<p> ksmooth # plotG </p>

9688a259-8ebd-4796-8805-bd6343023ed0 3 4 5 decimal

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

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 :

XY 18 10.982 - 39 10.013 - 4910 - 65 10.123 - 82 11.937 - 99 13.156 - 114 14.948 - 130 17.081 - 146 19.974 - 164 25.216 - 179 28.897 - 195 33.036 - 212 38.595 - 132 mat :

xy XY o 5 black plot :

x f XY 1 col XY 2 col x ainterp :

x λ 10 x ≤ (x 240 ≤ (& cases :

smoothed XY 18 10.982 - 39 10.013 - 4910 - 65 10.123 - 82 11.937 - 99 13.156 - 114 14.948 - 130 17.081 - 146 19.974 - 164 25.216 - 179 28.897 - 195 33.036 - 212 38.595 - 132 mat

raw XY 1811 - 3910 - 4910 - 6510 - 8212 - 9913 - 11415 - 13017 - 14620 - 16425 - 17929 - 19533 - 21239 - 132 mat

xy x f x λ * 2 1 sys

Tracer 15 ± 1 pixel

The Smath Gaussian 'ksmmooth'

t0 1 time :

<p> ksmooth # plotG </p>

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

Prepare and code the Smath project

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

bw 20 : (bandwidth ≡ W W : (isolate W ≡ XW X W augment : 31 line

W 11 mat

XW 18 10.965 - 39 10.022 - 49 10.012 - 65 10.225 - 82 11.9 - 99 13.276 - 114 14.929 - 130 17.143 - 146 19.968 - 164 25.386 - 179 28.838 - 195 33.033 - 212 38.22 - 132 mat