<p> TOC [Table of Content] ... from hyperlink </p>

d97f572c-b1b0-4016-9ba9-c3474647ffab 8 4 5 decimal

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

Part 1. Inclusive Table of Content

Table of Content data char size clr plot x β f n φ init iter Minimize data Error L H N xd data dt BarSize corr SSD δ TOC 11 1 line

includes itself TOC content.sm include 10

Example:
1. copy  Minimize(init,iter)
2. paste in "3. "
3. after 3. press space bar
4. only argument name is collected
5. You can fill as you wish ...
6. If you want to retrieve TOC,
       jump to the hyperlink below TOC 1. plot 2. φ 3. Minimize 4. Error 5. xd 6. BarSize 7. corr 8. SSD 9. δ 91 sys ≡

Part 2. Working with Table of Content [include]

Each new project starts here from new data set and model function

XY 104092030430260401925017052 mat :

Model function x β f β 1 el β 2 el x * exp * :

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

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

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

init 500 0.05 - 12 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 1 Y i el X i el β f / - eval : for X Δ augment 21 line :

SSD 512

β 504.902 0.023 - 21 mat

corr 0.9839

FIT range, populate U 060 0.1 range : i 1 U rows range vy i el U i el β f eval : for U vy augment 41 line :

Lifetime of the decay τ 1 β 2 el / abs : 43.4

data FIT 2 1 sys

Relative residuals

Residuals 0.5 BarSize 1 1 sys

Langmir model function x β f β 1 el x β 3 el^* 1 β 2 el x β 3 el^* + / (β 4 el^:

A most difficult data set to fit. For that one, Mathcad is no better, all sorts of coefficients will result ... LM no better either [ERR 0.32]

XY 0.5 0.1 20 3.341 50 6.429 100 9.366 200 12.184 300 13.645 500 15.393 1000 17.767 14001992 mat :

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

<= ConjugateGradient Vector Fnct 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 7574 0.4 45014 mat transpose :

iter 13 :

algo solving for β β init iter Minimize :

assign/isolate .. β β :

SSD 0.101

corr 1.003

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

FIT range, populate U 0150010 range : i 1 U rows range vy i el U i el β f eval : for U vy augment 41 line :

β 646.775 646.312 0.411 4607.136 41 mat

data FIT 2 1 sys

Relative residuals

Residuals 0.1 BarSize

will open a new Smath session from task bar: go back TOC.sm

TOC content.sm <p> TOC [Table of Content] ... from hyperlink </p>

TOC 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 : 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 : 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 : 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 : 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 : SSD Y i el X i el β f - (2^(i 1 XY rows sum : δ j 1 XY rows range Δ j el Y j el X j el β f - eval : for X Δ augment 21 line : 91 sys :