Theory and Methodology¶
Theory¶
Grasshopper utilizes tools in Geant4 to generate Monte Carlo (MC) particle simultions. In computing, a Monte Carlo algorithm is a randomized algorithm whose output can be incorrect to a certain range in probability. One such examples of an MC algorithm is the Karger–Stein algorithm.
The name refers to the grand casino in the Principality of Monaco at Monte Carlo, which is famous around the world as an icon of gambling. The term “Monte Carlo” was first introduced in 1947 by Nicholas Metropolis.
Las Vegas algorithms are the subset of Monte Carlo algorithms that can always produce the correct answer. Because they make random choices as part of their working, the time taken might vary between runs even with the same input.
Given a procedure for verifying whether the answer given by a Monte Carlo algorithm is correct, and that the analyical probability of a correct answer is bounded above zero, then with probability one running the algorithm repeatedly while testing the answers will eventually give a correct answer. Whether this process is a Las Vegas algorithm depends on whether halting with probability one is considered to satisfy the definition. [1]