Fitting custom functions to data - charts

Question

I have a series of data, for example:
0.767838478
0.702426493
0.733858228
0.703275979
0.651456058
0.62427187
0.742353261
0.646359026
0.695630431
0.659101665
0.598786652
0.592840135
0.59199059
which I know fits best to an equation of the form:
y=ae^(b*x)+c
How can I fit the custom function to this data?
Similar question had been already asked on LibreOffice forum without a proper answer. I would appreciate if you could help me know how to do this. Preferably answers applying to any custom function rather than workarounds to this specific case.

Answer 1

There are multiple possible solutions for this. But one approach would be the following:
For determining the aand b in the trend line function y = a*e^(b*x) there are solutions using native Calc functions (LINEST, EXP, LN).
So we could the y = a*e^(b*x)+c taking as y-c= a*e^(b*x) and so if we are knowing c, the solution for y = a*e^(b*x) could be taken too. How to know c? One approach is described in Exponential Curve Fitting. There approximation of b, a and then c are made.
I have the main part of the delphi code from Exponential Curve Fitting : source listing translated to StarBasic for Calc. The part of the fine tuning of c is not translated until now. To-Do for you as professional and enthusiast programmers.
Example:
Data:
x y
0 0.767838478
1 0.702426493
2 0.733858228
3 0.703275979
4 0.651456058
5 0.62427187
6 0.742353261
7 0.646359026
8 0.695630431
9 0.659101665
10 0.598786652
11 0.592840135
12 0.59199059
Formulas:
B17: =EXP(INDEX(LINEST(LN($B$2:$B$14),$A$2:$A$14),1,2))
C17: =INDEX(LINEST(LN($B$2:$B$14),$A$2:$A$14),1,1)
y = a*e^(b*x) is also the function used for the chart's trend line calculation.
B19: =INDEX(TRENDEXPPLUSC($B$2:$B$14,$A$2:$A$14),1,1)
C19: =INDEX(TRENDEXPPLUSC($B$2:$B$14,$A$2:$A$14),1,2)
D19: =INDEX(TRENDEXPPLUSC($B$2:$B$14,$A$2:$A$14),1,3)
Code:
function trendExpPlusC(rangey as variant, rangex as variant) as variant
'get values from ranges
redim x(ubound(rangex)-1) as double
redim y(ubound(rangex)-1) as double
for i = lbound(x) to ubound(x)
x(i) = rangex(i+1,1)
y(i) = rangey(i+1,1)
next
'make helper arrays
redim dx(ubound(x)-1) as double
redim dy(ubound(x)-1) as double
redim dxyx(ubound(x)-1) as double
redim dxyy(ubound(x)-1) as double
for i = lbound(x) to ubound(x)-1
dx(i) = x(i+1) - x(i)
dy(i) = y(i+1) - y(i)
dxyx(i) = (x(i+1) + x(i))/2
dxyy(i) = dy(i) / dx(i)
next
'approximate b
s = 0
errcnt = 0
for i = lbound(dxyx) to ubound(dxyx)-1
on error goto errorhandler
s = s + log(abs(dxyy(i+1) / dxyy(i))) / (dxyx(i+1) - dxyx(i))
on error goto 0
next
b = s / (ubound(dxyx) - errcnt)
'approximate a
s = 0
errcnt = 0
for i = lbound(dx) to ubound(dx)
on error goto errorhandler
s = s + dy(i) / (exp(b * x(i+1)) - exp(b * x(i)))
on error goto 0
next
a = s / (ubound(dx) + 1 - errcnt)
'approximate c
s = 0
errcnt = 0
for i = lbound(x) to ubound(x)
on error goto errorhandler
s = s + y(i) - a * exp(b * x(i))
on error goto 0
next
c = s / (ubound(x) + 1 - errcnt)
'make y for (y - c) = a*e^(b*x)
for i = lbound(x) to ubound(x)
y(i) = log(abs(y(i) - c))
next
'get a and b from LINEST for (y - c) = a*e^(b*x)
oFunctionAccess = createUnoService( "com.sun.star.sheet.FunctionAccess" )
args = array(array(y), array(x))
ab = oFunctionAccess.CallFunction("LINEST", args)
if a < 0 then a = -exp(ab(0)(1)) else a = exp(ab(0)(1))
b = ab(0)(0)
trendExpPlusC = array(a, b, c)
exit function
errorhandler:
errcnt = errcnt + 1
resume next
end function

Answer 2

The formula y = beax is the exponential regression equation for LibreOffice chart trend lines.

Answer 3

LibreOffice exports all settings
All the settings of LibreOffice, all in the LibreOffice folder.
C:\Users\a←When installing the operating system, the name
entered.\AppData←File Manager ~ "Hidden project" to open, the AppData
folder will be displayed.\Roaming\LibreOffice
Back up the LibreOffice folder, when reinstalling, put the LibreOffice folder in its original place.
Note:
1. If the installation is preview edition, because the name of preview edition is LibreOfficeDev, so the LibreOfficeDev folder will be
displayed.
2. Formal edition can be installed together with preview edition, if both formal edition and preview edition are installed, LibreOffice
folder and LibreOfficeDev folder will be displayed.
3. To clear all settings, just delete the LibreOffice folder, then open the program, a new LibreOffice folder will be created.
LibreOffice exports a single toolbar I made
Common path
C:\Users\a←When installing the operating system, the name
entered.\AppData←File Manager ~ "Hidden project" to open, the AppData
folder will be
displayed.\Roaming\LibreOffice\4\user\config\soffice.cfg\modules\Please
connect the branch path of the individual software below.
Branch path
\modules\StartModule\toolbar\The "Start" toolbar I made is placed here.
\modules\swriter\toolbar\The "writer" toolbar I made is placed here.
\modules\scalc\toolbar\The "calc" toolbar I made is placed here.
\modules\simpress\toolbar\The "impress" toolbar I made is placed here.
\modules\sdraw\toolbar\The "draw" toolbar I made is placed here.
\modules\smath\toolbar\The "math" toolbar I made is placed here.
\modules\dbapp\toolbar\The "base" toolbar I made is placed here.
Backup file, when reinstalling, put the file in the original place.
Note:
Because of the toolbar that I made myself, default file name, will automatically use Numbering, so to open the file, can know the name of
the toolbar.
The front file name "custom_toolbar_" cannot be changed, change will cause error, behind's file name can be changed. For example:
custom_toolbar_c01611ed.xml→custom_toolbar_AAA.xml.
Do well of toolbar, can be copied to other places to use. For example: In the "writer" Do well of toolbar, can be copied to "calc"
places to use.
LibreOffice self-made symbol toolbar
Step 1 Start "Recording Macros function" Tools\Options\Advanced\Enable macro recording（Tick）, in the
"Tools\Macros", the "Record Macro" option will appear.
Step 2 Recording Macros Tools\Macros\Record Macro→Recording action (click "Ω" to enter symbol→select symbol→Insert)→Stop
Recording→The name Macros stored in "Module1" is Main→Modify Main
name→Save.
Step 3 Add item new toolbar Tools\Customize\Toolbar→Add→Enter a name (example: symbol)→OK, the new toolbar will appear in the top
left.
Step 4 Will Macros Add item new toolbar Tools\Customize\Toolbar\Category\Macros\My
Macros\Standard\Module1\Main→Click "Main"→Add item→Modify→Rename (can
be named with symbol)→OK→OK.