= FitUtil =

== Overview ==
`FitUtil` is a Dyalog Unicode Workspace (v16) that contains useful functions related to curve fitting. The regressions performed are:
{{{
 1. Linear:      Y' = a + b×X
 2. Exponential: Y' = a × exp(b×X)
 3. Power:       Y' = a × X*b
 4. Logarithmic: Y' = a + b×ln(X)
 5. Parabolic:   Y' = a + b×X + c×X*2
 6. Cubic:       Y' = a + b×X + c×X*2 + d×X*3
 7. Linear through origin:    Y' = 0 + b×X
 8. Parabolic through origin: Y' = 0 + b×X + c×X*2
 9. Cubic through origin:     Y' = 0 + b×X + c×X*2 + d×X*3
10. Weibull:                  Y' = a × exp(b×X*c)
}}}

The first 9 curve fittings are a least square fit using the APL's domino operator (`⌹`). The Weibull regression is obtained by iterations and may not converge to a solution all the time. The main functions are `FIT` and `TFIT`.  Both will perform 10 different curve fittings on a set of X and Y values. The function `TFIT` will removed the non significant points by performing a Student test on the data.

The results are stored in a global nested variable called `∆FIT` or `∆TFIT` depending of the main function used. `FIT` and `TFIT` will present the results of the curve fittings in the APL session, the function SHOW will present them graphically using the variables `∆FIT` or `∆TFIT`. It uses WPF and the Syncfusion libraries.

The usage of the functions is as follow:
{{{
      x FIT y    ⍝ Normal regression

      x TFIT y   ⍝ Will remove the non significant points before performing the regressions

}}}
For example for the following values of X1 and Y1:
{{{
      X1
0.5497 0.817 0.999 1.19 2.78 5.53 10.21 16.59 22.56 99.7 200 1000 1500 5000
      Y1
19.191 17.672 17.063 16.613 14.602 13.25 12.418 11.859 11.512 9.75 9.008 7.309 6.836 5.765
}}}
The following is written in the session:
{{{
      X1 FIT Y1

------------------------------------------------------------------------------------------
CALCULATION OF THE CORRELATION'S COEFFICIENTS
------------------------------------------------------------------------------------------
1. LINEAR:          Y' = 13.454 + ¯0.0019732×X   (r² = 0.388)


2. EXPONENTIAL:     Y' = 12.989 × exp(¯0.00020156×X)   (r² = 0.522)


3. POWER:           Y' = 17.034 × X*¯0.12515   (r² = 0.996)


4. LOGARITHMIC:     Y' = 16.631 + ¯1.3954×ln(X)   (r² = 0.963)


5. PARABOLIC:       Y' = 14.235 + ¯0.0077116×X + 0.0000012078×X*2   (r² = 0.599)


6. CUBIC:           Regression not possible


7. LINEAR @(0,0):    Y' = 0 + 0.0017639×X   (r² = 0.000)


8. PARABOLIC @(0,0): Y' = 0 + 0.096933×X + ¯0.000020817×X*2   (r² = 0.000)


9. CUBIC @(0,0):     Y' = 0 + 0.46267×X + ¯0.00044524×X*2 + 7.0616E¯8×X*3   (r² = 0.000)


10.WEIBULL:          Y' = 0.34555 × exp(3.9069 × X*¯0.036282)   (r² = 0.996)


------------------------------------------------------------------------------------------
THE BEST REGRESSION IS No 3: POWER
------------------------------------------------------------------------------------------
}}}
With the following WPF Window will be showing the results graphically:
{{attachment:FIT.png || width=1220}}

To remove the non significant points before doing the regressions:
{{{
      X1 TFIT Y1

------------------------------------------------------------------------------------------
    SAME REGRESSIONS WITH THE NON SIGNIFICANT POINT(S) REMOVED:
------------------------------------------------------------------------------------------
1. LINEAR:          Y' = 12.746 + ¯0.0013976×X   (r² = 0.871)
   The Following Points were Removed: 1 2 3 4 10 11 12 13


2. EXPONENTIAL:     Y' = 12.706 × exp(¯0.00015817×X)   (r² = 0.936)
   The Following Points were Removed: 1 2 3 4 10 11 12 13


3. POWER:           Y' = 17.09 × X*¯0.12548   (r² = 0.999)
   The Following Points were Removed: 1 5 6 7 11


4. LOGARITHMIC:     Y' = 16.703 + ¯1.3586×ln(X)   (r² = 0.990)
   The Following Points were Removed: 1 2 5 6 7 8 9


5. PARABOLIC:       Y' = 13.39 + ¯0.0061933×X + 9.3462E¯7×X*2   (r² = 0.953)
   The Following Points were Removed: 1 2 3 4 8 9 10 11


6. CUBIC:           Regression Not possible


7. LINEAR @(0,0):    Y' = 0 + 0.0016421×X   (r² = 0.000)
   The Following Points were Removed: 1 2 3 4 5 6 7 8 9 10 11


8. PARABOLIC @(0,0): Y' = 0 + 0.4465×X + ¯0.000089216×X*2   (r² = 0.000)
   The Following Points were Removed: 12 13


9. CUBIC @(0,0):     Y' = 0 + 8.3272×X + ¯0.40538×X*2 + 0.000080744×X*3   (r² = 0.000)
   The Following Points were Removed: 10 11 12 13


10.WEIBULL:          Y' = 0.025474 × exp(6.5082 × X*¯0.020864)   (r² = 0.999)
   The Following Points were Removed: 1 5 6 9 10 11


------------------------------------------------------------------------------------------
THE BEST REGRESSION IS No 10: WEIBULL
------------------------------------------------------------------------------------------
}}}
With the following WPF Window will be showing the results graphically:
{{attachment:TFIT.png || width=1220}}

This Workspace is also a demonstration of how to:
 1. Build a WPF program.
 1. Use Syncfusion's !SfChart to show the Plots.
 1. How to bind a !DataSet created from APL data.
 1. Customize the Look of the Tabs.
 1. Capture a screen and save it to disk.
 1. Capture a screen and print it.


== How to download FitUtil ==

 1. Download [[attachment:FitUtilv16.dws]] (Dyalog Unicode v16)

== Version Information ==
{{{
February 2016   - Initial version (1.0)
October 2017    - Bug in Xaml fixed
}}}

== Version Information ==
||Original author: ||Pierre Gilbert ||
||Responsible: ||PierreGilbert ||
||Email: || <<MailTo(apgil AT SPAMFREE videotron DOT ca)>> ||

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CategoryDyalog - CategoryDyalogDotNet - CategoryDyalogWpfUtilities - CategoryDotNet