This is a fork from https://github.com/marcusps/ExpmV.jl, implementing the evaluation for multiple values of the parameter
t.
This is a Julia translation of the MATLAB implementation of Al-Mohy and Higham's
function for computing expm(t*A)*v when A is sparse, without explicitly computing expm(A).
If t is a StepRangeLen object (i. e. a linspace), use an optimized algorithm to output the result for all t.
The original code can be found at Matlabcentral File Exchange, and the theory is explained in the following article:
Computing the Action of the Matrix Exponential, with an Application to Exponential Integrators, Awad H. Al-Mohy and Nicholas J. Higham, SIAM Journal on Scientific Computing 2011 33:2, 488-511. (preprint)
Install into Julia using the package manager:
Pkg.add("ExpmV")expmv(t, A, v)Eg. t = 1., or t = linspace(0, 1, 100).
This benchmark shows the performance of ExpmV compared to Expokit.jl and the builtin dense expm of Julia, for complex matrices with (confidence interval 5%). The benchmark is done using BenchmarkTools.jl and the script in benchmark/compare.jl.
| Matrix rows | Expm |
Expokit |
Expmv |
|---|---|---|---|
| 32 | 158.495 μs | 30.100 μs | 53.609 μs |
| 64 | 856.923 μs | 52.036 μs | 58.536 μs |
| 128 | 7.805 ms | 537.083 μs | 80.650 μs |
| 256 | 40.027 ms | 2.993 ms | 112.047 μs |
| 512 | 277.680 ms | 3.195 ms | 218.490 μs |
| 1024 | 1.902 s | 4.267 ms | 571.590 μs |
| Matrix rows | Expm |
Expokit |
Expmv |
|---|---|---|---|
| 32 | 31.147 μs | 12.144 μs | 55.103 μs |
| 64 | 471.424 μs | 15.816 μs | 53.599 μs |
| 128 | 7.368 ms | 34.339 μs | 60.320 μs |
| 256 | 27.817 ms | 61.137 μs | 76.773 μs |
| 512 | 325.282 ms | 182.016 μs | 142.402 μs |
| 1024 | 1.568 s | 2.137 ms | 306.293 μs |
Released under the BSD 2-clause license used in Al-Mohy and Higham's original code.