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

36009407-263d-46bf-a71a-cd9a2e0186bd 10 6 5 fraction

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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 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 : x β f x β f : x β φ x β φ transpose : 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 + : 151 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 :

These data are the result of a NIST study involving semiconductor electron mobility. The response variable is a measure of electron mobility, and the predictor variable is the natural log of the density. http://www.itl.nist.gov/div898/strd/nls/data/LINKS/i-thurber.shtml

XY 2.981 - 84.248 2.921 - 87.264 2.912 - 87.185 2.84 - 89.076 2.797 - 89.608 2.702 - 89.868 2.699 - 90.101 2.633 - 92.405 2.481 - 95.854 2.363 - 100.696 2.322 - 101.06 1.501 - 401.672 1.46 - 390.724 1.274 - 567.534 1.212 - 635.316 1.1 - 7330.54 1.046 - 759.087 0.915 - 894.206 0.714 - 990.785 0.566 - 1090 0.545 - 1080 0.4 - 1120 0.309 - 1180 0.109 - 1260 0.103 - 1270 0.01 1290 0.119 1330 0.377 1350 0.79 1420 0.963 1430 1.006 1420 1.115 1440 1.572 1460 1.841 1470 2.047 1450 2.2 1460362 mat :

Mathcad 11 Levenberg-Marquardt is more robust. NIST persits with a rational fraction, that must be rejected compared to SGompertz. Observe the two flat datum.

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

<= Model function

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 :

Project Note:: SGompertz is "infinitely reactive" In this document, the fit was done manually .

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

β 901375 1.6 1.25 - 41 mat :

Range & populate the discrete fit

L 8 - :

H 5 :

N 199 :

U L H N xd :

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

901375 1.6 1.25 - 41 mat

801400 1.5 1.25 - 41 mat

MyFit U FIT augment :

data X Y . 12 black plotG :

Title 0.5 1000 SGompertz fit Thurber 12 black 15 mat :

data MyFit Title 3 1 sys

β 901375 1.6 1.25 - 41 mat :

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

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

x β f data 2 1 sys