<p> Hermite Interpolation modules </p>

816941d9-248c-4296-b334-ebf162e2c0b5 23 4 5 decimal

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

Hermite . . . reverse interpolation, discrete, clean

]]>

Data set sourceTopUser2000 New 11.637 311.0177 64.07 295.6239 100.9516 280.2301 120.1979 264.8363 126.5569 245.9867 119.6988 218.6548 112.9347 203.261 105.8145 187.8672 92.4534 157.0796 81.1751 126.292 71.9373 95.5044 61.1175 49.323 52.4659 0132 mat :

Xo New 1 col : Yo New 2 col : 12 mat

support New . 14 black plot :

Reverse data sets are common in physicochemical. Ordinary interpolation [cinterp/ainterp] will fail, fail miserably. Thiele is not candidate in this demo. Hermite, the sole option AFAIK, exceptional rendering. Animation more from suite ...

Xo New 1 col : Yo New 2 col : 12 mat

Global definition
fetched from below
collapsed area ... support New . 14 black plot :

0.01 over populate demo t 01 0.1 range :

t rows 11

truncate t rows 2 - : 9

<p> Hermite Interpolation modules </p>

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 :

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 :

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 :

subspaces is '1' for interpolation sub 1 :

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

isolate Hermite Hermite :

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

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 :

Ω rows 140

Ω Ω t rows Ω rows truncate - (range 12 range el :

Hermite produces discrete export interpolated values. At this point for convenience you can interpolate cinterp/ainterp from piecewise each branch adapted from 'All values project'

Ω support 2 1 sys

Hermite interpolation 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 . . . reverse interpolation, suite . . .

]]>

contour Ω :

XY 126.6 24612 mat :

τ 1 contour rows range :

t NX contour 1 col t el : t NY contour 2 col t el : 12 mat

t 1 ≡ path t NX t NY 1 2 mat : path path t NX t NY 1 2 mat stack : if XY 1 1 el XY 1 2 el + 40 red 1 5 mat support 3 1 sys

data Ω :

Locate 1rst exact value in vector V x col FindIdx j 1 : V j col el x ≠ j j 1 + : while j 0 ≡ inexistant j V j col el 12 mat if 31 line :

All values project

data data rows row 52.4659 012 mat

data 1 col Max 126.5569

data 1 row 11.637 311.0177 12 mat

# # # FindIdx

key data 1 col Max : col 1 : 12 mat

idxkey data 1 col key col FindIdx :

row of Max(X) idxkey 41 126.5569 12 mat

XY data idxkey 11 el row : 126.6 24612 mat

XY XY eval :

Scalar piecewise interpolation ...

sub_1 data 141 range 12 range el : 11 mat sub_2 data 42 data rows range 12 range el : ux sub_1 1 col : uy sub_1 2 col : 12 mat vx sub_2 1 col : vy sub_2 2 col : 12 mat x f ux uy x ainterp : x Φ vx vy x ainterp : x λ1 1 11.64 x ≤ (x 126.6 ≤ (& cases : x λ2 1 x 126.6 ≤ (x 52.5 ≥ (& cases : 81 sys

sub_1 sub_2 126.6 246 + 40 black 1 5 mat 3 1 sys

x f x λ1 * x 11.64 126.6 int 33480

x Φ x λ2 * x 52.5 126.6 int 10358

u 96 : u f 12 mat v 72 : v Φ 12 mat 21 mat 96 282.78 12 mat 72 95.74 12 mat 21 mat

11.64 u ≤ (u 126.6 ≤ (&

Bivalent interpolation wrt [u, v] ... ► Experiment u ≡ v

x f x λ1 * x Φ x λ2 * u u f + 20 black 1 5 mat v v Φ + 20 black 1 5 mat 4 1 sys

126.6 24612 mat

v 126.6 ≤ (52.5 v ≤ (&

jmG: 20230220