Quickguide EXP Problem

This page is part of the Quickguide Manual. See Quickguide.

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

Exponential models treated in TOMLAB.

$f(t)=\sum \limits _{i}^{p}\alpha _{i}e^{-\beta _{i}t}$	$\alpha _{i}\geq 0$	$0\leq \beta _{1}<\beta _{2}<...<\beta _{p}$.
$f(t)=\sum \limits _{i}^{p}\alpha _{i}(1-e^{-\beta _{i}t})$	$\alpha _{i}\geq 0$	$0\leq \beta _{1}<\beta _{2}<...<\beta _{p}$.
$f(t)=\sum \limits _{i}^{p}t\alpha _{i}e^{-\beta _{i}t}$	$\alpha _{i}\geq 0$	$0\leq \beta _{1}<\beta _{2}<...<\beta _{p}$.
$f(t)=\sum \limits _{i}^{p}(t\alpha _{i}-\gamma _{i})e^{-\beta _{i}t}$	$\alpha _{i},\gamma _{i}\geq 0$	$0\leq \beta _{1}<\beta _{2}<...<\beta _{p}$.
$f(t)=\sum \limits _{i}^{p}t\alpha _{i}e^{-\beta _{i}(t-\gamma _{i})}$	$\alpha _{i}\geq 0$	$0\leq \beta _{1}<\beta _{2}<...<\beta _{p}$.

Example problem:

The vectors t, y contain the following data:

${\begin{array}{|r|rrrrrrrrr|}t_{i}&0&1.00&2.00&4.00&6.00&8.00&10.00&15.00&20.00\\y_{i}&905.10&620.36&270.17&154.68&106.74&80.92&69.98&62.50&56.29\\\end{array}}$

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

$f(t)=\alpha _{1}e^{-\beta _{1}t}+\alpha _{2}e^{-\beta _{2}t},$

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 = 'snopt';
 %Result = tomRun('expSolve',Prob,1);