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

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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 41 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 :

Bar plot unicolor style, bar width user. data dt BarSize v data 2 col : t v bar t dt - 0 t dt - v t dt + v t dt + 042 mat : j 1 data rows range j 1 ≡ B data j 1 el data j 2 el bar : B B data j 1 el data j 2 el bar stack : if 11 line for B 41 line :

XY 0.1 0.02 0.2 0.08 0.3 0.16 0.4 0.26 0.5 0.37 0.6 0.48 0.7 0.62 0.8 0.76 0.9 0.82 1 1.09 102 mat :

user adjust around  4.5
given data set is freaked
thus unreliable for fit x β f β 1 el x 4.5 / sin (β 2 el^* :

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

<= Gradient Vector Function x β φ x β f 2 φ :

X XY 1 col : Y XY 2 col : data X Y o 5 black plotG : 31 line

β 8.5 1.5 21 mat :

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

re-inject to iterate manually

Collect initial & successive 'β' β x 4.5 / sin 8.5 1.5 21 mat 21 mat 10.9646 1.5639 21 mat # # # # 16 mat ≡

range/populate L 0 : H 1.25 : N 99 : 13 mat U L H N xd : 21 line

β 10.9646 1.5639 21 mat

<= recast the scalar model x fit x β f :

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

Absolute residuals α Residuals i 1 Y rows range Δ i el Y i el X i el fit - eval : for X α Δ * augment 21 line :

data FIT 2 Residuals 0.01 BarSize 3 1 sys

0.0 β f 0.2 β f 21 mat 0 0.08 21 mat

For cnvenience => we affect the residuals with a zoom factor 'α'

n Y rows :

SSD = "Sum Square Differences" SSD Y i el X i el fit - (2^(i 1 n sum :

very excellent SSD SSD 0.009

unary sine hysterisis model t f 1 t 4 sqrt * 8 / sin (3^* :

plot x f x c * 1 x 4 / sin (2^* x c * 1 x 4 / sin (4^* x c * 1 x 4 / sin (0.25^* x c * 41 sys :

x c 10 x ≤ (x 2 π * ≤ (& cases :

plot 1 1 sys

There are limitless hysteresis models. This one is the simplest for demo and possible applications.