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

089c4c3f-4f18-4a19-9353-3c5192f21097 9 6 5 fraction

&[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 : 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 :

XY 0.1 10 0.2 5 0.3 3.333 0.4 2.5 0.5 2 0.6 1.667 0.7 1.429 0.8 1.25 0.9 1.111 112 0.5 3 0.333 4 0.25 5 0.2 142 mat :

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

<= 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 :

β 110141 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

In Mathcad 11 & earlier SSE = Sum Square Error Type E= after a Mineer fit

Range & populate the discrete fit

L 0.05 :

H 10 :

N 99 :

U L H N xd :

Collect initial & successive 'β'

β 0.0001 - 1.0002 6.4223 105 -^* - 4.5597 106 -^* 41 mat

β 110141 mat 0.0001 - 1.0002 6.4223 105 -^* - 4.5597 106 -^* 41 mat # # # 15 mat ≡

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

MyFit U FIT augment :

data X Y . 12 black plotG :

0.05 β f 20.0146

data MyFit 2 1 sys

This is just an exercise. Simplify the coefficients, export the function that sampled the data set ... 1/x

β 0.0001 - 1.0002 6.4223 105 -^* - 4.5597 106 -^* 41 mat :

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

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