Am I doing this right? (a Math formula to Matlab language)

I needed to calculate this formula:

So I wrote a function in order to do that:

(P is x and P^ is y):

function NS = nash_sat(x, y)
% This function calculates Nash-Sutcliffe efficiency coefficient
%   Detailed explanation goes here
A = sum (x-y).^2;
B = sum (x-(mean(x)).^2;
fraction = (A/B);
NS = 1-fraction;
end

This is the first time I type a math formula in Matlab. I want to know if I typed the formula in the function correctly or not.

Thank you so much.

Answer 1

[James Tursa]

You are on the right track, but have typos in the code due to parentheses issues.

A = sum( (x - y).^2 );
B = sum( (x - mean(x)).^2 );

[BN]

Thank you so much

Answer 2

[Giuseppe Inghilterra]

Hi,

A and B terms are wrong.

What you wrote is the square of sum of differences. Instead formula is the sum of square of differences.

The code should be written as follow:

A = sum((x-y).^2);
B = sum((x-(mean(x))).^2); 
fraction = (A/B);
NS = 1-fraction;

Pay attention also to space left between "sum" and "(x-y)" in your code: it is not correct.

Answer 3

[akca -]

function NS = nash_sat1(x, y)
% This function calculates Nash-Sutcliffe efficiency coefficient
%   Detailed explanation goes here
A = sum((minus(x,y)).^2);
B = sum((minus(x,(mean(x))).^2));
fraction = (A./B);  %Element-Wise
NS = 1-fraction;
end