3f4e3c49-62ef-4555-bdee-a835525680ca 10 6 5 auto

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

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 :

σ 0.3708158988058244 :

The Gaussian "Ksmooth"

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

This is the Gaussian "Ksmooth" kernel found in many CAS tool box. You may want to customise 'σ'.. no use for. The bandwidth 'bw' does it indirectly. The symbolic expansion of "Ksmooth" is huge out of imagination. Better not try or on few points [3]. Parameter 'bw' is the only smoothing governor, bw = σ works well for this demo, but will be user/data adapted. The data set in demo is peanut. On much longer ones, Smath pedals for a while. Observe that we help rctifying the Y's ordinates by constraining two points.

Gaussian Ksmooth Kernel

x K

XY 0.175 317.303 0.35 195.232 0.525 124.387 0.7 43.733 0.875 40.463 1.05 55.722 1.225 90.599 1.4 115.668 1.575 184.332 1.75 140.736 1.925 100.409 2.1 57.902 2.275 42.643 2.45 58.992 2.625 98.229 2.8 206.131 2.975 316.212 3.15 345.64 3.325 284.605 3.5 235.559 3.675 90.599 3.85 35.014 4.025 36.104 4.2 11.035 242 mat :

Xo XY 1 col :

X XY 1 col :

Yo XY 2 col :

Y XY 2 col :

n X rows :

n 24

bw σ :

j X Y Ksmooth μ j 11 line : X i el X μ el - bw / K Y i el * (i 1 X rows sum X i el X μ el - bw / K (i 1 X rows sum / 21 line :

Y 9 el 230 :

Y 19 el 350 :

W j 1 X rows range s j el j X Y Ksmooth eval : constrain 1rst node s 1 el Y 1 el : 31 line for s 21 line :

XW X W augment :

vx X :

vy XW 2 col :

XW XW 1 col XW 2 col o 7 red plotG :

XY X Yo + 7 black plotG :

t 0.175 4.2 0.180 range :

t rows 805

Cfit i 1 t rows range u i el t i el : v i el vx vy t i el cinterp eval : 21 line for u v augment 21 line :

Ksmooth cspline populated

Cfit XW XY 3 1 sys