histogram of signals gaps width (Matlab) - matlab

Question

I am looking for algorithm (effective + vectorized) how to find histogram of gaps (NaN) width in the following manner:
signals are represented by (Nsamples x Nsig) array
gaps in signal are encoded by NaN's
width of gaps: is number of consecutive NaN's in the signal
gaps width histogram: is frequency of gaps with specific widths in signals
And the following conditions are fullfilled:
[Nsamples,Nsig ]= size(signals)
isequal(size(signals),size(gapwidthhist)) % true
isequal(sum(gapwidthhist.*(1:Nsamples)',1),sum(isnan(signals),1)) % true
Of course, compressed form of gapwidthhist (represented by two cells: "gapwidthhist_compressed_widths" and "gapwidthhist_compressed_freqs") is required too.
Example:
signals = [1.1 NaN NaN NaN -1.4 NaN 8.3 NaN NaN NaN NaN 1.5 NaN NaN; % signal No. 1
NaN 2.2 NaN 4.9 NaN 8.2 NaN NaN NaN NaN NaN 2.4 NaN NaN]' % signal No. 2
gapwidthhist = [1 1 1 1 0 0 0 0 0 0 0 0 0 0; % gap histogram for signal No. 1
3 1 0 0 1 0 0 0 0 0 0 0 0 0]' % gap histogram for signal No. 2
where integer histogram bins (gap widths) are 1:Nsamples (Nsamples=14).
Coresponding compressed gap histogram looks like:
gapwidthhist_compressed_widths = cell(1,Nsig)
gapwidthhist_compressed_widths =
1×2 cell array
{[1 2 3 4]} {[1 2 5]}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
gapwidthhist_compressed_freqs = cell(1, Nsig)
gapwidthhist_compressed_freqs =
1×2 cell array
{[1 1 1 1]} {[3 1 1]}
Typical problem dimension:
Nsamples = 1e5 - 1e6
Nsig = 1e2 - 1e3.
Thanks in advance for any help.
Added remark: My so far best solution is the following code:
signals = [1.1 NaN NaN NaN -1.4 NaN 8.3 NaN NaN NaN NaN 1.5 NaN NaN; % signal No. 1
NaN 2.2 NaN 4.9 NaN 8.2 NaN NaN NaN NaN NaN 2.4 NaN NaN; % signal No. 2
1 NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN]' % signal No. 3
[numData, numSignals] = size(signals)
gapwidthhist = zeros(numData, numSignals);
for column = 1 : numSignals
thisSignal = signals(:, column); % Extract this column.
% Find lengths of all NAN runs
props = regionprops(isnan(thisSignal), 'Area');
allLengths = [props.Area]
edges = [1:max(allLengths), inf]
hc = histcounts(allLengths, edges)
% Load up gapwidthhist
for k2 = 1 : length(hc)
gapwidthhist(k2, column) = hc(k2);
end
end
% What it is:
gapwidthhist'
But I am looking mainly for pure Matlab code without any built-in matlab functions (like "regionprops" from Image Processing Toolbox)!!!

Answer 1

This is much more simple Matlab implementation but still not optimal (+ not vectorized):
signals = [1.1 NaN NaN NaN -1.4 NaN 8.3 NaN NaN NaN NaN 1.5 NaN NaN; % signal No. 1
NaN 2.2 NaN 4.9 NaN 8.2 NaN NaN NaN NaN NaN 2.4 NaN NaN; % signal No. 2
1 NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN]'; % signal No. 3
signals
[numData, numSignals] = size(signals);
gapwidthhist = zeros(numData, numSignals);
gaps = zeros(numData+1,numSignals);
auxnan = isnan(signals);
for i = 1:numSignals
c = 0;
for j = 1:numData
if auxnan(j,i)
c = c + 1;
else
gaps(j,i) = c;
c = 0;
end
end
gaps(numData+1,i) = c;
gapwidthhist(:,i) = histcounts(gaps(:,i),1:numData+1);
end
gapwidthhist
Thanks to #breaker for help.
Any idea how to optimize (vectorize) this code to be more effective?

Answer 2

Here is a slightly more vectorized version that may be a bit quicker. I use Octave, so I don't know how much MATLAB's JIT compiler will optimize the inner loop in the other approach.
% Set up the data
signals = [1.1 NaN NaN NaN -1.4 NaN 8.3 NaN NaN NaN NaN 1.5 NaN NaN; % signal No. 1
NaN 2.2 NaN 4.9 NaN 8.2 NaN NaN NaN NaN NaN 2.4 NaN NaN; % signal No. 2
1 NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN]'; % signal No. 3
signals
[numData, numSignals] = size(signals);
gapwidthhist = zeros(numData, numSignals);
gaps = zeros(numData+1,numSignals);
auxnan = ~isnan(signals); % We want non-NaN values to be 1
for i = 1:numSignals
difflist = diff(find([1; auxnan(:,i); 1])) - 1; % get the gap lengths
gapList = difflist(find(difflist)); % keep only the non-zero gaps
for c = gapList.' % need row vector to loop over elements
gapwidthhist(c,i) = gapwidthhist(c,i) + 1; % each gap length increments the histogram
end
end
gapwidthhist
Here's the program flow:
First, negate the auxnan array so that NaN is 0 and non-NaN is 1.
In the outer loop, pad each column with 1's on top and bottom to capture strings of NaN at the beginning and end of the signal.
Use find to get the indices of the 1 (non-NaN) elements.
Take the diff of the indices.
A diff of 1 means no gap and a diff greater than 1 gives the length of the gap plus 1, so subtract 1 from the diff result.
Use the results (indices) of find to get the values of the nonzero elements. These are the gap widths.
Now loop through the values and accumulate the results in the histogram. You might try replacing this inner loop with accumarray to see if that speeds things up any.

Answer 3

May be final solution:
signals = [1.1 NaN NaN NaN -1.4 NaN 8.3 NaN NaN NaN NaN 1.5 NaN NaN; % signal No. 1
NaN 2.2 NaN 4.9 NaN 8.2 NaN NaN NaN NaN NaN 2.4 NaN NaN; % signal No. 2
1 NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN]'; % signal No. 3
signals
[numData, numSignals] = size(signals);
gapwidthhist = zeros(numData, numSignals);
auxnan = isnan(signals);
for i = 1:numSignals
c = 0;
for j = 1:numData
if auxnan(j,i)
c = c + 1;
else
if c > 0
gapwidthhist(c,i) = gapwidthhist(c,i) + 1;
c = 0;
end
end
end
if c > 0
gapwidthhist(c,i) = gapwidthhist(c,i) + 1;
end
end
gapwidthhist
Open question: how to modify the code where outer for-loop should be able to use parfor-loop?