<p> Minimize Conjugate-Gradient </p>

1f7a7902-1e12-439f-9626-2d13b548dcd0 2 15 12 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 :

Verhulst logistic to fit AntColony: 'data' from American Scientist, Jan-Feb 1995

colony 500 :

<= Verhulst model function x β f colony β 1 el 11 β 2 el / 1 - (β 3 el x β 4 el - (* - exp * + / + :

XY 15002110032050 3.5 38004540058700610550711200811100911900102 mat :

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

<= Gradient Vector Function x β φ x β f 4 φ :

X XY 1 col : Y XY 2 col : n XY rows : 31 line

L 0 : H 10 : N 199 : 13 mat U L H N xd : 21 line

init 11000 0.75 1.25 514 mat transpose :

iter 5 :

algo solving for β β init iter Minimize :

assign/isolate .. β β :

Absolute  residuals 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 450072

β 10989.3643 0.7447 1.3487 4.9812 41 mat

corr 1.004

bar δ 0.05 BarSize :

bar

FIT i 1 U rows range vy i el U i el β f eval : for U vy augment 21 line :

data XY . 12 black plot :

Verhulst logistic to fit AntColony from American Scientist, Jan-Feb 1995

data FIT 2 1 sys

Ant data set XY 15002110032050 3.5 38004540058700610550711200811100911900102 mat :

colony 500 : β 10990 0.749 1.348 541 mat : 21 mat

x β f colony β 1 el 11 β 2 el / 1 - (β 3 el x β 4 el - (* - exp * + / + :