plot(data,#,size,#)

5c87ef03-a2e5-4f69-bfc0-3d7e24c2b06d 108 4 5 decimal

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

plot(data,#,size,#)

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 :

f(x,β) NOT compatible: L-M, Genfit Conjugate Gradient, al_nleqsolve . . . Mathcad

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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 : 12 mat xy XY . 12 black plot : 21 line

NOT compatible Smath Conjugate Gradient x β f 1 β 1 el x β 4 el - (β 2 el x β 4 el - (β 3 el x * -^*^* β 5 el + / :

β 11172 1.2502 51 mat :

Q U 2.8 3.2 2.801 range : j 1 U rows range vy j el U j el β f eval : for U vy augment 31 line :

2.93 β f 0.759

Transmute model fit ... for undocumented reaction/reactants

xy Q 2.94 0.664 + 100 blue 1 5 mat 2.944 0.622 o 5 black 1 5 mat 4 1 sys

Absolute  residuals δ j 2 XY rows 1 - (range vx j 1 - el X j el : vy j 1 - el Y j el : Δ j 1 - el Y j el X j el β f - eval : 31 line for vx vy Δ augment 21 line :

δ 2.4 0.8 0 2.8 0.8 0 2.91 0.8 0 2.92 0.797 0.001 2.93 0.759 0 2.94 0.664 0 2.95 0.568 0 2.96 0.506 0 2.97 0.472 0 2.98 0.456 0.001 2.99 0.448 03 0.444 0 3.2 0.444 0 3.6 0.444 0143 mat

Near vertical @ datum '0', bracket wisely. x β f 0.8 0.444 + (2 / - 0 ≡ x 2.75 3.925 solve 2.944031

Σ X 2.8 3.2 2.81 range : i 1 X rows range cumul i el x β f x X 1 el X i el int eval : for X cumul augment 31 line :

Σ Σ :

Σ Σ rows row 3.2 0.2297 12 mat

Near vertical @ datum '0', bracket wisely. x β f (x 2 diff 0 ≡ x 2.93 2.95 solve 2.93953334937398

Improve root accuracy

Locate the point of inflexion diff((f(x,β)),x,2) scaled 0.01

x β f x diff 0.01 x β f x 2 diff * 2.9395 20 2.9395 20 - 2 2 mat 3 1 sys

x f x β f 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

xn 2.93953325280976

xn f 5.6 1011 -^* -

n 44

2.939533 β f 0.668982

NOT compatible Smath Conjugate Gradient x β xo f 1 β 1 el x xo - (β 2 el x xo - (β 3 el x * -^*^* β 4 el + / :

β 1117 1.25 41 mat :

Hyper reflexive model function 1 β 1 el x β 4 el - (β 2 el x β 4 el - (β 3 el x * -^*^* β 5 el + /

Transmute model fit ... for undocumented reaction/reactants

x β 1.95 f x β 1.975 f x β 2 f x β 2.025 f x β 2.05 f x β 2.075 f xy 7 1 sys

11172 1.2502 51 mat

===== Good fit by hand =====

plot(data,#,size,#)

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 :

XY 0100 0.1 100 0.2 100 0.3 100 0.4 100 0.5 100 0.6 100 0.7 100 0.8 99.03 0.9 83.62 1 52.49 1.1 27.49 1.2 13.52 1.3 6.61 1.4 3.3 1.5 1.69 1.6 0.89 1.7 0.48 1.8 0.27 1.9 0.16 2 0.09 212 mat :

The English hat model function m n x J 1001 n x n + (m^* + / :

even m 14 :

n 0.125 :

data XY . 12 black plot :

You may constrain the plot starting @ '0'

data m n x J 2 1 sys

X XY 1 col : Y XY 2 col : 12 mat

Absolute  residuals δ j 1 XY rows range vx j el X j el : vy j el Y j el : Δxy j el Y j el m n X j el J - eval : 31 line for vx vy Δxy augment 21 line :

δ 01000 0.1 1000 0.2 1000 0.3 1000 0.4 100 0.002 0.5 100 0.017 0.6 100 0.138 0.7 100 0.839 0.8 99.03 3.058 0.9 83.62 1.369 - 1 52.49 8.109 - 1.1 27.49 4.337 - 1.2 13.52 0.054 1.3 6.61 1.29 1.4 3.3 1.172 1.5 1.69 0.804 1.6 0.89 0.504 1.7 0.48 0.304 1.8 0.27 0.187 1.9 0.16 0.119 2 0.09 0.069 213 mat

01000 0.1 1000 0.2 1000 0.3 1000 0.4 100 0.002 0.5 100 0.017 0.6 100 0.138 0.7 100 0.839 0.8 99.03 3.058 0.9 83.62 1.369 - 1 52.49 8.109 - 1.1 27.49 4.337 - 1.2 13.52 0.054 1.3 6.61 1.29 1.4 3.3 1.172 1.5 1.69 0.804 1.6 0.89 0.504 1.7 0.48 0.304 1.8 0.27 0.187 1.9 0.16 0.119 2 0.09 0.069 213 mat

k 0.609318 : xo 0.405489 : n 7.488356 : 31 mat

99 x xo - k / (n^- unsolved Smath WIN 7 plots OK Mathcad WIN XP 21 sys ≡

99 x xo - k / ( n ^ -