How to fine numerical gradient

I have a function f(x,y). Following is just a sample function explaining how I save f(x,y) value in a 2D array.

clear; clc;

xs = linspace(1,2,100);
ys = linspace(1,3,100);

fun_values = zeros(100,100);

for ix = 1:100
    x = xs(ix);
    for iy = 1:100
        y = ys(iy);
        fun_values(ix,iy) = x^2+y^2;
    end
end

I want to calculate and . I am confused what is the correct way to use gradient() function given the way how I store values in fun_values variable.

Answer 1

[Chunru]

clear; clc;
xs = linspace(1,2,100);
ys = linspace(1,3,100)';        % transpose here
fun_values = zeros(100,100);
%{
for ix = 1:100
    x = xs(ix);
    for iy = 1:100
        y = ys(iy);
        fun_values(ix,iy) = x^2+y^2;
    end
end
%}

% Try use array operation instead of loops
fun_values = xs.^2 + ys.^2;

% Gradient
[Fx, Fy] = gradient(fun_values, xs, ys);

[Luqman Saleem]

@Chunru It worked. thank you

Answer 2

[VBBV]

There is another way to find the numerical gradient for the given function

clear; clc;
xs = linspace(1,2,100);
ys = linspace(1,3,100)';        % transpose here
fun_values = zeros(100,100);

[Xs, Ys] = meshgrid(xs,ys);

% Try use array operation instead of loops
fun_values = Xs.^2 + Ys.^2;
% Gradient
[Fx, Fy] = gradient(fun_values)

Fx = 100×100

0.0203 0.0204 0.0206 0.0208 0.0210 0.0212 0.0214 0.0216 0.0218 0.0220 0.0222 0.0224 0.0227 0.0229 0.0231 0.0233 0.0235 0.0237 0.0239 0.0241 0.0243 0.0245 0.0247 0.0249 0.0251 0.0253 0.0255 0.0257 0.0259 0.0261 0.0203 0.0204 0.0206 0.0208 0.0210 0.0212 0.0214 0.0216 0.0218 0.0220 0.0222 0.0224 0.0227 0.0229 0.0231 0.0233 0.0235 0.0237 0.0239 0.0241 0.0243 0.0245 0.0247 0.0249 0.0251 0.0253 0.0255 0.0257 0.0259 0.0261 0.0203 0.0204 0.0206 0.0208 0.0210 0.0212 0.0214 0.0216 0.0218 0.0220 0.0222 0.0224 0.0227 0.0229 0.0231 0.0233 0.0235 0.0237 0.0239 0.0241 0.0243 0.0245 0.0247 0.0249 0.0251 0.0253 0.0255 0.0257 0.0259 0.0261 0.0203 0.0204 0.0206 0.0208 0.0210 0.0212 0.0214 0.0216 0.0218 0.0220 0.0222 0.0224 0.0227 0.0229 0.0231 0.0233 0.0235 0.0237 0.0239 0.0241 0.0243 0.0245 0.0247 0.0249 0.0251 0.0253 0.0255 0.0257 0.0259 0.0261 0.0203 0.0204 0.0206 0.0208 0.0210 0.0212 0.0214 0.0216 0.0218 0.0220 0.0222 0.0224 0.0227 0.0229 0.0231 0.0233 0.0235 0.0237 0.0239 0.0241 0.0243 0.0245 0.0247 0.0249 0.0251 0.0253 0.0255 0.0257 0.0259 0.0261 0.0203 0.0204 0.0206 0.0208 0.0210 0.0212 0.0214 0.0216 0.0218 0.0220 0.0222 0.0224 0.0227 0.0229 0.0231 0.0233 0.0235 0.0237 0.0239 0.0241 0.0243 0.0245 0.0247 0.0249 0.0251 0.0253 0.0255 0.0257 0.0259 0.0261 0.0203 0.0204 0.0206 0.0208 0.0210 0.0212 0.0214 0.0216 0.0218 0.0220 0.0222 0.0224 0.0227 0.0229 0.0231 0.0233 0.0235 0.0237 0.0239 0.0241 0.0243 0.0245 0.0247 0.0249 0.0251 0.0253 0.0255 0.0257 0.0259 0.0261 0.0203 0.0204 0.0206 0.0208 0.0210 0.0212 0.0214 0.0216 0.0218 0.0220 0.0222 0.0224 0.0227 0.0229 0.0231 0.0233 0.0235 0.0237 0.0239 0.0241 0.0243 0.0245 0.0247 0.0249 0.0251 0.0253 0.0255 0.0257 0.0259 0.0261 0.0203 0.0204 0.0206 0.0208 0.0210 0.0212 0.0214 0.0216 0.0218 0.0220 0.0222 0.0224 0.0227 0.0229 0.0231 0.0233 0.0235 0.0237 0.0239 0.0241 0.0243 0.0245 0.0247 0.0249 0.0251 0.0253 0.0255 0.0257 0.0259 0.0261 0.0203 0.0204 0.0206 0.0208 0.0210 0.0212 0.0214 0.0216 0.0218 0.0220 0.0222 0.0224 0.0227 0.0229 0.0231 0.0233 0.0235 0.0237 0.0239 0.0241 0.0243 0.0245 0.0247 0.0249 0.0251 0.0253 0.0255 0.0257 0.0259 0.0261

Fy = 100×100

0.0408 0.0408 0.0408 0.0408 0.0408 0.0408 0.0408 0.0408 0.0408 0.0408 0.0408 0.0408 0.0408 0.0408 0.0408 0.0408 0.0408 0.0408 0.0408 0.0408 0.0408 0.0408 0.0408 0.0408 0.0408 0.0408 0.0408 0.0408 0.0408 0.0408 0.0412 0.0412 0.0412 0.0412 0.0412 0.0412 0.0412 0.0412 0.0412 0.0412 0.0412 0.0412 0.0412 0.0412 0.0412 0.0412 0.0412 0.0412 0.0412 0.0412 0.0412 0.0412 0.0412 0.0412 0.0412 0.0412 0.0412 0.0412 0.0412 0.0412 0.0420 0.0420 0.0420 0.0420 0.0420 0.0420 0.0420 0.0420 0.0420 0.0420 0.0420 0.0420 0.0420 0.0420 0.0420 0.0420 0.0420 0.0420 0.0420 0.0420 0.0420 0.0420 0.0420 0.0420 0.0420 0.0420 0.0420 0.0420 0.0420 0.0420 0.0429 0.0429 0.0429 0.0429 0.0429 0.0429 0.0429 0.0429 0.0429 0.0429 0.0429 0.0429 0.0429 0.0429 0.0429 0.0429 0.0429 0.0429 0.0429 0.0429 0.0429 0.0429 0.0429 0.0429 0.0429 0.0429 0.0429 0.0429 0.0429 0.0429 0.0437 0.0437 0.0437 0.0437 0.0437 0.0437 0.0437 0.0437 0.0437 0.0437 0.0437 0.0437 0.0437 0.0437 0.0437 0.0437 0.0437 0.0437 0.0437 0.0437 0.0437 0.0437 0.0437 0.0437 0.0437 0.0437 0.0437 0.0437 0.0437 0.0437 0.0445 0.0445 0.0445 0.0445 0.0445 0.0445 0.0445 0.0445 0.0445 0.0445 0.0445 0.0445 0.0445 0.0445 0.0445 0.0445 0.0445 0.0445 0.0445 0.0445 0.0445 0.0445 0.0445 0.0445 0.0445 0.0445 0.0445 0.0445 0.0445 0.0445 0.0453 0.0453 0.0453 0.0453 0.0453 0.0453 0.0453 0.0453 0.0453 0.0453 0.0453 0.0453 0.0453 0.0453 0.0453 0.0453 0.0453 0.0453 0.0453 0.0453 0.0453 0.0453 0.0453 0.0453 0.0453 0.0453 0.0453 0.0453 0.0453 0.0453 0.0461 0.0461 0.0461 0.0461 0.0461 0.0461 0.0461 0.0461 0.0461 0.0461 0.0461 0.0461 0.0461 0.0461 0.0461 0.0461 0.0461 0.0461 0.0461 0.0461 0.0461 0.0461 0.0461 0.0461 0.0461 0.0461 0.0461 0.0461 0.0461 0.0461 0.0469 0.0469 0.0469 0.0469 0.0469 0.0469 0.0469 0.0469 0.0469 0.0469 0.0469 0.0469 0.0469 0.0469 0.0469 0.0469 0.0469 0.0469 0.0469 0.0469 0.0469 0.0469 0.0469 0.0469 0.0469 0.0469 0.0469 0.0469 0.0469 0.0469 0.0478 0.0478 0.0478 0.0478 0.0478 0.0478 0.0478 0.0478 0.0478 0.0478 0.0478 0.0478 0.0478 0.0478 0.0478 0.0478 0.0478 0.0478 0.0478 0.0478 0.0478 0.0478 0.0478 0.0478 0.0478 0.0478 0.0478 0.0478 0.0478 0.0478

[Luqman Saleem]

It worked. thank you