Vector processing

D. Fincham and B. J. Ralston, Molecular dynamics simulation using the Cray-1 vector processing computer , Comp. Phys. Comm., Vol 23, no 2, 127-34, 1981. 

Figure 5.26 (A) The two 90° pulses are applied with an intervening variable

The CRAY-1 vector processing computer at the Science Research Council s (S.E.R.C) Daresbury Laboratory, is at the centre of a network providing large scale computational facilities for Universities in the United Kingdom. This is the only supercomputer available at present to Quantum Chemists in the U.K., and this article will therefore be restricted to experience gained on the CRAY-1, although this experience will undoubtedly be relevant to future applications on machines such as the ICL Distributed Array Processor (DAP) (see reference (2) for a detailed description) and the CDC Cyber 203/205. 

Full details of the algorithm have been given elsewhere (37). Here, we indicate the features of the calculation which take advantage of vector processing facilities. The inner most DO loop of the program forms intermediates of the type... 

Third-order calculations are considered in the next section. This is followed by a brief discussion of the computation of higher-order terms and of the evaluation of bubble diagrams which are required when molecular properties are calculated or when a reference function other than the closed-shell Hartree-Fock function is employed. The impact of the new generation of computers, which have vector processing capabilities, on many-body perturbative calculations is discussed very briefly in the final section. 

The algorithms devised to perform many-body perturbation calculations are well suited to vector processing computers such as the CRAY l. 141 >159 The scalar... 

R. Vogelsang, M. Schoen, and C. Hoheisel, Comput. Phys. Commun., 30, 235 (1983). Vectorisation of Molecular Dynamics Fortran Programs Using the Cyber 205 Vector Processing Computer. 

M. Schoen, Comput. Phys. Commun., 52, 175 (1989). Structure of a Simple Molecular Dynamics Fortran Program Optimized for Cray Vector Processing Computers. 

D. C. Rapaport, Comput. Phys. Commun., 62, 198 (1991). Multi-Million Particle Molecular Dynamics. I. Design Considerations for Vector Processing. 

As a consequence, from the point of view of this rotating frame, a nucleus at site A processes at frequency (vq — Va), whereas a nucleus at site B processes at frequency (vb — Vo) that is, the two nuclei (actually their magnetization vectors) process in opposite directions. We imagine several possible cases. 

Figure 5 J2. (a) Amplitude modulation requires both counter-rotating vectors (p = 1 coherences) be retained during ti. The resultant signal (greyed) is modulated in ampUtude along the y—axis as the vectors process, (b) Phase modulation results if only one vector (p - 1 or p = —1) is retained as the phase angle 9 varies as the vector processes.

In real experiments after Fourier transformed the lineshapes are mixtures of absorptive and dispersive signals and are related to the delayed FID acquisition (first-order phase error). The delayed acquisition is a consequence of the minimum time required to change the spectrometer from transmit to receive mode, during this delay the magnetization vectors process according to their chemical shift frequencies. The zero-order phase error arises because of the phase difference between the magnetization vectors and the receiver. In NMR-SIM the delayed acquisition is not necessary because the ideal spectrometer approach does not require any switching time and the first order phase correction is normally zero if no other sources of phase deviations are present. 

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