The solver that uses DASKR, a variant of DASSL.

See sim for the interface.

The solver that uses Sundials.

See sim for the interface.

sim is the name of the default solver used to simulate Sims models and also shows the generic simulation API for available solvers (currently dasslsim and sunsim). The default solver is currently dasslsim if DASSL is available.

sim has many method definitions to accomodate solutions based on intermediate model representations. Also, both positional and keyword arguments are supported (use one or the other after the first argument).

sim(m::Model, tstop::Float64=1.0, Nsteps::Int=500, reltol::Float64=1e-4, abstol::Float64=1e-4, init::Symbol=:Ya_Ydp, alg::Bool=true)
sim(m::Model; tstop::Float64=1.0, Nsteps::Int=500, reltol::Float64=1e-4, abstol::Float64=1e-4, init::Symbol=:Ya_Ydp, alg::Bool=true)
sim(m::Sim, tstop::Float64=1.0, Nsteps::Int=500, reltol::Float64=1e-4, abstol::Float64=1e-4, init::Symbol=:Ya_Ydp, alg::Bool=true)
sim(m::Sim; tstop::Float64=1.0, Nsteps::Int=500, reltol::Float64=1e-4, abstol::Float64=1e-4, init::Symbol=:Ya_Ydp, alg::Bool=true)
sim(m::SimState, tstop::Float64=1.0, Nsteps::Int=500, reltol::Float64=1e-4, abstol::Float64=1e-4, init::Symbol=:Ya_Ydp, alg::Bool=true)
sim(m::SimState; tstop::Float64=1.0, Nsteps::Int=500, reltol::Float64=1e-4, abstol::Float64=1e-4, init::Symbol=:Ya_Ydp, alg::Bool=true)

Arguments

• m::Model : a Model

• sm::Sim : a simulation object

• ss::SimState : a simulation object

• tstop::Float64 : the simulation stopping time [secs], default = 1.0

• Nsteps::Int : the number of simulation steps, default = 500

• reltol::Float64 : the relative tolerance, default = 1e-4

• abstol::Float64 : the absolute tolerance, default = 1e-4

• init : initialization of the model; options include:

  • :none : no initialization

  • :Ya_Ydp : given Y_d, calculate Y_a and Y'_d (the default)

  • :Y : given Y', calculate Y

  • alg : indicates whether algebraic variables should be included in the error estimate (default is true)

Returns

• ::SimResult : the simulation result

The result can be plotted with Plots.jl.

Details

The main steps in converting to a model and doing a simulation are:

eqs::EquationSet = elaborate(m::Model)   # flatten the model
sm::Sim = create_sim(eqs::EquationSet)   # prepare for simulation
sm::SimState = create_simstate(sm::Sim)  # prepare for simulation II
y::SimResult = sim(ss::SimState)         # simulate

The following are equivalent:

y = sim(create_simstate(create_sim(elaborate(m))))
y = sim(m)

Example

using Sims
function Vanderpol()
    y = Unknown(1.0, "y")   # The 1.0 is the initial value. "y" is for plotting.
    x = Unknown("x")        # The initial value is zero if not given.
    # The following gives the return value which is a list of equations.
    # Expressions with Unknowns are kept as expressions. Expressions of
    # regular variables are evaluated immediately (like normal).
    @equations begin
        # The -1.0 in der(x, -1.0) is the initial value for the derivative 
        der(x, -1.0) = (1 - y^2) * x - y 
        der(y) = x
    end
end

v = Vanderpol()       # returns the hierarchical model
y = sunsim(v, 50.0)

plot(y)

A representation of a flattened model, normally created with elaborate(model). sim uses an elaborated model for simulations.

Contains the hierarchical equations, flattened equations, flattened initial equations, events, event response functions, and a map of Unknown nodes.

elaborate is the main elaboration function that returns a flattened model representation that can be used by sim.

elaborate(a::Model)

Arguments

• a::Model : the input model

Returns

• ::EquationSet : the flattened model

Details

The main steps in flattening are:

• Replace fixed initial values.

• Flatten models and populate eq.equations.

• Pull out InitialEquations and populate eq.initialequations

• Pull out Events and populate eq.events.

• Handle StructuralEvents.

• Collect nodes and populate eq.nodeMap.

• Strip out MExpr's from expressions.

• Remove empty equations.

There is currently no real symbolic processing (sorting, index reduction, or any of the other stuff a fancy modeling tool would do).

In EquationSet, model contains equations and StructuralEvents. When a StructuralEvent triggers, the entire model is elaborated again. The first step is to replace StructuralEvents that have activated with their new_relation in model. Then, the rest of the EquationSet is reflattened using model as the starting point.

The set of functions used in the DAE solution. Includes an initial set of equations, a residual function, and several functions for detecting and responding to events.

All functions take (t,y,yp) as arguments. {TODO: is this still right?}

A type for holding several simulation objects needed for simulation, normally created with create_sim(eqs).

The top level type for holding all simulation objects needed for simulation, including a Sim. Normally created with create_simstate(sim).

create_sim converts a model to a Sim.

create_sim(m::Model)
create_sim(eq::EquationSet)

Arguments

• m::Model : a Model

• eq::EquationSet : a flattened model

Returns

• ::Sim : a simulation object

create_simstate converts a Sim is the main conversion function that returns a SimState, a simulation object with state history.

create_simstate(m::Model)
create_simstate(eq::EquationSet)
create_simstate(sm::Sim)

Arguments

• m::Model : a Model

• eq::EquationSet : a flattened model

• sm::Sim : a simulation object

Returns

• ::Sim : a simulation object

A type holding simulation results from sim, dasslsim, or sunsim. Includes a matrix of results and a vector of column names.