I have simulated a lipid bilayer. The trajectory has about 20000 frames. Each frame contains 128 lipids where 64 lipids reside in the upper layer and the rest in the lower layer. I want to calculate an average vector representing all the head-groups of the lipid in only on the upper layer. Something like P-N vector in DPPC molecule.
My doubt is in calculating the average vector in only one frame. I can calculate the P-N vector for each lipid in upper layer from one frame. For these vectors I want to get an average vector.
How I shall go about this?
I have tried to add each component of the vectors and divide with the total number of lipids in one layer (64). Like sum up all the 64 Vx, Vy, and Vz and divide with 64. But this way misleading from what I want.
Is there any rational way to get the average vector?
I have thought about using unit vector. But I am not so sure if this would give the average vector either.
I hope to get some help to this simple conceptual question.
Many thanks in advance.
Regards
Vijay,
Average vector is simply a vector of component-wise averages, so the way you think about computing it is right. If you can elaborate on why you think this way is 'misleading' then we could discuss it in more details.
Dear Maxim,
I say misleading because, for example, if I add 5 vectors its components-wise what I shall get is the resultant vector. And when I divide the resultant vector by the number of vectors involved ( in this case 5) what I will get is still the resultant vector but smaller in term of magnitude.
Is this resultant vector equal to average vector ?
Yes, this vector is the average vector you want. However, magnitude might be not important depending on what you want to compute, e.g. angle that is formed between this 'average vector' and some axis.
Thanks for the answer. I also got some info from http://math.stackexchange.com/questions/80923/average-of-multiple-vectors.
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