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MCSLMonte Carlo simulation
language
Diego GarciaEita Shuto
Yunling WangChong Zhai
Outline of Presentation
• Introduction of language
• Language tutorial and examples
• Architectural design and implementation
• Summary and lessons learned
Monte Carlo methods
a class of computational algorithms that rely on repeated random sampling to compute their results.
Why interested with it?• widely used• good performance• possibly the only • efficient approach
Applications• Physics
– high energy particle physics, quantum many-body problem, transportation theory
• Mathematics – Integration, Optimization, Inverse problems, Computational
mathematics
• Computer science – Las Vegas algorithm, LURCH, Computer Go, General Game
Playing
• Finance– Option, instrument, portfolio or investment
Algorithm of MCSL
• Generation particular distributed psedu-random numbers (or low discrepancy sequence)
• Evaluate the function by sampling with these numbers
• Aggregate results! (weight might be counted, variational method or conditional acceptance might be considered)
Advantages
• Fast Random number algorithm (with good performance also)
• Other than iteration, consider all samples as a single vector
• Built-in Function to simplify aggregate process with different conditioning.
Example One Calculation of “π” = 3.14159265358979323846…
Sample code for Calculate Pi
Example 2-Pollard's rho algorithm
Sample code for Factorization
Language Implementation
Architectural Design andImplementation
Testing Cases
Summary and lessons learned• We have a language specification and a compiler
of Monte Carlo Simulation! It has…• Random type and type conversion• Useful builtin libraries, such as an iteration function…
• Teamwork and effective project management• SVN (Subversion) on Googlecode• Incremental Development Approach• Functional Language, Ocaml• Tiring work, supporting many data types
Thank You!
• MCSL Team• Columbia University• Dec 19th, 2008
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