Solving a function handle using solve or fsolve. How do I avoid error like 'Undefined function or variable' ?

Hello, I am trying to solve composite pulse problem using function handle and get the values of phi_0,phi_1,phi_2,phi_3,phi_4 and O by solving six equations after differentiation.

phi_5= 0;

a = @(O)cos(O/2);
b = @(O)-1i*sin(O/2);
ai = @(O)a(O);
bi = @(O)-b(O);
U0 = @(O,phi_0)[a(O),b(O)*exp(-1i*phi_0); -bi(O)*exp(1i*phi_0),ai(O)];
U1 = @(O,phi_1)[a(O),b(O)*exp(-1i*phi_1); -bi(O)*exp(1i*phi_1),ai(O)];
U2 = @(O,phi_2)[a(O),b(O)*exp(-1i*phi_2); -bi(O)*exp(1i*phi_2),ai(O)];
U3 = @(O,phi_3)[a(O),b(O)*exp(-1i*phi_3); -bi(O)*exp(1i*phi_3),ai(O)];
U4 = @(O,phi_4)[a(O),b(O)*exp(-1i*phi_4); -bi(O)*exp(1i*phi_4),ai(O)];
U5 = @(O)[a(O),b(O)*exp(-1i*phi_5); -bi(O)*exp(1i*phi_5),ai(O)];

U = @(phi_0,phi_1,phi_2,phi_3,phi_4,O)U5(O)*U4(O,phi_4)*U3(O,phi_3)*U2(O,phi_2)*U1(O,phi_1)*U0(O,phi_0);

U_11 = @(phi_0,phi_1,phi_2,phi_3,phi_4,O)U(1,1); 
U21 = @(phi_0,phi_1,phi_2,phi_3,phi_4,O)U(2,1);

U11 = inline('U_11','phi_0','phi_1','phi_2','phi_3','phi_4','O');
%u11 = symfun(U11,[O,phi_0,phi_1,phi_2]);
%u21 = symfun(U21,[O,phi_0,phi_1,phi_2]);
dU11_1 = @(phi_0,phi_1,phi_2,phi_3,phi_4,O)diff(sym(U11),O,1);
dU11_2 = @(phi_0,phi_1,phi_2,phi_3,phi_4,O)diff(sym(U11),O,2);
dU11_3 = @(phi_0,phi_1,phi_2,phi_3,phi_4,O)diff(sym(U11),O,3);
dU11_4 = @(phi_0,phi_1,phi_2,phi_3,phi_4,O)diff(sym(U11),O,4);
dU11_5 = @(phi_0,phi_1,phi_2,phi_3,phi_4,O)diff(sym(U11),O,5);
dU11_6 = @(phi_0,phi_1,phi_2,phi_3,phi_4,O)diff(sym(U11),O,6);
dU11_7 = @(phi_0,phi_1,phi_2,phi_3,phi_4,O)diff(sym(U11),O,7);
dU11_8 = @(phi_0,phi_1,phi_2,phi_3,phi_4,O)diff(sym(U11),O,8);
dU11_9 = @(phi_0,phi_1,phi_2,phi_3,phi_4,O)diff(sym(U11),O,9);

U_eqn1 = @(phi_0,phi_1,phi_2,phi_3,phi_4,O)dU11_1;
U_eqn2 = @(phi_0,phi_1,phi_2,phi_3,phi_4,O)dU11_2;
U_eqn3 = @(phi_0,phi_1,phi_2,phi_3,phi_4,O)dU11_3;
U_eqn4 = @(phi_0,phi_1,phi_2,phi_3,phi_4,O)dU11_4;
U_eqn5 = @(phi_0,phi_1,phi_2,phi_3,phi_4,O)dU11_5;
U_eqn6 = @(phi_0,phi_1,phi_2,phi_3,phi_4,O)dU11_6;
U_eqn7 = @(phi_0,phi_1,phi_2,phi_3,phi_4,O)dU11_7;
U_eqn8 = @(phi_0,phi_1,phi_2,phi_3,phi_4,O)dU11_8;
U_eqn9 = @(phi_0,phi_1,phi_2,phi_3,phi_4,O)dU11_9;

U_eqn0 = @(phi_0,phi_1,phi_2,phi_3,phi_4,O)U_11;

%Phase 
[O1,phiA,phiB,phiC,phiD,phiE] = solve(U_eqn1(phi_0,phi_1,phi_2,phi_3,phi_4,O),U_eqn3(phi_0,phi_1,phi_2,phi_3,phi_4,O),U_eqn5(phi_0,phi_1,phi_2,phi_3,phi_4,O),U_eqn7(phi_0,phi_1,phi_2,phi_3,phi_4,O),U_eqn9(phi_0,phi_1,phi_2,phi_3,phi_4,O),U_eqn0(phi_0,phi_1,phi_2,phi_3,phi_4,O),phi_0,phi_1,phi_2,phi_3,phi_4,O);

I want to solve the six equations ( in the last line of the code)using either solve or fsolve command? but I am getting this error.

Undefined function or variable 'phi_0'

Answer 1

[Walter Roberson]

Do not use function handle notation for symbolic functions or symbolic expressions. You can differentiate a symbolic expression and you can differentiate a symbolic function, but you probably cannot differentiate a function handle.

I particularly recommend against using inline() with symbolic expressions.

I would also certainly recommend against using O as a variable name: it is much too easily confused with 0 .

Remember that when you have

dU11_1 = @(phi_0,phi_1,phi_2,phi_3,phi_4,O)diff(sym(U11),O,1);

U_eqn1 = @(phi_0,phi_1,phi_2,phi_3,phi_4,O)dU11_1;

then you are saying that U_eqn1 should be a function that takes 6 variables, ignores them, and returns the function handle dU11_1 . Naming a function handle returns the function handle. If you want the function to be applied to the variables you need to invoke the function handle,

    U_eqn1 = @(phi_0,phi_1,phi_2,phi_3,phi_4,O) dU11_1(phi_0,phi_1,phi_2,phi_3,phi_4,O)

... and if you are going to do that then why bother creating a new function handle? Why not at most use

    U_eqn1 = dU11_1

which would copy the function handle.