<p> plot </p>

e7611178-72ac-4baa-8794-1fd501860d61 5 4 5 decimal

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

Cholesky for Engineer . . .

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data char size clr plot k 1 data rows range r3 k el char : r4 k el size : r5 k el clr : 13 mat for data r3 r4 r5 augment 21 line :

clear M M 0 :

data 020305070901005014015016017022032027 mat transpose :

Cholesky fitting vector
1. add/delete components
2. manipulate exponents
       ± successful. x φ 1 x x 2^x 3^41 mat :

Cholesky companion solver .. inclusive X data 1 col : Y data 2 col : 12 mat XY data . 14 black plot : 21 line j 1 x φ length range i 1 X length range M i j el X i el φ j el : for for b M transpose M * (1 -^eval M transpose Y * * : fit u 20 - 12019 - range : i 1 u rows range vy i el u i el f eval : for u vy augment 31 line : 41 line

b 48.547319 7.421749 0.163574 - 0.001157 41 mat

M transpose M * not commutative ≡

M transpose Y * not commutative ≡

isolate/export

Cholesky fitting vector
1. add/delete components
2. manipulate exponents
       ± successful. x φ 1 x x 2^x 3^41 mat :

b 48.547319 7.421749 0.163574 - 0.001157 41 mat :

<= recast the scalar model x f b x φ * :

data lo mesh hi cubic X data 1 col : Y data 2 col : 12 mat XY data . 14 black plot : 21 line j 1 x φ length range i 1 X length range M i j el X i el φ j el : for for b M transpose M * (1 -^eval M transpose * Y * : fit u lo hi mesh range : i 1 u rows range vy i el u i el f eval : for u vy augment 31 line : 41 line :

fit x f XY 3 1 sys

export data 20 - 19 - 120 cubic :

export 20 - 174.5733 - 19 - 159.452 - 18 - 144.7898 - 17 - 130.5796 - 16 - 116.8147 - 52 mat

data char size clr plot 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 :

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 :

Example of Non-linear Fit [Adapted from Smath source]. We will fit a model fnct using the CholeskyMatrixSolver

t0 1 time :

T 236.3 253.4 261.5 270.4 280.6 288.4 299.1 315.2 333.6 353.1 101 mat :

P 1510204060100200400760101 mat :

Install 'Y' non-linear i 1 P length range Y i el P i el log10 : for

Y 0 0.699 1 1.301 1.6021 1.7782 2 2.301 2.6021 2.8808 101 mat

i 1 P length range : NL i Y augment : 21 sys

NL o 5 blue plot

In this non-linear fit, the all thing is about installing 'Y' the non-linear component.

Just to show what equation we are fitting i.e: the model function to fit data points

P log10 b 1 el b 2 el T / + b 3 el T log10 * + b 4 el T 2^* + ≡

[1]

x φ 1000 x x log10 x 2^41 mat :

Memo 100 x x log10 x 2^51 mat

Prepare Cholesky n T length : k x φ length : 21 line

n k 21 mat 10421 mat

Cholesky  solver Num. j 1 k range i 1 n range X i j el T i el φ j el : for for Φ X transpose X * : d X transpose Y * : b Φ 1 -^eval d * : 41 line

Let recast the model function in [1]
to eliminate the log10 x fit 10 b x φ *^eval :

i 1 n range Pc i el T i el fit eval : for

Deviations @ support points Δ i 1 T length range res i el P i el T i el fit - eval : for P res augment 21 line :

b 0.288666886318 - 0.341588684153 - 149.943525856756 0.000241564906 41 mat

2.8867 - 0.3416 - 149.9436 0.0002 41 mat

T 236.3 253.4 261.5 270.4 280.6 288.4 299.1 315.2 333.6 353.1 101 mat

P 1510204060100200400760101 mat

Pc 0.98 5.26 10.25 19.66 37.86 59.07 101.67 204.6 401.83 753.59 101 mat

Δ 1 0.02 5 0.26 - 10 0.25 - 20 0.34 40 2.14 60 0.93 100 1.67 - 200 4.6 - 400 1.83 - 760 6.41 102 mat

Δ 2 BarSize

L H N xd U 0 : dx H L - N / : i 1 N 1 + range U i el L dx - (dx i * + : for U 41 line :

U 225375300 xd :

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

1 time t0 - 0.7 s *

data T P augment o 5 black plot :

x c 1225 x ≤ (x 375 ≤ (& cases :

Complete plot: data points + the fitted model

data FIT 2 1 sys

Export this formula for the remaining of project.
Transport high decimals [b]... high 'x' in x^2 x q 10 b 2 el b 1 el x φ 1 el * b 2 el / x + (* b 3 el x log10 * + b 4 el x 2^* + (^:

data x q x c * 2 1 sys

300 fit 300 q 21 mat 106.083 106.083 21 mat