Lines Of Fortran Research Articles

A Robust Algebraic Domain Decomposition Preconditioner for Sparse Normal Equations

Solving the normal equations corresponding to large sparse linear least-squares problems is an important and challenging problem. For very large problems, an iterative solver is needed and, in general, a preconditioner is required to achieve good convergence. In recent years, a number of preconditioners have been proposed. These are largely serial, and reported results demonstrate that none of the commonly used preconditioners for the normal equations matrix is capable of solving all sparse least-squares problems. Our interest is thus in designing new preconditioners for the normal equations that are efficient and robust and can be implemented in parallel. Our proposed preconditioners can be constructed efficiently and algebraically without any knowledge of the problem and without any assumption on the least-squares matrix except that it is sparse. We exploit the structure of the symmetric positive definite normal equations matrix and use the concept of algebraic local symmetric positive semidefinite splittings to introduce two-level Schwarz preconditioners for least-squares problems. The condition number of the preconditioned normal equations matrix is shown to be theoretically bounded independently of the number of subdomains in the splitting. This upper bound can be adjusted using a single parameter $\tau$ that the user can specify. We discuss how the new preconditioners can be implemented on top of the PETSc library using only 150 lines of Fortran, C, or Python code. Problems arising from practical applications are used to compare the performance of the proposed new preconditioner with that of other preconditioners.

Improved algorithm for calculating high accuracy values of the Chandrasekhar function

Improved algorithm for calculating high accuracy values of the Chandrasekhar function

State-Transition Diagrams for Biologists

It is clearly in the tradition of biologists to conceptualize the dynamical evolution of biological systems in terms of state-transitions of biological objects. This paper is mainly concerned with (but obviously not limited too) the immunological branch of biology and shows how the adoption of UML (Unified Modeling Language) state-transition diagrams can ease the modeling, the understanding, the coding, the manipulation or the documentation of population-based immune software model generally defined as a set of ordinary differential equations (ODE), describing the evolution in time of populations of various biological objects. Moreover, that same UML adoption naturally entails a far from negligible representational economy since one graphical item of the diagram might have to be repeated in various places of the mathematical model. First, the main graphical elements of the UML state-transition diagram and how they can be mapped onto a corresponding ODE mathematical model are presented. Then, two already published immune models of thymocyte behavior and time evolution in the thymus, the first one originally conceived as an ODE population-based model whereas the second one as an agent-based one, are refactored and expressed in a state-transition form so as to make them much easier to understand and their respective code easier to access, to modify and run. As an illustrative proof, for any immunologist, it should be possible to understand faithfully enough what the two software models are supposed to reproduce and how they execute with no need to plunge into the Java or Fortran lines.

L2CXCV: A Fortran 77 package for least squares convex/concave data smoothing

Fortran 77 software is given for least squares smoothing to data values contaminated by random errors subject to one sign change in the second divided differences of the smoothed values, where the location of the sign change is also unknown of the optimization problem. A highly useful description of the constraints is that they follow from the assumption of initially increasing and subsequently decreasing rates of change, or vice versa, of the process considered. The underlying algorithm partitions the data into two disjoint sets of adjacent data and calculates the required fit by solving a strictly convex quadratic programming problem for each set. The piecewise linear interpolant to the fit is convex on the first set and concave on the other one. The partition into suitable sets is achieved by a finite iterative algorithm, which is made quite efficient because of the interactions of the quadratic programming problems on consecutive data. The algorithm obtains the solution by employing no more quadratic programming calculations over subranges of data than twice the number of the divided differences constraints. The quadratic programming technique makes use of active sets and takes advantage of a B-spline representation of the smoothed values that allows some efficient updating procedures. The entire code required to implement the method is 2920 Fortran lines. The package has been tested on a variety of data sets and it has performed very efficiently, terminating in an overall number of active set changes over subranges of data that is only proportional to the number of data. The results suggest that the package can be used for very large numbers of data values. Some examples with output are provided to help new users and exhibit certain features of the software. Important applications of the smoothing technique may be found in calculating a sigmoid approximation, which is a common topic in various contexts in applications in disciplines like physics, economics, biology and engineering. Distribution material that includes single and double precision versions of the code, driver programs, technical details of the implementation of the software package and test examples that demonstrate the use of the software is available in an accompanying ASCII file.

An automatic differentiation platform: Odyssée

Numerous automatic differentiation strategies can be imagined to produce all kind of derivative programs under a wide range of complexity constraints, but there is no way to prototype and evaluate them on real size applications with reasonable effort. Since the development of an automatic differentiation platform is prohibitively expensive, using an existing platform to share investments between the different research teams is a good solution. Odyssée is an open automatic differentiation tool that enables the development of program analysis as well as program transformation for automatic differentiation. It has been used to differentiate large size industrial programs (300 000 lines of Fortran 77) and to prototype diverse new automatic differentiation algorithms. Its source is now freely available, a cooperative research project can therefore be based on it without financial or contractual constraint.

Extending the functionality of the general‐purpose finite element package SEPRAN by automatic differentiation

AbstractFrom an abstract point of view, a numerical simulation implements a mathematical function that produces some output from some given input. Derivatives (or sensitivities) of the function's output with respect to its input can be obtained—free from truncation error—by using a technique called automatic differentiation. Given a computer code in a high‐level programming language like Fortran, C, or C++, automatic differentiation generates another code capable of computing not only the original function but also its derivatives. Thus, the application of automatic differentiation significantly extends the functionality of a simulation package. For instance, automatic differentiation enables, in a completely mechanical fashion, the usage of derivative‐based optimization algorithms where the evaluation of the objective function comprises some given large‐scale engineering simulation. In this paper, the automatic differentiation tool ADIFOR is used to transform the general‐purpose finite element package SEPRAN. In doing so, we automatically transform the given 400000 lines of Fortran 77 into a new program consisting of 600000 lines of Fortran 77. We compare our approach with a traditional approach based on numerical differentiation and quantify its advantages in terms of accuracy and computational efficiency for a standard fluid flow problem. Copyright © 2003 John Wiley & Sons, Ltd.

Computing sensitivities of the electrostatic potential by automatic differentiation

Abstract Given a computer model for the electrostatic potential in an L-shaped region with media of different dielectric permeabilities in two subregions, we are interested in the robustness of the simulation by identifying the rate of change of the potential with respect to a change in the permeabilities. Such sensitivity analyses, assessing the rate of change of certain model outputs implied by varying certain model inputs, can be carried out by computing the corresponding partial derivatives. In large-scale computational physics, the underlying computer model is typically available as a complicated computer code in a high-level programming language such as Fortran, C, or C++. To obtain accurate and efficient derivatives of functions given in this form, we use a technique called automatic or algorithmic differentiation. Unlike numerical differentiation based on divided differences, derivatives generated by automatic differentiation are free of truncation error. Here, the automatic differentiation tool Adifor is used to transform the given computer model—implemented with the general purpose finite element package SEPRAN—into a new computer code computing the derivatives of the electrostatic potential with respect to the dielectric permeabilities. In doing so, we automatically translate 400,000 lines of Fortran 77 into a new program consisting of 600,000 lines of Fortran 77. We compare our approach with a traditional approach based on numerical differentiation and quantify its advantages in terms of accuracy and computational efficiency.

Program to generate and evaluate three-phase structure-invariant ω estimates from single-wavelength anomalous dispersion data

A direct-methods computer program for evaluating three-phase structure invariants for single-wavelength anomalous dispersion data is described. The entire program was coded in 570 lines of Fortran, is highly automated and requires a minimal amount of user-supplied input data.

Sensitivity analysis of the MM5 weather model using automatic differentiation

We present a general method for using automatic differentiation to facilitate model sensitivity analysis. Automatic differentiation techniques augment, in a completely mechanical fashion, an existing code such that it also simultaneously and efficiently computes derivatives. Our method allows the sensitivities of the code’s outputs to its parameters and inputs to be determined with minimal human effort by exploiting the relationship between differentiation and formal perturbation theory. Employing this methodology, we performed a sensitivity study of the MM5 code, a mesoscale weather model jointly developed by Penn State University and the National Center for Atmospheric Research, that is composed of roughly 40,000 lines of Fortran 77 code. Our results show that automatic differentiation-computed sensitivities exhibit superior accuracy compared to divided difference approximations computed from finite-amplitude perturbations. We also comment on a numerically induced precursor wave that would almost certainly have been undetectable if one used a divided difference method. © 1996 American Institute of Physics.

Comparing ada and FORTRAN lines of code: Some experimental results

This paper presents the results of a study comparing pairs of functionally equivalent programs written in the FORTRAN and Ada languages. We found the Ada programs to require more lines of code than their functionally equivalent FORTRAN counterparts. However, we also observed that the overhead for Ada diminishes as program size increases. Our limited data suggested that there may be a cross-over point beyond which the size of an Ada program would be smaller than a functionally equivalent FORTRAN program. We explore some of the reasons for these economies of scale when using Ada. The implications of our findings on software cost estimating are also discussed.

Porting a three-dimensional semiconductor device modelling program to the Intel iPSC/860 hypercube

EVEREST is a three-dimensional device modelling package used to study the electrical behaviour of semiconductor devices. A set of partial differential equations describing the current flow within the device is solved using a mixed mesh of tetrahedral and hexahedral elements. The highly non-linear nature of the equations requires that a flexible solution strategy be used to make the software robust and efficient. Within the solution process large sparse non-symmetric linear systems are solved using iterative solvers such as CGS with preconditioning. Run times of many hours or even days are required for realistic devices on current workstations. EVEREST consists of over 100 000 lines of Fortran and was developed for scalar architectures. The main aim of this work was to investigate how such an application could be adapted to run on the iPSC/860. A review of some of the possible parallelisation techniques is made. Most techniques for the parallel implementation of such mesh based calculations on MIMD machines involve a partitioning of the mesh. An extension of an algorithm due to Farhat has been implemented in a pre-processor to partition the device meshes used by EVEREST. Aspects of load balancing and the need to minimise the number of interface nodes in the decomposition are discussed. Some initial results using the partitioned mesh to perform the system matrix assembly are presented. Methods that could be used to implement a parallel preconditioned CGS solver on the iPSC/860 are reviewed and some performance estimates made using the results of certain BBS tests on this machine.

A Fokker-Planck code for the numerical solution of the plasma heating and the current drive problems with synergetic effects

A code developed to solve the quasilinear 2-D Fokker-Planck equation and previously applied to study the synergetic effect of lower hybrid current drive (LHCD) with electron cyclotron (EC) heating [Comput. Phys. Commun. 55 (1989) 253] is generalized to solve the current drive problem involving the synergetic effect of fast waves with electron cyclotron waves or of fast waves (FW) with lower hybrid waves. The code is relativistic and is no longer than about 170 FORTRAN lines. The input data for this code requires specifying parameters given in about five lines. The code uses the finite element library PDE-PROTRAN, or its new version PDE2D to solve the differential equation directly on a 2-D domain.

The multiflow trace scheduling compiler

The Multiflow compiler uses the trace scheduling algorithm to find and exploit instruction-level parallelism beyond basic blocks. The compiler generates code for VLIW computers that issue up to 28 operations each cycle and maintain more than 50 operations in flight. At Multiflow the compiler generated code for eight different target machine architectures and compiled over 50 million lines of Fortran and C applications and systems code. The requirement of finding large amounts of parallelism in ordinary programs, the trace scheduling algorithm, and the many unique features of the Multiflow hardware placed novel demands on the compiler. New techniques in instruction scheduling, register allocation, memory-bank management, and intermediate-code optimizations were developed, as were refinements to reduce the overhead of trace scheduling. This article describes the Multiflow compiler and reports on the Multiflow practice and experience with compiling for instruction-level parallelism beyond basic blocks.

A fast normal random number generator

A method is presented for generating pseudorandom numbers with a normal distribution. The technique uses the ratio of uniform deviates method discovered by Kinderman and Monahan with an improved set of bounding curves. An optimized quadratic fit reduces the expected number of logarithm evaluations to 0.012 per normal deviate. The method gives a theoretically correct distribution and can be implemented in 15 lines of FORTRAN. Timing and source size comparisons are made with other methods for generating normal deviates. The proposed algorithm compares favorably with some of the better algorithms.

On predicting the fate of radioactive caesium in soil beneath grassland

SUMMARYA simple mechanistic model is developed for predicting the fate of radioactive caesium in the soil beneath grassland. A continuity equation is derived describing the diffusion, leaching and reaction of caesium in soil, with uptake by a uniformly distributed root system. The soil reaction is characterized by three phases: an instantaneous exchange, a moderately‐fast reversible reaction and a slow reversible reaction. The time‐dependent reactions and root uptake have first‐order kinetics. It is shown that caesium is unlikely to be removed from the root zone by leaching and diffusion, even under prolonged high rainfall. Therefore, since the rates of the soil reactions and root uptake are much greater than the rates of diffusion and leaching, it is not necessary to calculate the concentration profile to find the rate of uptake. The computer program for the model is just 30 lines of fortran, and requires only a few seconds of micro‐computer CPU time for each year of simulation.Some predicted rates of plant uptake and distributions in the soil are given. It is seen that the fate of the caesium is markedly influenced by soil parameters dependent on soil clay content, clay mineralogy, organic matter content, cation saturation and pH, and by the rooting density. The predicted rates of uptake vary from about 0.5% to 50% per annum, which is compatible with data reported elsewhere. The predictions are intended to expose gaps in knowledge of the fate of caesium in soil: in particular, the mobility of sorbed radio‐nuclides on soil surfaces needs further study. Predictions are not given for the fate of caesium in any real situations because insufficient data are available.

Implementation and Performance of the Large-Scale Finite Element Code Sesam On a Wide Range of Scientific Computers

SESAM is a large, commercial finite ele ment package for structural analysis that includes SESTRA, an analysis portion of approximately 280,000 lines of FORTRAN 77 statements. We discuss the issues of por tability and efficiency in implementing this code on a wide range of computers, in cluding the FPS-164, GRAY X-MP, CDC Cyber 205, Amdahl VP1200, IBM 3090/VF, and NEC SX-2. Performance data are re lated to the different architectures and the degree of code tuning. SESAM requires large amounts of direct access secondary storage. The use of FORTRAN I/O can sig nificantly decrease performance, as mea sured by both CPU time and elapsed time. We discuss how different levels of I/O support on scientific computers affect the potentially large gap between CPU time and elapsed time.

Interfacing similarity search software with the sequence retrieval system ACNUC

A method of interfacing sequence similarity search software with the fast sequence retrieval system ACNUC is described. The method is written in FORTRAN 77 and is straightforward to implement because no text-processing code is required--a minimum of 12 extra lines of FORTRAN provided the interface for most applications. The method is also efficient, since sequences are located by simple indexing techniques, with no linear searches of large database files necessary.

A performace evaluation of three supercomputers, Fujitsu VP-200, Hitachi S810/20 and the Cray X-MP/24

The Los Alamos benchmark set has been executed on two Japanese supercomputers, Fujitsu's VP-200 and Hitachi's S810/20, as well as on the American-made CRAY X-MP/24. The benchmark set is a collection of CPU intensive codes that approach benchmarking at three levels: (1) Timing of elementary vector operations whose analysis provides basic data about the vector architecture and compiler (2) Timing of characteristic code excerpts (1000 to 3000 FORTRAN lines). These codes vary from linear equation solvers to physics simulations of particle transport and hydrodynamics. (3) Timing of characteristic real codes (10,000 to 20,000 lines of FORTRAN), some of which have been partitioned for execution on multiprocessor architectures. These codes were not used in this benchmark. The time alloted to the evaluations was one week per machine. The codes were run in two modes: (1) original mode in which only changes necessary to execute the codes correctly were allowed and (2) “tuned” mode in which minor FORTRAN changes or compiler directives were allowed. All the benchmarks (even the CRAY X-MP/24) were single processor tests. No I/O or throughput measurements were made. The results of the benchmarks can be analyzed in terms of scalar speed, raw vector speed, and, finally, overall performance. The scalar speed of the VP-200 and X-MP/24 were roughly comparable. Scalar timings differed by, at most, 30 percent, and we concluded that differences of this magnitude could be overcome by a couple of versions of compiler changes. Hitachi's S810/20, however, was a factor of 2 slower in scalar performance. The vector speed of the machines are viewed at two different ranges of vector length. The VP-200 and CRAY X-MP performed equally on short vectors (vector length 10), while the S810 was 50 percent slower. On long vectors (1000 length), the Japanese machines outperformed the X-MP by a factor of 2 or 3. Final conclusions about the machines, however, are based on the overall performance of codes that contain a mixture of scalar and vector modes. In this regime, Amdahl's Law applies and raw vector speed is rarely the determining factor. On the majority of our benchmark set and, particularly, on the more important codes, the VP-200 and an X-MP/24 single processor performed comparably. The Hitachi S810/20 was generally a factor of 2 slower.

An improved three‐noded triangular element for plate bending

AbstractA new three‐noded triangular element for plate bending is described. The element is based on an earlier stress‐smoothed triangular element due to Razzaque,1 but extra internal ‘bubble’ functions are included to make it more flexible. The accuracy of the new element is compared with that of a number of other high‐performance triangular elements. It is concluded that the present element and that due to Hansen, Bergan and Syvertsen2 are the two most accurate triangular thin plate elements currently available. The extra lines of FORTRAN required to convert Razzaque's shape function subroutine to that for the new element are given, thus making the new element easy to implement in any general‐purpose finite element program.

Fitting a Gallon into a Pint Pot! Or Creating Overlaid Programs under CP/M

This paper is a case study describing the implementation of a system of programs composed of 17,000 lines of FORTRAN on a Z80A microcomputer. A detailed description of the methods used is given including an assembler listing of the overlaying routine.