Vectorizing for loops in Matlab

Question

I'm not too sure if this is possible, but my understanding of Matlab could certainly be better.

I have some code I wish to vectorize as it's causing quite a bottleneck in my program. It's part of an optimisation routine which has many possible configurations of Short Term Average (STA), Long Term Average (LTA) and Sensitivity (OnSense) to run through.

Time is in vector format, FL2onSS is the main data (an Nx1 double), FL2onSSSTA is its STA (NxSTA double), FL2onSSThresh is its Threshold value (NxLTAxOnSense double)

The idea is to calculate a Red alarm matrix which will be 4D - The alarmStatexSTAxLTAxOnSense that is used throughout the rest of the program.

Red = zeros(length(FL2onSS), length(STA), length(LTA), length(OnSense), 'double');
for i=1:length(STA)
    for j=1:length(LTA)
        for k=1:length(OnSense)
            Red(:,i,j,k) = calcRedAlarm(Time, FL2onSS, FL2onSSSTA(:,i), FL2onSSThresh(:,j,k));
        end
    end
end

I've currently got this repeating a function in an attempt to get a bit more speed out of it, but obviously it will be better if the entire thing can be vectorised. In other words I do not need to keep the function if there is a better solution.

function [Red] = calcRedAlarm(Time, FL2onSS, FL2onSSSTA, FL2onSSThresh)

% Calculate Alarms
% Alarm triggers when STA > Threshold

zeroSize = length(FL2onSS);

%Precompose
Red = zeros(zeroSize, 1, 'double');

for i=2:zeroSize
    %Because of time chunks being butted up against each other, alarms can
    %go off when they shouldn't. To fix this, timeDiff has been
    %calculated to check if the last date is different to the current by 5
    %seconds. If it isn't, don't generate an alarm as there is either a
    %validity or time gap.
    timeDiff = etime(Time(i,:), Time(i-1,:));
    if FL2onSSSTA(i) > FL2onSSThresh(i) && FL2onSSThresh(i) ~= 0 && timeDiff == 5 
        %If Short Term Avg is > Threshold, Trigger
        Red(i) = 1;
    elseif FL2onSSSTA(i) < FL2onSSThresh(i) && FL2onSSThresh(i) ~= 0 && timeDiff == 5
        %If Short Term Avg is < Threshold, Turn off
        Red(i) = 0;
    else
        %Otherwise keep current state
        Red(i) = Red(i-1);
    end
end
end

The code is simple enough so I won't explain it any further, if you need elucidation on what a particular line is doing let me know.

Thanks in advance.

Answer 1

The trick is to bring all your data to the same form, using mostly repmat and permute. Then the logic is the simple part.

I needed a nasty trick to implement the last part (if none of the conditions hold, use the last results). usually that sort of logic is done using a cumsum. I had to use another matrix of 2.^n to make sure the values that are defined are used (so that +1,+1,-1 will really give 1,1,0) - just look at the code :)

%// define size variables for better readability
N = length(Time);
M = length(STA);
O = length(LTA);
P = length(OnSense);

%// transform the main data to same dimentions (3d matrices)
%// note that I flatten FL2onSSThresh to be 2D first, to make things simpler. 
%// anyway you don't use the fact that its 3D except traversing it.
FL2onSSThresh2 = reshape(FL2onSSThresh, [N, O*P]);
FL2onSSThresh3 = repmat(FL2onSSThresh2, [1, 1, M]);
FL2onSSSTA3 = permute(repmat(FL2onSSSTA, [1, 1, O*P]), [1, 3, 2]);
timeDiff = diff(datenum(Time))*24*60*60;
timeDiff3 = repmat(timeDiff, [1, O*P, M]);
%// we also remove the 1st plain from each of the matrices (the vector equiv of running i=2:zeroSize
FL2onSSThresh3 = FL2onSSThresh3(2:end, :, :);
FL2onSSSTA3 = FL2onSSSTA3(2:end, :, :);

Red3 = zeros(N-1, O*P, M, 'double');

%// now the logic in vector form
%// note the chage of && (logical operator) to & (binary operator)
Red3((FL2onSSSTA3 > FL2onSSThresh3) & (FL2onSSThresh3 ~= 0) & (timeDiff3 == 5)) = 1;
Red3((FL2onSSSTA3 < FL2onSSThresh3) & (FL2onSSThresh3 ~= 0) & (timeDiff3 == 5)) = -1;
%// now you have a matrix with +1 where alarm should start, and -1 where it should end.

%// add the 0s at the begining
Red3 = [zeros(1, O*P, M); Red3];

%// reshape back to the same shape
Red2 = reshape(Red3, [N, O, P, M]);
Red2 = permute(Red2, [1, 4, 2, 3]);

%// and now some nasty trick to convert the start/end data to 1 where alarm is on, and 0 where it is off.
Weights = 2.^repmat((1:N)', [1, M, O, P]); %// ' damn SO syntax highlighting. learn MATLAB already!
Red = (sign(cumsum(Weights.*Red2))+1)==2;

%// and we are done. 
%// print sum(Red(:)!=OldRed(:)), where OldRed is Red calculated in non vector form to test this.