The python library parses mathematical functions that are exported from mathematica. The mathematical operations are represented within the flow_equation_parser.py file as a tree. This tree can be used to generate code in any programming language to perform the same mathematical operation. We do this here on the example of a set of ordinary differential equations and convert the equation into Thrust code that can be run with CUDA on a GPU.
Note that based on the flow_equation_parser, the code can be straightforwardly extended to support other programming languages and types of equations.
So far, the library needs to be build locally. This can be done by running
cd path_to_mathematica_parser/
pip install --use-feature=in-tree-build .We consider as and example a lorentz attractor:
with:
which results in a chaotic solution.
The equations are exported from the Mathematica file with the FullForm (see mathematica_notebooks/lorentz_attractor.nb). The resulting output is (see examples/flow_equations/lorentz_attractor):
List[Equal[Derivative[1][x][k], Times[10.`, Plus[Times[-1, x[k]], y[k]]]], Equal[Derivative[1][y][k], Plus[Times[-1, y[k]], Times[x[k], Plus[28.`, Times[-1, z[k]]]]]], Equal[Derivative[1][z][k], Plus[Times[x[k], y[k]], Times[Rational[-8, 3], z[k]]]]]
Note that in this case k refers to the time.
By executing the following python code in the top-level directory of the repository:
from mathematicaparser.odevisualization.generators import generate_equations
generate_equations("lorentz_attractor", "./examples/flow_equations/lorentz_attractor/")the mathematicaparser.core.flow_euquation_parser.FlowEquationParser class generates a tree in a pandas dataframe out of the above expression (example for the first ordinary differential equation):
Based on this tree, thrust cuda code is generated with the help of the modules of mathematicaparser.odevisualization
void LorentzAttractorFlowEquation0::operator() (devdat::DimensionIteratorC &derivatives, const devdat::DevDatC &variables)
{
thrust::transform(variables[0].begin(), variables[0].end(), variables[1].begin(), derivatives.begin(), [] __host__ __device__ (const cudaT &val1, const cudaT &val2) { return 10 * ((-1 * val1) + val2); });
}The computation of the first ordinary differential equation can be recognized in the lambda expression of the flow equation of the code snippet.
- numpy
- pandas
- ODEVisualization (https://github.com/statphysandml/ODEVisualization)
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