Is there any way to scale histogram elements so instead of simple count get weighted sum within bins?

Let's say I have an array of values: xy=[11,12,13,14,15,11] and an array of bins xyuni=[11,12,13,14,15] and an array of intensities int=[1,1,1,1,1,0.5].

What I would like to calculate is a histogram of xy values within the bins xyuni scaled by the intensities int, so the output I would like to get is:

[1.5,1,1,1,1].

Is there a simple way of doing this? Using histc, I can get the uniform-weighted histogram and bin indices from:

[hstres,binindices] = histc(xy,xyuni)

which gives

histres=[2,1,1,1,1] binindices=[1,2,3,4,5,1]

but I can't think of an easy way to scale by intensity. In reality I have really big arrays so am hoping to avoid a loop (the simple way would be to just loop over bin indices and sum/scale by intensity within the loop to calculate the weighted histogram that way but that would take too long with my really long arrays).

Any suggestions for a vectorized solution?

[Jemima Puddleduck]

I would like to know the answer to this question too!!!

https://uk.mathworks.com/matlabcentral/answers/291105-how-to-make-histogram-with-volume-instead-of-frequency

Answer 1

[Azzi Abdelmalek]

Edit

xy=[11.1,12.3,13.2,14.2,15.5,11.8]
xyuni=[11,12,13,14,15,16] 
int=[1,1,1,1,1,0.5]
[a,b]=histc(xy,xyuni)
c=accumarray(b',int')
out=[c;zeros(numel(a)-numel(c),1)]

[Matthew Lawrence]

I might have over simplified in my example:

if xy=[11.1,12.3,13.2,14.2,15.5,11.8] and xyuni=[11,12,13,14,15,16] and intensity=[1,1,1,1,1,0.5],

I would like to get [1.5,1,1,1,1,0] as the answer, but histc gives [2,1,1,1,1,0].

My bad as my first example was way too simple.

[Azzi Abdelmalek]

Look at edited answer

[topolowa]

Hi Azzi, thanks for your coment. How would you do it if you want to bin X and Y coordinates scaled using Z values. X, Y, Z are vectors. thanks a lot!

Answer 2

[andrepiz]

you can use histweight available on MATLAB exchange.

The call would be:

[bins, counts, edges] = histweight(xy, int)

Note that it is not vectorized and bins must be uniformly spaced.

Example for random points attached.

Disclaimer: I am the author of the toolbox.