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How to fine numerical gradient

조회 수: 9 (최근 30일)
Luqman Saleem
Luqman Saleem 2024년 3월 20일
댓글: Luqman Saleem 2024년 3월 21일
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.

채택된 답변

Chunru
Chunru 2024년 3월 21일
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);

추가 답변 (1개)

VBBV
VBBV 2024년 3월 21일
편집: VBBV 2024년 3월 21일
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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