system_derivatives: Calculate Derivatives for Differential Quantities

Description

Solving a BioCro model using one of R's available differential equation solvers

Usage

system_derivatives(
    parameters = list(),
    drivers,
    direct_module_names = list(),
    differential_module_names = list()
  )

Value

The return value of system_derivatives is a function with three inputs (t, differential_quantities, and parms) that returns derivatives for each of the differential quantities in the dynamical system determined by the original inputs (parameters, drivers,

direct_module_names, and differential_module_names).

This function signature and the requirements for its inputs are set by the

LSODES function from the deSolve package. The t input should be a single time value and the differential_quantities input should be a vector with the names of the differential quantities defined by the modules. parms is required by LSODES, but we don't use it for anything.

This function can be passed to LSODES as an alternative integration method, rather than using one of BioCro's built-in solvers.

Arguments

parameters: Identical to the corresponding argument from run_biocro.
drivers: Identical to the corresponding argument from run_biocro.
direct_module_names: Identical to the corresponding argument from run_biocro.
differential_module_names: Identical to the corresponding argument from run_biocro.

Details

system_derivatives accepts the same input arguments as run_biocro with the exceptions of ode_solver and initial_values; this function is intended to be passed to an ODE solver in R, which will solve for the system's time dependence as its diffferential quantities evolve from their initial values, so ode_solver and initial_values are not required here.

When using one of the pre-defined crop growth models, it may be helpful to use the with command to pass arguments to system_derivatives; see the documentation for crop_model_definitions for more information.

Examples

Run this code

# Note: Example 3 below may take several minutes to run. Patience is required!

# Example 1: calculating a single derivative using a soybean model

soybean_system <- system_derivatives(
  soybean$parameters,
  soybean_weather$'2002',
  soybean$direct_modules,
  soybean$differential_modules
)

derivs <- soybean_system(0, unlist(soybean$initial_values), NULL)

# Example 2: a simple oscillator with only one module

times = seq(0, 5, by = 1) # times spaced by `timestep`

oscillator_system_derivatives <- system_derivatives(
  list(
    timestep = 1,
    mass = 1,
    spring_constant = 1
  ),
  data.frame(time = times),
  c(),
  'BioCro:harmonic_oscillator'
)

result <- as.data.frame(deSolve::lsodes(
  c(position=0, velocity=1),
  times,
  oscillator_system_derivatives
))

lattice::xyplot(
  position + velocity ~ time,
  type='l',
  auto=TRUE,
  data=result
)

# Example 3: solving 500 hours of a soybean simulation. This will run slowly
# compared to a regular call to `run_biocro`.

# \donttest{

soybean_system <- system_derivatives(
  soybean$parameters,
  soybean_weather$'2002',
  soybean$direct_modules,
  soybean$differential_modules
)

times = seq(from=0, to=500, by=1)

result <- as.data.frame(deSolve::lsodes(unlist(soybean$initial_values), times, soybean_system))

lattice::xyplot(Leaf + Stem ~ time, type='l', auto=TRUE, data=result)
# }