Sundials for Julia

Introduction

Sundials.jl is a Julia package that interfaces to the Sundials library. Sundials (the C library and this package) provides the following:

• CVODES - for integration and sensitivity analysis of ODEs. CVODES treats stiff and nonstiff ODE systems of the form y' = f(t,y,p), y(t0) = y0(p), where p is a set of parameters.
• IDAS - for integration and sensitivity analysis of DAEs. IDAS treats DAE systems of the form F(t,y,y',p) = 0, y(t0) = y0(p), y'(t0) = y0'(p)
• KINSOL - for solution of nonlinear algebraic systems. KINSOL treats nonlinear systems of the form F(u) = 0

Note that CVODES and IDAS contain all functions provided by CVODE and IDA (for integration without sensitivity analysis). If you need to use the latter, you can set enable_sensitivities=false in deps/build.jl and (re)build the package.

Julia is a fast, Matlab-like language that is well suited to modeling and simulations. It's particularly suited for use with Sundials because the functions representing the system will run at nearly the speed of C functions. Julia functions are compiled on the fly (JIT), so it is also possible to quickly recompile a system to model structural changes to the system.

I use Sundials in Sims, a Julia package to support equation-based modeling for simulations. Sims is like a lite version of Modelica. Sims can currently use Sundials or DASSL.

Installation

Within Julia, use the package manager:

Pkg.add("Sundials")

This should download and install the Sundials libraries and register the package. On Windows precompiled binaries are used, while on Unix and OSX Sundials is built from its sources (provided the necessary tools are available). If you have Sundials already installed, make sure that Julia can find it, e.g., via

push!(Sys.DL_LOAD_PATH, "/opt/local/lib")

before you install the package. Downloading and/or re-building of the library can be triggered by Pkg.build("Sundials") if anything goes wrong.

To test the installation use

Pkg.test("Sundials")

which currently runs some of the examples in the examples directory.

API

This package closely follows the Sundials C API. At a slightly higher level, many (but not all) Sundials.jl functions support passing Julia objects (like Arrays) instead of Sundials objects (like N_Vectors). See src/Sundials.jl for examples of how the higher-level interfacing works.

The Julia package Clang.jl was used to wrap Sundials. This directly uses Sundials' headers sort-of like SWIG. This is great work by Isaiah--it didn't take me much work to package a pretty complete interface to Sundials. For the wrapping code, see src/wrap_sundials.jl.

Because of Clang.jl, Sundials.jl provides good coverage of the Sundials library (the serial version).

Simplified Functions

Three functions kinsol, cvode, and idasol are provided as high-level, very simple functions. Note that the latter two functions were previously called ode and ida. Here is an example for cvode:

using Sundials

function f(t, y, ydot)
    ydot[1] = -0.04*y[1] + 1.0e4*y[2]*y[3]
    ydot[3] = 3.0e7*y[2]*y[2]
    ydot[2] = -ydot[1] - ydot[3]
end

t = [0.0, 4 * logspace(-1., 7., 9)]
res = Sundials.cvode(f, [1.0, 0.0, 0.0], t)

There are two supported keyword arguments, reltol, and abstol, for cvode and idasol. These functions will probably be deprecated, in order to create a unified API for ODE solvers under ODE.jl

Examples

See the examples directory.

Three-Body Problem is a notebook with a more thoroughly explained example.

Status

Please note that this is a developer preview. There could be bugs, and everything is subject to change. Of note are:

• The API that matches the Sundials C API should be stable.
• The simplified API is not stable.
• There is no documentation for this package. Please see the general C documentation for Sundials. The API should be identical.
• Macros like DENSE_ELEM are not available.
• Nothing is (yet) exported from the module. You need to put Sundials. in front of everything.
• Parts of the Sundials API that access C structures are difficult. One can use the StrPack package to read or write to these structures, but nothing is built into this package. See this CVODE example.
• The parallel versions of Sundials have been wrapped, but I doubt that they are usable from Julia. They need to be integrated with MPI.jl
• More work could be done to provide a better interface to N_Vectors.