Error in T12 (line 35) surf(X, Y, fplot) and I have no idea what I was wrong

Question

Ngo Ha Gia Bao 2022-5-17

0
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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1721435-error-in-t12-line-35-surf-x-y-fplot-and-i-have-no-idea-what-i-was-wrong

回答： KSSV 2022-5-17

clc
clear
close all
syms x y
f = @(x,y)(x.^2+y.^2+x.*y-12*log(x)-10*log(y));
fx = diff(f,x);
fy = diff(f,y);
[xc,yc] = solve(fx,fy,x,y,'real',true);
[m,n] = size([xc,yc]);
fxx = diff(fx,x);
fyy = diff(fy,y);
fxy = diff(fx,y);
D = fxx*fyy - fxy^2;
%print
for i = 1:m
 if subs(D,{x,y},{xc(i),yc(i)}) > 0
 if subs(fxx,{x,y},{xc(i),yc(i)}) > 0
 fprintf('(%f,%f,%f) is local minimum\n',xc(i),yc(i),f(xc(i),yc(i)));
 else
 fprintf('(%f,%f,%f) is local maximum\n',xc(i),yc(i),f(xc(i),yc(i)));
 end
 elseif subs(D,{x,y},{xc(1),yc(1)}) < 0
 fprintf('(%f,%f,%f) is saddle point\n',xc(i),yc(i),f(xc(i),yc(i)));
 else
 fprintf('(%f,%f,%f) is unknown\n',xc(i),yc(i),f(xc(i),yc(i)));
 end
 
end
%Sketch
xx = linspace(-1.2, 1.2, 100);
yy = linspace(-1.2, 1.2, 100);
[X,Y] = meshgrid(xx, yy);
fplot = X^2+Y^2-12*log(X)-10*log(Y)+X*Y;
figure
surf(X, Y, fplot)
hold on
for i = 1:m
 plot3(xc(i),yc(i),f(xc(i),yc(i)),'r*')
end

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Answer 1

KSSV 2022-5-17

0
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1721435-error-in-t12-line-35-surf-x-y-fplot-and-i-have-no-idea-what-i-was-wrong#answer_965785

在 MATLAB Online 中打开

clc

clear

close all

syms x y

f = @(x,y)(x.^2+y.^2+x.*y-12*log(x)-10*log(y));

fx = diff(f,x);

fy = diff(f,y);

[xc,yc] = solve(fx,fy,x,y,'real',true);

[m,n] = size([xc,yc]);

fxx = diff(fx,x);

fyy = diff(fy,y);

fxy = diff(fx,y);

D = fxx*fyy - fxy^2;

%print

for i = 1:m

if subs(D,{x,y},{xc(i),yc(i)}) > 0

if subs(fxx,{x,y},{xc(i),yc(i)}) > 0

fprintf('(%f,%f,%f) is local minimum\n',xc(i),yc(i),f(xc(i),yc(i)));

else

fprintf('(%f,%f,%f) is local maximum\n',xc(i),yc(i),f(xc(i),yc(i)));

end

elseif subs(D,{x,y},{xc(1),yc(1)}) < 0

fprintf('(%f,%f,%f) is saddle point\n',xc(i),yc(i),f(xc(i),yc(i)));

else

fprintf('(%f,%f,%f) is unknown\n',xc(i),yc(i),f(xc(i),yc(i)));

end

(-2.044027,-1.782708,-3.360401) is local minimum (3.389486,-3.238614,-15.399595) is local minimum (2.044027,1.782708,-3.360401) is local minimum (-3.389486,3.238614,-15.399595) is local minimum

%Sketch

xx = linspace(-1.2, 1.2, 100);

yy = linspace(-1.2, 1.2, 100);

[X,Y] = meshgrid(xx, yy);

Z = X.^2+Y.^2-12*log(X)-10*log(Y)+X.*Y; %<---- element by element operations

figure

surf(X, Y, abs(Z))

hold on

for i = 1:m

plot3(xc(i),yc(i),f(xc(i),yc(i)),'r*')

end

Warning: Imaginary parts of complex X, Y, and/or Z arguments ignored