Members of the Forum:
If I plot the points of a sine curve thusly
'type point;pensize 5' plot 1 o. 8%~i:49
I get a nice graph but, due the nature of the sine function, points near the
inflection points are more closely spaced than those further away. How can
I adjust my input points to get more evenly-spaced (for simplicity, on the
X-axis) outputs? I'd like a method I could use for any arbitrary function.
Here's a simple attempt wherein I try to remove the point closest to the one
before it and insert a point midway between the two most widely separated
points:
NB.* evenOut: adjust inputs to fnc so outputs more evenly spaced.
evenOut=: 1 : 0
diffs=. |2-~/\u y
'whi wlo'=. diffs i. (>./,<./)diffs
wlo=. wlo-wlo=<:#y NB. Don't remove endpoint
y=. (0 (>:whi)}1$~>:#y)#^:_1 y
y=. (u -:+/y{~whi+0 2) (>:whi)}y
y=. (<<<>:wlo){y
)
evenOut_test_=: 3 : 0
tsts=. 0 1 10,0 10 11,:0 5 10
assert. (] evenOut"1 tsts)-:(5.5 5 5) 1}&.|:tsts
)
If I could get a satisfactory version of this two-point substituter, it
might work to apply it repeatedly until the point differences stabilize.
I'm satisfied with the result for these simple test cases:
]tsts=. 0 1 10,0 10 11,:0 5 10
0 1 10
0 10 11
0 5 10
] evenOut"1 tsts
0 5.5 10
0 5 11
0 5 10
(Testing with verb "]" for simplicity). However, this result
] evenOut 0 2 4 5
0 1 2 5
isn't as good; a result like "0 2 3
5" might be better in this case. We could define a measure of evenness:
msrEveness=: 13 : '%:+/*:2-/\|2-/\y'
to quantify this preference (where a lower measure is better). This shows
us that of the three possibilities,
msrEveness ] evenOut 0 2 4 5
2
msrEveness 0 2 4 5
1
msrEveness 0 2 3 5
1.4142136
the initial arrangement is best. An arrangement like this
msrEveness 0 5r3 10r3 5
0
is optimal in this case (we want to retain the endpoints unchanged).
Any ideas on how to approach this?
--
Devon McCormick, CFA
^me^ at acm.
org is my
preferred e-mail
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