Carlos L-M algorithm

50d46fa6-e0c0-404d-842d-f44d33589cc9 59 6 5 decimal

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

HEADER ITER S:x.1 S:x.2 S:x.3 Res1 μ dnor 17 mat :

t0 1 time :

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 Function i 1 m range jj i 1 el f i el x 1 el diff : jj i 2 el f i el x 2 el diff : jj i 3 el f i el x 3 el diff : 31 line for

can be grouped but 
NOT collected {X derf jj : X fx f : Eps 1016 -^: tol Eps sqrt x normi * : 41 line

cont 0 : dnor 1 : update 1 : 13 mat μ 0.01 : μ1 100 : 12 mat 21 mat

LM like other methods 
needs be initialized. x 20030 0.4 - 31 mat :

Carlos L-M algorithm

dnor tol > update 1 ≡ f x fx : J x derf : jtj J transpose J * : res f norme (2^: 41 line continue if a jtj μ n identity * + : s a 1 -^J transpose f * (* : b x s - : f1 b fx : res1 f1 norme (2^μ1 / : 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 μ1 * : Sol cont 6 el μ : Sol cont 7 el dnor : μ μ 10 / : update 1 : 131 line μ μ 10 * : update 0 : 21 line if 71 line while

M n Mround i 1 M rows range j 1 M cols range m i j el M i j el n round : for for m 21 line :

Sol Sol 9 Mround :

15 D independent "round Sol" x 196.186261720221 49.0916394489396 0.313569729960875 - 31 mat

196.186261720221 49.09163944894 0.313569729961 - 31 mat

1 time t0 - 2 s *

Mround Sol res1 res μ1 μ update dnor cont tol Eps i m n t0 HEADER lastError Mround Sol res1 f1 b s res x μ1 μ update dnor cont tol Eps fx f i m n X y t t0 HEADER lastError res1 res μ1 μ update dnor cont tol Eps i m n t0

Solution
Sol
1	147.568723194	30.915753991	-0.333046612	23586.350335244	0.01	0.355300742
2	174.854929697	41.322472852	-0.311831819	320.952854408	0.001	0.156050542
3	194.416358743	48.327112423	-0.313449578	19.720323863	0.0001	0.100616168
4	196.131762436	49.079231125	-0.313590424	2.665761493	0.00001	0.00874618
5	196.185537218	49.091542376	-0.313570099	2.587301123	0.000001	0.000274102
6	196.186255881	49.091638512	-0.313569733	2.587277397	0.0000001	0.000003663
7	196.18626172	49.091639449	-0.31356973	2.587277395	0.00000001	0.00000003
#
ITER	S:x.1	S:x.2	S:x.3	Res1	μ	dnor
#
#
#

Sol 1 147.568723194 30.915753991 0.333046612 - 23586.350335244 0.01 0.355300742 2 174.854929697 41.322472852 0.311831819 - 320.952854408 0.001 0.156050542 3 194.416358743 48.327112423 0.313449578 - 19.720323863 0.0001 0.100616168 4 196.131762436 49.079231125 0.313590424 - 2.665761493 1105 -^* 0.00874618 5 196.185537218 49.091542376 0.313570099 - 2.587301123 1106 -^* 0.000274102 6 196.186255881 49.091638512 0.313569733 - 2.587277397 1107 -^* 3.663 106 -^* 7 196.18626172 49.091639449 0.31356973 - 2.587277395 1108 -^* 3108 -^* 77 mat

plotG(data,char,size,clr)

data char size clr plotG k 1 data rows range r3 k el char : r4 k el size : r5 k el clr : 31 line for data r3 r4 r5 augment 21 line :

α 20030 0.4 - 31 mat :

x α init α 1 el 1 α 2 el x α 3 el * exp * + / :

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 :

β 196.186261720221 49.09163944894 0.313569729961 - 31 mat :

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

XY t y augment : data XY o 5 black plotG : 21 line

data x β f x α init 3 1 sys