User has to enter total number N>5 of points for approximation. It is convenient
to store the data in a file when one has a large number of points.
It should be the text file (with .txt extension), which contains exactly 3N numbers
separated by white space or new line ("Enter"). Note that two integer numbers without separator
will be read as one number, for example "23" and "67" will be read as "2367".
Two float numbers without separator could be corrupted, for example "0.34" and "3.5"
typed as "0.343.5" can be read as "0.343" and "0.5". We check the format of input numbers
and in the most cases one will get an error message if the format is not valid,
but it is the responsibility of the user to prepare the input data properly.
First N numbers should correspond to x-coordinates of given points, the second set
of N numbers should correspond to y-coordinates and the third set
of N numbers should correspond to z-coordinates. User can arrange them in any order,
but first x-coordinate (first point) should correspond to first y-coordinate and to first z-coordinate etc.
One can use "Browse" to select the required file and click "Upload" to submit.
On the next page user should enter four parameters of approximation, which allow to define the process of calculation. The first couple (qx and qy) corresponds to two substitutions X=xqx and Y=yqy which are used in the approximation. Parameters ex and ey are used in substitutions X=exp(ex*x) and Y=exp(ey*y). If input for any parameter is equal to 0, then this parameter is calculated as the value delivering the minimum of residual sum of squares. Otherwise the selected value of this parameter is fixed in the calculation. In particular, if qx=0, qy=0, ex=0, ey=0 then all these parameters are considered as variables in the following domains [0.1, 2] for qx, qy and [-1, 1] for ex, ey.
Values of these parameters can be changed on this page and you can proceed to another calculation for the same input data just by clicking the 'Calculate' button. The calculation takes several seconds.