How to find the previous position in an array where a value is met?

Question

Shuo Zhang 2019-8-28

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评论： darova 2019-8-28

Hi everyone,

As it is said in the title, I'd like to find the previous position(not the last position) in an array where a value is met. I have a program that works but I'm looking for improvement or optimazations of my program.

To be specific, let's suppose I have an array A=[1 0 1 0 0 0 0 1 1 1 0 0 0 0 1] and I'd like to fill in values in another array B based on values in A.

The rule is, if A(i)=1, then B(i)=1;

if A(i)=0, find the index of the previous element in A which is 1, and compute the difference between that index and current index number. If the difference is larger than 1 and no larger than 3, B(i)=2; otherwise B(i)=0;

For example, when i=5, the index of previous element in A which is 1 is 3, then 5-3=2<3, so B(5)=2; when i=7, the index of previouse element in A which is 1 is 3, then 7-3=4>3, so B(7)=0;

So in the end, I hope to have an array B=[1 0 1 0 2 2 0 1 1 1 0 2 2 0 1];

Here is what my current program looks like

A=[1 0 1 0 0 0 0 1 1 1 0 0 0 0 1];
B=NaN(length(A),1);
for i=1:length(A)
    if A(i)==1
        B(i)=1;
    else
        if i-find(B==1,1,'last')>1 && i-find(B==1,1,'last')<=3
            B(i)=2;
        else
            B(i)=0;
        end
    end
end

The program works well. However the thing is, in future calculations, the length of array A could be as large as 1.5million and there will be some other calculations with indefinite amount of elements in the inner loop. So it's really time-comsuming to execute this find command in each iteration(last time I tried, it took 8hrs to compute for 500000 data points).

I tried to break the program into two one-layer-if-statements by allocating zero value to all data that satisfies the conditon in the inner loop and start another loop through them to find for which element I should specify 2 instead of 0. However, the problem is, the command find(X,n,direction) could only find the last position of an array where a value is met. So it always returns number 15 as it is the last position where value 1 appears in array A. I'm wondering, is there any other command that finds the index of the previous position where a value is met? For example, when i=5, the command would return number 3 while when i=11:14, it would return 10?

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darova 2019-8-28

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Shouldn't B array be like that?

B=[1 0 1 0 2 3 0 1 1 1 0 2 3 0 1];

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Answer 1

Johannes Fischer 2019-8-28

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编辑：Johannes Fischer 2019-8-28

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This is an ideal playgrouond to see how you can increase speed by avoiding for loops.

% My idea is to create an array, that in each field contains the value to
% the index of the previous '1' in A. To get there, I first get the indices
% where A is 1:
A=[1 0 1 0 0 0 0 1 1 1 0 0 0 0 1];
I = 1:numel(A);
AA = I;
AA(A==0)=0;
% AA = [1 0 3 0 0 0 0 8 9 10 0 0 0 0 15];
% Now the idea is to fill the zeros in AA with the value that preceeds
% contiguous zeros to get to Last = [1 1 3 3 3 3 3 8 9 10 10 10 10 10 15];
% Im not sure this is the most efficient or easiest to understand way but
% here is the idea: use cumsum() to propagate the information of the
% previous index along the array. For that to work the array must be
% prepared such that at index 8 there is a 5 that will add up to 8 = 5+3.
% The 5 in this case also is the number of zeros +1 between the 3 and 8 in
% AA. Since the indices are linearly increasing, we can get it by taking
% diff() where AA is not equal to 0.
d = [1 diff(AA(AA~=0))];
% you did not specify what to do if A(1) is 0. My approach only works when
% A(1) is 1
% now place the values in d at the position where A is equal to 1
a = A;
a(A~=0) = d;
% and calculate the cumulative sum
Last = cumsum(a);
% To get the distance to the last '1' in A its merely
diffToLast = I-Last;
% Followed by
B = zeros(1, numel(A));
B(A==1) = 1;
B(diffToLast == 2 | diffToLast == 3) = 2;

edit: restructured added more commentary to code.

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Johannes Fischer 2019-8-28

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As I said, that case wasnt specified, but if you replace with

if A(1) == 1
    d = [1 diff(AA(AA~=0))];
else
    d = [find(A==1, 1, 'first') diff(AA(AA~=0))];
end

the results for B should be identical except for the values before the second '1' in A. For the others, the result assumes that A(-1) is 1.

darova 2019-8-28

Understood. Works fine!

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Answer 2

darova 2019-8-28

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编辑：darova 2019-8-28

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Probably Johannes's version could be faster but mine is simpler to understand

clc,clear
A = randi([0 1],10,1);
    % divide array into sections
ind = find(abs(diff(A))>0);
    % ignore first zeros
if A(1) == 0
    ind(1) = [];
end
    % if last element is zero - add index
if A(end) == 0
    ind(end+1) = length(A);
end
B = A;
for i = 1:2:length(ind)
    i1 = ind(i)+1;          % first zero in current section
    i2 = ind(i+1);          % last zero
    if i1+0 < i2            % if second zero exists
        B(i1+1) = 2;        % replace 2d zero with '2'
    end
    if i1+1 < i2            % if third zero exists
        B(i1+2) = 2;        % replace 3d zero with '2'
    end
end
[A B]

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darova 2019-8-28

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Shorter version. Same idea as Johannes: numerate zeros

clc,clear
A = randi([0 1], 1, 10);
A1 = A*0;
i1 = find(A,1,'first');     % start from first '1'
for i = i1:length(A)
    if A(i) == 0
        k = k + 1;
    else
        k = 0;
    end
    A1(i) = k;
end
B = A;
B(A1==2 | A1==3) = 2;
[A;B]'