find_loops_vset {LoopDetectR}

Loop detection for an ODE model at multiple sets of variables

Description

Determines loop lists for an ODE system given by a function and at multiple sets of variables. Loop lists are reported if signs of Jacobian matrix have changed.

Usage

find_loops_vset(
  fun,
  vset,
  ...,
  max_num_loops = 1e+05,
  compute_full_list = TRUE
)

Arguments

fun

Function defining the ODE system, returns the vector dx/dt. May depend on further parameters in ....

vset

List of variable values at which the loops are determined.

...

Further parameters except variable values to the function fun, none called x.

max_num_loops

Positive numeric value indicating the maximal number of loops that are reported in a loop list. Default: 10^5.

compute_full_list

Logical value indicating whether for each Jacobian matrix with any different sign the loop list is computed (TRUE, default), or whether further checks are performed to ensure that loops may be altered.

Details

The supplied function can take more arguments, but only the variables are allowed to be named x (they can also be named differently). The Jacobian matrices are computed for each of the variable values defined in vset using the jacobian function from the NumDeriv package with option method = 'complex', i.e. using a complex-step approach. If compute_full_list = TRUE (default), loop lists are not re-computed for Jacobians that clearly do not allow for altered loop lists. This is the case if no new regulation appear and only signs of regulations are altered that are not member of any loop. Loop lists can still be identical for different Jacobians, e.g. if two sign switches occur that are both affecting the same loops.

If there is only one class of Jacobian matrix (i.e. the signs of the Jacobian matrix are the same for all entries in vset), loop_rep and jac_rep will have only one entry each. The number of entries for loop_rep_index and jac_rep_index corresponds to the length of vset. Only if compute_full_list is set to FALSE, loop_rep can contain fewer elements than jac_rep, otherwise both have the same number of elements.

Value

A list with four entries:

• loop_rep List of loop lists.

• loop_rep_index Vector of integer numbers returning the index of the loop list in loop_rep belonging to each entry in vset.

• jac_rep List of signed Jacobian matrices.

• jac_rep_index Vector of integer numbers returning the index of the Jacobian matrix in jac_rep belonging to each entry in vset.

Examples

#default call to determine loops from an ODE model given by a function
#read in example functions
data("func_POSm4")
#the loaded function func_POSm4 takes arguments t, x, klin, knonlin
res_tab <- find_loops_vset(func_POSm4,vset=list(c(1,1,1,1)),t=1,
klin=c(1,2,0.5,1,2,0.1,3,2,3),knonlin=c(1,2))
#computed loop list:
res_tab$loop_rep[[1]] #or res_tab[[1]][[1]]

#determine loops from an ODE model over the course of a solution
#read in the example function defining the bacterial cell cycle
data("func_li08")
#kinetic parameter values are defined within the function
#read in a set of variable values (the solution of func_li08 with events)
data("li08_solution")
#transform the solution (columns: variables) to the correct list format
#and remove the time (first column)
li08_sol_list <- as.list(as.data.frame(t(li08_solution[,-1])))
res_tab <- find_loops_vset(func_li08,vset=li08_sol_list,t=1,
compute_full_list=FALSE)