I've searched and there are many answers to this kind of question, suggesting functions like arrayfun, bsxfun, and so on. I haven't been able to resolve the issue due to dimension mismatches (and probably a fundamental misunderstanding as to how MATLAB treats anonymous function handles).
I have a generic function handle of more than one variable:
f = #(x,y) (some function of x, y)
Heuristically, I would like to define a new function handle like
g = #(x) sum(f(x,1:3))
More precisely, the following does exactly what I need, but is tedious to write out for larger arrays (say, 1:10 instead of 1:3):
g = #(x) f(x,1)+f(x,2)+f(x,3)
I tried something like
g = #(x) sum(arrayfun(#(y) f(x,y), 1:3))
but this does not work as soon as the size of x exceeds 1x1.
Thanks in advance.
Assuming you cannot change the definition of f to be more vector-friendly, you can use your last solution by specifying a non-uniform output and converting the output cell array to a matrix:
g = #(x) sum(cell2mat(arrayfun(#(y) f(x,y), 1:3,'UniformOutput',false)),2);
This should work well if f(x,y) outputs column vectors and you wish to sum them together. For rows vectors, you can use
g = #(x) sum(cell2mat(arrayfun(#(y) f(x,y), 1:3,'UniformOutput',false).'));
If the arrays are higher in dimension, I actually think a function accumulator would be quicker and easier. For example, consider the (extremely simple) function:
function acc = accumfun(f,y)
acc = f(y(1));
for k = 2:numel(y)
acc = acc + f(y(k));
end
end
Then, you can make the one-liner
g = #(x) accumfun(#(y) f(x,y),y);
Related
I'm pretty new to matlab, so I'm guessing there is some shortcut way to do this but I cant seem to find it
results = eqs\soltns;
A = results(1);
B = results(2);
C = results(3);
D = results(4);
E = results(5);
F = results(6);
soltns is a 6x1 vector and eqs is a 6x6 matrix, and I want the results of the operation in their own separate variables. It didn't let me save it like
[A, B, C, D, E, F] = eqs\soltns;
Which I feel like would make sense, but it doesn't work.
Up to now, I have never come across a MATLAB function doing this directly (but maybe I'm missing something?). So, my solution would be to write a function distribute on my own.
E.g. as follows:
result = [ 1 2 3 4 5 6 ];
[A,B,C,D,E,F] = distribute( result );
function varargout = distribute( vals )
assert( nargout <= numel( vals ), 'To many output arguments' )
varargout = arrayfun( #(X) {X}, vals(:) );
end
Explanation:
nargout is special variable in MATLAB function calls. Its value is equal to the number of output parameters that distribute is called with. So, the check nargout <= numel( vals ) evaluates if enough elements are given in vals to distribute them to the output variables and raises an assertion otherwise.
arrayfun( #(X) {X}, vals(:) ) converts vals to a cell array. The conversion is necessary as varargout is also a special variable in MATLAB's function calls, which must be a cell array.
The special thing about varargout is that MATLAB assigns the individual cells of varargout to the individual output parameters, i.e. in the above call to [A,B,C,D,E,F] as desired.
Note:
In general, I think such expanding of variables is seldom useful. MATLAB is optimized for processing of arrays, separating them to individual variables often only complicates things.
Note 2:
If result is a cell array, i.e. result = {1,2,3,4,5,6}, MATLAB actually allows to split its cells by [A,B,C,D,E,F] = result{:};
One way as long as you know the size of results in advance:
results = num2cell(eqs\soltns);
[A,B,C,D,E,F] = results{:};
This has to be done in two steps because MATLAB does not allow for indexing directly the results of a function call.
But note that this method is hard to generalize for arbitrary sizes. If the size of results is unknown in advance, it would probably be best to leave results as a vector in your downstream code.
I want to save the (x,y) coordinates in a grid network that are visited by different individuals. Let say I have 1000 individuals and the network size is x = 1:100 and y=1:100. I am using Dict() and here is a sample code about what I want to do:
individuals = 1:1000
x = 1:100
y = 1:100
function Visited_nodes()
nodes_of_inds =Dict{Int64, Array{Tuple{Int64, Int64}}}()
for ind in individuals
dum_array = Array{Tuple{Int64, Int64}}(0)
for i in x
for j in y
if rand()<0.2 # some conditions
push!(dum_array, (i,j))
end
end
end
nodes_of_inds[ind]=unique(dum_array)
end
return nodes_of_inds
end
#time nodes_of_inds = Visited_nodes()
# result: 1.742297 seconds (12.31 M allocations: 607.035 MB, 6.72% gc time)
But this is not efficient. I appreciate any advice how to make it more efficient.
Please see the performance tips. Very first piece of advice there: avoid global variables. individuals, x, and y are all non-constant global variables. Make them arguments to your function instead. That change alone speeds up your function by an order of magnitude.
By construction, you're not going to have any duplicate tuples in your dum_array, so you don't need to call unique. That shaves off another factor of two.
Finally, Array{T} isn't a concrete type. Julia's arrays also encode the dimensionality as a type parameter, which must be included for the dictionary of arrays to be efficient. Use Array{T, 1} or Vector{T} instead. This isn't a major consideration within the time of this function, though.
The major thing that's left is just the O(length(individuals)*length(x)*length(y)) computational complexity. Doing anything ten million times will add up quickly, no matter how efficient it is.
#Matt B., thanks for your response. About the global variables, I tried a simplified version of my code and it did not help the performance.
Let say I read my input data from a couple of csv files and I have three functions with different arguments:
function Read_input_data()
# read input data
individuals = readcsv("file1")
x = readcsv("file2")
y = readcsv("file3")
A = readcsv("file4")
B = readcsv("file5") # and a few other files
# call different functions
result_1 = Function1(individuals , x, y)
result_2 = Function2(result_1 ,y, A, B)
result_3 = Function3(result_2 , individuals, A, B)
return result_1, result_2, result_3
end
result_1, result_2, result_3 = Read_input_data()
I do not know why the performance is not better compared to when I define everything global! I appreciate any if you can comment about this!
In MATLAB, I would like to extract a nested field for each index of a 1 x n struct (a nonscalar struct) and receive the output as a 1 x n cell array. As a simple example, suppose I start with the following struct s:
s(1).f1.fa = 'foo';
s(2).f1.fa = 'yedd';
s(1).f1.fb = 'raf';
s(2).f1.fb = 'da';
s(1).f2 = 'bok';
s(2).f2 = 'kemb';
I can produce my desired 1 x 2 cell array c using a for-loop:
n = length(s);
c = cell(1,n);
for k = 1:n
c{k} = s(k).f1.fa;
end
If I wanted to do analogously for a non-nested field, for example f2, then I could "vectorize" the operation (see this question), writing simply:
c = {s.f2};
However the same approach does not appear to work for nested fields. What then are possible ways to vectorize the above for-loop?
You cannot really vectorize it. The problem is that Matlab does not allow most forms of nested indexing, including []..
The most concise / readable option would be to concatenate s.f1 results in a structure array using [...], and then index into the new structure array with a separate call:
x = [s.f1]; c = {x.fa};
If you have a Mapping Toolbox, you could use extractfield to perform the second indexing in one expression:
c = extractfield([s.f1], 'fa');
Alternatively you could write a one-liner using arrayfun - here's a couple of options:
c = arrayfun(#(x) x.f1.fa, s, 'uni', false);
c = arrayfun(#(x) x.fa, [s.f1], 'uni', false);
Note that arrayfun and similar functions are generally slower than explicit for loops. So if the performance is critical, time / profile your code, before making a decision to get rid of the loop.
I've done quite a bit of searching and haven't been able to find a satisfactory answer so far, so I'm sorry if this question has already been raised.
I'm stuck on how to sum over the dimensions of an array. I have array A(w0,lambda,2048,2048), and I would like to be able to define a second array U(w0, 2048, 2048) which is composed of the sum of A over dimension lambda.
So far I have been defining both A and U as follows:
A = zeros(length(w0),length(lambda),2048,2048);
U = zeros(length(w0),2048,2048);
for ii = 1:length(w0) % Scan through spot sizes
for aa = 1:length(lambda) % Scan through wavelengths
A(ii,aa,:,:) = ASM(w0(ii),lambda(aa),z1,z2);
end
U(ii,:,:) = sum(A,2);
end
Where ASM is just a function. z1 and z2 are defined earlier, and not relevant here.
I have been trying to come up with other possible ways of finding U(w0,2048,2048) as the sum over the second dimension of A (lambda), but haven't been successful...
Thanks for any pointers, and sorry again if this has already been resolved!
James.
From the sounds of it, you just want:
U = squeeze(sum(A, 2));
squeeze() eliminates singleton dimensions.
Here are two alternative solutions:
U = reshape(sum(A, 2), [length(w0) 2048 2048]);
or:
U = sum(A, 2);
U = U(:, 1, :, :);
Try using 'sum' function with a dimension argument, and collapse result on the desired dimensions.
z = rand(2,3,2,2);
q = sum(z,2); %sum all 3 matrices of size 2x2x2 to get 2x1x2x2 result
zz = q(:,1,:,:); %zz is now 2x2x2, by collapsing the dimension 2.
I often find myself wanting to collapse an n-dimensional matrix across one dimension using a custom function, and can't figure out if there is a concise incantation I can use to do this.
For example, when parsing an image, I often want to do something like this. (Note! Illustrative example only. I know about rgb2gray for this specific case.)
img = imread('whatever.jpg');
s = size(img);
for i=1:s(1)
for j=1:s(2)
bw_img(i,j) = mean(img(i,j,:));
end
end
I would love to express this as something like:
bw = on(color, 3, #mean);
or
bw(:,:,1) = mean(color);
Is there a short way to do this?
EDIT: Apparently mean already does this; I want to be able to do this for any function I've written. E.g.,
...
filtered_img(i,j) = reddish_tint(img(i,j,:));
...
where
function out = reddish_tint(in)
out = in(1) * 0.5 + in(2) * 0.25 + in(3) * 0.25;
end
Many basic MATLAB functions, like MEAN, MAX, MIN, SUM, etc., are designed to operate across a specific dimension:
bw = mean(img,3); %# Mean across dimension 3
You can also take advantage of the fact that MATLAB arithmetic operators are designed to operate in an element-wise fashion on matrices. For example, the operation in your function reddish_tint can be applied to all pixels of your image with this single line:
filtered_img = 0.5.*img(:,:,1)+0.25.*img(:,:,2)+0.25.*img(:,:,3);
To handle a more general case where you want to apply a function to an arbitrary dimension of an N-dimensional matrix, you will probably want to write your function such that it accepts an additional input argument for which dimension to operate over (like the above-mentioned MATLAB functions do) and then uses some simple logic (i.e. if-else statements) and element-wise matrix operations to apply its computations to the proper dimension of the matrix.
Although I would not suggest using it, there is a quick-and-dirty solution, but it's rather ugly and computationally more expensive. You can use the function NUM2CELL to collect values along a dimension of your array into cells of a cell array, then apply your function to each cell using the function CELLFUN:
cellArray = num2cell(img,3); %# Collect values in dimension 3 into cells
filtered_img = cellfun(#reddish_tint,cellArray); %# Apply function to each cell
I wrote a helper function called 'vecfun' that might be useful for this, if it's what you're trying to achieve?
link
You could use BSXFUN for at least some of your tasks. It performs an element-wise operation among two arrays by expanding the size 1 - dimensions to match the size in the other array. The 'reddish tint' function would become
reddish_image = bsxfun(#times,img,cat(3,0.5,0.25,0.25));
filtered_img = sum(reddish_image,3);
All the above statement requires in order to work is that the third dimension of img has size 1 or 3. Number and size of the other dimensions can be chosen freely.
If you are consistently trying to apply a function to a vector comprised by the 3 dimension in a block of images, I recommend using a pair reshapes, for instance:
Img = rand(480,640,3);
sz = size(Img);
output = reshape(myFavoriteFunction(reshape(Img,[prod(sz(1:2)),sz(3)])'),sz);
This way you can swap in any function that operates on matrices along their first dimension.
edit.
The above code will crash if you input an image which has only one layer: The function below can fix it.
function o = nLayerImage2MatrixOfPixels(i)
%function o = nLayerImage2MatrixOfPixels(i)
s = size(i);
if(length(s) == 2)
s3 = 1;
else
s3 = s(3);
end
o = reshape(i,[s(1)*s(2),s(3)])';
Well, if you are only concerned with multiplying vectors together you could just use the dot product, like this:
bw(:,:,1)*[0.3;0.2;0.5]
taking care that the shapes of your vectors conform.