<p> Genfit Utilities </p>

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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 :

Bar plot unicolor style, bar width user. data dt BarSize v data 2 col : t v bar t dt - 0 t dt - v t dt + v t dt + 042 mat : j 1 data rows range j 1 ≡ B data j 1 el data j 2 el bar : B B data j 1 el data j 2 el bar stack : if 11 line for B 41 line :

XY 9.65 0.0082 24 0.129 62.63 3.223 104.46 14.377 134.79 25.853 157.76 35.06 176.25 42.31 191.48 48.06 207.58 53.78 229.92 61.1 254.22 68.23 278.83 74.6 302.02 79.88 324.42 84.4 347.02 88.43 371.3 92.2 162 mat :

Model f(x,β) => Courtesy Jean Giraud. ------------------------------------ Reference: Kirby, R., NIST (1979). Scanning electron microscope line width standards.

Model function x β f β 1 el β 2 el 1 β 3 el x β 4 el - β 5 el / (2^* + / + :

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

<= Gradient Vector Function x β φ x β f 5 φ :

range/populate L 0 : H 400 : N 400 : 13 mat U L H N xd : 21 line

126126 - 92760051 mat 126.314 126.762 - 8.734 27.699 615.942 51 mat # 13 mat

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

β β 1 el 126126 - 92760051 mat : iter 6 : 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 :

Absolute  residuals δ j 1 XY rows range Δ j el Y j el X j el β f - eval : for X Δ augment 21 line :

β 126.314 126.762 - 8.734 27.699 615.942 51 mat

bar δ 2.5 BarSize (:

bar

SSD = "Sum Square Differences" SSD Y i el X i el β f - (2^(i 1 n sum : 0.74

Kirby i 1 U rows range vy i el U i el β f eval : for U vy augment 21 line :

Kirbydata X Y . 12 black plotG : Title 19240 Transmute fit to Kirby2 12 black 15 mat : 21 line

Absolute  residuals δ j 1 XY rows range Δ j el Y j el X j el β f - eval : for X 100 Δ * augment 21 line :

bar δ 1.5 BarSize (:

δ Error

bar Kirby Kirbydata Title 4 1 sys