How to fine numerical gradient

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Luqman Saleem
Luqman Saleem 2024-3-20
评论： Luqman Saleem 2024-3-21
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.

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采纳的回答

Chunru
Chunru 2024-3-21
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);

更多回答（1 个）

VBBV
VBBV 2024-3-21
编辑：VBBV 2024-3-21
Ran in:
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

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