## Finding Sequences of 1's values

### James (view profile)

on 21 Sep 2011
Latest activity Answered by Jos (10584)

on 18 Mar 2014

### Image Analyst (view profile)

I have a matrix of values, for example: [0 0 0 0 0 0 1 1 1 0 0 0 0 0 1 1 0 0 0 0 1 1 1 1 1 0 0 ...]

In practice this is a vector (1 row by somewhere around 80000 columns). I need to output a vector with the duration of these 'bursts' of 1's. For example, the output for the above would be: [3 2 5 ...]

Background: I have a time series where all the 1's are values above a threshold and all the 0's are values below a threshold. So by doing this I'm trying to investigate the duration of these extreme events.

Can anyone tell me how I can do this?

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### Image Analyst (view profile)

on 21 Sep 2011

If you have the Image Processing Toolbox, just call bwconncomp() or bwlabel(), then call regionprops() asking for 'Area' and then extract the areas from the structure. Three lines.

```labeledMatrix = bwlabel(data);
measurements = regionprops(labeledMatrix, 'Area');
allAreas = [measurements.Area];
```

Jan Simon

### Jan Simon (view profile)

on 22 Sep 2011

data = round(rand(1, 80000))
regionprops (Image Analyst): 0.55 sec
Vectorized FINDSTR(DIFF): 0.0081 sec
Cleaned loop (Derek + Jan): 0.0048 sec
(Measured under Matlab 2009a, WinXP, 2.3GHz Core2Duo)

### Derek O'Connor (view profile)

on 21 Sep 2011

If you don't have any toolboxes then this plain Matlab function may help. It is based loosely on the WordCount procedure in Kernighan & Plauger [1981], Software Tools in Pascal, ©Bell Labs, Addison-Wesley, page 17.

For n = 10^8 it takes about 4 secs (single core) 2.3GHz, R2008a 64bit on Windows 7.

```function [start, len, k1] = ZeroOnesCount(v)
%
% Determine the position and length of each 1-string in v,
% where v is a vector of 1s and 0s
% Derek O'Connor 21 Sep 2011
%
n = length(v);
start = zeros(1,n);            % where each 1-string starts
len = zeros(1,n);              % length of each 1-string
k1= 0;                         % count of 1-strings
inOnes = false;
for k = 1:n
if v(k) == 0               % not in 1-string
inOnes = false;
elseif ~inOnes             % start of new 1-string
inOnes = true;
k1 = k1+1;
start(k1) = k;
len(k1) = 1;
else                       % still in 1-string
len(k1) = len(k1)+1;
end
end
%-------------  ZeroOnesCount ----------------------------
```
```>> v = [0 0 0 0 0 0 1 1 1 0 0 0 0 0 1 1 0 0 0 0 1 1 1 1 1 0 0];
>> [start,len,k1] = ZeroOnesCount(v);disp([start(1:k1); len(1:k1)]);
7    15    21
3     2     5
```

Jan Simon

### Jan Simon (view profile)

on 22 Sep 2011

To get the answer needed by the OP, collecting "start" is not needed, but occupies n*8 bytes in the memory.
But the idea to create a loop is efficient. +1

### James (view profile)

on 21 Sep 2011

Thanks, that worked perfect!

### Derek O'Connor (view profile)

on 22 Sep 2011

This is a more general and simpler solution than my previous answer.

```%-------------------------------------------------------
function [start, val, len, rn] = RunsCount(v)
%
% Determine the length of each val-run in v,
% where v is a vector of 'values'
% Example 1: RunsCount([2 2 2 1 1 9 8 8 3 3 3 3]) gives
% start     1     4     6     7     9
% val       2     1     9     8     3
% len       3     2     1     2     4
% Example 2: RunsCount(['aaaabbaacccbbb']);
% start     1     5     7     9    12
% val      97    98    97    99    98
% len       4     2     2     3     3
%
% Derek O'Connor 22 Sep 2011
%
n = length(v);
val = zeros(1,n);           % run value
len = zeros(1,n);           % run length
start = zeros(1,n);         % pos. in v where run starts
start(1) = 1;
rk = 1;                     % number in run
rn = 1;                     % number of runs
for k = 2:n
if  v(k) == v(k-1)      % in run
rk = rk+1;
else                    % end of run
val(rn) = v(k-1);
len(rn) = rk;
rk = 1;             % v(k) is start of
rn = rn+1;          % next run
start(rn) = k;      % position of start in v
end
end
val(rn) = v(n);             % last run
len(rn) = n - sum(len);
%
%------------- End RunsCount ----------------------------
```

EDIT : Pre-allocated all output arrays. Changed loop counter from i to k.

Jan Simon

### Jan Simon (view profile)

on 22 Sep 2011

Without pre-allocating "val", "len" and "start", this code will be very slow for a large input due to the huge memory footprint. Therefore I'd prefer your other solution.

### Jan Simon (view profile)

on 22 Sep 2011

A modified version of Derek's solution:

```function len = CountOnes(v)
n      = length(v);
len    = zeros(1,n);         % length of each 1-string
k1     = 0;                  % count of 1-strings
inOnes = false;
s      = 0;
```
```for k = 1:n
if v(k)                    % not in 1-string
s       = s + 1;         % increase the counter
inOnes  = true;
elseif inOnes              % leave the ones block
k1      = k1 + 1;
len(k1) = s;
s       = 0;             % reset the counter
inOnes  = false;
end
end
len = len(1:k1);
```

And this is a vectorized approach:

```function len = CountOnes_vectorized(v)
v   = diff([0, x, 0]);
len = findstr(v, -1) - findstr(v, 1);
```

It looks nice, but is 45% slower than the loop method for the 80'000 elements needed by the OP.

[EDITED] New version with a nested loop:

```function len = CountOnes2(v)
n   = length(v);
len = zeros(1, ceil(n/2), 'uint32');
j   = 0;
```
```k = 1;
while k <= n
if v(k)
a = k;
k = k + 1;
while k <= n && v(k)
k = k + 1;
end
j      = j + 1;
len(j) = k - a;
end
k = k + 1;
end
len = len(1:j);
```

Leendert

### Leendert (view profile)

on 12 Mar 2014

Hi Jan,

I would like to ask you some 'dummy' questions about your function. Hope you have the time to answer them. I see the function works fine, but I can't figure out how it works! :) And I would like to rebuild it to count each run of consecutive zeros in an array.

• What does " if v(k) " and "&& v(k)" test for? I only know if structure with operators like >,<, == and so on.
• You have used a while loop. In what way is this better than a for loop?

It would be great if your could post the function with (extensive/dummy understandable) comments on what each line does.

Hope to learn from you!

Jan Simon

### Jan Simon (view profile)

on 17 Mar 2014

@Leendert: The expression "a > 0" replies a logical value TRUE or FALSE. Using "if v(k)" as expression is a shortcut for "if v(k) ~= 0".

Leendert

### Leendert (view profile)

on 18 Mar 2014

@Jan: Thanx a million now it was a piece of cake to rewrite it!

### Derek O'Connor (view profile)

on 22 Sep 2011

Jan,

I'm using the Add-an-Answer window because the comment window is hard to use for all but short, text-only replies.

I posted an older version of RunsCount (no pre-allocation) by mistake. At that time I wasn't sure how long the output arrays should be. The size varies with the input but the worst is n, so pre-allocate the output arrays of length n.

I take your point that the array start, etc., are not necessary, but I suspect this information might be needed in other applications of these counters. Anyway, to compare your modification with ZeroOnesCount and RunsCount, I stripped out all but the output array len(1,n).

RC3 is RunsCount with start and val array and their ops stripped out

ZOC2 is ZeroOnesCount with start array and its ops stripped out.

COJ is CountOnes, Jan's modification of ZOCorig

The table below are the normalized average times, averaged over 100 runs The final row gives the actual average times for n = 10^8.

`                      Normalized Average Times`
```               n        RC3       ZOCorig    ZOC2      COJ
-----------------------------------------------
10^3       1.53        3.84       1       1.16
10^4       1.26        1.49       1       1.11
10^5       1.19        1.24       1       1.15
10^6       1.15        1.25       1       1.31
10^7       1.15        1.24       1       1.32
10^8       1.14        1.26       1       1.32
-----------------------------------------------
Actual(secs)10^8       3.84        4.23       3.36    4.44```

I was surprised by this result: ZOC2 is uniformly better than COJ.

I profiled both functions with n = 10^8 and compared statement counts (timing info is ignored because it is useless for comparisons).

`                  COJ                                   ZOC2`
```         1  10 for k = 1:n                     1  11 for k = 1:n
100000000  11   if v(k)               100000000  12     if v(k) == 0
49999019   12     s       = s + 1;    50000981   13       inOnes = false;
49999019   13     inOnes  = true;     49999019   14     elseif ~inOnes
50000981   14   elseif inOnes         25002599   15       inOnes = true;
25002599   15     k1      = k1 + 1;   25002599   16       k1 = k1+1;
25002599   16     len(k1) = s;        25002599   17       len(k1) = 1;
25002599   17     s       = 0;        24996420   18     else
25002599   18     inOnes  = false;    24996420   19       len(k1) = len(k1)+1;
25002599   19   end                   24996420   20     end
100000000  20 end                     100000000  21 end```

At first glance there seems to be very little difference in the counts: if-elseif about the same, inOnes = true-false, about the same.

The only difference I can see is that COJ does about 75x10^6 ops on the counter s (lines 12,17) which are not done by ZOC2. However, ZOC2 does about 25x10^6 ops extra on len (line 19) which are not done by COJ.

Thus COJ is doing about 50x10^6 extra assignment operations. This would seem to account for the difference between the two functions.

Derek O'Connor

### Derek O'Connor (view profile)

on 23 Sep 2011

None of the functions in the timing tests above uses uint32, so your comment is not about these results but about new functions that use uint32. If you have written new functions and done timing tests then please don't be coy, let us have your results.

Indeed, given COJ and ZOC2 are designed for zeros and ones, why not use uint16, uint8, uint4, and last, but not least, UINT1 -- the bit vector?

Your second comment, unlike your first comment, is about ZOC2 ('your function'), when you ask "Does your function catch the last 1? E.g. what is the reply for [1]?" Again you are being coy. Have you found that ZOC2 does not work for this contrived example? If so tell us. Better still, tell us how to fix it.

Walter Roberson

### Walter Roberson (view profile)

on 23 Sep 2011

uint4 and uint1 are not defined by MATLAB.

Jan Simon

### Jan Simon (view profile)

on 23 Sep 2011

@Walter: I think Derek bantered me with the UINT1 because he thought, that I had changed the topic durign the process of measurement.

### Jos (10584) (view profile)

on 18 Mar 2014

Another idea, not tested for speed:

```A = [0 0 0 0 0 0 1 1 1 0 0 0 0 0 1 1 0 0 0 0 1 1 1 1 1 0 0]
```
```B = cumsum(a)
tf = B(2:end) == B(1:end-1) & A(1:end-1)==1
result = diff([0 B(tf)])
```

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