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A typical alternative for dense array storage is to use Iliffe vectors, which typically store pointers to elements in the same row contiguously (like row-major order), but not the rows themselves. They are used in (ordered by age): Java, [14] C#/CLI/.Net, Scala, [15] and Swift.
MATLAB supports both external and internal implicit iteration using either "native" arrays or cell arrays. In the case of external iteration where the onus is on the user to advance the traversal and request next elements, one can define a set of elements within an array storage structure and traverse the elements using the for-loop construct ...
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 ...
The array elements 0..i-1 contain constructed objects. The array element i is about to be constructed, and the following elements are uninitialized. Shape analysis can approximate this situation using a summary for the first set of elements, a materialized memory location for element i, and a summary for the remaining uninitialized locations ...
The number of possible parenthesizations is given by the (n–1) th Catalan number, which is O(4 n / n 3/2), so checking each possible parenthesization (brute force) would require a run-time that is exponential in the number of matrices, which is very slow and impractical for large n. A quicker solution to this problem can be achieved by ...
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.
Function rank is an important concept to array programming languages in general, by analogy to tensor rank in mathematics: functions that operate on data may be classified by the number of dimensions they act on. Ordinary multiplication, for example, is a scalar ranked function because it operates on zero-dimensional data (individual numbers).
When a statement in one iteration of a loop depends in some way on a statement in a different iteration of the same loop, a loop-carried dependence exists. [1] [2] [3] However, if a statement in one iteration of a loop depends only on a statement in the same iteration of the loop, this creates a loop independent dependence. [1] [2] [3]