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import itertools
import numpy as np
from polymatrix.denserepr.impl import DenseReprBufferImpl, DenseReprImpl
from polymatrix.expression.expression import Expression
from polymatrix.expression.mixins.expressionbasemixin import ExpressionBaseMixin
from polymatrix.expressionstate.abc import ExpressionState
from polymatrix.expression.utils.getvariableindices import get_variable_indices_from_variable
from polymatrix.statemonad.init import init_state_monad
from polymatrix.statemonad.mixins import StateMonadMixin
from polymatrix.denserepr.utils.monomialtoindex import variable_indices_to_column_index
def from_polymatrix(
expressions: Expression | tuple[Expression],
variables: Expression = None,
sorted: bool = None,
) -> StateMonadMixin[ExpressionState, tuple[tuple[tuple[np.ndarray, ...], ...], tuple[int, ...]]]:
if isinstance(expressions, Expression):
expressions = (expressions,)
assert isinstance(variables, ExpressionBaseMixin) or variables is None, f'{variables=}'
def func(state: ExpressionState):
def acc_underlying_application(acc, v):
state, underlying_list = acc
state, underlying = v.apply(state)
assert underlying.shape[1] == 1, f'{underlying.shape[1]=} is not 1'
return state, underlying_list + (underlying,)
*_, (state, polymatrix_list) = tuple(itertools.accumulate(
expressions,
acc_underlying_application,
initial=(state, tuple()),
))
if variables is None:
sorted_variable_index = tuple()
else:
state, variable_index = get_variable_indices_from_variable(state, variables)
if sorted:
tagged_variable_index = tuple((offset, state.get_name_from_offset(offset)) for offset in variable_index)
sorted_variable_index = tuple(v[0] for v in sorted(tagged_variable_index, key=lambda v: v[1]))
else:
sorted_variable_index = variable_index
sorted_variable_index_set = set(sorted_variable_index)
if len(sorted_variable_index) != len(sorted_variable_index_set):
duplicates = tuple(state.get_name_from_offset(var) for var in sorted_variable_index_set if 1 < sorted_variable_index.count(var))
raise Exception(f'{duplicates=}. Make sure you give a unique name for each variables.')
variable_index_map = {old: new for new, old in enumerate(sorted_variable_index)}
n_param = len(sorted_variable_index)
def gen_numpy_matrices():
for polymatrix in polymatrix_list:
n_row = polymatrix.shape[0]
buffer = DenseReprBufferImpl(
data={},
n_row=n_row,
n_param=n_param,
)
for row in range(n_row):
polymatrix_terms = polymatrix.get_poly(row, 0)
if polymatrix_terms is None:
continue
if len(polymatrix_terms) == 0:
buffer.add(row, 0, 0, 0)
else:
for monomial, value in polymatrix_terms.items():
def gen_new_monomial():
for var, count in monomial:
try:
index = variable_index_map[var]
except KeyError:
# todo: improve this error message!
raise KeyError(f'{var=} ({state.get_key_from_offset(var)}) is incompatible with {variable_index_map=}')
for _ in range(count):
yield index
new_variable_indices = tuple(gen_new_monomial())
cols = variable_indices_to_column_index(n_param, new_variable_indices)
col_value = value / len(cols)
for col in cols:
degree = sum(count for _, count in monomial)
buffer.add(row, col, degree, col_value)
yield buffer
underlying_matrices = tuple(gen_numpy_matrices())
def gen_auxillary_equations():
for key, monomial_terms in state.auxillary_equations.items():
if key in sorted_variable_index:
yield key, monomial_terms
auxillary_equations = tuple(gen_auxillary_equations())
n_row = len(auxillary_equations)
if n_row == 0:
auxillary_matrix_equations = None
else:
buffer = DenseReprBufferImpl(
data={},
n_row=n_row,
n_param=n_param,
)
for row, (key, monomial_terms) in enumerate(auxillary_equations):
for monomial, value in monomial_terms.items():
new_monomial = tuple(variable_index_map[var] for var, count in monomial for _ in range(count))
cols = variable_indices_to_column_index(n_param, new_monomial)
col_value = value / len(cols)
for col in cols:
buffer.add(row, col, sum(count for _, count in monomial), col_value)
auxillary_matrix_equations = buffer
result = DenseReprImpl(
data=underlying_matrices,
aux_data=auxillary_matrix_equations,
variable_mapping=sorted_variable_index,
state=state,
)
return state, result
return init_state_monad(func)
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