The Kartesio Handbook

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Table of Contents

1. Introduction
2. Kartesio quick start guide
3. Regression
4. Neural Network
5. Other useful things
6. Questions and Answers
7. How can I contribute?
8. Credits and License
A. Installation
How to obtain Kartesio
Web Presence
Compilation and Installation

Kartesio is a program for calculating best fit curves with experimental points using regression algorithms or neural networks. It is free and licensed under the Public License.

Kartesio has a simple interface that allows you to plot points and a curve. The curve is usually calculated by the program, but you can also write it by yourself.

As soon as you open Kartesio, you will get a blank table and a blank plot. This is also the same screen you can get in every moment just clicking on (FileNew). You can try to best fit your experimental points with a regression algorithm or a neural network, using the tools in the appropriate tab. Please note that regression algorithm needs maxima to be installed on your computer, while the neural network method needs ZorbaNeural.

Kartesio main window

You should start adding your points to the table. Obviously, a bidimensional point is identified with two coordinates (on X and Y axis).

Adding points

In the Regression tab, you can write a generic function that will be used by Kartesio as a model for the fitting curve. The function must be written with the variables x and y, and with variable coefficients (represented by letters). Obviously, you can also write numeric coefficients. Please take note that the function must be biuniqe.

Writing a generic function

Clicking the Best fit button, Kartesio will start to calculate coefficients for the function you wrote, trying to best fit the experimental points. The final function will appear the edit box close to the bottom edge of the window.

Best fit done

After the fit operation, points and the curve will be automatically plotted. Anyway, you may prefer to change to plotted area to see better the image. This can be done using the four spinboxes: Xmin is the minimum value of X axis, and Xmax is the maximum value. For example, if you write respectively 0 and 1, then the plot will start from 0 and end to 1. The same logic works for Y axis.

A closer look

If you change plot limits, you may need to change also the resolution: if the resolution of the plot is too little, you will see every curve as a single line. If the resolution is too high you will waste a lot of CPU time to draw the plot.

Higher resolution

The neural network method works like the regression one, but you can not write you own function: you must choose it from a list. This list, anyway, contains practically every kind of function you may want (periodic functions are not usable with a neural network).

Choosing the correct function

Usually, back propagation training is just what you need. For this reason it is checked by default. Just modify the number of iterations (it should not be too high, or the process may end up with way too strange value) and then press the Calculate button. Please take note that the neural network, exactly as a human brain, may give you different results: if you press the Calculate button more than once and you will find out that the network calculates every time a different best fitting curve.

Back propagation training

If you are not satisfied by the back propagation training result, you could also use the genetic algorithm training. This can be done simply checking the appropriate checkbox. Genetic algorithm training takes a lot more CPU resources, so you better use a very low iterations number (not more than 500).

Genetic algorithm training

Sometimes it is useful to redraw the plot. For example, it is if you have manually changed the best fitting curve or if you edited some points and you don't want to recalculate the fitting function. Just use the Draw Plot button.

Draw plot

To know how much the fitting curve is different from your experimental points, you can look at the root mean square error. To add it to the plot, it is needed to check the checkbox Show RMS error. Then press the Draw Plot button to redraw the plot: it should contain a red label with the RMS error.

Showing RMS error
6.1. Will I ever have to pay for Kartesio?


Will I ever have to pay for Kartesio?

No, never. Kartesio is licensed under the GPL, so you will never have to pay for this program.

7.1. Find some bugs or give some suggestions


Find some bugs or give some suggestions

If you find any bugs in the program, or have a few suggestions for improvements, please let me know at


Program Copyright, 2010-2011 Luca Tringali