This uses RxODE family of objects, file, or model specification to solve a ODE system.

rxControl(
scale = NULL,
method = c("liblsoda", "lsoda", "dop853"),
transitAbs = NULL,
atol = 1e-08,
rtol = 1e-06,
maxsteps = 70000L,
hmin = 0L,
hmax = NA,
hmaxSd = 0,
hini = 0,
maxordn = 12L,
maxords = 5L,
...,
cores,
covsInterpolation = c("locf", "linear", "nocb", "midpoint"),
matrix = FALSE,
sigma = NULL,
sigmaLower = -Inf,
sigmaUpper = Inf,
nCoresRV = 1L,
sigmaIsChol = FALSE,
nDisplayProgress = 10000L,
amountUnits = NA_character_,
timeUnits = "hours",
stiff,
theta = NULL,
thetaLower = -Inf,
thetaUpper = Inf,
eta = NULL,
stateTrim = Inf,
updateObject = FALSE,
omega = NULL,
omegaIsChol = FALSE,
omegaLower = -Inf,
omegaUpper = Inf,
nSub = 1L,
thetaMat = NULL,
thetaIsChol = FALSE,
nStud = 1L,
dfSub = 0,
dfObs = 0,
returnType = c("rxSolve", "matrix", "data.frame", "data.frame.TBS", "data.table",
"tbl", "tibble"),
seed = NULL,
nsim = NULL,
minSS = 10L,
maxSS = 1000L,
infSSstep = 12,
strictSS = TRUE,
params = NULL,
events = NULL,
istateReset = TRUE,
subsetNonmem = TRUE,
linLog = FALSE,
maxAtolRtolFactor = 0.1,
from = NULL,
to = NULL,
by = NULL,
length.out = NULL,
iCov = NULL,
keep = NULL,
drop = NULL,
idFactor = TRUE,
mxhnil = 0,
hmxi = 0,
warnIdSort = TRUE,
warnDrop = TRUE,
ssAtol = 1e-08,
ssRtol = 1e-06,
safeZero = TRUE
)

rxSolve(object, ...)

# S3 method for default
rxSolve(object, params = NULL, events = NULL, inits = NULL, ...)

# S3 method for rxSolve
update(object, ...)

# S3 method for RxODE
predict(object, ...)

# S3 method for rxSolve
predict(object, ...)

# S3 method for rxEt
predict(object, ...)

# S3 method for rxParams
predict(object, ...)

# S3 method for RxODE
simulate(object, nsim = 1L, seed = NULL, ...)

# S3 method for rxSolve
simulate(object, nsim = 1L, seed = NULL, ...)

# S3 method for rxParams
simulate(object, nsim = 1L, seed = NULL, ...)

# S3 method for rxSolve
solve(a, b, ...)

# S3 method for RxODE
solve(a, b, ...)

# S3 method for rxParams
solve(a, b, ...)

# S3 method for rxEt
solve(a, b, ...)

## Arguments

scale a numeric named vector with scaling for ode parameters of the system. The names must correspond to the parameter identifiers in the ODE specification. Each of the ODE variables will be divided by the scaling factor. For example scale=c(center=2) will divide the center ODE variable by 2. The method for solving ODEs. Currently this supports: "liblsoda" thread safe lsoda. This supports parallel thread-based solving, and ignores user Jacobian specification. "lsoda" -- LSODA solver. Does not support parallel thread-based solving, but allows user Jacobian specification. "dop853" -- DOP853 solver. Does not support parallel thread-based solving nor user Jacobain specification boolean indicating if this is a transit compartment absorption a numeric absolute tolerance (1e-8 by default) used by the ODE solver to determine if a good solution has been achieved; This is also used in the solved linear model to check if prior doses do not add anything to the solution. a numeric relative tolerance (1e-6 by default) used by the ODE solver to determine if a good solution has been achieved. This is also used in the solved linear model to check if prior doses do not add anything to the solution. maximum number of (internally defined) steps allowed during one call to the solver. (5000 by default) The minimum absolute step size allowed. The default value is 0. The maximum absolute step size allowed. When hmax=NA (default), uses the average difference (+hmaxSd*sd) in times and sampling events. When hmax=NULL RxODE uses the maximum difference in times in your sampling and events. The value 0 is equivalent to infinite maximum absolute step size. The number of standard deviations of the time difference to add to hmax. The default is 0 The step size to be attempted on the first step. The default value is determined by the solver (when hini = 0) The maximum order to be allowed for the nonstiff (Adams) method. The default is 12. It can be between 1 and 12. The maximum order to be allowed for the stiff (BDF) method. The default value is 5. This can be between 1 and 5. Other arguments including scaling factors for each compartment. This includes S# = numeric will scale a compartment # by a dividing the compartment amount by the scale factor, like NONMEM. Number of cores used in parallel ODE solving. This defaults to the number or system cores determined by rxCores for methods that support parallel solving (ie thread-safe methods like "liblsoda"). specifies the interpolation method for time-varying covariates. When solving ODEs it often samples times outside the sampling time specified in events. When this happens, the time varying covariates are interpolated. Currently this can be: "linear" interpolation (the default), which interpolates the covariate by solving the line between the observed covariates and extrapolating the new covariate value. "constant" -- Last observation carried forward. "NOCB" -- Next Observation Carried Backward. This is the same method that NONMEM uses. "midpoint" Last observation carried forward to midpoint; Next observation carried backward to midpoint. A boolean indicating if covariates should be added to the output matrix or data frame. By default this is disabled. A boolean indicating if a matrix should be returned instead of the RxODE's solved object. Named sigma covariance or Cholesky decomposition of a covariance matrix. The names of the columns indicate parameters that are simulated. These are simulated for every observation in the solved system. Degrees of freedom of the sigma t-distribution. By default it is equivalent to Inf, or a normal distribution. Lower bounds for simulated unexplained variability (by default -Inf) Upper bounds for simulated unexplained variability (by default Inf) Number of cores used for the simulation of the sigma variables. By default this is 1. This uses the package rmvn and rmvt. To reproduce the results you need to run on the same platform with the same number of cores. This is the reason this is set to be one, regardless of what the number of cores are used in threaded ODE solving. Boolean indicating if the sigma is in the Cholesky decomposition instead of a symmetric covariance An integer indicating the minimum number of c-based solves before a progress bar is shown. By default this is 10,000. This supplies the dose units of a data frame supplied instead of an event table. This is for importing the data as an RxODE event table. This supplies the time units of a data frame supplied instead of an event table. This is for importing the data as an RxODE event table. a logical (TRUE by default) indicating whether the ODE system is stiff or not. For stiff ODE systems (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). A vector of parameters that will be named THETA[#] and added to parameters Lower bounds for simulated population parameter variability (by default -Inf) Upper bounds for simulated population unexplained variability (by default Inf) A vector of parameters that will be named ETA[#] and added to parameters Boolean indicating if the solve should add RxODE EVID and related columns. This will also include dosing information and estimates at the doses. Be default, RxODE only includes estimates at the observations. (default FALSE). When addDosing is NULL, only include EVID=0 on solve and exclude any model-times or EVID=2. If addDosing is NA the classic RxODE EVID events. When addDosing is TRUE add the event information in NONMEM-style format; If subsetNonmem=FALSE RxODE will also extra event types (EVID) for ending infusion and modeled times: EVID=-1 when the modeled rate infusions are turned off (matches rate=-1) EVID=-2 When the modeled duration infusions are turned off (matches rate=-2) EVID=-10 When the specified rate infusions are turned off (matches rate>0) EVID=-20 When the specified dur infusions are turned off (matches dur>0) EVID=101,102,103,... Modeled time where 101 is the first model time, 102 is the second etc. When amounts/concentrations in one of the states are above this value, trim them to be this value. By default Inf. Also trims to -stateTrim for large negative amounts/concentrations. If you want to trim between a range say c(0, 2000000) you may specify 2 values with a lower and upper range to make sure all state values are in the reasonable range. This is an internally used flag to update the RxODE solved object (when supplying an RxODE solved object) as well as returning a new object. You probably should not modify it's FALSE default unless you are willing to have unexpected results. Estimate of Covariance matrix. When omega is a list, assume it is a block matrix and convert it to a full matrix for simulations. The degrees of freedom of a t-distribution for simulation. By default this is NULL which is equivalent to Inf degrees, or to simulate from a normal distribution instead of a t-distribution. Indicates if the omega supplied is a Cholesky decomposed matrix instead of the traditional symmetric matrix. Lower bounds for simulated ETAs (by default -Inf) Upper bounds for simulated ETAs (by default Inf) Number between subject variabilities (ETAs) simulated for every realization of the parameters. Named theta matrix. The degrees of freedom of a t-distribution for simulation. By default this is NULL which is equivalent to Inf degrees, or to simulate from a normal distribution instead of a t-distribution. Indicates if the theta supplied is a Cholesky decomposed matrix instead of the traditional symmetric matrix. Number virtual studies to characterize uncertainty in estimated parameters. Degrees of freedom to sample the between subject variability matrix from the inverse Wishart distribution (scaled) or scaled inverse chi squared distribution. Degrees of freedom to sample the unexplained variability matrix from the inverse Wishart distribution (scaled) or scaled inverse chi squared distribution. This tells what type of object is returned. The currently supported types are: "rxSolve" (default) will return a reactive data frame that can change easily change different pieces of the solve and update the data frame. This is the currently standard solving method in RxODE, is used for rxSolve(object, ...), solve(object,...), "data.frame" -- returns a plain, non-reactive data frame; Currently very slightly faster than returnType="matrix" "matrix" -- returns a plain matrix with column names attached to the solved object. This is what is used object$run as well as object$solve "data.table" -- returns a data.table; The data.table is created by reference (ie setDt()), which should be fast. "tbl" or "tibble" returns a tibble format. an object specifying if and how the random number generator should be initialized represents the number of simulations. For RxODE, if you supply single subject event tables (created with eventTable) Minimum number of iterations for a steady-state dose Maximum number of iterations for a steady-state dose Step size for determining if a constant infusion has reached steady state. By default this is large value, 420. Boolean indicating if a strict steady-state is required. If a strict steady-state is (TRUE) required then at least minSS doses are administered and the total number of steady states doses will continue until maxSS is reached, or atol and rtol for every compartment have been reached. However, if ODE solving problems occur after the minSS has been reached the whole subject is considered an invalid solve. If strictSS is FALSE then as long as minSS has been reached the last good solve before ODE solving problems occur is considered the steady state, even though either atol, rtol or maxSS have not been achieved. 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; an eventTable object describing the input (e.g., doses) to the dynamic system and observation sampling time points (see eventTable); When TRUE, reset the ISTATE variable to 1 for lsoda and liblsoda with doses, like deSolve; When FALSE, do not reset the ISTATE variable with doses. subset to NONMEM compatible EVIDs only. By default TRUE. Boolean indicating if linear compartment models be calculated more accurately in the log-space (slower) By default this is off (FALSE) The maximum atol/rtol that FOCEi and other routines may adjust to. By default 0.1 When there is no observations in the event table, start observations at this value. By default this is zero. When there is no observations in the event table, end observations at this value. By default this is 24 + maximum dose time. When there are no observations in the event table, this is the amount to increment for the observations between from and to. The number of observations to create if there isn't any observations in the event table. By default this is 200. A data frame of individual non-time varying covariates to combine with the params to form a parameter data.frame. Columns to keep from either the input dataset or the iCov dataset. With the iCov dataset, the column is kept once per line. For the input dataset, if any records are added to the data LOCF (Last Observation Carried forward) imputation is performed. Columns to drop from the output This boolean indicates if original ID values should be maintained. This changes the default sequentially ordered ID to a factor with the original ID values in the original dataset. By default this is enabled. maximum number of messages printed (per problem) warning that T + H = T on a step (H = step size). This must be positive to result in a non-default value. The default value is 0 (or infinite). inverse of the maximum absolute value of H to be used. hmxi = 0.0 is allowed and corresponds to an infinite hmax (default). hmin and hmxi may be changed at any time, but will not take effect until the next change of H is considered. This option is only considered with method=liblsoda. Warn if the ID is not present and RxODE assumes the order of the parameters/iCov are the same as the order of the parameters in the input dataset. Warn if column(s) were supposed to be dropped, but were not present. Steady state atol convergence factor. Can be a vector based on each state. Steady state rtol convergence factor. Can be a vector based on each state. Use safe zero divide and log routines. By default this is turned on but you may turn it off if you wish. is a either a RxODE family of objects, or a file-name with a RxODE model specification, or a string with a RxODE model specification. 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); when using solve, this is equivalent to the object argument. If you specify object later in the argument list it overwrites this parameter. when using solve, this is equivalent to the params argument. If you specify params as a named argument, this overwrites the output

## Value

An “rxSolve” solve object that stores the solved value in 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 assignments in the RxODE model code). It also stores information about the call to allow dynamic updating of the solved object.

The operations for the object are similar to a data-frame, but expand the \$ and [[""]] access operators and assignment operators to resolve based on different parameter values, initial conditions, solver parameters, or events (by updating the time variable).

You can call the eventTable methods on the solved object to update the event table and resolve the system of equations.

## References

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).

RxODE