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Created page with 'Hi, I guess limiting is only useful when there's enough room for all groups. Eg.: the calculation makes sense only if: <code>(1) ∀ i: Li >= Gi</code> Otherwise, the gro…'
Hi,
I guess limiting is only useful when there's enough room for all groups. Eg.: the calculation makes sense only if:
<code>(1) ∀ i: Li >= Gi</code>
Otherwise, the group limit is to strict.Obviously it's required that:
<code>(2) ∑ Gi <= R </code>
, and the above condition is enough:
<code>(3) L1 = (1/N-1) * ((R-G2)+(R-G3)+...+(R-Gn) - (N-2)*(R-G1)) > G1 </code>
⇔
<code>(4) ((R-G2)+(R-G3)+...+(R-Gn) - (N-2)*(R-G1)) > (N-1)*G1</code>
⇔
<code>(5) (N-1)*R-(G2+G3+...+Gn)-(N-2)*R+(N-2)*G1 > (N-1)*G1</code>
⇔
<code>(6) R - (G2+G3+...+Gn) + (N-2)*G1 > (N-1)*G1</code>
⇔
<code>(7) R > G2+G3+...+Gn+G1</code>
Thus limiting is only useful if the trivial condition under (2) holds.
Cheers,
Gyula
I guess limiting is only useful when there's enough room for all groups. Eg.: the calculation makes sense only if:
<code>(1) ∀ i: Li >= Gi</code>
Otherwise, the group limit is to strict.Obviously it's required that:
<code>(2) ∑ Gi <= R </code>
, and the above condition is enough:
<code>(3) L1 = (1/N-1) * ((R-G2)+(R-G3)+...+(R-Gn) - (N-2)*(R-G1)) > G1 </code>
⇔
<code>(4) ((R-G2)+(R-G3)+...+(R-Gn) - (N-2)*(R-G1)) > (N-1)*G1</code>
⇔
<code>(5) (N-1)*R-(G2+G3+...+Gn)-(N-2)*R+(N-2)*G1 > (N-1)*G1</code>
⇔
<code>(6) R - (G2+G3+...+Gn) + (N-2)*G1 > (N-1)*G1</code>
⇔
<code>(7) R > G2+G3+...+Gn+G1</code>
Thus limiting is only useful if the trivial condition under (2) holds.
Cheers,
Gyula