In my Matlab code I have an object-array of 'masses' which are an object of a class which describes the mass, speed, accerleration etc.
To speed up the simulation I want to reduce the usage of for-loops with using more vector operations. One of the operations is to get the distance of the current mass to all others.
I would like to solve it like that:
%position is a vector with x and y values e.g. [1 2]
%repeat the current mass as many times as there are other masses to compare with
currentMassPosition = repmat(obj(currentMass).position, length(obj), 2);
distanceCurrentMassToOthersArray = obj(:).position - currentMassPosition;
I cannot use the colon-indexing operation on the object array. Currently i use a for-loop where I iterate through every single object. Do you have any tips to optimise that without using a for loop?
I hope my question was clear enough, otherwise I will optimise it ;).
I used this code to reproduce your problem. For future questions please try to include such examples into your question:
classdef A
properties
position
end
methods
function obj=A()
obj.position=1;
end
end
end
.
%example code to reproduce
x(1)=A
x(2)=A
x(3)=A
%line which causes the problem
x(:).position-3
To understand why this is not working, take a look at the output of x(:).position, just type it into the console. You get multiple ans values, indicating a comma separated list of multiple values. If you use [x(:).position] instead, you get an array of doubles. The correct code is:
[x(:).position]-3
I am a newbie to Matlab and I am currently trying to optimize a nested for loop as below. The loop is currently running forever for my input.
for i = 1:size(mat,1)
for j = 1:size(mat,2)
mat(i,j) = some_mapping(mat(i,j)+1);
end
end
However I can't find a way to vectorize it. I have tried bsxfun and arrayfun but it does not seem to work (or even run more slowly than the loop).
Maybe I was doing it in a wrong way. Any help is appreciated!
As suggested by Andras Deak, if some_mapping is simply a look-up-table operation, then
mat = some_mapping( mat+1 );
Notes:
- In order of the mapping to work, the values of mat must be integers in the range [0..numel(some_mapping)-1].
- The size of some_mapping does not affect the size of the result, it will be identical in size to mat.
Last week I asked the following:
https://stackoverflow.com/questions/32658199/vectorizing-gibbs-sampler-in-matlab
Perhaps it was not that clear what I want to do, so this might be more clear.
I would like to vectorize a "for" loop in matlab, where some variables inside of the loop are bidirectionally related. So, here is an example:
A=2;
B=3;
for i=1:10000
A=3*B;
B=exp(A*(-1/2))
end
Thank you once again for your time.
A quick Excel calculation indicates that this quickly converges to 0.483908 (after much less than 10000 loops - so one way of speeding it up would be to check for convergence). If A and B are always 2 and 3 respectively, you could just replace the loop with this value.
Alternatively, using some series analysis you might be able to come up with an analytical expression for B when i is large - although with the nested exponents deriving this is a bit beyond my own abilities!
Edit
A bit of googling reveals this. Wikipedia states that for a tetration of x to infinity (i.e. x^x^x^x^x...), the solution y satisfies y = x^y. In your case, for example, 0.483908 = e^(-3/2)^0.483908, so 0.483908 is a solution. Not sure how you would exploit this though.
Wikipedia also gives a convergence condition, which might be of use to you: x lies between e^-e and e^1/e.
Final Edit (?)
Turns out you need Lambert's W function to solve for equations of the form of y = x^y. There seems to be no native function for this, but there seems to be something in the FileExchange - see here and here.
parfor is a convenient way to distribute independent iterations of intensive computations among several "workers". One meaningful restriction is that parfor-loops cannot be nested, and invariably, that is the answer to similar questions like there and there.
Why parallelization across loop boundaries is so desirable
Consider the following piece of code where iterations take a highly variable amount of time on a machine that allows 4 workers. Both loops iterate over 6 values, clearly hard to share among 4.
for row = 1:6
parfor col = 1:6
somefun(row, col);
end
end
It seems like a good idea to choose the inner loop for parfor because individual calls to somefun are more variable than iterations of the outer loop. But what if the run time for each call to somefun is very similar? What if there are trends in run time and we have three nested loops? These questions come up regularly, and people go to extremes.
Pattern needed for combining loops
Ideally, somefun is run for all pairs of row and col, and workers should get busy irrespectively of which iterand is being varied. The solution should look like
parfor p = allpairs(1:6, 1:6)
somefun(p(1), p(2));
end
Unfortunately, even if I knew which builtin function creates a matrix with all combinations of row and col, MATLAB would complain with an error The range of a parfor statement must be a row vector. Yet, for would not complain and nicely iterate over columns. An easy workaround would be to create that matrix and then index it with parfor:
p = allpairs(1:6, 1:6);
parfor k = 1:size(pairs, 2)
row = p(k, 1);
col = p(k, 2);
somefun(row, col);
end
What is the builtin function in place of allpairs that I am looking for? Is there a convenient idiomatic pattern that someone has come up with?
MrAzzman already pointed out how to linearise nested loops. Here is a general solution to linearise n nested loops.
1) Assuming you have a simple nested loop structure like this:
%dummy function for demonstration purposes
f=#(a,b,c)([a,b,c]);
%three loops
X=cell(4,5,6);
for a=1:size(X,1);
for b=1:size(X,2);
for c=1:size(X,3);
X{a,b,c}=f(a,b,c);
end
end
end
2) Basic linearisation using a for loop:
%linearized conventional loop
X=cell(4,5,6);
iterations=size(X);
for ix=1:prod(iterations)
[a,b,c]=ind2sub(iterations,ix);
X{a,b,c}=f(a,b,c);
end
3) Linearisation using a parfor loop.
%linearized parfor loop
X=cell(4,5,6);
iterations=size(X);
parfor ix=1:prod(iterations)
[a,b,c]=ind2sub(iterations,ix);
X{ix}=f(a,b,c);
end
4) Using the second version with a conventional for loop, the order in which the iterations are executed is altered. If anything relies on this you have to reverse the order of the indices.
%linearized conventional loop
X=cell(4,5,6);
iterations=fliplr(size(X));
for ix=1:prod(iterations)
[c,b,a]=ind2sub(iterations,ix);
X{a,b,c}=f(a,b,c);
end
Reversing the order when using a parfor loop is irrelevant. You can not rely on the order of execution at all. If you think it makes a difference, you can not use parfor.
You should be able to do this with bsxfun. I believe that bsxfun will parallelise code where possible (see here for more information), in which case you should be able to do the following:
bsxfun(#somefun,(1:6)',1:6);
You would probably want to benchmark this though.
Alternatively, you could do something like the following:
function parfor_allpairs(fun, num_rows, num_cols)
parfor i=1:(num_rows*num_cols)
fun(mod(i-1,num_rows)+1,floor(i/num_cols)+1);
end
then call with:
parfor_allpairs(#somefun,6,6);
Based on the answers from #DanielR and #MrAzzaman, I am posting two functions, iterlin and iterget in place of prod and ind2sub that allow iteration over ranges also if those do not start from one. An example for the pattern becomes
rng = [1, 4; 2, 7; 3, 10];
parfor k = iterlin(rng)
[plate, row, col] = iterget(rng, k);
% time-consuming computations here %
end
The script will process the wells in rows 2 to 7 and columns 3 to 10 on plates 1 to 4 without any workers idling while more wells are waiting to be processed. In hope that this helps someone, I deposited iterlin and iterget at the MATLAB File Exchange.
I've got an ODE system working perfectly. But now, I want in each iteration, sort in ascending order the solution vector. I've tried many ways but I could not do it. Does anyone know how to do?
Here is a simplified code:
function dtemp = tanque1(t,temp)
for i=1:N
if i==1
dtemp(i)=(((-k(i)*At*(temp(i)-temp(i+1)))/(y))-(U*As(i)*(temp(i)-Tamb)))/(ro(i)*vol_nodo*cp(i));
end
if i>1 && i<N
dtemp(i)=(((k(i)*At*(temp(i-1)-temp(i)))/(y))-((k(i)*At*(temp(i)-temp(i+1)))/(y))-(U*As(i)*(temp(i)-Tamb)))/(ro(i)*vol_nodo*cp(i));
end
if i==N
dtemp(i)=(((k(i)*At*(temp(i-1)-temp(i)))/(y))-(U*As(i)*(temp(i)-Tamb)))/(ro(i)*vol_nodo*cp(i));
end
end
end
Test Script:
inicial=343.15*ones(200,1);
[t temp]=ode45(#tanque1,0:360:18000,inicial);
It looks like you have three different sets of differential equations depending on the index i of the solution vector. I don't think you mean "sort," but rather a more efficient way to implement what you've already done - basically vectorization. Provided I haven't accidentally made any typos (you should check), the following should do what you need:
function dtemp = tanque1(t,temp)
dtemp(1) = (-k(1)*At*(temp(1)-temp(2))/y-U*As(1)*(temp(1)-Tamb))/(ro(1)*vol_nodo*cp(1));
dtemp(2:N-1) = (k(2:N-1).*(diff(temp(1:N-1))-diff(temp(2:N)))*At/y-U*As(2:N-1).*(temp(2:N-1)-Tamb))./(vol_nodo*ro(2:N-1).*cp(2:N-1));
dtemp(N) = (k(N)*At*(temp(N-1)-temp(N))/y-U*As(N)*(temp(N)-Tamb))/(ro(N)*vol_nodo*cp(N));
You'll still need to define N and the other parameters and ensure that temp is returned as a column vector. You could also try replacing N with the end keyword, which might be faster. The two uses of diff make the code shorter, but, depending on the value of N, they may also speed up the calculation. They could be replaced with temp(1:N-2)-temp(2:N-1) and temp(2:N-1)-temp(3:N). It may be possible to collapse these down to a single vectorized equation, but I'll leave that as an exercise for you to attempt if you like.
Note that I also removed a great many unnecessary parentheses for clarity. As you learn Matlab you'll to get used to the order of operations and figure out when parentheses are needed.