Given an array of $A=[1,2,4, -5, -10, 34]$ and $A_{size} = 6$, how can I write mathematically the sum only of non-negative values? For example $S$ like $\sum_{i=1}^n (sign(A_i)\times A_i)$ but mathematically in formula ?
Sum of non-negative elements in array
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linear-algebra
summation
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0What about $\sum_{A_i \geq 0} A_i$? – 2017-01-03
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0Do you want the sum of the non negative values (that would be $1+2+4+34$ in your example, or the sum of the absolute values (which is what your expression - probably - gives, in your example that would be $1+2+4+5+10+34$)? – 2017-01-03
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0only non negative so 1,2,4,34 – 2017-01-03
1 Answers
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You can write it as:
$$S^-=\frac{\sum_{i=1}^n (A_i - |A_i|)}{2}$$ $$S^+=\frac{\sum_{i=1}^n (A_i + |A_i|)}{2}$$
where $S^-$ is sum of negative elements and $S^+$ is sum of all positive elements.
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0This is what I was needed, thanks. – 2017-01-03
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0Possibly clearer as $\sum_i \min(A_i,0)$ and $\sum_i \max(A_i,0)$. – 2017-01-03