how to calculate the summation of a function having two variables.

I want to calculate:

in Matlab and I have f(x,y),(for example: f(x,y) = 2y*sin(x), N =50) how can I calculate f(x) in Matlab? I need it for minimizing f(x) with fminunc command.

Answer 1

[Star Strider]

The summation is across ‘f(x,y)’, not only ‘y’, so the function must work for all values of the arguments. The only way to do this is to create both arguments as matrices, since the multiplication will only work for matrices of the same size, then sum across the ‘y’ matrix.

One approach:

N = 50;
x = linspace(0, 10*pi, 250);                            % Define ‘x’
[X,Y] = ndgrid(x, (1:N));                               % Define (x,y) As Matrices
fxy = @(x,y) sum(2*y.*sin(x),2);                        % Define ‘f(x,y)’, Sum Across Rows (‘y’)
fx = @(x) fxy(x,Y);                                     % Define ‘f(x)’ Given ‘y’

plot(X, fx(X))
grid

The summation is across the rows because that is how the ndgrid function creates the matrices, as I have defined them here.

Even if this is homework, the approach would not be obvious for someone with little experience in these sorts of MATLAB calculations.