How to pass multiple vectors (possibly a matrix) to pdepe and output a respective vector matrix?

Hi!

I have a matrix of parameters (lets say a design of experiments) which I would like to pass to pdepe and obtain a numerical output. That output will be used to calculate the flux and the flux is multipled by a bunch of constants to obtain my quanitity of interest. I want to then bunch up the quanity of the interest in a vector of similar dimensions to the experimental output to be able to fit coefficients to my coupled equations.

I need a way to pass my parameter matrix (lets say) x to obtain my I_num.

[Torsten]

You don't even need to start. Having six measurement data to fit six parameters makes no sense at all.

[Hashim]

I am sorry I should've said I have a matrix of values (not parameters). I want to initialize my pdes using this matrix and get a numerical output. The actual number of experimental points I have against this input is 17. For now my major concern is to get numerical output against the matrix i.e. every array of that matrix initializes the pde and spits out a output. This output is used to calculate the quantity of interest so against every array initialization I get a 1*1 solution. After I have the initialization I can then perhaps start thinking about the fitting to my extended dataset.

[Torsten]

I read about your PDE system here:

https://de.mathworks.com/matlabcentral/answers/1707965-how-can-i-adjust-the-output-of-my-pdepe-function-for-nlinfit?s_tid=prof_contriblnk

What are the parameters you want to fit (beta0) ? For what variable(s) do you have measurement data over time (is alphaa = time) ?

[Hashim]

No alphaa is not time varied rather these are the values that are supposed to be passed to pdepe (initialize icfun etc. etc.). Beta0 are the initial estimates of the parameters and beeta is the parameter vector which I want to fit. The first value of I_num needs be concatenated to form a 1*6 vector that should be passed to the fitting function so it can fit to I_exp. But for that to happen I need to get Ur solution for the whole matrix of alphaa.

[Torsten]

Pass the values of alphaa to the functions of pdepe where they are needed, e.g.

icfun = @(x) Uinit(x,alphaa(1))
sol = pdepe(m,pdefun,icfun,bcfun,xmesh,tspan,options)

function u0 = Uinit(x,alphaa)
  u0 = alphaa;
end

[Hashim]

alphaa     = [2.00000000000000e-06,3.46000000000000e-06,3.54444000000000e-07;
              6.00000000000000e-06,4.46000000000000e-06,4.54444000000000e-07;
              7.00000000000000e-06,5.46000000000000e-06,5.54444000000000e-07;
              8.00000000000000e-06,6.46000000000000e-06,6.54444000000000e-07;
              9.00000000000000e-06,7.46000000000000e-06,7.54444000000000e-07;
              7.00000000000000e-06,8.46000000000000e-06,8.54444000000000e-07];

Let's say this is our alphaa respectively for every row N I want a solution matrix. This is what I am struggling with atm. Using this solution matrix I want to calculate I_num which would be a vector 6*1. I am trying to use a loop with no success so far. Looks like this so far:

for i=1:length(tspan)
ic_arg(i)  = {@(x)alphaa(i,1).*ones(size(N)) ; @(x)alphaa(i,2).*ones(size(N)); ...
              @(x)alphaa(i,3).*ones(size(N))}; 
IC(i)      =  @(x)PDE_PSw_EK_IC(x, ic_arg(i)); 
BC         =  @(xl, yl, xr, yr, t)PDE_PSw_EK_BC(xl, yl, xr, yr, t, epsilon, alphaa); 

optns      = odeset('MaxStep',1e-00,'RelTol',1e-7,'AbsTol',1e-7); 
sol1(i)    = pdepe(m, @(x, t, y, DyDx)PDE_PSt_EK(x, t, y, DyDx, beeta, alphaa), ... 
                   IC(i), BC, x, tspan, optns);
end

Pretty sure i will have to loop through my BCfun as well considering it has terms from alphaa as well.

Answer 1

[Torsten]

optns  = odeset('MaxStep',1e-00,'RelTol',1e-7,'AbsTol',1e-7);
for i=1:size(alphaa,1)
    INIT = @(x) alphaa(i,1:3);
    BC = @(xl, yl, xr, yr, t)PDE_PSw_EK_BC(xl, yl, xr, yr, t, epsilon, alphaa);
    PDE = @(x, t, y, DyDx)PDE_PSt_EK(x, t, y, DyDx, beeta, alphaa)
    sol{i} = pdepe(m, PDE,INIT, BC, x, tspan, optns);
end