def __pow__(self,other):
if self.interv_class == "M":
if other%2 == 0:
maximo = max(abs(self.inf),abs(self.sup))
return Interv_single(0,up(lambda:maximo**other))
else:
return Interv_single(down(lambda:self.inf**other),up(lambda:self.sup**other))
else: # N, P, Z, E
return Interv_single(down(lambda:self.inf**other),up(lambda:self.sup**other))
def __pow__(self, other):
if self.interv_class == "M":
if other % 2 == 0:
maximo = max(abs(self.inf), abs(self.sup))
return Interv_single(0, up(lambda: maximo**other))
else:
return Interv_single(down(lambda: self.inf**other),
up(lambda: self.sup**other))
else: # N, P, Z, E
return Interv_single(down(lambda: self.inf**other),
up(lambda: self.sup**other))
def __mul__(self, other):
inf = 0
sup = 0
c1 = self.interv_class
c2 = other.interv_class
if c1 == "E" or c2 == "E":
inf = float("nan")
sup = float("nan")
elif c1 == 'Z' or c2 == 'Z':
inf = 0
sup = 0
elif c1 in self._P_:
if c2 in self._P_:
inf = down(lambda: self.inf * other.inf)
sup = up(lambda: self.sup * other.sup)
elif c2 == 'M':
inf = down(lambda: self.sup * other.inf)
sup = up(lambda: self.sup * other.sup)
else: #c2 in self._N_:
inf = down(lambda: self.sup * other.inf)
sup = up(lambda: self.inf * other.sup)
elif c1 == 'M':
if c2 in self._P_:
inf = down(lambda: self.inf * other.sup)
sup = up(lambda: self.sup * other.sup)
elif c2 == 'M':
inf = min(down(lambda: self.inf * other.sup),
down(lambda: self.sup * other.inf))
sup = max(up(lambda: self.sup * other.sup),
up(lambda: self.inf * other.inf))
else: #c2 in N
inf = down(lambda: self.sup * other.inf)
sup = up(lambda: self.inf * other.inf)
else: #c1 in N
if c2 in self._P_:
inf = down(lambda: self.inf * other.sup)
sup = up(lambda: self.sup * other.inf)
elif c2 == 'M':
inf = down(lambda: self.inf * other.sup)
sup = up(lambda: self.inf * other.inf)
else: #c2 in N
inf = down(lambda: self.sup * other.sup)
sup = up(lambda: self.inf * other.inf)
return Interv_single(inf, sup)
def __mul__(self,other):
inf = 0
sup = 0
c1 = self.interv_class
c2 = other.interv_class
if c1 == "E" or c2 == "E":
inf = float("nan")
sup = float("nan")
elif c1 == 'Z' or c2 == 'Z':
inf = 0
sup = 0
elif c1 in self._P_:
if c2 in self._P_:
inf = down(lambda: self.inf * other.inf)
sup = up(lambda: self.sup * other.sup)
elif c2 == 'M':
inf = down(lambda: self.sup * other.inf)
sup = up(lambda: self.sup * other.sup)
else: #c2 in self._N_:
inf = down(lambda: self.sup * other.inf)
sup = up(lambda: self.inf * other.sup)
elif c1 == 'M':
if c2 in self._P_:
inf = down(lambda: self.inf * other.sup)
sup = up(lambda: self.sup * other.sup)
elif c2 == 'M':
inf = min(down(lambda: self.inf * other.sup), down(lambda: self.sup * other.inf))
sup = max(up(lambda: self.sup * other.sup), up(lambda: self.inf * other.inf))
else: #c2 in N
inf = down(lambda: self.sup * other.inf)
sup = up(lambda: self.inf * other.inf)
else: #c1 in N
if c2 in self._P_:
inf = down(lambda: self.inf * other.sup)
sup = up(lambda: self.sup * other.inf)
elif c2 == 'M':
inf = down(lambda: self.inf * other.sup)
sup = up(lambda: self.inf * other.inf)
else: #c2 in N
inf = down(lambda: self.sup * other.sup)
sup = up(lambda: self.inf * other.inf)
return Interv_single(inf,sup)
def __sub__(self, other):
return Interv_single(down(lambda: self.inf - other.sup),
up(lambda: (self.sup - other.inf)))
def __add__(self, other):
return Interv_single(down(lambda: self.inf + other.inf),
up(lambda: (self.sup + other.sup)))
def __div__(self, other):
inf = 0
sup = 0
c1 = self.interv_class
c2 = other.interv_class
if c2 == "E" or c1 == "E":
inf = float("nan")
sup = float("nan")
elif c2 == "Z":
inf = float("nan")
sup = float("nan")
elif c1 == "Z":
inf = 0
sup = 0
elif c2 == "P0":
if c1 == "P1":
inf = down(lambda: self.inf / other.sup)
sup = float("+inf")
elif c1 == "P0":
inf = 0
sup = float("+inf")
elif c1 == "M":
inf = float("-inf")
sup = float("inf")
elif c1 == "N0":
inf = float("-inf")
sup = 0
else: #c1 == "N1":
inf = float("-inf")
sup = up(lambda: self.sup / other.sup)
elif c2 == "P1":
if c1 == "P1":
inf = down(lambda: self.inf / other.sup)
sup = up(lambda: self.sup / other.inf)
elif c1 == "P0":
inf = 0
sup = up(lambda: self.sup / other.inf)
elif c1 == "M":
inf = down(lambda: self.inf / other.inf)
sup = up(lambda: self.sup / other.inf)
elif c1 == "N0":
inf = down(lambda: self.inf / other.inf)
sup = 0
else: #c1 == "N1":
inf = down(lambda: self.inf / other.inf)
sup = up(lambda: self.sup / other.sup)
elif c2 == "M":
inf = float("-inf")
sup = float("inf")
elif c2 == "N0":
if c1 == "P1":
inf = float("-inf")
sup = up(lambda: self.inf / other.inf)
elif c1 == "P0":
inf = float("-inf")
sup = 0
elif c1 == "M":
inf = float("-inf")
sup = float("inf")
elif c1 == "N0":
inf = 0
sup = float("+inf")
else: #c1 == "N1":
inf = down(lambda: self.sup / other.inf)
sup = float("+inf")
elif c2 == "N1":
if c1 == "P1":
inf = down(lambda: self.sup / other.sup)
sup = up(lambda: self.inf / other.inf)
elif c1 == "P0":
inf = down(lambda: self.sup / other.sup)
sup = 0
elif c1 == "M":
inf = down(lambda: self.sup / other.sup)
sup = up(lambda: self.inf / other.sup)
elif c1 == "N0":
inf = 0
sup = up(lambda: self.inf / other.sup)
else: #c1 == "N1":
inf = down(lambda: self.sup / other.inf)
sup = up(lambda: self.inf / other.sup)
return Interv_single(inf, sup)
def __sub__(self,other):
return Interv_single(down(lambda: self.inf - other.sup), up(lambda: (self.sup - other.inf)))
def __add__(self,other):
return Interv_single(down(lambda: self.inf + other.inf), up(lambda:(self.sup + other.sup)))
def __div__(self,other):
inf = 0
sup = 0
c1 = self.interv_class
c2 = other.interv_class
if c2 == "E" or c1 == "E":
inf = float("nan")
sup = float("nan")
elif c2 == "Z":
inf = float("nan")
sup = float("nan")
elif c1 == "Z":
inf = 0
sup = 0
elif c2 == "P0":
if c1 == "P1":
inf = down(lambda: self.inf / other.sup)
sup = float("+inf")
elif c1 == "P0":
inf = 0
sup = float("+inf")
elif c1 == "M":
inf = float("-inf")
sup = float("inf")
elif c1 == "N0":
inf = float("-inf")
sup = 0
else: #c1 == "N1":
inf = float("-inf")
sup = up(lambda: self.sup / other.sup)
elif c2 == "P1":
if c1 == "P1":
inf = down(lambda: self.inf / other.sup)
sup = up(lambda: self.sup / other.inf)
elif c1 == "P0":
inf = 0
sup = up(lambda: self.sup / other.inf)
elif c1 == "M":
inf = down(lambda: self.inf / other.inf)
sup = up(lambda: self.sup / other.inf)
elif c1 == "N0":
inf = down(lambda: self.inf / other.inf)
sup = 0
else: #c1 == "N1":
inf = down(lambda: self.inf / other.inf)
sup = up(lambda: self.sup / other.sup)
elif c2 == "M":
inf = float("-inf")
sup = float("inf")
elif c2 == "N0":
if c1 == "P1":
inf = float("-inf")
sup = up(lambda: self.inf / other.inf)
elif c1 == "P0":
inf = float("-inf")
sup = 0
elif c1 == "M":
inf = float("-inf")
sup = float("inf")
elif c1 == "N0":
inf = 0
sup = float("+inf")
else: #c1 == "N1":
inf = down(lambda: self.sup / other.inf)
sup = float("+inf")
elif c2 == "N1":
if c1 == "P1":
inf = down(lambda: self.sup / other.sup)
sup = up(lambda: self.inf / other.inf)
elif c1 == "P0":
inf = down(lambda: self.sup / other.sup)
sup = 0
elif c1 == "M":
inf = down(lambda: self.sup / other.sup)
sup = up(lambda: self.inf / other.sup)
elif c1 == "N0":
inf = 0
sup = up(lambda: self.inf / other.sup)
else: #c1 == "N1":
inf = down(lambda: self.sup / other.inf)
sup = up(lambda: self.inf / other.sup)
return Interv_single(inf,sup)