Parenthesizing arrays

Type declaration—Must be placed after CONST sequence and before variable declarations used to define nev (not predefined) data types either as a range of values or as specific values within parentheses and to define arrays, records, and files. User-defined scalar types are ordered in increasing lefl to right sequence. For example. 

The actual values of these concentrations depend on a whole array of unknown parameters, but their relative values depend only on the valence of the counterions. The entries outside parentheses in Table 13.1 are the values of the CCC relative to the value for the monovalent electrolyte in the same set of experiments. These are seen to be remarkably consistent for the divalent ions and acceptably close together for trivalent and tetravalent counterions. 

A matrix is a rectangular array of terms (numbers or symbols) called elements which are written between parentheses or double lines, e.g. 

The structure is bonded to a substrate 24 which is chosen to have a coefficient of thermal expansion that is selected for providing the resultant read-out chip assembly with an effective coefficient of thermal expansion that is approximately the same as an HgCdTe detector array 36. The substrate material may be GaAs (4.5-5.9 x 10"6 m/mK), CdTe, Ge (5.5-6.4 x 10"6 m/mK), and a-plane sapphire (3.5-7 5 x 10" m/mK) where the coefficients of thermal expansion are given in parentheses. The coefficients of thermal expansion for silicon, HgCdTe and epoxy are 1.2 x 10"6 m/mK, 3.8-4.5 x 1 O 6m/mK and 30-50 x 10"6 m/mK, respectively. Next, the substrate 16 is removed and aluminium pads 34a are formed. Indium bumps 34b are cold welded to corresponding indium bumps 36b. 

You can refer to the complete array by using the array variable name in your code. Sometimes the array name can be used with parentheses, other times without parentheses. 

Only one argument can follow the ParamArray keyword, and it must be the last one in the function s list of arguments. The argument declared by the ParamArray keyword is an array of Variant elements. Empty parentheses are required. 

Variable is the name assigned to the array. Subscripts are the dimensions of the array an array can have up to 60 dimensions. Each dimension has a default lower value of zero a single number for a dimension is taken as the upper limit. Use lowerTo upper to specify a range that does not begin at zero. Use Dim with empty parentheses to specify an array whose dimensions are defined within a procedure by means of the ReDim statement. 

A matrix is an array of elements., comprising n rows and m columns, enclosed in parentheses (round brackets). By convention, matrices are named using bold typeface letters of upper or lower case, such as A or b, so we could, for example, label the matrices above as ... 

Figure 7.3. Cross-validation results of a noisy three-way array. LBO and EM are abbreviations of leave-bar-out and expectation maximization, respectively. The numbers between parentheses correspond to the size of the Tucker3 model, e.g. (2,2,2) means a Tucker3 (2,2,2) model.

This array we may represent by the symbol f or (/J, We enclose it in parentheses to distinguish it from a determinant, with which it should not be confused. 

The concept of a subroutine with an explicit interface-, the aiyuments of the subroutine are a comma-separated list in parentheses following the subroutine s name. They are dummies in the sense that the subroutine takes whatever objects it finds in these locations and performs the operations on them as if they were C, R, m and nocc. Obviously the objects passed to scfR should be of the correct type (array, integer or whatever). 

Perl lists are closely related to arrays. Lists are a set of constants or variables enclosed in parentheses. An example of a list of strings would be ("one", "two", "buckle my shoe"), whereas an example of a list of variables would be ( a, b, c). A list that combines variables, constant strings, and constant numbers might be something like ( a, "the Roman empire", 3.141592 6, ipath). Lists can be thought of as being related to array variables in the same way that the constant 123.4 might be related to the scalar variable total. 

The ideal spinel structure consists of a cubic closely packed array of anions, with one-eighth of the tetrahedral and one-half of the octahedral interstices occupied by cations, so that the cation to anion ratio is 3 4. In a binary oxidic spinel, AB2O4, two extreme distributions of cations among the available sites are possible the normal distribution, A(B2)04, and the inverse distribution, B(AB)04 in each case the ions in parentheses occupy octahedral sites. Intermediate distributions also are known, in particular the random or statistical distribution Ai/3B2/3(A2/3B4 )04. It is Convenient to characterize the cation distribution by specifying the fraction of tetrahedral sites, x, occupied by B cations, i.e., Ai cBx(A cB2-x)04. The parameter x equals 0, 2/3 and 1 for normal, random and inverse spinel, respectively. In the substitution spinels some of... 

The original BASIC allowed the use of single letters as array names (arrays are also called lists and tables or, in mathematical circles, vectors and matrices). A single letter with an attached subscript in parentheses represented an array element. The following complete program, which prints the squares of the whole numbers from 1-8, uses a singly subscripted array (i.e., a list or vector) ... 

The simplest rule for understanding a declaration is to remember that if you use the item just as it is declared it will have the simple type mentioned in the left part of the declaration. The next step is to learn the meanings of the three operators that are used in many declarations a pair of parentheses indicates a function, square brackets indicate an array, and the asterisk indicates a pointer. Also remember that things to the right of a variable name (parentheses and square brackets) bind more tightly than things to the left. 

FIGURE 2.19 Comparison of friction force vs. pull-off force on platinum and silicon asperity arrays using data from fig. 2.18. The friction forces measured on each material were fitted with a line that passes through the origin. The gradient of each approximated line is shown in the parentheses in the inset box. 

A matrix is an ordered array of elements satisfying certain algebraic rules. We write our matrices with parentheses on the left and right of the array. Unless otherwise stated, we restrict the elements to be numbers (which need not be real). In general, however, as long as the rules of matrix algebra can be observed, there is no restriction on what the elements may be. In expression (9-1), we have written a matrix in three ways ... 

The function mean returns arithmetic mean of arrays (vector, matrix or list). The first call of this function in Fig. 6.41 is made in common form as a function. Two parentheses appear (it is like saying salt is salty) that may confuse a novice user when the mean function is invoked. The user will try to delete excess parentheses not understanding why it is impossible to do. The solution is to call the matrix function (the function whose... 

Caution must be exercised with array names since the s3mthesizer may strip ofifiieir parentheses. For example, an array signal element A(0) would be converted to AO by the compiler. This will cause an error if a scalar signal has also been named AO. Therefore, avoid using names that end in a number, such as LOAD or D6, when also using array types. This also applies to variables and constants. 

The empty parentheses after InputNumbers identify it as an array argument, and the dummy Nums becomes an array structure of whatever length InputNumbers happens to be. These parentheses are not essential but they help to document the array argument. 

To illustrate the use of ReDim, one more version of the example program is shown. The input data format is changed so that the very first number in the list is not one of the numbers to be averaged, but it indicates how many numbers there are (and thus the required size of the array that holds the numbers). In this version, the dimension of InputNumbers is left blank (note the empty parentheses), and then the following statement makes the dimension what it needs to be ... 

Dim InputNumbers ( As Double array of numbers the Enpty parentheses)... 

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