Nested foreach in NetLogo - netlogo

Question

I am trying to calculate the Gini coefficient of a set of numbers. The Gini coefficient is half the mean absolute difference. That is, for every possible pair of numbers in the list, I need to take their absolute difference and add these differences together (and some other stuff). This is my code
to-report calc-Gini [list-Values]
let sumdiff 0
foreach list-Values
[ foreach list-Values
[ set sumdiff sumdiff + abs ( ?1 - ?2 )
]
]
report 0.5 * sumdiff / (mean list-Values * (length list-Values) ^ 2)
end
When I test it (eg show calc-Gini (list 1 2 3)) I get an error "task expected 2 inputs, but only got 1" on the second foreach.
I think the problem is that NetLogo wants to run through the foreach loops simultaneously. So if the list length is N, then it creates only N pairs (that is, first item in list1 and first item in list2, then the second item in each list etc) which is where the requirement for equal length lists comes from. But I need it to work with the N^2 pairs obtained by crossing the lists.
How can I make the nested foreach do what I want and/or is some other primitive more appropriate?

Answer 1

NetLogo doesn't have a mechanism for binding ?1 and ?2 to an outer and an inner task. When it sees ?1 and ?2 in your code, it expects that both inputs will come from the inner task. And since the inner foreach only provides one input, NetLogo complains.
You can get around that problem by simply assigning the input of the outer foreach to a local variable:
to-report calc-Gini [list-Values]
let sumdiff 0
foreach list-Values
[ let v ?
foreach list-Values
[ set sumdiff sumdiff + abs ( v - ? )
]
]
report 0.5 * sumdiff / (mean list-Values * (length list-Values) ^ 2)
end
That being said, here is an alternative implementation:
to-report calc-gini [ xs ]
report 0.5 * sum map [ sum-diff ? xs ] xs / (mean xs * (length xs) ^ 2)
end
to-report sum-diff [ x xs ]
report sum map [ abs (x - ?) ] xs
end

Answer 2

I can't solve your nested foreach approach, but this might be an alternative way to do your calculation:
If you use ordered data, you can use this equation for the Gini coefficient (given a vector $y$ with $y_i$, $i=1,...,n$)
$$ G(y) = \frac{1}{n} (n + 1 - 2 * \frac{ \sum_{i=1}^{n} (n + 1 - i) y_{i} }{ \sum_{i=1}^{n} y_i} $$
and the following reporter should deliver the result in NetLogo:
to-report calc-Gini [list-Values]
let values sort list-Values ; making sure values are in a non-decreasing order
let n length values
let i 1
let numerator []
foreach values
[ set numerator lput ( (n + 1 - i) * ? ) numerator
set i i + 1
]
report 1 / n * ( n + 1 - 2 * (sum(numerator) / sum(values)) )
end