9ab0f125-0d79-4d41-ad3e-9a1b00ffd8ed 8 3 5 decimal

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

doctored by Carlos
to enable recursive N 2 k matrix ≡ M nr nc matrix ≡ 21 sys

2D simplex integration

k gencm1 N 2 k matrix : i 1 k range N 1 i el i 1 - : N 2 i el k i - : 21 line for N 31 line :

Sanity checked 5 gencm1 012344321025 mat

M last M transpose 1 col rows :

nr nc v genm M nr nc matrix : i 1 nr range j 1 nc range M i j el v : for for M 31 line :

330 genm 00000000033 mat

410 genm 000041 mat

M idx M transpose 1 col rows :

without submatrix(...) tip from Carlos n k gencm n 1 ≡ k gencm1 M n 1 + 10 genm : i 0 k range N n 1 - k 1 + (i - gencm : w N idx 1 - : O 1 w 1 + i genm : N O N stack : M M N augment : 51 line for w M idx 0 - : M 1 n 1 + (range 2 w range el 41 line if 11 line :

15 gencm 012344321025 mat

Only true for n=2 and any 'k'

24 gencm 11 mat 000001111222334012340123012010432103210210100315 mat 11 mat

21 gencm 00101010033 mat

22 gencm 00011201201021010036 mat

23 gencm 000011122301230120103210210100310 mat

n s weights d 2 s * 1 + : i 0 s range w i 1 + el 1 - (i^22 s * -^* d n + 2 i * - (d^i! (d n + i - (! (* / * : for w 31 line :

n s pts d 2 s * 1 + : i 1 s range M n s i - gencm : M M 2 n 1 + 1 M idx 0 - submatrix : Pt i el 2 M * 1 + d n + 2 i * - / : 31 line for Pt 31 line :

n s pts Smath code: RemToDo n 2 ≠ n s pts cases :

... [F9] recalculate WS does NOT clear error message once generated

Some sanities vs MCD

23 pts 0.143 0.429 0.714 0.143 0.429 0.143 0.714 0.429 0.143 0.429 0.143 0.143 26 mat 0.2 0.6 0.2 0.6 0.2 0.2 23 mat 0.333 0.333 21 mat 31 mat

22 pts 0.2 0.6 0.2 0.6 0.2 0.2 23 mat 0.333 0.333 21 mat 21 mat

24 pts 0.111 0.333 0.556 0.778 0.111 0.333 0.556 0.111 0.333 0.111 0.778 0.556 0.333 0.111 0.556 0.333 0.111 0.333 0.111 0.111 210 mat 0.143 0.429 0.714 0.143 0.429 0.143 0.714 0.429 0.143 0.429 0.143 0.143 26 mat 0.2 0.6 0.2 0.6 0.2 0.2 23 mat 0.333 0.333 21 mat 41 mat

25 pts 0.091 0.273 0.455 0.636 0.818 0.091 0.273 0.455 0.636 0.091 0.273 0.455 0.091 0.273 0.091 0.818 0.636 0.455 0.273 0.091 0.636 0.455 0.273 0.091 0.455 0.273 0.091 0.273 0.091 0.091 215 mat 0.111 0.333 0.556 0.778 0.111 0.333 0.556 0.111 0.333 0.111 0.778 0.556 0.333 0.111 0.556 0.333 0.111 0.333 0.111 0.111 210 mat 0.143 0.429 0.714 0.143 0.429 0.143 0.714 0.429 0.143 0.429 0.143 0.143 26 mat 0.2 0.6 0.2 0.6 0.2 0.2 23 mat 0.333 0.333 21 mat 51 mat

Project demo ============

Simplex integration algorithm f n s ∫ v 0 : Pt n s pts : w n s 1 - weights : i 1 w rows range P Pt i el : v v w i el P j col f j 1 P idx sum * + : 21 line for v 51 line :

x f e x 1 el^0.5 x 2 el (3^- (* :

t0 1 time :

s > 7 ... numerical instability n 2 : s 7 : 12 mat

sanity ... 0.299449943475250 f n s ∫ 0.29944994347527

1 time t0 - 0.5 s *