<p> Plot data utility </p>

18862025-8c52-41df-8e52-132609f7ba76 30 4 3 decimal

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

T P char size color plotG n T length : plot T 1 el P 1 el char size color augment : i 2 n range plot plot T i el P i el char size color augment stack : for plot 41 line :

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 * - :

This project demonstrates the Cholesky numerical matrix property applied to a non linear model function in the sense of Legendre-Gauss LestSquares [LS]. The φ(x,β) is a vector of the model function at top, then stacked with the derivatives wrt each parameter. For the numerical evaluation, the β precedes. To view the full literal expansion, export the two f(x,β) & φ(x,β) w/o the β's ... paste in blank sheet and evaluate symbolic φ(x,β). The most difficult part of fitting a data set is the choice of the model function. It may take days/months/years/never !!! This data set is some kind of Pharmacokinetics stuff. Start with the initial β parameters to get a first rough fit, then re-plug the calculated β in itself ... two re-injections are enough to fit this data set, but that will depend upon the closeness of the initial fit. This example illustrates and concludes the model from a reasonably populated data set [too many points per region deteriorate the fit]

data 1106 -^* 0.51 0.82 1.02 1.23 1.43 1.85 2.05 2.36 4.52 9.22 0.78 0.8 0.92 1.14 1.26 1.28 1.22 1.16 1.12 1.08 1.08 211 mat transpose :

X data 1 col :

Y data 2 col :

0.5 Y 1 el 1414 mat transpose

=>=> initial β

x β φ x β f x β f β 1 el diff x β f β 2 el diff x β f β 3 el diff x β f β 4 el diff 51 mat :

β 0.7819 1.0676 1.2636 4.8488 41 mat :

<= re-inject β from below

n X length :

n 11

k x β φ length :

k 5

L H N xd N+1 pts L...H dx H L - N / : i 1 N 1 + range U i el L dx - (dx i * + : for U 21 line 31 line :

j 1 k range i 1 n range M i j el X i el β φ j 1 + el : for for

i 1 Y length range vx i el X i el β f : for

Φ M transpose M * :

d M transpose Y vx - (* :

L X 1 el :

H X X length el :

Δβ Φ 1 -^eval d * :

N 100 :

U L H N xd :

β β Δβ + :

<= ... the active β

x fit x β f eval :

=>=> plug in β above

init next fit 0.5 0.78 1441 mat 0.7819 1.0676 1.2636 4.8488 41 mat 0.7775 1.0727 1.2782 4.8027 41 mat 23 mat

FIT i 1 U rows range FIT i el U i el fit eval : for FIT 21 line :

β 0.7775 1.0727 1.2782 4.8027 41 mat

MyFit U FIT augment :

data X Y o 8 blue plotG :

Title 21 Model fit in Pharmacokinetics 12 black 15 mat :

data MyFit Y 11 el Y 1 el Title 5 1 sys

jmGiraud: July, 22, 2015

n 11

k 5

β 0.7819 1.0676 1.2636 4.8488 41 mat :

M 0 :

vx 0 :

Φ 0 :

d 0 :

Δβ 0 :

X Y β f N New Niterate 1 N range j 1 k range i 1 n range M i j el X i el β φ j 1 + el eval : for for i 1 Y length range vx i el X i el β f eval : for Φ M transpose M * eval : d M transpose Y vx - (* eval : Δβ Φ 1 -^eval d * : β β Δβ + : 61 line for β 21 line :

M transpose Y vx - (* eval

M transpose M * eval

# eval

M transpose M *

M transpose Y vx - (*

X Y β f 2 New does not work ? ≡

The symbolic literal expansion is so voluminous that it will be imprudent to script.