Elias at 22:32, 17 January 2012

2012-01-17T22:32:11Z

← Older revision		Revision as of 17:32, 17 January 2012
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	Exponential fitting problems are a set of special problems normally solved by ''expSolve''. Several different models are treated in <span class="roman">TOMLAB</span>:		Exponential fitting problems are a set of special problems normally solved by ''expSolve''. Several different models are treated in <span class="roman">TOMLAB</span>:

	~~<figtable id="tab:expModels">~~
	{\| class="wikitable"		{\| class="wikitable"
	\|+<caption>Exponential models treated in TOMLAB.</caption>		\|+<caption>Exponential models treated in TOMLAB.</caption>
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	\|<math>f(t) = \sum\limits_i^p t \alpha_i e^{-\beta_i (t - \gamma_i)}</math>\|\|<math>\alpha_i \geq 0</math>\|\|<math>0\leq\beta_1<\beta_2< ... <\beta_p</math>.		\|<math>f(t) = \sum\limits_i^p t \alpha_i e^{-\beta_i (t - \gamma_i)}</math>\|\|<math>\alpha_i \geq 0</math>\|\|<math>0\leq\beta_1<\beta_2< ... <\beta_p</math>.
	\|}		\|}
	~~</figtable>~~

	Example problem:		Example problem:
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	Open the file for viewing, and execute expQG in Matlab.		Open the file for viewing, and execute expQG in Matlab.

	<~~syntaxhighlight~~ lang="matlab">		<source lang="matlab">
	% expQG is a small example problem for defining and solving exponential		% expQG is a small example problem for defining and solving exponential
	% fitting problems using the TOMLAB format. See the TOMLAB manual for		% fitting problems using the TOMLAB format. See the TOMLAB manual for
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	%Prob.SolverL2 = 'snopt';		%Prob.SolverL2 = 'snopt';
	%Result = tomRun('expSolve',Prob,1);		%Result = tomRun('expSolve',Prob,1);
	</~~syntaxhighlight~~>		</source>

Elias: Created page with "{{Part Of Manual|title=the Quickguide Manual|link=Quickguide}} Exponential fitting problems are a set of special problems normally solved by ''expSolve''. Several ..."

2011-08-11T07:18:07Z

Created page with "{{Part Of Manual|title=the Quickguide Manual|link=Quickguide}} Exponential fitting problems are a set of special problems normally solved by ''expSolve''. Several ..."

New page

{{Part Of Manual|title=the Quickguide Manual|link=[[Quickguide|Quickguide]]}}
Exponential fitting problems are a set of special problems normally solved by ''expSolve''. Several different models are treated in <span class="roman">TOMLAB</span>:

<figtable id="tab:expModels">
{| class="wikitable"
|+<caption>Exponential models treated in TOMLAB.</caption>
|<math>f(t) = \sum\limits_i^p \alpha_i e^{-\beta_i t}</math>||<math>\alpha_i
\geq 0</math>||<math>0\leq\beta_1<\beta_2< ... <\beta_p</math>.
|-
|<math>f(t) = \sum\limits_i^p \alpha_i(1-e^{-\beta_i t})</math>||<math>\alpha_i
\geq 0</math>||<math>0\leq\beta_1<\beta_2< ... <\beta_p</math>.
|-
|<math>f(t) = \sum\limits_i^p t \alpha_i e^{-\beta_i t}</math>||<math>\alpha_i \geq0</math>||<math>0\leq\beta_1<\beta_2< ... <\beta_p</math>.
|-
|<math>f(t) = \sum\limits_i^p (t \alpha_i-\gamma_i) e^{-\beta_i t}</math>||<math>\alpha_i,\gamma_i \geq 0</math>||<math>0\leq\beta_1<\beta_2< ... <\beta_p</math>.
|-
|<math>f(t) = \sum\limits_i^p t \alpha_i e^{-\beta_i (t - \gamma_i)}</math>||<math>\alpha_i \geq 0</math>||<math>0\leq\beta_1<\beta_2< ... <\beta_p</math>.
|}
</figtable>

Example problem:

The vectors ''t'', ''y'' contain the following data:

<math>
\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}
</math>

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

<math>
f(t) = \alpha_1 e^{-\beta_1 t} + \alpha_2 e^{-\beta_2 t},
</math>

The following file defines and solves the problem in TOMLAB.

'''File: '''<span class="roman">tomlab/quickguide/expQG.m</span>

Open the file for viewing, and execute expQG in Matlab.

<syntaxhighlight lang="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);
</syntaxhighlight>

Quickguide EXP Problem - Revision history

Elias at 22:32, 17 January 2012

Elias: Created page with "{{Part Of Manual|title=the Quickguide Manual|link=Quickguide}} Exponential fitting problems are a set of special problems normally solved by ''expSolve''. Several ..."