在 MATLAB 中对循环进行矢量化

Question

我不太确定这是否可能，但我对 MATLAB 的理解肯定会更好。

我有一些代码希望矢量化，因为它在我的程序中造成了相当大的瓶颈。它是优化例程的一部分，它有许多可能的短期平均 (STA)、长期平均 (LTA) 和灵敏度 (OnSense) 配置来运行。

时间是矢量格式，FL2onSS是主要数据（一个Nx1双精度），FL2onSSSTA是它的STA（NxSTA双精度），FL2onSSThresh是它的阈值（NxLTAxOnSense双精度）

这个想法是计算一个红色警报矩阵，它将是 4D - 在整个程序的其余部分中使用的 alarmStatexSTAxLTAxOnSense。

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

我目前有这个重复的功能，试图从中获得更快的速度，但显然如果整个事情可以矢量化会更好。换句话说，如果有更好的解决方案，我不需要保留该功能。

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

代码很简单，我就不多解释了。如果您需要说明特定行的作用，请告诉我。

Answer 1

诀窍是将所有数据放入同一个表单，主要使用 repmat 和 permute。那么逻辑就是简单的部分。

我需要一个讨厌的技巧来实现最后一部分（如果条件都不成立，则使用最后的结果）。通常这种逻辑是使用 cumsum 完成的。我必须使用另一个 2.^n 矩阵来确保使用定义的值（这样 +1,+1,-1 将真正给出 1,1,0） - 只需查看代码 :)

%// 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.