plotG(vx,vy,char,size,color)

b0444fd7-e9ab-403b-a1ef-8b08819dc42b 8 4 5 decimal

&[DATE] &[TIME] - &[FILENAME]

Both optimiz NONE ... construct/export continued fraction

Thiele on length of support points 'j' j K X x Cfr N j 1 + el K j 1 + el : c j el N j el : a j el K j el : jj j 1 - (0 range c jj el a jj 1 + el : a jj el K jj el x X jj el - c jj el / + : 21 line for a 1 el 51 line :

symbolic expansion of Thiele 'Cfr' algo style 6 K X x Cfr K 1 el x X 1 el - K 2 el x X 2 el - K 3 el x X 3 el - K 4 el x X 4 el - K 5 el x X 5 el - K 6 el / + / + / + / + / +

https://en.wikipedia.org/wiki/Thorvald_N._Thiele

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plotG(vx,vy,char,size,color)

vx vy char size color plotG n vx length : plot vx 1 el vy 1 el char size color augment : i 2 n range plot plot vx i el vy i el char size color augment stack : for plot 41 line :

The best I could do
before applying 'ksmoth'
Turquoise  ... ► 
 ▼  recovered from 'ksmooth' DATA 0.25 0.024 0.00025 0.2867 0.031 0.000424 0.333 0.041 0.000762 0.4 0.056 0.0016 0.5 0.08 0.0035 0.667 0.116 0.0083 63 mat :

0.25 0.0003146 0.2867 0.0004373 0.333 0.0007311 0.4 0.0015377 0.5 0.003491 0.667 0.0083 62 mat

DATA 0.25 0.0003146 0.2867 0.0004373 0.333 0.0007311 0.4 0.0015377 0.5 0.003491 0.667 0.0083 62 mat :

XY DATA 1 col DATA 2 col augment :

length Thiele j XY rows : 6

X Y Δ Thiele ε 1018 -^: n X rows : i 1 n range M i 1 el Y i el : for j 2 n range i j n range dM M i j 1 - el M j 1 - j 1 - el - : dM dM abs ε < ε M i j el X i el X j 1 - el - dM / : if : 21 line for for i 1 n range c i 1 el X i el : c i 2 el M i i el : 21 line for Δ 0 ≡ c M if 61 line :

Thiele on length of support points 'j' K X x Cfr N j 1 + el K j 1 + el : c j el N j el : a j el K j el : jj j 1 - (0 range c jj el a jj 1 + el : a jj el K jj el x X jj el - c jj el / + : 21 line for a 1 el 51 line :

symbolic expansion of Thiele  algo style K X x Cfr K 1 el x X 1 el - K 2 el x X 2 el - K 3 el x X 3 el - K 4 el x X 4 el - K 5 el x X 5 el - K 6 el / + / + / + / + / +

recast the Cf on the system  [K,X,x] x Cf K X x Cfr :

support points X XY 1 col : Y XY 2 col : 21 sys

Thiele K's coefficients
@ support points X X Y 0 Thiele 0.25 0.0003146 0.2867 299.103504482478 0.333 0.000463817280381 - 0.4 375.899988395261 - 0.5 0.002245387732925 0.667 91.7082923240027 62 mat

Thiele K's continued fraction K X Y 0 Thiele 2 col :

K K 9 round vectorize :

X XY 1 col : Y XY 2 col : 12 mat support X Y . 14 black plotG : 21 line

Thiele x 0.25 1 0.251 range : i 1 x rows range v i el x i el Cf eval : for x v augment 31 line :

Experimental projects should be collected 'raw' transmitted as such ... NO processing. The measuring devices must be at least of 10 times greater accuracy than the neasured.

at this point, you can safely 'ainterp' Thiele ...

support Thiele 2 1 sys

The Smath Gaussian 'ksmmooth'

t0 1 time :

ksmooth # plotG

data char size clr plot k 1 data rows range r3 k el char : r4 k el size : r5 k el clr : 13 mat for data r3 r4 r5 augment 21 line :

σ 0.3708158988058244 :

The Gaussian ksmooth

d K 12 π * sqrt σ * / d 2^2 σ 2^* / - exp * :

Smath recognises the silent 'bw', something
like the Mathcad "global definition". j X Y Ksmooth X i el X j el - bw / K Y i el * (i 1 X rows sum X i el X j el - bw / K (i 1 X rows sum / :

Gaussian Ksmooth Kernel

x K

X Y bw 13 mat

W j 1 X rows range s j el j X Y Ksmooth eval : for s 21 line :

W 11 mat

DATA 0.25 0.024 0.00025 0.2867 0.031 0.000424 0.333 0.041 0.000762 0.4 0.056 0.0016 0.5 0.08 0.0035 0.667 0.116 0.0083 63 mat :

XY DATA 1 col DATA 3 col augment :

Prepare and code the Smath project

X XY 1 col : Y XY 2 col : 21 line

bw 0.0825 : (bandwidth ≡ W W : (isolate W ≡ XW X W augment : 31 line

W 11 mat

XW 0.25 0.0003146 0.2867 0.0004373 0.333 0.0007311 0.4 0.0015377 0.5 0.003491 0.667 0.0083 62 mat

The working path: collect & return [X,Y]=>[bw]=>[Ksmooth(j,X,Y,bw)]=>[W]=>[XW]

XW XW o 7 red plot : raw XY . 9 black plot : 21 line

===== Finish/collect the project =====

spline join/mesh the smoothed data set Cfit t 0.25 1 0.256 range : i 1 t rows range v i el X W t i el cinterp eval : for t v augment 31 line :

collect plot plot Cfit raw XW 31 sys :

1 time t0 - 1 s *

plot