# How to fine numerical gradient

4 views (last 30 days)
Luqman Saleem on 20 Mar 2024
Commented: Luqman Saleem on 21 Mar 2024
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.

Chunru on 21 Mar 2024
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;
[Fx, Fy] = gradient(fun_values, xs, ys);
Luqman Saleem on 21 Mar 2024
@Chunru It worked. thank you

VBBV on 21 Mar 2024
Edited: VBBV on 21 Mar 2024
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;
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 on 21 Mar 2024
It worked. thank you

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