Algo(L,H,N,f(■ ),range,n)

434cda78-d199-4a42-b4ec-69d8b94fffd3 39 4 5 decimal

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

Algo(L,H,N,f(■ ),range,n) Algo(L,H,N,f(■ ),range,n)

L H N # f range n Algo U 0 : dx H L - N 1 - / : i 1 N 1 + (range U i el L dx - (dx i * + : for j 1 range range u j el U j el : y j el U j el f eval : 21 line for u n round vectorize y n round vectorize augment 51 line :

4 appVersion 0.98.6179.21440 ≡

define as scalar fnct x q 0.01 x 3^(* :

start end mesh x f Xend decimals Algo

x sqrt start at 0 ≡

plot 10 - 1001000 x q 2006 Algo :

plot x q 2 1 sys

plot 1 row plot plot rows row 21 mat 10 - 10 - 12 mat 11.9119 16.9022 12 mat 21 mat

plot 10 - 10 - 9.88989 - 9.673294 - 9.77978 - 9.353782 - 9.66967 - 9.041384 - 9.55956 - 8.736021 - 9.449449 - 8.437611 - 62 mat

algo style for command line
add 'n' fractional 'f'
to Origin 'O' ... O n f X O O : i 0 n range R i el O i f * + : for R 31 line :

X 0.125 - 10 0.125 X :

Type. 0

X transpose 0 0.125 0.25 0.375 0.5 0.625 0.75 0.875 1 1.125 110 mat

L H N xd U 0 : dx H L - N 1 - / : 12 mat i 1 N range U i el L dx - (dx i * + : for U 31 line :

L 1.785686 : H 14.245529 : N 100 : 13 mat x L H N xd : 21 line

Type. 1

x rows 100

L H N Xd xd 0 : k 0 N range xd k 1 + el L H L - N / (k * + : for xd 31 line :

4 Discretizers algo style

matter of preference wrt application.

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Type. 2

L Δ N inc X 0 : i 0 N range X i 1 + el L Δ i * + : for X 31 line :

U 1 - 110 Xd :

Type. 3

Δ 2 - 0.1 12 inc :

U transpose 1 - 0.8 - 0.6 - 0.4 - 0.2 - 0 0.2 0.4 0.6 0.8 1111 mat

Δ transpose 2 - 1.9 - 1.8 - 1.7 - 1.6 - 1.5 - 1.4 - 1.3 - 1.2 - 1.1 - 1 - 0.9 - 0.8 - 113 mat

Create/Export . . . user meshed table

export this section

]]> Subdivide ... strip repeated

Subdivide a range in 'n' intervals ... demo n pivot interval j 1 n 1 + (range h j el pivot - pivot j * + n / : for h 21 line :

Strip repeated in vector data Strip v data 1 col : k 0 : i 1 data rows 1 - (range v i 1 + el v i el ≠ R k k 1 + : el v i el : 11 line end of strip recover last u 21 line if 11 line for R X X cols el stack 41 line :

Subdivide X vector in 'n' subintervals X n split i 2 X cols (range determine 'p' the pivots pp i el X i el X i 1 - el - (: uu i 1 - el n pp i el * pp i el interval : 31 line for recompose the subdivided X v uu 1 el X 1 el + : j 2 uu rows range v v uu j el X j el + (stack : for v 51 line :

subdivide X 'n'
collect 'V' X 021013 mat : n 5 : 12 mat V X n split Strip : 21 sys

Table x V : i 1 x rows range v i el x i el (sqrt eval : for hpa x v 3 round vectorize augment : header X Y 12 mat : header hpa stack 51 line :

Table X Y 00 0.2 0.447 0.4 0.632 0.6 0.775 0.8 0.894 11 1.2 1.095 1.4 1.183 1.6 1.265 1.8 1.342 2 1.414 122 mat

Remember ... Pivot system needs 3 points. The central point can be any in between the extremas.

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 :

Subdivide a range in 'n' intervals ... demo n pivot interval j 1 n 1 + (range h j el pivot - pivot j * + n / : for h 21 line :

Strip repeated in vector

X 35913 mat : u1 16 X 2 el X 1 el - interval : u2 8 X 3 el X 2 el - interval : data u1 X 1 el + u2 X 2 el + stack : New data Strip : 51 sys

===========

data Strip strip repeated in  col u data 1 col : k 0 : i 1 u rows 1 - (range u i 1 + el u i el ≤ (u i 1 + el u i el ≥ (¤ S k k 1 + : el u i el : 11 line end of strip recover last u 21 line if 11 line for 21 line S X 3 el stack 41 line :

New 3 3.125 3.25 3.375 3.5 3.625 3.75 3.875 4 4.125 4.25 4.375 4.5 4.625 4.75 4.875 5 5.5 181 mat

idx 1 New rows range : xy idx New augment : xy xy o 4 red plot : 31 sys

New rows 25

in the range 3..5 ► 16 intervals. in the range 5..9 ► 8 intervals

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 :

Subdivide a range in 'n' intervals ... demo n pivot interval j 1 n 1 + (range h j el pivot - pivot j * + n / : for h 21 line :

pivot SubRange ct 1 : i 1 pivot cols range a ct el pivot i el : ct ct 1 + : 21 line for Unest a v a 1 el : j 2 a rows range v v a j el stack : for v 61 line :

n 6 : p 1 : 12 mat

u n p interval :

subdivide a user collection ▼ pivot u 0.75 - u + 1 - u + 0.375 - u + 14 mat :

u 0 0.1667 0.3333 0.5 0.6667 0.8333 171 mat

i 1 pivot SubRange rows range : U pivot SubRange : (collected vector ≡ xy i U augment : Sub xy o 5 black plot : 41 sys

U 0 0.1667 0.3333 0.5 0.6667 0.8333 1 0.75 - 0.5833 - 0.4167 - 0.25 - 0.0833 - 121 mat

Sub xy 2 1 sys

pivot 0 0.1667 0.3333 0.5 0.6667 0.8333 171 mat 0.75 - 0.5833 - 0.4167 - 0.25 - 0.0833 - 0.0833 0.25 71 mat 1 - 0.8333 - 0.6667 - 0.5 - 0.3333 - 0.1667 - 071 mat 0.375 - 0.2083 - 0.0417 - 0.125 0.2917 0.4583 0.625 71 mat 14 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 :

Subdivide a range in 'n' intervals ... demo n pivot interval j 1 n 1 + (range h j el pivot - pivot j * + n / : for h 21 line :

n 9 : p 1 : 12 mat

u n p interval : j 0 u rows 1 - (range : xy j u augment : pts xy o 5 red plot : 41 sys

Observe results ▼ ......... ▼

pts 5 0.5555556 + 20 blue 1 5 mat 2 1 sys

u 0 0.111111111111111 0.222222222222222 0.333333333333333 0.444444444444444 0.555555555555556 0.666666666666667 0.777777777777778 0.888888888888889 1101 mat

u 0 0.1 0.2 0.3 0.4 0.6 0.7 0.8 0.9 1101 mat

u 9 * 0.000000000000000 1.000000000000000 2.000000000000000 3.000000000000000 4.000000000000000 5.000000000000000 6.000000000000000 7.000000000000000 8.000000000000000 9.000000000000000 101 mat

subdivided @ pivot [0,3,7,11] pivot u 3 u + 7 u + 11 u + 14 mat :

i 1 pivot SubRange rows range : Y pivot SubRange : XY i Y augment : Sub XY o 5 black plot : 41 sys

Sub

pivot 0 0.1111 0.2222 0.3333 0.4444 0.5556 0.6667 0.7778 0.8889 1101 mat 3 3.1111 3.2222 3.3333 3.4444 3.5556 3.6667 3.7778 3.8889 4101 mat 7 7.1111 7.2222 7.3333 7.4444 7.5556 7.6667 7.7778 7.8889 8101 mat 11 11.1111 11.2222 11.3333 11.4444 11.5556 11.6667 11.7778 11.8889 12101 mat 14 mat

Subdivide a range in 'n' intervals ... demo n pivot interval j 1 n 1 + (range h j el pivot - pivot j * + n / : for h 21 line :

User subdivide X-integer pivot range

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subdivide X 'n'
subdivided 'X' X 37912171816 mat : n 2 : 12 mat V X n split Strip : 21 sys

V 11 mat 3 3.5 4 4.5 5 5.5 6 6.5 7 7.5 8 8.5 9 9.5 10 10.5 11 11.5 12 12.5 13 13.5 14 14.5 15 15.5 16 16.5 17 17.5 9311 mat 11 mat

V rows 31

X X cols el X 1 el - (n * 1 + 31

XY X transpose X transpose augment : pts XY o 7 black plot : xy V V augment : mesh xy . 9 red plot : 41 sys

pts mesh 2 1 sys

User . . . subdivide pair wise 2D vectors

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data sub subspace j 1 data rows 1 - (range Vsub j el i 1 sub range vx i el data j el i sub / data 1 j + el data j el - (* + : for vx 21 line eval : 11 line for v Vsub 1 el : j 2 Vsub rows range v v Vsub j el stack : for data 1 el v stack 31 line 21 line :

user original polygon Xo 0.5 - 123456718 mat transpose : Yo 6 7.5 7.5 1.25 1.25 64718 mat transpose : 21 sys

fragment subspaces sub 10 :

New Xo sub subspace Yo sub subspace augment : XoYo Xo Yo augment : XY New : 12 mat XoYo XoYo o 7 black plot : XY XY . 10 red plot : x f New 1 col New 2 col x linterp : 51 sys

isolate New New :

ω 4.5 :

x f XoYo XY ω ω f + 40 black 1 5 mat 4 1 sys

sanity ω ω f 12 mat 4.5 3.625 12 mat

Subdivide a range in 'n' intervals ... demo n pivot interval j 1 n 1 + (range h j el pivot - pivot j * + n / : for h 21 line :

NUMERIC hi 483 interval : lo 162 - interval reverse : 21 sys

rename/isolate Lo lo : Hi hi : 21 sys

x f x 3^:

data_hi Hi Hi f vectorize augment : data_lo Lo Lo f vectorize augment : 21 sys

alternate plot: line/points

data_lo data_hi 2 1 sys

data data_lo data_hi stack :

XY Strip strip col pairwise repeated '0' end data data rows row : XY XY 1 csort : uu XY 1 col : vv XY 2 col : 12 mat k 0 : i 1 uu rows 1 - (range uu i 1 + el uu i el ≥ (vv i 1 + el vv i el ≠ (& collect k k 1 + : el uu i el vv i el 12 mat : 11 line end of strip if 11 line for 21 line Un-nest the stripped collect Un collect 1 el : j 2 collect rows range Un Un collect j el stack : for Un end stack 91 line :

Export data Strip :

Subdivide a range in 'n' intervals ... demo n pivot interval j 1 n 1 + (range h j el pivot - pivot j * + n / : for h 21 line :

Strip repeated in vector data Strip v data 1 col : k 0 : i 1 data rows 1 - (range v i 1 + el v i el ≠ R k k 1 + : el v i el : 11 line end of strip recover last u 21 line if 11 line for R X 3 el stack 41 line :

123 interval transpose 103 interval transpose 43 interval transpose 31 mat 0 0.25 0.5 0.75 1 1.25 1.5 1.75 2 2.25 2.5 2.75 3113 mat 0 0.3 0.6 0.9 1.2 1.5 1.8 2.1 2.4 2.7 3111 mat 0 0.75 1.5 2.25 315 mat 31 mat

X 37913 mat : u1 8 X 2 el X 1 el - interval : u2 4 X 3 el X 2 el - interval : u3 16 X 3 el X 1 el - interval : data u1 X 1 el + u2 X 2 el + stack : New data Strip : 61 sys

New 3 3.5 4 4.5 5 5.5 6 6.5 7 7.5 8 8.5 9131 mat

u1 0 0.5 1 1.5 2 2.5 3 3.5 491 mat

u2 0 0.5 1 1.5 251 mat

u3 0 0.375 0.75 1.125 1.5 1.875 2.25 2.625 3 3.375 3.75 4.125 4.5 4.875 5.25 5.625 6171 mat