

• p is the parameter vector.
• parindex: see Indices, above.
• pt is the vector wherein the results will be returned.