Create a dynamic ODE-based model object suitably for translation into fast C code

```
RxODE(model, modName = basename(wd), wd = ifelse(RxODE.cache.directory ==
".", getwd(), RxODE.cache.directory), filename = NULL, do.compile = NULL,
extraC = NULL, debug = FALSE, calcJac = NULL, calcSens = NULL,
collapseModel = FALSE, ...)
```

model

This is the ODE model specification. It can be:

a string containing the set of ordinary differential equations (ODE) and other expressions defining the changes in the dynamic system.

a file name where the ODE system equation is contained

An ODE expression enclosed in

`{}`

(see also the `filename`

argument). For
details, see the sections “Details” and
“`RxODE Syntax`

” below.

modName

a string to be used as the model name. This string
is used for naming various aspects of the computations,
including generating C symbol names, dynamic libraries,
etc. Therefore, it is necessary that `modName`

consists of
simple ASCII alphanumeric characters starting with a letter.

wd

character string with a working directory where to
create a subdirectory according to `modName`

. When
specified, a subdirectoy named after the
“`modName.d`

” will be created and populated with a
C file, a dynamic loading library, plus various other working
files. If missing, the files are created (and removed) in the
temporary directory, and the RxODE DLL for the model is
created in the current directory named `rx_????_platform`

, for
example `rx_129f8f97fb94a87ca49ca8dafe691e1e_i386.dll`

filename

A file name or connection object where the
ODE-based model specification resides. Only one of `model`

or `filename`

may be specified.

do.compile

logical specifying whether to carry out the
parsing of the ODE into C code and its compilation. Default is
`TRUE`

extraC

Extra c code to include in the model. This can be
useful to specify functions in the model. These C functions
should usually take `double`

precision arguments, and
return `double`

precision values.

debug

is a boolean indicating if the executable should be compiled with verbose debugging information turned on.

calcJac

boolean indicating if RxODE will calculate the Jacobain according to the specified ODEs.

calcSens

boolean indicating if RxODE will calculate the sennsitivities according to the specified ODEs.

collapseModel

boolean indicating if RxODE will remove all LHS variables when calculating sensitivities.

...

any other arguments are passed to the function
`readLines`

, (e.g., encoding).

The “Rx” in the name `RxODE`

is meant to suggest the
abbreviation *Rx* for a medical prescription, and thus to
suggest the package emphasis on pharmacometrics modeling, including
pharmacokinetics (PK), pharmacodynamics (PD), disease progression,
drug-disease modeling, etc.

The ODE-based model specification may be coded inside a character
string or in a text file, see Section *RxODE Syntax* below for
coding details. An internal `RxODE`

compilation manager
object translates the ODE system into C, compiles it, and
dynamically loads the object code into the current R session. The
call to `RxODE`

produces an object of class `RxODE`

which
consists of a list-like structure (closure) with various member
functions (see Section *Value* below).

For evaluating `RxODE`

models, two types of inputs may be
provided: a required set of time points for querying the state of
the ODE system and an optional set of doses (input amounts). These
inputs are combined into a single *event table* object created
with the function `eventTable`

.

An object (closure) of class “`RxODE`

” (see Chambers and Temple Lang (2001))
consisting of the following list of strings and functions:

the name of the model (a copy of the input argument).

a character string holding the source model specification.

a function that returns a list with 3 character
vectors, `params`

, `state`

, and `lhs`

of variable names used in the model
specification. These will be output when the model is computed (i.e., the ODE solved by integration).

this function solves (integrates) the ODE. This
is done by passing the code to `rxSolve`

.
This is as if you called `rxSolve(RxODEobject, ...)`

,
but returns a matrix instead of a rxSolve object.

`params`

: a numeric named vector with values for every parameter
in the ODE system; the names must correspond to the parameter
identifiers used in the ODE specification;

`events`

: an `eventTable`

object describing the
input (e.g., doses) to the dynamic system and observation
sampling time points (see `eventTable`

);

`inits`

: a vector of initial values of the state variables
(e.g., amounts in each compartment), and the order in this vector
must be the same as the state variables (e.g., PK/PD compartments);

`stiff`

: a logical (`TRUE`

by default) indicating whether
the ODE system is stifff or not.

For stiff ODE sytems (`stiff = TRUE`

), `RxODE`

uses
the LSODA (Livermore Solver for Ordinary Differential Equations)
Fortran package, which implements an automatic method switching
for stiff and non-stiff problems along the integration interval,
authored by Hindmarsh and Petzold (2003).

For non-stiff systems (`stiff = FALSE`

), `RxODE`

uses DOP853,
an explicit Runge-Kutta method of order 8(5, 3) of Dormand and Prince
as implemented in C by Hairer and Wanner (1993).

`trans_abs`

: a logical (`FALSE`

by default) indicating
whether to fit a transit absorption term
(TODO: need further documentation and example);

`atol`

: a numeric absolute tolerance (1e-08 by default);

`rtol`

: a numeric relative tolerance (1e-06 by default).e

The output of “solve” is a matrix with as many rows as there are sampled time points and as many columns as system variables (as defined by the ODEs and additional assigments in the RxODE model code).

a function that (naively) checks for model validity, namely that the C object code reflects the latest model specification.

a string with the version of the `RxODE`

object (not the package).

a function with one `force = FALSE`

argument
that dynamically loads the object code if needed.

a function with no argument that unloads the model object code.

removes all created model files, including C and DDL files.
The model object is no longer valid and should be removed, e.g.,
`rm(m1)`

.

deprecated, use `solve`

.

deprecated.

deprecated.

deprecated.

internal (not user callable) function.

An `RxODE`

model specification consists of one or more
statements terminated by semi-colons, ‘`;`

’, and
optional comments (comments are delimited by `#`

and an
end-of-line marker). **NB:** Comments are not allowed inside
statements.

A block of statements is a set of statements delimeted by curly
braces, ‘`{ ... }`

’. Statements can be either
assignments or conditional `if`

statements. Assignment
statements can be: (1) “simple” assignmets, where the left
hand is an identifier (i.e., variable), (2) special
“time-derivative” assignments, where the left hand specifies
the change of that variable with respect to time e.g.,
`d/dt(depot)`

, or (3) special “jacobian” assignments,
where the left hand specifies the change of of the ODE with respect
to one of the parameters, e.g. `df(depot)/dy(kel)`

. The
“jacobian” assignments are not required, and are only useful
for very stiff differential systems.

Expressions in assignment and ‘`if`

’ statements can be
numeric or logical (no character expressions are currently
supported). Numeric expressions can include the following numeric
operators (‘`+`

’, ‘`-`

’, ‘`*`

’,
‘`/`

’, ‘`^`

’), and those mathematical
functions defined in the C or the R math libraries (e.g.,
`fabs`

, `exp`

, `log`

, `sin`

). (Notice that the
modulo operator ‘`%`

’ is currently not supported.)

Identifiers in an `RxODE`

model specification can refer to:

state variables in the dynamic system (e.g., compartments in a pharmacokinetics/pharamcodynamics model);

implied input variable,

`t`

(time),`podo`

(oral dose, for absorption models), and`tlast`

(last time point);model parameters, (

`ka`

rate of absorption,`CL`

clearance, etc.);`pi`

, for the constant pi.others, as created by assignments as part of the model specification.

Identifiers consists of case-sensitive alphanumeric characters,
plus the underscore ‘_’ character. **NB:** the dot
‘.’ character is **not** a valid character identifier.

The values of these variables at pre-specified time points are
saved as part of the fitted/integrated/solved model (see
`eventTable`

, in particular its member function
`add.sampling`

that defines a set of time points at which to
capture a snapshot of the syste via the values of these variables).

The ODE specification mini-language is parsed with the help of the
open source tool *DParser*, Plevyak (2015).

Chamber, J. M. and Temple Lang, D. (2001)
*Object Oriented Programming in R*.
R News, Vol. 1, No. 3, September 2001.
https://cran.r-project.org/doc/Rnews/Rnews_2001-3.pdf.

Hindmarsh, A. C.
*ODEPACK, A Systematized Collection of ODE Solvers*.
Scientific Computing, R. S. Stepleman et al. (Eds.),
North-Holland, Amsterdam, 1983, pp. 55-64.

Petzold, L. R.
*Automatic Selection of Methods for Solving Stiff and Nonstiff
Systems of Ordinary Differential Equations*.
Siam J. Sci. Stat. Comput. 4 (1983), pp. 136-148.

Hairer, E., Norsett, S. P., and Wanner, G.
*Solving ordinary differential equations I, nonstiff problems*.
2nd edition, Springer Series in Computational Mathematics,
Springer-Verlag (1993).

Plevyek, J.
*Dparser*, http://dparser.sourceforge.net. Web. 12 Oct. 2015.

```
# NOT RUN {
# Step 1 - Create a model specification
ode <- "
# A 4-compartment model, 3 PK and a PD (effect) compartment
# (notice state variable names 'depot', 'centr', 'peri', 'eff')
C2 = centr/V2;
C3 = peri/V3;
d/dt(depot) =-KA*depot;
d/dt(centr) = KA*depot - CL*C2 - Q*C2 + Q*C3;
d/dt(peri) = Q*C2 - Q*C3;
d/dt(eff) = Kin - Kout*(1-C2/(EC50+C2))*eff;
"
m1 <- RxODE(model = ode, modName = "m1")
print(m1)
# Step 2 - Create the model input as an EventTable,
# including dosing and observation (sampling) events
# QD (once daily) dosing for 5 days.
qd <- eventTable(amount.units = "ug", time.units = "hours")
qd$add.dosing(dose = 10000, nbr.doses = 5, dosing.interval = 24)
# Sample the system hourly during the first day, every 8 hours
# then after
qd$add.sampling(0:24)
qd$add.sampling(seq(from = 24+8, to = 5*24, by = 8))
# Step 3 - set starting parameter estimates and initial
# values of the state
theta <-
c(KA = .291, CL = 18.6,
V2 = 40.2, Q = 10.5, V3 = 297.0,
Kin = 1.0, Kout = 1.0, EC50 = 200.0)
# init state variable
inits <- c(0, 0, 0, 1);
# Step 4 - Fit the model to the data
qd.cp <- m1$solve(theta, events = qd, inits)
head(qd.cp)
# This returns a matrix. Note that you can also
# solve using name initial values. For example:
inits <- c(eff = 1);
qd.cp <- solve(m1, theta, events = qd, inits);
# }
```

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