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An array data structure can be mathematically modeled as an abstract data structure (an abstract array) with two operations get(A, I): the data stored in the element of the array A whose indices are the integer tuple I. set(A, I, V): the array that results by setting the value of that element to V. These operations are required to satisfy the ...
defines a variable named array (or assigns a new value to an existing variable with the name array) which is an array consisting of the values 1, 3, 5, 7, and 9. That is, the array starts at 1 (the initial value), increments with each step from the previous value by 2 (the increment value), and stops once it reaches (or is about to exceed) 9 ...
Thus, if the array is seen as a function on a set of possible index combinations, it is the dimension of the space of which its domain is a discrete subset. Thus a one-dimensional array is a list of data, a two-dimensional array is a rectangle of data, [12] a three-dimensional array a block of data, etc.
In addition to support for vectorized arithmetic and relational operations, these languages also vectorize common mathematical functions such as sine. For example, if x is an array, then y = sin (x) will result in an array y whose elements are sine of the corresponding elements of the array x. Vectorized index operations are also supported.
In array languages, operations are generalized to apply to both scalars and arrays. Thus, a+b expresses the sum of two scalars if a and b are scalars, or the sum of two arrays if they are arrays. An array language simplifies programming but possibly at a cost known as the abstraction penalty.
For instance, within the loop a reference to element I of an array would likely employ the auxiliary variable (especially if it were held in a machine register), but if I is a parameter to some routine (for instance, a print-statement to reveal its value), it would likely be a reference to the proper variable I instead. It is best to avoid such ...
MATLAB was created in the 1970s by Cleve Moler, who was chairman of the computer science department at the University of New Mexico at the time. It was a free tool for academics. Jack Little, who would eventually set up the company, came across the tool while he was a graduate student in electrical engineering at Stanford University.
The findgen function in the above example returns a one-dimensional array of floating point numbers, with values equal to a series of integers starting at 0.. Note that the operation in the second line applies in a vectorized manner to the whole 100-element array created in the first line, analogous to the way general-purpose array programming languages (such as APL, J or K) would do it.