How can I use equations from a matrix, using symbolic variables, inside the function file for ode45 ?

I want to use time dependent equations directly from a matrix (i.e. product of matrices) in the function file. keeping it simple using 2*2 matrices.

%function file

function dbdt =timedb(t,b)
global w0 l1 d gc gm1 phi
dbdt=zeros(4,1);
g=l1^2/d;
a=[-g*sin(phi) w0-g*cos(phi);-w0-g*cos(phi) g*sin(phi)-gm1];
syms b11 b12 b21 b22
b=[b11 b12; b21 b22];
syms t
% dbrdt=diff(b)./diff(t);
dbrdt=a*b+b*a.';
%if I write 
%dbdt=a*b+b*a.';%error is: TIMEDV must return a column vector.
%I want to use compcat form smthing like this 
dbdt(1) = dbrdt(1,1);
dbdt(2)=dbrdt(1,2);
dbdt(3)=dbrdt(2,1);
dbdt(4)=dbrdt(2,2);

Manually it can be done like this which works well.

%         dbdt(1) = 2*A(1,1)*b(1)+A(1,2)*b(2)+b(3)*A(1,2);
%         dbdt(2)=A(1,1)*b(2)+A(1,2)*b(4)+b(1)*A(2,1)+b(2)*A(2,2);
%         dbdt(3)=A(2,1)*b(1)+A(2,2)*b(3)+b(3)*A(1,1)+b(4)*A(1,2);
%         dbdt(4)=A(2,1)*b(2)+2*A(2,2)*b(4)+b(3)*A(2,1);
% with initial conditions
% b1_0=1;
% b2_0=0;
% b3_0=0;
% b4_0=0;

but I want to use compact from of equtions, using the syms, as in the previosu part.

My main file looks like this

b11_0=1;
b12_0=0;
b21_0=0;
b22_0=0;
bb=[b11_0, b12_0, b21_0 b22_0];
[T,B]=ode45('timedb',tspan,bb);

it gives error:

Unable to perform assignment because value of type 'sym' is not convertible to 'double'. How can I solve this issue?

[Torsten]

By removing the syms lines in your function file and replacing

[T,B] = ode45(...

by

[T,B] = ode45(@(t,b)timedb(t,b(1),b(2),b(3),b(4)),tspan,bb)

and

function dbdt = ...

by

function dbdt(t,b11,b12,b21,b22)

and by defining the undefined variable geff somewhere.

[Anil Kumar]

Dear Torsten, thanks!. is it the only solution if I have 16 (4*4), 36(6*6) or many such euqtaions instead of four here? I hope you understand that as the dimension of matrices go up, this may not be a suitable way.

sorry that geff is a typo, removing it.

[Torsten]

If you have more equations, use

[T,B] = ode45(@timedb,tspan,bb)

function dbdt = timedb(t,bvec)

and in the code

b = reshape(bvec,sqrt(numel(b)),sqrt(numel(b)))

[Anil Kumar]

Dear Torsten, Indeed helpful, thanks!. Few minor typos there, hilighted text here:

1) first commnet, function dbdt=timedb(t,b11,b12,b21,b22)

2) second comment, b = reshape(bvec,sqrt(numel(bvec)),sqrt(numel(bvec)))

[Torsten]

Maybe the reshape command gives the transposed matrix of B.

Then use reshape(...).'

[Anil Kumar]

Dear Torsten, Thanks!. Wroking perfect. there was a typo, removing that unnecessary comment.

Answer 1

[Steven Lord]

It is possible to perform calculations using symbolic variables inside the function file whose handle you pass into ode45 as the first argument. However whether or not you perform the calculations symbolically inside your function file, your function file must return a double column vector.

Looking specifically at what you've written, these lines are problematic.

syms b11 b12 b21 b22
b=[b11 b12; b21 b22];
syms t

ode45 will call your function with inputs and inside your function those inputs are known as t and b. These lines I've quoted overwrite those inputs with symbolic variables, so you're completely ignoring what ode45 asked you to compute.