# How to sum a series of functions generated from data

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Jonathan Davidson on 25 Apr 2019
Answered: Mark Sherstan on 25 Apr 2019
I have some 2D XRD data in array form(details don't matter).
Essentially I have a list of peak intensities, and miller indices h,k
I wish to plot the paterson function which in this case is Where u and v are coordinates on the unit mesh.
Converting u,v to x,y and plotting them is straightforward. But I can't seem to get a handle on how to do the summation.
My initial attempt was to define a Paterson function for each individual reflection in my dataset, and then sum them together.
However it seems Matlab isn't happy having u and v defined in the way I have done.
clear all
%define unit mesh
a = 20.46;
b = 9.99;
gamma = 34.12;
%create array
x = [-2*a:1:2*a];
y = [-2*a:1:2*a];
%define u and v
u = x - y*cot(gamma*pi/180);
v = y*csc(gamma*pi/180);
%import data and create Paterson for each reflection
for N =1 : size(data,1);
peakn = data(N,1);
F = data(N,2);
h = data(N,3);
k = data(N,4);
Paterson(N,u,v) = F^2*cos(2*pi*(h*u+k*v));
end

Mark Sherstan on 25 Apr 2019
The variable Paterson requires intergers as indices not doubles hence the error. Consider changing that last section as follows:
%import data and create Paterson for each reflection
for N =1 : size(data,1);
peakn = data(N,1);
F = data(N,2);
h = data(N,3);
k = data(N,4);
Paterson(N,:) = [u v F^2*cos(2*pi*(h*u+k*v))];
end