Subroutines libraries

Due to its modularity, the software comes in many parts (shown in Fig. 9). The Chemkin package is composed of four important pieces the Interpreter, the Thermodynamic Data Base, the Linking File, and the Gas-Phase Subroutine Library. The Interpreter is a program that first reads the user s symbolic description of the reaction mechanism. It then extracts thermodynamic information for the species involved from the Thermodynamic Data Base. The user may add to or modify the information in the data base by input to the Interpreter. In addition to printed output, the Interpreter writes a Linking File, which contains all the pertinent information on the elements, species, and reactions in the mechanism. 

Once the Interpreter has been executed and the Linking File created, the user is ready to use the Gas-Phase Subroutine Library. These subroutines are called... 

Several numerical subroutine libraries contain safeguarded Newton codes using the ideas previously discussed. When first and second derivatives can be computed quickly and accurately, a good safeguarded Newton code is fast, reliable, and locates a local optimum very accurately. We discuss this NLP software in Section 8.9. 

Hopper, M. J. Harwell Subroutine Library, A.E.R.E., Harwell, Didcot, UK. 

The use of literate programming methods leads naturally to structure and standardization in computer code. In turn, this structure leads to subroutine libraries and we describe the specification of a basic tensor algebra subroutine library, which we have recently developed, and which we expect to prove useful in a range of applications. 

For a problem involving surface chemistry, the next step is to execute the Surface Chemkin Interpreter, which reads the user s symbolic description of the surface-reaction mechanism. Required thermodynamic data can come from the same Thermodynamic Database used by Chemkin or from a separate Thermodynamic Database compiled for surface species. Both Interpreters provide the capability to add to or override the data in the database by user input in the reaction description. The Surface Chemkin Interpreter extracts all needed information about gas-phase species from the Chemkin Linking File. (Thus the Chemkin Interpreter must be executed before the Surface Chemkin Interpreter.) Like the Chemkin Interpreter, the Surface Chemkin Interpreter also provides a printed output and a Linking File. Again, the Surface Linking File is read by an initialization subroutine in the Surface Subroutine Library that makes the surface-reaction mechanism information available to all other subroutines in the Library. 

An analytic expression for the reduced creep function, obtained from Eq. (3.11) with Eq. (3.6) for the linear array, is shown in Table 4 Eq. (T4). Je is the elastic equilibrium compliance and y (1/2, w) is the incomplete gamma function of order 1/2, extensively tabulated and available in most computer subroutine libraries. The last term accounts for contribution of plastic flow, where present. Reduced creep functions (recoverable and including flow contributions) are plotted in Fig. 4 as a function of Z. The... 

At the next level, the subroutine library that the user works with remains functionally constant, but its internal structure will directly take into account differences in hardware. This allows some portability, but puts the burden of support for different devices on the system/1ibrary manager. 

The hierarchical code organization is illustrated in Fig. 18.3. This is by code series and then individual codes. ADAS provides extensive Fortran and IDL subroutine libraries which are available for use in a user s own codes and analysis programs. The IDL subroutines support the user s interface to interactive ADAS and graphical presentation of results. Modular basic atomic calculation routines, utilities and access routines to the ADAS data classes are mostly provided in Fortran but generally with IDL versions which use the Fortran through C wrappers. In particular reaEadf .pro and run-adas.pro IDL procedures give access to ADAS data or run ADAS codes at the IDL command line - independent of interactive ADAS. The libraries now include 700 subroutines. 

This completes the derivation of the derivatives needed for the gradient of the energy functional. The compact matrix forms of these results can be manipulated using matrix algebra and are readily implemented using optimized computer subroutine libraries. 

In order to understand formal relationships the basic coupling of two angular momenta is expressed in terms of the Clebsch—Gordan coefficients. In setting up the algebra for computation it is more convenient to use the 3-j symbols. Calculations of the Wigner symbols and the Clebsch—Gordan coefficients are found in subroutine libraries. See, for example, Soper (1989). 

The important properties of these functions are given for example by Antosiewicz (1973) and calculations are in subroutine libraries, for example Barnett et al. (1974). 

We consider it as the problem of diagonalising a finite matrix, the computation of which is available in subroutine libraries, for example Anderson et al. (1992), by truncating the basis to a finite set of states j). The eigenvector components j n) are fully defined by requiring that the eigenvectors n) are normalised. 

It is not necessary for the physicist to know how to compute the Coulomb functions. They are found in subroutine libraries, for example Barnett et al. (1974). A sufficient idea of their form is obtained by putting j = L = 0 in (4.62), when they are seen to be sinp and cosp respectively. The potential terms dilate or compress the sine and cosine waves, resulting in an overall phase shift at long range. 

For certain mathematical functions and operations it is necessary for the physicist to know their context, definition and mathematical properties, which we treat in the book. He does not need to know how to calculate them or to control their calculation. Numerical values of functions such as sinx have traditionally been taken from table books or slide rules. Modern computational facilities have enabled us to extend this concept, for example, to Coulomb functions, associated Legendre polynomials, Clebsch—Gordan and related coefficients, matrix inversion and diagonali-sation and Gaussian quadratures. The subroutine library has replaced the table book. We give references to suitable library subroutines. 

PRODD Profile Refinement of Diffraction Data using the Cambridge Crystallographic Subroutine Library (CCSL),... 

The components of represent stochastic displacements and are obtained using the multivariate Gaussian random number generator GGNSM from the IMSL subroutine library (30). p ° is the initial hydrodynamic interaction tensor between subunits iJand j. Although the exact form of D. is generally unknown, it is approximated here using the Oseen tensor with slip boundary conditions. This representation has been shown to provide a reasonable and simple point force description of the relative diffusion of finite spheres at small separations (31). In this case, one has... 

Subroutines for calculating the singular value decomposition may be found in all popular subroutine libraries (IMSL, NAGlib, Numerical Recipes). Our current code calls subroutines from the IMSL library however, a modest amount of recoding would convert them for use with NAGlib or even with the subroutines available with Numerical Recipes. We will provide copies of our code requests should be sent via Internet to rtr-t- osu.edu. 

M. J. Hopper, Harwell Subroutine Library, AERE-R7477. At. Energy Res. Estab., Harwell, Berkshire, U.K. (1973) also Suppl. No. 1 (1974). 

C. B. Bailey and R. E. Jones, Brief Instructions for Using the Sandia Numerical Mathematical Subroutine Library on the CDC6600, SLA-74-0095. Sandia Lab., Albuquerque, New Mexico, 1974. 

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