Tranform a systems of equations to for loop

Hello everyone, I hav the following systems of equations:

syms Qc Qh Qm1 Qm2 Qm3 T1 T2 T3

eqn1 = Qm1 - Qc == q0 - Pc - qw/2 ; 
eqn2 = T1 + Rc*Qc == T0;

eqn3 = T2 - T1 + R1/2*Qm1 == R1/2*q0; 
eqn4 = T2 - Rg0/2*Qm1 + Rg0/2*Qm2 == T0;

eqn5 = T3 - T2 + R1/2*Qm2 == R1/2*q0; 
eqn6 = T3 - Rg0/2*Qm2 + Rg0/2*Qm3 == T0;

eqn7 = Qh + Qm3 == Ph - q0 + qw/2;
eqn8 = T3 - Rh*Qh == T0;

[A,B] = equationsToMatrix([eqn1, eqn2, eqn3, eqn4, eqn5, eqn6, eqn7, eqn8], [Qc Qh Qm1 Qm2 Qm3 T1 T2 T3]); 

X = linsolve(A,B); 

Is there a way to transform these systems of equations to a simpler and faster way to calculate the unknwowns variables (like a for loop)?

Thanks in advance!

Answer 1

[Walter Roberson]

No, linsolve is pretty efficient.

[letoppina]

Thanks. What if I want to solve the equations with one or more changing variables (for isntance, for different values of q0)? Is there a way to do so?

[Walter Roberson]

Changing q0 changes the constants, b, in an A*x=b setup. You can solve for multiple at the same time by using a matrix for b, one column for each different q0 value.

If you have the same A matrix but there are reasons why you do not have the q0 values available all at the same time, then see decomposition()

[letoppina]

Could you show me how to code it? I am a beginner in matlab

[Walter Roberson]

q0vals = [-1, 0, 1];

syms Pc Ph q0 qw R1 Rc Rg0 Rh T0   %replace these with actual constants

syms Qc Qh Qm1 Qm2 Qm3 T1 T2 T3

eqn1 = Qm1 - Qc == q0 - Pc - qw/2 ; 
eqn2 = T1 + Rc*Qc == T0;

eqn3 = T2 - T1 + R1/2*Qm1 == R1/2*q0; 
eqn4 = T2 - Rg0/2*Qm1 + Rg0/2*Qm2 == T0;

eqn5 = T3 - T2 + R1/2*Qm2 == R1/2*q0; 
eqn6 = T3 - Rg0/2*Qm2 + Rg0/2*Qm3 == T0;

eqn7 = Qh + Qm3 == Ph - q0 + qw/2;
eqn8 = T3 - Rh*Qh == T0;

[A,B] = equationsToMatrix([eqn1, eqn2, eqn3, eqn4, eqn5, eqn6, eqn7, eqn8], [Qc Qh Qm1 Qm2 Qm3 T1 T2 T3]); 

Bmat = subs(B, q0, q0vals)

Bmat = 

X = simplify(A\Bmat);

X

X =