Im trying to make a n-nested loop method in Julia
function fun(n::Int64)
#nloops n i d->1:3 begin\n
#nexprs n j->(print(i_j))\n
end
end
But the #nloops definition is limited to
_nloops(::Int64, ::Symbol, ::Expr, ::Expr...)
and I get the error
_nloops(::Symbol, ::Symbol, ::Expr, ::Expr)
Is there any way to make this work? Any help greatly appreciated
EDIT:
What I ended up doing was using the combinations method
For my problem, I needed to get all k-combinations of indices to pull values from an array, so the loops would had to look like
for i_1 in 1:100
for i_2 in i_1:100
...
for i_k in i_[k-1]:100
The number of loops needs to be a compile-time constant – a numeric literal, in fact: the code generated for the function body cannot depend on a function argument. Julia's generated functions won't help either since n is just a plain value and not part of the type of any argument. Your best bet for having the number of nested loops depend on a runtime value like n is to use recursion.
In julia-0.4 and above, you can now do this:
function fun(n::Int)
for I in CartesianRange(ntuple(d->1:3, n))
#show I
end
end
In most cases you don't need the Base.Cartesian macros anymore (although there are still some exceptions). It's worth noting that, just as described in StefanKarpinski's answer, this loop will not be "type stable" because n is not a compile-time constant; if performance matters, you can use the "function barrier technique." See http://julialang.org/blog/2016/02/iteration for more information about all topics related to these matters.
Related
I want to be able to allow users of my package to define functions in a more mathematical manner, and I think a macro is the right direction. The problem is as follows. The code allows the users to define functions which are then used in specialized solvers to solve PDEs. However, to make things easier for the solver, some of the inputs are "matrices" in ways that you wouldn't normally wouldn't think they would be. For example, the solvers can take in functions f(x,t), but x[:,1] is what you'd think of as x and x[:,2] is what you'd think of as y (and sometimes it is 3D).
The bigger issues is that when the PDE is nonlinear, I place everything in a u vector, when in many cases (like Reaction-Diffusion equations) these things are named. So in this general case, I'd like to be able to write
#mathdefine f(RA,RABP,RAR,x,y,t) = RA*RABP + RA*x + RAR*t
and have it translate to
f(u,x,t) = u[:,1].*u[:,2] + u[:,1].*x[:,1] + u[:,3]*t
I am not up to snuff on my macro-foo, so I was hoping someone could get me started (or if macros are not the right way to approach this, explain why).
It's not too hard if the user has to give what is being translated to what, but I'd like to have it be as clean to use as possible, so somehow know that it's to the spatial variables and so everything before is part of a u, but after is part of x.
The trick to macro "find/replace" is just to pass off processing to a recursive function that updates the expression args. Your signature will come in as a bunch of symbols, so you can loop through the call signature and add to two dicts, mapping variable name to column index. Then recursively replace the arg tree when you see any of the variables. This is untested:
function replace_vars!(expr::Expr, xd::Dict{Symbol,Int}, ud::Dict{Symbol,Int})
for (i,arg) in enumerate(expr.args)
if haskey(xd, arg)
expr.arg[i] = :(x[:,$(xd[arg])])
elseif haskey(ud, arg)
expr.arg[i] = :(u[:,$(ud[arg])])
elseif isa(arg,Expr)
replace_vars!(arg, xd, ud)
end
end
end
macro mathdefine(expr)
# todo: loop through function signature (expr.args[1]?) to build xd/ud
replace_vars!(expr)
expr
end
I left a little homework for you, but this should get you started.
I would like to call a macro in a Julia package (#defNLExpr in JuMP) using an argument that is runtime dependent. The argument is an expression that depends on the runtime parameter n. The only way that I can think of doing this is something like the following:
macro macro1(x)
y=length(x.args);
return esc(:(k=$y-1))
end
macro macro2(n)
x="0";
for i=1:n
x="$x+$i"
end
x=parse(x);
return :(#macro1($x))
end
n=rand(1:3)
println(n)
if (n==1)
#macro2(1)
elseif (n==2)
#macro2(2)
elseif (n==3)
#macro2(3)
else
error("expected n in 1:3")
end
println(k)
Here I have assumed that my runtime n will always be in the range 1-3. I use macro2 to build-up all possible expressions for these different possible values of n, and call the external macro (which I have replaced by the simplified macro1 here) for each of them. The calls to macro1 are in if statements, so only the correct one (determined from the value of n at runtime) will actually be executed.
Although this seems to work, is there a more efficient way of achieving this?
Seems that you might be looking for eval? Be aware that it should be used with care though, and that it not very fast since it has to income the compiler each time it is called.
If it's a limitation to you that it evaluates the expression in global scope then, there are some ways to work around that.
I'm trying to evaluate some matrix multiplications in MuPAD. The output is using sigmas as placeholders for the matrix elements since they are long expressions (I assume that's the reason). Is there a way to get MuPAD to display the individual matrix elements as (in my case) the exponential functions that they really are, regardless of the length of the expression?
Below is an example of a case where MuPAD is using sigmas instead of the actual exponential functions. I would like to be able to see what the individual matrix elements of TotT^4 really are.
The commands I executed in the MuPAD interface that lead up to TotT^4 are:
T1 := matrix([[exp((J+B/2)/T),exp(-(J+B/6)/T)],[exp((-J+B/6)/T),exp((J-B/2)/T)]])
T2 := matrix([[exp((J1+B/2)/T),exp(-(J1+B/6)/T)],[exp((-J1+B/6)/T),exp((J1-B/2)/T)]])
T1d := linalg::transpose(T1)
TotT := T1d*T2
The class of your variable can be obtain via type(totT): Dom::Matrix. You may want to look at the many methods of this class in the documentation. As far as I can tell, this issue has something to do with the pretty printing of the class's print method. Other classes exhibit this same substitution, so it may be a function of the overloaded print. I was not able to change the behavior by adjusting setPrintMaxSize, PRETTYPRINT, TEXTWIDTH, or any of the optional arguments to print. You might still try yourself as there are many permutations.
I also tried using the expand function. expand(TotT,IgnoreAnalyticConstraints) nearly works though it could have undesirable effects in some cases if things were expanded too much. Calling simplify does get rid go the substitutions, but it also changes the nature of some of the entries by simplifying. It is probably also not a general solution to this issue.
One way that does work, but is ugly, is to use the expr2text method, which returns a result as a string:
expr2text(TotT)
which returns
"matrix([[exp((B/6 - J)/T)*exp((B/6 - J1)/T) + exp((B/2 + J)/T)*exp((B/2 + J1)/T), ...
exp(-(B/2 - J1)/T)*exp((B/6 - J)/T) + exp((B/2 + J)/T)*exp(-(B/6 + J1)/T)], ...
[exp(-(B/2 - J)/T)*exp((B/6 - J1)/T) + exp((B/2 + J1)/T)*exp(-(B/6 + J)/T), ...
exp(-(B/2 - J)/T)*exp(-(B/2 - J1)/T) + exp(-(B/6 + J)/T)*exp(-(B/6 + J1)/T)]])"
I think that this question would be a good one to ask over at Matlab Central or by filing a service request if you have a license with support.
How to simplify a given boolean expression with many variables (>10) so that the number of occurrences of each variable is minimized?
In my scenario, the value of a variable has to be considered ephemeral, that is, has to recomputed for each access (while still being static of course). I therefor need to minimize the number of times a variable has to be evaluated before trying to solve the function.
Consider the function
f(A,B,C,D,E,F) = (ABC)+(ABCD)+(ABEF)
Recursively using the distributive and absorption law one comes up with
f'(A,B,C,E,F) = AB(C+(EF))
I'm now wondering if there is an algorithm or method to solve this task in minimal runtime.
Using only Quine-McCluskey in the example above gives
f'(A,B,C,E,F) = (ABEF) + (ABC)
which is not optimal for my case. Is it save to assume that simplifying with QM first and then use algebra like above to reduce further is optimal?
I usually use Wolfram Alpha for this sort of thing.
Try Logic Friday 1
It features multi-level design of boolean circuits.
For your example, input and output look as follows:
You can use an online boolean expression calculator like https://www.dcode.fr/boolean-expressions-calculator
You can refer to Any good boolean expression simplifiers out there? it will definitely help.
Is there an idiomatic way in Matlab to bind the value of an expression to the nth return value of another expression?
For example, say I want an array of indices corresponding to the maximum value of a number of vectors stored in a cell array. I can do that by
function I = max_index(varargin)
[~,I]=max(varargin{:});
cellfun(#max_index, my_data);
But this requires one to define a function (max_index) specific for each case one wants to select a particular return value in an expression. I can of course define a generic function that does what I want:
function y = nth_return(n,fun,varargin)
[vals{1:n}] = fun(varargin{:});
y = vals{n};
And call it like:
cellfun(#(x) nth_return(2,#max,x), my_data)
Adding such functions, however, makes code snippets less portable and harder to understand. Is there an idiomatic to achieve the same result without having to rely on the custom nth_return function?
This is as far as I know not possible in another way as with the solutions you mention. So just use the syntax:
[~,I]=max(var);
Or indeed create an extra function. But I would also suggest against this. Just write the extra line of code, in case you want to use the output in another function. I found two earlier questions on stackoverflow, which adress the same topic, and seem to confirm that this is not possible.
Skipping outputs with anonymous function in MATLAB
How to elegantly ignore some return values of a MATLAB function?
The reason why the ~ operator was added to MATLAB some versions ago was to prevent you from saving variables you do not need. If there would be a syntax like the one you are searching for, this would not have been necessary.