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Adds annotations and formula notes

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LSaldyt
2017-09-29 15:01:57 -06:00
parent 665bf1f778
commit fa8b493948
1 changed files with 69 additions and 25 deletions
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94
copycat/temperature.py
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@ -223,34 +223,78 @@ class Temperature(object):
f = ((10 - sqrt(100 - self.value()))/100 + 1) * value
For the original LISP program:
; This function is a filter: it inputs a value (from 0 to 100) and returns
; a probability (from 0 - 1) based on that value and the temperature.
*********************************************************
; When the temperature is 0, the result is (/ value 100), but at higher
; temperatures, values below 50 get raised and values above 50 get lowered
; as a function of temperature.
**********************************************************
; I think this whole formula could probably be simplified.
**********************************************************
; This function is a filter: it inputs a value (from 0 to 100) and returns
; a probability (from 0 - 1) based on that value and the temperature. When
; the temperature is 0, the result is (/ value 100), but at higher
; temperatures, values below 50 get raised and values above 50 get lowered
; as a function of temperature.
; I think this whole formula could probably be simplified.
(setq result
(cond ((= prob 0) 0)
((<= prob .5)
(setq low-prob-factor (max 1 (truncate (abs (log prob 10)))))
(min (+ prob
(* (/ (- 10 (sqrt (fake-reciprocal *temperature*)))
100)
(- (expt 10 (- (1- low-prob-factor))) prob)))
.5))
((= prob .5) .5)
((> prob .5)
(max (- 1
(+ (- 1 prob)
(defun get-temperature-adjusted-probability (prob &aux low-prob-factor
result)
(setq result
(cond ((= prob 0) 0)
((<= prob .5)
(setq low-prob-factor (max 1 (truncate (abs (log prob 10)))))
(min (+ prob
(* (/ (- 10 (sqrt (fake-reciprocal *temperature*)))
100)
(- 1 (- 1 prob)))))
.5))))
result)
100)
(- (expt 10 (- (1- low-prob-factor))) prob)))
.5))
((= prob .5) .5)
((> prob .5)
(max (- 1
(+ (- 1 prob)
(* (/ (- 10 (sqrt (fake-reciprocal *temperature*)))
100)
(- 1 (- 1 prob)))))
.5))))
result)
Which was tested using:
(defun test-get-temperature-adjusted-probability (prob)
(with-open-file (ostream "testfile" :direction :output
:if-does-not-exist :create
:if-exists :append)
(format ostream "prob: ~a~&" prob)
(loop for temp in '(0 10 20 30 40 50 60 70 80 90 100) do
(setq *temperature* temp)
(format ostream "Temperature: ~a; probability ~a~&"
temp (float (get-temperature-adjusted-probability prob))))
(format ostream "~%")))
Interpretation:
Importantly, the values of .5 in both the min and max correspond to the mid-cutoff of 50:
i.e. 'values below 50 get raised and values above 50 get lowered'
Still, it is interesting to note that changing 'return max(f, 0.0) to max(f, 0.5) has no significant effect on the distribution
It looks like the function below preserves most of the functionality of the original lisp.
However, the comments themselves agree that the formula is overly complicated.
prob = value # Slightly more descriptive (and less ambiguous), will change argument
# Temperature, potentially clamped
temp = self.value()
# A scaling factor (between 0 and infinity), based on temperature (i.e. 100/coldness)
if temp == 100: # Avoid dividing by zero
factor = float('inf')
else:
factor = 100 / (100 - temp)
if prob == .5:
return .5
elif prob > .5:
prob = prob / factor
elif prob < .5:
prob = prob * factor
return max(min(prob, 0), 1) # Normalize between 0 and 1. TODO: make scaling factor more reasonable
"""
if value == 0 or value == 0.5 or self.value() == 0:
return value
if value < 0.5: