ad800385-d583-4298-a62e-9f6a879d9016 34 4 5 decimal

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

Example: 1

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 :

vu 0.01 9 0.1 range :

vu rows 100

x fnct Quick i 1 vu rows range vy i el vu i el fnct eval : 11 line for vu vy augment 21 line :

low high N logpts linear-log populate step high low / 10 log N / : i 1 N range x i el low 10 step i *^* : for x 41 line :

q 0.01 10100 logpts :

q f q :

x F x :

X x F Quick 1 col : Y x F Quick 2 col : 21 line

L q q f augment : vx L 1 col : vy L 2 col : 31 line

n 0.25 :

P X Y n^vectorize + 12 red plotG : V vx vy n^vectorize o 5 black plotG : Table vx vy n^vectorize augment : 31 line

red is the linear discrete ... black 'o' is the log discrete. 'red' is underpopulated in the low region.

P V 2 1 sys

log-Linear populate the low region

L 1 1 sys Table

vy 2^vectorize 0.0001 0.0001 0.0002 0.0002 0.0002 0.0002 0.0003 0.0003 0.0003 0.0004 0.0005 0.0005 0.0006 0.0007 0.0008 0.0009 0.001 0.0012 0.0014 0.0016 0.0018 0.0021 0.0024 231 mat

low high N logpts step high low / 10 log N / : i 1 N range x i el low 10 step i *^* : for x 41 line :

u 0.01 10100 logpts : data u u reverse augment : 21 line

data 1 1 sys

Example: 2

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 :

vu 0.01 9 0.1 range :

vu rows 100

x fnct Quick i 1 vu rows range vy i el vu i el fnct eval : 11 line for vu vy augment 21 line :

low high N logpts linear-log populate step high low / 10 log N / : i 1 N range x i el low 10 step i *^* : for x 41 line :

q 0.01 10100 logpts :

q f q :

x F x :

X x F Quick 1 col : Y x F Quick 2 col : 21 line

L q q f augment : vx L 1 col : vy L 2 col : 31 line

n 0.25 - :

P X Y n^vectorize + 12 red plotG : V vx vy n^vectorize o 5 black plotG : Table vx vy n^vectorize augment : 31 line

red is the linear discrete ... black 'o' is the log discrete. 'red' is underpopulated in the low region.

P V 2 1 sys

log-Linear populate the low region

L 1 1 sys

The 'N' discretiser.

set N = even/odd to escape divide by 0 maybe other singularities.

Space split discretzer L H N xd U 0 : dx H L - N / : i 1 N 1 + (range U i el L dx - (dx i * + : for U 41 line :

L 5 - : H 5 : N 9 : 31 line

Incremental discretiser L inc N Δ n 1 N range v n el L inc - (n inc * + : for v 21 line :

U L H N xd :

j 01 0.1 range :

U 5 - 3.8889 - 2.7778 - 1.6667 - 0.5556 - 0.5556 1.6667 2.7778 3.8889 5101 mat

0 0.1 11 Δ 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1111 mat

j 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1111 mat