87110e5d-4134-472d-b7d2-e68f2d8fa6bc 17 6 9 decimal

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

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 11 0.2978 11.5 0.2755 12 0.2546 12.5 0.2354 13 0.2176 13.5 0.2012 14 0.186 14.5 0.172 15 0.159 15.5 0.147 16 0.1359 16.5 0.1256 17 0.1162 17.5 0.1074 18 0.0993 18.5 0.0918 19 0.0849 19.5 0.0785 20 0.0726 192 mat :

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

Model function

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

x β φ x β f 3 φ :

<= ConjugateGradient Vector Fnct

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

β 0.0001376 1.67547 6.36715 31 mat :

0.1 - 1531 mat

β length 3

re-inject to iterate manually

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

FIT range, populate U 1021 10.01 range : i 1 U rows range FIT i el U i el β f eval : for U FIT augment 41 line :

β 0.00013756 1.675475195 6.367153135 31 mat

Collect initial & successive 'β' β # # # # # 15 mat ≡

β 0.0001376 1.67547 6.36715 31 mat :

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 :

data X Y . 12 black plotG :

data FIT 2 1 sys

Relative residuals

Residuals Error Residuals 2 1 sys

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

β SSD 0.000000024

RMS difference β SSD n / sqrt 0.000035

Lifetime of  decay τ 1 β 2 el / abs : 0.6