eldo_user

Monte Carlo Analysis
Sampling Plan Methods
Sampling Plan Methods
The goal of Monte Carlo analysis is usually to estimate the distribution of a measure of
performance defined over a circuit.
The sampling plan methods available in Eldo Monte Carlo analysis are specified with the
SAMPLING parameter of the .MC command, as follows:
• Standard Monte Carlo uses a pseudo-random number generator to draw the input
sample. This is the random input used by default in Eldo. It comes from a pseudorandom
generator that outputs numbers between 0 and 1, which are assumed to imitate a
sequence of uniform random variables between 0 and 1. These numbers are then
transformed to follow the probability distributions specified by the model.
• Importance Sampling Monte Carlo uses a dedicated method for computing tail
probabilities. This method is specified using the MCPROB and MCBOUND functions.
Importance sampling uses the same pseudorandom generator as standard Monte Carlo
sampling. The pilot runs are standard MC runs, and the standard post-analysis is
performed on these runs.
• Quasi-Monte Carlo Method is an empirical sampling method based on Monte Carlo, but
using low discrepancy point sets instead of pseudorandom numbers. This improved (and
deterministic) sampling scheme roughly ‘fill the space’ in a better way.
• Latin Hypercube Sampling may be considered as a particular case of stratified sampling.
The purpose of stratified sampling is to achieve a better coverage of the sample space of
the input factors.
• Model-Based Monte Carlo Simulation is a variability analysis where the sampling plan
is optimized with respect to the number of random input variables and a user-defined
budget of runs.
Standard Monte Carlo
There are two different random number generators in Eldo depending on the argument
DATAFLOW of the .MC command.
When DATAFLOW=0 Eldo uses the drand48 routine provided in the standard C library, and
when DATAFLOW=1 the RNARRY routine described in D.E. Knuth, The Art of Computer
Programming (3rd edition, Addison Wesley, vol 2, Seminumerical algorithms, Chap 3).
The pseudo-random generator proposed with DATAFLOW=1 belongs to the family of lagged
Fibonacci generators. It overcomes some well-known weaknesses of the linear congruential
generator used in the drand48 routine. Specifically, if we build d-dimensional vectors from
consecutive random numbers (X i , X i+1 , …, X i+d ), then the points will lie on a relatively small
number of hyperplanes. This is due to the fact that the low-order bits of the generated numbers
have very short periods. Using this routine attempts to satisfy three objectives:
Eldo® User's Manual, 15.3 451