<content> ksmooth # plotG </content>

4a4abc96-5c50-4fcd-9391-50ebe264f33e 37 4 5 false false 0 0 decimal

&[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 * :

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 :

Gaussian Ksmooth Kernel

x K

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

<content> linfit modules </content>

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 :

Applicable parts are: Optimiz "numeric" XY f φ β βlinfit X XY 1 col : Y XY 2 col : n XY rows : k x β φ length 1 - : vx raw initial vector fit i 1 X length range vx i el X i el β f eval : for M-> Cholesky Gradient Matrix j 1 k range i 1 n range M i j el X i el β φ j 1 + el eval : for for Cholesky solver [LS] Φ M transpose M * : d M transpose Y vx - (* : Δβ Φ 1 -^eval d * : b β Δβ + : 131 line :

Vector gradient ... Optimiz Symbolic x β f n φ ct 1 : i 1 n range PD ct el x β f (β ct el diff : stack f(x,β) & PD V 1 el x β f : V i 1 + el PD i el : 21 line ct ct 1 + : 41 line for V 31 line :

set N = even/odd to escape divide
by 0 maybe other singularities.

L H N xd U 0 : dx H L - N / : i 1 N 1 + range U i el L dx - (dx i * + : for U 41 line :

XY 02116121212209932120421135209862067720718207092056102083112090122072132064142081152074162054172056182058192061202 mat :

The Gaussian ksmooth

X XY 1 col : Y XY 2 col : Yo XY 2 col : 31 line

bw 6 : bandwidth ≡ XW X W augment : vx X : vy XW 2 col : 41 line

XW 0 2113.3 1 2111.7 2 2109.2 3 2105.2 4 2099.4 5 2092.1 6 2084.7 7 2078.6 8 2075.1 9 2073.9 10 2074.1 11 2074.4 12207413 2072.5 14 2070.1 15 2067.2 16 2064.4 17206218 2060.5 19 2059.6 202 mat

XW vx vy o 6 black plotG : XY X Yo + 7 black plotG : 21 line

===== Finish/collect the ksmooth =====

spline join/mesh the smoothed data set Cfit t 0201 range : i 1 t rows range v i el vx vy t i el cinterp eval : for t v augment 31 line :

collect plot plot XY Cfit XW 31 sys :

plot

XY 02116121212209932120421135209862067720718207092056102083112090122072132064142081152074162054172056182058192061202 mat :

Fit a model function to "raw corn Thermies"

X XY 1 col : Y XY 2 col : 12 mat data X Y . 4 black plotG : 21 line

Model function compatible for the 'linfit' ... x β f β 1 el β 2 el x - β 3 el / exp * + :

x β φ x β f 3 φ :

Manual iterative 'linfit'
The auto-iterative Genfit not
offered but easier, suffers
same difficult 'β' initials

β 2053.8627 69.7619 8.0527 31 mat :

β XY f φ β βlinfit :

β 2053.73812 70.002057 8.049043 31 mat

200070531 mat 2056.5192 65.8728 7.1785 31 mat 2053.8627 69.7619 8.0527 31 mat 2053.7381 70.0021 8.049 31 mat # 15 mat

Levenberg-Marquardtfrom OriginLab yo 2053.74 : A 70.0025 : t1 8.0493 : 31 sys

selected for themain document EXPORT x Decay yo A x - t1 / exp * + :

L t 020 0.1 range : i 1 t rows range u i el t i el : v i el t i el Decay eval : 21 line for u v augment 31 line :

plot XY Cfit x Decay data XW 51 sys :

plot

x D x Decay x diff :

x D2 x Decay x 2 diff :

x ∫ ω Decay ω x - x int :

more scalar maths suite

u 6 :

in-siyu command-line track 0 u D u u D u 032 mat :

x D track 2 1 sys

u u D 12 mat 6 4.127 - 12 mat

u 16 :

in-siyu command-line track 0 u ∫ u u ∫ u 032 mat :

Thermies 1 :

x ∫ track 2 1 sys

click to see ... ■ empty place holder 9 ∫ 14 ∫ 19 ∫ 31 sys 38507606148395931 sys

u u ∫ 12 mat 166975512 mat

result appended of user unit ... 9 ∫ 14 ∫ 19 ∫ 31 sys Thermies 38507606148395931 sys

In this example, Thermies is unary.
Make it @ will appended result .

ωx Cfit 1 col : ωy Cfit 2 col : 12 mat x spline ωx ωy x cinterp : 21 sys

u 6.5 :

in-situ command-line track 0 u spline u u spline u 032 mat :

XW x spline track 3 1 sys

u u spline 12 mat 6.5 2081.4 12 mat

XW 0 2113.3 1 2111.7 2 2109.2 3 2105.2 4 2099.4 5 2092.1 6 2084.7 7 2078.6 8 2075.1 9 2073.9 10 2074.1 11 2074.4 12207413 2072.5 14 2070.1 15 2067.2 16 2064.4 17206218 2060.5 19 2059.6 202 mat ≡

jmG: 20231120