D2 ... D3

7276fb4d-2525-43d4-95b2-ac2b721d3204 17 15 12 decimal

&[DATE] &[TIME] - &[FILENAME]

D2 ... D3

0.38 -

D2 00 0.021 2.22 0.04 3.375 0.059 3.789 0.079 3.782 0.099 3.538 0.12 3.164 0.141 2.754 0.164 2.322 0.188 1.919 0.213 1.552 0.237 1.253 0.263 0.991 0.29 0.77 0.318 0.595 0.346 0.456 0.377 0.341 0.406 0.257 0.437 0.192 0.47 0.14 0.509 0.096 0.545 0.068 0.591 0.044 0.645 0.026 0.918 0.002 1.125 0 1.154 0272 mat :

D3 0 10.861 0.021 6.056 0.04 3.327 0.059 1.687 0.079 0.706 0.099 0.133 0.12 0.187 - 0.141 0.338 - 0.164 0.395 - 0.188 0.394 - 0.213 0.362 - 0.237 0.32 - 0.263 0.272 - 0.29 0.226 - 0.318 0.185 - 0.346 0.149 - 0.377 0.118 - 0.406 0.093 - 0.437 0.073 - 0.47 0.056 - 0.509 0.041 - 0.545 0.031 - 0.591 0.022 - 0.645 0.014 - 0.918 0.002 - 1.125 0 1.154 0272 mat :

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 :

Plot 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 :

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 :

ListCollect

data list ListCollect collects index list select list : ct 1 : i select a ct el data i 1 el : b ct el data i 2 el : ct ct 1 + : 31 line for a b augment 51 line :

data char size clr plot k 1 data rows range r3 k el char : r4 k el size : r5 k el clr : 13 mat for data r3 r4 r5 augment 21 line :

XY D3 :

===== D3 data set =====

D3 rows 27

model function
plug in ia(x,β):= β 1 el β 2 el x - β 3 el + β 5 el / exp x - β 3 el + (β 4 el β 5 el + β 4 el β 5 el * / * exp - (* -

1. selct the support points
2. collect for LM list 1514222515 mat : uv XY list ListCollect : 21 sys

raw XY o 5 black plot : support uv . 15 blue plot : 21 line

support raw 2 1 sys

uv 0 10.861 0.079 0.706 0.29 0.226 - 0.545 0.031 - 0.918 0.002 - 52 mat

x uv 1 col : y uv 2 col : 21 sys

Disable for selective fit ... enable for 'global'

clear as required from previous use x y β Clear 1

3 appVersion 0.98.6179 ≡ Document_Timing 1.3 min ≡ 21 line

global fit x XY 1 col : y XY 2 col : 21 sys

3. global Levenberg-Marquardt

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model function ... plug in ia(x,β):= β 1 el β 2 el x - β 3 el + β 5 el / exp x - β 3 el + (β 4 el β 5 el + β 4 el β 5 el * / * exp - (* -

β β 1 el β 2 el β 3 el β 4 el β 5 el 15 mat transpose :

n β length : m x length : 21 line

initialise the solver init 01 0.1 0.075 0.1 15 mat transpose :

t0 1 time :

typical for this example tol 0.00001 :

L-M Components => algo solves 'β'

x β ia β 1 el β 2 el x - β 3 el + β 5 el / exp x - β 3 el + (β 4 el β 5 el + β 4 el β 5 el * / * exp - (* - : ................................... i 1 m range ΦΦ i el x i el β ia y i el - : for β Φ ΦΦ : 21 line ................................... i 1 m range j 1 n range β j el β j el h + : jjh1 x i el β ia y i el - : β j el β j el 2 h * - : jjh2 x i el β ia y i el - : jjh0 i j el jjh1 jjh2 - 2 h * / : β j el β j el h + : 61 line for 11 line for ................................. β derfhφ jjh0 : 71 line

h tol : μ 0.01 : μ1 100 : 31 sys

cont 0 : dnor 1 : update 1 : 31 line dnor tol > update 1 ≡ f init Φ : J init derfhφ : jtj J transpose J * : res f norme (2^: 41 line if 11 line a jtj μ n identity * + : s1 a 1 -^J transpose f * (* : b1 init s1 - (: f1 b1 Φ : SSD f1 norme (2^μ1 / : 51 line SSD res < init b1 : f f1 : 12 mat dnor s1 normi init normi / : cont cont 1 + : Sol cont 1 el cont : z 1 n range Sol cont z 1 + el init z el : 11 line for Sol cont n 2 + el SSD μ1 * : Sol cont n 3 + el μ : Sol cont n 4 + el dnor : μ μ 10 / : update 1 : 101 line μ μ 10 * : update 0 : 21 line if 31 line while 21 line

assign 'β' from solved 'init' β init :

reflexive parameters 'β' global 70 sec 21 sys selected 4 sec 21 sys 0.0047 - 1.13381 0.10605 0.06714 0.11621 51 mat 0.00049 - 1.04812 0.10625 0.06299 0.12409 51 mat 22 mat

recover @ 'tol' β β 5 round vectorize :

1 time t0 - 80 s *

β 0.0047 - 1.13381 0.10605 0.06714 0.11621 51 mat

x c 10 x ≤ (x 2 ≤ (& cases :

x f β 1 el β 2 el x - β 3 el + β 5 el / exp x - β 3 el + (β 4 el β 5 el + β 4 el β 5 el * / * exp - (* - :

Absolute  residuals δ X XY 1 col : Y XY 2 col : 12 mat j 1 XY rows range Δ j el Y j el X j el f - eval : for X Δ augment 31 line :

raw x f x c * support 3 1 sys

δ 11 mat 0 0.014 - 0.021 0.052 0.04 0.02 - 0.059 0.034 - 0.079 0.001 0.099 0.004 0.12 0.006 0.141 0.007 0.164 0.008 0.188 0.006 0.213 0.003 0.237 0 0.263 0.002 - 0.29 0.003 - 0.318 0.005 - 0.346 0.005 - 0.377 0.005 - 0.406 0.003 - 0.437 0.003 - 0.47 0.002 - 0.509 0.001 - 0.545 0 0.591 0 0.645 0.002 0.918 0.004 1.125 0.005 1.154 0.005 272 mat 11 mat

0.014 - 0.052 0.02 - 0.034 - 0.001 0.004 0.006 0.007 0.008 0.006 0.003 0 0.002 - 0.003 - 0.005 - 0.005 - 0.005 - 0.003 - 0.003 - 0.002 - 0.001 - 00 0.002 0.004 0.005 0.005 271 mat