Function Utilities

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How to iterate Smath Genfit Minimize

Function Utilities

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 15002110032050 3.5 38004540058700610550711200811100911900102 mat :

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

Verhulst logistic to fit AntColony: 'data' from American Scientist, Jan-Feb 1995

From the look, the observed population is irregular but not to matter that Verhulst logistic should have been recognised by Amarican Scientist !

colony 500 :

Verhulst model to "ant colony" x β f colony β 1 el 11 β 2 el / 1 - (β 3 el x β 4 el - (* - exp * + / + :

<= Model function

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

x β φ x β f 4 φ :

<= Gradient Vector Function

β β 1 el 11000 0.75 1.25 541 mat : iter 2 : 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 i 1 XY rows range Δ i el Y i el X i el β f - 0 round eval : for X Y Δ augment 21 line :

δ 1500148 - 211005332050289 - 3.5 3800198454001195870010 - 61055049 - 71120044 - 811100326 - 911900426103 mat

FIT U 010 0.05 range : i 1 U rows range FIT i el U i el β f eval : for U FIT augment 31 line :

β 10991.701 0.75 1.344 5.012 41 mat

data X Y . 12 black plotG :

data FIT 2 1 sys

Δelta X δ 3 col augment : stem Δelta Error : 21 line

0 stem 2 1 sys BarSize Unicolor QuickPlot or any color X_Y

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 :

MyBar Δelta 0.075 BarSize :

Mutual deviation between data set and rational fit.

0 MyBar 2 1 sys