<p> Genfit modules </p>

10e91c16-197f-4769-bcf7-4351a187706f 50 3 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 :

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 :

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 :

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 :

Fit Lorentz multi-peak model

Lorentz model peak fit x β f β 1 el 2 β 2 el π / * β 4 el 4 x β 3 el - (2^* β 4 el (2^+ / * (+ 2 β 5 el π / * β 7 el 4 x β 6 el - (2^* β 7 el (2^+ / * (+ 2 β 8 el π / * β 10 el 4 x β 9 el - (2^* β 10 el (2^+ / * (+ :

XY 0.1 6.905 0.3 10.567 0.5 18.504 0.7 39.878 0.8 64.004 0.9 101.6 1 126.706 1.1 101.822 1.2 64.451 1.3 40.556 1.5 19.673 1.7 12.293 1.9 9.293 3 15.124 3.2 21.711 3.4 34.35 3.6 60.908 3.7 84.199 3.8 116.214 3.9 150.8 4 167.442 4.1 150.756 4.2 116.126 4.3 84.065 4.4 60.726 4.6 34.065 4.8 21.306 5 14.572 5.5 7.542 6 5.847 6.5 10.223 6.7 22.186 6.8 42.04 6.9 101.908 7 201.789 7.1 101.681 7.2 41.582 7.3 21.492 7.5 9.026 7.7 6.026 8 3.014 8.5 1.711 9 1.175 9.5 0.883 10 0.699 452 mat :

If you have spectroscopic/chromatographic sampled data, this Smath document may be profitable to your project. The Genfit Minimize(XY,f,φ,β)wrt SSD(β)is robust enough. The peak centers are first identified, then initialise to preserve the peaks.

MCD 11 0 78.54 1 0.4 157.08 4 0.6 62.832 7 0.2 101 mat

ConjugateGradient vector function x β φ x β f 10 φ :

X XY 1 col : Y XY 2 col : n XY rows : data X Y . 12 black plotG : 41 line

β β 1 el 0801 0.4 1504 0.5 607 0.2 110 mat transpose : iter 3 : i 1 : i iter ≤ β i 1 + el XY f φ β i el Minimize : i i 1 + : 21 line while β β iter el : 51 line :

β β :

β 0.06 78.445 1 0.4 156.887 4 0.599 62.792 7 0.2 101 mat

plot data x β f 10115022 mat 40420022 mat 70725022 mat 51 sys :

FIT range, populate U 010 0.01 range : i 1 U rows range FIT i el U i el β f eval : for U FIT augment 41 line :

x y axes x y / - :

plot XY x β f 1 0 1 150 2 2 mat 4 0 4 200 2 2 mat 7 0 7 250 2 2 mat axes 6 1 sys

Discrete analytical insight

data Σ Finite differences Cumul Integ'n vx data 1 col : vy data 2 col : Y 1 el 0 : i 2 vx rows range Δx i el vx i el vx i 1 - el - : Y i el Y i 1 - el 12 / vy i 1 - el vy i el + (Δx i el * (* + : 21 line for vx Y augment 61 line :

data D data Derivative BackSubstitut'n X data 1 col : Y data 2 col : n X rows : D 1 el 0 : D n el 0 : i 2 n 1 - (range D i el 0.5 Y i 1 - el Y i el - X i 1 - el X i el - / Y i el Y i 1 - el - X i el X i 1 - el - / + (* : for D 1 el D 2 el : D n el D D rows el : X D augment 101 line :

Cumulative Integration

FIT Σ FIT 2 1 sys

Finite differences derivative

FIT D

Laser model fit

c 22 ln sqrt / :

x B p x Xo - (2 ln * B W 2^* - eval :

A 166.937 436.795 126.295 31 mat :

B 0.00013405 0.000010719 0.000355983 31 mat :

W 443.03334 : Xo 1994.32623 : offset 107.5887 : 31 sys

x c 14000 - x ≤ (x 40000 ≤ (& cases :

x Laser A i el 1 c x B i el p * W / erf + (* B i el - (x B i el p 2 ln / * exp * i 13 sum offset + :

Laser [560 TOPO/HDA NC's] Read more: Genfit Convolution Laser

x Laser x c * Xo 750 + 30 red 1 5 mat 2 1 sys