plotG(vx,vy,char,size,color)

12659175-bac0-46ef-a326-25aa6231aeb8 15 4 5 decimal

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

vx vy char size color plotG n vx length : plot vx 1 el vy 1 el char size color augment : i 2 n range plot plot vx i el vy i el char size color augment stack : for plot 41 line :

Carbon12 0.175 317.303 0.35 195.232 0.525 124.387 0.7 43.733 0.875 40.463 1.05 55.722 1.225 90.599 1.4 115.668 1.575 184.332 1.75 140.736 1.925 100.409 2.1 57.902 2.275 42.643 2.45 58.992 2.625 98.229 2.8 206.131 2.975 316.212 3.15 345.64 3.325 284.605 3.5 235.559 3.675 90.599 3.85 35.014 4.025 36.104 4.2 11.035 242 mat :

Xo Carbon12 1 col :

X Carbon12 1 col :

Yo Carbon12 2 col :

Y Carbon12 2 col :

n X rows :

n 24

t0 1 time :

ρ 0.525 : m 2.5 : μ 0 : σ 0.385 : 41 sys

X 2 el 0.315 : Y 9 el 230 : 21 line

r m ρ * - ρ - ρ m ρ * 14 mat transpose :

visible Lagrange iterated product x L x r 1 el - (x r 2 el - (* x r 3 el - (* x r 4 el - (* :

r 1.3125 - 0.525 - 0.525 1.3125 41 mat

x μ σ dnorm 12 π * σ * sqrt / 12 σ 2^* / x μ - (2^* - exp * :

Kernel exposed page: 4 x Kernel x L x μ σ dnorm * :

bw 1 :

weighted moving average smoothing kernel j X Y Sup X i el X j el - bw / Kernel Y i el * (i 1 X rows sum X i el X j el - bw / Kernel (i 1 X rows sum / :

W j 1 X rows range s j el j X Y Sup eval : constrain 1rst node s 1 el 301.5 : 31 line for s 21 line :

W W :

XW X W augment : vx Xo : vy XW 2 col : Δ Yo W - : 41 line

t 0.175 4.2 0.185 range :

t rows 403

Cfit i 1 t rows range u i el t i el : v i el vx vy t i el cinterp eval : 21 line for u v augment 21 line :

C12 Xo Yo + 7 blue plotG : XW XW 1 col XW 2 col o 7 blak plotG : Title 1360 Carbon α 12 12 black 15 mat : 31 sys

1 time t0 - 3.6 s *

FD Derivative

data Deriv data Derivative BackSubstitution X data 1 col : Y data 2 col : n X rows : deriv 1 el 0 : deriv n el 0 : i 2 n 1 - range deriv i el 0.5 Y i 1 - el Y i el - X i 1 - el X i el - / Y i el Y i 1 - el - X i el X i 1 - el - / + (* : for deriv 1 el deriv 2 el : deriv n el deriv n 1 - el : X deriv augment 101 line :

0 Cfit C12 XW Title 5 1 sys Cfit Deriv 0 2 1 sys Stem construct

iii 1 Δ rows range P iii el 3 : P Δ rows el 2 : 21 line for

ii 1 Δ rows range v ii el ii : for

i 1 v length range YΔ 3 i * el Δ i el : for

Core component of the stem style P v replicate Mathcad 8 Pro. Treasury k 1 : i 1 v length range P i el 1 ≡ continue j 1 P i el range T k j + el v i el : for k k P i el + : 21 line if for T 41 line :

datum 0 :

u P v replicate :

V u YΔ augment :

Δx P Xo replicate :

Residuals Δx V 2 col augment :

β 1403.4 6.8679 3.4766 4.6785 0.10541 5.9138 1.0965 2933.1 33.952 0.32404 4.1246 0.50485 14.081 131 mat :

Title 145 Cα12 SuperSmoothlet 12 black 15 mat :

Residuals on SuperSmoothlet... extensible at will.

Residuals datum Title 3 1 sys

Δ Max Δ Min 21 mat 22 27.9 - 21 mat

Padé rational fraction from Cfit, converted J_Fraction x J β 1 el β 8 el x β 2 el - β 9 el x β 3 el + β 10 el x β 4 el - β 11 el x β 5 el + β 12 el x β 6 el - β 13 el x β 7 el + / + / - / + / - / + / - :

x q 0.175 x ≤ (x 4.2 ≤ (& x J eval out of range if :

x D 0.175 x ≤ (x 4.2 ≤ (& x J (x diff eval out of range if :

D(x) takes 3 min to plot instead: plot Dinf(x,h,f)

x q 0.5 x D * 2 1 sys

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 :

range/discretise L 0.175 : H 4.2 : N 400 : 13 mat U L H N xd : 21 sys

x fnct Q i 1 U rows range vx i el U i el : vy i el U i el fnct eval : 21 line for vx vy augment 21 line :

Ω x J Q :

Convolution Derivative  on Padé J_Fraction.
The J_Fraction is collected from Mathcad 11 Φ U Δeriv_f dx U 2 el U 1 el - : scale 1 - 2 dx * / : f 1 - 0113 mat transpose : dy Φ 2 col f al_convr1d : dy dy 2 dy rows 1 - 11 submatrix : Deriv U scale dy * augment : Deriv Deriv 2 Deriv rows 1 - 12 submatrix : 71 line :

h 0.001 : x f x J : 21 line

x c 1 0.175 x ≤ (x 4.2 ≤ (& cases :

x h f Dinf 0.5 x h - f x f - x h - (x - / x f x h - f - x x h - (- / + (* :

Discretised function

C12 Ω 2 1 sys

Scalar infinitesimal derivative

0 x h f Dinf x c * 2 1 sys

Convolution derivative wrt J(x)

0 Ω U Δeriv_f 2 1 sys

convolution over J(x) convolutionn over W

Derivative by Convolution: adapted from Martin Kraska.

Derivative convolution on "Cfit" SuperSmoothlet data Δeriv Vx data 1 col : Vy data 2 col : dx Vx 2 el Vx 1 el - : scale 1 - 2 dx * / : f 1 - 0113 mat transpose : Dy Vy f al_convr1d : Dy Dy 2 Dy rows 1 - 11 submatrix : Deriv Vx scale Dy * augment : Deriv Deriv 2 Deriv rows 1 - 12 submatrix : 91 line :

1 time t0 - min 3.1

0 Cfit Δeriv 2 1 sys

x c 12 - x ≤ (x 2 ≤ (& cases :

Expose the smoothing kernel(x)

x Kernel x c * r 2 el 0.125 r 2 el 0.125 - 2 2 mat r 3 el 0.125 r 3 el 0.125 - 2 2 mat 3 1 sys

jmGiraud: 2015/10/06