def __mul__(self, other):
"""Handles logic of multiplying signs.
Cases:
ZERO * ANYTHING = ZERO
UNKNOWN * NON-ZERO = UNKNOWN
POSITIVE * NEGATIVE = NEGATIVE
POSITIVE * POSITIVE = POSITIVE
NEGATIVE * NEGATIVE = POSITIVE
Args:
self: The Sign of the left-hand multiplier.
other: The Sign of the right-hand multiplier.
Returns:
The Sign of the product.
"""
neg_mat = bu.dot(self.neg_mat, other.pos_mat) | \
bu.dot(self.pos_mat, other.neg_mat)
pos_mat = bu.dot(self.neg_mat, other.neg_mat) | \
bu.dot(self.pos_mat, other.pos_mat)
# Reduce 1x1 matrices to scalars.
neg_mat = bu.to_scalar(neg_mat)
pos_mat = bu.to_scalar(pos_mat)
return Sign(neg_mat, pos_mat)
def sign_mul(sign, curv):
"""Handles logic of sign by curvature multiplication.
Cases:
ZERO * ANYTHING = CONSTANT
NON-ZERO * AFFINE/CONSTANT = AFFINE/CONSTANT
UNKNOWN * NON-AFFINE = UNKNOWN
POSITIVE * ANYTHING = ANYTHING
NEGATIVE * CONVEX = CONCAVE
NEGATIVE * CONCAVE = CONVEX
Args:
sign: The Sign of the left-hand multiplier.
curv: The Curvature of the right-hand multiplier.
Returns:
The Curvature of the product.
"""
cvx_mat = bu.dot(sign.pos_mat, curv.cvx_mat) | \
bu.dot(sign.neg_mat, curv.conc_mat)
conc_mat = bu.dot(sign.pos_mat, curv.conc_mat) | \
bu.dot(sign.neg_mat, curv.cvx_mat)
nonconst_mat = bu.dot(sign.pos_mat, curv.nonconst_mat) | \
bu.dot(sign.neg_mat, curv.nonconst_mat)
# Simplify 1x1 matrices to scalars.
cvx_mat = bu.to_scalar(cvx_mat)
conc_mat = bu.to_scalar(conc_mat)
nonconst_mat = bu.to_scalar(nonconst_mat)
return Curvature(cvx_mat, conc_mat, nonconst_mat)
def __mul__(self, other):
"""Handles logic of multiplying signs.
Cases:
ZERO * ANYTHING = ZERO
UNKNOWN * NON-ZERO = UNKNOWN
POSITIVE * NEGATIVE = NEGATIVE
POSITIVE * POSITIVE = POSITIVE
NEGATIVE * NEGATIVE = POSITIVE
Args:
self: The Sign of the left-hand multiplier.
other: The Sign of the right-hand multiplier.
Returns:
The Sign of the product.
"""
neg_mat = bu.dot(self.neg_mat, other.pos_mat) | \
bu.dot(self.pos_mat, other.neg_mat)
pos_mat = bu.dot(self.neg_mat, other.neg_mat) | \
bu.dot(self.pos_mat, other.pos_mat)
# Reduce 1x1 matrices to scalars.
neg_mat = bu.to_scalar(neg_mat)
pos_mat = bu.to_scalar(pos_mat)
return Sign(neg_mat, pos_mat)
def sign_mul(sign, curv):
"""Handles logic of sign by curvature multiplication.
Cases:
ZERO * ANYTHING = CONSTANT
NON-ZERO * AFFINE/CONSTANT = AFFINE/CONSTANT
UNKNOWN * NON-AFFINE = UNKNOWN
POSITIVE * ANYTHING = ANYTHING
NEGATIVE * CONVEX = CONCAVE
NEGATIVE * CONCAVE = CONVEX
Args:
sign: The Sign of the left-hand multiplier.
curv: The Curvature of the right-hand multiplier.
Returns:
The Curvature of the product.
"""
cvx_mat = bu.dot(sign.pos_mat, curv.cvx_mat) | \
bu.dot(sign.neg_mat, curv.conc_mat)
conc_mat = bu.dot(sign.pos_mat, curv.conc_mat) | \
bu.dot(sign.neg_mat, curv.cvx_mat)
nonconst_mat = bu.dot(sign.pos_mat, curv.nonconst_mat) | \
bu.dot(sign.neg_mat, curv.nonconst_mat)
# Simplify 1x1 matrices to scalars.
cvx_mat = bu.to_scalar(cvx_mat)
conc_mat = bu.to_scalar(conc_mat)
nonconst_mat = bu.to_scalar(nonconst_mat)
return Curvature(cvx_mat, conc_mat, nonconst_mat)
def __getitem__(self, key):
"""Determines the DCP attributes of an index/slice.
Args:
key: A (slice, slice) tuple.
Returns:
The DCPAttr of the index/slice into the matrix expression.
"""
shape = Shape(*ku.size(key, self.shape))
# Reduce 1x1 matrices to scalars.
neg_mat = bu.to_scalar(bu.index(self.sign.neg_mat, key))
pos_mat = bu.to_scalar(bu.index(self.sign.pos_mat, key))
cvx_mat = bu.to_scalar(bu.index(self.curvature.cvx_mat, key))
conc_mat = bu.to_scalar(bu.index(self.curvature.conc_mat, key))
nonconst_mat = bu.to_scalar(bu.index(self.curvature.nonconst_mat, key))
return DCPAttr(Sign(neg_mat, pos_mat), Curvature(cvx_mat, conc_mat, nonconst_mat), shape)
def __getitem__(self, key):
"""Determines the DCP attributes of an index/slice.
Args:
key: A (slice, slice) tuple.
Returns:
The DCPAttr of the index/slice into the matrix expression.
"""
shape = Shape(*ku.size(key, self.shape))
# Reduce 1x1 matrices to scalars.
neg_mat = bu.to_scalar(bu.index(self.sign.neg_mat, key))
pos_mat = bu.to_scalar(bu.index(self.sign.pos_mat, key))
cvx_mat = bu.to_scalar(bu.index(self.curvature.cvx_mat, key))
conc_mat = bu.to_scalar(bu.index(self.curvature.conc_mat, key))
nonconst_mat = bu.to_scalar(bu.index(self.curvature.nonconst_mat, key))
return DCPAttr(Sign(neg_mat, pos_mat),
Curvature(cvx_mat, conc_mat, nonconst_mat), shape)