PlotG, xd(l,h,n)

5c87ef03-a2e5-4f69-bfc0-3d7e24c2b06d 66 4 5 decimal

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

PlotG, xd(l,h,n)

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 :

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 :

a 1 : b 1 : c 17 : yo 1.25 : xo 2 : 51 line

L 2.4 : H 4 : N 200 : U L H N xd : 41 line

XY 2 0.8 2.4 0.8 2.8 0.8 2.91 0.8 2.92 0.797 2.93 0.759 2.94 0.664 2.95 0.568 2.96 0.506 2.97 0.472 2.98 0.456 2.99 0.448 3 0.444 3.2 0.444 3.6 0.444 4 0.444 162 mat :

X XY 1 col :

Y XY 2 col :

x chemist 1 yo a x xo - (b x xo - (c x * -^*^* + / :

Q i 1 U rows range vy i el U i el chemist eval : for U vy augment 21 line :

i 2 X rows range V i 1 - el X i el chemist eval : for

Note: f(x) divides by 0 for x = 2. Get a longer plot by escaping U=2 ... A most curious model that fits 16 exactly: 3 parameters

xy X Y . 12 black plotG :

No matter the secrecy around the "chemical reaction", the data set is rmarkably well collectd with just enough samples, well distributed.

Chemist Transmute Model Fit ... not quite a titration curve from undocumented chemical reaction/reactants {Channel 101 ?]

xy Q 2.9395 0.6691 + 100 blue 1 5 mat 3 1 sys

V 0.8 0.8 0.8 0.797 0.759 0.664 0.568 0.506 0.472 0.456 0.448 0.444 0.444 0.444 141 mat

U 2.4 2.408 2.416 2.424 2.432 2.44 2.448 2.456 2.464 2.472 2.48 2.488 2.496 2.504 2.512 2.52 2.528 2.536 2.544 2.552 2.56 2.568 2.576 2.584 2.592 251 mat

"No real roots" => unsane answer ! We can get an
answer by bracketing wisely. x chemist (x 2 diff 0 ≡ x 2.93 2.95 solve 2.939533

2.939533 chemist 0.669072

Y mwfft 9.646 0.584312 1.541009 i * - 0.053087 - 0.363668 i * - 0.250203 0.208152 i * - 0.183 0.215 i * - 0.162435 0.116535 i * - 0.183087 0.067668 i * - 0.179051 0.037392 i * - 0.176 0.179051 0.037392 i * + 0.183087 0.067668 i * + 0.162435 0.116535 i * + 0.183 0.215 i * + 0.250203 0.208152 i * + 0.053087 - 0.363668 i * + 0.584312 1.541009 i * + 161 mat

i 1 X rows range vx i el i : for

Fo Y mwfft mwabs :

Spectrum is missing stem style

0.25 vx Fo . 10 red plotG 2 1 sys

Improve root accuracy

Locate the point of inflexion

x chemist x diff 0.01 x chemist x 2 diff * 2.939 20 2.939 20 - 2 2 mat 3 1 sys

x f x chemist x 2 diff :

a 2.93 : b 2.95 : xn b a + (2 / : 31 line

ε 1010 -^:

Dichotomy n 0 : xn f abs ε > xn f a f * 0 ≤ b xn : a xn : if xn b a + (2 / : n n 1 + : 31 line while 31 line

.. sanity ..

xn 2.939532646

xn f 7.6 1011 -^*

n 84

Genfit Algo

Applicable parts are: Optimiz "numeric" data f φ β βNlin u data 1 col : v data 2 col : n data rows : k x β φ length 1 - : vx-> raw initial vector fit i 1 u length range ev i el u i el β f eval : for M-> Cholesky GradientMatrix j 1 k range i 1 n range M i j el u i el β φ j 1 + el eval : for for CholeskySolver LeastSquares Φ M transpose M * : d M transpose v ev - (* : Δβ Φ 1 -^eval d * : out β Δβ + : 131 line :

Vector gradient ... Optimiz Symbolic x β f n φ V 0 : ct 1 : j 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 j 1 + el PD j el : 21 line ct ct 1 + : 41 line for V 41 line :

Genfit does NOT support repeated samples

data 2 0.8 2.4 0.8 2.8 0.8 2.91 0.8 2.92 0.797 2.93 0.759 2.94 0.664 2.95 0.568 2.96 0.506 2.97 0.472 2.98 0.456 2.99 0.448 3 0.444 3.2 0.444 3.6 0.444 4 0.444 162 mat :

In this Genfit demo, we have successively attempted 'xo' and repeadedly run for 'β'. The model is weird like hell the fit is a task of patience. Amazing, that this secret data set has been cracked with an exact fit wrt the accuracy of the proposed samples.

data data 41312 submatrix :

xo 2.0 :

Model function x β f 1 β 1 el 1 x xo - (1 x xo - (β 2 el x * -^*^* + / :

in φ(x,β,f,n) -> set 'n' to last index β # el ≡

x β φ x β f 2 φ :

β 11221 mat :

11221 mat

1.215372 14.516826 21 mat

1.262638 16.84531 21 mat

1.24958 16.996408 21 mat

1.25 1721 mat

Genfit coeff's of fit β data f φ β βNlin :

β 1.215372 14.516826 21 mat

1.24958 16.996408 21 mat 1.25 1721 mat

Spectrum stemX 1 Fo rows 2 / Floor 1 + range : i 1 stemX rows range stem i el stemX i el Fo i el stemX i el 022 mat : for stem 31 line :

spectrum Spectrum 1 el Spectrum 2 el Spectrum 3 el Spectrum 4 el Spectrum 5 el Spectrum 6 el Spectrum 7 el Spectrum 8 el Spectrum 9 el 91 sys :

Fo 9.646 1.648 0.368 0.325 0.282 0.2 0.195 0.183 0.176 0.183 0.195 0.2 0.282 0.325 0.368 1.648 161 mat

spectrum