numeric solution to matrix ODE with matrix

I am now trying to solve a matrix ODE numerically, let's simplify my problem as follows:

 %{ I don't know the best way to define a 4*4 matrix function%}
syms rho11(t) rho12(t) rho13(t) rho14(t);
syms rho21(t) rho22(t) rho23(t) rho24(t);
syms rho31(t) rho32(t) rho33(t) rho34(t);
syms rho41(t) rho42(t) rho43(t) rho44(t); 
 %{ rho is a 4*4 matrix, each element is a function of time %}
rho=[rho11, rho12, rho13, rho14;rho21, rho22, rho23, rho24;rho31, rho32, rho33, rho34;rho41, rho42, rho43, rho44];

 %{ define constant matrix %}
 s2p=zeros(4,4);s1p=zeros(4,4);
 s2p(1,2)=1;s2p(3,4)=1;s1p(1,3)=1;s1p(2,4)=1;
 init=zeros(4,4);init(2,2)=1;

 %{now we need to solve the following ODE %}
 d(rho)/dt=-(rho *s1p - rho *s2p); 
 %{initial condition:%} rho(0)=init

I know one way is to transform the matrix to a vector, but the actual equation I am doing is too complex to transform it myself. Can anybody tell me the code to make this transformation and solve the ODE? Thanks!

Answer 1

[James Tursa]

Generally, the only thing you need to use for this is the reshape function. It doesn't matter how "complex" your matrix stuff is. E.g.,

% Define all of your matrix stuff here
% Reshape the matrix inputs into vectors
% Call ode with the vector inputs
% Reshape the ode vector outputs as desired.

And then in your derivative function

% function signature here (gets vector inputs from the solver)
% reshape the vector inputs to matrices as needed
% do your matrix operations
% reshape the matrix derivative into vector for output

[Jieyu You]

Thank you! Now I can transform my equation to y'(t)=A(y1,y2...yn), where y(t) is a vector. Can you give me more details on how to further transform it to y'(t)=A*y(t)?