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#coding=utf-8
#
# Kokompe Interval Algebra module for Python
#
# Smári McCarthy <smari@yaxic.org>
# Based on interval.cpp by Ara Knaian <ara@mit.edu>
#
# Copyright © FAB Foundation, 2008.
# Copyright © Massachusetts Institute of Technology, 2007.
#
class Interval:
"""
Implements real interval algebra.
We store two values: a and b.
Agnostic towards infinity.
Real numbers are considered to be intervals of length 0 and
intervals of length 0 are considered to be real numbers.
"""
def __init__(self, a=None, b=None):
#
# Data invariant: a < b
#
self.a = a
self.b = b
pass
def SetRealInterval(self, a, b):
"""
We demand correct order on a, b here, but elsewhere we're agnostic.
"""
if (b < a):
raise OutOfOrderException
self.a = a
self.b = b
pass
def SetRealNumber(self, a):
"""
Change an interval into a real number.
"""
self.a = a
self.b = a
return None
def GetCenter(self):
"""
Return arithmetic average of the interval.
"""
return (self.a+self.b)*0.5
def GetLength(self):
"""
Length of interval. Uses British Rail metric.
"""
return abs(self.b-self.a)
def GetUpper(self):
"""
Returns upper value.
"""
return self.a
def GetLower(self):
"""
Returns lower value.
"""
return self.a
def Overlaps(self, other):
"""
Returns true if two Intervals overlap.
"""
if not isinstance(other, Interval):
raise TypeError("Only Intervals can overlap with Intervals.")
return ( ((other.a >= self.a) and (other.a <= self.b)) or ((self.a >= other.a) and (self.a <= other.b)) );
def IsRealNumber(self):
"""
Returns true if the Interval represents a real number.
"""
if self.a == self.b:
return True
return False
def GetRealValue(self):
"""
Returns real value iff the Interval represents a real number. Otherwise returns None.
"""
if not self.IsRealNumber():
return None
return self.a
def __add__(self, other):
"""
Add two intervals to get their vector sum.
Add a real number to an interval to lengthen it.
"""
c = Interval()
if type(other) == int or type(other) == float:
c.SetRealInterval(self.a, self.b+other)
elif isinstance(other, Interval):
c.SetRealInterval(self.a+other.a, self.b+self.b)
if c.b < c.a:
temp = c.a
c.a = c.b
c.b = temp
else:
raise TypeError("You can only add Intervals or real numbers from Intervals")
return c
def __sub__(self, other):
"""
Subtract two intervals to get their vector difference.
Subtract a real number from an Interval to shorten it.
"""
c = Interval()
if type(other) == int or type(other) == float:
c.SetRealInterval(self.a, self.b-other)
elif isinstance(other, Interval):
c.SetRealInterval(self.a-other.b, self.b-other.a)
if c.b < c.a:
temp = c.a
c.a = c.b
c.b = temp
else:
raise TypeError("You can only subtract Intervals or real numbers from Intervals")
return c
def __mul__(self, other):
"""
Multiply an Interval with with:
a) Another Interval.
For Intervals A, B, then
A·B = [a1, a2]·[b1, b2]
= [min(a1b1, a1b2, a2b1, a2b2), max(a1b1, a1b2, a2b1, a2b2)]
b) A boolean value.
For Interval A and bool b. Ab = ( (b => A) ^ (¬b => 0) )
c) A real number.
For Interval A and real c, cA = c[a1, a2] = [ca1, ca2].
"""
i = Interval()
if isinstance(other, Interval):
opts = [self.a * other.a, self.a * other.b, self.b * other.a, self.b * other.b]
i.SetRealInterval(min(opts), max(opts))
elif type(other) == bool:
if other == True:
i.SetRealInterval(self.a, self.b)
else:
i.SetRealInterval(0, 0)
elif type(other) == int or type(other) == float:
i.SetRealInterval(self.a * other, self.b * other)
else:
raise TypeException("Right side of multiplication with Interval is defined for Interval, bool, int and float.")
return i
def __div__(self, other):
"""
Divide an Interval by:
a) Another Interval.
For Intervals A, B; 0 \notin B, then
A/B = [a1, a2]·[b1, b2]
= [min(a1/b1, a1/b2, a2/b1, a2/b2), max(a1/b1, a1/b2, a2/b1, a2/b2)]
b) A real number.
For Interval A an real c, A/c = 1/c * [a1, a2]. See multiplication (__mul__) for resolution.
"""
i = Interval()
if isinstance(other, Interval):
if other.a == 0 or other.b == 0:
raise ZeroDivisionError("Interval division by zero-Interval [a,0] or [a,0]")
i = opts = [self.a / other.a, self.a / other.b, self.b / other.a, self.b / other.b]
i.SetRealInterval(min(opts), max(opts))
elif type(other) == int or type(other) == float:
if other == 0:
raise ZeroDivisionError("Interval division by zero")
i.SetRealInterval(self.a / other, self.b / other)
else:
raise TypeException("Right side of division for Interval is defined for Interval, int and float.")
return i
def __pow__(self, other):
# FIXME: Unimplemented
raise NotImplemented
def __lshift__(self, other):
"""
Left shift operator shifts the Interval left by the value of 'other', without changing it's length.
"""
i = Interval()
if type(other) == int or type(other) == float:
i.SetRealInterval(self.a - other, self.b - other)
else:
raise TypeError("You can only shift Intervals by real numbers")
return i
def __rshift__(self, other):
"""
Right shift operator shifts the Interval right by the value of 'other', without changing it's length.
"""
i = Interval()
if type(other) == int or type(other) == float:
i.SetRealInterval(self.a + other, self.b + other)
else:
raise TypeError("You can only shift Intervals by real numbers")
return i
def __and__(self, other):
"""
a & b : Returns the largest contiguous interval shared by both intervals, or an
empty interval if they are disjoint.
"""
if not isinstance(other, Interval):
raise TypeError("Interval and only works on two intervals.")
if not self.Overlaps(other):
return Interval()
start = max(self.a, other.a)
end = min(self.b, other.b)
return Interval(start, end)
def __xor__(self, other):
"""
a ^ b : Returns the longest contiguous interval covered by a or b but not both.
Returns an empty interval if they overlap perfectly.
"""
if not isinstance(other, Interval):
raise TypeError("Interval xor only works on two intervals.")
i = Interval()
if self.a == other.a and self.b == other.b:
return i
# FIXME: Not complete.
def __or__(self, other):
"""
a | b : Returns the longest contiguous interval that consists of either a or b or both.
Returns an empty interval iff both a and b are empty.
"""
if not isinstance(other, Interval):
raise TypeError("Interval or only works on two intervals.")
i = Interval()
if not self.Overlaps(other):
if self.GetLength() > other.GetLength():
i.a = self.a
i.b = self.b
else:
i.a = other.a
i.b = other.b
return i
if (self.a < other.a):
start = self.a
else:
start = other.a
if (self.b > other.b):
end = self.b
else:
end = other.b
i.SetRealInterval(start, end)
return i
def __iadd__(self, other):
self.SetRealInterval(self.a+other.a, self.b+self.b)
return self
def __isub__(self, other):
self.SetRealInterval(self.a-other.b, self.b-other.a)
return self
def __imul__(self, other):
# FIXME: Unimplemented
raise NotImplemented
def __idiv__(self, other):
# FIXME: Unimplemented
raise NotImplemented
def __ipow__(self, other):
# FIXME: Unimplemented
raise NotImplemented
def __ilshift__(self, other):
if type(other) == int or type(other) == float:
self.a -= other
self.b -= other
return self
def __irshift__(self, other):
if type(other) == int or type(other) == float:
self.a += other
self.b += other
return self
def __iand__(self, other):
# FIXME: Unimplemented
raise NotImplemented
def __ixor__(self, other):
# FIXME: Unimplemented
raise NotImplemented
def __ior__(self, other):
# FIXME: Unimplemented
raise NotImplemented
def __invert__(self):
"""
Mirrors the interval over the 0 point.
"""
i = Interval()
i.b = -self.a
i.a = -self.b
return i
def __str__(self):
return "[%lf, %lf]" % (self.a, self.b)
def __lt__(self, other):
# FIXME: Unimplemented
raise NotImplemented
def __le__(self, other):
# FIXME: Unimplemented
raise NotImplemented
def __eq__(self, other):
return (self.a == other.a) and (self.b == other.b)
def __ne__(self, other):
return (self.a != other.a) or (self.b != other.b)
def __gt__(self, other):
# FIXME: Unimplemented
raise NotImplemented
def __ge__(self, other):
# FIXME: Unimplemented
raise NotImplemented
def __hash__(self):
# FIXME: Bad implementation
return self.a + self.b + (self.a.__hash__() ^ self.b.__hash__()) + self.GetLength()
class OutOfOrderException(Exception):
def __init__(self):
print "On a closed interval [a,b], a < b."
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