data [145 pairs]

773bb184-932f-4f34-b250-6310dddf283a 15 4 5 decimal

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

Plot points 4 Styles ...

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

~ 12 times faster than plotG(,,,,,) a b c spec . 12 red 13 mat : plot data a b c spec pts : 21 line

1. Plenty of named colors from X_Y Smath 2. More web colors from "Rapid Tables"

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 :

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 :

X 1 1.5 2 2.5 351 mat :

Y 4532451 mat :

Symbol . : size 14 : clr black : 13 mat

Often convenient to nest

fill-in matrix(5*3)
specify 'selected' plotSample Symbol size clr Symbol size clr Symbol size clr + 40 blue Symbol size clr 53 mat :

x f X Y x cinterp : Data X Y plotSample augment : 21 sys

data NestRows j 1 data rows range nest j 1 el data j row : for nest 21 line :

Data x f 2 1 sys

Data NestRows 14.14 black 15 mat 1.5 5.14 black 15 mat 23.14 black 15 mat 2.5 2 + 40 blue 15 mat 34.14 black 15 mat 51 mat

Data 14.14 black 1.5 5.14 black 23.14 black 2.5 2 + 40 blue 34.14 black 55 mat

Plot points Style 4 ...

data [145 pairs]

XY 0 0.152 0.006944 0.063 0.014 0.098 0.021 0.263 0.028 0.125 0.035 0.107 0.042 0 0.049 0.25 0.056 0.071 0.063 0.259 0.069 0.286 0.076 0.205 0.083 0.295 0.09 0.214 0.097 0.188 0.104 0.152 0.111 0.295 0.118 0.214 0.125 0.125 0.132 0.098 0.139 0.107 0.146 0.357 0.153 0.473 0.160 0.214 0.167 0.232 0.174 0.259 0.181 0.268 0.188 0.196 0.194 0.152 0.201 0.179 0.208 0.241 0.215 0.143 0.222 0.196 0.229 0.321 0.236 0.134 0.243 0.179 0.25 0.107 0.257 0.071 0.264 0.143 0.271 0.152 0.278 0.330 0.285 0.339 0.292 0.170 0.299 0.268 0.306 0.348 0.313 0.268 0.319 0.143 0.326 0.080 0.333 0.045 0.340 0.143 0.347 0.205 0.354 0.036 0.361 0.00893 0.368 0.027 0.375 0.063 0.382 0.045 0.389 0.116 0.396 0.107 0.403 0.259 0.410 0.339 0.417 0.143 0.424 0.036 0.431 0.134 0.438 0.223 0.444 0.268 0.451 0.286 0.458 0.196 0.465 0.223 0.472 0.170 0.479 0.259 0.486 0.393 0.493 0.295 0.5 0.268 0.507 0.134 0.514 0.330 0.521 0.402 0.528 0.366 0.535 0.259 0.542 0.366 0.549 0.321 0.556 0.366 0.563 0.438 0.569 0.527 0.576 0.455 0.583 0.455 0.590 0.527 0.597 0.509 0.604 0.509 0.611 0.643 0.618 0.527 0.625 0.366 0.632 0.375 0.639 0.375 0.646 0.375 0.653 0.286 0.660 0.402 0.667 0.482 0.674 0.536 0.681 0.313 0.688 0.313 0.694 0.241 0.701 0.509 0.708 0.563 0.715 0.500 0.722 0.464 0.729 0.500 0.736 0.491 0.743 0.518 0.750 0.259 0.757 0.330 0.764 0.411 0.771 0.402 0.778 0.384 0.785 0.500 0.792 0.446 0.799 0.304 0.806 0.438 0.813 0.554 0.819 0.321 0.826 0.366 0.833 0.286 0.84 0.527 0.847 0.446 0.854 0.527 0.861 0.571 0.868 0.589 0.875 0.527 0.882 0.688 0.889 0.500 0.896 0.482 0.903 0.563 0.910 0.688 0.917 0.696 0.924 0.634 0.931 0.777 0.938 0.732 0.944 0.598 0.951 0.643 0.958 0.705 0.965 0.813 0.972 0.670 0.979 0.857 0.986 1 0.993 0.777 1 0.732 1452 mat :

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

t0 1 time :

Hyperfast/compact
independent in-situ a b c spec . 10 black 13 mat : data XY a b c spec pts : 21 sys

style '4' plot data

data

1 time t0 - 0.4 s *

Int(f,a,b,n)

Simpson Integrator in the Romberg Transform Domain [0,1] <= [a,b] ...  
... integrates  Smath ainterp(X,Y,x), cinterp(X,Y,x), cubic(x) from  l_p_c_spline 
Integration accuracy from user command line 'n' ... NUMERIC f a b n Int w s b a - (34 / 2 w * 1 - (* 14 / 2 w * 1 - (3^* - 12 / + (* a + : w G w s f 12 w * 1 - (2^- (* : ... α 0 : β 1 : h β α - n / : 15 mat Simpson 13 / h 2 / α G β G + (* h α k h * + G k 1 n 1 - sum * + (* 23 / h * α h 2 / - k h * + G k 1 n sum * + eval : 32 / b a - (* Simpson * 41 line :

b1 3.4445 - : b2 1.5 : β 4 - : 13 mat x spline1 β x * 2 β * b1 + (x 2^* - β b1 + (x 3^* + : x spline2 β x * 2 β * b2 + (x 2^* - β b2 + (x 3^* + : 31 sys

x λ 10 x ≤ (x 1 ≤ (& cases :

x arc1 1 x spline1 x diff (2^+ sqrt : x arc2 1 x spline2 x diff (2^+ sqrt : 21 sys

n 100 :

x f x arc1 :

dorso f 01 n Int : 1.82603

x spline1 x λ * x spline2 x λ * 2 1 sys

x f x arc2 :

torso f 01 n Int : 1.82604

1. Prepare the project

N 1000 : (Density of random ≡

xmax 1 : xmin 0 : 21 line

ymax 0.5 : ymin 1 - : 21 line

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

x y1 x spline1 : x y2 x spline2 : 21 line

2. Fill critical region

A function that tests an arbitrary point 
for its membership in the critical region. x y Test y x y2 - 0 ≥ (y x y1 - 0 ≥ (- :

#A0A0A0

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 :

Pts Pts eval :

t0 1 time :

Hyperfast/compact independent in-situ a b c spec . 8 #A0A0A0 13 mat : pts Pts a b c spec pts : 21 sys

1 time t0 - 12 s *

x y1 0 ≡ x 0.5 0.6 solve 0.53731

Elastic Dolphin [jmG, Sophie Germain]

x y1 x λ * x y2 x λ * pts 0.875 0.125 . 15 black 1 5 mat 4 1 sys

dorso torso 21 mat 1.826 1.826 21 mat