I need to choose. Consider this:
a . i . j
where a is an array of arrays. The first or closest index i selects an inner
array of a, and the second, fastest moving index j selects an element
of the inner array.
To scan the inner elements contiguously we must use he formula
linear_index = i * N + j
If you view it like this:
// j=0,1,2
( (0,1,2), // i = 0
(3,4,5), // i =1
(6,7,8) ) // i=2
i is selecting a row, and j a column. In this view a "top level"
array is a column vector. Actually I personally see it the other
way, that is, I see a row of columns. YMMV :)
Now, remember there is a more fundamental way
to do projections:
j (i a)
because the dot (.) notation is just reverse application.
So here's the problem: if we convert the array of arrays to
a matrix, that is a single linear array with a tuple argument,
what order do the indices go in?
If we take:
a . i . j ==> mat(a) . (i,j)
preserving the index order, then we unfortunately get this as equivalent:
(i,j) mat(a)
I ask this question because at the moment Felix is bugged:
it uses both orderings in different places, so now is the time
to fix the order.
I like this rule:
int ^ N ^ M => int ^ (N * M)
which is what I thought was implemented (but apparently in
some places M and N are swapped).
Note this rule is equivalent to:
a . i . j ==> a . (j,i)
because the first applied index i eliminates the M leaving int ^ N.
So roughly: if we preserve the index order for the type notation
we have to swap it for the index values (relative to the dot notation:
the order is preserved for the functional notation).
--
john skaller
skal...@users.sourceforge.net
http://felix-lang.org
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