Array Data Structures

An Array is the eqnivalent of a subscripted variable. There are one-, two-, or even higher-dimensional arrays. As with scalar variables, arrays are declared in a Dim statement as in 

In this example, the array x consists of 5 elements x(0), x(l), x(2), x(3), and X (4). By default, the first subscript is 0. However, starting at zero can lead to confusion, and it is recommended to always include 

Then subscripts begin with 1, which many find more natnral. For those comfortable with subscripts starting at zero, this option need not be nsed. For all programs in this book use, Option Base 1 is used. 

For a two-dimensional array (matrix), an example declaration is as follows  

The matrix y has 3 rows and 4 colnmns (assnming subscripts start at 1). 

---

The keyword DIM is used to specify the data type of a variable. When Option Explicit is used (as is always recommended), the type of every variable in the program must be specified explicitly. Later it will be seen that DIM is also used to specify an Array data structure. Table 2.2 summarizes some of the VBA built-in data types. Only the types most often used are included. A full list of data types can be viewed via the Help system. 

For the data of streams and equipment models, ASPEN utilizes a plex data structure of the type proposed by Evans, et al. (3) Information is stored in blocks of contiguous locations known as beads. Beads of any length are created dynamically from a pool of free storage which may be thought of as a lengthy FORTRAN array. The combination of the preprocessor approach and the plex data structure has resulted in the absence of dimensional constraints on the system. There are no maximum numbers of streams, components, models, stages in a column, etc. except as limited by the total memory available. 

Both PCA and MCR-ALS can be easily extended to complex data arrays ordered in more than two ways or modes, giving three-way data arrays (data cubes or parallelepipeds) or multiway data arrays. In PCA and MCR-ALS, the multiway data set is unfolded prior to data analysis to give an augmented two-way data matrix. After analysis is complete, the resolved two-way profiles can be regrouped to recover the profiles in the three modes. The current state of the art in multiway data analysis includes, however, other methods where the structure of the multiway data array is explicitly built into the model and fixed during the resolution process. Among these... 

Much of numerical computation in chemistry revolves about numerical multilinear algebra. By this term I denote the manipulation of arrays whose dimension may exceed two. Mindful of Richard and Ledgard s admonition (16) that language design should never be overly ambitious, I propose only data structures, operations, and syntax for programming multilinear algebra. Multilin exceeds Bohlender s Pascal extension in two ways its provision for more than two dimensions, and its explicit declaration of data representations. 

C. Pottle, M. S. Pottle, R. W. Tuttle, R. J. Kinch, and H. A. Scheraga, / Cornput. Chem., 1, 46 (1980). Conformational Analysis of Proteins Algorithms and Data Structures for Array Processing. 

Among the current limitations of Linda, those important to computational chemistry applications are failure to provide information on where or how tuples are stored or accessed lack of structure within tuple space, making it hard to maintain modularity a requirement to match general tuples, leading to inefficiencies in memory usage and communication even for simple data structures (e.g., a distributed array) lack of primitives for efficient global operations (e.g., reduction and broadcast) and requiring the compiler to detect and optimize these constructs. There are many current directions of related research. 

Data Parallel Describing a programming model in which tasks are assigned to processes based on the distribution of the various data structures (e.g., arrays and matrices). 

A large variety of methods, developed with a specific goal to solve the crystal structure from diffraction data, can be divided into two major groups. The first group entails techniques that are applicable in direct space by constructing a model of the crystal structure from considerations other than the available array of structure amplitudes. These include ... 

Although PCA reduces the number of genes involved, the results largely depend on the data distribution and the variance-covariance of the data. The identified principal components do not always have useful sample prediction capabilities for example, they often do not capture phenotype structures (86). The poor predictive capabilities of PCA with array data arise because the genes accounting for most of the variance in the data are frequently not the most informative of the class distinction of interest. 

Because of these complexities, we will start by describing a simplified Array-Express model - ArrayExpressB, after which we will add the details of the Ar-rayExpressC model. Some users may not need to implement the ArrayExpressC model for their particular purposes. We encourage users to assess whether the ArrayExpressB model is sufficient or not (data structured according to the ArrayExpressB model can be later imported into the ArrayExpressC model compliant database). Also, a whole range of intermediate models between the two extremes is possible. In fact, these models should be critically assessed by users and adjusted to the particular needs of their laboratories. 

As described above, not all three-way data can be meaningfully approximated as low-rank trilinear, and consequently multi-way methods may be divided into two groups based on whether or not the methods require low-rank trilinear data structure. It is therefore important to perform a preliminary analysis to determine the inner structure of a three-way array before choosing a suitable resolution method. The models discussed in this paper are listed in Table 2, also stating whether or not a given model requires low-rank trilinear data and therefore results in direct chemically meaningful solutions. 

Some of the more advanced methods described in this book require a more specific use of the RDBMS. The choice made for this book is PostgreSQL. In cases where a particular feature of PostgreSQL is used, a note is added to alert the reader. For example, the array data type in SQL2003 is implemented in PostgreSQL very differently than in Oracle. The list matches function described in a later chapter of this book returns an array of integers that denote which atoms in a structure match a substructure query. The integration of this function into SQL would be handled quite differently in PostgreSQL, Oracle and MySQL. 

The following fragment of code implements this procedure assuming the above data structures and that dfact(i+l) supplies (2i — 1) and the original contraction coefficients are in the array c. 

Consult the STRUCTURES information for a detailed description of the data structures used by the integral generation routines only arguments specific to this routine are described here. ngriLx Input The explicit first dimension of the array eta in the program which calls genint. nbfns Input The number of basis functions. 

C Computer system handling the operation of (he robotic arm D, valve system B, adressing of reagents and solvents. In addition, the data (structural and spatial) of the products synthesised in a parallel array is handled electronically (typically with ISIS Base or similar database)... 

---