warning all the time, don't know what is wrong

Question

Xiao yang 2024-3-22

0
链接

此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/2097841-warning-all-the-time-don-t-know-what-is-wrong

评论： Dyuman Joshi 2024-3-29

在 MATLAB Online 中打开

syms m n p a x y z lambda real

g = x + y + z -a;

L = (x).^m.*(y).^n.*(z).^p - lambda.*g

L =

Lx = diff(L,x)

Lx =

Ly = diff(L,y)

Ly =

Lz = diff(L,z)

Lz =

sol = solve([Lx==0,Ly==0,Lz==0,g==0],[x y z lambda])

Warning: Unable to find explicit solution. For options, see help.

sol = struct with fields:

x: [0x1 sym] y: [0x1 sym] z: [0x1 sym] lambda: [0x1 sym]

sol.x

ans = Empty sym: 0-by-1

sol.y

ans = Empty sym: 0-by-1

sol.z

ans = Empty sym: 0-by-1

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Xiao yang 2024-3-22

I can hand solve this problem, dont know what'wrong the code

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Answer 1

Walter Roberson 2024-3-22

0
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/2097841-warning-all-the-time-don-t-know-what-is-wrong#answer_1429786

移动：Walter Roberson 2024-3-22

在 MATLAB Online 中打开

The 0^n and 0^(m-1) occur because there are not constraints on m and n, so there is the possibility that 0^0 is being generated, and 0^0 is 1 whereas 0^anything_else is 0

syms m n p a x y z lambda real

g = x + y + z -a;

L = (x).^m.*(y).^n.*(z).^p - lambda.*g;

Lx = diff(L,x);

Ly = diff(L,y);

Lz = diff(L,z);

eqns = [Lx==0,Ly==0,Lz==0,g==0];

partial_lambda = solve(eqns(1), lambda, 'returnconditions', true);

%partial_lambda.conditions

eqns2 = subs(eqns(2:end), lambda, partial_lambda.lambda);

partial_x = solve(eqns2(3), x);

eqns3 = subs(eqns2([1:2 4:end]), x, partial_x);

partial_y = solve(eqns3(1), y, 'returnconditions', true);

%partial_y.y

%partial_y.conditions

eqns4 = subs(eqns3(2:end), y, partial_y.y);

syms parameter1 parameter2 real

partial_z1 = subs(solve(eqns4(1,1), z, 'returnconditions', true), sym('x'), parameter1);

partial_z2 = subs(solve(eqns4(2,1), z, 'returnconditions', true), sym('x'), parameter2);

partial_z3 = solve(eqns4(3,1), z, 'returnconditions', true);

%partial_z3.z

%partial_z3.conditions

back_z1 = partial_z1.z;

back_y1 = subs(partial_y.y(1), z, back_z1);

back_x1 = subs(partial_x, {y, z}, {back_y1, back_z1});

back_lambda1 = subs(partial_lambda, {x, y, z}, {back_x1, back_y1, back_z1});

solution1 = [x == back_x1, y == back_y1, z == back_z1, lambda == back_lambda1.lambda]

solution1 =

back_z2 = partial_z2.z;

back_y2 = subs(partial_y.y(2), z, back_z2);

back_x2 = subs(partial_x, {y, z}, {back_y2, back_z2});

back_lambda2 = subs(partial_lambda, {x, y, z}, {back_x2, back_y2, back_z2});

solution2 = [x == back_x2, y == back_y2, z == back_z2, lambda == back_lambda2.lambda]

solution2 =

back_z3a = partial_z3.z(1);

back_y3a = subs(partial_y.y(3), z, back_z3a);

back_x3a = subs(partial_x, {y, z}, {back_y3a, back_z3a});

back_lambda3a = subs(partial_lambda, {x, y, z}, {back_x3a, back_y3a, back_z3a});

solution3a = [x == back_x3a, y == back_y3a, z == back_z3a, lambda == back_lambda3a.lambda]

solution3a =

back_z3b = partial_z3.z(2);

back_y3b = subs(partial_y.y(3), z, back_z3b);

back_x3b = subs(partial_x, {y, z}, {back_y3b, back_z3b});

back_lambda3b = subs(partial_lambda, {x, y, z}, {back_x3b, back_y3b, back_z3b});

solution3b = [x == back_x3b, y == back_y3b, z == back_z3b, lambda == back_lambda3b.lambda]

solution3b =

back_z3c = partial_z3.z(3);

back_y3c = subs(partial_y.y(3), z, back_z3c);

back_x3c = subs(partial_x, {y, z}, {back_y3c, back_z3c});

back_lambda3c = subs(partial_lambda, {x, y, z}, {back_x3c, back_y3c, back_z3c});

solution3c = [x == back_x3c, y == back_y3c, z == back_z3c, lambda == back_lambda3c.lambda]

solution3c =

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Walter Roberson 2024-3-24

在 MATLAB Online 中打开

That is one of the solutions. There are 5 solutions in total.

syms m n p a x y z lambda real

g = x + y + z -a;

L = (x).^m.*(y).^n.*(z).^p - lambda.*g;

Lx = diff(L,x);

Ly = diff(L,y);

Lz = diff(L,z);

eqns = [Lx==0,Ly==0,Lz==0,g==0];

partial_lambda = solve(eqns(1), lambda, 'returnconditions', true);

%partial_lambda.conditions

eqns2 = subs(eqns(2:end), lambda, partial_lambda.lambda);

partial_x = solve(eqns2(3), x);

eqns3 = subs(eqns2([1:2 4:end]), x, partial_x);

partial_y = solve(eqns3(1), y, 'returnconditions', true);

%partial_y.y

%partial_y.conditions

eqns4 = subs(eqns3(2:end), y, partial_y.y);

syms parameter1 parameter2 real

partial_z1 = subs(solve(eqns4(1,1), z, 'returnconditions', true), sym('x'), parameter1);

partial_z2 = subs(solve(eqns4(2,1), z, 'returnconditions', true), sym('x'), parameter2);

partial_z3 = solve(eqns4(3,1), z, 'returnconditions', true);

%partial_z3.z

%partial_z3.conditions

back_z1 = simplify(partial_z1.z);

back_y1 = simplify(subs(partial_y.y(1), z, back_z1));

back_x1 = simplify(subs(partial_x, {y, z}, {back_y1, back_z1}));

back_lambda1 = subs(partial_lambda, {x, y, z}, {back_x1, back_y1, back_z1});

solution1 = [x == back_x1, y == back_y1, z == back_z1, lambda == simplify(back_lambda1.lambda)]

solution1 =

back_z2 = simplify(partial_z2.z);

back_y2 = simplify(subs(partial_y.y(2), z, back_z2));

back_x2 = simplify(subs(partial_x, {y, z}, {back_y2, back_z2}));

back_lambda2 = subs(partial_lambda, {x, y, z}, {back_x2, back_y2, back_z2});

solution2 = [x == back_x2, y == back_y2, z == back_z2, lambda == simplify(back_lambda2.lambda)]

solution2 =

back_z3a = simplify(partial_z3.z(1));

back_y3a = simplify(subs(partial_y.y(3), z, back_z3a));

back_x3a = simplify(subs(partial_x, {y, z}, {back_y3a, back_z3a}));

back_lambda3a = subs(partial_lambda, {x, y, z}, {back_x3a, back_y3a, back_z3a});

solution3a = [x == back_x3a, y == back_y3a, z == back_z3a, lambda == simplify(back_lambda3a.lambda)]

solution3a =

back_z3b = simplify(partial_z3.z(2));

back_y3b = simplify(subs(partial_y.y(3), z, back_z3b));

back_x3b = simplify(subs(partial_x, {y, z}, {back_y3b, back_z3b}));

back_lambda3b = subs(partial_lambda, {x, y, z}, {back_x3b, back_y3b, back_z3b});

solution3b = [x == back_x3b, y == back_y3b, z == back_z3b, lambda == simplify(back_lambda3b.lambda)]

solution3b =

back_z3c = simplify(partial_z3.z(3));

back_y3c = simplify(subs(partial_y.y(3), z, back_z3c));

back_x3c = simplify(subs(partial_x, {y, z}, {back_y3c, back_z3c}));

back_lambda3c = subs(partial_lambda, {x, y, z}, {back_x3c, back_y3c, back_z3c});

solution3c = [x == back_x3c, y == back_y3c, z == back_z3c, lambda == simplify(back_lambda3c.lambda)]

solution3c =

Xiao yang 2024-3-28

thank you very much

Dyuman Joshi 2024-3-29

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