plot(data,char,size,clr) ..... lookup(data,value,col)

e34e9610-0f0a-4939-9705-ae2c570c9dda 41 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 :

simply indexes the row(s) containing "value in col" data value col lookup k 1 : j k data rows range data j col el value ≡ index k el j : k k 1 + : 21 line 0 if for index IsDefined index No value(s) match error if 31 line :

data spec pts i 1 data rows range p i el a b c spec : for Unest 'p' v p 1 el : j 2 p rows range v v p j el stack : for data v augment 51 line :

The IRS Project

4 appVersion 0.98.6179.21440 ≡

The Internal Revenue Service (IRS) is a U.S. government agency responsible for the collection of taxes and enforcement of tax laws.

Age 707172737475767778798081828384858687888990919293949596979899100311 mat :

Dist 27.4 26.5 25.6 24.7 23.8 22.9 22.0 21.2 20.3 19.5 18.7 17.9 17.1 16.3 15.5 14.8 14.1 13.4 12.7 12.0 11.4 10.8 10.2 9.6 9.1 8.6 8.1 7.6 7.1 6.7 6.3 311 mat :

Where is the old man 85 ?
@ index 'idx' in 'Age' age 85 : idx Age age 1 lookup : 21 sys

X Age ln vectorize : Y Dist ln vectorize : 12 mat XY X Y augment : x f X Y x linterp : x c 1 X min x ≤ (x X max ≤ (& cases : data XY o 5 black plot : 51 sys

IRSoldMan X idx el Y idx el 21 mat :

old_Man X idx el Y idx el X idx el 0.5 - X idx el Y idx el X idx el - Y idx el 42 mat :

Age rows 31

N 2000 : (Density of random ≡ x y1 x f : 21 line

index 1 to explode for value

xmax X 31 el : xmin X idx el : 21 line

ymax Y idx el 1 el : ymin 0 : 21 line

space_x xmax xmin - (: space_y ymax ymin - (: 21 line

A function that tests an arbitrary point 
for its membership in the critical region. x y Test y x y1 + 0 ≥ (y x y1 - 0 ≤ (* :

A routine that finds an array of N random 
pairs in the critical region. Pts the routine is a compressor it maintains density 'N' within the variable region i 1 N range x 1 Random space_x * xmin + 1 el : y 1 Random space_y * ymin + 1 el : 1 x y Test - x 1 Random space_x * xmin + 1 el : y 1 Random space_y * ymin + 1 el : 21 line while P i 1 el x : P i 2 el y : 51 line for P 51 line :

any web color

a b c spec . 8 #A0A0A0 13 mat : pts Pts a b c spec pts : 21 sys

old_Man x f x c * data pts 4 1 sys

left over oldMan ! x f x age ln 100 ln int 0.373

x f x 70 ln 100 ln int 0.962

IRSoldMan 4.443 11 mat 2.695 11 mat 21 mat

# f L Δ N Δinc X 0 : i 1 N range X i 1 + el L Δ i * + : X 1 el L : 21 line for i 1 X rows range vy i el X i el f eval : for X vy augment 41 line :

L 70 ln : Δ 100 ln 70 ln - 100 / : N 101 : 13 mat F x f L Δ N Δinc : 21 sys

F 1 row F N row 21 mat 4.248 3.311 12 mat 4.605 1.841 12 mat 21 mat

data set for integration

data 4.248 3.311 4.252 3.302 4.256 3.294 4.259 3.285 4.263 3.277 4.266 3.268 4.27 3.259 4.273 3.251 4.277 3.242 4.281 3.232 4.284 3.223 4.288 3.214 4.291 3.205 4.295 3.195 4.298 3.185 4.302 3.175 4.306 3.165 4.309 3.155 4.313 3.145 4.316 3.135 4.32 3.124 4.323 3.113 4.327 3.102 4.331 3.092 4.334 3.082 4.338 3.071 4.341 3.061 4.345 3.051 4.348 3.039 4.352 3.027 4.355 3.015 4.359 3.003 4.363 2.992 4.366 2.981 4.37 2.969 4.373 2.957 4.377 2.946 4.38 2.934 4.384 2.921 4.388 2.909 4.391 2.896 4.395 2.884 4.398 2.87 4.402 2.857 4.405 2.844 4.409 2.83 4.413 2.816 4.416 2.802 4.42 2.788 4.423 2.773 4.427 2.758 4.43 2.743 4.434 2.729 4.438 2.715 4.441 2.701 4.445 2.686 4.448 2.672 4.452 2.657 4.455 2.642 4.459 2.626 4.463 2.61 4.466 2.595 4.47 2.578 4.473 2.561 4.477 2.544 4.48 2.527 4.484 2.509 4.487 2.491 4.491 2.474 4.495 2.458 4.498 2.441 4.502 2.424 4.505 2.407 4.509 2.389 4.512 2.371 4.516 2.353 4.52 2.334 4.523 2.315 4.527 2.295 4.53 2.275 4.534 2.256 4.537 2.238 4.541 2.22 4.545 2.202 4.548 2.183 4.552 2.164 4.555 2.144 4.559 2.124 4.562 2.103 4.566 2.082 4.57 2.06 4.573 2.038 4.577 2.015 4.58 1.992 4.584 1.968 4.587 1.947 4.591 1.926 4.594 1.906 4.598 1.884 4.602 1.862 4.605 1.841 4.609 1.819 1022 mat :

Data set from foreign source

data Σ Finite differences Cumul Integ'n vx data 1 col : vy data 2 col : Y 1 el 0 : i 2 vx rows range Δx i el vx i el vx i 1 - el - : Y i el Y i 1 - el 12 / vy i 1 - el vy i el + (Δx i el * (* + : 21 line for vx Y augment 61 line :

data Σ 70 ln 0.5 70 ln 0.25 - 2 2 mat 100 ln 1.25 100 ln 0.25 - 2 2 mat 3 1 sys

data Σ N row 4.605 0.963 12 mat

data Deriv data Derivative BackSubstitution X data 1 col : Y data 2 col : n X rows : deriv 1 el 0 : deriv n el 0 : i 2 n 1 - (range deriv i el 0.5 Y i 1 + el Y i el - X i 1 + el X i el - / Y i el Y i 1 - el - X i el X i 1 - el - / + (* : for deriv 1 el deriv 2 el : deriv n el deriv deriv rows el : X 1 deriv * augment 101 line :

linterp is not smooth. For this particular example linterp f(x) would have to be recast via a model fit function

data Deriv 70 ln 5 70 ln 10 - 2 2 mat 100 ln 5 100 ln 10 - 2 2 mat 3 1 sys plotG, discrete poly

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

Low High step x fnct inc U Low High step range : i 1 U rows range f i el U i el fnct : for U f augment 31 line :

XY 4.248 3.311 4.263 3.277 4.277 3.243 4.29 3.207 4.304 3.17 4.317 3.131 4.331 3.091 4.344 3.054 4.357 3.011 4.369 2.97 4.382 2.929 4.394 2.885 4.407 2.839 4.419 2.791 4.431 2.741 4.443 2.695 4.454 2.646 4.466 2.595 4.477 2.542 4.489 2.485 4.5 2.434 4.511 2.38 4.522 2.322 4.533 2.262 4.543 2.208 4.554 2.152 4.564 2.092 4.575 2.028 4.585 1.96 4.595 1.902 4.605 1.841 312 mat :

X XY 1 col : Y XY 2 col : pts X Y o 5 black plotG : 31 line

Polyfit model x φ 1 x x 2^x 3^41 mat :

any value ≠ 0

Low High step # f inc U Low High step range : i 1 U rows range f i el U i el f : for U f augment 31 line :

Cholesky companion solver j 1 x φ length range i 1 X length range M i j el X i el φ j el : for for Φ M transpose M * : d M transpose Y * : b Φ 1 -^eval d * : 41 line

b 260.258345 192.298714 - 48.362475 4.080319 - 41 mat

M transpose M * not commutative ≡ M transpose Y * not commutative ≡ 21 sys

<= recast the scalar model x fit b x φ * :

Poly X Min X Max 4.25 x fit inc :

Rough polyfit: by inspection OK, respecting Lagrange

pts Poly 2 1 sys

260.258345 192.298714 - 48.362475 4.080319 - 41 mat 1 x x 2^x 3^41 mat *

rate of change IRS wrt age [70 ... 100]

x fit x diff x c * 70 ln 1 70 ln 10 - 2 2 mat 100 ln 1 100 ln 10 - 2 2 mat 4 1 sys

More statistical insight

SSD = "Sum Square Differences" SSD Y i el X i el fit - (2^(i 1 X rows sum : 0.00015

χ X Mean : μ Y Mean : n XY rows : 31 line

χ μ n 31 mat 4.437065 2.651419 3131 mat

Pearson’s correlation coefficient corr 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 fit eval μ - (* (i 1 n sum X i el χ - (2^(i 1 n sum X i el fit eval μ - (2^(i 1 n sum * sqrt / / : 1.00000

correlation between [X,Y data]

correlation between [X,fitted model]

hatch

Erzeugt eine Matrix für die Darstellung vertikaler Linien zwischen den Funktionen f(x) und 
g(x) im Bereich von x1 bis x2 mit 2*n Linien. Generates a matrix for 2*n vertical lines (hatching) between functions f(x) and g(x)
in x-range from x1 to x2 f g x.1 x.2 N hatch dx x.2 x.1 - N / (: h x.1 x.1 f x.1 x.1 g 22 mat : x x.1 x.2 dx - x.1 dx + range h h x dx 2 / + x dx 2 / + g x dx 2 / + x dx 2 / + f x dx + x dx + f x dx + x dx + g 42 mat stack : for h 41 line :

x f 260.258345 192.298714 x * - 48.362475 x 2^* + 4.080319 x 3^* - : x g 0 x * : 21 sys

IRSoldMan age IRSoldMan stack :

Predictive left over IRS for the oldMan [85] up to 100

old_Man x f x c * x f x g X idx el ( 1 el X Max 20 hatch age ln 0.25 age 1 3 mat 5 1 sys

IRSoldMan 85 4.443 11 mat 2.695 11 mat 31 mat

observe index X idx el (1 el 4.443

index 1 to explode

Possible model fit to this IRS arc

XY 4.248 3.311 4.263 3.277 4.277 3.243 4.29 3.207 4.304 3.17 4.317 3.131 4.331 3.091 4.344 3.054 4.357 3.011 4.369 2.97 4.382 2.929 4.394 2.885 4.407 2.839 4.419 2.791 4.431 2.741 4.443 2.695 4.454 2.646 4.466 2.595 4.477 2.542 4.489 2.485 4.5 2.434 4.511 2.38 4.522 2.322 4.533 2.262 4.543 2.208 4.554 2.152 4.564 2.092 4.575 2.028 4.585 1.96 4.595 1.902 4.605 1.841 312 mat :

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 :

a 0.485 : b 0.725 - : xo 0.1625 : n 0.96 : d 1.7 : 51 sys

model too reactive for any auto-optimization
here: => fitted manually a b xo n d x model a b x xo + (n^-^(* d + Re :

XY o 5 black plot a b xo n d x model 2 1 sys