def __mul__(self, other):
"""Determines the DCP attributes of two expressions multiplied together.
Assumes one of the arguments has constant curvature.
Args:
self: The DCPAttr of the left-hand expression.
other: The DCPAttr of the right-hand expression.
Returns:
The DCPAttr of the product.
"""
shape = self.shape * other.shape
sign = self.sign * other.sign
if self.curvature.is_constant():
curvature = Curvature.sign_mul(self.sign, other.curvature)
else:
curvature = Curvature.sign_mul(other.sign, self.curvature)
return DCPAttr(sign, curvature, shape)
def __mul__(self, other):
"""Determines the DCP attributes of two expressions multiplied together.
Assumes one of the arguments has constant curvature.
Args:
self: The DCPAttr of the left-hand expression.
other: The DCPAttr of the right-hand expression.
Returns:
The DCPAttr of the product.
"""
shape = self.shape * other.shape
sign = self.sign * other.sign
if self.curvature.is_constant():
curvature = Curvature.sign_mul(self.sign, other.curvature)
else:
curvature = Curvature.sign_mul(other.sign, self.curvature)
return DCPAttr(sign, curvature, shape)
def mul_elemwise(lh_expr, rh_expr):
"""Determines the DCP attributes of expressions multiplied elementwise.
Assumes the left-hand argument has constant curvature and both
arguments have the same shape.
Args:
lh_expr: The DCPAttr of the left-hand expression.
rh_expr: The DCPAttr of the right-hand expression.
Returns:
The DCPAttr of the product.
"""
shape = lh_expr.shape + rh_expr.shape
sign = lh_expr.sign * rh_expr.sign
curvature = Curvature.sign_mul(lh_expr.sign, rh_expr.curvature)
return DCPAttr(sign, curvature, shape)
def mul_elemwise(lh_expr, rh_expr):
"""Determines the DCP attributes of expressions multiplied elementwise.
Assumes the left-hand argument has constant curvature and both
arguments have the same shape.
Args:
lh_expr: The DCPAttr of the left-hand expression.
rh_expr: The DCPAttr of the right-hand expression.
Returns:
The DCPAttr of the product.
"""
shape = lh_expr.shape + rh_expr.shape
sign = lh_expr.sign * rh_expr.sign
curvature = Curvature.sign_mul(lh_expr.sign, rh_expr.curvature)
return DCPAttr(sign, curvature, shape)
def dcp_curvature(monotonicity, func_curvature, arg_sign, arg_curvature):
"""Applies DCP composition rules to determine curvature in each argument.
Composition rules:
Key: Function curvature + monotonicity + argument curvature
== curvature in argument
anything + anything + constant == constant
anything + anything + affine == original curvature
convex/affine + increasing + convex == convex
convex/affine + decreasing + concave == convex
concave/affine + increasing + concave == concave
concave/affine + decreasing + convex == concave
Notes: Increasing (decreasing) means non-decreasing (non-increasing).
Any combinations not covered by the rules result in a
nonconvex expression.
Args:
monotonicity: The monotonicity of the function in the given argument.
func_curvature: The curvature of the function.
arg_sign: The sign of the given argument.
arg_curvature: The curvature of the given argument.
Returns:
The Curvature of the composition of function and arguments.
"""
if arg_curvature.is_constant():
return Curvature.CONSTANT
elif monotonicity == INCREASING:
return func_curvature + arg_curvature
elif monotonicity == DECREASING:
return func_curvature - arg_curvature
# Absolute value style monotonicity.
elif monotonicity == SIGNED and \
func_curvature.is_convex():
conc_mat = arg_sign.neg_mat & arg_curvature.cvx_mat | \
arg_sign.pos_mat & arg_curvature.conc_mat
return Curvature(np.bool_(True), conc_mat, np.bool_(True))
else: # non-monotonic
return func_curvature + arg_curvature - arg_curvature
