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benchmarks/Jumps/VR_Aggregator_Benchmark.jmd

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# Introduction
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This document benchmarks the performance of variable rate jumps in `JumpProcesses.jl` and visualizes example solution trajectories for the test cases from `variable_rate_test.jl`. The benchmark compares `VR_Direct` and `VR_FRM` aggregators, while the visualization shows state variables vs. time to verify simulation behavior.
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**Note**: If you encounter a precompilation error due to method overwriting in `JumpProcesses.jl`, add `__precompile__(false)` to `/home/siva/Desktop/julia/JumpProcesses.jl/src/JumpProcesses.jl` and clear the compilation cache (`rm -rf ~/.julia/compiled`).
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This document benchmarks the performance of variable rate jumps in `JumpProcesses.jl` and
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visualizes example solution trajectories for the test cases from `variable_rate_test.jl`.
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The benchmark compares `VR_Direct` and `VR_FRM` aggregators, while the visualization shows
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state variables vs. time to verify simulation behavior.
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The test cases are:
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1. **Scalar ODE with Variable Rate Jumps**: Solved with `Tsit5` and `Rosenbrock23` (with/without autodiff).
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2. **Scalar SDE with Variable Rate Jumps**: Solved with `SRIW1`.
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3. **SDE with Parameter-Switching Jump**: Solved with `SRA1`.
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4. **ODE with Constant Rate Jump**: Solved with `Tsit5`.
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5. **ODE with Variable Rate Jumps (Alternative Rate)**: Solved with `Tsit5`.
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6. **SDE with Variable Rate Jumps (Alternative Rate)**: Solved with `SRIW1`.
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7. **Matrix ODE with Variable Rate Jump**: Solved with `Tsit5`.
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8. **Complex ODE with Variable Rate Jump**: Solved with `Tsit5`.
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3. **ODE with Constant Rate Jump**: Solved with `Tsit5`.
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4. **ODE with Variable Rate Jumps (Alternative Rate)**: Solved with `Tsit5`.
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5. **SDE with Variable Rate Jumps (Alternative Rate)**: Solved with `SRIW1`.
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6. **Complex ODE with Variable Rate Jump**: Solved with `Tsit5`.
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For visualization, we solve one trajectory per test case with 2 jumps. For benchmarking, we vary jumps from 1 to 20, running 100 trajectories per configuration.
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For visualization, we solve one trajectory per test case with 2 jumps. For benchmarking,
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we vary jumps from 1 to 20, running 100 trajectories per configuration.
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# Benchmark and Visualization Setup
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