This is relatively straightforward with the bsxfun function. Here, there are two calls to it, one for the altitude and one for the wind velocities. Each creates a matrix of its arguments, so that the structure of ‘u_ratios’ for example is:
u(1)/u(1) u(2)/u(1) ...
u(1)/u(2) u(2)/u(2)
u(1)/u(3) u(2)/u(3)
: .
: .
with the corresponding structure for ‘h_ratios’. The ‘alpha’ calculation then dies element-wise division of these the log of each matrix, producing the output. Note: the diagonals of ‘alpha’ are NaN because they are the results of log(1)/log(1) = 0/0 = NaN. So you may want to eliminate the NaN values on the main diagonal of ‘alpha_mtx_nan’. I did this by creating ‘alpha_mtx’ with -1 on the main diagnonal instead. The NaN values will cause problems with the calculations, so use either matrix. I opted not to ‘collapse’ the matrix by eliminating the main diagonal.
The Code:
u = sort(randi(25, 1, 11), 'descend'); % Create Wind Velocities (m/s)
h = [200 150 100 80 60 50 40 30 38 20 10]; % Altitude (m)
u_ratios = bsxfun(@rdivide, u, u'); % Divide ‘Rows’ Of ‘u’ By Columns Of ‘u'’
h_ratios = bsxfun(@rdivide, h, h'); % Divide ‘Rows’ Of ‘h’ By Columns Of ‘h'’
alpha_mtx_nan = log(u_ratios) ./ log(h_ratios);
alpha_mtx = triu(alpha_mtx_nan,1) + tril(alpha_mtx_nan,-1) + diag(-ones(1,size(alpha_mtx_nan,1),1));
