# How to create a histogram without using the matlab function

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Ole le 28 Fév 2020
Commenté : Ole le 1 Mar 2020
How to create a histogram without using the matlab hist function.
Given scattered data x = randn(1,100); y = randn(1,100);
with coresponding phase p = randn(1,100), having phase phase = exp(1i*p);
would like to create uniform grid, add the phase for the data points that are inside each bin.
This is to create a na intensity plot or coherent sum of the scattered data.
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Guillaume le 1 Mar 2020
@Ole, can you give a formal mathematical definition of what it is you want to calculate for a bin, because as you can see we're a bit confused.
Ole le 1 Mar 2020
There is scatted data (points) in space given as vectors x, y. Let say we discretize the data and in each bin (pixel) fall a set of points {x(k), y(k)}. Each point x(k), y(k) is associated with phase exp(1i*p(k)). In each bin (n,m) I would like to sum the phases for the points that fall inside the bin {x(k), y(k)} -> sum( exp(1i*p(k)) ). So the out put is a matrix M(n,m) that is with reduced size because of the binning and the values of the matrix are M(n,m) = sum( exp(1i*p(k)) ). And would like also to have the number of points x(k), y(k) that are in n,m bin (what histogram does).

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### Réponse acceptée

Guillaume le 1 Mar 2020
As Steven said, use discretize to find the bin indices and then one of the many aggregation functions in matlab. With 3 vector inputs, I'd use the older accumarray:
%demo data and bin definitions
x = randn(1, 100);
y = randn(1, 100);
p = randn(1, 100);
phase = exp(1i*p);
xedges = [-Inf, -3:3, +Inf]; %there will be one less bin that there are edges
yedges = [-Inf, -3:3, +Inf]; %see documentation of discretize
%histogram building
destrow = discretize(y, ybins);
destcol = discretize(x, xbins);
phasehistogram = accummaray([destrow, destcol], phase, [numel(ybins), numel(xbins)] - 1);
Or you could put the vectors in a table, and call groupsummary which would do the binning and summing for you:
%demo data and bin definitions
x = randn(1, 100);
y = randn(1, 100);
p = randn(1, 100);
phase = exp(1i*p);
xedges = [-Inf, -3:3, +Inf]; %there will be one less bin that there are edges
yedges = [-Inf, -3:3, +Inf]; %see documentation of discretize
%table construction and histogram:
phasetable = table(x, y, phase);
phasehistogram = groupsummary(phasetable, {'x', 'y'}, {xedges, yedges}, 'sum', 'phase');
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Ole le 1 Mar 2020
Thank you

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### Plus de réponses (1)

Steven Lord le 28 Fév 2020
Consider using discretize to bin the data then passing that grouping information into groupsummary or splitapply.
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