plotG(vx,vy,char,size,color) ... Hermite Polyline modules

bc0d8348-9429-4952-b63f-2e4a2afa9d77 5 4 5 decimal

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

Table_2 1 0.16 0.022 1.5 0.26 0.043 2 0.34 0.06 2.5 0.38 0.07 3 0.43 0.078 3.5 0.47 0.086 4 0.49 0.091 73 mat :

Table_1 0.25 0.024 0.0003 0.286 0.031 0.0005 0.333 0.041 0.0008 0.4 0.056 0.0016 0.5 0.08 0.0035 0.667 0.116 0.0083 63 mat :

Your data set are not very true, Thiele tells me that at least once. As naive interpolation looks, as much it may turn freak ! Col [3] Table_1 is missing significant decimals. Col [3] Table_2 is not so bad.

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 Table_1 1 col : Y Table_1 2 col : 12 mat XY X Y augment : support XY . 14 black plot : 31 sys

Clear K 0 : Table 0 : 12 mat

Thiele table of inverse differences ... Carlos i 1 Y rows range Table i 1 el Y i el : for j 2 Y rows range i j Y rows range Table i j el X j 1 - el X i el - Table j 1 - j 1 - el Table i j 1 - el - / : cont j : 21 line break try for for i 1 cont range K i el Table i i el : for 31 line

K K 6 round vectorize :

... NUMERIC ...

K 0.024 5.142857 0.180419 - 0.958052 - 0.357843 - 0.100838 61 mat

isolate 'K' K K eval :

Thiele on length of support points 'j' K X x Cfr j K rows 1 - : N j 1 + el K j 1 + el : c j el N j el : a j el K j el : jj j 1 - (1 range c jj el a jj 1 + el : a jj el K jj el x X jj el - c jj el / + : 21 line for a 1 el 61 line :

isolated 'K'

Recast inclusive of
parameters K's , X's x f K X x Cfr :

NUMERIC

SYMBOLIC

x λ 10 x ≤ (x 1 ≤ (& cases :

x f x 0 0.25 solve 0.1312

x f x λ * 0.1312 0.125 0.1312 0.125 - 2 2 mat support 3 1 sys

X Table_2 1 col : Y Table_2 2 col : 12 mat XY X Y augment : support XY . 14 black plot : 31 sys

Clear K 0 : Table 0 : 12 mat

Thiele table of inverse differences ... Carlos i 1 Y rows range Table i 1 el Y i el : for j 2 Y rows range i j Y rows range Table i j el X j 1 - el X i el - Table j 1 - j 1 - el Table i j 1 - el - / : cont j : 21 line break try for for i 1 cont range K i el Table i i el : for 31 line

K K 6 round vectorize :

... NUMERIC ...

K 0.16 5 0.9 1.428571 - 0.229091 - 37.444196 0.008303 - 71 mat

isolate 'K' K K eval :

Thiele on length of support points 'j' K X x Cfr j K rows 1 - : N j 1 + el K j 1 + el : c j el N j el : a j el K j el : jj j 1 - (1 range c jj el a jj 1 + el : a jj el K jj el x X jj el - c jj el / + : 21 line for a 1 el 61 line :

isolated 'K'

Recast inclusive of
parameters K's , X's x f K X x Cfr :

NUMERIC

SYMBOLIC

x λ 10 x ≤ (x 5 ≤ (& cases :

x f x 01 solve 0.4676

x f x λ * 0.4676 0.25 0.4679 0.25 - 2 2 mat support 3 1 sys

X Table_2 1 col : Y Table_2 3 col : 12 mat XY X Y augment : support XY . 14 black plot : 31 sys

Clear K 0 : Table 0 : 12 mat

Thiele table of inverse differences ... Carlos i 1 Y rows range Table i 1 el Y i el : for j 2 Y rows range i j Y rows range Table i j el X j 1 - el X i el - Table j 1 - j 1 - el Table i j 1 - el - / : cont j : 21 line break try for for i 1 cont range K i el Table i i el : for 31 line

K K 6 round vectorize :

... NUMERIC ...

K 0.022 23.809524 0.1995 7.680492 - 0.084389 - 35.100476 0.006778 71 mat

isolate 'K' K K eval :

Thiele on length of support points 'j' K X x Cfr j K rows 1 - : N j 1 + el K j 1 + el : c j el N j el : a j el K j el : jj j 1 - (1 range c jj el a jj 1 + el : a jj el K jj el x X jj el - c jj el / + : 21 line for a 1 el 61 line :

isolated 'K'

Recast inclusive of
parameters K's , X's x f K X x Cfr :

NUMERIC

SYMBOLIC

x λ 10 x ≤ (x 4 ≤ (& cases :

x f x λ * support 2 1 sys plotG(vx,vy,char,size,color) ... Hermite Polyline modules

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 :

z n RepEnd m z rows : i 1 n range w i el z 1 el : for i n 1 + (m n + (range w i el z i n - el : for i m n + 1 + (m 2 n * + (range w i el z m el : for w 51 line :

data Strip nest stripped in 'R' u data 1 col : v data 2 col : k 0 : i 1 data rows 1 - range v i 1 + el v i el ≤ (v i 1 + el v i el ≥ (¤ R k k 1 + : el u i el v i el 12 mat : 11 line Undefined if 11 line for 21 line Un-nest R v R 1 el : j 2 R rows range v v R j el stack : for v 81 line :

M Unwrap V M 1 col : i 2 M cols range V V M i col stack : for V 31 line :

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 v 31 line 21 line :

Round OFF Matrix/Vector M n Round i 1 M rows range m i el M i el n round : for m 21 line :

Table_1 0.25 0.024 0.0003 0.286 0.031 0.0005 0.333 0.041 0.0008 0.4 0.056 0.0016 0.5 0.08 0.0035 0.667 0.116 0.0083 63 mat :

Polyline construct

r 2 : X X r RepEnd : Y Y r RepEnd : 31 sys

x c 10 x ≤ (x 1 ≤ (& cases :

interpolate 16 / t 3^- 3 t 2^* + 2 t * - 3 t 3^* 6 t 2^* - 3 t * - 6 + 3 t 3^* - 3 t 2^* + 6 t * + t 3^t - 41 mat *

Hermite PolyLine t P 16 / t 3^- 3 t 2^* + 2 t * - 3 t 3^* 6 t 2^* - 3 t * - 6 + 3 t 3^* - 3 t 2^* + 6 t * + t 3^t - 41 mat * :

Hermite basis cubics 0...1

x P 1 el x c * x P 2 el x c * x P 3 el x c * x P 4 el x c * 4 1 sys

polyline 16 / t 3^- 3 t 2^* + 3 t * - 1 + (3 t 3^* 6 t 2^* - 4 + (3 t 3^* - 3 t 2^* + 3 t * + 1 + (t 3^41 mat *

t j XP t P 1 el X j el * t P 2 el X j 1 + el * + t P 3 el X j 2 + el * + t P 4 el X j 3 + el * + : t j YP t P 1 el Y j el * t P 2 el Y j 1 + el * + t P 3 el Y j 2 + el * + t P 4 el Y j 3 + el * + : 21 sys

U j 1 X rows r 1 + (- (range : ct 1 : j j i 1 t rows range Hx i ct el t i el j XP eval : for ct ct 1 + : 21 line for Hx 41 line :

V j 1 X rows r 1 + (- (range : ct 1 : j j i 1 t rows range Hy i ct el t i el j YP eval : for ct ct 1 + : 21 line for Hy 41 line :

collect the project xy U Unwrap V Unwrap augment : contour xy Strip : 21 sys

Xo Table_1 1 col : Yo Table_1 3 col : 21 sys

subspaces is '1' for interpolation sub 1 :

New Xo sub subspace Yo sub subspace augment : New Xo 1 el Yo 1 el 12 mat New stack : 21 line

isolate New New :

X New 1 col : Y New 2 col : 21 line

t 01 0.1 range :

Polyline construct

r 2 : X X r RepEnd : Y Y r RepEnd : 31 sys

x c 10 x ≤ (x 1 ≤ (& cases :

interpolate 16 / t 3^- 3 t 2^* + 2 t * - 3 t 3^* 6 t 2^* - 3 t * - 6 + 3 t 3^* - 3 t 2^* + 6 t * + t 3^t - 41 mat *

Hermite PolyLine t P 16 / t 3^- 3 t 2^* + 2 t * - 3 t 3^* 6 t 2^* - 3 t * - 6 + 3 t 3^* - 3 t 2^* + 6 t * + t 3^t - 41 mat * :

Hermite basis cubics 0...1

x P 1 el x c * x P 2 el x c * x P 3 el x c * x P 4 el x c * 4 1 sys

polyline 16 / t 3^- 3 t 2^* + 3 t * - 1 + (3 t 3^* 6 t 2^* - 4 + (3 t 3^* - 3 t 2^* + 3 t * + 1 + (t 3^41 mat *

t j XP t P 1 el X j el * t P 2 el X j 1 + el * + t P 3 el X j 2 + el * + t P 4 el X j 3 + el * + : t j YP t P 1 el Y j el * t P 2 el Y j 1 + el * + t P 3 el Y j 2 + el * + t P 4 el Y j 3 + el * + : 21 sys

U j 1 X rows r 1 + (- (range : ct 1 : j j i 1 t rows range Hx i ct el t i el j XP eval : for ct ct 1 + : 21 line for Hx 41 line :

V j 1 X rows r 1 + (- (range : ct 1 : j j i 1 t rows range Hy i ct el t i el j YP eval : for ct ct 1 + : 21 line for Hy 41 line :

collect the project xy U Unwrap V Unwrap augment : contour xy Strip : 21 sys

Ω contour :

XY X Y . 14 black plotG : XoYo Xo Yo + 15 black plotG : 21 line

contour rows 70

vx Ω 1 col : vy Ω 2 col : 12 mat x spline vx vy x ainterp : x λ 1 0.196 x ≤ (x 1 ≤ (& cases : 31 line

ainterp [Akima] is unique compatible

x spline x 0.125 0.25 solve 0.196

0.3 spline 0.0006

Ω x spline x λ * XY 3 1 sys