<p> Genfit Utilities </p>

d5d18636-56ae-4475-a911-5c8594dff199 17 6 9 decimal

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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 41 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 minimize 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 init 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 LS Φ M transpose M * : d M transpose Y vx - (* : Δβ Φ 1 -^eval d * : b β Δβ + : 151 line :

Alt+0126 data n ~ data n col :

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 :

Samples expected exact 15 D XY 011 0.840896415253715 203 1.18920711500272 - 42 - 5 1.68179283050743 - 607 2.37841423000544 849 3.36358566101486 100112 mat :

x β f β 1 el x * exp β 2 el x * β 3 el + sin * :

Model function

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

x β φ x β f 3 φ :

<= Gradient Vector Function

X XY 1 col : Y XY 2 col : 21 line

β 0.17328679514 π 4 / π 2 / 31 mat :

0.15 π 4 / π 2 / 31 mat

<= ..... initial β ........ .... iterate manually ..... <= <= re-inject the last 'β'

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

re-inject to iterate manually

β 0.17328679514 0.785398163397 1.570796326795 31 mat

data X Y . 12 black plotG :

data x β f β 1 el x * exp β 1 el x * exp - 4 1 sys

Notes on the fitting session: 1. The phase shift β3 is π/2. 2. We try β2 magnitude π/4 3. If we are correct, only the exponential growth β1 need be found. This will arise when the Δ's will equate 0 Have we done right ? YES => exact fit !

Δ π 4 / β 2 el - π 2 / β 3 el - 21 mat : 0 3.8 1016 -^* 21 mat

9 β f 3.36358566101485

data x β f β 1 el x * exp β 1 el x * exp - 4 1 sys