Plot Utilities

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Plot 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 :

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 :

L-M <= courtesy ... Carlos 2018_09_20

HEADER ITER S:x.1 S:x.2 S:x.3 S:x.4 Res1 μ dnor 18 mat :

t 1012 -^0.51 0.82 1.02 1.23 1.43 1.85 2.05 2.36 4.52 9.22 111 mat :

y 0.78 0.8 0.92 1.14 1.26 1.28 1.22 1.16 1.12 1.08 1.08 111 mat :

model function to fit wrt data set x β f β 2 el β 1 el β 2 el - 1 x β 3 el / (β 4 el^+ / + β 1 el β 2 el - 1 x β 3 el / (β 4 el^+ (2^/ x β 3 el / (β 4 el^* β 4 el * - (:

X x 1 el x 2 el x 3 el x 4 el 41 mat :

n X length : m t length : 21 line

3 appVersion 0.98.6179 ≡ Timing_LM ~ 1 min ≡ ConjugateGradient 6 s ≡ 31 line

t0 1 time :

L-M Components

t X ia X 2 el X 1 el X 2 el - 1 t X 3 el / (X 4 el^+ / + X 1 el X 2 el - 1 t X 3 el / (X 4 el^+ (2^/ t X 3 el / (X 4 el^* X 4 el * - :

i 1 m range ΦΦ i el t i el X ia y i el - : for X Φ ΦΦ : 21 line

i 1 m range j 1 n range X j el X j el h + : jjh1 t i el X ia y i el - : X j el X j el 2 h * - : jjh2 t i el X ia y i el - : jjh0 i j el jjh1 jjh2 - 2 h * / : X j el X j el h + : 61 line for 11 line for

X derfhφ jjh0 :

initialise the solver x 111414 mat transpose :

[ShortVersion] ... the data Table has been removed from the original.

Eps 1106 -^* :

L-M algorithm

h Eps sqrt abs : μ 0.01 : μ1 104.5069 : 31 sys

tol Eps sqrt x normi * :

cont 0 : dnor 1 : update 1 : 31 line dnor tol > update 1 ≡ f x Φ : J x derfhφ : jtj J transpose J * : res f norme (2^: 41 line if 11 line a jtj μ n identity * + : s1 a 1 -^J transpose f * (* : b1 x s1 - (: f1 b1 Φ : res1 f1 norme (2^μ1 / : 51 line res1 res < x b1 : f f1 : 12 mat dnor s1 normi x normi / : cont cont 1 + : Sol cont 1 el cont : z 1 n range Sol cont z 1 + el x z el : 11 line for Sol cont n 2 + el res1 μ1 * : Sol cont n 3 + el μ : Sol cont n 4 + el dnor : μ μ 10 / : update 1 : 101 line μ μ 10 * : update 0 : 21 line if 31 line while 21 line

β x : 0.77736 1.072743 1.278167 4.80147 41 mat

X t : Y y : 12 mat

corr

corr Pearson correlation χ X Mean : μ Y Mean : n X 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 :

SSD = "Sum Square Differences" SSD y i el t i el β f - (2^(i 1 n sum :

FIT U 020 0.05 range : i 1 U rows range vy i el U i el β f eval : for U vy augment 31 line :

tol 0.004

β 0.777 1.073 1.278 4.801 41 mat

0.777333 1.072745 1.278124 4.800763 41 mat

corr 1.079

SSD 0.001

1 time t0 - min 0.9

Absolute residuals Residuals i 1 t rows range Δ i el y i el t i el β f - 3 round : for t Δ augment 21 line :

t y augment FIT 2 1 sys

Absolute residuals

Residuals 0.025 BarSize 1 1 sys

1 time t0 - min 1.1

Conjugate Gradient

]]> Minimize Conjugate-Gradient

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 :

3 appVersion 0.98.6179 ≡ Timing 7 sec ≡ 21 line

clear ln0 undefined ε 1015 -^:

XY ε 0.78 0.51 0.8 0.82 0.92 1.02 1.14 1.23 1.26 1.43 1.28 1.85 1.22 2.05 1.16 2.36 1.12 4.52 1.08 9.22 1.08 112 mat :

x β f β 2 el β 1 el β 2 el - 1 x β 3 el / (β 4 el^+ / + β 1 el β 2 el - 1 x β 3 el / (β 4 el^+ (2^/ x β 3 el / (β 4 el^* β 4 el * - :

t0 1 time :

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

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

init 0.5 11114 mat transpose :

iter 9 :

algo solving for β β init iter Minimize :

assign/isolate .. β β :

1 time t0 - s 6

SSD 0.0015

Absolute  residuals δ Δ 0 : j 1 XY rows range Δ j el Y j el X j el β f - 3 round eval : for X Δ augment 31 line :

corr 1.0794

.... L-M
identical CG 
wrt Residuals 0.777335509074769 1.07274497889379 1.27812699550013 4.80082359179995 41 mat

bar δ 0.0375 BarSize (:

FIT U 010 0.025 range : i 1 U rows range vy i el U i el β f eval : for U vy augment 31 line :

β 0.77735 1.07274 1.27815 4.80111 41 mat

bar

data XY o 5 black plot :

Title 21 Pharmacokinetics 12 black 15 mat :

collect 1.08 FIT 0.78 data Title 51 sys :

collect