Transcript Analisys … A Curve Fitting Application A Mathematica® based regression analysis program Overview • Experimental scientists all over the world need to find models for describing.

Analisys …
A Curve Fitting Application
A Mathematica® based regression analysis
program
Overview
• Experimental scientists all over the world need to
find models for describing their experimental
data...
• Analisys is a curve fitting application:
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It fits a theoretical model function to a given set of
experimental data
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It performs regression analysis over the resulting fit
Features & Benefits
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Very advanced mathematical system
Straightforward Data Entry
2D and 3D Data Plotting
Multi-dimensional Regression Model Capability
Automatic classification of model to select the
best suited method for optimization; either linear,
non-linear separable, or non-linear non-separable.
• Sophisticated Data Manipulation
Features & Benefits
• Minimizing the sum of squares is done with a
program based on Mathematica's built-in
FindMinimum function
• RPC Technology is used to connect to the
kernel and execute expressions
• Very flexible grid functionality, such as: copying,
pasting, inserting, sorting(ascending or
descending), reversing, and deleting grid data.
Features & Benefits
• Detailed regression report is produced after fitting
including:
Specifications of the model and the method used in
fitting
+ Estimates of the parameters, their standard errors, and
confidence intervals
+ General statistical diagnostics that include the norm of
residuals, estimated variance, asymptotic correlation
and covariance matrices
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Features & Benefits
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(continued)
A table comparing experimental values with predicted
ones, and the corresponding weighted residuals
Features & Benefits
Now, to an overview of the application’s user
interface features...
Features & Benefits
• Selecting ‘New’ from File Menu the following
dialog box appears, from which one of the two
options: “Direct Data Entry”, “Data From File”
can be chosen, as shown beneath.
Features & Benefits
• ‘Perform Regression’ item in the Options menu
causes a dialog box to appear, after finishing with
this dialog a series of dialog boxes appear to guide
the user through that process.
Features & Benefits
• The results of the fitting process that appear in the
‘Results’ dialog can be saved to a text file.
Features & Benefits
• If the ‘Plot while Iterating’ option in the ‘Options’
dialog box was checked, the process of numerical
fitting will be accompanied by plotting the
progress results...
Features & Benefits
• Other features include:
1) 2D or 3D Data Plotting
2) Evaluating expressions using Mathematica’s Kernel
Features & Benefits
3) Whole files containing Mathematica Expressions
can also be evaluated!
Features & Benefits
4) Sophisticated data manipulation can be performed
on grid data
Features & Benefits
• Even the splash screen was carefully designed
with the comprehensive nature of the application
in mind.
Applications
• Scientists and engineers can benefit from this
application
• Separable non-linear models especially appear in
nuclear magnetic resonance practice and in semiconductor physics (e.g. common-base transistor
(an npn-transistor))
I(V,T)  I 01[e A1V 1]  I 02 [e A2V 1]
Where I0i are the linear parameters and Ai are the
non-linear parameters at constant temperature
Specifications
• This following table shows the results for different
commercial applications versus Analisys results: