I need to partition an input vector v into smaller series of subvectors each containing the whole array of a periodic pattern given by a local sum of successive elements in the array.

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Radu Mihail 2016-2-26

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评论： Radu Mihail 2016-3-2

I need to partition an input vector v into smaller series of subvectors each containing the whole array of a periodic pattern given by a local sum of successive elements in the array. I am recording some oscillations in a biological system. The vectors that I analyze represent an array of successive timings between followed events and under some stimulation they follow a certain periodicity . The pattern has two main characteristics: 1- the oscillations are periodic according to period reflected in a constant sum of successive elements of the array that repeats itself. The period varies from one vector to another and cannot be predicted ahead. Hence it is not the same for all vectors 2- many elements in the array are iterated because the system stabilizes at a constant oscillation pattern from which we can easily see the period. However the subvector of the whole pattern is more extended starting with the very early elements whose periodicity are respected by the sum of consecutive elements even if they do not follow exactly the iteration. For example this is a typical vector

v = [14  97  38  41  22   6  27  55  55  22  33  22   6  27  22  33  55   1  35  19  22  33  22  33  22  33  22  33  22  33  55  12  18  23  67  92  12]

in this case the periodicity of oscillation is 55. Note that

22+33 = 22+6+27 = 1+35+19 = 55

I need to extract the subvector with all elements for which the sum of consecutive elements is 55 which is a

a = [22  6  27  55  55  22  33  22   6  27  22  33  55   1  35  19  22  33  22  33  22  33  22  33  22  33  55]

and the starting and ending indices of the subvector from the original vector

i=[5 31]

I have no words to thank you for any suggestion on how to tackle this!

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采纳的回答

Stephen23 2016-2-26

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https://ww2.mathworks.cn/matlabcentral/answers/270138-i-need-to-partition-an-input-vector-v-into-smaller-series-of-subvectors-each-containing-the-whole-a#answer_211303

编辑：Stephen23 2016-2-26

在 MATLAB Online 中打开

v = [14,97,38,41,22,6,27,55,55,22,33,22,6,27,22,33,55,1,35,19,22,33,22,33,22,33,22,33,22,33,55,12,18,23,67,92,12];
N = 55;
idx = v==N;
tmp = v;
for k = 2:numel(v);
    tmp = v + [0,tmp(1:end-1)];
    idy = find(tmp==N);
    idz = bsxfun(@minus,idy(:),k-1:-1:0).';
    idx(idz) = true;
end
out = v(idx);

and check the output:

% test:
a = [22,6,27,55,55,22,33,22,6,27,22,33,55,1,35,19,22,33,22,33,22,33,22,33,22,33,55]
isequal(a,out)

and get the indices:

find(idx,1,'first')
find(idx,1,'last')

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Stephen23 2016-2-29

在 MATLAB Online 中打开

@Radu Mihail: sorry, but your one hundred and twenty six line communication via my user page does not help. It includes three copies of my answer code, screeds of unformatted code, and lots of your random comments. Please understand: I am happy to help you, but you really need to consider how you present your information. What you sent me is basically unreadable without me spending two hours trying to decipher it. Please be clear and precise with what you need. 126 lines of text does not help you.

I gave you a very precise request in my last comment: three or four examples like this:

N = 7;
v = [1 7 6 7 7 2 7 6 5 7 1];
out = ??? % I need to know this too

Please make a comment giving these examples. If you also want to explain your requirements, then please be short and precise, something like this:

Return the largest group of consecutive elements meeting the requirements:

the group must contain at least 10 elements.
sequential values may add up to the periodicity.
these sequential values must be ascending in value.
etc

Also note that you have introduced a new condition which was not in your original question: that multiples of the periodicity are also required. Is there any limit to this? Are any multiples allowed? If so, then 2 is likely to be the most common periodicity.

Radu Mihail 2016-3-1

编辑：Stephen23 2016-3-1

在 MATLAB Online 中打开

Sorry Stephen. I apologize for my overzealous answer. I will give the following 3 examples of soft problems: Ex1 and Ex2 have sum of consecutive terms differ from N

Ex1

N = 14
v = [4,2,1,5,7,1,1,6,14,7,14,7,14,7,7,7,7,1,6,7,1,6,7,7,7,7,7,7,7,1,6,7,1,6,7,1,6,7]
out = [1,5,7,1,1,14,14,14,7,7,7,7,1,6,7,1,6,7,7,7,7,7,7,7,1,6,7,1,6,7,1,6,7]

The first a=[1,5,7,1,1] indices [3,7] Here 1+5+7+1+1=15,which is wrong ,then the next subvector is 14=N

Ex 2

N = 81
v = [1,17,36,6,34,6,35,6,38,12,11,14,13,43,11,14,13,31,12,11,14,56,11,14,13,14,17,23,24,17,70,11,9,61,11,9,72,3,61,6,11]
out [6,34,6,35,6,38,12,11,14,13,43,11,14,13,31,12,11,14,56,11,14,13,14,17,23,24,17,70,11,9,61,11,9,72,3,61,6,11]

The first subvector, a is good for its successive terms all equal with N = 81

a = [ 6,34,6,35,6,38,12,11,14,13,43,11,14,13,31,12,11,14,56,11,14] 
indices[4,24]

for the sum of consecutive adjacent terms equal

N=81 = 6+34+6+35 = 6+38+12+11 +14 = 13+43 +11+ 14 = 56+11+14=81

BUT, THE NEXT subvector b

b = [13,14,17,23,24,17,70,11,9,61,11,9,72,3,61,6,11]

has problems

13+14+17+23 = 67<81<13+14+17+23+24 = 91

Ex3 there are vectors that the program cannot process

N = 244
v =[2,3,15,15,117,15,15,62,2,3,15,15,117,15,15,62,2,3,15,15,117,15,15,62,2,3,15,15,102,15,15,15,62,2,3]
out Subscript indices must either be real positive integers or logicals.

Stephen23 2016-3-2

I have attached to this comment one function (named split) and one test script. I believe that the function does what you want, based on your examples.

The test script runs every example you have given me here, and compare the functions output with the expected output. They all pass :)

Radu Mihail 2016-3-2