plot(data,char,size,clr)

50bd4ae6-e705-406b-bf17-69308ebf987b 6 4 5 decimal

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

data 1850 1.97 108^* 2.62 109^* 1851 1.99 108^* 2.71 109^* 1852 2.08 108^* 2.76 109^* 1853 2.17 108^* 2.83 109^* 1854 2.55 108^* 2.89 109^* 1855 2.60 108^* 2.90 109^* 1856 2.77 108^* 2.95 109^* 73 mat :

XY data 1 col 1850 - data 2 col 108 -^* augment :

UV data 1 col 1850 - data 3 col 109 -^* augment :

XY UV 2 1 sys

XY 0 1.97 1 1.99 2 2.08 3 2.17 4 2.55 5 2.6 6 2.77 72 mat

plot(data,char,size,clr)

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 :

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

x φ 1 x x 2^31 mat :

Cholesky companion solver j 1 x φ length range i 1 X length range M i j el X i el φ j el : for for Φ M transpose M * : d M transpose Y * : 12 mat b Φ 1 -^eval d * : 31 line

b 1.933333 0.065357 0.013452 31 mat

M transpose M * not commutative ≡

M transpose Y * not commutative ≡

recast the fit x p b 1 el b 2 el x * + b 3 el x 2^* + :

x λ 1 X 1 el x ≤ (x X X rows el ≤ (& cases :

XY . 10 black plot x p x λ * 2 1 sys Minimize Conjugate-Gradient

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 :

init iter Minimize XY f φ β LS X XY 1 col : Y XY 2 col : n XY rows : k x β φ length 1 - : vx-> raw initial vector fit i 1 X length range vx i el X i el β f eval : for M-> Cholesky GradientMatrix j 1 k range i 1 n range M i j el X i el β φ j 1 + el eval : for for CholeskySolver LeastSquares Φ M transpose M * : d M transpose Y vx - (* : Δβ Φ 1 -^eval d * : b β Δβ + : 131 line : β 1 el init : i 1 : i iter ≤ β i 1 + el XY f φ β i el LS : i i 1 + : 21 line while β β iter el : 41 line β 31 line :

Vector Gradient ... Optimiz Symbolic
seemingly a scalar kernel  not 
recognized in program loop x β f n φ ct 1 : i 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 i 1 + el PD i el : 21 line ct ct 1 + : 41 line for V 31 line :

Error stem plot for QuickPlot unicolor data Error stemX 1 data rows range : i 1 stemX rows range stem i el data i 1 el data i 2 el data i 1 el 022 mat : for i 1 stem rows 1 - range stem i el stem i el stem i 1 + (1 el 1 el 012 mat stack : for V stem 1 el : j 2 stem rows 1 - range V V stem j el stack : for V V data data rows row stack : 71 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 :

Bar plot unicolor style, bar width user. data dt BarSize v data 2 col : t v bar t dt - 0 t dt - v t dt + v t dt + 042 mat : j 1 data rows range j 1 ≡ B data j 1 el data j 2 el bar : B B data j 1 el data j 2 el bar stack : if 11 line for B 41 line :

corr Pearson correlation χ X Mean : μ Y Mean : n XY rows : 13 mat X i el χ - (Y i el μ - (* (i 1 n sum X i el χ - (2^(i 1 n sum Y i el μ - (2^(i 1 n sum * sqrt / X i el χ - (X i el β f eval μ - (* (i 1 n sum X i el χ - (2^(i 1 n sum X i el β f eval μ - (2^(i 1 n sum * sqrt / / 31 line :

correlation between [X,Y data]

correlation ... [X,fitted model]

Absolute  residuals observer
fetches β from calculated δ j 1 XY rows range Δ j el Y j el X j el β f - eval : for X Δ augment 21 line :

SSD = "Sum Square Differences" SSD Y i el X i el β f - (2^(i 1 XY rows sum :

Otherwise Pearson independent of f(x,ParameterName) x y corr n x length : xy x y * vectorize : x2 x x * vectorize : y2 y y * vectorize : n xy sum (* x sum (y sum (* - n x2 sum (* x sum (2^- (n y2 sum (* y sum (2^- (* (sqrt / 51 line :

Fit ii 1 n range Fit ii el X ii el β f : for Fit 21 line :

<= Exp model function x β f β 1 el β 2 el e β 3 el x *^* + :

XY 0 1.97 1 1.99 2 2.08 3 2.17 4 2.55 5 2.6 6 2.77 72 mat :

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

<= Gradient Vector Function x β φ x β f 3 φ :

init 2 0.75 0.1 13 mat transpose :

iter 9 :

algo solving for β β init iter Minimize :

assign/isolate .. β β :

β 1.3801 0.5392 0.1631 31 mat

XY . 10 black plot x p x λ * x β f x λ * 3 1 sys