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 Res1 μ dnor 17 mat :

t 123456789101112121 mat :

y 5.308 7.24 9.638 12.866 17.069 23.192 31.443 38.558 50.156 62.948 75.995 91.972 121 mat :

X x 1 el x 2 el x 3 el 31 mat :

n X length :

m t length :

Function adjusted to the data i 1 m range f i el X 1 el 1 X 2 el e t i el X 3 el *^* + (/ y i el eval - : for

Jacobian matrix for finite differences i 1 m range fh i el X 1 el h1 + 1 X 2 el h2 + (e t i el X 3 el h3 + (*^* + (/ y i el eval - : for X h1 h2 h3 fxh fh : i 1 m range jjh i 1 el X h1 00 fxh i el X h1 - 00 fxh i el - 2 h1 * / : jjh i 2 el X 0 h2 0 fxh i el X 0 h2 - 0 fxh i el - 2 h2 * / : jjh i 3 el X 00 h3 fxh i el X 00 h3 - fxh i el - 2 h3 * / : 31 line for X derfh jjh : 41 line

X fx f :

x β fO β 1 el 1 β 2 el β 3 el x * exp * + / :

cont 0 :

Eps 1.110 1016 -^* :

tol Eps sqrt x normi * :

dnor 1 :

h1 Eps sqrt abs :

h2 Eps sqrt abs :

h3 Eps sqrt abs :

update 1 :

x 20030 0.4 - 31 mat :

mu 0.01 :

mu1 104.5069 :

L-M algorithm

dnor tol > update 1 ≡ f x fx : J x derfh : jtj J transpose J * : res f norme (2^: 41 line continue if a jtj mu n identity * + : s a 1 -^J transpose f * (* : b x s - : f1 b fx : res1 f1 norme (2^mu1 / : res1 res < x b : f f1 : dnor s normi x normi / : cont cont 1 + : Sol cont 1 el cont : Sol cont 2 el x 1 el : Sol cont 3 el x 2 el : Sol cont 4 el x 3 el : Sol cont 5 el res1 mu1 * : Sol cont 6 el mu : Sol cont 7 el dnor : mu mu 10 / : update 1 : 131 line mu mu 10 * : update 0 : 21 line if 71 line while

Sol res1 mu1 mu h3 h2 h1 dnor tol Eps fO HEADER t0 BarSize plotG Sol res1 f1 b s mu1 mu x h3 h2 h1 dnor tol Eps fO fx fxh fh f X y t HEADER t0 BarSize plotG res1 mu1 mu dnor tol Eps fO t0

Solution
Sol
1.000000000	147.568761094	30.915753670	-0.333046521	23586.350335244	0.010000000	0.355300394
2.000000000	174.855106628	41.322493572	-0.311831737	320.951846601	0.001000000	0.156051179
3.000000000	194.416410267	48.327126814	-0.313449574	19.720114405	0.000100000	0.100615496
4.000000000	196.131795647	49.079232849	-0.313590402	2.665759318	0.000010000	0.008746085
5.000000000	196.185482594	49.091533552	-0.313570124	2.587301125	0.000001000	0.000273654
6.000000000	196.186492952	49.091663840	-0.313569598	2.587277397	0.000000100	0.000005150
7.000000000	196.186235213	49.091638051	-0.313569748	2.587277395	0.000000010	0.000001314
#
ITER	S:x.1	S:x.2	S:x.3	Res1	μ	dnor
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data t y . 12 black plotG :

1 time t0 - 0.2810 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 Sol cont 2 el Sol cont 3 el Sol cont 4 el 31 mat : 196.186235213146 49.0916380508869 0.313569747935126 - 31 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 : 0.01

RMS difference SSD n / sqrt 0.1

Relative residuals

Residuals 0.1 BarSize 1 1 sys