MATLAB: cumulative geometric mean

Question

I have a 2x3 matrix m = [1.1, 2.0, 0.5 ; 0.9, 1.5, 1.1];. I need to compute a cumulative geometric mean along the second dimension, i.e. the resulting matrix results must also have the same dimension (2x3). It's basically comparable to using cumprod with the extensions that I need to take the 1/n power where n is the column number.

results must look like this:

[(1.1)^(1/1), (1.1 * 2.0)^(1/2), (1.1 * 2.0 * 0.5)^(1/3) ;
 (0.9)^(1/1), (0.9 * 1.5)^(1/2), (0.9 * 1.5 * 1.1)^(1/3)]

results = cumprod(m,2) delivers the multiplication components. However, what's the most clever way in order to take the appropriate powers?

Answer 1

Use the power of bsxfun -

bsxfun(@power, cumprod(m,2), 1./(1:size(m,2)))

Sample run -

>> m
m =
    1.1000    2.0000    0.5000
    0.9000    1.5000    1.1000
>> bsxfun(@power, cumprod(m,2), 1./(1:size(m,2)))
ans =
    1.1000    1.4832    1.0323
    0.9000    1.1619    1.1409
>> [(1.1)^(1/1), (1.1 * 2.0)^(1/2), (1.1 * 2.0 * 0.5)^(1/3) ;
    (0.9)^(1/1), (0.9 * 1.5)^(1/2), (0.9 * 1.5 * 1.1)^(1/3)]
ans =
    1.1000    1.4832    1.0323
    0.9000    1.1619    1.1409

On newer MATLAB versions, with implicit-expansion, the expression would simplify to -

cumprod(m,2).^ (1./(1:size(m,2)))