def __call__(self, *args):
while type(args[0]) is list: args = args[0]
assert len(args) == 2
p = args[0]
x = args[1]
if p == 0 or p == 1:
return p
elif 0 < p < 1:
if isinstance(x, expr):
return expr(self, [scalar(p), x])
else:
if x<1:
raise ValueError('power_pos called with exponent %f < 1' %x)
return pow(max(p,0), x)
elif p > 1:
if isinstance(x, expr):
return expr(self, [scalar(p), x])
else:
if x<1:
raise ValueError('power_pos called with exponent %f < 1' %x)
return pow(max(0,p), x)
else:
raise ValueError('power called with negative base %f' %p)
def __call__(self, *args):
while type(args[0]) is list:
args = args[0]
assert len(args) == 2
p = args[0]
x = args[1]
if p == 0 or p == 1:
return p
elif 0 < p < 1:
if isinstance(x, expr):
return expr(self, [scalar(p), x])
else:
if x < 1:
raise ValueError('power_pos called with exponent %f < 1' %
x)
return pow(max(p, 0), x)
elif p > 1:
if isinstance(x, expr):
return expr(self, [scalar(p), x])
else:
if x < 1:
raise ValueError('power_pos called with exponent %f < 1' %
x)
return pow(max(0, p), x)
else:
raise ValueError('power called with negative base %f' % p)
def __call__(self, *args):
while type(args[0]) is list: args = args[0]
assert len(args) == 2
x = args[0]
y = args[1]
if isNumber(x) and isNumber(y):
if y==0: raise ValueError('Division by zero in quadratic over linear')
return x*x/y
if isNumber(x): x = scalar(x)
if isNumber(y): y = scalar(y)
return expr(self, [x, y])
def __init__(self, lhs, relop, rhs):
assert relop in [EQ, LT, GT]
if isNumber(lhs): lhs = scalar(lhs)
if isNumber(rhs): rhs = scalar(rhs)
if relop == EQ:
assert lhs.is_affine() and rhs.is_affine()
if relop == LT:
assert lhs.is_convex() and rhs.is_concave()
if relop == GT:
assert lhs.is_concave() and rhs.is_convex()
self.lhs = lhs
self.rhs = rhs
self.relop = relop
def __init__(self, lhs, relop, rhs):
assert relop in [EQ, LT, GT]
if isNumber(lhs): lhs = scalar(lhs)
if isNumber(rhs): rhs = scalar(rhs)
if relop == EQ:
assert lhs.is_affine() and rhs.is_affine()
if relop == LT:
assert lhs.is_convex() and rhs.is_concave()
if relop == GT:
assert lhs.is_concave() and rhs.is_convex()
self.lhs = lhs
self.rhs = rhs
self.relop = relop
def __call__(self, *args):
while type(args[0]) is list: args = args[0]
assert len(args) == 2
x = args[0]
y = args[1]
if isNumber(x) and isNumber(y):
if x<=0 or y<=0:
raise ValueError('relative entropy called with negative arguments x = %f , y = %f' % (x,y))
print (x,y)
return x*math.log(float(x)/y)
if isNumber(x): x = scalar(x)
if isNumber(y): y = scalar(y)
return expr(self,[x,y])
def __call__(self, *args):
while type(args[0]) is list:
args = args[0]
assert len(args) == 2
x = args[0]
y = args[1]
if isNumber(x) and isNumber(y):
if x <= 0 or y <= 0:
raise ValueError(
'relative entropy called with negative arguments x = %f , y = %f'
% (x, y))
print(x, y)
return x * math.log(float(x) / y)
if isNumber(x): x = scalar(x)
if isNumber(y): y = scalar(y)
return expr(self, [x, y])
def __call__(self, *args):
while type(args[0]) is list: args = args[0]
assert len(args) == 1 or len(args) == 2
if len(args) == 1: args.append(1.0)
assert isNumber(args[1]) and args[1] >= 0
x = args[0]
M = args[1]
if isinstance(x, expr):
return expr(self, [x, scalar(M)])
elif math.fabs(x) <= M:
return x*x
else:
return M*(2.0*math.fabs(x)-M)
def __call__(self, *args):
while type(args[0]) is list: args = args[0]
x = args
flag = False
for xi in x:
if isinstance(xi, expr):
flag = True
break
if not flag: return math.sqrt(sum([xi**2.0 for xi in x]))
y = []
for i in range(len(x)):
if isNumber(x[i]): y.append(scalar(x[i]))
else: y.append(x[i])
return expr(self, y)
def __call__(self, *args):
while type(args[0]) is list:
args = args[0]
assert len(args) == 1 or len(args) == 2
if len(args) == 1: args.append(1.0)
assert isNumber(args[1]) and args[1] >= 0
x = args[0]
M = args[1]
if isinstance(x, expr):
return expr(self, [x, scalar(M)])
elif math.fabs(x) <= M:
return math.fabs(x)
else:
return (x * x + M * M) / (2.0 * M)
def __call__(self,*args):
while type(args[0]) is list: args = args[0]
assert len(args) == 2
x = args[0]
p = args[1]
if p == 0: return 1;
if p == 1: return x;
if isinstance(x,expr):
return expr(self,[x, scalar(p)])
else:
if p<1:
raise ValueError('pow_pos called with exponent %f <1' %p)
else:
return pow(max(x,0),p)
def __call__(self,*args):
while type(args[0]) is list: args = args[0]
x = args
n = float(len(args))
flag = False
for xi in x:
if isinstance(xi, expr):
flag = True
break
if not flag:
for xi in x:
if xi == 0: return 0
if xi < 0: raise ValueError('geometric mean called with'
'a vector containing a negative entry')
return math.exp(sum([math.log(xi)/n for xi in x]))
y = []
for i in range(len(x)):
if isNumber(x[i]): y.append(scalar(x[i]))
else: y.append(x[i])
return expr(self, y)