Plot Utilities

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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 :

t0 1 time :

HEADER ITER S:x.1 S:x.2 S:x.3 S:x.4 Res1 μ dnor 18 mat :

t 1012 -^0.51 0.82 1.02 1.23 1.43 1.85 2.05 2.36 4.52 9.22 111 mat :

y 0.78 0.8 0.92 1.14 1.26 1.28 1.22 1.16 1.12 1.08 1.08 111 mat :

X x 1 el x 2 el x 3 el x 4 el 41 mat :

model function to fit wrt data set β 2 el β 1 el β 2 el - 1 x β 3 el / (β 4 el^+ / + β 1 el β 2 el - 1 x β 3 el / (β 4 el^+ (2^/ x β 3 el / (β 4 el^* β 4 el * -

n X length :

m t length :

t X ia X 2 el X 1 el X 2 el - 1 t X 3 el / (X 4 el^+ / + X 1 el X 2 el - 1 t X 3 el / (X 4 el^+ (2^/ t X 3 el / (X 4 el^* X 4 el * - :

i 1 m range ΦΦ i el t i el X ia y i el - : for

X Φ ΦΦ :

x β fO β 2 el β 1 el β 2 el - 1 x β 3 el / (β 4 el^+ / + β 1 el β 2 el - 1 x β 3 el / (β 4 el^+ (2^/ x β 3 el / (β 4 el^* β 4 el * - :

i 1 m range j 1 n range X j el X j el h + : jjh1 t i el X ia y i el - : X j el X j el 2 h * - : jjh2 t i el X ia y i el - : jjh0 i j el jjh1 jjh2 - 2 h * / : X j el X j el h + : 61 line for 11 line for

X derfhφ jjh0 :

cont 0 :

Eps 1.110 1016 -^* :

tol Eps sqrt x normi * :

dnor 1 :

h Eps sqrt abs :

update 1 :

x 111441 mat :

mu 0.01 :

mu1 104.5069 :

L-M algorithm

dnor tol > update 1 ≡ f x Φ : J x derfhφ : jtj J transpose J * : res f norme (2^: 41 line if 11 line a jtj mu n identity * + : s1 a 1 -^J transpose f * (* : b1 x s1 - (: f1 b1 Φ : res1 f1 norme (2^mu1 / : 51 line res1 res < x b1 : f f1 : dnor s1 normi x normi / : cont cont 1 + : Sol cont 1 el cont : z 1 n range Sol cont z 1 + el x z el : 11 line for Sol cont n 2 + el res1 mu1 * : Sol cont n 3 + el mu : Sol cont n 4 + el dnor : mu mu 10 / : update 1 : 111 line mu mu 10 * : update 0 : 21 line if 31 line while

Sol res1 mu1 mu h dnor tol Eps jjh2 jjh1 fO ia HEADER t0 BarSize plotG Sol res1 f1 b1 s1 f mu1 mu x h dnor tol Eps jjh2 jjh1 fO Φ ΦΦ ia X y t HEADER t0 BarSize plotG res1 mu1 mu dnor tol Eps jjh2 jjh1 fO ia t0

Solution
Sol
1.000000000	0.751606093	1.064630120	1.000000000	4.000000000	0.361600000	0.010000000	0.062098477
2.000000000	0.786150005	1.076663782	1.283581853	3.768826812	0.068120175	0.001000000	0.075244066
3.000000000	0.782836608	1.069166075	1.281062529	4.873550231	0.014535736	0.000100000	0.226677343
4.000000000	0.777152813	1.072748099	1.277745875	4.792963461	0.001792014	0.000010000	0.016813558
5.000000000	0.777360214	1.072743417	1.278167400	4.801470193	0.001492837	0.000001000	0.001771693
6.000000000	0.777333306	1.072745143	1.278123670	4.800763155	0.001492349	0.000000100	0.000147276
7.000000000	0.777335675	1.072744974	1.278127288	4.800827785	0.001492346	0.000000010	0.000013462
8.000000000	0.777335479	1.072744985	1.278126969	4.800822550	0.001492346	0.000000001	0.000001090
9.000000000	0.777335491	1.072744985	1.278126992	4.800822873	0.001492346	0.000000000	0.000000067
10.000000000	0.777335483	1.072744986	1.278126983	4.800822612	0.001492346	0.000000000	0.000000054
11.000000000	0.777335492	1.072744985	1.278126991	4.800822908	0.001492346	0.000000000	0.000000062
12.000000000	0.777335498	1.072744984	1.278126994	4.800823111	0.001492346	0.000000000	0.000000042
#
ITER	S:x.1	S:x.2	S:x.3	S:x.4	Res1	μ	dnor
#
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#

data t y . 12 black plotG :

1 time t0 - 17.856 s *

FIT range, populate U 020 0.01 range : i 1 U rows range vy i el U i el β fO eval : for U vy augment 41 line :

β x : 0.777335498374467 1.07274498351951 1.27812699407994 4.80082311066275 41 mat

Relative residuals Residuals i 1 t rows range Δ i el 1 y i el t i el β fO / - eval : for t Δ augment 21 line :

data FIT 2 1 sys

SSD = "Sum Square Differences" SSD y i el t i el β fO - (2^(i 1 n sum : 0

RMS difference SSD n / sqrt 0

Relative residuals

Residuals 0.1 BarSize 1 1 sys