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Application of Numerical Methods to Selected Model Equations
Published in Dale A. Anderson, John C. Tannehill, Richard H. Pletcher, Munipalli Ramakanth, Vijaya Shankar, Computational Fluid Mechanics and Heat Transfer, 2020
Dale A. Anderson, John C. Tannehill, Richard H. Pletcher, Munipalli Ramakanth, Vijaya Shankar
Another strategy that is sometimes used in iterative schemes is to split the update sweep into two or more separate DO loops. Such an approach can permit the loops to be processed efficiently by vector machines. Vector processing is less common today than it was a few years ago, but the concept is worth summarizing here. The vectorization occurs in FORTRAN DO loops (only in the innermost loop if the loops are nested) and can be thought of as a simultaneous execution of the statements in the DO loop for all values of the DO parameter. If the statements in the DO loop are recursive in nature, that is, the right-hand side of the statement contains results previously computed in the loop, then the compiler rejects that loop for vectorization because an apparent error would occur if the statements were executed simultaneously. Vectorization naturally speeds up the algorithm and is a desirable feature. An example of a vectorizable FORTRAN DO loop is do10j=1,nja(j)=b(j)∗c+d10continue
Introduction to Python
Published in Dr Arzhang Angoshtari, Ali Gerami Matin, Finite Element Methods in Civil and Mechanical Engineering, 2020
Dr Arzhang Angoshtari, Ali Gerami Matin
An important feature of Numpy is vectorization, that is, instead of using loops over arrays, many NumPy operations can be directly preformed on arrays. Vectorization is useful for speeding up heavy numerical computations. As an example, suppose that we want to compute f(x)=exsin(x2), where x belongs to a uniform mesh of [0,1] with 2,000,000 vertices. In the following, we preform a standard loop version and a vectorized version of this computation and compare the time spent on each version.
Parallel Architectures
Published in Pranabananda Chakraborty, Computer Organisation and Architecture, 2020
A vector processor executes vector instructions giving rise to vector processing on the ordered set of scalar data items. It is distinguished from scalar processing which operates on one or one pair of data. A typical vector operation might add two 32-element (a1, a2, …, a32 and b1, b2, …, b32) floating-point vectors to obtain a single 32-element (c1, c2, …, c32) vector result. The vector instruction is equivalent to an entire loop, in which each of the iterations computes one of the 32 elements of the result and updates the indices and then branches back to the beginning to continue, and all these happen per clock cycle continuously. A schematic structure of a vector ALU is illustrated in Figure 10.30. The conversion from scalar code to vector code is called vectorization.
A scalable Bayesian framework for large-scale sensor-driven network anomaly detection
Published in IISE Transactions, 2023
After the parallelization clusters are found, the MCMC operations within each cluster require many repetitive steps (e.g., finding α) for many nodes at the same time. One approach that can utilize parallel operations on a CPU is vectorization that can potentially lead to the elimination of many for loops. In this subsection, we propose a series of steps to convert the proposed MCMC operations on a set of nodes into efficient and high-performance vectorized operations and matrix operations, which are supported by a typical CPU. For large networks and when GPU units are available, we can potentially speed up the MCMC even further. To further accelerate the convergence of the MCMC, we can also run multiple chains on several CPU units. Recall Ωc as the set of nodes in the cth cluster where they can be sampled together. Below, we introduce a series of vectorization steps for the proposed MCMC sampler. The target of the first step of vectorization is to generate vector where αi is the acceptance probability in the Metropolis–Hastings algorithm as follows: