<p> Genfit Functions ... plotG ... xd(L,H,N) </p>

b24146d4-45b1-47b2-b215-ad9fbf7418c1 21 4 5 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 :

L H N xd U 0 : dx H L - N / : i 1 N 1 + range U i el L dx - (dx i * + : for U 21 line 31 line :

Module xd(L,H,N) is a discretiser for use in-situ [user spec's]: range [L,H], density [N].

Applicable parts are: Optimiz "numeric" XY f φ β βNlin 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 GradientMatrix j 1 k range i 1 n range M i j el X i el β φ j 1 + el eval : for for CholeskySolver LeastSquares 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 :

Data 9.65 0.0082 24 0.129 62.63 3.223 104.46 14.377 134.79 25.853 157.76 35.06 176.25 42.31 191.48 48.06 207.58 53.78 229.92 61.1 254.22 68.23 278.83 74.6 302.02 79.88 324.42 84.4 347.02 88.43 371.3 92.2 162 mat :

...This fit results from 'data reduction Y/X, from which the model is developped and reconstructed Kir(x)... Kirby2(x)*x. The reduced Y/X looks weird to fit, OVNI model will digest. Observe this model 'pins' the fit to datum 0 ! Reference: Kirby, R., NIST (1979). Scanning electron microscope line width standards.

μ 3 :

x β f β 1 el x β 2 el^* β 3 el x β 4 el - (1 μ -^* - exp * x β 4 el - (μ -^* :

Model function

XY 9.65 0.00085 24 0.00538 62.63 0.0515 104.46 0.1376 134.79 0.1918 157.76 0.2222 176.25 0.2401 191.48 0.251 207.58 0.2591 229.92 0.2657 254.22 0.2684 278.83 0.2675 302.02 0.2645 324.42 0.2602 347.02 0.2548 371.3 0.2483 162 mat :

in φ(x,β,f,n) -> set 'n' to last index β # el ≡

x β φ x β f 4 φ :

<= Gradient Vector Function

X XY 1 col :

Y XY 2 col :

β 2672.58 1.6 54440.1 89.72 - 41 mat :

3000 1.5 5500090 - 41 mat

<= ..... initial β ........ .... iterate manually ..... <= <= re-inject the last 'β'

β length 4

Genfit coeff's of fit β XY f φ β βNlin :

re-inject to iterate manually

range/populate L 0 : H 500 : N 199 : U L H N xd : 41 line

β 2836.32 1.57 54333.71 89.33 - 41 mat

the recovered function x β f x * ≡

Collect initial & successive 'β'

FIT i 1 U rows range FIT i el U i el β f U i el * eval : for FIT 21 line :

β 3000 1.5 5500090 - 41 mat 2672.58 1.6 54440.1 89.72 - 41 mat 2836.32 1.57 54333.71 89.33 - 41 mat # # 15 mat ≡

MyFit U FIT augment :

data Data 1 col Data 2 col . 12 black plotG :

Title 19045 Transmute OVNI fit to Kirby2 12 black 15 mat :

data MyFit Title 3 1 sys XY

μ 3 :

β 2836.32 1.57 54333.71 89.33 - 41 mat :

Check the export  for enough decimals x β f x β 1 el x β 2 el^* β 3 el x β 4 el - (1 μ -^* - exp * x β 4 el - (μ -^* (* :

Resd i 1 Y rows range resd i el Y i el X i el β f X i el * eval - : for Y resd augment 21 line :

x β f data 2 1 sys