<p> Minimize Conjugate-Gradient </p>

00f90e2f-ed17-4cb0-8d4d-11a7b2b32ef1 30 4 5 decimal

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

Suggestive cost of pollutants ...

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

XY 001 1.58 2 4.82 3 10.25 4 18.1 5 28.3 6 40.72 7 55.19 8 71.61 9 89.87 10 109.92 112 mat :

Experimental

closely flat foot parabola x β f β 1 el x * 1 x 1.5 - β 3 el / exp + ln (β 2 el^(* 0 + :

<= ConjugateGradient Vector Fnct x β φ x β f 3 φ :

X XY 1 col : Y XY 2 col : 12 mat data XY . 14 black plot : n XY rows : 31 line

hyper robust wrt initials init 11113 mat transpose :

iter 6 :

algo solving for β β init iter Minimize :

assign/isolate .. β β :

SSD 0.00006

corr 1.00000

Absolute residuals ΔR i 1 XY rows range Δf i el Y i el X i el β f - eval : for X Δf augment 21 line :

FIT range, populate U 011 0.01 range : i 1 U rows range vy i el U i el β f eval : for U vy augment 41 line :

β 2.607467 0.769103 1.309392 31 mat

ΔR 001 0.0023 2 0.002 3 0.0034 - 4 0.0018 5 0.0032 - 6 0.0024 7 0.0018 - 8 0.0036 9 0.0019 - 100112 mat

001 0.0023 2 0.002 3 0.0034 - 4 0.0018 5 0.0032 - 6 0.0024 7 0.0018 - 8 0.0036 9 0.0019 - 100112 mat

data FIT 2 1 sys

This project was done for the Mathsoft Collaboratory. Surprisingly well guesstimated from Originator source. Original data have been subjected to a first fitting pass.

... add nodes labels & track explorer

Create your own vector size n Vect n 1 ≡ size ct 1 : j 1 n range a ct 1 el size : ct ct 1 + : 21 line for v a 1 el : k 2 a rows range v v a k el stack : for v 51 line if :

x f x β f :

track 'u' on the cost curve.
'u 3.5' partial pollutant 4.
i.e: ½ pollutant 4 treated. u 3.5 : track 01006100 u u f 32 mat : 21 sys

Alternate values/positions

XY 2 col 0 1.58 4.82 10.25 18.1 28.3 40.72 55.19 71.61 89.87 109.92 111 mat

nodes XY 2 col :

Enable for position nodes XY 1 col :

NodesLabel nodes var2str vectorize : vx XY 1 col : vy XY 2 col : 12 mat n vx rows : Graph nodes vy augment : 41 line

Unable to group ? 6 40.72 12 mat

nodes_label vx vy NodesLabel 9 n Vect black n Vect augment :

◄ Composite plot for convenience.

track FIT data nodes_label 0 50 0 20 - 2 2 mat 7 1 sys

u u f 12 mat 3.5 13.87 12 mat