Find consecutive values in a vector that are above a threshold

Hi everyone,

I have a vector of monthly values. I would now like to identify periods of months where the values exceeded my threshold for 5 months. I know I can find all the individual months with the find function but how do I add this extra condition saying, only show me their position if five months in a row exceeded the threshold?

thank you so much for any hint. Sandra

[Azzi Abdelmalek]

Can you explain with an example?

Answer 1

[Matt Kindig]

One way:

s = RandStream('mcg16807','Seed',0);
RandStream.setDefaultStream(s);  %set seed so example is reproducible
monthdata = rand(1,30);   %random data
threshold = 0.4;  %for example
aboveThreshold = (monthdata > threshold);  %where above threshold
%aboveThreshold is a logical array, where 1 when above threshold, 0, below.
%we thus want to calculate the difference between rising and falling edges
aboveThreshold = [false, aboveThreshold, false];  %pad with 0's at ends
edges = diff(aboveThreshold);
rising = find(edges==1);     %rising/falling edges
falling = find(edges==-1);  
spanWidth = falling - rising;  %width of span of 1's (above threshold)
wideEnough = spanWidth >= 5;   
startPos = rising(wideEnough);    %start of each span
endPos = falling(wideEnough)-1;   %end of each span
%all points which are in the 5-month span (i.e. between startPos and endPos).
allInSpan = cell2mat(arrayfun(@(x,y) x:1:y, startPos, endPos, 'uni', false));

EDIT: Made more robust for case where first point is above threshold as well.

[Matt Kindig]

Or, if you have the Image Processing Toolbox, you can simply do:

aboveThreshold = (monthdata > threshold);
spanLocs = bwlabel(aboveThreshold);   %identify contiguous ones
spanLength = regionprops(spanLocs, 'area');  %length of each span
spanLength = [ spanLength.Area];
goodSpans = find(SpanLength>=5);   %get only spans of 5+ points
allInSpans = find(ismember(spanLocs, goodSpans));  %indices of these spans

[Image Analyst]

I like this method (of course). And I voted for you.

[Sandra]

I have the processing toolbox. Thank you for this solution. A really neat approach!

[Peacerich]

For those of you who don't have the Image Processing Toolbox you can rewrite those parts as follows:

aboveThreshold = (monthdata > threshold);
thresholdChange = [aboveThreshold(1) diff(aboveThreshold)];
thresholdChange(thresholdChange==-1) = 0;
spanLocs = cumsum(thresholdChange);
spanLocs(~aboveThreshold) = 0;
aboveThresholdIndex = find(aboveThreshold==1);
notConsecutiveIndex = [true diff(aboveThresholdIndex) ~= 1];
sumIndex = cumsum(notConsecutiveIndex);
spanLength = histc(sumIndex, 1:sumIndex(end));
goodSpans = find(spanLength>=5);
allInSpans = find(ismember(spanLocs, goodSpans));

Answer 2

[Youssef Khmou]

hi you can find function with multiple output that show the indices :

 v=1:10;
 [r,c]=find(r>5);

c represents the indices not the values , to make it more clear :

 v=wrev(v);
 [r,c]=find(r>5);