在 MATLAB 中向量化 for 循环

Question

我不太确定这是否可行，但我对 MATLAB 的理解肯定会更好。

我有一些代码希望进行矢量化，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，该例程具有多种可能的短期平均值 (STA)、长期平均值 (LTA) 和灵敏度 (OnSense) 配置可供运行。

时间采用矢量格式，FL2onSS 是主要数据（Nx1 双精度），FL2onSSSTA 是其 STA（NxSTA 双精度），FL2onSSThresh 是其阈值（NxLTAxOnSense 双精度）。

想法是计算 4D 的红色警报矩阵 - AlarmStatexSTAxLTAxOnSense 在程序的其余部分中使用。

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

我目前已经重复了一个函数，试图提高它的速度，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，所以我不会进一步解释。如果您需要说明特定线路正在做什么，请告诉我。

Answer 1

诀窍是将所有数据转化为相同的形式，主要使用repmat 和permute。那么逻辑就是简单的部分。

我需要一个令人讨厌的技巧来实现最后一部分（如果没有一个条件成立，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） - 只需看看代码:)

%// 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.