This is a wrapper of the odeintr R package using symengine objects to specify the ODE system and C code generation functionality from symengine to generate the C++ source. The dxdt function and defined == S4 method allow one to intuitively specify the ODE system with symengine objects. The ODESystem will generate C++ source and compile on the fly with Rcpp. Then predict can be used to get results.

dxdt(x)

# S4 method for DxdtOdeConstructor,ANY
==(e1, e2)

ODESystem(
  odesys,
  ...,
  method = "rk5_i",
  atol = 1e-06,
  rtol = 1e-06,
  compile = TRUE
)

# S4 method for ODESystem
predict(object, init, duration, step_size = 1, start = 0)

Arguments

x

A SymEngine Basic object of type Symbol or a R object that will be converted to Symbol(x).

e1

A DxdtOdeConstructor S4 object which can be returned by `dxdt`.

e2

A Basic object or an R object that will be converted to `S(e2)`.

odesys, ...

DxdtOde S4 objects that can be returned with `dxdt(x) == rhs`. Or `odesys` can be a list of DxdtOde S4 objects when there is no dot arguments.

method, atol, rtol

Passed to `odeintr::compile_sys`.

compile

Logical, whether to compile the C++ source. Useful if you only want to obtain the code.

object

A ODESystem S4 object.

init

A numeric vector specifying the initial conditions. It can be named with the variable names or it can be unnamed but in the same of order of equations.

duration, step_size, start

Passed to the function generated by `odeintr::compile_sys`.

Value

dxdt returns a DxdtOdeConstructor S4 object.

S4 method of `==` for "DxdtOdeConstructor" returns a DxdtOde S4 object.

`ODESystem` returns a ODESystem S4 object.

`predict` returns a dataframe.

Examples

# A differential equation specified with dxdt and == x <- Symbol("x") eq <- dxdt(x) == 1/exp(x) print(eq)
#> Ordinary differential equation: #> d(x)/dt == 1.0*exp(-x)
# \donttest{ ## Lorenz system use_vars(x, y, z)
#> Initializing ‘x’, ‘y’, ‘z’
sigma <- 10 rho <- 28 beta <- 8/3 lorenz_sys <- ODESystem( dxdt(x) == sigma * (y - x), dxdt(y) == (rho - z) * x - y, dxdt(z) == - beta * z + x * y ) res <- predict( lorenz_sys, init = c(x = 1, y = 1, z = 1), duration = 100, step_size = 0.001 ) plot(res[, c(2, 4)], type = 'l', col = "steelblue", main = "Lorenz Attractor")
# }