How do I feed ODE45 a cell array ?

I am trying to solve an ODE which consists of function handles. In order to formulate the equation of state vector derivative of the System of 1st order ODEs, I collect these function handles in a cell array. It is not possible to store them in a normal array as far as I know. How do I feed the cell Array, which contains all the function handles to the ODE45 solver or do it differently?

Scheme of the problem:

%create cell and state array
state = @(x,y,z) [x;y;z];
Cell_array = cell(3);

%column selector
select_column = @(M, col_index) M(:,col_index);

%Define Matrix Functions, here 2 examples of Matrices
Matrix_1 = @(state) [1,1,state(1); 1,1,sin(state(2));1,1,state(3)];
Matrix_2 = @(state) [state(1),0,0; 0,state(2),0; 0,0, state(2)];

%select the columns 
M1_c1 = @(state) select_column(Matrix_1(state),1);
M1_c2 = @(state) select_column(Matrix_1(state),2);
M1_c3 = @(state) select_column(Matrix_1(state),3);

%differential equations
state_dot_1 =  @(state) Matrix_2(state) * M1_c1(state);
state_dot_2 =  @(state) Matrix_2(state) * M1_c2(state);
state_dot_3 =  @(state) Matrix_2(state) * M1_c3(state);

%fill cell array with differential equations 
Cell_array{1} = state_dot_1;
Cell_array{2} = state_dot_2;
Cell_array{3} = state_dot_3;

I would now like to feed that cell_array to an ODE solver. This doesn't work. But using a normal array doesn't work either for these function handles. Does anyone know a work around ? I'm new to matlab and programming in general.

[Torsten]

Maybe you could tell us first which ODE system you are trying to solve.

You have 3 unknown state variables, but state_dot_1, state_dot_2 and state_dot_3 together give 9 equations.

Or do you want to call the ODE integrator three times - once for each state_dot_i ?

[Lennart Göppinger]

First of all thank you for your quick reply.

You're right, that scheme is wrong. It should have been the rows of Matrix_2.

So for state_dot_1 it is the first row of matrix_2 multiplied by the column vector, for state_dot_2 it is the 2nd row of Matrix_2 multiplied by the column vector and so on. This would then give us 3 equations for 3 states with the Cell_array containing these 3 equations. How do I feed that Cell_array to the ODE solver ?

Sorry for the confusion.

[James Tursa]

@Lennart Göppinger I'm not sure I completely follow this. Why can't you create a function handle that unwraps the cell array function handles appropriately given the state input to create the derivative output, and feed that to the ODE integrator? Notionally, something like

f = @(t,y) [Cell_array{1}(y);Cell_array{2}(y);Cell_array{3}(y)]

... or whatever variation of this that produces a column vector output.

Answer 1

[Torsten]

Use state_dot as the function that you pass to the integrator.

I followed your coding - the problem setup could have been much easier.

%column selector
select_column = @(M, col_index) M(:,col_index);
select_row = @(M,row_index)M(row_index,:);
%Define Matrix Functions, here 2 examples of Matrices
Matrix_1 = @(state) [1,1,state(1); 1,1,sin(state(2));1,1,state(3)];
Matrix_2 = @(state) [state(1),0,0; 0,state(2),0; 0,0, state(2)];
%select the columns 
M1_c1 = @(state) select_column(Matrix_1(state),1);
M1_c2 = @(state) select_column(Matrix_1(state),2);
M1_c3 = @(state) select_column(Matrix_1(state),3);
%select the rows
M2_r1 = @(state) select_row(Matrix_2(state),1);
M2_r2 = @(state) select_row(Matrix_2(state),2);
M2_r3 = @(state) select_row(Matrix_2(state),3);
%differential equations
state_dot_1 =  @(state) M2_r1(state) * M1_c1(state);
state_dot_2 =  @(state) M2_r2(state) * M1_c2(state);
state_dot_3 =  @(state) M2_r3(state) * M1_c3(state);
state_dot = @(~,state)[state_dot_1(state);state_dot_2(state);state_dot_3(state)];
state_dot(0,[1 2 3])

ans = 3x1

1 2 6

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[Lennart Göppinger]

thank you very much for your help, that worked!