<p> Genfit Utilities </p>

909fc023-c157-4a1b-88aa-9dfef5a56f84 15 4 5 decimal

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vx vy char size clr plotG n vx length : plot vx 1 el vy 1 el char size clr augment : i 2 n range plot plot vx i el vy i el char size clr augment stack : for plot 41 line :

Error stem plot for QuickPlot unicolor data Error stemX 1 data rows range : i 1 stemX rows range stem i el data i 1 el data i 2 el data i 1 el 022 mat : for i 1 stem rows 1 - range stem i el stem i el stem i 1 + (1 el 1 el 012 mat stack : for V stem 1 el : j 2 stem rows 1 - range V V stem j el stack : for V V data data rows row stack : 71 line :

Applicable parts are: Optimiz "numeric" XY f φ β Minimize 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 :

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].

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 0.25 37.8 0.3 40 0.35 41.9 0.4 43.4 0.45 44.7 0.5 45.8 0.55 46.7 0.6 47.5 0.65 48.3 0.7 48.9 0.75 49.5 0.8 50 0.85 50.5 0.9 51 0.95 51.3 1 51.7 1.05 52 1.1 52.4 1.15 52.6 1.2 52.9 1.25 53.1 1.31 53.4 1.36 53.6 232 mat :

<= Model function x β f 0 β 1 el 1 β 3 el β 2 el x * - exp * - (* + :

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

<= ConjugateGradient Vector Fnct x β φ x β f 3 φ :

X XY 1 col : Y XY 2 col : n XY rows : 31 line

β 54.41055 2.443014 0.550449 31 mat :

1rst iterate 523 0.75 31 mat

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

re-inject to iterate manually

FIT range, populate U 0 1.5 0.01 range : i 1 U rows range FIT i el U i el β f eval : for U FIT augment 41 line :

β 54.425024 2.443162 0.550061 31 mat

data X Y . 12 black plotG :

data FIT 2 1 sys

Relative residuals Residuals i 1 XY rows range Δ i el 1 Y i el X i el β f / - eval : for X Δ augment 21 line :

Residuals Error

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

β SSD 0.634