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import abc
import dataclasses
from polymatrix.polymatrix.init import init_poly_matrix
from polymatrix.expression.mixins.expressionbasemixin import ExpressionBaseMixin
from polymatrix.expressionstate.mixins import ExpressionStateMixin
from polymatrix.polymatrix.mixins import PolyMatrixMixin
from polymatrix.expression.utils.getvariableindices import get_variable_indices_from_variable
from polymatrix.expression.utils.splitmonomialindices import split_monomial_indices
class QuadraticMonomialsExprMixin(ExpressionBaseMixin):
"""
Maps a polynomial matrix
underlying = [
[x y ],
[x + x^2],
]
into a vector of monomials
output = [1, x, y]
in variable
variables = [x, y].
"""
@property
@abc.abstractclassmethod
def underlying(self) -> ExpressionBaseMixin:
...
@property
@abc.abstractmethod
def variables(self) -> ExpressionBaseMixin:
...
# overwrites the abstract method of `ExpressionBaseMixin`
def apply(
self,
state: ExpressionStateMixin,
) -> tuple[ExpressionStateMixin, PolyMatrixMixin]:
state, underlying = self.underlying.apply(state=state)
state, variable_indices = get_variable_indices_from_variable(state, self.variables)
def gen_sos_monomials():
for row in range(underlying.shape[0]):
for col in range(underlying.shape[1]):
polynomial = underlying.get_poly(row, col)
if polynomial is None:
continue
for monomial in polynomial.keys():
x_monomial = tuple((var_idx, count) for var_idx, count in monomial if var_idx in variable_indices)
left, right = split_monomial_indices(x_monomial)
yield left
yield right
sos_monomials = tuple(sorted(set(gen_sos_monomials()), key=lambda m: (len(m), m)))
def gen_terms():
for index, monomial in enumerate(sos_monomials):
yield (index, 0), {monomial: 1.0}
terms = dict(gen_terms())
poly_matrix = init_poly_matrix(
terms=terms,
shape=(len(sos_monomials), 1),
)
state = dataclasses.replace(
state,
cache=state.cache | {self: poly_matrix},
)
return state, poly_matrix
|
