5029b6d2-1995-46f3-8b4f-bb217d37ff4c 32 4 5 decimal

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

Joukowsky . . . Air foil . . . Stream lines

. . . adapted from Steven Finch [Mathsoft]

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isolate for re-use in R(u)
'n' extends  blue ◄ ►  Joukowski air foil.
Try 'n 80' ... 'n 100' 10 min. n 60 : k 0 n range : u 0.05 n 2 / k - (* vectorize eval : 31 sys

A j 14 range k 1 n 1 + (range A j k el u k el j 0.05 i * (* + eval : for for A 21 line :

Isolate to speed up A A eval :

z T z z Re sign z 2^1 - sqrt * + : z R z z 1 + sign z 2^1 - sqrt * + : 21 sys

U j 14 range k 1 n 1 + (range U j k el A j k el T eval : for for U 21 line :

t0 1 time :

specific components M u R vectorize eval : L U - eval : N M - : 31 sys

1 time t0 - 1.6 s *

'a' &  'b' between 0 .. 1
'c' between 1 .. 5 a 0.6 : b 0.4 : c 1 : 13 mat f c a 1 + (2^b 2^+ sqrt * : 21 sys

t0 1 time :

SYMBOLIC faster W M N augment U transpose augment L transpose augment transpose :

1 time t0 - 2 s *

H f W * a - b i * + :

z J 0.5 z 1 z / + (* eval :

Collect 10 streamlines S H J vectorize eval : stream S 110 range 1 n 1 + (range el : stream stream transpose : 31 sys

lines data UnestV v data 1 el : j 2 data rows range v v data j el stack : for v 31 line : ii 1 stream rows range j 1 stream cols range lines ii j el stream ii j el Re stream ii j el Im augment eval : for for lines j 1 lines cols range myV 1 j el lines j col UnestV : for myV 51 line :

Isolate to speed up lines lines eval :

t0 1 time :

blue lines 1 col eval : red lines 2 col eval : 21 sys

1 time t0 - 0.06 s *

M c DelRow N 0 : ct 1 : n 1 M rows range n c ≠ N ct 1 el M n row : ct ct 1 + : 21 line Unest 'N' if for v N 1 el : j 2 N rows range v v N j el stack : for v 61 line :

blue red lines 3 col eval 3 1 sys

the row to be deleted from 'lines' r n 2 / 1 + : 31

t0 1 time :

index 1 to explode  col(lines,#) J lines 3 col eval 1 el r DelRow lines 4 col eval 1 el r DelRow lines 5 col eval 1 el r DelRow lines 6 col eval 1 el r DelRow 00 lines 7 col eval 1 el r DelRow lines 8 col eval 1 el r DelRow lines 9 col eval 1 el r DelRow lines 10 col eval 1 el r DelRow 101 sys :

blue red J 3 1 sys

x y axes x y / - :

1 time t0 - 5 s *

blue red J axes 4 1 sys