edb012c4-7dfa-4a16-b452-1280cf2ba7aa 5 6 6 decimal

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

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 :

t0 1 time :

Fitting a model by fitting the reduced data set

Fitting data is "an art [F.B. Hildebrand]". Models don't abund in literature, NIST is very poor to useless. Data reduction is often a good route. In this example, the sampled data are col_1, col_2. We divide col 'Y' by col 'X' to get col 'R', the reduced data. The fitting session will be exercised on 'XR'. The final fit is recovered by reverse engineering the fit, i.e: multiply by 'X'. This data set does not lack points. What we have here is some kind of "reaction rate", but the theoretical reaction rate model does not have enough parameters to fit. In this demo, parameters are from OriginLab. An Smath "Genfit" session would do as well. The data set is typical of an alcotest. The driver was tested above Canadian limit [80mg/l], continued tested for complete history.

algo style matrices: elements wise between matrices u v Vectorise i 1 u rows range j 1 u cols range M i j el u i j el v i j el algo eval : for for M 21 line :

Reduce data set u v algo u v / :

XY 2 col XY 1 col Vectorise

XYR 13.125 154.614 11.780114 34.026 246.218 7.236172 55.446 252.327 4.55086 76.021 242.368 3.188172 92.273 191.45 2.074821 105.182 152.065 1.445732 117.288 142.612 1.215913 127.59 121.356 0.95114 137.523 117.018 0.850898 147.304 115.21 0.782124 103 mat :

OriginLab coefficients yo 0.02024 : A1 14.848 : t1 47.1 : A2 4.376 : t2 6.158 : 15 mat

Reduced fit x f yo A1 x t1 / - exp * + A2 x t2 / - exp * + :

Recovered fit x q x x f * :

Reduced data set to fit XR XYR 1 col XYR 3 col . 10 black plotG :

Original data set, for recovery XY XYR 1 col XYR 2 col . 10 black plotG :

x limit 80 :

x q x limit - 0 ≡ x 150175 solve 162.4

'solve' does not support eval(,) in f(x)

Copy/paste OriginLab param.

y0 0.02024 0.3204 A1 14.84776 2.3454 t1 47.09886 7.9083 A2 4.3761 74.783 t2 6.15757 57.482

Reduce x 1020011 range : i 1 x rows range R i el x i el f eval : for x R augment 31 line :

Fit x 02501 range : i 1 x rows range fit i el x i el q eval : for x fit augment 31 line :

The fitted reduced data set

XR Reduce 2 1 sys

Fit of the original data set

XY Fit 2 1 sys

The scalar model fit

x q 162.4 80 + 30 red 1 5 mat 2 1 sys

1 time t0 - 1.2 sec *

Data: Data1_B Model: ExpDec2 Equation: y = A1*exp(-x/t1) + A2*exp(-x/t2) + y0 Weighting: y No weighting Chi^2/DoF = 0.0188 R^2 = 0.99919 y0 0.02024 0.32036 A1 14.84776 2.3454 t1 47.09886 7.90829 A2 4.3761 74.78261 t2 6.15757 57.4818