<p> Minimize Conjugate-Gradient </p>

81b545ba-8a8d-489b-acb9-5e9779924056 5 4 5 decimal

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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 :

Minimize model "ConjugateGradient" wrt parameters [β's]

45 0.0959 80 0.4741 120 1.9867 160 6.1814 210 19.0739 52 mat

45 0.0959 80 0.4741 120 1.9867 160 6.1814 180 10.0263 52 mat

Model function x β f 0.0061078 β 1 el x * x β 2 el + / exp * :

XY 180 10.0263 230 27.9679 300 85.8771 350 165.2916 373.707 220.0012 52 mat :

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

<= ConjugateGradient Vector Fnct x β φ x β f 2 φ :

180 10.0263 230 27.9679 300 85.8771 350 165.2916 373.707 220.0012 52 mat

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

init 1524012 mat transpose :

iter 5 :

algo solving for β β init iter Minimize :

assign/isolate .. β β :

Relative residuals Residuals i 1 XY rows range Δ i el Y i el X i el β f - : for X Δ augment 21 line :

SSD 3

β 17.451 248.083 21 mat

corr 0.9989

FIT range, populate U 210374211 range : i 1 U rows range vy i el U i el β f eval : for U vy augment 41 line :

data FIT 2 1 sys

Relative residuals

Residuals 0.5 BarSize 1 1 sys