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Solves a general system of ordinary differential equations (ODEs) using an algorithm by L. F. Shampine and M. K. Gordon:
y′(t) = f(t, y(t))
The code was originally translated from the Netlib version with the aid of f2c.
Download the latest tarball and run:
make PREFIX=/usr/local install
Replace /usr/local (the default PREFIX) with wherever you want it to be installed. Afterward, the library will be installed to $PREFIX/lib/libsgode.so and the header files will be installed to $PREFIX/include/sg_ode/.
Arch Linux users can use the PKGBUILD script instead.
To include the headers in your source code, write:
#include <sg_ode/ode.h>Be sure that $PREFIX/include is part of your header search path (-I $PREFIX/include).
To link with the library, pass -l sgode and make sure $PREFIX/lib is part of your library search path (-L $PREFIX/include).
The tests/main.c directory provides a generic test driver for integrating ODE equations using this library. It must be linked with either tests/harmonic_oscillator.c, tests/jacobian_elliptic_a.c, or tests/jacobian_elliptic_b.c to create a full program.
To support parallelization, the algorithm utilizes an abstract vector interface that is sufficiently generic to support single-threaded, multi-threaded, and distributed vector representations without significantly compromising performance. The actual implementations are provided by a vector driver.
To keep the library lightweight and dependency-free, the library comes with only a driver for the trivial vector representation. It should be straightforward to implement a driver for a distributed vector representation for say MPI.
The core of the abstract vector interface lies in a single higher-order function that we have uncreatively named operate. Here is a sketch of its type signature with the boring parts omitted for clarity:
void operate(Accum total,
void f(Accum subtotal,
const Accum input,
double data[m][n],
size_t n),
Vector vectors[m],
size_t m);The function operate performs a map-like (i.e. element-wise) operation over m vectors followed by a fold (accumulate/reduce) operation over all the elements. The actual operation is specified by f, which performs the desired operation over a set of m subvectors of length n and also accumulates the value of input as well as the value of the subvector elements into the subtotal.
- L. K. Shampine and M. K. Gordon, Computer Solution of Ordinary Differential Equations: The Initial Value Problem (Freeman, 1975), ISBN: 0716704617.