"Solve" for optimization problem does not store linear parameters
4 views (last 30 days)
Show older comments
I am fitting a function to some data I simulated. I managed to get intelligent constraints that help the fit quite a bit, even with a lot of noise.
This is the function; DF1 and DF2 are constant, c(1) and c(2) are linear, while lam(1), lam(2), lam(3) and lam(4) are nonlinear. I am following the procedure explained here (https://it.mathworks.com/help/optim/ug/nonlinear-data-fitting-problem-based-example.html#NonlinearDataFittingProblemBasedExample-4) to split linear and nonlinear parameters.
% Create a function that computes the value of the response at times t when the parameters are c and lam
temp1 = 1 - exp(-t / lam(1));
temp2 = exp(-t / lam(2));
temp3 = 1 - exp(-t / lam(3));
temp4 = exp(-t / lam(4));
diffun = (temp1 .* temp2) * DF1 * c(1) + (temp3 .* temp4) * DF2 * c(2);
This is the code that I came up with, but it's not working because it does not store correctly the two values for c.
To generate the data:
function [EPSC, IPSC, CPSC, t] = generate_current(G_max_chl, G_max_glu, EGlu, EChl, Vm, tau_rise_In, tau_decay_In, tau_rise_Ex, tau_decay_Ex,tmax)
dt = 0.1; % time step duration (ms)
t = 0:dt:tmax-dt;
% Compute compound current
IPSC = ((G_max_chl) .* ((1 - exp(-t / tau_rise_In)) .* exp(-t / tau_decay_In)) * (Vm - EChl));
EPSC = ((G_max_glu) .* ((1 - exp(-t / tau_rise_Ex)) .* exp(-t / tau_decay_Ex)) * (Vm - EGlu));
CPSC = IPSC + EPSC;
end
To fit the function:
% Simulated data
[EPSC,IPSC,CPSC,t] = generate_current(80,15,0,-70,-30,0.44,15,0.73,3,120);
ydata = awgn(CPSC,25,'measured'); % Add white noise
ydata = ydata';
t = t';
% Values
Vm = -30; DF1 = Vm +70; DF2 = Vm;
% Initial values for fitting
gmc = 40; gmg = 20; tde = 0.2; tdi = 8; tre = 1.56; tri = 3;
% Objective function
c = optimvar('c',2); % Linear parameters
lam = optimvar('lam',4); % Nonlinear parameters
% Bounds
c.LowerBound = [0, 0];
c.UpperBound = [200, 200];
lam.LowerBound = [0.16,7.4,1.1,2.6];
lam.UpperBound = [0.29,8.4,2.3,3.3];
x0.c = [gmc,gmg]; % Starting values
x0.lam = [tri,tdi,tre,tde]; % Starting values
% Create a function that computes the value of the response at times t when the parameters are c and lam
temp1 = 1 - exp(-t / lam(1));
temp2 = exp(-t / lam(2));
temp3 = 1 - exp(-t / lam(3));
temp4 = exp(-t / lam(4));
diffun = (temp1 .* temp2) * DF1 * c(1) + (temp3 .* temp4) * DF2 * c(2);
%Solve the problem
%To do so, first convert the fitvector function to an optimization expression using fcn2optimexpr.
F2 = fcn2optimexpr(@(x) fitvector(x,t,ydata),lam,'OutputSize',[length(t),1]);
% Create a new optimization problem with objective as the sum of squared differences between the converted fitvector function and the data y
ssqprob = optimproblem('Objective',sum((F2 - ydata).^2));
[sol,fval,exitflag,output] = solve(ssqprob,x0)
% Plot
resp = evaluate(diffun,sol);
hold on
plot(t,resp)
hold off
Fitvector function:
function yEst = fitvector(lam,xdata,ydata)
temp1 = 1 - exp(-xdata / lam(1));
temp2 = exp(-xdata / lam(2));
temp3 = 1 - exp(-xdata / lam(3));
temp4 = exp(-xdata / lam(4));
A(:,1) = temp1 .* temp2 * 40; % DF1 is 40
A(:,2) = temp3 .* temp4 * -30; % DF2 is -30
c = A\ydata; % solve A*c = y for linear parameters c
yEst = A*c; % return the estimated response based on c
Not sure what I am doing wrong, because I get this error:
Error using optim.problemdef.OptimizationExpression/evaluate
Second argument must contain values for variable 'c'.
Error in SplittFit (line 44)
resp = evaluate(diffun,sol);
0 Comments
Answers (1)
Matt J
on 27 Mar 2021
Have you looked at what sol contains? I'm willing to bet it contains values for lam, but not c. Your objective F2 is only a function of lam, after all, is it not?
0 Comments
See Also
Categories
Find more on Optimization in Help Center and File Exchange
Community Treasure Hunt
Find the treasures in MATLAB Central and discover how the community can help you!
Start Hunting!