Max and Min values within vectors in a cell matrix

Hi everyone. I'm a strong user of MATLAB Answers and I've searched a lot to find an answer to this particular question but I couldn't... I need to find max and min values within vectors that are in a cell matrix. The cell matrix is quite big Nx865x351 where N will not be bigger than 10. Each cell has a vector (1xM, with M variable from vector to vector) or it can be an empty vector (so vectors in the different cells HAVE NOT the same size). So, for each 'N' I want to find the max and min value of all the values in the vectors contained in the 865x351 subpart of the cell matrix. I managed to do it in some way (written below) but I definitevely don't like it, I think there must be a faster and better way. At the end I just want 2 vectors with the max and min values for each N position. In the code

%pos_number=N
%power_critical_all -> cell matrix Nx865x351

min_interf=zeros(1,pos_number);
max_interf=zeros(1,pos_number);

mn = cellfun(@(x) min(x(:)),power_critical_all,'UniformOutput',0);
mx = cellfun(@(x) max(x(:)),power_critical_all,'UniformOutput',0);

% here I replace empty vectors by NaNs because cell2mat doesn't work then if I don't do it
mn(cellfun(@isempty,mn))={NaN};
mx(cellfun(@isempty,mx))={NaN};

mn=cell2mat(mn);
mx=cell2mat(mx);

for i=1:pos_number
    min_interf(i)=min(mn(i,:));
    max_interf(i)=max(mx(i,:));
end

An annex to this question (not so important but if someone knows how to...): what if I have the case that each vector (not an empty one, obviously) within a cell of the cell matrix has two rows and I just want to get the min and max values from the second row?

I hope I explain myself correctly and thanks in advance for your comments!

[Jan]

CELLFUN(@isempty) is much slower than CELLFUN('isempty').

All your cell elements are vectors. Then CELLFUN(@min) is about 4 times faster than CELLFUN(@(x) min(x(:)).

Answer 1

[Andrei Bobrov]

variant

N = size(C,1);
out = zeros(N,2);
for i1 = 1:N
    p1 = [C{i1,:,:}];
    out(i1,:) = [min(p1) max(p1)];
end

[Jan]

"[C{i1,:,:}]" will work, because Juan stated: "Each cell has a vector (1xM, with M variable from vector to vector)".

Unfortunatly MATLABs HORZCAT function (called for "[...]") does not pre-allocate the output sufficiently. But the C-Mex http://www.mathworks.com/matlabcentral/fileexchange/28916-cell2vec does such that it can be twice as fast.

But HORZCAT is not the bottleneck of this method, because it needs to allocate a lot of temporary memory.

[Juan Grosso]

with the data I have now is working but I will have different data soon... do you think (with disregard of the computation time) I'll have a problem with the code provided by Andrei in some situations? The vectors in the cell matrix are not larger than 1x12 (that is M<=12 always). Thanks!

[Andrei Bobrov]

Hi Jan! Thank you very much for your helpful comment.

[Jan]

@Juan: Andrei's code is a good choice.

Some speed measurements:

Your original code: 8.75 sec

Your code with CELLFUN('isempty'): 7.87 sec

Your code with CELLFUN('isempty') and CELLFUN(@max): 3.01 sec

Andrei: 0.84 sec

Andrei with Cell2Vec C-Mex: 0.42 sec

Jan with MinMaxElem C-Mex: 0.60 sec

Interpretation: Using CELLFUN efficiently accelerates the program by a factor 3.

Although the MinMaxElem function does not need temporary memory, the data vectors with N<=12 are so tiny, that the overhead of calling a Mex is too time-consuming.

But the advantage of pre-allocation in CELL2VEC is impressive. Or to be more precise: It is disappointing, that such a basic function as MATLAB's HORZCAT is weakly implemented.

While the speedup of 8.75 to 0.84 will be important, it is questionable, if the installation of a compiler is useful to get further 0.42 seconds.

[Juan Grosso]

Excellent explanation and predisposition from you! I will take into account your solution for further developments, now I cannot use a compiler... Thanks a lot, man!

[Jan]

For 32 bit MATLAB, MacOS and Linux a compiler is always available, but not for 64-bit Windows systems. I curious if LCC64 will be bundled in the future.

[Juan Grosso]

Dear Andrei or Jan,

I'd like to add a question to this one. I'd need now to be able to get where the min/max value were found, that is in which cell of the 865x351 possible for each N.

I've been trying for a while but no luck...

I'd be grateful if you can give me an advice.

Thanks in advance!

[Amalia adiba]

Dear Andrei and Juan I have same problem, but in my case, vector is 2xM, cell = {[1:5 6:10],[10:15 16:20],[21:25 26:30]} how to find max and min value for each vector?? and the answer may be like this: max =[5 10 15 20 25 30] min=[1 6 10 16 21 26] thanks in advance and sorry for comment a new question

Answer 2

[Jan]

I'm using a C-Mex for finding the Min/Max elements in a set of arrays: FEX: MinMaxElem :

% C is a {Nx865x351} cell.
minValue = zeros(1, N);
maxValue = zeros(1, N);   % [EDITED]: was "minValue" a 2nd time
for i = 1:N
  [minValue(i), maxValue(i)] = MinMaxElem(C{i, :, :});
end

Getting Min and Max at the same time is much faster than obtaining them separately: For the sequence [1, 2, 3] the first element is the Min and the Max, for the following elements it is enough to check, if it is the new Max - if so, a check for a new Min value can be omitted!

[Juan Grosso]

Hi Jan, thank you very much. I've never used a C-Mex so I have to read a little bit in order to make it work. I tried to run the code you provide me and I got some errors.

[Jan]

Please post the error messages, such that we can give an advice.

Using a C-Mex is not hard: Install a C-compiler (I struggled just for 2 days to install MSVC2010+SDK7.1+SP1, 64 bit. Actually it is trivial, but there are bugs in the SP1 installers provided by Microsoft.), run "mex -setup", download the FEX submission, run "mex -O MinMaxElem.c". Or you can download the pre-compiled DLL from my webpage, but this works for 32 bit only at the moment.

[Juan Grosso]

The error was just because I don't have a compiler installed in this laptop (of my work place) and I cannot install anything here.

Since other persons will use the code I'm doing now, I should follow Andrei's advice which is simpler and doesn't use external files and it's way faster than my code.

Anyway thanks a lot for your help Jan!