Calculate mean for uneven weighting in matlab -

i want calculate mean of field of tracers in matlab, cells make field different size. example, tracer field is:

t =   1 3 5 8  2 1 4 3  2 1 9 1  20 8 3 1 

and have 2 more fields, dx , dy describe size of cells make t.

dx =  1 1 2 3  1 1 2 3  1 1 2 3  1 1 2 3 

and

dy =   3 3 3 3  3 3 3 3  2 2 2 2  1 1 1 1 

so, intuitively, dx , dy tell me bottom left hand corner of tracer field t should have smallest contribution calculate of mean of t, while top right hand corner should have greatest contribution.

i tried mean(mean(t)), overweights importance of bottom left corner of t, etc. after bit of investigation figured i'd thorough , calculate mean manually, , including weightings, using this:

t_mean_i = sum(t*dx)./sum(dx) 

and similar dy, cell width in y-direction. however, i'm not sure how implement this.

edit: here more detail question.

my grid 260*380 cells, size(dy) = size(dx) = 260-by-380. tracer field calculated dividing surface flux field, sflux sized salinity field, salt. so, size(sflux) = size(salt) = 260-by-380-by-1000, time dimension has length 1000.

i want find mean of sflux(:,:)./salt(:,:,ii) including weighting of cell width fields, dx , dy, @ each timestep ii. (i won't use for-loop this, don't worry!!)

am on right track i'm doing? or think wrong? please feel free ask clarification.

cheers!

mean , sum operate along single dimension. apply them on entire matrix, convert data column vector first using colon operator (:), example:

w = dx .* dy; sum(w(:)) 

to obtain desired mean each layer in 3-d array, like:

t = sflux ./ salt; %// tracer field w = dx .* dy;      %// weights t_mean = sum(reshape(bsxfun(@times, t, w), [], size(t, 3))) / sum(w(:)); 

this produces array t_mean elements corresponding mean values @ each time step.

explanation: bsxfun(@times, t, w) multiples each layer element-wise weights. resulting weighted 3-d array reshaped 2-d array, each column converted different column (similar colon operator), , normalized sum of weights.