How can I graph this Lagrange Equation?

Question

Sena 2022-10-27

0
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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1836978-how-can-i-graph-this-lagrange-equation

评论： Sena 2022-11-13

采纳的回答： Jayant Gangwar

My code works and gives results, but there is a problem with the graph, it is blank, how can I fix it?

syms x1 x2 x3 y1 y2 lambda

g = x1+x2+x3+y1+y2 - 10;

L = 12*x1-x1^2+8*x2-x2^2+18*x3-3*x3^2+24*y1-y1^2+10*y2-5*y2^2+lambda*g;

Lx1 = diff(L,x1);

Lx2 = diff(L,x2);

Lx3 = diff(L,x3);

Ly1= diff(L,y1);

Ly2= diff(L,y2);

Llambda = diff(L,lambda);

s = solve([Lx1,Lx2,Lx3,Ly1,Ly2, Llambda])

Lopt = subs(L,[x1,x2,x3,y1,y2,lambda],[s.x1,s.x2,s.x3,s.y1,s.y2,s.lambda])

%solution is over. lets make a graph.

drawingrange=[-10,10];

fig=figure;

hold on;

set(fig,'defaultLineLineWidth',5);

axis equal;

%2D graphs

fcontour(Lopt,drawingrange);

h=gplot(g,drawingrange);

fprintf('number of solutions:%i\n', size(s.lambda,1));

for i=1:size(s.lambda,1)

fprintf('x1%i, x2%i, x3%i, y1%i, y2%i, lambda%i: %f\t;%f\t;%f\t;%f\t;%f\t;%f\t',...

i,i,i,i,i,i,double(s.x1(i)),double(s.x2(i)),double(s.x3(i)),...

double(s.y1(i)),double(s.y2(i)),double(s.lambda(i)))

end

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Torsten 2022-10-27

How do you want to plot a function that depends on 5 or 6 independent variables ?

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Answer 1

Jayant Gangwar 2022-11-3

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此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1836978-how-can-i-graph-this-lagrange-equation#answer_1090403

Hi Sena,

"fcontour" function can be used to plot the contour lines of symbolic expression f(x,y), which means that it is suitable to plot a symbolic expression with no more than 2 independent variables, but you are trying to use it to plot an expression with 6 independent variables because of which it is outputting an empty graph.

To visualize your solution, it would require a 6D space which is not possible.

Please refer to this MATLAB answer for more information on how you can visualize your solution by breaking it into parts.