<p> XY data set </p>

09482963-2a40-416e-a67b-1c04f466f7c6 19 3 5 auto

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

<p> XY data set </p>

XY 1 4.18 2 4.67 3 5.3 4 5.37 5 5.45 6 5.74 7 5.65 8 5.84 9 6.36 10 6.38 11 6.31 12 6.46 13 6.48 14 6.59 15 6.74 16 6.56 17 6.85 18 6.53 19 6.68 20 7.01 21 6.82 22 6.65 23 6.95 24 7.12 25 7.14 26 6.91 27 6.94 28 7.23 29 6.9 30 7.39 31 6.94 312 mat :

<p> linfit modules </p>

vx vy a b c plotG a char ≡ b size ≡ c color ≡ 13 mat n vx length : plot vx 1 el vy 1 el a b c augment : i 2 n range plot plot vx i el vy i el a b c augment stack : for plot 51 line :

Applicable parts are: Optimiz "numeric" XY f φ β βlinfit X XY 1 col : Y XY 2 col : n XY rows : k x β φ length 1 - : vx raw initial vector fit i 1 X length range vx i el X i el β f eval : for M-> Cholesky Gradient Mat j 1 k range i 1 n range M i j el X i el β φ j 1 + el eval : for for Cholesky solver [LS] Φ M transpose M * : d M transpose Y vx - (* : Δβ Φ 1 -^eval d * : b β Δβ + : 131 line :

Vector gradient ... Optimiz Symbolic x β f n φ ct 1 : i 1 n range PD ct el x β f (β ct el diff : stack f(x,β) & PD V 1 el x β f : V i 1 + el PD i el : 21 line ct ct 1 + : 41 line for V 31 line :

Part 1: Dress the "linfit" solver

X XY 1 col : Y XY 2 col : data X Y o 5 black plotG : 31 line

1. model combination x β p β 1 el β 2 el x ln * β 3 el x sqrt * 31 mat :

<= leading fnct is '1'

n x β p rows ≡

n 3 :

2. Collect  the model function x β f x β p n el n 13 sum 11 line :

view the expanded linfit model x β f β 2 el x ln * β 3 el x sqrt * + β 1 el +

Part 2: Execute the "linfit" solver

initialise the solver β 11113 mat transpose :

<= assign/create the vector gradient x β φ x β f n φ :

assign the solver β XY f φ β βlinfit :

coefficients of the model vector fnct's β 4.183 0.996 0.079 - 31 mat

recast the solved "linfit model" x β fit 1 x ln x sqrt 31 mat β * :

data x β fit 2 1 sys