## 29EXP Problem

Exponential fitting problems are a set of special problems normally solved by expSolve. Several different models are treated in TOMLAB:

Table 1: Exponential models treated in TOMLAB.

f(t) = Σip αi e−βi t, αi ≥ 0, 0≤β12< ... <βp.
f(t) = Σip αi(1−e−βi t), αi ≥ 0, 0≤β12< ... <βp.
f(t) = Σip t αi e−βi t, αi ≥ 0, 0≤β12< ... <βp.
f(t) = Σip (t αi−γi) e−βi t, αii ≥ 0, 0≤β12< ... <βp.
f(t) = Σip t αi e−βi (t − γi), αi ≥ 0, 0≤β12< ... <βp.

Example problem:

The vectors t, y contain the following data:
 ti 0 1 2 4 6 8 10 15 20 yi 905.1 620.36 270.17 154.68 106.74 80.92 69.98 62.5 56.29

Setup and solve the problem of fitting the data to a two-term exponential model:

f(t) = α1 e−β1 t + α2 e−β2 t,

The following file defines and solves the problem in TOMLAB.

File: tomlab/quickguide/expQG.m

Open the file for viewing, and execute expQG in Matlab.
```% expQG is a small example problem for defining and solving exponential
% fitting problems using the TOMLAB format. See the TOMLAB manual for
% options.

% f(t) = alpha(1)*exp(-beta(1)*t) + alpha(2)*exp(beta(2)*t)

t = [0 1.00 2.00 4.00 6.00 8.00 10.00 15.00 20.00]';
y = [905.10 620.36 270.17 154.68 106.74 80.92 69.98 62.50 56.29]';
p      = 2;                         % Two terms
Name   = 'Simple two-term exp fit'; % Problem name, can be anything
wType  = 0;                         % No weighting
SepAlg = 0;                         % Separable problem
Prob = expAssign(p,Name,t,y,wType,[],SepAlg);

Prob.SolverL2 = 'nlssol';
Result = tomRun('expSolve',Prob,1);
%Prob.SolverL2 = 'snopt7';
%Result = tomRun('expSolve',Prob,1);```