Find numerical gradient of a function

function [y] = sumsqu(xx)

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% SUM SQUARES FUNCTION
%
% INPUT:
%
% xx = [x1, x2, ..., xd]
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

d = length(xx);
sum = 0;
for ii = 1:d
  xi = xx(ii);
  sum = sum + ii*xi^2;
end

y = sum;

end

Above is the code for d variables. Whenever I call the function I get the sum as expected. Now I want to find the numerical gradient of the function. But since the function is returning a scalar value, gradient is returning 0 obviously. What can I do so that gradient first evaluates in its variable form then return an array corresponding to x1 x2 x3....xd?

As you can see in the picture, I want it in that order. And I also want d as a variable so that code can be generic. Hope you understood my problem. Thank you

Answer 1

[Star Strider]

If I understand correctly what you want to do, this is one approach:

xx = randi(9,1,3)                               % Create ‘x’ Argument
cfs = (1:numel(xx))                             % Coefficient Vector
f = (xx.^2).*cfs                                % Calculate ‘f’
delf = xx .* (cfs*2)                            % Calculate Gradient
fsum = sum(f)                                   % Calculate Sum Of ‘f’

Please do not name your variable ‘sum’. This is the name of an important built-in function, and ‘overshadowing’ it with a function name will cause you significan problems if you then want to use the function later in your code.

[Tusar Jit Medhi]

Ok, I don't know how to ask this.

So this is the function. I want to find the gradient of the function for any value of d. So how do I implement this as a function file? Thank you. i will vary from 1 to d.

[Star Strider]

One possibility:

function [fsum,delf] = sumsq(xx)
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% SUM SQUARES FUNCTION
%
% INPUT:
%
% xx = [x1, x2, ..., xd]
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

cfs = (1:numel(xx))                             % Coefficient Vector
f = (xx.^2).*cfs                                % Calculate ‘f’
delf = xx .* (cfs*2)                            % Calculate Gradient
fsum = sum(f)                                   % Calculate Sum Of ‘f’
end

I simply wrapped my code in the function code you used.