将矢量值加起来直到阈值，然后重新开始

Question

我有一个向量 a = [1 3 4 2 1 5 6 3 2]。现在我想用 a 的 cumsum 创建一个新向量 'b'，但是在达到阈值后，比方说 5，cumsum 应该重置并重新开始，直到达到阈值，所以新向量应该是这样的：

b = [1 4 4 2 3 5 6 3 5]

有什么想法吗？

Answer 1

计算累计和并替换符合您条件的索引值。

 a = [1 3 4 2 1 5 6 3 2] ;

 b = [1 4 4 2 3 5 6 3 5] ;

 iwant = a ;
 a_sum = cumsum(a) ;
 iwant(a_sum<5) = a_sum(a_sum<5) ;

Answer 2

一种方法是使用循环。您创建第一个累积和 cs，然后只要 cs 中的元素大于您的阈值 th，您就用其余元素上的累积和中的元素替换它们在 a.

因为 a 中的一些元素可能比 th 大，除非我们也消除这些元素，否则这个循环将是无限的。

这是一个带有 while 循环的简单解决方案：

a = [1 3 4 2 1 5 6 3 2];
th = 5;
cs = cumsum(a);
while any(cs>th & cs~=a) % if 'cs' has values larger that 'th',
                       % and there are any values smaller than th left in 'a'
    % sum all the values in 'a' that are after 'cs' reached 'th',
    % excluding values that are larger then 'th'
    cs(cs>th & cs~=a) = cumsum(a(cs>th & cs~=a));
end

Answer 3

通过规范化 cumsum with the threshold and flooring you can get grouping indizes for accumarray 的参数，然后可以cumsumming groupwise:

t = 5;
a = [1 3 4 2 1 5 6 3 2];

%// cumulative sum of normalized vector a 
n = cumsum(a/t);
%// subs for accumarray
subs = floor( n ) + 1;
%// cumsum of every group
aout = accumarray( subs(:), (1:numel(subs)).', [], @(x) {cumsum(a(x))});
%// gather results;
b = [aout{:}]

Answer 4

您可以构建一个稀疏矩阵，当它乘以原始向量时，returns 就是累积和。我没有将此解决方案与其他解决方案进行计时，但我强烈怀疑这将是大型 a 数组中最快的。

% Original data
a = [1 3 4 2 1 5 6 3 2];
% Threshold
th = 5;
% Cumulative sum corrected by threshold
b = cumsum(a)/th;
% Group indices to be summed by checking for equality,
% rounded down, between each cumsum value and its next value. We add one to
% prevent NaNs from occuring in the next step. 
c = cumsum(floor(b) ~= floor([0,b(1:end-1)]))+1;
% Build the sparse matrix, remove all values that are in the upper
% triangle.
S = tril(sparse(c.'./c == 1));
% In case you use matlab 2016a or older:
% S = tril(sparse(bsxfun(@rdivide,c.',c) == 1));
% Matrix multiplication to create o.
o = S*a.';

将矢量值加起来直到阈值，然后重新开始

Sum up vector values till threshold, then start again

arrays

matlab

cumsum