<p> Minimize Conjugate-Gradient </p>

e74e6f3f-b332-45e2-a016-fdb9cf39ba45 12 3 12 decimal

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

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 :

Pile-Redux 'a4' XY 1.3 9.812 1.4 6.375 1.5 4.89 1.6 4.063 1.7 3.535 1.8 3.169 1.9 2.9 2 2.694 2.1 2.532 2.2 2.4 2.3 2.292 2.4 2.2 2.5 2.122 2.6 2.055 2.7 1.997 2.8 1.946 3.2 1.79 3.6 1.685 4 1.61 4.4 1.553 4.8 1.509 5.2 1.473 5.6 1.444 6 1.42 6.4 1.399 6.8 1.381 7.2 1.366 7.6 1.352 8 1.34 8.4 1.33 8.8 1.32 9.2 1.312 9.6 1.304 10 1.297 342 mat :

Transmute model to Pile-Redux

a 1.15 : b 0.005 - : c 1.4 : d 1 : 14 mat

x f a b x * + c x d + / + :

x c 11 x ≤ cases :

data XY o 5 black plot :

data x 2.125 - f x c * 2 1 sys

symbolic model fit
recast as parametric x 2.125 - f 1792018578 x * - (9 - 8 x * + (* + 16009 - 8 x * + (* /

Next ... rational parametric fit

<p> Minimize Conjugate-Gradient </p>

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 :

# # log

parametric model fit x β f β 1 el β 3 el β 4 el x * - (β 5 el - β 4 el x * + (* + β 2 el β 5 el - β 4 el x * + (* / :

<= ConjugateGradient Vector Fnct x β φ x β f 5 φ :

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

init 17920160018578915 mat transpose :

iter 3 :

algo solving for β β init iter Minimize :

assign/isolate .. β β :

SSD 0.0332

corr 0.998

FIT range, populate U 1.3 12 1.31 range : i 1 U rows range vy i el U i el β f eval : for U vy augment 41 line :

β 69066.5941 6061.2614 6995.5633 8.7912 10.0930 51 mat

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

data FIT 2 1 sys

Absolute residuals

Residuals 0.005 BarSize 1 1 sys