How to fine numerical gradient

Question

Luqman Saleem 2024-3-20

0
链接

此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/2096991-how-to-fine-numerical-gradient

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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Answer 1

Chunru 2024-3-21

1
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/2096991-how-to-fine-numerical-gradient#answer_1428536

在 MATLAB Online 中打开

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);

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Luqman Saleem 2024-3-21

@Chunru It worked. thank you

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Answer 2

VBBV 2024-3-21

0
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/2096991-how-to-fine-numerical-gradient#answer_1428546

编辑：VBBV 2024-3-21

在 MATLAB Online 中打开

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