<p> plotG(vx,vy,a,b,c) </p>

08736142-5817-4c56-9b4a-c72079da49b6 17 3 5 decimal

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

vx vy a b c plotG a char ≡ b size ≡ c color ≡ 13 mat n vx length : plot vx 1 el vy 1 el a b c augment : i 2 n range plot plot vx i el vy i el a b c augment stack : for plot 51 line :

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 :

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 :

5 gencm1 012344321025 mat

330 genm 00000000033 mat

Carlos added,
enables recursive N 2 k matrix ≡ M nr nc matrix ≡ 21 sys

M idx M transpose 1 col rows :

5 gencm1 idx 5

Carlos  'submat' M 1 n 1 + (range 2 w range el M 1 n 1 + (2 w submatrix ≡

330 genm idx 3

without submatrix(...) 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

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 :

sanity 15 D 33 weights 0.043058311287478 0.090299823633157 - 0.054241071428571 0.008465608465608 - 41 mat

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

Specific for n=1

n s 1 + (i - gencm

14 pts 0.875 0.625 0.375 0.125 14 mat 0.8333 0.5 0.1667 13 mat 0.75 0.25 12 mat 0.5 11 mat 41 mat

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

Specific for n=2

n s i - gencm

show 27 pts : simplex show 1 el transpose : vx simplex 1 col : vy simplex 2 col : 41 line

min simplex Min : 0.067

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

S vx vy o 5 red plotG :

simplex 0 0 0 1 1 1 1 0 0 0 5 2 mat 0.2 1 0.2 0 2 2 mat S 4 1 sys

The doctored triple integration

23 gencm 000011122301230120103210210100310 mat

n s pts d 2 s * 1 + : v 11113 mat transpose : i 0 s range M n s i - gencm : M M 2 n 1 + 1 M idx submatrix : Pt i el 2 M * 1 + v augment : Pt s 1 + el v : scale i 1 + el 1 d n + 2 i * - / : 51 line for Pt scale * vectorize 41 line :

Specific for n=3

's' pilots accuracy of ∫(f)

n 3 : s 4 : 12 mat

pts n s pts :

Simplex  triple integration algorithm f ∫ v 0 : Pt pts : w n s 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 :

Simplex integration is on the 0 .. 1

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

t0 1 time :

sanity ... 0.129622968748757 f ∫ 0.129622968748766

1 time t0 - 0.2 s *

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 :

pts from Smath simplex

fetches [n, s] from above

sanity 15 D n s 1 - weights 0.043058311287478 0.090299823633157 - 0.054241071428571 0.008465608465608 - 41 mat