Assume I have a Manipulate with two dynamic variables and I want to put the corresponding controls in a Row for aesthetics reason. I can think of two ways to do it as follows:
Row[Control/#{{{a,a_in},a_min,a_max},{{b,b_in},b_min,b_bmax}}]
or
Row[{Control[{{a,a_in},a_min,a_max}],Control[{{b,b_in},b_min,b_bmax}]}]
The issue is that in the first case after the 1st run of the cell containing Manipulate with that line the variables a, b become having defined value (a_in and b_in) respectively and for further evaluation are not recognized as variables of Manipulate, while in the other case a and b remain undefined and serve correctly as dynamic variables.
I expect that the Map (/#) somehow changes the order of evaluation in the expression and that the variable "leaks" outside the Row, gets told by Manipulate to have a value and takes it on. While on the other hand the simple Control[] correctly encloses a control option and nothing "leaks". Yet I find this claim possibly false and unsatisfyingly vague (thus hard to generalize and understand Mathematica better, which I would like to).
Can someone explain why that happens or point me to some other insightful answer (I guess this is not the first time this issue came up, but I can't form a proper query to google for it.)?
(This question regards search/6.)
I was wondering if there is a way -rather than manual tracing- to pause the execution of search/6 every time a new solution for a single variable was found?
I would like to accomplish this to further investigate what is happening during search in constrained models.
For example, if you are trying to solve the classic sudoku problem, and you have written a set of constraints and a print method for your board, it can be useful to print the board after setting the constraints, but before searching, in order to evaluate the strongness of your constraints. However, once search is called to solve the sudoku, you don't really have an overview of the single results being built underneath unless you do a trace.
It would be very useful if something was possible in the likes of:
(this is just an abstract example)
% Let's imagine this is a (very poorly) constrained sudoku board
?- problem(Sudoku),constraint(Sudoku),print(Sudoku).
[[1,3,_,2,_,_,7,4,_],
[_,2,5,_,1,_,_,_,_],
[4,8,_,_,6,_,_,5,_],
[_,_,_,7,8,_,2,1,_],
[5,_,_,_,9,_,3,7,_],
[9,_,_,_,3,_,_,_,5],
[_,4,_,_,_,6,8,9,_],
[_,5,3,_,_,1,4,_,_],
[6,_,_,_,_,_,_,_,_]]
Now for the search:
?- problem(Sudoku),constraint(Sudoku),search_pause(Sudoku,BT),print(Sudoku,BT).
[[1,3,6,2,_,_,7,4,_],
[_,2,5,_,1,_,_,_,_],
[4,8,_,_,6,_,_,5,_],
[_,_,_,7,8,_,2,1,_],
[5,_,_,_,9,_,3,7,_],
[9,_,_,_,3,_,_,_,5],
[_,4,_,_,_,6,8,9,_],
[_,5,3,_,_,1,4,_,_],
[6,_,_,_,_,_,_,_,_]]
Board[1,3] = 6
Backtracks = 1
more ;
Using existing Visualization tools
Have a look at the Visualization Tools Manual. You can get the kind of matrix display you want by adding a viewable_create/2 annotation to your code, and launching a Visualisation Client from TkECLiPSe's Tools-menu.
Using your own instrumented search routine
You can replace the indomain_xxx choice methods in search/6 with a user-defined one where you can print information before and/or after propagation.
If that is not enough, you can replace the whole built-in search/6 with your own, which is not too difficult, see e.g. the ECLiPSe Tutorial chapter on tree search or my answer to this question.
Tracing using data-driven facilities
Using ECLiPSe's data-driven control facilities, you can quite easily display information when certain things happen to your variables. In the simplest case you do something on variable instantiation:
?- suspend(printf("X was instantiated to %w%n",[X]), 1, X->inst),
writeln(start), X=3, writeln(end).
start
X was instantiated to 3
end
Based on this idea, you can write code that allows you to follow labeling and propagation steps even when they happen inside a black-box search routine. See the link for details.
EDIT to try to address #user2864740's edit and comment: I am wondering if there is any information particularly relevant to 0.4rc1/rc2 or in particular a strategy or suggestion from one of the Julia developers more recent than those cited below (particularly #StefanKarpinski's Jan 2014 answer in #6 below). Thx
Please see e.g.
https://groups.google.com/forum/#!topic/julia-users/pCuDx6jNJzU
https://groups.google.com/forum/#!topic/julia-users/2kLNdQTGZcA
https://groups.google.com/forum/#!msg/julia-dev/JEiH96ofclY/_amm9Cah6YAJ
https://github.com/JuliaLang/julia/pull/10269
https://github.com/JuliaLang/julia/issues/1090
Can I add type information to arguments that are functions in Julia?
Performance penalty using anonymous function in Julia
(As a fairly inexperienced Julia user) my best synthesis of this information, some of which seems to be dated, is that the best practice is either "avoid doing this" or "use FastAnonymous.jl."
I'm wondering what the bleeding edge latest and greatest way to handle this is.
[Longer version:]
In particular, suppose I have a big hierarchy of functions. I would like to be able to do something like
function transform(function_one::Function{from A to B},
function_two::Function{from B to C},
function_three::Function{from A to D})
function::Function{from Set{A} to Dict{C,D}}(set_of_As::Set{A})
Dict{C,D}([function_two(function_one(a)) => function_three(a)
for a in set_of_As])
end
end
Please don't take the code too literally. This is a narrow example of a more general form of transformation I'd like to be able to do regardless of the actual specifics of the transformation, BUT I'd like to do it in such a way that I don't have to worry (too much) about checking the performance (that is, beyond the normal worries I'd apply in any non-function-with-function-as-parameter case) each time I write a function that behaves this way.
For example, in my ideal world, the correct answer would be "so long as you annotate each input function with #anon before you call this function with those functions as arguments, then you're going to do as well as you can without tuning to the specific case of the concrete arguments you're passing."
If that's true, great--I'm just wondering if that's the right interpretation, or if not, if there is some resource I could read on this topic that is closer to a "logically" presented synthesis than the collection of links here (which are more a stream of collective consciousness or history of thought on this issue).
The answer is still "use FastAnonymous.jl," or create "functor types" manually (see NumericFuns.jl).
If you're using julia 0.4, FastAnonymous.jl works essentially the same way that official "fast closures" will eventually work in base julia. See https://github.com/JuliaLang/julia/issues/11452#issuecomment-125854499.
(FastAnonymous is implemented in a very different way on julia 0.3, and has many more weaknesses.)
In relationship to this thread, this is also what i am kind of trying to do but i have had a bit more leeway in this.
My problem is i am currently working on a defining program (for my ti-89 titanium) to write out the definitions of variables. However, considering i had indefinite amounts of variables to add, i thought using the define function over and over again would waste memory and processing power. So my thinking was Save the variable to another variable to be defined in a later portion of the program.
prompt x
lbl x_d_r
x_d_r->q:Goto def
lbl def
define expr(q)[1]=x
where x_d_r has no assigned value. So the program was supposed to use the defined string as a list value to be x. However the obvious error came about.
So i played around on the home screen and program screen for a bit and came across entry(1) and ans(1). See back on the ti-83 (or 84) i could basically go (If i remember correctly)
disp q*1
x->ans(1)
However ans(1) on a ti-89 titanium is based upon the last answer submitted to the homescreen. Even then, ans(1) or entry(1) gets replaced in the program by just that. Lucky me, i found a way to avoid this.
Prgm
expr(char(120)&char(22)&char(97)&char(110)&char(115)&char(40)&char(49)&char(41))
EndPrgm
For those that do not know, this is simply expressing x->ans(1) which is a way for the code to transmit ans(1) within a program without removing the code to say so.
But it still does not work as a value needs to be sent to the home screen in order for it to record properly. This is one of those advantages that the ti-84 or ti-83 i wish it still had on the titanium. So i have spent some time searching for ways how i can display values of q to the home screen from within a program.
So far i learned that functions when used straight from the home screen return the value of q to the same place. However i have no way of implementing this in an actual program as the function does not wish to transmit the value to the home screen, and its rather useless within the program.
Secondly i have found this website which details methods of such ways to return values to the homescreen. While method 1 seems to hold promise, i do not seem to have any way of accessing that folder/program. Most likely because it is one that he made and has not shared its location on the pdf. I do like the expr("q"&":stop"), but q is not evaluated out so maybe i would have to rework it somehow.
While this was happening, i thought some other ideas could be using the paste key within a program but i have no idea how to implement stuff found from getkey let alone how the second and grab buttons factor in.
Or i could somehow have the ans(1) look to someplace else other than the home screen. Preferably to the i/0 screen but maybe to some other list or data matrix.
Anybody have any ideas on how to relay a value to the homescreen be it through function, pasting or something, and have the program i defined earlier define it as a value?
UPDATE+1
Ok i am beginning to question if maybe i am making it more complex than it needs to be...
After all, i am only going for just x->x_d_r[1], which is already defined elsewhere. So does it beat x->q:Goto def
Lbl def
Define expr(q)=x
(Or something like that which calls to a history recording program to define values?)
in terms of processing speed and memory count?
Got it. See here for what i was really trying to do.
So as an explanation of what the main problem was again, i wanted to be able to post a string value of q to be defined by another value of x.
The expr( function is quite a powerful tool on the ti-89 and like the person in that other forum, underestimated it. See what the person was trying to do was
InputStr "Function:",f(x)
expr(f)→f(x)
And was later answered by reworking it as
InputStr "function", n
expr(n & "->f(x)")
The expression tool just simply expresses what is in the parentheses. So during break periods in school today, i reworked in my head thinking "What if i tried rewriting the parenthesis out so it reads Expr("x->"&String(q))?
Lo-and-behold it works. Tested it with the fuller version of define to get
td()
Prgm
Prompt X
x_d_r->q
expr("x->"&string(q)&"[1]")
Disp x_d_r[1]
Delvar x_d_r
EndPrgm
Tried, tested and true. Works all the way. See what i think is happening is that anything that is not within the quotes is evaluated immediately in an expression while the the quoted objects are simply expressed and added later in response to the "&" key. Furthermore it makes sense if i was to describe it more with english; "Express x to be stored into the string of q's respective table".
While for variables sake i would have to look into ways to make x_d_r local only to the program without compensating the fact that the x_d_r portion is not considered a store value when executing x_d_r->q. But knowing what i know now i could probably do
expr("q"+"x_d_r"&->a)
expr("x->"&string(a)-"q"&"[1]")
In order to bypass that problem.
I've been working on a programme to solve any maximisation LPP using the Revised Simplex Method. I have a problem with it though as I'm trying to input a sequence to solve the problem of non-basic variables.
My code is as follows:
matmax:=proc(tableau,basic)
local pivot,T,nbv,n,m,b;
T:=evalm(tableau);
n:=coldim(T); m:=rowdim(T);
b:=evalm(basic);
print(evalm(T));
nbv:={seq(i,i=2..n-1)}minus{seq(b[i],i=1..m)};
pivot:=getpiv(T,nbv);
while not pivot=FAIL do
b[pivot[1]]:=pivot[2];
T:=evalm(gauss(col(T,pivot[2]),pivot[1])&*T);
print(evalm(T));
nbv:={seq(i,i=2,..n-1)}minus{seq(b[i],i=1..m)};
pivot:=getpiv(T,nbv);
od;
[evalm(T),evalm(b)];
end;
The gauss and getpiv commands are procedures written to work in this programme, these work fine. However upon executing this procedure Maple returns with the message "Error, (in matmax) unable to execute seq" If anyone can give me any help on how to fix this problem it would be greatly appreciated.
If you have not loaded the linalg package before calling your matxmax then commands like coldim will simplify not work and not produce the integer results for n and m that are expected when using those in the bound of the seq calls. I believe that is why your seq error occurs, because n and m are not being assigned integer intermediate results like you expect.
You could try to remedy this by either loading the package before calling matmax, with with(linalg). But that is not so robust, and there are scenarios where it might not work. The with command won't work within a procedure body, so you can't put that inside the defn of proc matmax.
You could insert a line into matmax above, say, the local declaration line, like,
uses linalg;
That would make coldim and friends from the linalg package work. Unfortunately you've used the name pivot as a local variable, and that clashes with the pivot export from linalg package. So that simple fix via uses is not quite enough. You could use some name other than pivot, and that simple uses line, sure.
My own preference would be to make everything fully explicit, so that later on you or anyone else reading the code can understand it more clearly, even if it's longer. So I would use linalg[coldim] instead of coldim, and so on for the other exports uses from the linalg package within matmax.
Having said all the above, you should know that the linalg package is deprecated in modern Maple and that LinearAlgebra is the new package that offers the functionality you seem to be using. The command names are longer, but using the newer package means that you don't need all those evalm calls (or anything like it).
The problem could lie in your gauss and getpiv commands as they may not work with your procedure, could you expand on what they do?