Thanks for the reply. I don't think I was clear enough with my initial question
though so have given the example below:
###################################################################################
Consider
lists := []
lists[1] := [1,2,3]
lists[2] := [4,5]
I would now like to iterate over the cartesian product of `lists[1]` and
`lists[2]` i.e. `[[1,4],[1,5],[2,4],[2,5],[3,4],[3,5]]`.
For an example this small, you could simply store the cartesian product itself
in a list and iterate over that. This obviously becomes very inefficient if we
have more lists with a larger number of values.
A better way is, if we have `n` lists and `size_rc[i] := Size(list[i])`, we can
avoid storing/calculating the Cartesian product with
base := List([1..n], x -> 1); #We store the iteration step state in base
while base <> size_rc do
#Perform whatever list[i][base[i]] calculations here
#Execute the incrementor
base[1] := base[1] + 1;
for j in [2..n] do
if base[j-1] = size_rc[j-1] + 1 then
base[j] := base[j] + 1;
base[j-1] := 1;
fi;
od;
od;
then at each loop of the while `base` contains the values we need.
However this is still far slower than the Python implementation I mentioned
before. I was wondering if there was a way in GAP to speed up this iteration
(maybe by pointing to the memory locations of the lists)?
Thanks,
Rob
________________________________________
From: Alexander Konovalov [[email protected]]
Sent: 16 January 2014 22:01
To: Wolstenholme, Robert
Cc: [email protected]
Subject: Re: [GAP Forum] Iteration Over Lists of Lists
On 16 Jan 2014, at 20:03, "Wolstenholme, Robert"
<[email protected]> wrote:
> Is there a way in GAP to 'quickly' iterate of lists of lists i.e. like the
> Python itertools.product() function?
>
Yes, see `21.20 Operations for Lists' from the GAP Reference Manual. You may
enter `?Operations for Lists' in GAP or see it online at
http://www.gap-system.org/Manuals/doc/ref/chap21.html#X7DF510F7848CBBFD
A random example just to expose the syntax and some functions:
gap> l:=List([1..10],i -> [1..i]);
[ [ 1 ], [ 1, 2 ], [ 1 .. 3 ], [ 1 .. 4 ], [ 1 .. 5 ], [ 1 .. 6 ],
[ 1 .. 7 ], [ 1 .. 8 ], [ 1 .. 9 ], [ 1 .. 10 ] ]
gap> Sum( List( l, x -> Product( List( x, Fibonacci ) ) ) );
124819000
HTH,
Alexander
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