<p> bSpline modules </p>

8faa2807-288a-4063-9931-3c697ac4c03e 18 4 5 decimal

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

bSpline . . . interpolation for native Smath

]]>

data 0 0.00794 0.1 0.012 0.2 0.02 0.3 0.048 0.4 0.17 0.46 0.556 62 mat :

X data 1 col : Y data 2 col : 12 mat

reserve the end point Xn X X length el :

mesh/populate the bSpline data
managed in collapsed 'bSpline' ► Δ 0.025 :

ζ X 1 el X length 1 - (Δ range (≡

<p> bSpline modules </p>

u b 0 u 2 - ≤ 16 / 2 u + (3^* 2 - u ≤ (u 1 - ≤ (& 16 / 2 u + (3^* 23 / 1 u + (3^* - 1 - u ≤ (u 0 ≤ (& 23 / 1 u - (3^* - 16 / 2 u - (3^* + 0 u ≤ (u 1 ≤ (& 16 / 2 u - (3^* 1 u ≤ (u 2 ≤ (& 0 cases :

The Gaussian b-spline

Gaussian basis 'b-spline'

2 - x ≤ x 2 ≤ & x b Undefined if

0 b 0.6667

u v Bsp v m el u m - b * (m 1 v rows sum :

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 :

X X 2 RepEnd : Y Y 2 RepEnd : 21 line

u ox u X Bsp : u oy u Y Bsp : 21 line

bSpline ζ X 1 el X length 1 - (Δ range : i 1 ζ rows range vx i el ζ i el ox eval : vy i el ζ i el oy eval : 21 line for vx vy augment 31 line :

X length 1 - 9

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 :

store/isolate bSpline bSpline eval :

bSpline rows 361

Truncate low region lo 21 Δ / * (1 + : 81

bSpline bSpline lo bSpline rows range 12 range el :

bSpline rows 281

eventual cinterp bx bSpline 1 col eval : by bSpline 2 col eval : 21 sys

support data o 7 black plot :

x f bx by x cinterp : x λ 1 X 1 el x ≤ (x Xn ≤ (& cases : 21 sys

bSpline 1 row bSpline bSpline rows row 21 sys 0 0.0079 12 mat 0.46 0.556 12 mat 21 sys

'bSpline' is a clean data set for export.

bSpline support 2 1 sys support x f x λ * 2 1 sys

Σ U X 1 el Xn X 1 el 0.01 + range : i 1 U rows range Cumul i el x f x U 1 el U i el int eval : for U Cumul augment 31 line :

store/isolate Σ Σ eval :

acc 100 x f x X 1 el Xn int 0.0422

Σ rows 47

Σ Σ rows row 0.46 0.0422 12 mat

jmG 20230106