APL Programs Research Articles

Avoiding the bit-reversed ordering in parallel multi-digit multiplication based on FFT

The paper for the parallel model of computation, a modification of the method of implementing the multiplication of multi-digit integers based on the fast Fourier transform (FFT) avoiding the bit-reversed ordering is proposed. The paper researches the calculation of FFT according to the “butterfly” scheme based on decimation-in- frequency and decimation-in-time methods, an input signal with elements in direct and bit-reversed order, with an increase and decrease in the number Fourier series coefficients at each step of the "butterfly", the use of a list of Fourier series coefficients in direct and bit-reversed order. The standard FFT-based multiplication algorithm uses the same “butterfly” operation to compute the forward and inverse Fourier transforms. The paper analyzes two combinations of the FFTFDN–FFTTBN and FFTFBN–FFTTDN “butterfly” calculation schemes for calculating forward and inverse discrete Fourier transforms (DFT) in the case of implementing the multi-digit operation in parallel computational model to exclude bit-reversed permutation. A scheme for distributing calculations among four processors is proposed, in which forward and inverse Fourier transform calculations are localized within one parallel processor. The proposed modification does not reduce the computational complexity in terms of the number of complex operations, but due to the exclusion of bit-reversed permutation, the number of synchronization commands between processors and data is reduced, which reduces the algorithm execution time. The scheme can be adapted to distribute the computations among a larger number of processors. Four algorithms for implementing FFT based on decimation-in-frequency and decimation-in-time methods, an input vector with elements in direct and bit-reversed orders are presented. To check the result of the calculation, the algorithm of multiplication avoiding the steps of bit-reversed ordering was implemented in the APL programming language. An example of calculation is given in the form of a table.

Automatic generation of APL programs

This paper describes the use of grammatical evolution to generate APL programs which perform some pre-required function.

APL.NET encryption HOWTO

The article outlines the key points of building a Dyalog APL interface to the GNU Privacy Guard (GnuPG), a tool for cryptographic privacy and authentication. The main purpose of the interface is to use the GnuPG's functionality to encrypt data and create digital signatures directly from APL programs. The article briefly describes .NET classes that form the core of the interface and provide effective means to manage processes running on a computer. It also contains a number of examples demonstrating usage of the interface and the underlying ideas.

The making of the MCM/70 microcomputer

MCM/70, manufactured by Micro Computer Machines (MCM), was a small desktop microcomputer designed to provide the APL programming language environment for business, scientific, and educational use. MCM was among the first companies to fully recognize and act upon microprocessor technology's immense potential for developing a new generation of cost-effective computing systems. This article discusses the pioneering work on personal microcomputers conducted at MCM in the early 1970s and, in particular, the making of the MCM/70 microcomputer.

A SAS macro for the analysis of cell survival curves

This paper describes a SAS macro for the statistical analyses of cell survival data obtained after radiation treatment using the methods of R.E. Tarone et al. (Mutation Research 111 (1983) 79–96). These analyses are usually required on a routine basis by all biomedical research laboratories involved in cell survival assays generating dose–response curves aimed at characterizing radiosensitive mutant cell strains or individuals whose body cells exhibit enhanced sensitivity to radiation and other genotoxic agents. Statistical methods of linear regression are applied to data from repeated experiments with a cell line/strain and weighted estimates of a common slope and its variance are obtained. The methods are currently implemented in two APL programs. These programs are not easily accessible to most biomedical statisticians and researchers because APL is not a common software tool for statistical analysis. Implementation of these methods in SAS, a widely used commercial software for statistical analysis, is expected to help resolve this issue. We illustrate the application of the macro using an example data set obtained in our laboratory, and hope that other investigators may find it useful in analyzing their data.

Applied Physics Laboratory participation in SAX99: Experiment design and execution

The main goals of the APL program in SAX99 were to measure and improve our ability to model acoustic propagation within, high-frequency backscattering from, and penetration into sand sediments. To prepare for these measurements, new equipment and experimental procedures were developed. For the penetration studies, simulations were used extensively to guide the experiment design in order to ensure that the measurements would be useful for addressing our goals. Illustrations will be given of how simulations were used to support the experiment design. The APL experimental equipment used in SAX99 will be described, and the experimental procedures will be presented. Finally, the resulting data set will be summarized. [Work supported by ONR.]

An interface between Java and APL

This paper discusses an interface between the Java and APL languages. It is in the form of a report on some technology that has been developed for SHARP APL, though there are no aspects of the technology that are particularly special to that dialect of APL.The interface (called, for the purposes of this paper, the "APL-Java Interface") is a general facility for allowing APL programs and Java programs to work together. The project was started because it occurred to us that there is now a substantial body of Java-based technology that solves many of the problems that we needed to address for APL, particularly in the area of program interoperability; and, since this Java-based technology is both widely (and, in many cases, freely) available, and portable across the platforms that are of most concern to us, it would make a lot of sense to try to develop a general way to access this technology from APL. If that could be done, we could largely avoid re-inventing the wheel in a whole set of instances, by capitalizing on existing Java-based solutions. As a simple example, rather than implementing the standard XML parser in APL (which is certainly possible), we could simply use one of the several existing Java implementations.There are four parts to this paper:• A very brief discussion of Java is given.• An overview of the APL-Java Interface is presented, with some examples.• Some practical uses for the interface are presented.Some aspects of the interface that are of some technical interest are discussed.• The dialect of APL used in code examples in this paper is SHARP APL.A knowledge of Java will certainly help with this paper, but the dependency on such knowledge is not all that heavy, so it is quite likely that most of the paper's points can be grasped given just the few simple Java notions listed below.

An APL ompiler

Even if APL is the best-suited programming language for multi-dimensional data, nowadays computer applications additionally require complex graphical user interfaces, internet and database access. Combining software written in C, C++ or Java with interpreted APL programs is difficult. A homogeneous solution has been found by automatically converting APL programs into native C code. A complete APL2 like system including interpreter and session manager has been implemented in ISO C from scratch based on the standard C library. It is the property of the author and not yet commercially available. It has been successfully compiled on several operating systems. The built in system call APL2C allows one to compile any APL function including all referenced functions or operators within the workspace into native C code and completely removes the interpreter using direct calls to the C coded APL primitives. Only obvious restrictions (no runtime execution of character arrays or dynamic creation of functions via FX ) apply. In addition, a makefile is created to enable the simple build of standalone executable files. The C files, generated by APL2C, can be easily mixed with other C/C++ source files and compiled on any platform provided that the required library for the APL primitives is available.

The killer app

I've been a programmer for over 30 years, often at the leading edge, never in a classic IT shop. I've worked with several vendors' mainframes, midis and micros, for big firms, small firms, central government, educational establishments, and for myself; in colleges, universities, laboratories and classrooms; in England, in Europe, and in the USA. I've been involved in some total flops, but in one or two real successes too. I could never tell from the outset which it was going to be. The more I see of the software industry, the less I feel I know anything about it. Giving a talk like this is sticking my neck out.But plus ça change… plus ça la même chose. I think I've seen enough by now, and maybe my experience will interest somebody. We've all dreamed of writing the APL program which will make our fortunes. I've had to launder my examples, to protect the guilty along with the innocent. But where I name names, what I have to say is already in the public domain. I've omitted a detailed reference --- this will have to await the book. Most of the principles I've discerned I'm going to present as the experience of two fictitious, companies, Company A, Company B.Company A is not just based on one particular company I've known. Nor is Company B. I bought a honeycomb once. It said on the back 'Produce of more than one country'. I thought, what a marvellous thing --- the dear little bees had actually co-operated in an International Honeycomb! A lesson to us all. But my fictitious companies really are a blend. Not an International Beehive. (Not even IBM was like that.)

Accelerating APL programs with SAC

The paper investigates, how S AC , a purely functional language based on C syntax, relates to A PL in terms of expressiveness and run-time behavior. To do so, three different excerpts of real world A PL programs are examined. It is shown that after defining the required A PL primitives in S AC , the example programs can be re-written in S AC with an almost one-to-one correspondence. Run-time comparisons between interpreting A PL programs and compiled S AC programs show that speedups due to compilation vary between 2 and 500 for three representative benchmark programs.

First flight

This paper discusses a proposed beginner-level APL tutorial program that can be delivered as an APL program or as an internet web site. The need for developing automated APL learning is presented, and cognitive as well as constructivist instructional design issues are reviewed. Implementation issues are discussed for APL-only and for combined APL and HTML approaches.

The use of Markov discontinuous processes in the pricing of derivative securities

The paper deals with one of the most important fields of research in modern financial theory: the valuation of derivatives. The aim of the work is the use of a discontinuous Markov process to model the dynamics of stock prices and, consequently to discover the right price of the derivative instruments, in place of the traditional binomial multiplicative process used frequently in many discrete models. At the end of the work various applications are presented. In them the stochastic process of the stock prices is modelled with the use of a simple and powerful APL program. In the applications APL shows all its capacity of calculation and matrix manipulation for mathematical uses.

The permutation distribution of the Friedman test

In this article an algorithm is presented to compute the exact permutation distribution of the nonparametric Friedman test for the two-way layout with possible stochastic dependencies within rows. Apart from regular convolution methods this algorithm uses the rich algebraic structure of the full permutation group. This leads to a substantial reduction of the computational workload. The algorithm makes use of some mathematical operators on k-dimentional arrays which all are available in the computer language APL (take, transpose and ravel). However, these operators are explained in detail in this article to facilitate understanding without knowledge of APL. APL programs are provided.

Cross-tabulation algorithms

The cross-tabulation technique is a common tool for data analysis and other statistical purposes. But when the datasets are large the standard software such as spreadsheet programs cannot process all the data or the database programs are too slow. It is therefore necessary to offer efficient APL programs which are well designed for cross-tabulations. There are various algorithms in APL but which ones are appropriate for such tasks?

Linear programming in APL

Linear programming in APL

Precision Intervals for Estimates of the Difference in Success Rates for Binary Random Variables Based on the Permutation Principle

AbstractFisher's exact test is a very commonly applied test in clinical trials with a binary outcome variable (e.g. success/failure). However confidence statements about the difference of success rates are usually based on the normal approximation. This may sometimes lead to the confusing statement that the test is statistically significant at a prespecified level while the corresponding confidence interval includes the zero difference and vice versa. Here, we construct precision intervals for the difference of success rates from two independent samples based on the permutation principle which are in perfect agreement with the discrete (permutation) test and compare it to examples from the literature. APL programs are provided.

A parallel processed scheme for the eigenproblem of positive definite matrices

This paper deals with the eigenproblem of positive definite matrices. A numerical algorithm, to find the largest eigenvalues of a full positive definite matrix using Householder reflections, is described. The proposed algorithm can be used to find all the eigenvalues of a symmetric matrix or at least the first few largest ones. The scheme is proved to be convergent and the convergence rate is calculated. The full matrix is operated upon, at each iteration; hence one could use the APL programming language to write down a very brief code to implement the program.

Aberth's method for the parallel iterative finding of polynomial zeros

Aberth's method for the iterative finding of polynomial zeros using simultaneous interacting guesses is seen to be the systematic use of Newton's method under Parallel Anticipatory Implicit Deflation (PAID), changing the single polynomial problem into that for a system of rational functions. It offers the prospect of parallel execution, discourages coincident convergences, and subjects all iterates to the same algorithm, without the uneven roundoff error accumulation due to deflation typical in serial iterative methods. Yet it converges slowly to multiple zeros, and consumes far more total computing power than serial methods. Factors hindering convergence include problem symmetry and clustering of iterates, alleviated by asymmetric initial guesses and an immediate updating strategy, as seen through the speedup in the experimental APL program PAIDAX.

A Stochastic Analysis of State Transitions in an Air-Space Management System

This paper explores the application of stochastic process ideas to answer some fundamental questions about a state system which arises in the Mode Select Beacon System (Mode-S), an air-space management system. A series of models is developed, based on semi-Markov processes, population models, and Monte Carlo simulation. Computer programs in the APL programming language to implement the models and to process the resulting data are developed. The output of the models illuminate the behavior of the state system by providing predictions with confidence bounds about the movements of aircraft among the states over time.

A constrained optimal control program in APL

This note formulates a dynamic control model which optimizes a quadratic objective functional subject to linear constraints and solves in APL. Besides giving the optimal objective function value, the APL program computes values of the gain matrices, the Riccati equations, the state variables and the control variables. The power, compactness and flexibility of the APL program are undoubted when compared with other software. The most useful result of the exercise is that the APL program can be easily modified to the exact requirements of the individual researcher, faculty member, consultant and student.