370c454c-2813-436f-addc-d91706d8d852 57 3 5 auto

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

Filling a statistical region [PDF]

t0 1 time :

Prepare the project

Construct the project

xo x f 1150 x xo - (2^* + / :

xo 0.5 : N 1000 : sx 0.25 : 31 line

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 :

xmin sx : xmax 1 sx - : 12 mat ymin 0 : ymax 1 : 12 mat 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 xo x f ≤ (x xmax ≤ (* :

PDF x 01 0.0025 range : i 1 x rows range y i el xo x i el f eval : 11 line for x y augment 31 line :

A routine that finds an array of N random 
pairs in the critical region. Pts 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 21 line :

a b c spec . 6 #808080 13 mat :

fill Pts a b c spec pts :

Domain

Xmin sx 1 sx 0.25 - 22 mat :

Xmax xmax 1 xmax 0.25 - 22 mat :

Xo xo 1 xo 022 mat :

plot PDF fill Xmin Xmax Xo 51 sys :

fill 1.549864 1014^* 2.5 1014^* / 2.898754 1014^* 51014^* / . 6 #808080 3.044805 1014^* 81014^* / 6.247425 1013^* 1.25 1014^* / . 6 #808080 1.451902 1014^* 41014^* / 6.11164 1013^* 21014^* / . 6 #808080 5.855885 1013^* 21014^* / 2.246462 1013^* 11015^* / . 6 #808080 1.184142 1014^* 2.5 1014^* / 1.308656 1013^* 51013^* / . 6 #808080 5.434784 1013^* 81013^* / 3.699058 1013^* 1.25 1014^* / . 6 #808080 4.819939 1013^* 11014^* / 1.505305 1013^* 41013^* / . 6 #808080 4.704003 1013^* 11014^* / 8.571531 1014^* 11015^* / . 6 #808080 85 mat

1 time t0 - 20.4 s *

Filling a region of a PDF

plot

Simulate a noisy experimental data set

Noisy data sets are often used to test filter modules. So, here is a typical construction. We just take a smaller magnitude of the noise. It represents a good resolution of the measuring chain that must be at least 10 times more accurate [resolution] than the sampled data. Noise from measurement is due to digital "quantization" whether "quantizaton" is from visual or digital.

Superpose noise on a function data n rnd μ n 11 line : 2 μ Random * 1 - 21 line : x 01 0.01 range : i 1 x rows range y i el xo x i el f eval : rn x rows rnd : 21 line for x y 0.1 rn * + (augment 41 line :

Create an experimental noisy data set

data PDF 2 1 sys