Plot Utilities

a097b6ec-c2ac-47cf-9171-93ac2b8381c9 23 4 5 decimal

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

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 :

L-M => courtesy from Carlos 2018_09_20

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 :

model function to fit wrt data set x β f 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 * - (:

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

n X length : m t length : 21 line

3 appVersion 0.98.6179 ≡ Timing 2.6 min ≡ 21 line

t0 1 time :

L-M Components

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 : 21 line

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 :

Initialize/prepare the solver

x 111441 mat :

h Eps sqrt abs : μ 0.01 : μ1 104.5069 : 31 sys

cont 0 : dnor 1 : update 1 : 31 sys

Eps 1.110 1016 -^* : tol Eps sqrt x normi * : 21 sys

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 μ n identity * + : s1 a 1 -^J transpose f * (* : b1 x s1 - (: f1 b1 Φ : res1 f1 norme (2^μ1 / : 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 μ1 * : Sol cont n 3 + el μ : Sol cont n 4 + el dnor : μ μ 10 / : update 1 : 111 line μ μ 10 * : update 0 : 21 line if 31 line while

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

β x : 0.777335491943527 1.07274498420879 1.27812698620318 4.80082292277248 41 mat

Absolute residuals Residuals i 1 t rows range Δ i el y i el t i el β f - eval : for t Δ augment 21 line :

t y augment FIT 2 1 sys

SSD = "Sum Square Differences" SSD y i el t i el β f - (2^(i 1 n sum : 0.001

Absolute residuals

Residuals 0.0125 BarSize 1 1 sys

1 time t0 - min 2.6

SSD Residuals FIT z Sol res1 f1 res J f tol Eps update dnor cont μ1 μ h derfhφ jjh0 jjh2 jjh1 j Φ ΦΦ i ia t0 m n y t HEADER BarSize plotG lastError SSD Residuals β FIT z Sol res1 f1 b1 s1 res f tol Eps update dnor cont μ1 μ h x jjh2 jjh1 j Φ ΦΦ i ia t0 m n X y t HEADER BarSize plotG lastError SSD z res1 f1 res f tol Eps update dnor cont μ1 μ jjh2 jjh1 j Φ ΦΦ i ia t0 m n y t

Solution
Sol
1	0.751606098373314	1.06463012061639	1	4	0.3616	0.01	0.062098475406672
2	0.786150012398853	1.07666378918754	1.2835818335219	3.76882704975777	0.068120175292209	0.001	0.075244055982917
3	0.782836586314748	1.06916608168721	1.28106244933058	4.87354901194094	0.014535728181673	0.0001	0.226677101117976
4	0.77715281509938	1.07274810002247	1.277745884033	4.79296365160128	0.001792013656741	0.00001	0.016813263399718
5	0.77736020978112	1.07274341759434	1.27816739278205	4.80147006377349	0.001492836718061	0.000001	0.001771626618355
6	0.777333308506676	1.07274514203954	1.27812366979063	4.8007632378208	0.00149234894242	0.0000001	0.000147231995766
7	0.777335696749448	1.0727449696537	1.27812730110826	4.80082849596204	0.001492345537774	0.00000001	0.00001359309988
8	0.77733547035501	1.07274498630926	1.27812695867521	4.80082230899589	0.001492345511046	0.000000001	0.000001288730503
9	0.777335505637514	1.07274498253841	1.2781269991947	4.8008233248154	0.001492345510804	0.0000000001	0.000000211592781
10	0.77733549238836	1.07274498443261	1.27812699079356	4.80082292604909	0.001492345510804	0.00000000001	0.000000083062077
11	0.777335491943527	1.07274498420879	1.27812698620318	4.80082292277247	0.001492345510802	0.000000000001	0.000000000956165
#
ITER	S:x.1	S:x.2	S:x.3	S:x.4	Res1	μ	dnor
#
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HEADER ITER β1 β2 β3 β4 Res1 μ dnor 18 mat :

System HEADER Sol stack :

System ITER β1 β2 β3 β4 Res1 μ 1 0.7516 1.0646 14 0.3616 0.01 2 0.7862 1.0767 1.2836 3.7688 0.0681 0.001 3 0.7828 1.0692 1.2811 4.8735 0.0145 0.0001 4 0.7772 1.0727 1.2777 4.793 0.0018 1105 -^* 5 0.7774 1.0727 1.2782 4.8015 0.0015 1106 -^* 6 0.7773 1.0727 1.2781 4.8008 0.0015 1107 -^* 7 0.7773 1.0727 1.2781 4.8008 0.0015 1108 -^* 8 0.7773 1.0727 1.2781 4.8008 0.0015 1109 -^* 9 0.7773 1.0727 1.2781 4.8008 0.0015 11010 -^* 10 0.7773 1.0727 1.2781 4.8008 0.0015 11011 -^* 11 0.7773 1.0727 1.2781 4.8008 0.0015 11012 -^* 127 mat