Browsing by Author "Sarno, Riyanarto"

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    A comparison of vectorizable discrete sampling methods in Monte Carlo applications
    (1995) Sarno, Riyanarto; Bhavsar, Virendra, C.; Hussein, Esam, M., A.
    The performance of various vectorizable discrete random-sampling methods, along with the commonly used inverse sampling method, is assessed on a vector machine. Monte Carlo applications involving, one-dimensional, two-dimensional and multi-dimensional probability tables are used in the investigation. Various forms of the weighted sampling method and methods that transform the original probability table are examined. It is found that some form of weighted sampling is efficient, when the original probability distribution is not far from uniform or can be approximated analytically. Table transformation methods, though require additional memory storage, are best suited in applications where multi-dimensional tables are involved. Keywords: Discrete sampling, Weighted sampling, Monte Carlo simulations, Vector processing.
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    Design and analysis of vectorized Monte Carlo codes
    (1989) Sarno, Riyanarto; Bhavsar, Virendra, C.; Banerjee, Pradeep, K.
    Vectorized Monte Carlo codes use a set of vectors, generally referred to as a stack in the literature, to hold the attribute values of the entities carrying out random walks. This paper presents schemes for optimizing the performance of stack processing in Monte Carlo codes and carries out their execution time analyses. The proposed four schemes are: (i) continuous inspection of the stack with no stack compression, (ii) continuous inspection of the stack with stack compression, (iii) periodical inspection of the stack with no stack compression, and (iv) periodical inspection of the stack with stack compression. The execution time analysis of the continuous schemes is carried out using some results from Order Statistics, and that of the periodical inspection schemes is carried out using some results from Markovian decision processes. Under some assumptions, one of them being that the time required for random walk computations is exponentially distributed, closed-form expressions for the expected execution time are obtained. The theoretical performance of the proposed schemes is illustrated and concluding remarks are given. Finally, the performance of the schemes is illustrated through vectorizing few Monte Carlo codes and running them on IBM 3090-180VF. Keywords: Markovian decision processes, Monte Carlo codes, order statistics, parallel processing, supercomputing, vector processing
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    Discrete sampling methods for vector Monte Carlo codes
    (1992) Sarno, Riyanarto
    Sampling from an arbitrary discrete distribution in Monte Carlo calculations often requires a considerable amount of computing time on sequential computers as it involves table lookup computation. The vectorization of some existing discrete sampling methods is investigated, in an attempt to speed them up. These methods are applied to various problems including a large sparse system of linear equations and neutron transport problems. The codes are written in VS Fortran and implemented on the IBM 3090-lSOVF. Their performance for scalar and vector processing is evaluated based on both statistical and computational criteria. To overcome the computational drawbacks of these sampling methods, this thesis proposes a discrete sampling method, named the weighted sampling method, which is especially suited for vector processing. This method utilizes a uniform distribution to construct samples from a probability table. Each sample is subsequently adjusted so that unbiased estimates are obtained. The proposed method enhances the vectorizability of the vector Monte Carlo codes, and achieves better performance for the scalar as well as vector processing in comparison to those of the other sampling methods for the examined problems. Four variants of the weighted sampling method are also developed. These variants involve stretching of a probability table, sampling from known nonuniform distributions and the combination of two sampling methods. For this purpose, the study of vectorizing the random number generation from binomial and geometric distributions is carried out. It is demonstrated that these variants significantly increase the efficiency of Monte Carlo solutions by reducing the sample variance and decreasing the processing time through vectorization.