Function Utilities

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Function Utilities

vx vy char size clr plotG n vx length : plot vx 1 el vy 1 el char size clr augment : i 2 n range plot plot vx i el vy i el char size clr augment stack : for plot 41 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 :

Applicable parts are: Optimiz "numeric" XY f φ β Minimize 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 :

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 :

Module xd(L,H,N) is a discretiser for use in-situ [user spec's]: range [L,H], density [N].

Vector gradient ... Optimiz Symbolic 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 :

½ range

XY 00600 0.133 1200 0.189 1800 0.2323 2400 0.2691 3000 0.3017 3600 0.3314 4200 0.3588 4800 0.3844 5400 0.4086 6000 0.4316 6600 0.4536 7200 0.4746 7800 0.4949 8400 0.5145 9000 0.5335 9600 0.5519 10200 0.5699 10800 0.5873 11400 0.6044 12000 0.621 12600 0.6373 13200 0.6533 13800 0.669 14400 0.6844 15000 0.6995 15600 0.7143 16200 0.7289 16800 0.7433 17400 0.7575 18000 0.7715 18600 0.7853 19200 0.7989 19800 0.8123 20400 0.8256 21000 0.8387 21600 0.8517 22200 0.8645 22800 0.8772 23400 0.8897 24000 0.9022 24600 0.9145 25200 0.9267 25800 0.9388 26400 0.9507 27000 0.9626 27600 0.9744 28200 0.9861 28800 0.9977 29400 1.0092 30000 1.0206 30600 1.0319 31200 1.0431 532 mat :

XY 005000 0.3926 10000 0.5639 15000 0.6995 20000 0.8167 25000 0.9226 30000 1.0206 35000 1.1127 40000 1.2003 45000 1.2844 50000 1.3657 55000 1.4448 60000 1.5219 65000 1.5977 70000 1.6722 75000 1.7458 80000 1.8187 85000 1.8911 90000 1.9632 95000 2.0353 1105^* 2.1074 1.05 105^* 2.1798 1.1 105^* 2.2527 232 mat :

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

ε 0.001 :

Verhulst model to "ant colony" x β f β 1 el x ε + (* (β 2 el^:

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

x β φ x β f 2 φ :

β β 1 el 0.000035 0.6 21 mat : iter 3 : i 1 : i iter ≤ β i 1 + el XY f φ β i el Minimize : i i 1 + : 21 line while β β iter el : 51 line :

β β :

Absolute residuals δ i 1 XY rows range Δ i el Y i el X i el β f - 2 round eval : for X Y Δ augment 21 line :

δ 000600 0.133 0.01 1200 0.189 0.01 1800 0.2323 0.01 2400 0.2691 03000 0.3017 03600 0.3314 04200 0.3588 04800 0.3844 05400 0.4086 06000 0.4316 06600 0.4536 07200 0.4746 0133 mat

FIT U 030000500 range : i 1 U rows range FIT i el U i el β f eval : for U FIT augment 31 line :

β 3.438 105 -^* 0.534 21 mat

data X Y . 12 black plotG :

data FIT 2 1 sys

Δelta X δ 3 col augment : stem Δelta Error : 21 line

0 stem 2 1 sys