MATLAB: Extracting variables from symbolic expression in a matrix form

divisionmatrixmatrix manipulationsymbolicSymbolic Math Toolbox

I have a long equation in symbolic math toolbox which has the following form:

A*u1+B*u2+C*u3

A, B and C are long relationships consisting of symbolic variables. I would like to extract the A B C in from u1, u2 and u3 and write them in a matrix form. In other words I would like to shape a relationship such us

[A B C]*{u}

where u is

u=[u1;u2;u3]

How can I do that?

Best Answer

You could use coeffs but the output is a bit of a nuisance for multivariates.

You could call into MuPAD and use coeff.

But really, the easiest way is likely to use

A = subs(Expression, {u2,u3}, {0,0});
B = subs(Expression, {u1,u3}, {0,0});
C = subs(Expression, {u1,u2}, {0,0});

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MATLAB: Matlab sorts tensor product of variables automatically

Symbolic variables always stand in for scalar values, never for matrices. Scalar values are commutative under multiplication so the order of the scalar variables does not matter.

It would be quite a bit of work to get the symbolic toolbox to handle this situation.

You will need to substitute arrays of symbolic variables with fixed size and compute based on those. This will obscure your equations for sure.

MATLAB: Solving system of equations with parameters

Like sir Walter says I think you should be using ode solvers to solve the problem because it clearly is a system of odes:

tspan=[0 1];  % time span 
ic=[0;1;0;0;0;0;0;0;0;0;0;0]; % initial conditions
[t,x]=ode45(@myod,tspan,ic);  % function call
plot(t,x(:,1)) % likewise another 11 solutions can be plotted
function dSdt = myod(t,x)  % function definition
 S0=x(1);
 S1=x(2);
 S2=x(3);
 S3=x(4);
 S4=x(5);
 S5=x(6);
 S6=x(7);
 S7=x(8);
 S8=x(9);
 S9=x(10);
 S10=x(11);
 S11=x(12);
Ca_sr_conc  = 1.3e-3;
MgATP_conc  = 5e-3;  
MgADP_conc  = 36e-6; 
Pi_conc     = 1e-3;  
Ca=1e-3;  % change it to your value
Ca_cyt_conc = 140e-9; 
k_S0_S1   = 4e7;   
k_S1_S0   = 450;   
k_S1_S2   = 120;   
k_S2_S1   = 25;    
k_S2_S3   = 1e8;   
k_S3_S2   = 16;    
k_S3_S4   = 2e7;  
k_S4_S3   = 40;   
k_S4_S5   = 135;   
k_S5_S4   = 765;   
k_S5_S6   = 15;    
k_S6_S5   = 7.5e4;
k_S6_S7   = 1.5; k_S7_S6   = 2.0;
k_S7_S8   = 350; 
k_S8_S7   = 1.2e5;
k_S8_S9   = 160;   
k_S9_S8   = 250;   
k_S9_S10  = 300;
k_S10_S9  = 9e4;   
k_S10_S11 = 60;    
k_S11_S10 = 60;    
k_S11_S0  = 250;   
k_S0_S11  = 2.7e5; 
dSdt  = [ ((k_S11_S0 * S11) + (k_S1_S0 * S1)) - ((Ca_cyt_conc* k_S0_S1 + Pi_conc * k_S0_S11) * S0);
((Ca_cyt_conc* k_S0_S1 * S0) + (k_S2_S1 * S2)) - ((k_S1_S0 + k_S1_S2) * S1);
((k_S1_S2 * S1) + (k_S3_S2 * S3)) - ((k_S2_S1 + Ca* k_S2_S3) * S2);
((Ca_cyt_conc* k_S2_S3 * S2) + (k_S4_S3 * S4)) - ((k_S3_S2 + MgATP_conc * k_S3_S4) * S3);
((MgATP_conc * k_S3_S4 * S3) + (k_S5_S4 * S5)) - ((k_S4_S3 + k_S4_S5) * S4);
((k_S4_S5 * S4) + (k_S6_S5 * MgADP_conc * S6)) - ((k_S5_S4 + k_S5_S6) * S5);
((k_S5_S6 * S5) + (k_S7_S6 * S7)) - ((k_S6_S5 * MgADP_conc + k_S6_S7) * S6);
((k_S6_S7 * S6) + (Ca_sr_conc * k_S8_S7 * S8)) - ((k_S7_S6 * MgADP_conc + k_S7_S8) * S7);
((k_S7_S8 * S7) + (k_S9_S8 * S9)) - ((Ca_sr_conc * k_S8_S7 + k_S8_S9) * S8);
((k_S8_S9 * S9) + (Ca_sr_conc * k_S10_S9 * S10)) - ((k_S9_S8 + k_S9_S10) * S9);
((k_S9_S10 * S9) + (k_S11_S10 * S11)) - ((k_S10_S11 + Ca_sr_conc * k_S10_S9) * S10);
((k_S10_S11 * S10) + (Pi_conc * k_S0_S11 * S0)) - ((k_S11_S0 + k_S11_S10) * S11)];
end

Best Answer

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