how to use erlang lists:map function - erlang

The following is a erlang function. I don't understand how lists:map function is used here.
Could someone please explain?
% perform M runs with N calls to F in each run.
% For each of the M runs, determine the average time per call.
% Return, the average and standard deviation of these M results.
time_it(F, N, M) ->
G = fun() -> F(), ok end,
NN = lists:seq(1, N),
MM = lists:seq(1, M),
T = lists:map(
fun(_) ->
T0 = now(), % start timer
[ G() || _ <- NN ], % make N calls to F
1.0e-6*timer:now_diff(now(), T0)/N % average time per call
end,
MM
),
{ avg(T), std(T) }.
Thanks.
also, I don't know the proper syntax when using this function. For example, I have a dummy() function take 1 parameter. I get an error while trying to time the dummy function.
moduleName:time_it(moduleName:dummy/1, 10, 100).
the above would evaluate to illegal expression.
Actually, now with the correct syntax, the function can be invoked correctly with:
moduleName:time_it(fun moduleName:dummy/1, 10, 100).
However, it will throw a exception saying invoking dummy function without passing any parameter. I think this line is the villain, [ G() || _ <- NN ], I have no idea how to fix it.

map is used here to execute the function
T0 = now(), % start timer
[ G() || _ <- NN ], % make N calls to F
1.0e-6*timer:now_diff(now(), T0)/N % average time per call
for each element of MM. map will return a new list of the same size, where each element of the new list is the result of applying the above function to the corresponding element of MM.
You can invoke time_it like:
moduleName:time_it(fun moduleName:dummy/1, 10, 100).

The purpose of lists:map in the time_it function is just to run the inner function M times. When you see this pattern:
L = lists:seq(1,M),
lists:map(fun(_)-> Foo() end, L)
It just means call Foo() again and again M times, and return the results of each call in a list. It actually makes a list of integers [1,2,3,...N] and then calls Foo() once for each member of the list.
The author of time_it does this same trick again, because time_it needs to call the function you give it N*M times. So inside the outer loop that runs M times they use a different technique to run the inner loop N times:
L = lists:seq(1,N),
[Foo() || _ <- L]
This has exactly the same result as the code above, but this time Foo is called N times.
The reason you are having trouble using time_it with your dummy function is that time_it takes a function with 0 parameters, not 1. So you need to make a dummy function and call it like this:
dummy() ->
%% do something here you want to measure
ok.
measure_dummy() ->
time_it(fun someModule:dummy/0, 10, 100).

If you have a function moduleName:dummy/1 you can do one of the following
If you can edit time_it/3, then make it call F(constant_parameter) instead of F(). I assume this is the case.
Otherwise, call M1:time_it(fun() -> M2:dummy(constant_parameter) end, N, M).
dummy will not be called directly, but only by F inside time_it.

results(N, F) when N >= 0 -> results(N, F, []).
results(0, _, Acc) -> lists:reverse(Acc);
results(N, F, Acc) -> results(N-1, F, [F() | Acc]).
repeat(0, F) -> ok;
repeat(N, F) when N > 0 ->
F(),
repeat(N-1, F).
With these:
T = results(M, fun () ->
T0 = now(),
repeat(N, G),
1.0e-6 * timer:now_diff(now(), T0)/N
end)
Make sense, now?

Related

How to evaluate the first element of a tuple ONLY if elements in the tuple are identical in Erlang?

Let's say our Variable Five is a tuple of five elements.
How do we write an expression that evaluates to (and prints) the first element, but only if all five elements are identical?
For example, given this following tuple:
Five = {4, 4, 4, 4, 4}.
I'm trying to use element(_,_). Statement as:
element(1, Five) =:= element(2, Five).
But this only give me the evaluation of the first element VS the 2nd one, not all together.
Any idea how I can evaluate the first one with all the other elements the same time?
{ .................. } = Five, ....................
If you know the size of the tuple (e.g. 5 as in your example), you could pattern match using the same variable:
case Five of
{X, X, X, X, X} -> io:format("~w", [X]), X;
_Otherwise -> ok
end
Of course, the same can be done in function clauses.
If the size of the tuple is unknown, one way would be to convert it to a list using tuple_to_list/1 and, for example, use lists:all/2:
[H | T] = tuple_to_list(Five),
IsSame = lists:all(fun (E) -> E =:= H end, T),
case IsSame of
true -> io:format("~w", [H]), H;
false -> ok
end

Erlang inference

The following source doesn't compile because Stopover is unbound.
I'm new to Erlang, how can I rewrite it?
-module(distances).
-export([ path/2 ]).
path( madrid, paris ) ->
{ km, 1049 };
path( paris, moscou ) ->
{ km, 2482 };
path( moscou, berlin ) ->
{ km, 1603 };
path( From, To ) ->
path( From, Stopover ) + path( Stopover, To ).
The usage of this module maybe:
path( madrid, moscou ).
And the epected answer should be { km, 3531}.
The following source doesn't compile because Stopover is unbound.
I'm new to Erlang, how can I rewrite it?
Look at this code:
-module(a).
-compile(export_all).
do_stuff() ->
Stopover.
Here's what happens when I try to compile it:
a.erl:5: variable 'Stopover' is unbound
The variable Stopover was never assigned a value, so erlang has no idea what should be returned by the function do_stuff(). You are doing something similar here:
path( From, Stopover ) + path( Stopover, To ).
The variables From and To are parameter variables for the function path(), and when path() is called, e.g. path(madrid, moscow), then madrid will be assigned to the variable From, and moscow will be assigned to the variable To. Note, however, that nowhere do you assign any value to the variable Stopover.
You need to redefine path() to look like this:
path(From, To, Stopover) ->
Next, you should try to see if adding tuples actually works:
2> {km, 5} + {km, 3}.
** exception error: an error occurred when evaluating an arithmetic expression
in operator +/2
called as {km,5} + {km,3}
3>
Nope!
What you need to do is use pattern matching to extract the distance, an integer, from each tuple, then add the two integers:
{km, Distance1} = path( From, Stopover ),
... = path(Stopover, To),
{km, Distance1 + Distance2}.
This question is already answered by #7stud, and I was wondering how to implement such a path search in erlang. Here is a possible solution:
-module(distances).
-export([ path/2,getTowns/0,start/1, stop/0 ]).
path(From,To) ->
Paths = getPath(),
path(From,To,maps:get(orderedTuple(From,To), Paths, not_found),Paths).
% distanceServer in charge to keep the liste of known distances
% server interfaces
start(Towns) ->
{ok,List} = file:consult(Towns),
Paths = lists:foldl(fun({A,B,D},Acc) -> maps:put(orderedTuple(A,B), D, Acc) end,#{},List),
start(Paths,distance_server).
stop() ->
distance_server ! stop.
getTowns() ->
K = maps:keys(getPath()),
L = lists:usort(lists:flatten([[A,B] || {A,B} <- K])),
io:format("list of towns :~n~p~n~n",[L]).
getPath() ->
distance_server ! {getPath,self()},
receive
Path -> Path
end.
% server fuctions
start(Paths,Server) ->
Pid = spawn(fun() -> distanceServer(Paths) end),
register(Server, Pid).
distanceServer(Path) ->
receive
stop -> stop;
{getPath,From} ->
From ! Path,
distanceServer(Path)
end.
% Searching path
path(From,To,not_found,Paths) -> % if not in the known list, seach for the shortest path
{KM,P} = searchBestPath({0,[From]},To,maps:keys(Paths),{no_dist,no_path}),
case P of
no_path -> not_found;
_ -> {lists:reverse(P),KM}
end;
path(From,To,KM,_) -> % else give the result. Assumption: the known path contains always the best one.
{[From,To],KM}.
searchBestPath({N,[To|_]}=Path,To,_,{BestD,_}) when N < BestD -> Path; % keep the new path if it is better
searchBestPath({N,_},_,_,{BestD,_}=Best) when N >= BestD -> Best; % cancel search if the path so far is longer or equal to the best found
searchBestPath({D,[H|_]=PathSoFar},To,Remaining,Best) ->
Next = [remove(H,{A,B}) || {A,B} <- Remaining, (A =:= H) orelse (B =:= H)], % list of all possible next steps
case Next of
[] -> Best;
Next -> lists:foldl(
fun(X,Acc) ->
{_,ND} = path(H,X), % will always match
R = Remaining -- [orderedTuple(H,X)], % necessary to avoid possible infinite loop in the first search
searchBestPath({D+ND,[X|PathSoFar]},To,R,Acc) % evaluate path for all possible next steps
end,
Best,Next)
end.
% helpers
orderedTuple(A,B) when B > A -> {A,B};
orderedTuple(A,B) -> {B,A}.
remove(X,{X,B}) -> B;
remove(X,{A,X}) -> A.
it uses an external file to define the "known distances", I have used this one for test:
{paris,lyon,465}.
{lyon,marseille,314}.
{marseille,nice,198}.
{marseille,toulouse,404}.
{toulouse,bordeaux,244}.
{bordeaux,paris,568}.
{bordeaux,nantes,347}.
{nantes,paris,385}.
{paris,lille,225}.
{paris,strasbourg,491}.
{lille,strasbourg,525}.
{lille,bruxelles,120}.
{rennes,brest,244}.
{rennes,paris,351}.
{rennes,nantes,113}.
and the result in the shell:
1> c(distances).
{ok,distances}
2> distances:start("distances.txt").
true
3> distances:getTowns().
list of towns :
[bordeaux,brest,bruxelles,lille,lyon,marseille,nantes,nice,paris,rennes,
strasbourg,toulouse]
ok
4> distances:path(bordeaux,bruxelles).
{[bordeaux,paris,lille,bruxelles],913}
5> distances:path(nice,bruxelles).
{[nice,marseille,lyon,paris,lille,bruxelles],1322}
6> distances:path(moscou,paris).
not_found
7> distances:stop().
stop
8>
next step could be to increase the list of known distances each time a new request is done.

Erlang; list comprehension without duplicates

I am doing somthing horrible but I don't know how to make it better.
I am forming all pairwise sums of the elements of a List called SomeList, but I don't want to see duplicates ( I guess I want "all possible pairwise sums" ):
sets:to_list(sets:from_list([A+B || A <- SomeList, B <- SomeList]))
SomeList does NOT contain duplicates.
This works, but is horribly inefficient, because the original list before the set conversion is GIGANTIC.
Is there a better way to do this?
You could simply use lists:usort/1
lists:usort([X+Y || X <- L, Y <- L]).
if the chance to have duplicates is very high, then you can generate the sum using 2 loops and store the sum in an ets set (or using map, I didn't check the performance of both).
7> Inloop = fun Inloop(_,[],_) -> ok; Inloop(Store,[H|T],X) -> ets:insert(Store,{X+H}), Inloop(Store,T,X) end.
#Fun<erl_eval.42.54118792>
8> Outloop = fun Outloop(Store,[],_) -> ok; Outloop(Store,[H|T],List) -> Inloop(Store,List,H), Outloop(Store,T,List) end.
#Fun<erl_eval.42.54118792>
9> Makesum = fun(L) -> S = ets:new(temp,[set]), Outloop(S,L,L), R =ets:foldl(fun({X},Acc) -> [X|Acc] end,[],S), ets:delete(S), R end.
#Fun<erl_eval.6.54118792>
10> Makesum(lists:seq(1,10)).
[15,13,8,11,20,14,16,12,7,3,10,9,19,18,4,17,6,2,5]
11> lists:sort(Makesum(lists:seq(1,10))).
[2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20]
12>
This module will allow you to compare times of execution when using list comprehension, sets or ets. You can of course add additional functions to this comparison:
-module(pairwise).
-export([start/2]).
start(Type, X) ->
L = lists:seq(1, X),
timer:tc(fun do/2, [Type, L]).
do(compr, L) ->
sets:to_list(sets:from_list([A+B || A <- L, B <- L]));
do(set, L) ->
F = fun(Sum, Set) -> sets:add_element(Sum, Set) end,
R = fun(Set) -> sets:to_list(Set) end,
do(L, L, sets:new(), {F, R});
do(ets, L) ->
F = fun(Sum, Tab) -> ets:insert(Tab, {Sum}), Tab end,
R = fun(Tab) ->
Fun = fun({X}, Acc) -> [X|Acc] end,
Res = ets:foldl(Fun, [], Tab),
ets:delete(Tab),
Res
end,
do(L, L, ets:new(?MODULE, []), {F, R}).
do([A|AT], [B|BT], S, {F, _} = Funs) -> do([A|AT], BT, F(A+B, S), Funs);
do([_AT], [], S, {_, R}) -> R(S);
do([_A|AT], [], S, Funs) -> do(AT, AT, S, Funs).
Results:
36> {_, Res1} = pairwise:start(compr, 20).
{282,
[16,32,3,19,35,6,22,38,9,25,12,28,15,31,2,18,34,5,21,37,8,
24,40,11,27,14,30|...]}
37> {_, Res2} = pairwise:start(set, 20).
{155,
[16,32,3,19,35,6,22,38,9,25,12,28,15,31,2,18,34,5,21,37,8,
24,40,11,27,14,30|...]}
38> {_, Res3} = pairwise:start(ets, 20).
{96,
[15,25,13,8,21,24,40,11,26,20,14,28,23,16,12,39,34,36,7,32,
35,3,33,10,9,19,18|...]}
39> R1=lists:usort(Res1), R2=lists:usort(Res2), R3=lists:usort(Res3).
[2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,
24,25,26,27,28,29,30|...]
40> R1 = R2 = R3.
[2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,
24,25,26,27,28,29,30|...]
The last line is to compare that all functions return the same result but sorted differently.
First number in each resulted tuple is the time of execution as returned from timer:tc(fun do/2, [Type, L]).. In this example it's 282 for list comprehension, 155 for sets and 96 for ets.
An effective way is to use foldl instead of lists comprehension, because in this case you nedd a state on each step
sets:to_list(
lists:foldl(fun(A, S1) ->
lists:foldl(fun(B, S2) ->
sets:add_element(A+B, S2)
end, S1, SomeListA)
end, sets:new(), SomeListB)).
This solution keeps it relatively fast and makes use of as much pre-written library code as possible.
Note that I use lists:zip/2 here rather than numeric +, only to illustrate that this approach works for any kind of non-repeating permutation of a unique list. You may only care about arithmetic, but if you want more, this can do it.
-export([permute_unique/1]).
permute_unique([]) ->
[];
permute_unique([A|Ab]) ->
lists:zip(lists:duplicate(length(Ab)+1, A), [A|Ab])
++
permute_unique(Ab).
%to sum integers, replace the lists:zip... line with
% [B+C || {B,C} <- lists:zip(lists:duplicate(length(Ab)+1, A), [A|Ab])]
%to perform normal arithmetic and yield a numeric value for each element
I am not sure what you consider gigantic - you will end up with N*(N+1)/2 total elements in the permuted list for a unique list of N original elements, so this gets big really fast.
I did some basic performance testing of this, using an Intel (Haswell) Core i7 # 4GHz with 32GB of memory, running Erlang/OTP 17 64-bit.
5001 elements in the list took between 2 and 5 seconds according to timer:tc/1.
10001 elements in the list took between 15 and 17 seconds, and required about 9GB of memory. This generates a list of 50,015,001 elements.
15001 elements in the list took between 21 and 25 seconds, and required about 19GB of memory.
20001 elements in the list took 49 seconds in one run, and peaked at about 30GB of memory, with about 200 million elements in the result. That is the limit of what I can test.

F# Interesting Behavior of Curried Function

I have a function
// Will perform a given function twice
let twice f = (fun x -> f (f x))
Then I have something like.
// Take x add 1
let f x = x+1
Depending on how I call twice it behaves differently do to left associativity.
(twice (twice (twice (twice f)))) 0;; // Outputs 16
twice twice twice twice f 0;; // Outputs 65536
If I add another twice my program does a StackOverflow, but so far it seems to behave without a pattern, which drives me crazy.
Let k be the number of times twice is called.
Un-curried is 2^k to get the answer.
Curried is extremely odd. Hypothesis 1: When the number of calls is less than 4 it looks like 2^(2^(k-1)), but when k is 4 it behaves like 2^(2^k)
Does anyone see the pattern? Or can you run it past k = 4 to prove it?
This is simple precedence rules behaving weirdly (the hint is 65536=2^16). In the second case you are actually creating an exponential number of calls to f rather than the linear increase you expected.
When you expand one layer on the second case you get
twice twice twice (twice twice twice (f)) 0
and the number of terms will grow exponentially as you write more twice
Indeed, it's all about associativity. When you write,
let x1 = twice twice twice twice f 0
It's equal to
let x11 = (((twice twice) twice) twice) f 0
This leads to exponential growth of call order: each twice call is supposed to call f x two times. Instead, it recursively calls itself, and only the most inner call would invoke f.
You may look at the prototype of the function:
let y1: ( _ -> _ -> int) = twice twice twice twice
// val y1: ((int -> int) -> int -> int)
The minimal code to make the associativity work well would be:
// note we need to specify a type here
let y2: ( _ -> _ -> int) = twice >> twice >> twice >> twice
// the same with all arguments
let x2 = (twice >> twice >> twice >> twice) f 0
or
let y3 = f |> twice |> twice |> twice |> twice
let x3 = (f |> twice |> twice |> twice |> twice) 0

F# Tail Recursive Function Example

I am new to F# and was reading about tail recursive functions and was hoping someone could give me two different implementations of a function foo - one that is tail recursive and one that isn't so that I can better understand the principle.
Start with a simple task, like mapping items from 'a to 'b in a list. We want to write a function which has the signature
val map: ('a -> 'b) -> 'a list -> 'b list
Where
map (fun x -> x * 2) [1;2;3;4;5] == [2;4;6;8;10]
Start with non-tail recursive version:
let rec map f = function
| [] -> []
| x::xs -> f x::map f xs
This isn't tail recursive because function still has work to do after making the recursive call. :: is syntactic sugar for List.Cons(f x, map f xs).
The function's non-recursive nature might be a little more obvious if I re-wrote the last line as | x::xs -> let temp = map f xs; f x::temp -- obviously its doing work after the recursive call.
Use an accumulator variable to make it tail recursive:
let map f l =
let rec loop acc = function
| [] -> List.rev acc
| x::xs -> loop (f x::acc) xs
loop [] l
Here's we're building up a new list in a variable acc. Since the list gets built up in reverse, we need to reverse the output list before giving it back to the user.
If you're in for a little mind warp, you can use continuation passing to write the code more succinctly:
let map f l =
let rec loop cont = function
| [] -> cont []
| x::xs -> loop ( fun acc -> cont (f x::acc) ) xs
loop id l
Since the call to loop and cont are the last functions called with no additional work, they're tail-recursive.
This works because the continuation cont is captured by a new continuation, which in turn is captured by another, resulting in a sort of tree-like data structure as follows:
(fun acc -> (f 1)::acc)
((fun acc -> (f 2)::acc)
((fun acc -> (f 3)::acc)
((fun acc -> (f 4)::acc)
((fun acc -> (f 5)::acc)
(id [])))))
which builds up a list in-order without requiring you to reverse it.
For what its worth, start writing functions in non-tail recursive way, they're easier to read and work with.
If you have a big list to go through, use an accumulator variable.
If you can't find a way to use an accumulator in a convenient way and you don't have any other options at your disposal, use continuations. I personally consider non-trivial, heavy use of continuations hard to read.
An attempt at a shorter explanation than in the other examples:
let rec foo n =
match n with
| 0 -> 0
| _ -> 2 + foo (n-1)
let rec bar acc n =
match n with
| 0 -> acc
| _ -> bar (acc+2) (n-1)
Here, foo is not tail-recursive, because foo has to call foo recursively in order to evaluate 2+foo(n-1) and return it.
However, bar ís tail-recursive, because bar doesn't have to use the return value of the recursive call in order to return a value. It can just let the recursively called bar return its value immediately (without returning all the way up though the calling stack). The compiler sees this and optimized this by rewriting the recursion into a loop.
Changing the last line in bar into something like | _ -> 2 + (bar (acc+2) (n-1)) would again destroy the function being tail-recursive, since 2 + leads to an action that needs to be done after the recursive call is finished.
Here is a more obvious example, compare it to what you would normally do for a factorial.
let factorial n =
let rec fact n acc =
match n with
| 0 -> acc
| _ -> fact (n-1) (acc*n)
fact n 1
This one is a bit complex, but the idea is that you have an accumulator that keeps a running tally, rather than modifying the return value.
Additionally, this style of wrapping is usually a good idea, that way your caller doesn't need to worry about seeding the accumulator (note that fact is local to the function)
I'm learning F# too.
The following are non-tail recursive and tail recursive function to calculate the fibonacci numbers.
Non-tail recursive version
let rec fib = function
| n when n < 2 -> 1
| n -> fib(n-1) + fib(n-2);;
Tail recursive version
let fib n =
let rec tfib n1 n2 = function
| 0 -> n1
| n -> tfib n2 (n2 + n1) (n - 1)
tfib 0 1 n;;
Note: since the fibanacci number could grow really fast you could replace last line tfib 0 1 n to
tfib 0I 1I n to take advantage of Numerics.BigInteger Structure in F#
Also, when testing, don't forget that indirect tail recursion (tailcall) is turned off by default when compiling in Debug mode. This can cause tailcall recursion to overflow the stack in Debug mode but not in Release mode.

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