This program estimates the integral of a function using Monte Carlo integration with OpenMP for parallelization. It calculates the integral over a given range, computes statistical values like variance, standard deviation, and relative error, and stores the results in a CSV file. The integral is computed in batches, where each batch has an increasing number of random samples (histories).
- Option 1: Compile and run the program using
./run.sh - Option 2: Compile using a FORTRAN compiler.
run.shuses OpenMP so the -fopenmp tag must be added to the custom command. However, this is not strictly necessary
aandb: These define the lower and upper bounds of the definite integral.batches: This is the number of times the integration is repeated with increasing histories.histories: Initial number of random points (histories) to calculate the integral for the first batch.hist_factor: Increases the value of histories by a factor every new batch.
lit_val: The known or exact value of the integral for comparison. (required for percent error calculation)
The program generates a CSV file named results.csv containing the results of each batch. It includes:
- Batch number
- Calculated integral (IMC value)
- Number of histories used in that batch
- Variance
- Standard deviation (stdv)
- Relative error (rel_err)
- Batch execution time
The function being integrated is in terms of a one variable f(x) funciton. You can modify it by editing the f(x) function inside the program:
function f(x) result(y)
real(dp) :: x, y
y = x ! Modify this to integrate a different function
end function f- matplotlib
- pandas
- numpy