plotG

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plotG

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 :

The Hermite cubic spline demo

XY 0 0.00794 0.1 0.012 0.2 0.022 0.3 0.048 0.4 0.167 0.5 1 0.6 0.167 0.7 0.048 0.8 0.022 0.9 0.012 1 0.00794 112 mat :

X XY 1 col : Y XY 2 col : data X Y + 10 black plotG : 31 line

α 2.75 : β 0.5 : γ 0.1303 : 31 line

D 1 el 0.025 : D 2 el 0.070 : D 3 el γ : D 4 el β : D 5 el α : 51 line

D 6 el 0 : D 7 el α - : D 8 el β - : D 9 el γ - : D 10 el 0.070 - : D 11 el 0 : 61 line

π 0.5 0.1303 31 line

D, Comments

D D 1 el D 2 el D 3 el D 4 el D 5 el D 6 el D 7 el D 8 el D 9 el D 10 el D 11 el 111 mat :

D 0.025 0.07 0.1303 0.5 2.75 0 2.75 - 0.5 - 0.1303 - 0.07 - 0111 mat

This Hermite cubic spline is the Draftsman spline. It has nothing to do with the other Hermite you will find in the web and math literature. This data set is from a pure symmetric function. The infinitesimal derivative allows inspection for the quality of fit. More advanced techniques apply to add points but not introduced in this "curiosity document". Most interesting is the introduction of an index in the argument H(j,u) and the scalar interpolation module J(u,Xdata) and the nesting H(J(u,X),u). Note the Smath ainterp(X,Y,x) is a good candidate. The orange and violet cubic don't please me !

Hermite

b n D rows : i 1 n 1 - range b i el 3 Y i 1 + el * X i 1 + el X i el - (D i 1 + el * - 2 D i el * X i 1 + el X i el - (* - 3 Y i el * - X i 1 + el X i el - (2^/ : for b 31 line :

a n D rows : i 1 n 1 - range a i el D i 1 + el X i 1 + el * D i 1 + el X i el * - 2 Y i 1 + el * - D i el X i 1 + el * + D i el X i el * - 2 Y i el * + X i 1 + el X i el - (3^/ : for a 31 line :

local assigment # 11 line :

j u H i j : a i el u X i el - (3^* b i el u X i el - (2^* + D i el u X i el - (* + Y i el + 21 line :

'J' => index of segment(s) u Xdata J search index n Xdata rows : u Xdata 1 el ≤ n 1 : u Xdata n el ≥ n n 1 - : resume next if if i 1 n range u Xdata i el ≤ break close if for J i 1 - (: 51 line :

Nest/check/interpolate

u InterpHermite u X J u H :

u 0.3 :

u InterpHermite 0.048

x f x InterpHermite :

Global segments

Global segments & pts plot

Data X Y . 13 black plotG :

plot 1 x H 2 x H 3 x H 4 x H 5 x H 6 x H 7 x H 8 x H 9 x H Data 101 sys :

Hermite cubic segments

plot

mirror 4 x H 5 x H 6 x H 7 x H Data 101 sys :

Hermite cubic segments

mirror

21 H 90 H 21 mat 0.337 0.337 21 mat

31 H 80 H 21 mat 5.898 5.898 21 mat

41 H 70 H 21 mat 29.357 29.357 21 mat

Y 4 el 4 X 4 el H - Y 5 el 4 X 5 el H - 21 mat 0021 mat

fit t 1012 -^1.25 0.01 range : i 1 t rows range y i el t i el f eval : for t y augment 31 line :

A t 1012 -^1 0.01 range : i 1 t rows range y i el X Y t i el ainterp eval : for t y augment 31 line :

1012 -^f 1 f 21 mat 0.00794 0.00794 21 mat

fit A data 0.35 0.1075 o 95 green 1 5 mat 4 1 sys

The Hermite α circle X 5 el X 4 el + 2 / Y 5 el Y 4 el + 2 / 21 mat 0.35 0.1075 21 mat

This Hermite adventure does not speak to the 1rst time reader. The α circle represents the difficult part of an experiment in in pure and applied physics [undisclosed] of length X1... X5. This region was considered not accurately fittable by models and excluding rational fraction by lack of support points. The entire data set is a Gaussian ... figure what it is .

h 0.000001 :

Recast the FD deriv in scalar form to support
the  internal "if"  ... success. f x h deriv 0.5 x h - f x f - x h - (x - / x f x h - f - x x h - (- / + (* eval :

x f x h deriv 0 2 1 sys

f 0.5 h deriv 0.000222