<p> Genfit modules </p>

10e91c16-197f-4769-bcf7-4351a187706f 36 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 :

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

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

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 0801 0.4 1504 0.5 607 0.2 101 mat :

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

β 0.32 78.148 1 0.399 154.619 4 0.582 62.622 7 0.2 101 mat

FIT range, populate U 010 0.025 range : i 1 U rows range FIT i el U i el β f eval : for U FIT augment 41 line :

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

plot

Discrete analytical insight

data Σ Finite differences Cumul Integration 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 :

Cumulative Integral

FIT Σ FIT 2 1 sys

data Deriv data Derivative BackSubstitution X data 1 col : Y data 2 col : n X rows : deriv 1 el 0 : deriv n el 0 : i 2 n 1 - range deriv 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 deriv 1 el deriv 2 el : deriv n el deriv deriv rows el : X deriv augment 101 line :

FIT Deriv