cumsum有上限和下限？(cumsum with upper & lower limits?)

 我想找到一种矢量化的方式来计算向量的累积和，但是有上限和下限。 
 
 在我的情况下，输入只包含1和-1。 你可以在你的答案中使用这个假设。 当然，更普遍的解决方案也是受欢迎的。 
 
 例如： 
 
x     = [1 1 1 1 -1 -1 -1 -1 -1 -1];
upper = 3;
lower = 0;
s     = cumsum(x)                    %// Ordinary cumsum.
s =
     1     2     3     4     3     2     1     0    -1    -2

y     = cumsumlim(x, upper, lower)   %// Cumsum with limits.
y =
     1     2     3     3     2     1     0     0     0     0
                 ^                       ^
                 |                       |
            upper limit             lower limit
 
 当累积和达到上限（第三个元素）时，它不会再增加。 同样，当累计和达到下限（在第七元素）时，它不会再减少。 一个for循环版本会是这样的： 
 
function y = cumsumlim(x, upper, lower)

y = zeros(size(x));
y(1) = x(1);

for i = 2 : numel(x)
    y(i) = y(i-1) + x(i);
    y(i) = min(y(i), upper);
    y(i) = max(y(i), lower);
end

end
 
 你有什么想法？ 

I'd like to find a vectorized way to calculate the cumulative sums of a vector, but with upper and lower limits.
 
In my case, the input only contains 1's and -1's. You can use this assumption in your answer. Of course, a more general solution is also welcome.
 
For example:
 
x     = [1 1 1 1 -1 -1 -1 -1 -1 -1];
upper = 3;
lower = 0;
s     = cumsum(x)                    %// Ordinary cumsum.
s =
     1     2     3     4     3     2     1     0    -1    -2

y     = cumsumlim(x, upper, lower)   %// Cumsum with limits.
y =
     1     2     3     3     2     1     0     0     0     0
                 ^                       ^
                 |                       |
            upper limit             lower limit
 
When the cumulative sum reaches the upper limit (at the 3rd element), it won't increase anymore. Likewise, when the cumulative sum reaches the lower limit (at the 7th element), it won't decrease anymore. A for-loop version would be like this:
 
function y = cumsumlim(x, upper, lower)

y = zeros(size(x));
y(1) = x(1);

for i = 2 : numel(x)
    y(i) = y(i-1) + x(i);
    y(i) = min(y(i), upper);
    y(i) = max(y(i), lower);
end

end
 
Do you have any ideas?

原文：https://stackoverflow.com/questions/31848337