<p> ListCollect </p>

bfdaf8c0-0cfe-4433-9389-1aba2fc4739d 4 6 12 decimal

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

data list ListCollect collects index list select list : ct 1 : i select a ct el data i 1 el : b ct el data i 2 el : ct ct 1 + : 31 line for a b augment 51 line :

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 304 0.1653 - 5 0.1313 6 0.219 7 0.8097 8 1.2045 9 1.302 10 2.1009 11 2.6004 12 3.7002 13 4.3001 112 mat :

1. selct the support points
2. collect for al_nleqsolve list 13791115 mat : xy XY list ListCollect : 21 sys

raw XY o 5 red plot : support xy + 20 blue plot : 21 line

raw support 2 1 sys

xy 305 0.131 9 1.302 11 2.6 13 4.3 52 mat

x xy 1 col : y xy 2 col : 21 sys

vector of guesses ... NOT easy ! X0 0.01 1 1.5 0515 mat transpose :

AlgLib Solver for a system of nonlinear equations(Uni) sol k 1 α f rows range u k el α k el : for α Jac u f u Jacobian : StepMax 0 : ε 109 -^: 12 mat u X0 StepMax ε α f α Jac al_nleqsolve : 41 line :

Model function.
Specific for the
flat low region. x α Φ α 1 el x * 1 x α 5 el - α 3 el / exp + ln (α 2 el^(* α 4 el + :

0.005 0.007 - 0.006 0.005 - 0.001 51 mat

Implicit equalities = 0 α f x 1 el α Φ y 1 el - x 2 el α Φ y 2 el - x 3 el α Φ y 3 el - x 4 el α Φ y 4 el - x 5 el α Φ y 5 el - 51 mat :

α sol : 0.10919 0.85833 1.61119 0.03206 - 7.12811 51 mat

Notes . . . Smath 6179

1. solves a system of [n equalities = n parameters.

2. The order of equalities is immaterial.

3. Guess wisely the best support equalities !

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The support points X XY 1 col : Y XY 2 col : 12 mat data XY o 5 black plot : 21 sys

sanity 0 α Φ 1 α Φ 2 α Φ 3 α Φ 41 mat : 0.032 - 0.028 - 0.018 - 0.003 41 mat

α f 0.003 0.005 - 0.005 0.005 - 0.001 51 mat

x c 10 x ≤ (x 15 ≤ (& cases :

optimize a bit 
to suit Φ(0,α)= 0 bias sanity sum 4 / : 0.019 -

user adjust '0' flat region bias 0.03206 - :

data x α Φ x c * bias - support 3 1 sys

Support points xy 305 0.131 9 1.302 11 2.6 13 4.3 52 mat

Conclusion . . .

The experimental model function is very

reactive. Attempting a refit from

Genfit Minimize is NOT convergent

and limited iter = 3.

al_nleqsove is a better choice.

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0 α Φ bias - 0

X 0 :

sanity flat '0' X α Φ X c * bias - 0.000002 -