This is a read-only-page

These operators where posted by John Scholes on November the 4th 2006 on Dyalog's web site:

? Variations on primitive scan: nvec?{axis}##.mscan nvec ? Minus scan. nvec?{axis}##.dscan nvec ? Divide scan. vect?(fn ##.ascan)vect ? Associative vector scan. array?{ascan}(fn ##.ascana)array ? Associative higher rank scan. Provided by Phil Last and Nicolas Delcros,these operators out-perform their primitive counterparts by scanning cumulatively from left to right. The primitive scan operator is defined as a vector of reductions: ¯¯¯¯¯¯¯¯¯ ??\? ? ??/¨(1 to??)?¨?? For example: +\3 1 4 1 6 ? +/¨(1 to 5)?¨?3 1 4 1 6 ? +/¨(3)(3 1)(3 1 4)(3 1 4 1)(3 1 4 1 6) ? (+/3)(+/3 1)(+/3 1 4)(+/3 1 4 1)(+/3 1 4 1 6) ? 3 4 8 9 15 Defn: An associative dyadic function f is one where:(A f B)f C ?? A f(B f C). ¯¯¯¯¯¯¯¯¯¯¯ For associative operand functions,such as + and ×, the interpreter can "cheat" by accumulating the result in a single left-to-right pass of the vector argument, but for non-associative functions, it is obliged to do it the slow way using reductions of increasingly longer sequences as above, resulting in an O(n×n) algorithm. Mscan and dscan provide linear O(n)functions to simulate-\and÷\respectively. -\?1000 ? slow primitive minus-scan. 1 ¯1 2 ¯2 3 ¯3 4 ¯4 5 ¯5 ... mscan?1000 ? quick minus-scan. 1 ¯1 2 ¯2 3 ¯3 4 ¯4 5 ¯5 ... ÷\?1000 ? slow primitive divide-scan. 1 0.5 1.5 0.375 1.875 0.3125 ... dscan?1000 ? quick divide-scan. 1 0.5 1.5 0.375 1.875 0.3125 ... In general, the interpreter can "cheat" only if it can determine that scan's operand function is associative. For example, even though dfn{?+?} is clearly associative, the interpreter cannot know this and so uses the slow O(n×n) method. In cases such as these, where it is known that the operand function is associative, ascan can be used to force a left-to-right cumulative O(n) scan. {?+?}\?10000 ? slow primitive scan. 1 3 6 10 15 21 28 36 45 55 ... {?+?}ascan?1000 ? quick associative scan. 1 3 6 10 15 21 28 36 45 55 ... Note that if the operand turns out to be non-associative, ascan will return a result that differs from primitive scan. {?-?}\?10 ? slow primitive scan. 1 ¯1 2 ¯2 3 ¯3 4 ¯4 5 ¯5 {?-?}ascan?10 ? quick left to right accumulation. 1 ¯1 ¯4 ¯8 ¯13 ¯19 ¯26 ¯34 ¯43 ¯53 nums??('one' 'two' 'three')('un' 'deux' 'trois')('yan' 'tan' 'tethera')