ExpSolve

Purpose

Solve exponential fitting problems for given number of terms p.

Calling Syntax

Prob = expAssign( ... );
Result = expSolve(Prob, PriLev); or
Result = tomRun('expSolve', PriLev);

Inputs

Prob	Problem created with expAssign.
PriLev	Print level in tomRun call.
Prob.SolverL2	Name of solver to use. If empty, TOMLAB selects dependent on license.

Outputs

Result	TOMLAB Result structure as returned by solver selected by input argument Solver.
LS	Statistical information about the solution. See TOMLAB Appendix B.

Description

expSolve solves a cls (constrained least squares) problem for exponential fitting formulates by expAssign. The problem is solved with a suitable or given cls solver.

The aim is to provide a quicker interface to exponential fitting, automating the process of setting up the problem structure and getting statistical data.

M-files Used

GetSolver, expInit, StatLS and expAssign

Examples

Assume that the Matlab vectors t, y contain the following data:

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

To set up and solve the problem of fitting the data to a two-term exponential model

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

give the following commands:

>> 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);

>> Result = tomRun('expSolve',Prob,1);
>> x = Result.x_k'

x =
          0.01          0.58         72.38        851.68

The $x$ vector contains the parameters as $x=[\beta _{1},\beta _{2},\alpha _{1},\alpha _{2}]$ so the solution may be visualized with

>> plot(t,y,'-*', t,x(3)*exp(-t*x(1)) + x(4)*exp(-t*x(2)) );

<figure id="fig:expData">

Results of fitting experimental data to two-term exponential model. Solid line: final model, dash-dot: data.

</figure>