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| author | Michael Schneeberger <michael.schneeberger@fhnw.ch> | 2022-04-04 14:47:50 +0200 |
|---|---|---|
| committer | Michael Schneeberger <michael.schneeberger@fhnw.ch> | 2022-04-04 14:47:50 +0200 |
| commit | 561997eaa73ad81ec2da63e6e62cdf776d87be4e (patch) | |
| tree | 6e37072a76772e70738f3572b63b5836688eeeb3 | |
| parent | bugfixes in KKT conditions (diff) | |
| download | polymatrix-561997eaa73ad81ec2da63e6e62cdf776d87be4e.tar.gz polymatrix-561997eaa73ad81ec2da63e6e62cdf776d87be4e.zip | |
implement polynomial matrix as an expression
135 files changed, 2970 insertions, 710 deletions
diff --git a/polymatrix/__init__.py b/polymatrix/__init__.py index e69de29..0f9bd81 100644 --- a/polymatrix/__init__.py +++ b/polymatrix/__init__.py @@ -0,0 +1,54 @@ +# import typing +# from polymatrix.init.initpolymatrixexpr import init_poly_matrix_expr +# from polymatrix.init.initpolymatrixparamexpr import init_poly_matrix_param_expr + + +from ast import Expression +from polymatrix.expression.init.initexpression import init_expression +from polymatrix.expression.init.initfromarrayexpr import init_from_array_expr +from polymatrix.expression.init.initkktexpr import init_kkt_expr +from polymatrix.expression.init.initvstackexpr import init_v_stack_expr + + +def from_( + data: tuple[tuple[float]], + # name: str, + # shape: tuple, + # degrees: tuple, + # re_index: typing.Callable[[int, int, int, tuple[int, ...]], tuple[int, int, int, tuple[int, ...], float]] = None, +): + return init_expression( + init_from_array_expr(data) + ) + + # return init_poly_matrix_expr( + # underlying=init_poly_matrix_param_expr( + # name=name, + # degrees=degrees, + # shape=shape, + # re_index=re_index, + # ) + # ) + +def v_stack( + expressions: tuple[Expression], +): + return init_expression( + init_v_stack_expr(expressions) + ) + + +def kkt( + cost: Expression, + equality: Expression, + variables: Expression +): + return init_expression( + init_kkt_expr( + cost=cost, + equality=equality, + variables=variables, + ) + ) + + diff --git a/polymatrix/addexpr.py b/polymatrix/addexpr.py new file mode 100644 index 0000000..983645e --- /dev/null +++ b/polymatrix/addexpr.py @@ -0,0 +1,4 @@ +from polymatrix.mixins.addexprmixin import AddExprMixin + +class AddExpr(AddExprMixin): + pass
\ No newline at end of file diff --git a/polymatrix/exprcontainer.py b/polymatrix/exprcontainer.py new file mode 100644 index 0000000..e5766f1 --- /dev/null +++ b/polymatrix/exprcontainer.py @@ -0,0 +1,10 @@ +import abc +import typing +from polymatrix.mixins.exprcontainermixin import ExprContainerMixin, ExprType + +class ExprContainer( + ExprContainerMixin[ExprType], + typing.Generic[ExprType], + abc.ABC, +): + pass diff --git a/polymatrix/expression/__init__.py b/polymatrix/expression/__init__.py new file mode 100644 index 0000000..e69de29 --- /dev/null +++ b/polymatrix/expression/__init__.py diff --git a/polymatrix/expression/derivativeexpr.py b/polymatrix/expression/derivativeexpr.py new file mode 100644 index 0000000..6805e4b --- /dev/null +++ b/polymatrix/expression/derivativeexpr.py @@ -0,0 +1,4 @@ +from polymatrix.expression.mixins.derivativeexprmixin import DerivativeExprMixin + +class DerivativeExpr(DerivativeExprMixin): + pass diff --git a/polymatrix/expression/derivativekey.py b/polymatrix/expression/derivativekey.py new file mode 100644 index 0000000..6d1fff8 --- /dev/null +++ b/polymatrix/expression/derivativekey.py @@ -0,0 +1,4 @@ +from polymatrix.expression.mixins.derivativekeymixin import DerivativeKeyMixin + +class DerivativeKey(DerivativeKeyMixin): + pass diff --git a/polymatrix/expression/determinantexpr.py b/polymatrix/expression/determinantexpr.py new file mode 100644 index 0000000..6e584f9 --- /dev/null +++ b/polymatrix/expression/determinantexpr.py @@ -0,0 +1,4 @@ +from polymatrix.expression.mixins.determinantexprmixin import DeterminantExprMixin + +class DeterminantExpr(DeterminantExprMixin): + pass diff --git a/polymatrix/expression/divisionexpr.py b/polymatrix/expression/divisionexpr.py new file mode 100644 index 0000000..63c95d9 --- /dev/null +++ b/polymatrix/expression/divisionexpr.py @@ -0,0 +1,4 @@ +from polymatrix.expression.mixins.divisionexprmixin import DivisionExprMixin + +class DivisionExpr(DivisionExprMixin): + pass diff --git a/polymatrix/expression/elemmultexpr.py b/polymatrix/expression/elemmultexpr.py new file mode 100644 index 0000000..1c8ef58 --- /dev/null +++ b/polymatrix/expression/elemmultexpr.py @@ -0,0 +1,4 @@ +from polymatrix.expression.mixins.elemmultexprmixin import ElemMultExprMixin + +class ElemMultExpr(ElemMultExprMixin): + pass diff --git a/polymatrix/expression/evalexpr.py b/polymatrix/expression/evalexpr.py new file mode 100644 index 0000000..0af72d1 --- /dev/null +++ b/polymatrix/expression/evalexpr.py @@ -0,0 +1,4 @@ +from polymatrix.expression.mixins.evalexprmixin import EvalExprMixin + +class EvalExpr(EvalExprMixin): + pass diff --git a/polymatrix/expression/expression.py b/polymatrix/expression/expression.py new file mode 100644 index 0000000..7f34637 --- /dev/null +++ b/polymatrix/expression/expression.py @@ -0,0 +1,4 @@ +from polymatrix.expression.mixins.expressionmixin import ExpressionMixin + +class Expression(ExpressionMixin): + pass diff --git a/polymatrix/expression/expressionstate.py b/polymatrix/expression/expressionstate.py new file mode 100644 index 0000000..e4b97aa --- /dev/null +++ b/polymatrix/expression/expressionstate.py @@ -0,0 +1,4 @@ +from polymatrix.expression.mixins.expressionstatemixin import ExpressionStateMixin + +class ExpressionState(ExpressionStateMixin): + pass diff --git a/polymatrix/expression/forallexpr.py b/polymatrix/expression/forallexpr.py new file mode 100644 index 0000000..972d553 --- /dev/null +++ b/polymatrix/expression/forallexpr.py @@ -0,0 +1,4 @@ +from polymatrix.expression.mixins.forallexprmixin import ForAllExprMixin + +class ForAllExpr(ForAllExprMixin): + pass diff --git a/polymatrix/expression/fromarrayexpr.py b/polymatrix/expression/fromarrayexpr.py new file mode 100644 index 0000000..b22792b --- /dev/null +++ b/polymatrix/expression/fromarrayexpr.py @@ -0,0 +1,4 @@ +from polymatrix.expression.mixins.fromarrayexprmixin import FromArrayExprMixin + +class FromArrayExpr(FromArrayExprMixin): + pass diff --git a/polymatrix/expression/getitemexpr.py b/polymatrix/expression/getitemexpr.py new file mode 100644 index 0000000..e7d32c2 --- /dev/null +++ b/polymatrix/expression/getitemexpr.py @@ -0,0 +1,4 @@ +from polymatrix.expression.mixins.getitemexprmixin import GetItemExprMixin + +class GetItemExpr(GetItemExprMixin): + pass diff --git a/polymatrix/expression/impl/derivativeexprimpl.py b/polymatrix/expression/impl/derivativeexprimpl.py new file mode 100644 index 0000000..87884ab --- /dev/null +++ b/polymatrix/expression/impl/derivativeexprimpl.py @@ -0,0 +1,10 @@ +import dataclass_abc +from polymatrix.expression.derivativeexpr import DerivativeExpr + +from polymatrix.expression.mixins.expressionbasemixin import ExpressionBaseMixin + +@dataclass_abc.dataclass_abc(frozen=True) +class DerivativeExprImpl(DerivativeExpr): + underlying: ExpressionBaseMixin + variables: tuple + introduce_derivatives: bool diff --git a/polymatrix/expression/impl/derivativekeyimpl.py b/polymatrix/expression/impl/derivativekeyimpl.py new file mode 100644 index 0000000..675503a --- /dev/null +++ b/polymatrix/expression/impl/derivativekeyimpl.py @@ -0,0 +1,8 @@ +import dataclass_abc +from polymatrix.expression.derivativekey import DerivativeKey + + +@dataclass_abc.dataclass_abc(frozen=True) +class DerivativeKeyImpl(DerivativeKey): + variable: int + with_respect_to: int diff --git a/polymatrix/expression/impl/determinantexprimpl.py b/polymatrix/expression/impl/determinantexprimpl.py new file mode 100644 index 0000000..3dc4ace --- /dev/null +++ b/polymatrix/expression/impl/determinantexprimpl.py @@ -0,0 +1,8 @@ +import dataclass_abc +from polymatrix.expression.determinantexpr import DeterminantExpr + +from polymatrix.expression.mixins.expressionbasemixin import ExpressionBaseMixin + +@dataclass_abc.dataclass_abc(frozen=True) +class DeterminantExprImpl(DeterminantExpr): + underlying: ExpressionBaseMixin diff --git a/polymatrix/expression/impl/divisionexprimpl.py b/polymatrix/expression/impl/divisionexprimpl.py new file mode 100644 index 0000000..c2c8966 --- /dev/null +++ b/polymatrix/expression/impl/divisionexprimpl.py @@ -0,0 +1,9 @@ +import dataclass_abc +from polymatrix.expression.divisionexpr import DivisionExpr + +from polymatrix.expression.mixins.expressionbasemixin import ExpressionBaseMixin + +@dataclass_abc.dataclass_abc(frozen=True) +class DivisionExprImpl(DivisionExpr): + left: ExpressionBaseMixin + right: ExpressionBaseMixin diff --git a/polymatrix/expression/impl/elemmultexprimpl.py b/polymatrix/expression/impl/elemmultexprimpl.py new file mode 100644 index 0000000..a9990e4 --- /dev/null +++ b/polymatrix/expression/impl/elemmultexprimpl.py @@ -0,0 +1,9 @@ +import dataclass_abc +from polymatrix.expression.elemmultexpr import ElemMultExpr + +from polymatrix.expression.mixins.expressionbasemixin import ExpressionBaseMixin + +@dataclass_abc.dataclass_abc(frozen=True) +class ElemMultExprImpl(ElemMultExpr): + left: ExpressionBaseMixin + right: ExpressionBaseMixin diff --git a/polymatrix/expression/impl/evalexprimpl.py b/polymatrix/expression/impl/evalexprimpl.py new file mode 100644 index 0000000..1730170 --- /dev/null +++ b/polymatrix/expression/impl/evalexprimpl.py @@ -0,0 +1,10 @@ +import dataclass_abc +from polymatrix.expression.evalexpr import EvalExpr + +from polymatrix.expression.mixins.expressionbasemixin import ExpressionBaseMixin + +@dataclass_abc.dataclass_abc(frozen=True) +class EvalExprImpl(EvalExpr): + underlying: ExpressionBaseMixin + variables: tuple + eval_values: tuple diff --git a/polymatrix/expression/impl/expressionimpl.py b/polymatrix/expression/impl/expressionimpl.py new file mode 100644 index 0000000..ab1da5d --- /dev/null +++ b/polymatrix/expression/impl/expressionimpl.py @@ -0,0 +1,8 @@ +import dataclass_abc +from polymatrix.expression.expression import Expression + +from polymatrix.expression.mixins.expressionbasemixin import ExpressionBaseMixin + +@dataclass_abc.dataclass_abc(frozen=True) +class ExpressionImpl(Expression): + underlying: ExpressionBaseMixin diff --git a/polymatrix/expression/impl/expressionstateimpl.py b/polymatrix/expression/impl/expressionstateimpl.py new file mode 100644 index 0000000..89afb56 --- /dev/null +++ b/polymatrix/expression/impl/expressionstateimpl.py @@ -0,0 +1,11 @@ +import dataclass_abc +from polymatrix.expression.expressionstate import ExpressionState + +from typing import Optional + +@dataclass_abc.dataclass_abc(frozen=True) +class ExpressionStateImpl(ExpressionState): + n_param: int + offset_dict: dict + auxillary_terms: tuple[dict[tuple[int], float]] + cached_polymatrix: dict diff --git a/polymatrix/expression/impl/forallexprimpl.py b/polymatrix/expression/impl/forallexprimpl.py new file mode 100644 index 0000000..0960479 --- /dev/null +++ b/polymatrix/expression/impl/forallexprimpl.py @@ -0,0 +1,9 @@ +import dataclass_abc +from polymatrix.expression.forallexpr import ForAllExpr + +from polymatrix.expression.mixins.expressionbasemixin import ExpressionBaseMixin + +@dataclass_abc.dataclass_abc(frozen=True) +class ForAllExprImpl(ForAllExpr): + underlying: ExpressionBaseMixin + variables: tuple diff --git a/polymatrix/expression/impl/fromarrayexprimpl.py b/polymatrix/expression/impl/fromarrayexprimpl.py new file mode 100644 index 0000000..7d7c45e --- /dev/null +++ b/polymatrix/expression/impl/fromarrayexprimpl.py @@ -0,0 +1,8 @@ +import dataclass_abc +from polymatrix.expression.fromarrayexpr import FromArrayExpr + +from numpy import array + +@dataclass_abc.dataclass_abc(frozen=True) +class FromArrayExprImpl(FromArrayExpr): + data: tuple[tuple[float]] diff --git a/polymatrix/expression/impl/getitemexprimpl.py b/polymatrix/expression/impl/getitemexprimpl.py new file mode 100644 index 0000000..b8972a9 --- /dev/null +++ b/polymatrix/expression/impl/getitemexprimpl.py @@ -0,0 +1,9 @@ +import dataclass_abc +from polymatrix.expression.getitemexpr import GetItemExpr + +from polymatrix.expression.mixins.expressionbasemixin import ExpressionBaseMixin + +@dataclass_abc.dataclass_abc(frozen=True) +class GetItemExprImpl(GetItemExpr): + underlying: ExpressionBaseMixin + index: tuple diff --git a/polymatrix/expression/impl/kktexprimpl.py b/polymatrix/expression/impl/kktexprimpl.py new file mode 100644 index 0000000..e7df9bf --- /dev/null +++ b/polymatrix/expression/impl/kktexprimpl.py @@ -0,0 +1,11 @@ +import dataclass_abc +from polymatrix.expression.kktexpr import KKTExpr + +from polymatrix.expression.mixins.expressionmixin import ExpressionMixin +from polymatrix.expression.mixins.expressionbasemixin import ExpressionBaseMixin + +@dataclass_abc.dataclass_abc(frozen=True) +class KKTExprImpl(KKTExpr): + cost: ExpressionMixin + equality: ExpressionMixin + variables: ExpressionBaseMixin diff --git a/polymatrix/expression/impl/parametrizesymbolsexprimpl.py b/polymatrix/expression/impl/parametrizesymbolsexprimpl.py new file mode 100644 index 0000000..af1fe3e --- /dev/null +++ b/polymatrix/expression/impl/parametrizesymbolsexprimpl.py @@ -0,0 +1,10 @@ +import dataclass_abc +from polymatrix.expression.parametrizesymbolsexpr import ParametrizeSymbolsExpr + +from polymatrix.expression.mixins.expressionbasemixin import ExpressionBaseMixin + +@dataclass_abc.dataclass_abc(frozen=True) +class ParametrizeSymbolsExprImpl(ParametrizeSymbolsExpr): + name: str + underlying: ExpressionBaseMixin + variables: tuple diff --git a/polymatrix/expression/impl/polymatriximpl.py b/polymatrix/expression/impl/polymatriximpl.py new file mode 100644 index 0000000..8dd6fca --- /dev/null +++ b/polymatrix/expression/impl/polymatriximpl.py @@ -0,0 +1,9 @@ +import dataclass_abc +from polymatrix.expression.polymatrix import PolyMatrix + + +@dataclass_abc.dataclass_abc(frozen=True) +class PolyMatrixImpl(PolyMatrix): + terms: dict + shape: tuple[int, ...] + # aux_terms: tuple[dict[tuple[int, ...], float]] diff --git a/polymatrix/expression/impl/quadraticinexprimpl.py b/polymatrix/expression/impl/quadraticinexprimpl.py new file mode 100644 index 0000000..8c7ac17 --- /dev/null +++ b/polymatrix/expression/impl/quadraticinexprimpl.py @@ -0,0 +1,9 @@ +import dataclass_abc +from polymatrix.expression.quadraticinexpr import QuadraticInExpr + +from polymatrix.expression.mixins.expressionbasemixin import ExpressionBaseMixin + +@dataclass_abc.dataclass_abc(frozen=True) +class QuadraticInExprImpl(QuadraticInExpr): + underlying: ExpressionBaseMixin + variables: tuple diff --git a/polymatrix/expression/impl/repmatexprimpl.py b/polymatrix/expression/impl/repmatexprimpl.py new file mode 100644 index 0000000..f8cee79 --- /dev/null +++ b/polymatrix/expression/impl/repmatexprimpl.py @@ -0,0 +1,9 @@ +import dataclass_abc +from polymatrix.expression.repmatexpr import RepMatExpr + +from polymatrix.expression.mixins.expressionbasemixin import ExpressionBaseMixin + +@dataclass_abc.dataclass_abc(frozen=True) +class RepMatExprImpl(RepMatExpr): + underlying: ExpressionBaseMixin + repetition: tuple diff --git a/polymatrix/expression/impl/transposeexprimpl.py b/polymatrix/expression/impl/transposeexprimpl.py new file mode 100644 index 0000000..59b1a53 --- /dev/null +++ b/polymatrix/expression/impl/transposeexprimpl.py @@ -0,0 +1,8 @@ +import dataclass_abc +from polymatrix.expression.transposeexpr import TransposeExpr + +from polymatrix.expression.mixins.expressionbasemixin import ExpressionBaseMixin + +@dataclass_abc.dataclass_abc(frozen=True) +class TransposeExprImpl(TransposeExpr): + underlying: ExpressionBaseMixin diff --git a/polymatrix/expression/impl/vstackexprimpl.py b/polymatrix/expression/impl/vstackexprimpl.py new file mode 100644 index 0000000..9ee582d --- /dev/null +++ b/polymatrix/expression/impl/vstackexprimpl.py @@ -0,0 +1,7 @@ +import dataclass_abc +from polymatrix.expression.vstackexpr import VStackExpr + + +@dataclass_abc.dataclass_abc(frozen=True) +class VStackExprImpl(VStackExpr): + underlying: tuple diff --git a/polymatrix/expression/init/initderivativeexpr.py b/polymatrix/expression/init/initderivativeexpr.py new file mode 100644 index 0000000..c640f47 --- /dev/null +++ b/polymatrix/expression/init/initderivativeexpr.py @@ -0,0 +1,17 @@ +from polymatrix.expression.mixins.expressionbasemixin import ExpressionBaseMixin +from polymatrix.expression.impl.derivativeexprimpl import DerivativeExprImpl + + +def init_derivative_expr( + underlying: ExpressionBaseMixin, + variables: tuple, + introduce_derivatives: bool = None, +): + if introduce_derivatives is None: + introduce_derivatives = False + + return DerivativeExprImpl( + underlying=underlying, + variables=variables, + introduce_derivatives=introduce_derivatives, +) diff --git a/polymatrix/expression/init/initderivativekey.py b/polymatrix/expression/init/initderivativekey.py new file mode 100644 index 0000000..db249ec --- /dev/null +++ b/polymatrix/expression/init/initderivativekey.py @@ -0,0 +1,11 @@ +from polymatrix.expression.impl.derivativekeyimpl import DerivativeKeyImpl + + +def init_derivative_key( + variable: int, + with_respect_to: int +): + return DerivativeKeyImpl( + variable=variable, + with_respect_to=with_respect_to, +) diff --git a/polymatrix/expression/init/initdeterminantexpr.py b/polymatrix/expression/init/initdeterminantexpr.py new file mode 100644 index 0000000..f0d1bb5 --- /dev/null +++ b/polymatrix/expression/init/initdeterminantexpr.py @@ -0,0 +1,10 @@ +from polymatrix.expression.mixins.expressionbasemixin import ExpressionBaseMixin +from polymatrix.expression.impl.determinantexprimpl import DeterminantExprImpl + + +def init_determinant_expr( + underlying: ExpressionBaseMixin, +): + return DeterminantExprImpl( + underlying=underlying, +) diff --git a/polymatrix/expression/init/initdivisionexpr.py b/polymatrix/expression/init/initdivisionexpr.py new file mode 100644 index 0000000..2a701a9 --- /dev/null +++ b/polymatrix/expression/init/initdivisionexpr.py @@ -0,0 +1,12 @@ +from polymatrix.expression.mixins.expressionbasemixin import ExpressionBaseMixin +from polymatrix.expression.impl.divisionexprimpl import DivisionExprImpl + + +def init_division_expr( + left: ExpressionBaseMixin, + right: ExpressionBaseMixin, +): + return DivisionExprImpl( + left=left, + right=right, +) diff --git a/polymatrix/expression/init/initelemmultexpr.py b/polymatrix/expression/init/initelemmultexpr.py new file mode 100644 index 0000000..ae0e85f --- /dev/null +++ b/polymatrix/expression/init/initelemmultexpr.py @@ -0,0 +1,12 @@ +from polymatrix.expression.mixins.expressionbasemixin import ExpressionBaseMixin +from polymatrix.expression.impl.elemmultexprimpl import ElemMultExprImpl + + +def init_elem_mult_expr( + left: ExpressionBaseMixin, + right: ExpressionBaseMixin, +): + return ElemMultExprImpl( + left=left, + right=right, +) diff --git a/polymatrix/expression/init/initevalexpr.py b/polymatrix/expression/init/initevalexpr.py new file mode 100644 index 0000000..deeb4e9 --- /dev/null +++ b/polymatrix/expression/init/initevalexpr.py @@ -0,0 +1,21 @@ +from tkinter import Variable +from polymatrix.expression.mixins.expressionbasemixin import ExpressionBaseMixin +from polymatrix.expression.impl.evalexprimpl import EvalExprImpl + + +def init_eval_expr( + underlying: ExpressionBaseMixin, + variables: tuple, + eval_values: tuple, +): + if not isinstance(variables, tuple): + variables = (variables,) + + if not isinstance(eval_values, tuple): + eval_values = (eval_values,) + + return EvalExprImpl( + underlying=underlying, + variables=variables, + eval_values=eval_values, +) diff --git a/polymatrix/expression/init/initexpression.py b/polymatrix/expression/init/initexpression.py new file mode 100644 index 0000000..7262e47 --- /dev/null +++ b/polymatrix/expression/init/initexpression.py @@ -0,0 +1,10 @@ +from polymatrix.expression.mixins.expressionbasemixin import ExpressionBaseMixin +from polymatrix.expression.impl.expressionimpl import ExpressionImpl + + +def init_expression( + underlying: ExpressionBaseMixin, +): + return ExpressionImpl( + underlying=underlying, +) diff --git a/polymatrix/expression/init/initexpressionstate.py b/polymatrix/expression/init/initexpressionstate.py new file mode 100644 index 0000000..a7d3aac --- /dev/null +++ b/polymatrix/expression/init/initexpressionstate.py @@ -0,0 +1,19 @@ +from polymatrix.expression.impl.expressionstateimpl import ExpressionStateImpl + + +def init_expression_state( + n_param: int = None, + offset_dict: dict = None, +): + if n_param is None: + n_param = 0 + + if offset_dict is None: + offset_dict = {} + + return ExpressionStateImpl( + n_param=n_param, + offset_dict=offset_dict, + auxillary_terms=tuple(), + cached_polymatrix={}, +) diff --git a/polymatrix/expression/init/initforallexpr.py b/polymatrix/expression/init/initforallexpr.py new file mode 100644 index 0000000..84388d2 --- /dev/null +++ b/polymatrix/expression/init/initforallexpr.py @@ -0,0 +1,12 @@ +from polymatrix.expression.mixins.expressionbasemixin import ExpressionBaseMixin +from polymatrix.expression.impl.forallexprimpl import ForAllExprImpl + + +def init_for_all_expr( + underlying: ExpressionBaseMixin, + variables: tuple, +): + return ForAllExprImpl( + underlying=underlying, + variables=variables, +) diff --git a/polymatrix/expression/init/initfromarrayexpr.py b/polymatrix/expression/init/initfromarrayexpr.py new file mode 100644 index 0000000..6aab26c --- /dev/null +++ b/polymatrix/expression/init/initfromarrayexpr.py @@ -0,0 +1,31 @@ +import typing +import numpy as np + +from polymatrix.expression.impl.fromarrayexprimpl import FromArrayExprImpl + + +def init_from_array_expr( + data: typing.Union[np.ndarray, tuple[tuple[float]]], +): + + match data: + case np.ndarray(): + data = tuple(tuple(i for i in row) for row in data) + + case tuple(): + + match data[0]: + + case tuple(): + n_col = len(data[0]) + assert all(len(col) == n_col for col in data) + + case _: + data = (data,) + + case _: + data = ((data,),) + + return FromArrayExprImpl( + data=data, + ) diff --git a/polymatrix/expression/init/initgetitemexpr.py b/polymatrix/expression/init/initgetitemexpr.py new file mode 100644 index 0000000..140fa3a --- /dev/null +++ b/polymatrix/expression/init/initgetitemexpr.py @@ -0,0 +1,12 @@ +from polymatrix.expression.mixins.expressionbasemixin import ExpressionBaseMixin +from polymatrix.expression.impl.getitemexprimpl import GetItemExprImpl + + +def init_get_item_expr( + underlying: ExpressionBaseMixin, + index: tuple, +): + return GetItemExprImpl( + underlying=underlying, + index=index, +) diff --git a/polymatrix/expression/init/initkktexpr.py b/polymatrix/expression/init/initkktexpr.py new file mode 100644 index 0000000..d8bfba8 --- /dev/null +++ b/polymatrix/expression/init/initkktexpr.py @@ -0,0 +1,15 @@ +from polymatrix.expression.mixins.expressionmixin import ExpressionMixin +from polymatrix.expression.mixins.expressionbasemixin import ExpressionBaseMixin +from polymatrix.expression.impl.kktexprimpl import KKTExprImpl + + +def init_kkt_expr( + cost: ExpressionMixin, + equality: ExpressionMixin, + variables: ExpressionBaseMixin, +): + return KKTExprImpl( + cost=cost, + equality=equality, + variables=variables, +) diff --git a/polymatrix/expression/init/initparametrizesymbolsexpr.py b/polymatrix/expression/init/initparametrizesymbolsexpr.py new file mode 100644 index 0000000..8d7db55 --- /dev/null +++ b/polymatrix/expression/init/initparametrizesymbolsexpr.py @@ -0,0 +1,14 @@ +from polymatrix.expression.mixins.expressionbasemixin import ExpressionBaseMixin +from polymatrix.expression.impl.parametrizesymbolsexprimpl import ParametrizeSymbolsExprImpl + + +def init_parametrize_symbols_expr( + name: str, + underlying: ExpressionBaseMixin, + variables: tuple, +): + return ParametrizeSymbolsExprImpl( + name=name, + underlying=underlying, + variables=variables, +) diff --git a/polymatrix/expression/init/initpolymatrix.py b/polymatrix/expression/init/initpolymatrix.py new file mode 100644 index 0000000..e6a6cde --- /dev/null +++ b/polymatrix/expression/init/initpolymatrix.py @@ -0,0 +1,16 @@ +from polymatrix.expression.impl.polymatriximpl import PolyMatrixImpl + + +def init_poly_matrix( + terms: dict, + shape: tuple, + aux_terms: tuple[dict[tuple[int, ...], float]] = None, +): + if aux_terms is None: + aux_terms = tuple() + + return PolyMatrixImpl( + terms=terms, + shape=shape, + # aux_terms=aux_terms, +) diff --git a/polymatrix/expression/init/initquadraticinexpr.py b/polymatrix/expression/init/initquadraticinexpr.py new file mode 100644 index 0000000..1e73745 --- /dev/null +++ b/polymatrix/expression/init/initquadraticinexpr.py @@ -0,0 +1,12 @@ +from polymatrix.expression.mixins.expressionbasemixin import ExpressionBaseMixin +from polymatrix.expression.impl.quadraticinexprimpl import QuadraticInExprImpl + + +def init_quadratic_in_expr( + underlying: ExpressionBaseMixin, + variables: tuple, +): + return QuadraticInExprImpl( + underlying=underlying, + variables=variables, +) diff --git a/polymatrix/expression/init/initrepmatexpr.py b/polymatrix/expression/init/initrepmatexpr.py new file mode 100644 index 0000000..2f7fb7c --- /dev/null +++ b/polymatrix/expression/init/initrepmatexpr.py @@ -0,0 +1,12 @@ +from polymatrix.expression.mixins.expressionbasemixin import ExpressionBaseMixin +from polymatrix.expression.impl.repmatexprimpl import RepMatExprImpl + + +def init_rep_mat_expr( + underlying: ExpressionBaseMixin, + repetition: tuple, +): + return RepMatExprImpl( + underlying=underlying, + repetition=repetition, +) diff --git a/polymatrix/expression/init/inittransposeexpr.py b/polymatrix/expression/init/inittransposeexpr.py new file mode 100644 index 0000000..9ca9d91 --- /dev/null +++ b/polymatrix/expression/init/inittransposeexpr.py @@ -0,0 +1,10 @@ +from polymatrix.expression.mixins.expressionbasemixin import ExpressionBaseMixin +from polymatrix.expression.impl.transposeexprimpl import TransposeExprImpl + + +def init_transpose_expr( + underlying: ExpressionBaseMixin, +): + return TransposeExprImpl( + underlying=underlying, +) diff --git a/polymatrix/expression/init/initvstackexpr.py b/polymatrix/expression/init/initvstackexpr.py new file mode 100644 index 0000000..1d7834e --- /dev/null +++ b/polymatrix/expression/init/initvstackexpr.py @@ -0,0 +1,9 @@ +from polymatrix.expression.impl.vstackexprimpl import VStackExprImpl + + +def init_v_stack_expr( + underlying: tuple, +): + return VStackExprImpl( + underlying=underlying, +) diff --git a/polymatrix/expression/kktexpr.py b/polymatrix/expression/kktexpr.py new file mode 100644 index 0000000..aa5be52 --- /dev/null +++ b/polymatrix/expression/kktexpr.py @@ -0,0 +1,4 @@ +from polymatrix.expression.mixins.kktexprmixin import KKTExprMixin + +class KKTExpr(KKTExprMixin): + pass diff --git a/polymatrix/expression/mixins/additionexprmixin.py b/polymatrix/expression/mixins/additionexprmixin.py new file mode 100644 index 0000000..776e952 --- /dev/null +++ b/polymatrix/expression/mixins/additionexprmixin.py @@ -0,0 +1,70 @@ + +import abc +import typing +import dataclass_abc + +from polymatrix.expression.init.initpolymatrix import init_poly_matrix +from polymatrix.expression.mixins.expressionbasemixin import ExpressionBaseMixin +from polymatrix.expression.polymatrix import PolyMatrix +from polymatrix.polymatrixexprstate import PolyMatrixExprState + + +class AddExprMixin(ExpressionBaseMixin): + @property + @abc.abstractmethod + def left(self) -> ExpressionBaseMixin: + ... + + @property + @abc.abstractmethod + def right(self) -> ExpressionBaseMixin: + ... + + # overwrites abstract method of `ExpressionBaseMixin` + @property + def shape(self) -> tuple[int, int]: + return self.left.shape + + # overwrites abstract method of `ExpressionBaseMixin` + def apply( + self, + state: PolyMatrixExprState, + ) -> tuple[PolyMatrixExprState, PolyMatrix]: + state, left = self.left.apply(state=state) + state, right = self.right.apply(state=state) + + assert left.shape == right.shape + + terms = {} + + for underlying in (left, right): + + for row in range(self.shape[0]): + for col in range(self.shape[1]): + + if (row, col) in terms: + terms_row_col = terms[row, col] + + else: + terms_row_col = {} + + try: + underlying_terms = underlying.get_poly(row, col) + except KeyError: + continue + + for monomial, value in underlying_terms.items(): + + if monomial not in terms_row_col: + terms_row_col[monomial] = 0 + + terms_row_col[monomial] += value + + terms[row, col] = terms_row_col + + poly_matrix = init_poly_matrix( + terms=terms, + shape=self.shape, + ) + + return state, poly_matrix diff --git a/polymatrix/expression/mixins/derivativeexprmixin.py b/polymatrix/expression/mixins/derivativeexprmixin.py new file mode 100644 index 0000000..516aa38 --- /dev/null +++ b/polymatrix/expression/mixins/derivativeexprmixin.py @@ -0,0 +1,155 @@ + +import abc +import collections +import typing +import dataclass_abc +from numpy import var +from polymatrix.expression.init.initderivativekey import init_derivative_key + +from polymatrix.expression.init.initpolymatrix import init_poly_matrix +from polymatrix.expression.mixins.expressionbasemixin import ExpressionBaseMixin +from polymatrix.expression.polymatrix import PolyMatrix +from polymatrix.polymatrixexprstate import PolyMatrixExprState + + +class DerivativeExprMixin(ExpressionBaseMixin): + @property + @abc.abstractmethod + def underlying(self) -> ExpressionBaseMixin: + ... + + @property + @abc.abstractmethod + def variables(self) -> typing.Union[tuple, ExpressionBaseMixin]: + ... + + @property + @abc.abstractmethod + def introduce_derivatives(self) -> bool: + ... + + # overwrites abstract method of `ExpressionBaseMixin` + @property + def shape(self) -> tuple[int, int]: + match self.variables: + case ExpressionBaseMixin(): + n_cols = self.variables.shape[0] + + case _: + n_cols = len(self.variables) + + return self.underlying.shape[0], n_cols + + # overwrites abstract method of `ExpressionBaseMixin` + def apply( + self, + state: PolyMatrixExprState, + ) -> tuple[PolyMatrixExprState, PolyMatrix]: + state = [state] + + state[0], underlying = self.underlying.apply(state=state[0]) + + match self.variables: + case ExpressionBaseMixin(): + assert self.variables.shape[1] == 1 + + state[0], variables = self.variables.apply(state[0]) + + def gen_indices(): + for row in range(variables.shape[0]): + for monomial in variables.get_poly(row, 0).keys(): + yield monomial[0] + + variable_indices = tuple(sorted(gen_indices())) + # print(f'{variable_indices=}') + + case _: + def gen_indices(): + for variable in self.variable: + if variable in state[0].offset_dict: + yield state[0].offset_dict[variable][0] + + variable_indices = tuple(sorted(gen_indices())) + + terms = {} + # aux_terms = [] + + for var_idx, variable in enumerate(variable_indices): + + def get_derivative_terms(monomial_terms): + + terms_row_col = {} + + for monomial, value in monomial_terms.items(): + + # count powers for each variable + monomial_cnt = dict(collections.Counter(monomial)) + + if variable not in monomial_cnt: + continue + + if self.introduce_derivatives: + variable_candidates = (variable,) + tuple(var for var in monomial_cnt.keys() if var not in variable_indices) + else: + variable_candidates = (variable,) + + for variable_candidate in variable_candidates: + + def generate_monomial(): + for current_variable, current_count in monomial_cnt.items(): + + if current_variable is variable_candidate: + sel_counter = current_count - 1 + + else: + sel_counter = current_count + + for _ in range(sel_counter): + yield current_variable + + if variable_candidate is not variable: + key = init_derivative_key( + variable=variable_candidate, + with_respect_to=var_idx, + ) + state[0] = state[0].register(key=key, n_param=1) + + yield state[0].offset_dict[key][0] + + col_monomial = tuple(generate_monomial()) + + if col_monomial not in terms_row_col: + terms_row_col[col_monomial] = 0 + + terms_row_col[col_monomial] += value * monomial_cnt[variable_candidate] + + return terms_row_col + + for row in range(self.shape[0]): + + try: + underlying_terms = underlying.get_poly(row, 0) + except KeyError: + continue + + derivative_terms = get_derivative_terms(underlying_terms) + + if 0 < len(derivative_terms): + terms[row, var_idx] = derivative_terms + + # if self.introduce_derivatives: + # for aux_monomial in underlying.aux_terms: + + # derivative_terms = get_derivative_terms(aux_monomial) + + # # todo: is this correct? + # if 1 < len(derivative_terms): + # aux_terms.append(derivative_terms) + + poly_matrix = init_poly_matrix( + terms=terms, + shape=self.shape, + # aux_terms=underlying.aux_terms + tuple(aux_terms), + ) + + return state[0], poly_matrix diff --git a/polymatrix/expression/mixins/derivativekeymixin.py b/polymatrix/expression/mixins/derivativekeymixin.py new file mode 100644 index 0000000..e0adddc --- /dev/null +++ b/polymatrix/expression/mixins/derivativekeymixin.py @@ -0,0 +1,12 @@ +import abc + +class DerivativeKeyMixin(abc.ABC): + @property + @abc.abstractmethod + def variable(self) -> int: + ... + + @property + @abc.abstractmethod + def with_respect_to(self) -> int: + ... diff --git a/polymatrix/expression/mixins/determinantexprmixin.py b/polymatrix/expression/mixins/determinantexprmixin.py new file mode 100644 index 0000000..8fe2536 --- /dev/null +++ b/polymatrix/expression/mixins/determinantexprmixin.py @@ -0,0 +1,115 @@ + +import abc +import collections +import dataclasses +from numpy import var + +from polymatrix.expression.init.initpolymatrix import init_poly_matrix +from polymatrix.expression.mixins.expressionbasemixin import ExpressionBaseMixin +from polymatrix.expression.polymatrix import PolyMatrix +from polymatrix.polymatrixexprstate import PolyMatrixExprState + + +class DeterminantExprMixin(ExpressionBaseMixin): + @property + @abc.abstractmethod + def underlying(self) -> ExpressionBaseMixin: + ... + + # overwrites abstract method of `ExpressionBaseMixin` + @property + def shape(self) -> tuple[int, int]: + return self.underlying.shape[0], 1 + + # overwrites abstract method of `ExpressionBaseMixin` + def apply( + self, + state: PolyMatrixExprState, + ) -> tuple[PolyMatrixExprState, PolyMatrix]: + if self in state.cached_polymatrix: + return state, state.cached_polymatrix[self] + + state, underlying = self.underlying.apply(state=state) + + assert underlying.shape[0] == underlying.shape[1] + + inequality_terms = {} + auxillary_terms = [] + + index_start = state.n_param + rel_index = 0 + + for row in range(self.shape[0]): + + current_inequality_terms = collections.defaultdict(float) + + # f in f-v^T@x-r^2 + # terms = underlying.get_poly(row, row) + try: + underlying_terms = underlying.get_poly(row, row) + except KeyError: + pass + else: + for monomial, value in underlying_terms.items(): + current_inequality_terms[monomial] += value + + for inner_row in range(row): + + # -v^T@x in f-v^T@x-r^2 + # terms = underlying.get_poly(row, inner_row) + try: + underlying_terms = underlying.get_poly(row, inner_row) + except KeyError: + pass + else: + for monomial, value in underlying_terms.items(): + new_monomial = monomial + (index_start + rel_index + inner_row,) + current_inequality_terms[new_monomial] -= value + + auxillary_term = collections.defaultdict(float) + + for inner_col in range(row): + + # P@x in P@x-v + key = tuple(reversed(sorted((inner_row, inner_col)))) + # terms = underlying.get_poly(*key) + try: + underlying_terms = underlying.get_poly(*key) + except KeyError: + pass + else: + for monomial, value in underlying_terms.items(): + new_monomial = monomial + (index_start + rel_index + inner_col,) + auxillary_term[new_monomial] += value + + # -v in P@x-v + # terms = underlying.get_poly(row, inner_row) + try: + underlying_terms = underlying.get_poly(row, inner_row) + except KeyError: + pass + else: + for monomial, value in underlying_terms.items(): + auxillary_term[monomial] -= value + + auxillary_terms.append(dict(auxillary_term)) + + rel_index += row + inequality_terms[row, 0] = dict(current_inequality_terms) + + state = state.register(rel_index) + + # print(f'{auxillary_terms=}') + + poly_matrix = init_poly_matrix( + terms=inequality_terms, + shape=self.shape, + ) + + state = dataclasses.replace( + state, + auxillary_terms=state.auxillary_terms + tuple(auxillary_terms), + cached_polymatrix=state.cached_polymatrix | {self: poly_matrix}, + ) + + return state, poly_matrix diff --git a/polymatrix/expression/mixins/divisionexprmixin.py b/polymatrix/expression/mixins/divisionexprmixin.py new file mode 100644 index 0000000..01d3505 --- /dev/null +++ b/polymatrix/expression/mixins/divisionexprmixin.py @@ -0,0 +1,81 @@ + +import abc +import dataclasses + +from polymatrix.expression.init.initpolymatrix import init_poly_matrix +from polymatrix.expression.mixins.expressionbasemixin import ExpressionBaseMixin +from polymatrix.expression.polymatrix import PolyMatrix +from polymatrix.polymatrixexprstate import PolyMatrixExprState + + +class DivisionExprMixin(ExpressionBaseMixin): + @property + @abc.abstractmethod + def left(self) -> ExpressionBaseMixin: + ... + + @property + @abc.abstractmethod + def right(self) -> ExpressionBaseMixin: + ... + + # overwrites abstract method of `ExpressionBaseMixin` + @property + def shape(self) -> tuple[int, int]: + return self.left.shape + + # overwrites abstract method of `ExpressionBaseMixin` + def apply( + self, + state: PolyMatrixExprState, + ) -> tuple[PolyMatrixExprState, PolyMatrix]: + if self in state.cached_polymatrix: + return state, state.cached_polymatrix[self] + + state, left = self.left.apply(state=state) + state, right = self.right.apply(state=state) + + assert right.shape == (1, 1) + + terms = {} + + division_variable = state.n_param + state = state.register(n_param=1) + + for row in range(self.shape[0]): + for col in range(self.shape[1]): + + try: + underlying_terms = left.get_poly(row, col) + except KeyError: + continue + + def gen_monomial_terms(): + for monomial, value in underlying_terms.items(): + yield monomial + (division_variable,), value + + terms[row, col] = dict(gen_monomial_terms()) + + def gen_auxillary_terms(): + for monomial, value in right.get_poly(0, 0).items(): + yield monomial + (division_variable,), value + + auxillary_terms = dict(gen_auxillary_terms()) + + if tuple() not in auxillary_terms: + auxillary_terms[tuple()] = 0 + + auxillary_terms[tuple()] -= 1 + + poly_matrix = init_poly_matrix( + terms=terms, + shape=self.shape, + ) + + state = dataclasses.replace( + state, + auxillary_terms=state.auxillary_terms + (auxillary_terms,), + cached_polymatrix=state.cached_polymatrix | {self: poly_matrix}, + ) + + return state, poly_matrix diff --git a/polymatrix/expression/mixins/elemmultexprmixin.py b/polymatrix/expression/mixins/elemmultexprmixin.py new file mode 100644 index 0000000..9684827 --- /dev/null +++ b/polymatrix/expression/mixins/elemmultexprmixin.py @@ -0,0 +1,74 @@ + +import abc +import itertools + +from polymatrix.expression.init.initpolymatrix import init_poly_matrix +from polymatrix.expression.mixins.expressionbasemixin import ExpressionBaseMixin +from polymatrix.expression.polymatrix import PolyMatrix +from polymatrix.polymatrixexprstate import PolyMatrixExprState + + +class ElemMultExprMixin(ExpressionBaseMixin): + @property + @abc.abstractmethod + def left(self) -> ExpressionBaseMixin: + ... + + @property + @abc.abstractmethod + def right(self) -> ExpressionBaseMixin: + ... + + # overwrites abstract method of `ExpressionBaseMixin` + @property + def shape(self) -> tuple[int, int]: + return self.left.shape + + # overwrites abstract method of `ExpressionBaseMixin` + def apply( + self, + state: PolyMatrixExprState, + ) -> tuple[PolyMatrixExprState, PolyMatrix]: + state, left = self.left.apply(state=state) + state, right = self.right.apply(state=state) + + assert right.shape == (1, 1) + + right_terms = right.get_poly(0, 0) + + terms = {} + + for poly_row in range(left.shape[0]): + for poly_col in range(left.shape[1]): + + terms_row_col = {} + + try: + left_terms = left.get_poly(poly_row, poly_col) + except KeyError: + continue + + for (left_monomial, left_value), (right_monomial, right_value) \ + in itertools.product(left_terms.items(), right_terms.items()): + + value = left_value * right_value + + if value == 0: + continue + + monomial = tuple(sorted(left_monomial + right_monomial)) + + if monomial not in terms_row_col: + terms_row_col[monomial] = 0 + + terms_row_col[monomial] += value + + if 0 < len(terms_row_col): + terms[poly_row, poly_col] = terms_row_col + + poly_matrix = init_poly_matrix( + terms=terms, + shape=self.shape, + ) + + return state, poly_matrix diff --git a/polymatrix/expression/mixins/evalexprmixin.py b/polymatrix/expression/mixins/evalexprmixin.py new file mode 100644 index 0000000..b945064 --- /dev/null +++ b/polymatrix/expression/mixins/evalexprmixin.py @@ -0,0 +1,93 @@ + +import abc +import itertools + +from polymatrix.expression.init.initpolymatrix import init_poly_matrix +from polymatrix.expression.mixins.expressionbasemixin import ExpressionBaseMixin +from polymatrix.expression.polymatrix import PolyMatrix +from polymatrix.polymatrixexprstate import PolyMatrixExprState + + +class EvalExprMixin(ExpressionBaseMixin): + @property + @abc.abstractmethod + def underlying(self) -> ExpressionBaseMixin: + ... + + @property + @abc.abstractmethod + def variables(self) -> tuple: + ... + + @property + @abc.abstractmethod + def eval_values(self) -> tuple[float, ...]: + ... + + # overwrites abstract method of `ExpressionBaseMixin` + @property + def shape(self) -> tuple[int, int]: + return self.underlying.shape + + # overwrites abstract method of `ExpressionBaseMixin` + def apply( + self, + state: PolyMatrixExprState, + ) -> tuple[PolyMatrixExprState, PolyMatrix]: + assert len(self.variables) == len(self.eval_values) + + state, underlying = self.underlying.apply(state=state) + + def gen_indices(): + for variable in self.variables: + if variable in state.offset_dict: + yield state.offset_dict[variable][0] + + variable_indices = tuple(sorted(gen_indices())) + + terms = {} + + for row in range(self.shape[0]): + for col in range(self.shape[1]): + + try: + underlying_terms = underlying.get_poly(row, col) + except KeyError: + continue + + terms_row_col = {} + + for monomial, value in underlying_terms.items(): + + def acc_monomial(acc, variable): + monomial, value = acc + + if variable in variable_indices: + index = variable_indices.index(variable) + new_value = value * self.eval_values[index] + return monomial, new_value + + else: + return monomial + (variable,), value + + *_, (new_monomial, new_value) = tuple(itertools.accumulate( + monomial, + acc_monomial, + initial=(tuple(), value), + )) + + # print(f'{new_monomial=}') + + if new_monomial not in terms_row_col: + terms_row_col[new_monomial] = 0 + + terms_row_col[new_monomial] += new_value + + terms[row, col] = terms_row_col + + poly_matrix = init_poly_matrix( + terms=terms, + shape=self.shape, + ) + + return state, poly_matrix diff --git a/polymatrix/expression/mixins/expressionbasemixin.py b/polymatrix/expression/mixins/expressionbasemixin.py new file mode 100644 index 0000000..d5109c0 --- /dev/null +++ b/polymatrix/expression/mixins/expressionbasemixin.py @@ -0,0 +1,17 @@ +import abc +from polymatrix.expression.mixins.expressionstatemixin import ExpressionStateMixin +from polymatrix.expression.mixins.polymatrixmixin import PolyMatrixMixin + + +class ExpressionBaseMixin( + abc.ABC, +): + + @property + @abc.abstractclassmethod + def shape(self) -> tuple[int, int]: + ... + + @abc.abstractmethod + def apply(self, state: ExpressionStateMixin) -> tuple[ExpressionStateMixin, PolyMatrixMixin]: + ... diff --git a/polymatrix/expression/mixins/expressionmixin.py b/polymatrix/expression/mixins/expressionmixin.py new file mode 100644 index 0000000..e50f660 --- /dev/null +++ b/polymatrix/expression/mixins/expressionmixin.py @@ -0,0 +1,213 @@ +import abc +import dataclasses +import typing +import numpy as np +from sympy import re +from polymatrix.expression.init.initderivativeexpr import init_derivative_expr +from polymatrix.expression.init.initdeterminantexpr import init_determinant_expr +from polymatrix.expression.init.initdivisionexpr import init_division_expr +from polymatrix.expression.init.initelemmultexpr import init_elem_mult_expr +from polymatrix.expression.init.initevalexpr import init_eval_expr +from polymatrix.expression.init.initforallexpr import init_for_all_expr +from polymatrix.expression.init.initfromarrayexpr import init_from_array_expr +from polymatrix.expression.init.initgetitemexpr import init_get_item_expr +from polymatrix.expression.init.initparametrizesymbolsexpr import init_parametrize_symbols_expr +from polymatrix.expression.init.initquadraticinexpr import init_quadratic_in_expr +from polymatrix.expression.init.initrepmatexpr import init_rep_mat_expr +from polymatrix.expression.init.inittransposeexpr import init_transpose_expr + +from polymatrix.init.initpolymatrixaddexpr import init_poly_matrix_add_expr +from polymatrix.init.initpolymatrixmultexpr import init_poly_matrix_mult_expr + +from polymatrix.expression.mixins.expressionbasemixin import ExpressionBaseMixin +from polymatrix.expression.polymatrix import PolyMatrix +from polymatrix.polymatrixexprstate import PolyMatrixExprState + + +class ExpressionMixin( + ExpressionBaseMixin, + abc.ABC, +): + + @property + @abc.abstractmethod + def underlying(self) -> ExpressionBaseMixin: + ... + + # overwrites abstract method of `PolyMatrixExprBaseMixin` + def apply(self, state: PolyMatrixExprState) -> tuple[PolyMatrixExprState, PolyMatrix]: + return self.underlying.apply(state) + + # overwrites abstract method of `PolyMatrixExprBaseMixin` + @property + def degrees(self) -> set[int]: + return self.underlying.degrees + + # overwrites abstract method of `PolyMatrixExprBaseMixin` + @property + def shape(self) -> tuple[int, int]: + return self.underlying.shape + + def __iter__(self): + for row in range(self.shape[0]): + yield self[row, 0] + + def __add__(self, other: ExpressionBaseMixin) -> 'ExpressionMixin': + # assert self.underlying.shape == other.shape, f'shapes {(self.shape, other.shape)} of polynomial matrix do not match!' + + if other is None: + return self + + return dataclasses.replace( + self, + underlying=init_poly_matrix_add_expr( + left=self.underlying, + right=other.underlying, + ), + ) + + def __radd__(self, other): + return self + other + + def __getattr__(self, name): + attr = getattr(self.underlying, name) + + if isinstance(attr, ExpressionBaseMixin): + return dataclasses.replace( + self, + underlying=attr, + ) + + else: + return attr + + def __mul__(self, other) -> 'ExpressionMixin': + # assert isinstance(other, float) + + right = init_from_array_expr(other) + + return dataclasses.replace( + self, + underlying=init_elem_mult_expr( + left=self.underlying, + right=right, + ), + ) + + def __rmul__(self, other): + return self * other + + def __matmul__(self, other: typing.Union[ExpressionBaseMixin, np.ndarray]) -> 'ExpressionMixin': + match other: + case ExpressionBaseMixin(): + right = other.underlying + case _: + right = init_from_array_expr(other) + + return dataclasses.replace( + self, + underlying=init_poly_matrix_mult_expr( + left=self.underlying, + right=right, + ), + ) + + def __truediv__(self, other: ExpressionBaseMixin): + return dataclasses.replace( + self, + underlying=init_division_expr( + left=self.underlying, + right=other, + ), + ) + + def __getitem__(self, key: tuple[int, int]): + return dataclasses.replace( + self, + underlying=init_get_item_expr( + underlying=self.underlying, + index=key, + ), + ) + + @property + def T(self) -> 'ExpressionMixin': + return dataclasses.replace( + self, + underlying=init_transpose_expr( + underlying=self.underlying, + ), + ) + + def parametrize(self, name: str, variables: tuple) -> 'ExpressionMixin': + return dataclasses.replace( + self, + underlying=init_parametrize_symbols_expr( + name=name, + underlying=self.underlying, + variables=variables, + ), + ) + + def rep_mat(self, n: int, m: int) -> 'ExpressionMixin': + return dataclasses.replace( + self, + underlying=init_rep_mat_expr( + underlying=self.underlying, + repetition=(n, m), + ), + ) + + def diff( + self, + variables: tuple, + introduce_derivatives: bool = None, + ) -> 'ExpressionMixin': + return dataclasses.replace( + self, + underlying=init_derivative_expr( + underlying=self.underlying, + variables=variables, + introduce_derivatives=introduce_derivatives, + ), + ) + + def for_all(self, variables: tuple) -> 'ExpressionMixin': + return dataclasses.replace( + self, + underlying=init_for_all_expr( + underlying=self.underlying, + variables=variables, + ), + ) + + def quadratic_in(self, variables: tuple) -> 'ExpressionMixin': + return dataclasses.replace( + self, + underlying=init_quadratic_in_expr( + underlying=self.underlying, + variables=variables, + ), + ) + + def determinant(self) -> 'ExpressionMixin': + return dataclasses.replace( + self, + underlying=init_determinant_expr( + underlying=self.underlying, + ), + ) + + def eval( + self, + variable: tuple, + value: tuple[float, ...], + ) -> 'ExpressionMixin': + return dataclasses.replace( + self, + underlying=init_eval_expr( + underlying=self.underlying, + variables=variable, + eval_values=value, + ), + ) diff --git a/polymatrix/expression/mixins/expressionstatemixin.py b/polymatrix/expression/mixins/expressionstatemixin.py new file mode 100644 index 0000000..67085d4 --- /dev/null +++ b/polymatrix/expression/mixins/expressionstatemixin.py @@ -0,0 +1,54 @@ +import abc +import itertools +import dataclasses +import typing + +import sympy + + +class ExpressionStateMixin(abc.ABC): + + @property + @abc.abstractmethod + def n_param(self) -> int: + """ + current number of parameters used in polynomial matrix expressions + """ + + ... + + @property + @abc.abstractmethod + def offset_dict(self) -> dict[tuple[typing.Any], tuple[int, int]]: + ... + + @property + @abc.abstractmethod + def auxillary_terms(self) -> tuple[dict[tuple[int], float]]: + ... + + @property + @abc.abstractmethod + def cached_polymatrix(self) -> dict: + ... + + def register( + self, + n_param: int, + key: typing.Any = None, + ) -> 'ExpressionStateMixin': + + if key is None: + updated_state = dataclasses.replace(self, n_param=self.n_param + n_param) + + elif key not in self.offset_dict: + updated_state = dataclasses.replace( + self, + offset_dict=self.offset_dict | {key: (self.n_param, self.n_param + n_param)}, + n_param=self.n_param + n_param, + ) + + else: + updated_state = self + + return updated_state diff --git a/polymatrix/expression/mixins/forallexprmixin.py b/polymatrix/expression/mixins/forallexprmixin.py new file mode 100644 index 0000000..4f5577c --- /dev/null +++ b/polymatrix/expression/mixins/forallexprmixin.py @@ -0,0 +1,72 @@ + +import abc +from numpy import var + +from polymatrix.expression.init.initpolymatrix import init_poly_matrix +from polymatrix.expression.mixins.expressionbasemixin import ExpressionBaseMixin +from polymatrix.expression.polymatrix import PolyMatrix +from polymatrix.polymatrixexprstate import PolyMatrixExprState + + +class ForAllExprMixin(ExpressionBaseMixin): + @property + @abc.abstractmethod + def underlying(self) -> ExpressionBaseMixin: + ... + + @property + @abc.abstractmethod + def variables(self) -> tuple: + ... + + # overwrites abstract method of `ExpressionBaseMixin` + @property + def shape(self) -> tuple[int, int]: + return self.underlying.shape + + # overwrites abstract method of `ExpressionBaseMixin` + def apply( + self, + state: PolyMatrixExprState, + ) -> tuple[PolyMatrixExprState, PolyMatrix]: + state, underlying = self.underlying.apply(state=state) + + variable_indices = tuple(state.offset_dict[variable][0] for variable in self.variables if variable in state.offset_dict) + + terms = {} + idx_row = 0 + + for row in range(self.shape[0]): + for col in range(self.shape[1]): + + try: + underlying_terms = underlying.get_poly(row, col) + except KeyError: + continue + + x_monomial_terms = {} + + for monomial, value in underlying_terms.items(): + + x_monomial = tuple(var_idx for var_idx in monomial if var_idx in variable_indices) + p_monomial = tuple(var_idx for var_idx in monomial if var_idx not in variable_indices) + + if x_monomial not in x_monomial_terms: + x_monomial_terms[x_monomial] = {} + + if p_monomial not in x_monomial_terms: + x_monomial_terms[x_monomial][p_monomial] = 0 + + x_monomial_terms[x_monomial][p_monomial] += value + + for data in x_monomial_terms.values(): + terms[idx_row, 0] = data + idx_row += 1 + + + poly_matrix = init_poly_matrix( + terms=terms, + shape=self.shape, + ) + + return state, poly_matrix diff --git a/polymatrix/expression/mixins/fromarrayexprmixin.py b/polymatrix/expression/mixins/fromarrayexprmixin.py new file mode 100644 index 0000000..0ae210d --- /dev/null +++ b/polymatrix/expression/mixins/fromarrayexprmixin.py @@ -0,0 +1,76 @@ + +import abc +import collections +import typing +import numpy as np +import dataclass_abc +from numpy import poly +import sympy +import functools + +from polymatrix.expression.init.initpolymatrix import init_poly_matrix +from polymatrix.expression.mixins.expressionbasemixin import ExpressionBaseMixin +from polymatrix.expression.mixins.expressionstatemixin import ExpressionStateMixin +from polymatrix.expression.mixins.polymatrixmixin import PolyMatrixMixin + + +class FromArrayExprMixin(ExpressionBaseMixin): + @property + @abc.abstractmethod + def data(self) -> tuple[tuple[float]]: + pass + + # overwrites abstract method of `PolyMatrixExprBaseMixin` + @property + def shape(self) -> tuple[int, int]: + return len(self.data), len(self.data[0]) + + # overwrites abstract method of `ExpressionBaseMixin` + def apply( + self, + state: ExpressionStateMixin, + ) -> tuple[ExpressionStateMixin, PolyMatrixMixin]: + + terms = {} + + for poly_row, col_data in enumerate(self.data): + for poly_col, poly_data in enumerate(col_data): + + try: + poly = sympy.poly(poly_data) + except sympy.polys.polyerrors.GeneratorsNeeded: + terms[poly_row, poly_col] = {tuple(): poly_data} + continue + + for symbol in poly.gens: + state = state.register(key=symbol, n_param=1) + + terms_row_col = {} + + # a5 x1 x3**2 -> c=a5, m_cnt=(1, 0, 2) + for value, monomial_count in zip(poly.coeffs(), poly.monoms()): + + if value == 0.0: + continue + + # m_cnt=(1, 0, 2) -> m=(0, 2, 2) + def gen_monomial(): + for rel_idx, p in enumerate(monomial_count): + + idx, _ = state.offset_dict[poly.gens[rel_idx]] + + for _ in range(p): + yield idx + + monomial = tuple(gen_monomial()) + + terms_row_col[monomial] = value + + terms[poly_row, poly_col] = terms_row_col + + poly_matrix = init_poly_matrix( + terms=terms, + shape=self.shape, + ) + + return state, poly_matrix diff --git a/polymatrix/expression/mixins/getitemexprmixin.py b/polymatrix/expression/mixins/getitemexprmixin.py new file mode 100644 index 0000000..9a521cb --- /dev/null +++ b/polymatrix/expression/mixins/getitemexprmixin.py @@ -0,0 +1,55 @@ + +import abc +import dataclasses +import typing +import dataclass_abc +from polymatrix.expression.mixins.polymatrixmixin import PolyMatrixMixin + +from polymatrix.expression.init.initpolymatrix import init_poly_matrix +from polymatrix.expression.mixins.expressionbasemixin import ExpressionBaseMixin +from polymatrix.expression.polymatrix import PolyMatrix +from polymatrix.polymatrixexprstate import PolyMatrixExprState + + +class GetItemExprMixin(ExpressionBaseMixin): + @property + @abc.abstractmethod + def underlying(self) -> ExpressionBaseMixin: + ... + + @property + @abc.abstractmethod + def index(self) -> tuple[int, int]: + ... + + # overwrites abstract method of `ExpressionBaseMixin` + @property + def shape(self) -> tuple[int, int]: + return 1, 1 + + # overwrites abstract method of `ExpressionBaseMixin` + def apply( + self, + state: PolyMatrixExprState, + ) -> tuple[PolyMatrixExprState, PolyMatrix]: + state, underlying = self.underlying.apply(state=state) + + @dataclass_abc.dataclass_abc(frozen=True) + class GetItemPolyMatrix(PolyMatrixMixin): + underlying: PolyMatrixMixin + index: tuple[int, int] + shape: tuple[int, int] + # aux_terms: tuple + + def get_poly(self, row: int, col: int) -> dict[tuple[int, ...], float]: + assert row == 0 and col == 0 + + return self.underlying.get_poly(self.index[0], self.index[1]) + + return state, GetItemPolyMatrix( + underlying=underlying, + shape=self.shape, + index=self.index, + # aux_terms=underlying.aux_terms, + ) +
\ No newline at end of file diff --git a/polymatrix/expression/mixins/kktexprmixin.py b/polymatrix/expression/mixins/kktexprmixin.py new file mode 100644 index 0000000..f6066d8 --- /dev/null +++ b/polymatrix/expression/mixins/kktexprmixin.py @@ -0,0 +1,126 @@ + +import abc +import itertools +from this import d +import typing +import dataclass_abc +from polymatrix.expression.derivativekey import DerivativeKey + +from polymatrix.expression.init.initpolymatrix import init_poly_matrix +from polymatrix.expression.mixins.expressionbasemixin import ExpressionBaseMixin +from polymatrix.expression.mixins.expressionmixin import ExpressionMixin +from polymatrix.expression.polymatrix import PolyMatrix +from polymatrix.polymatrixexprstate import PolyMatrixExprState + + +class KKTExprMixin(ExpressionBaseMixin): + @property + @abc.abstractmethod + def cost(self) -> ExpressionMixin: + ... + + @property + @abc.abstractmethod + def equality(self) -> ExpressionMixin: + ... + + @property + @abc.abstractmethod + def equality(self) -> ExpressionMixin: + ... + + @property + @abc.abstractmethod + def variables(self) -> ExpressionBaseMixin: + ... + + # overwrites abstract method of `ExpressionBaseMixin` + @property + def shape(self) -> tuple[int, int]: + return self.cost.shape[0] + self.equality.shape[0], 1 + + # overwrites abstract method of `ExpressionBaseMixin` + def apply( + self, + state: PolyMatrixExprState, + ) -> tuple[PolyMatrixExprState, PolyMatrix]: + + assert self.cost.shape == self.variables.shape + assert self.cost.shape[1] == 1 + + state, cost = self.cost.apply(state=state) + state, equality = self.equality.apply(state=state) + + state, equality_der = self.equality.diff( + self.variables, + introduce_derivatives=True, + ).apply(state) + + def acc_nu_variables(acc, v): + state, nu_variables = acc + + nu_variable = state.n_param + state = state.register(n_param=1) + + return state, nu_variables + [nu_variable] + + *_, (state, nu_variables) = tuple(itertools.accumulate( + range(self.equality.shape[0]), + acc_nu_variables, + initial=(state, []), + )) + + terms = {} + + n_row = cost.shape[0] + + for row in range(n_row): + try: + monomial_terms = cost.get_poly(row, 0) + except KeyError: + monomial_terms = {} + + for eq_idx, nu_variable in enumerate(nu_variables): + + try: + underlying_terms = equality_der.get_poly(eq_idx, row) + except KeyError: + continue + + for monomial, value in underlying_terms.items(): + new_monomial = monomial + (nu_variable,) + + if new_monomial not in monomial_terms: + monomial_terms[new_monomial] = 0 + + monomial_terms[new_monomial] += value + + terms[row, 0] = monomial_terms + + idx_start = n_row + + for row in range(equality.shape[0]): + + try: + underlying_terms = equality.get_poly(row, 0) + except KeyError: + continue + + terms[idx_start + row, 0] = underlying_terms + + idx_start += equality.shape[0] + + # for row, aux_term in enumerate(state.auxillary_terms): + # terms[idx_start + row, 0] = aux_term + + # idx_start += len(state.auxillary_terms) + + # derivatives = tuple(key for key in state.offset_dict.keys() if isinstance(key, DerivativeKey)) + # print(f'{derivatives=}') + + poly_matrix = init_poly_matrix( + terms=terms, + shape=(idx_start, 1), + ) + + return state, poly_matrix diff --git a/polymatrix/expression/mixins/matrixmultexprmixin.py b/polymatrix/expression/mixins/matrixmultexprmixin.py new file mode 100644 index 0000000..29eb4ac --- /dev/null +++ b/polymatrix/expression/mixins/matrixmultexprmixin.py @@ -0,0 +1,75 @@ + +import abc +import itertools + +from polymatrix.expression.init.initpolymatrix import init_poly_matrix +from polymatrix.expression.mixins.expressionbasemixin import ExpressionBaseMixin +from polymatrix.expression.polymatrix import PolyMatrix +from polymatrix.polymatrixexprstate import PolyMatrixExprState + + +class MatrixMultExprMixin(ExpressionBaseMixin): + @property + @abc.abstractmethod + def left(self) -> ExpressionBaseMixin: + ... + + @property + @abc.abstractmethod + def right(self) -> ExpressionBaseMixin: + ... + + # overwrites abstract method of `ExpressionBaseMixin` + @property + def shape(self) -> tuple[int, int]: + return (self.left.shape[0], self.right.shape[1]) + + # overwrites abstract method of `ExpressionBaseMixin` + def apply( + self, + state: PolyMatrixExprState, + ) -> tuple[PolyMatrixExprState, PolyMatrix]: + state, left = self.left.apply(state=state) + state, right = self.right.apply(state=state) + + assert left.shape[1] == right.shape[0] + + terms = {} + + for poly_row in range(left.shape[0]): + for poly_col in range(right.shape[1]): + + terms_row_col = {} + + for index_k in range(left.shape[1]): + + try: + left_terms = left.get_poly(poly_row, index_k) + right_terms = right.get_poly(index_k, poly_col) + except KeyError: + continue + + for (left_monomial, left_value), (right_monomial, right_value) \ + in itertools.product(left_terms.items(), right_terms.items()): + + value = left_value * right_value + + if value == 0: + continue + + monomial = tuple(sorted(left_monomial + right_monomial)) + + if monomial not in terms_row_col: + terms_row_col[monomial] = 0 + + terms_row_col[monomial] += value + + if 0 < len(terms_row_col): + terms[poly_row, poly_col] = terms_row_col + + poly_matrix = init_poly_matrix( + terms=terms, + shape=self.shape, + ) + + return state, poly_matrix diff --git a/polymatrix/expression/mixins/parametrizetermsexprmixin.py b/polymatrix/expression/mixins/parametrizetermsexprmixin.py new file mode 100644 index 0000000..fbee57c --- /dev/null +++ b/polymatrix/expression/mixins/parametrizetermsexprmixin.py @@ -0,0 +1,175 @@ + +import abc +import functools +import dataclass_abc +from polymatrix.expression.init.initexpressionstate import init_expression_state + +from polymatrix.expression.init.initpolymatrix import init_poly_matrix +from polymatrix.expression.mixins.expressionbasemixin import ExpressionBaseMixin +from polymatrix.expression.mixins.expressionstatemixin import ExpressionStateMixin +from polymatrix.expression.mixins.polymatrixmixin import PolyMatrixMixin + + +class ParametrizeTermsExprMixin(ExpressionBaseMixin): + @property + @abc.abstractclassmethod + def name(self) -> str: + ... + + @property + @abc.abstractclassmethod + def underlying(self) -> ExpressionBaseMixin: + ... + + @property + @abc.abstractclassmethod + def variables(self) -> tuple: + ... + + @property + def shape(self) -> tuple[int, int]: + return self.underlying.shape + + def _internal_apply(self, state: ExpressionStateMixin): + if not hasattr(self, '_terms'): + state, underlying = self.underlying.apply(state) + + for variable in self.variables: + state = state.register(key=variable, n_param=1) + + variable_indices = tuple(state.offset_dict[variable][0] for variable in self.variables if variable in state.offset_dict) + + idx_start = state.n_param + # print(f'{idx_start=}') + n_param = 0 + terms = {} + + for row in range(self.shape[0]): + for col in range(self.shape[1]): + + try: + underlying_terms = underlying.get_poly(row, col) + except KeyError: + continue + + terms_row_col = {} + collected_terms = [] + + for monomial, value in underlying_terms.items(): + + x_monomial = tuple(var_idx for var_idx in monomial if var_idx in variable_indices) + + if x_monomial not in collected_terms: + collected_terms.append(x_monomial) + + # print(f'{x_monomial=}') + # print(f'{collected_terms=}') + + idx = idx_start + n_param + collected_terms.index(x_monomial) + + new_monomial = monomial + (idx,) + + terms_row_col[new_monomial] = value + + n_param += len(collected_terms) + terms[row, col] = terms_row_col + + state = state.register(key=self, n_param=n_param) + + self._terms = terms + self._start_index = idx_start + # self._n_param = n_param + + return state, self._terms + + @property + def param(self) -> tuple[int, int]: + outer_self = self + + # precalculate number of parameters (used for `shape` attribute) + # --------------------------------- + # not pretty + + dummy_state = init_expression_state() + + dummy_state, underlying = self.underlying.apply(dummy_state) + + for variable in self.variables: + dummy_state = dummy_state.register(key=variable, n_param=1) + + variable_indices = tuple(dummy_state.offset_dict[variable][0] for variable in self.variables if variable in dummy_state.offset_dict) + + n_param = 0 + + for row in range(self.shape[0]): + for col in range(self.shape[1]): + + underlying_terms = underlying.get_poly(row, col) + + collected_terms = [] + + for monomial in underlying_terms.keys(): + + x_monomial = tuple(var_idx for var_idx in monomial if var_idx in variable_indices) + + if x_monomial not in collected_terms: + collected_terms.append(x_monomial) + + n_param += len(collected_terms) + + @dataclass_abc.dataclass_abc(frozen=True) + class ParameterExprMixin(ExpressionBaseMixin): + n_param: int + + @property + def shape(self) -> tuple[int, int]: + return self.n_param, 1 + + def apply( + self, + state: ExpressionStateMixin, + ) -> tuple[ExpressionStateMixin, PolyMatrixMixin]: + + state, _ = outer_self._internal_apply(state) + + def gen_monomials(): + for rel_index in range(self.n_param): + yield {(outer_self._start_index + rel_index,): 1} + + terms = {(row, 0): monomial_terms for row, monomial_terms in enumerate(gen_monomials())} + + poly_matrix = init_poly_matrix( + terms=terms, + shape=self.shape, + ) + + return state, poly_matrix + + return ParameterExprMixin( + n_param=n_param, + ) + + # # overwrite this method to customize indexing + # def re_index( + # self, + # degree: int, + # poly_col: int, + # poly_row: int, + # x_monomial: tuple[int, ...], + # ) -> tuple[int, int, tuple[int, ...], float]: + # return poly_col, poly_row, x_monomial, 1.0 + + # overwrites abstract method of `ExpressionBaseMixin` + def apply( + self, + state: ExpressionStateMixin, + ) -> tuple[ExpressionStateMixin, PolyMatrixMixin]: + + state, terms = self._internal_apply(state) + + poly_matrix = init_poly_matrix( + terms=terms, + shape=self.shape, + ) + + return state, poly_matrix diff --git a/polymatrix/expression/mixins/polymatrixasdictmixin.py b/polymatrix/expression/mixins/polymatrixasdictmixin.py new file mode 100644 index 0000000..6aea8ed --- /dev/null +++ b/polymatrix/expression/mixins/polymatrixasdictmixin.py @@ -0,0 +1,28 @@ +import abc + +from polymatrix.expression.mixins.polymatrixmixin import PolyMatrixMixin + + +class PolyMatrixAsDictMixin( + PolyMatrixMixin, + abc.ABC, +): + @property + @abc.abstractmethod + def terms(self) -> dict[tuple[int, int], dict[tuple[int, ...], float]]: + ... + + # overwrites abstract method of `PolyMatrixMixin` + def get_poly(self, row: int, col: int) -> dict[tuple[int, ...], float]: + # key = (row, col) + + # if key in self.terms: + # return self.terms[key] + + # else: + # return None + + try: + return self.terms[row, col] + except KeyError: + raise KeyError(f'{(row, col)} is not a key of {self.terms}') diff --git a/polymatrix/expression/mixins/polymatrixmixin.py b/polymatrix/expression/mixins/polymatrixmixin.py new file mode 100644 index 0000000..e5b803e --- /dev/null +++ b/polymatrix/expression/mixins/polymatrixmixin.py @@ -0,0 +1,109 @@ +import abc +import dataclasses +import itertools +import collections +import typing + + +class PolyMatrixMixin(abc.ABC): + @property + @abc.abstractclassmethod + def shape(self) -> tuple[int, int]: + ... + + @abc.abstractclassmethod + def get_poly(self, row: int, col: int) -> typing.Optional[dict[tuple[int, ...], float]]: + ... + + def reduce(self): + def gen_used_variables(): + for row in range(self.shape[0]): + for col in range(self.shape[1]): + + try: + underlying_terms = self.get_poly(row, col) + except KeyError: + continue + + for monomial in underlying_terms.keys(): + yield from monomial + + used_variables = set(gen_used_variables()) + + variable_index_reverse_map = tuple(sorted(used_variables)) + variable_index_map = {old: new for new, old in enumerate(variable_index_reverse_map)} + + + terms = {} + + for row in range(self.shape[0]): + for col in range(self.shape[1]): + + try: + underlying_terms = self.get_poly(row, col) + except KeyError: + continue + + def gen_updated_monomials(): + for monomial, value in underlying_terms.items(): + new_monomial = tuple(variable_index_map[var] for var in monomial) + yield new_monomial, value + + terms[row, col] = dict(gen_updated_monomials()) + + poly_matrix = dataclasses.replace( + self, + terms=terms, + shape=self.shape, + ) + + return poly_matrix, variable_index_reverse_map + + + # @property + # @abc.abstractmethod + # def terms(self) -> dict[tuple[int, int], dict[tuple[int, ...], dict[tuple[int, ...], float]]]: + # ... + + # @property + # @abc.abstractclassmethod + # def aux_terms(self) -> tuple[dict[tuple[int, ...], float]]: + # ... + + # def get_equality_equations( + # self, + # offset: int = None + # ) -> dict[int, list[tuple[list[int], float]]]: + # if offset is None: + # offset = 0 + + # to_eq_index_dict = {} + # equality_constraints = collections.defaultdict(list) + + # # def gen_key_equation_mapping(): + # for (poly_row, poly_col), terms_x_monomial in self.terms.items(): + # for x_monomial, terms_p_monomial in terms_x_monomial.items(): + # key = (poly_row, poly_col, x_monomial) + + # if key not in to_eq_index_dict: + # to_eq_index_dict[key] = offset + # offset += 1 + + # for p_monomial, value in terms_p_monomial.items(): + # equality_constraints[to_eq_index_dict[key]] += ((p_monomial, value),) + + # return equality_constraints + + # @property + # @abc.abstractmethod + # def degrees(self) -> set[int]: + # ... + + # @abc.abstractmethod + # def get_term( + # self, + # poly_col: int, + # poly_row: int, + # x_monomial: tuple[int, ...] + # ) -> PolyMatrixTerm: + # ... diff --git a/polymatrix/expression/mixins/quadraticinexprmixin.py b/polymatrix/expression/mixins/quadraticinexprmixin.py new file mode 100644 index 0000000..8f5555e --- /dev/null +++ b/polymatrix/expression/mixins/quadraticinexprmixin.py @@ -0,0 +1,72 @@ + +import abc + +from polymatrix.expression.init.initpolymatrix import init_poly_matrix +from polymatrix.expression.mixins.expressionbasemixin import ExpressionBaseMixin +from polymatrix.expression.polymatrix import PolyMatrix +from polymatrix.polymatrixexprstate import PolyMatrixExprState + + +class QuadraticInExprMixin(ExpressionBaseMixin): + @property + @abc.abstractmethod + def underlying(self) -> ExpressionBaseMixin: + ... + + @property + @abc.abstractmethod + def variables(self) -> tuple: + ... + + # overwrites abstract method of `ExpressionBaseMixin` + @property + def shape(self) -> tuple[int, int]: + return 2*(len(self.variables),) + + # overwrites abstract method of `ExpressionBaseMixin` + def apply( + self, + state: PolyMatrixExprState, + ) -> tuple[PolyMatrixExprState, PolyMatrix]: + state, underlying = self.underlying.apply(state=state) + + assert underlying.shape == (1, 1) + + variable_indices = tuple(state.offset_dict[variable][0] for variable in self.variables if variable in state.offset_dict) + + terms = {} + + for row in range(underlying.shape[0]): + for col in range(underlying.shape[1]): + + try: + underlying_terms = underlying.get_poly(row, col) + except KeyError: + continue + + for monomial, value in underlying_terms.items(): + + x_monomial = tuple(var_idx for var_idx in monomial if var_idx in variable_indices) + p_monomial = tuple(var_idx for var_idx in monomial if var_idx not in variable_indices) + + assert len(x_monomial) == 2 + assert tuple(sorted(x_monomial)) == x_monomial, f'{x_monomial} is not sorted' + + key = tuple(reversed(x_monomial)) + + if key not in terms: + terms[key] = {} + + monomial_terms = terms[key] + + if p_monomial not in monomial_terms: + monomial_terms[p_monomial] = 0 + + monomial_terms[p_monomial] += value + + poly_matrix = init_poly_matrix( + terms=terms, + shape=self.shape, + ) + + return state, poly_matrix diff --git a/polymatrix/expression/mixins/repmatexprmixin.py b/polymatrix/expression/mixins/repmatexprmixin.py new file mode 100644 index 0000000..aec0d48 --- /dev/null +++ b/polymatrix/expression/mixins/repmatexprmixin.py @@ -0,0 +1,49 @@ +import abc +import dataclass_abc + +from polymatrix.expression.mixins.expressionbasemixin import ExpressionBaseMixin +from polymatrix.expression.mixins.expressionstatemixin import ExpressionStateMixin +from polymatrix.expression.mixins.polymatrixmixin import PolyMatrixMixin + +class RepMatExprMixin(ExpressionBaseMixin): + @property + @abc.abstractclassmethod + def underlying(self) -> ExpressionBaseMixin: + ... + + @property + @abc.abstractclassmethod + def repetition(self) -> tuple[int, int]: + ... + + @property + def shape(self) -> tuple[int, int]: + return tuple(s*r for s, r in zip(self.underlying.shape, self.repetition)) + + # overwrites abstract method of `ExpressionBaseMixin` + def apply( + self, + state: ExpressionStateMixin, + ) -> tuple[ExpressionStateMixin, PolyMatrixMixin]: + + state, underlying = self.underlying.apply(state) + + @dataclass_abc.dataclass_abc(frozen=True) + class RepMatPolyMatrix(PolyMatrixMixin): + underlying: PolyMatrixMixin + shape: tuple[int, int] + # aux_terms: tuple + + def get_poly(self, row: int, col: int) -> dict[tuple[int, ...], float]: + n_row, n_col = underlying.shape + + rel_row = row % n_row + rel_col = col % n_col + + return self.underlying.get_poly(rel_row, rel_col) + + return state, RepMatPolyMatrix( + underlying=underlying, + shape=self.shape, + # aux_terms=underlying.aux_terms, + )
\ No newline at end of file diff --git a/polymatrix/expression/mixins/transposeexprmixin.py b/polymatrix/expression/mixins/transposeexprmixin.py new file mode 100644 index 0000000..63e6a3f --- /dev/null +++ b/polymatrix/expression/mixins/transposeexprmixin.py @@ -0,0 +1,43 @@ + +import abc +import dataclasses +import typing +import dataclass_abc +from polymatrix.expression.mixins.polymatrixmixin import PolyMatrixMixin + +from polymatrix.expression.init.initpolymatrix import init_poly_matrix +from polymatrix.expression.mixins.expressionbasemixin import ExpressionBaseMixin +from polymatrix.expression.polymatrix import PolyMatrix +from polymatrix.polymatrixexprstate import PolyMatrixExprState + + +class TransposeExprMixin(ExpressionBaseMixin): + @property + @abc.abstractmethod + def underlying(self) -> ExpressionBaseMixin: + ... + + # overwrites abstract method of `PolyMatrixExprBaseMixin` + @property + def shape(self) -> tuple[int, int]: + return self.underlying.shape[1], self.underlying.shape[0] + + # overwrites abstract method of `PolyMatrixExprBaseMixin` + def apply( + self, + state: PolyMatrixExprState, + ) -> tuple[PolyMatrixExprState, PolyMatrix]: + state, underlying = self.underlying.apply(state=state) + + @dataclass_abc.dataclass_abc(frozen=True) + class TransposePolyMatrix(PolyMatrixMixin): + underlying: PolyMatrixMixin + shape: tuple[int, int] + + def get_poly(self, row: int, col: int) -> dict[tuple[int, ...], float]: + return self.underlying.get_poly(col, row) + + return state, TransposePolyMatrix( + underlying=underlying, + shape=self.shape, + )
\ No newline at end of file diff --git a/polymatrix/expression/mixins/vstackexprmixin.py b/polymatrix/expression/mixins/vstackexprmixin.py new file mode 100644 index 0000000..381659c --- /dev/null +++ b/polymatrix/expression/mixins/vstackexprmixin.py @@ -0,0 +1,66 @@ + +import abc +import itertools +import dataclass_abc +from polymatrix.expression.mixins.polymatrixmixin import PolyMatrixMixin + +from polymatrix.expression.mixins.expressionbasemixin import ExpressionBaseMixin +from polymatrix.expression.polymatrix import PolyMatrix +from polymatrix.polymatrixexprstate import PolyMatrixExprState + + +class VStackExprMixin(ExpressionBaseMixin): + @property + @abc.abstractmethod + def underlying(self) -> tuple[ExpressionBaseMixin, ...]: + ... + + # overwrites abstract method of `ExpressionBaseMixin` + @property + def shape(self) -> tuple[int, int]: + n_row = sum(expr.shape[0] for expr in self.underlying) + return n_row, self.underlying[0].shape[1] + + # overwrites abstract method of `ExpressionBaseMixin` + def apply( + self, + state: PolyMatrixExprState, + ) -> tuple[PolyMatrixExprState, PolyMatrix]: + assert all(expr.shape[1] == self.underlying[0].shape[1] for expr in self.underlying) + + # todo: rename + underlying = [] + for expr in self.underlying: + state, polymat = expr.apply(state=state) + underlying.append(polymat) + + @dataclass_abc.dataclass_abc(frozen=True) + class VStackPolyMatrix(PolyMatrixMixin): + underlying: tuple[PolyMatrixMixin] + underlying_row_range: tuple[tuple[int, int], ...] + shape: tuple[int, int] + # aux_terms: tuple + + def get_poly(self, row: int, col: int) -> dict[tuple[int, ...], float]: + for polymat, (row_start, row_end) in zip(self.underlying, self.underlying_row_range): + if row_start <= row < row_end: + return polymat.get_poly( + row=row - row_start, + col=col, + ) + + raise Exception(f'row {row} is out of bounds') + + underlying_row_range = tuple(itertools.pairwise( + itertools.accumulate( + (expr.shape[0] for expr in self.underlying), + initial=0) + )) + + return state, VStackPolyMatrix( + underlying=underlying, + shape=self.shape, + underlying_row_range=underlying_row_range, + # aux_terms=tuple(aux_term for expr in underlying for aux_term in expr.aux_terms) + ) +
\ No newline at end of file diff --git a/polymatrix/expression/parametrizesymbolsexpr.py b/polymatrix/expression/parametrizesymbolsexpr.py new file mode 100644 index 0000000..a81ec23 --- /dev/null +++ b/polymatrix/expression/parametrizesymbolsexpr.py @@ -0,0 +1,4 @@ +from polymatrix.expression.mixins.parametrizetermsexprmixin import ParametrizeTermsExprMixin + +class ParametrizeSymbolsExpr(ParametrizeTermsExprMixin): + pass diff --git a/polymatrix/expression/polymatrix.py b/polymatrix/expression/polymatrix.py new file mode 100644 index 0000000..c044081 --- /dev/null +++ b/polymatrix/expression/polymatrix.py @@ -0,0 +1,4 @@ +from polymatrix.expression.mixins.polymatrixasdictmixin import PolyMatrixAsDictMixin + +class PolyMatrix(PolyMatrixAsDictMixin): + pass diff --git a/polymatrix/expression/quadraticinexpr.py b/polymatrix/expression/quadraticinexpr.py new file mode 100644 index 0000000..bab76f6 --- /dev/null +++ b/polymatrix/expression/quadraticinexpr.py @@ -0,0 +1,4 @@ +from polymatrix.expression.mixins.quadraticinexprmixin import QuadraticInExprMixin + +class QuadraticInExpr(QuadraticInExprMixin): + pass diff --git a/polymatrix/expression/repmatexpr.py b/polymatrix/expression/repmatexpr.py new file mode 100644 index 0000000..bb983be --- /dev/null +++ b/polymatrix/expression/repmatexpr.py @@ -0,0 +1,4 @@ +from polymatrix.expression.mixins.repmatexprmixin import RepMatExprMixin + +class RepMatExpr(RepMatExprMixin): + pass diff --git a/polymatrix/expression/transposeexpr.py b/polymatrix/expression/transposeexpr.py new file mode 100644 index 0000000..908a9e4 --- /dev/null +++ b/polymatrix/expression/transposeexpr.py @@ -0,0 +1,4 @@ +from polymatrix.expression.mixins.transposeexprmixin import TransposeExprMixin + +class TransposeExpr(TransposeExprMixin): + pass diff --git a/polymatrix/expression/vstackexpr.py b/polymatrix/expression/vstackexpr.py new file mode 100644 index 0000000..7e9a1d7 --- /dev/null +++ b/polymatrix/expression/vstackexpr.py @@ -0,0 +1,4 @@ +from polymatrix.expression.mixins.vstackexprmixin import VStackExprMixin + +class VStackExpr(VStackExprMixin): + pass diff --git a/polymatrix/impl/addexprimpl.py b/polymatrix/impl/addexprimpl.py new file mode 100644 index 0000000..a3d9e1f --- /dev/null +++ b/polymatrix/impl/addexprimpl.py @@ -0,0 +1,8 @@ +import dataclass_abc +from polymatrix.addexpr import AddExpr +from polymatrix.mixins.oldpolymatrixmixin import OldPolyMatrixMixin + +@dataclass_abc.dataclass_abc(frozen=True) +class AddExprImpl(AddExpr): + left: OldPolyMatrixMixin + right: OldPolyMatrixMixin diff --git a/polymatrix/impl/exprcontainerimpl.py b/polymatrix/impl/exprcontainerimpl.py new file mode 100644 index 0000000..0706150 --- /dev/null +++ b/polymatrix/impl/exprcontainerimpl.py @@ -0,0 +1,8 @@ +import dataclass_abc +from polymatrix.exprcontainer import ExprContainer +from polymatrix.mixins.exprcontainermixin import ExprType +from polymatrix.expression.mixins.expressionbasemixin import ExpressionBaseMixin + +@dataclass_abc.dataclass_abc(frozen=True) +class ExprContainerImpl(ExprContainer[ExprType]): + expr: ExpressionBaseMixin diff --git a/polymatrix/impl/multexprimpl.py b/polymatrix/impl/multexprimpl.py new file mode 100644 index 0000000..7401ffa --- /dev/null +++ b/polymatrix/impl/multexprimpl.py @@ -0,0 +1,8 @@ +import dataclass_abc +from polymatrix.mixins.oldpolymatrixmixin import OldPolyMatrixMixin +from polymatrix.multexpr import MultExpr + +@dataclass_abc.dataclass_abc(frozen=True) +class MultExprImpl(MultExpr): + left: OldPolyMatrixMixin + right: OldPolyMatrixMixin diff --git a/polymatrix/impl/polymatriximpl.py b/polymatrix/impl/oldpolymatriximpl.py index cc435e3..29590db 100644 --- a/polymatrix/impl/polymatriximpl.py +++ b/polymatrix/impl/oldpolymatriximpl.py @@ -1,11 +1,11 @@ import typing import dataclass_abc -from polymatrix.polymatrix import PolyMatrix +from polymatrix.oldpolymatrix import OldPolyMatrix @dataclass_abc.dataclass_abc(frozen=True, eq=False) -class PolyMatrixImpl(PolyMatrix): +class PolyMatrixImpl(OldPolyMatrix): name: str degrees: list[int] subs: dict[int, dict[tuple[int, int], float]] diff --git a/polymatrix/impl/optimizationimpl.py b/polymatrix/impl/optimizationimpl.py index ac78ea0..3243175 100644 --- a/polymatrix/impl/optimizationimpl.py +++ b/polymatrix/impl/optimizationimpl.py @@ -1,13 +1,13 @@ import dataclass_abc from polymatrix.optimization import Optimization -from polymatrix.optimizationstate import OptimizationState +from polymatrix.oldpolymatrixexprstate import OldPolyMatrixExprState @dataclass_abc.dataclass_abc(frozen=True, eq=False) class OptimizationImpl(Optimization): # n_var: int - state: OptimizationState + state: OldPolyMatrixExprState equality_constraints: dict[int, dict[tuple[int, int], float]] inequality_constraints: dict[int, dict[tuple[int, int], float]] auxillary_equality: dict[int, dict[tuple[int, int], float]] diff --git a/polymatrix/impl/optimizationstateimpl.py b/polymatrix/impl/optimizationstateimpl.py index 5ce8d11..acfaddb 100644 --- a/polymatrix/impl/optimizationstateimpl.py +++ b/polymatrix/impl/optimizationstateimpl.py @@ -1,11 +1,11 @@ import dataclass_abc -from polymatrix.optimizationstate import OptimizationState -from polymatrix.polymatrix import PolyMatrix +from polymatrix.oldpolymatrixexprstate import OldPolyMatrixExprStateMixin +from polymatrix.oldpolymatrix import OldPolyMatrix @dataclass_abc.dataclass_abc(frozen=True, eq=False) -class OptimizationStateImpl(OptimizationState): +class OptimizationStateImpl(OldPolyMatrixExprStateMixin): n_var: int n_param: int - offset_dict: dict[tuple[PolyMatrix, int], int] + offset_dict: dict[tuple[OldPolyMatrix, int], int] diff --git a/polymatrix/impl/polymatexprimpl.py b/polymatrix/impl/polymatexprimpl.py new file mode 100644 index 0000000..c0d6abb --- /dev/null +++ b/polymatrix/impl/polymatexprimpl.py @@ -0,0 +1,7 @@ +import dataclass_abc +from polymatrix.expression.polymatrix import PolyMatrix + +@dataclass_abc.dataclass_abc(frozen=True) +class PolyMatExprImpl(PolyMatrix): + terms: dict + shape: tuple diff --git a/polymatrix/impl/polymatrixaddexprimpl.py b/polymatrix/impl/polymatrixaddexprimpl.py new file mode 100644 index 0000000..f30495b --- /dev/null +++ b/polymatrix/impl/polymatrixaddexprimpl.py @@ -0,0 +1,9 @@ +import dataclass_abc +from polymatrix.polymatrixaddexpr import PolyMatrixAddExpr + +from polymatrix.expression.mixins.expressionbasemixin import ExpressionBaseMixin + +@dataclass_abc.dataclass_abc(frozen=True) +class PolyMatrixAddExprImpl(PolyMatrixAddExpr): + left: ExpressionBaseMixin + right: ExpressionBaseMixin diff --git a/polymatrix/impl/polymatrixarrayexprimpl.py b/polymatrix/impl/polymatrixarrayexprimpl.py new file mode 100644 index 0000000..a005129 --- /dev/null +++ b/polymatrix/impl/polymatrixarrayexprimpl.py @@ -0,0 +1,8 @@ +import dataclass_abc +from polymatrix.polymatrixarrayexpr import PolyMatrixArrayExpr + +from numpy import array + +@dataclass_abc.dataclass_abc(frozen=True) +class PolyMatrixArrayExprImpl(PolyMatrixArrayExpr): + data: array diff --git a/polymatrix/impl/polymatrixexprimpl.py b/polymatrix/impl/polymatrixexprimpl.py new file mode 100644 index 0000000..a5c52f0 --- /dev/null +++ b/polymatrix/impl/polymatrixexprimpl.py @@ -0,0 +1,8 @@ +import dataclass_abc +from polymatrix.polymatrixexpr import PolyMatrixExpr + +from polymatrix.expression.mixins.expressionbasemixin import ExpressionBaseMixin + +@dataclass_abc.dataclass_abc(frozen=True) +class PolyMatrixExprImpl(PolyMatrixExpr): + underlying: ExpressionBaseMixin diff --git a/polymatrix/impl/polymatrixexprstateimpl.py b/polymatrix/impl/polymatrixexprstateimpl.py new file mode 100644 index 0000000..25f5c52 --- /dev/null +++ b/polymatrix/impl/polymatrixexprstateimpl.py @@ -0,0 +1,12 @@ +import typing +import dataclass_abc +import sympy +from polymatrix.polymatrixexprstate import PolyMatrixExprState + + +@dataclass_abc.dataclass_abc(frozen=True) +class PolyMatrixExprStateImpl(PolyMatrixExprState): + n_var: int + n_param: int + offset_dict: dict + symbols: typing.Optional[sympy.Symbol] diff --git a/polymatrix/impl/polymatrixmultexprimpl.py b/polymatrix/impl/polymatrixmultexprimpl.py new file mode 100644 index 0000000..7f8375e --- /dev/null +++ b/polymatrix/impl/polymatrixmultexprimpl.py @@ -0,0 +1,9 @@ +import dataclass_abc +from polymatrix.polymatrixmultexpr import PolyMatrixMultExpr + +from polymatrix.expression.mixins.expressionbasemixin import ExpressionBaseMixin + +@dataclass_abc.dataclass_abc(frozen=True) +class PolyMatrixMultExprImpl(PolyMatrixMultExpr): + left: ExpressionBaseMixin + right: ExpressionBaseMixin diff --git a/polymatrix/impl/polymatrixparamexprimpl.py b/polymatrix/impl/polymatrixparamexprimpl.py new file mode 100644 index 0000000..afb5388 --- /dev/null +++ b/polymatrix/impl/polymatrixparamexprimpl.py @@ -0,0 +1,9 @@ +import dataclass_abc +from polymatrix.polymatrixparamexpr import PolyMatrixParamExpr + + +@dataclass_abc.dataclass_abc(frozen=True) +class PolyMatrixParamExprImpl(PolyMatrixParamExpr): + name: str + shape: tuple + degrees: tuple diff --git a/polymatrix/impl/polymatrixvalueimpl.py b/polymatrix/impl/polymatrixvalueimpl.py new file mode 100644 index 0000000..c0c9921 --- /dev/null +++ b/polymatrix/impl/polymatrixvalueimpl.py @@ -0,0 +1,7 @@ +import dataclass_abc +from polymatrix.polymatrixvalue import PolyMatrixTerm + +@dataclass_abc.dataclass_abc(frozen=True) +class PolyMatrixValueImpl(PolyMatrixTerm): + p_monomial: tuple + value: float diff --git a/polymatrix/impl/scalarmultexprimpl.py b/polymatrix/impl/scalarmultexprimpl.py new file mode 100644 index 0000000..42bec55 --- /dev/null +++ b/polymatrix/impl/scalarmultexprimpl.py @@ -0,0 +1,8 @@ +import dataclass_abc +from polymatrix.scalarmultexpr import ScalarMultExpr +from polymatrix.expression.mixins.expressionbasemixin import ExpressionBaseMixin + +@dataclass_abc.dataclass_abc(frozen=True) +class ScalarMultExprImpl(ScalarMultExpr): + left: float + right: ExpressionBaseMixin diff --git a/polymatrix/init/initaddexpr.py b/polymatrix/init/initaddexpr.py new file mode 100644 index 0000000..e660ed1 --- /dev/null +++ b/polymatrix/init/initaddexpr.py @@ -0,0 +1,11 @@ +from polymatrix.impl.addexprimpl import AddExprImpl +from polymatrix.mixins.oldpolymatrixmixin import OldPolyMatrixMixin + +def init_add_expr( + left: OldPolyMatrixMixin, + right: OldPolyMatrixMixin, +): + return AddExprImpl( + left=left, + right=right, +) diff --git a/polymatrix/init/initexprcontainer.py b/polymatrix/init/initexprcontainer.py new file mode 100644 index 0000000..f790705 --- /dev/null +++ b/polymatrix/init/initexprcontainer.py @@ -0,0 +1,9 @@ +from polymatrix.expression.mixins.expressionbasemixin import ExpressionBaseMixin +from polymatrix.impl.exprcontainerimpl import ExprContainerImpl + +def init_expr_container( + expr: ExpressionBaseMixin, +): + return ExprContainerImpl( + expr=expr, +) diff --git a/polymatrix/init/initmultexpr.py b/polymatrix/init/initmultexpr.py new file mode 100644 index 0000000..dfffd97 --- /dev/null +++ b/polymatrix/init/initmultexpr.py @@ -0,0 +1,11 @@ +from polymatrix.impl.multexprimpl import MultExprImpl +from polymatrix.mixins.oldpolymatrixmixin import OldPolyMatrixMixin + +def init_mult_expr( + left: OldPolyMatrixMixin, + right: OldPolyMatrixMixin, +): + return MultExprImpl( + left=left, + right=right, +) diff --git a/polymatrix/init/initoptimization.py b/polymatrix/init/initoptimization.py index 653d248..2a340eb 100644 --- a/polymatrix/init/initoptimization.py +++ b/polymatrix/init/initoptimization.py @@ -1,6 +1,6 @@ from polymatrix.impl.optimizationimpl import OptimizationImpl from polymatrix.init.initoptimizationstate import init_optimization_state -from polymatrix.optimizationstate import OptimizationState +from polymatrix.oldpolymatrixexprstate import OldPolyMatrixExprState def init_optimization( diff --git a/polymatrix/init/initoptimizationstate.py b/polymatrix/init/initoptimizationstate.py index 372e225..edfa33e 100644 --- a/polymatrix/init/initoptimizationstate.py +++ b/polymatrix/init/initoptimizationstate.py @@ -1,11 +1,11 @@ from polymatrix.impl.optimizationstateimpl import OptimizationStateImpl -from polymatrix.mixins.polymatrixmixin import PolyMatrixMixin +from polymatrix.mixins.oldpolymatrixmixin import OldPolyMatrixMixin def init_optimization_state( n_var: int, n_param: int = None, - offset_dict: dict[tuple[PolyMatrixMixin, int], int] = None, + offset_dict: dict[tuple[OldPolyMatrixMixin, int], int] = None, ): if n_param is None: n_param = 0 diff --git a/polymatrix/init/initpolymatexpr.py b/polymatrix/init/initpolymatexpr.py new file mode 100644 index 0000000..9f6cd20 --- /dev/null +++ b/polymatrix/init/initpolymatexpr.py @@ -0,0 +1,10 @@ +from polymatrix.impl.polymatexprimpl import PolyMatExprImpl + +def init_poly_mat_expr( + terms: dict, + shape: tuple, +): + return PolyMatExprImpl( + terms=terms, + shape=shape, +) diff --git a/polymatrix/init/initpolymatrixaddexpr.py b/polymatrix/init/initpolymatrixaddexpr.py new file mode 100644 index 0000000..43c2d1f --- /dev/null +++ b/polymatrix/init/initpolymatrixaddexpr.py @@ -0,0 +1,12 @@ +from polymatrix.expression.mixins.expressionbasemixin import ExpressionBaseMixin +from polymatrix.impl.polymatrixaddexprimpl import PolyMatrixAddExprImpl + + +def init_poly_matrix_add_expr( + left: ExpressionBaseMixin, + right: ExpressionBaseMixin, +): + return PolyMatrixAddExprImpl( + left=left, + right=right, +) diff --git a/polymatrix/init/initpolymatrixarrayexpr.py b/polymatrix/init/initpolymatrixarrayexpr.py new file mode 100644 index 0000000..8f7dbed --- /dev/null +++ b/polymatrix/init/initpolymatrixarrayexpr.py @@ -0,0 +1,10 @@ +from numpy import array +from polymatrix.impl.polymatrixarrayexprimpl import PolyMatrixArrayExprImpl + + +def init_poly_matrix_array_expr( + data: array, +): + return PolyMatrixArrayExprImpl( + data=data, +) diff --git a/polymatrix/init/initpolymatrixexpr.py b/polymatrix/init/initpolymatrixexpr.py new file mode 100644 index 0000000..2749bd3 --- /dev/null +++ b/polymatrix/init/initpolymatrixexpr.py @@ -0,0 +1,10 @@ +from polymatrix.expression.mixins.expressionbasemixin import ExpressionBaseMixin +from polymatrix.impl.polymatrixexprimpl import PolyMatrixExprImpl + + +def init_poly_matrix_expr( + underlying: ExpressionBaseMixin, +): + return PolyMatrixExprImpl( + underlying=underlying, +) diff --git a/polymatrix/init/initpolymatrixexprstate.py b/polymatrix/init/initpolymatrixexprstate.py new file mode 100644 index 0000000..03649c8 --- /dev/null +++ b/polymatrix/init/initpolymatrixexprstate.py @@ -0,0 +1,26 @@ +import sympy +from polymatrix.impl.polymatrixexprstateimpl import PolyMatrixExprStateImpl + +def init_poly_matrix_expr_state( + n_var: int = None, + n_param: int = None, + offset_dict: dict = None, + symbols: sympy.Symbol = None, +): + if n_var is None: + n_var = len(symbols) + elif symbols is not None: + assert n_var == len(symbols), f'{n_var} is not equal {len(symbols)}' + + if n_param is None: + n_param = 0 + + if offset_dict is None: + offset_dict = {} + + return PolyMatrixExprStateImpl( + n_var=n_var, + n_param=n_param, + offset_dict=offset_dict, + symbols=symbols, +) diff --git a/polymatrix/init/initpolymatrixmultexpr.py b/polymatrix/init/initpolymatrixmultexpr.py new file mode 100644 index 0000000..2c423c9 --- /dev/null +++ b/polymatrix/init/initpolymatrixmultexpr.py @@ -0,0 +1,12 @@ +from polymatrix.expression.mixins.expressionbasemixin import ExpressionBaseMixin +from polymatrix.impl.polymatrixmultexprimpl import PolyMatrixMultExprImpl + + +def init_poly_matrix_mult_expr( + left: ExpressionBaseMixin, + right: ExpressionBaseMixin, +): + return PolyMatrixMultExprImpl( + left=left, + right=right, +) diff --git a/polymatrix/init/initpolymatrixparamexpr.py b/polymatrix/init/initpolymatrixparamexpr.py new file mode 100644 index 0000000..7e1b6d7 --- /dev/null +++ b/polymatrix/init/initpolymatrixparamexpr.py @@ -0,0 +1,33 @@ +import typing +from polymatrix.impl.polymatrixparamexprimpl import PolyMatrixParamExprImpl + +def init_poly_matrix_param_expr( + name: str, + shape: tuple, + degrees: tuple, + re_index: typing.Callable[[int, int, int, tuple[int, ...]], tuple[int, int, int, tuple[int, ...], float]] = None, +): + + if re_index is None: + return PolyMatrixParamExprImpl( + name=name, + shape=shape, + degrees=degrees, + ) + + else: + class ExtendedPolyMatrixParamExprImpl(PolyMatrixParamExprImpl): + def re_index( + self, + degree: int, + poly_col: int, + poly_row: int, + x_monomial: tuple[int, ...], + ) -> tuple[int, int, tuple[int, ...], float]: + return re_index(degree, poly_col, poly_row, x_monomial) + + return ExtendedPolyMatrixParamExprImpl( + name=name, + shape=shape, + degrees=degrees, + ) diff --git a/polymatrix/init/initpolymatrixvalue.py b/polymatrix/init/initpolymatrixvalue.py new file mode 100644 index 0000000..570f399 --- /dev/null +++ b/polymatrix/init/initpolymatrixvalue.py @@ -0,0 +1,10 @@ +from polymatrix.impl.polymatrixvalueimpl import PolyMatrixValueImpl + +def init_poly_matrix_value( + p_monomial: tuple, + value: float, +): + return PolyMatrixValueImpl( + p_monomial=p_monomial, + value=value, +) diff --git a/polymatrix/init/initscalarmultexpr.py b/polymatrix/init/initscalarmultexpr.py new file mode 100644 index 0000000..a401758 --- /dev/null +++ b/polymatrix/init/initscalarmultexpr.py @@ -0,0 +1,11 @@ +from polymatrix.expression.mixins.expressionbasemixin import ExpressionBaseMixin +from polymatrix.impl.scalarmultexprimpl import ScalarMultExprImpl + +def init_scalar_mult_expr( + left: float, + right: ExpressionBaseMixin, +): + return ScalarMultExprImpl( + left=left, + right=right, +) diff --git a/polymatrix/init/initpolymatrix.py b/polymatrix/init/oldinitpolymatrix.py index edfe195..f1b2efd 100644 --- a/polymatrix/init/initpolymatrix.py +++ b/polymatrix/init/oldinitpolymatrix.py @@ -1,6 +1,7 @@ import typing -from polymatrix.impl.polymatriximpl import PolyMatrixImpl +from polymatrix.impl.oldpolymatriximpl import PolyMatrixImpl +from polymatrix.init.initexprcontainer import init_expr_container def init_poly_matrix( @@ -25,7 +26,7 @@ def init_poly_matrix( if is_negated is None: is_negated = False - return PolyMatrixImpl( + expr = PolyMatrixImpl( name=name, degrees=degrees, subs=subs, @@ -34,3 +35,5 @@ def init_poly_matrix( shape=shape, is_negated=is_negated, ) + + return init_expr_container(expr=expr) diff --git a/polymatrix/mixins/addexprmixin.py b/polymatrix/mixins/addexprmixin.py new file mode 100644 index 0000000..4156829 --- /dev/null +++ b/polymatrix/mixins/addexprmixin.py @@ -0,0 +1,16 @@ +import abc + +from polymatrix.mixins.oldpolymatrixexprmixin import OldPolyMatrixExprMixin + + +class AddExprMixin(OldPolyMatrixExprMixin, abc.ABC): + @property + @abc.abstractmethod + def left(self) -> OldPolyMatrixExprMixin: + ... + + @property + @abc.abstractmethod + def right(self) -> OldPolyMatrixExprMixin: + ... + diff --git a/polymatrix/mixins/exprcontainermixin.py b/polymatrix/mixins/exprcontainermixin.py new file mode 100644 index 0000000..b5dff91 --- /dev/null +++ b/polymatrix/mixins/exprcontainermixin.py @@ -0,0 +1,82 @@ +import abc +import dataclasses +import typing +from polymatrix.addexpr import AddExpr +from polymatrix.init.initaddexpr import init_add_expr +from polymatrix.init.initmultexpr import init_mult_expr +from polymatrix.init.initscalarmultexpr import init_scalar_mult_expr +from polymatrix.mixins.oldpolymatrixexprmixin import OldPolyMatrixExprMixin + +from polymatrix.multexpr import MultExpr +from polymatrix.scalarmultexpr import ScalarMultExpr + + +ExprType = typing.TypeVar('ExprType', bound=OldPolyMatrixExprMixin) + +class ExprContainerMixin( + typing.Generic[ExprType], + abc.ABC, +): + @property + @abc.abstractmethod + def expr(self) -> ExprType: + ... + + def __add__(self, other: 'ExprContainerMixin[ExprType]'): + return dataclasses.replace( + self, + expr=init_add_expr( + left=self.expr, + right=other.expr, + ), + ) + + def __sub__(self, other: 'ExprContainerMixin[ExprType]'): + return self + (-1.0) * other + + def __mul__(self, other: 'ExprContainerMixin[ExprType]'): + return dataclasses.replace( + self, + expr=init_mult_expr( + left=self.expr, + right=other.expr, + ), + ) + + def __rmul__(self, val: float): + return dataclasses.replace( + self, + expr=init_scalar_mult_expr( + left=val, + right=self.expr, + ), + ) + + def to_list(self) -> tuple[tuple[float, tuple[OldPolyMatrixExprMixin, ...]]]: + def get_mult_expr_list(expr: MultExpr) -> tuple[OldPolyMatrixExprMixin, ...]: + match expr: + case MultExpr(): + left = get_mult_expr_list(expr.left) + right = get_mult_expr_list(expr.right) + return left + right + case _: + return (expr,) + + def get_add_expr_list(expr: AddExpr) -> tuple[tuple[float, tuple[OldPolyMatrixExprMixin, ...]]]: + match expr: + case AddExpr(): + left = get_add_expr_list(expr.left) + right = get_add_expr_list(expr.right) + return left + right + case ScalarMultExpr(): + right = get_mult_expr_list(expr.right) + return ((expr.left, right),) + case MultExpr(): + left = get_mult_expr_list(expr.left) + right = get_mult_expr_list(expr.right) + return ((1.0, left + right),) + case _: + return ((1.0, (expr,)),) + + return get_add_expr_list(self.expr) +
\ No newline at end of file diff --git a/polymatrix/mixins/multexprmixin.py b/polymatrix/mixins/multexprmixin.py new file mode 100644 index 0000000..c9c45c2 --- /dev/null +++ b/polymatrix/mixins/multexprmixin.py @@ -0,0 +1,15 @@ +import abc + +from polymatrix.mixins.oldpolymatrixexprmixin import OldPolyMatrixExprMixin + + +class MultExprMixin(OldPolyMatrixExprMixin, abc.ABC): + @property + @abc.abstractmethod + def left(self) -> OldPolyMatrixExprMixin: + ... + + @property + @abc.abstractmethod + def right(self) -> OldPolyMatrixExprMixin: + ... diff --git a/polymatrix/mixins/oldpolymatrixexprmixin.py b/polymatrix/mixins/oldpolymatrixexprmixin.py new file mode 100644 index 0000000..6d5a029 --- /dev/null +++ b/polymatrix/mixins/oldpolymatrixexprmixin.py @@ -0,0 +1,2 @@ +class OldPolyMatrixExprMixin: + pass diff --git a/polymatrix/mixins/optimizationstatemixin.py b/polymatrix/mixins/oldpolymatrixexprstatemixin.py index 731477c..0b95092 100644 --- a/polymatrix/mixins/optimizationstatemixin.py +++ b/polymatrix/mixins/oldpolymatrixexprstatemixin.py @@ -2,11 +2,11 @@ import abc import itertools import dataclasses -from polymatrix.mixins.polymatrixmixin import PolyMatrixMixin +from polymatrix.mixins.oldpolymatrixmixin import OldPolyMatrixMixin from polymatrix.utils import monomial_to_index -class OptimizationStateMixin(abc.ABC): +class OldPolyMatrixExprStateMixin(abc.ABC): @property @abc.abstractmethod def n_var(self) -> int: @@ -27,7 +27,7 @@ class OptimizationStateMixin(abc.ABC): @property @abc.abstractmethod - def offset_dict(self) -> dict[tuple[PolyMatrixMixin, int], tuple[int, int]]: + def offset_dict(self) -> dict[tuple[OldPolyMatrixMixin, int], tuple[int, int]]: ... # @property @@ -35,7 +35,7 @@ class OptimizationStateMixin(abc.ABC): # def local_index_dict(self) -> dict[tuple[PolyMatrixMixin, int], dict[int, int]]: # ... - def get_polymat(self, p_index: int) -> tuple[PolyMatrixMixin, int, int]: + def get_polymat(self, p_index: int) -> tuple[OldPolyMatrixMixin, int, int]: for (polymat, degree), (start, end) in self.offset_dict.items(): if start <= p_index < end: return polymat, degree, p_index - start @@ -46,7 +46,7 @@ class OptimizationStateMixin(abc.ABC): # start_idx, end_idx = self.offset_dict[(polymat, degree)] # return end_idx - start_idx - def update_offsets(self, polymats: tuple[PolyMatrixMixin]) -> 'OptimizationStateMixin': + def update_offsets(self, polymats: tuple[OldPolyMatrixMixin]) -> 'OldPolyMatrixExprStateMixin': registered_polymats = set(polymat for polymat, _ in self.offset_dict.keys()) parametric_polymats = set(p for p in polymats if not p.is_constant and p not in registered_polymats) diff --git a/polymatrix/mixins/polymatrixmixin.py b/polymatrix/mixins/oldpolymatrixmixin.py index c569a22..dc33449 100644 --- a/polymatrix/mixins/polymatrixmixin.py +++ b/polymatrix/mixins/oldpolymatrixmixin.py @@ -5,7 +5,7 @@ import typing from matplotlib.pyplot import streamplot -class PolyMatrixMixin(abc.ABC): +class OldPolyMatrixMixin(abc.ABC): @property @abc.abstractmethod def name(self) -> str: diff --git a/polymatrix/mixins/optimizationmixin.py b/polymatrix/mixins/optimizationmixin.py index e44a36f..1a0febe 100644 --- a/polymatrix/mixins/optimizationmixin.py +++ b/polymatrix/mixins/optimizationmixin.py @@ -6,18 +6,17 @@ import itertools import more_itertools from sympy import Equivalent -from polymatrix.mixins.optimizationpipeopmixin import OptimizationPipeOpMixin -from polymatrix.mixins.optimizationstatemixin import OptimizationStateMixin +from polymatrix.exprcontainer import ExprContainer +from polymatrix.mixins.oldpolymatrixexprstatemixin import OldPolyMatrixExprStateMixin -from polymatrix.mixins.polymatrixmixin import PolyMatrixMixin -from polymatrix.polystruct import DegreeType +from polymatrix.oldpolymatrix import OldPolyMatrix from polymatrix.utils import monomial_to_index class OptimizationMixin(abc.ABC): @property @abc.abstractmethod - def state(self) -> OptimizationStateMixin: + def state(self) -> OldPolyMatrixExprStateMixin: ... @property @@ -39,45 +38,28 @@ class OptimizationMixin(abc.ABC): def n_var(self) -> int: return self.state.n_var - # @property - # def n_equality_constraints(self) -> int: - # if len(self.equality_constraints) == 0: - # return 0 - - # return max(eq for eq, _ in self.equality_constraints.items()) + 1 - - # @property - # def n_inequality_constraints(self) -> int: - # if len(self.inequality_constraints) == 0: - # return 0 - - # return max(eq for eq, _ in self.inequality_constraints.items()) + 1 - # # return max(key[0] for _, d_data in self.inequality_constraints.items() for key, _ in d_data.items()) + 1 - - # @property - # def n_auxillary_equality(self) -> int: - # if len(self.auxillary_equality) == 0: - # return 0 - - # return max(eq for eq, _ in self.auxillary_equality.items()) + 1 - # # return max(key[0] for _, d_data in self.auxillary_equality.items() for key, _ in d_data.items()) + 1 - # def pipe(self, *operators: OptimizationPipeOpMixin): # return functools.reduce(lambda obs, op: op(obs), operators, self) - def add_equality_constraints(self, expr: tuple[tuple[PolyMatrixMixin, ...], ...]): - for term in expr: + @staticmethod + def _get_equality_terms_from_expression( + expr: ExprContainer[OldPolyMatrix], + state: OldPolyMatrixExprStateMixin, + ) -> dict[tuple[int, tuple[int, ...], tuple[int, ...]], float]: + expr_list = expr.to_list() + + for _, term in expr_list: for left, right in itertools.pairwise(term): assert left.shape[1] == right.shape[0], f'{left} and {right} do not match' - all_polymats = tuple(polymat for term in expr for polymat in term) + all_polymats = tuple(polymat for _, term in expr_list for polymat in term) # update offsets with unseen polymats - state = self.state.update_offsets(all_polymats) + state = state.update_offsets(all_polymats) equality_constraint = collections.defaultdict(float) - for term in expr: + for _, term in expr_list: for degrees in itertools.product(*(polymat.degrees for polymat in term)): @@ -89,7 +71,7 @@ class OptimizationMixin(abc.ABC): # n_var = 2, degree = 3 # cominations = [(0, 0, 0), (0, 0, 1), (0, 1, 1), (1, 1, 1)] - for combination in itertools.combinations_with_replacement(range(self.n_var), total_degree): + for combination in itertools.combinations_with_replacement(range(state.n_var), total_degree): for x_monomial in more_itertools.distinct_permutations(combination): def acc_func(acc, v): @@ -108,7 +90,7 @@ class OptimizationMixin(abc.ABC): # (1,0) -> x2*x1 instead of (0,1)->x1*x2 if all(non_increasing(rel_x_monomial) for rel_x_monomial in rel_x_monomials): - col_defaults = [monomial_to_index(self.n_var, monom) for monom in rel_x_monomials] + col_defaults = [monomial_to_index(state.n_var, monom) for monom in rel_x_monomials] n_rows_col = itertools.chain((m.shape[0] for m in term), (term[-1].shape[1],)) @@ -131,7 +113,7 @@ class OptimizationMixin(abc.ABC): else: new_poly_row, new_poly_col, new_monom, factor = re_index - col = monomial_to_index(self.n_var, new_monom) + col = monomial_to_index(state.n_var, new_monom) if subs is not None: try: @@ -168,19 +150,38 @@ class OptimizationMixin(abc.ABC): continue poly_row = data[0][0] + poly_col = data[-1][1] p_monomial = tuple(sorted(d[2] for d in data if d[4] is None)) x_monomial_sorted = tuple(sorted(x_monomial)) - equality_constraint[poly_row, x_monomial_sorted, p_monomial] += value + equality_constraint[poly_row, poly_col, x_monomial_sorted, p_monomial] += value + + return equality_constraint, state + + @staticmethod + def _get_equality_equations_from_terms( + equality_terms: dict[tuple[int, int, tuple[int, ...], tuple[int, ...]], float], + ) -> dict[int, list[tuple[list[int], float]]]: + offset = 0 + equality_constraints = collections.defaultdict(list) - # eq_constr = collections.defaultdict(list) + for _, data in equality_terms.items(): + equation_set = set((poly_row, poly_col, x_monomial) for (poly_row, poly_col, x_monomial, _) in data.keys()) + to_eq_index_dict = {eq: offset + idx for idx, eq in enumerate(equation_set)} + offset += len(equation_set) - # for degree, d_data in eq_constr_buffer.items(): - # for (eq_idx, perm, p_monoms), val in d_data.items(): - # row = eq_to_rows[(eq_idx, perm)] - # eq_constr[row] += ((p_monoms, val),) + for (poly_row, poly_col, x_monomial, p_monomial), val in data.items(): + eq_index = to_eq_index_dict[(poly_row, poly_col, x_monomial)] + equality_constraints[eq_index] += ((p_monomial, val),) - # eq_data = dict(gen_eq_data()) + return equality_constraints + + def add_equality_constraints(self, expr: ExprContainer[OldPolyMatrix]): + + equality_constraint, state = self._get_equality_terms_from_expression( + expr=expr, + state=self.state + ) if len(self.equality_constraints) == 0: constraint_index = 0 @@ -193,9 +194,10 @@ class OptimizationMixin(abc.ABC): equality_constraints=self.equality_constraints | {constraint_index: equality_constraint}, ) - def add_inequality_constraints(self, expr): + def add_inequality_constraints(self, expr: ExprContainer[OldPolyMatrix]): + # all_polymats = tuple(polymat for term in expr for polymat in term) - polymat = expr[0][0] + polymat = expr.expr all_polymats = (polymat,) # update offsets with unseen polymats @@ -275,22 +277,11 @@ class OptimizationMixin(abc.ABC): return dataclasses.replace(self, inequality_constraints=ineq_constr_buffer, auxillary_equality=aux_eq_buffer, state=state) - def get_equality_constraints(self): - offset = 0 - equality_constraints = collections.defaultdict(list) - - for _, data in self.equality_constraints.items(): - equation_set = set((poly_row, x_monomial) for (poly_row, x_monomial, _) in data.keys()) - to_eq_index_dict = {eq: offset + idx for idx, eq in enumerate(equation_set)} - offset += len(equation_set) - - for (poly_row, x_monomial, p_monomial), val in data.items(): - eq_index = to_eq_index_dict[(poly_row, x_monomial)] - equality_constraints[eq_index] += ((p_monomial, val),) - - return equality_constraints - - def minimize(self, cost_func=None): + def minimize( + self, + cost: tuple[ExprContainer[OldPolyMatrix], ...], + t: float, + ): """ - assume sum of squares cost function on variables x - introduce nu/lambda for each equality/inequality @@ -303,10 +294,20 @@ class OptimizationMixin(abc.ABC): > r1 * r2 > P @ x = v """ + + state = [self.state] - state = self.state + def gen_terms(): + for idx, expr in enumerate(cost): + sum_of_squares, state[0] = self._get_equality_terms_from_expression( + expr=expr, + state=state[0] + ) + yield idx, sum_of_squares + # print(dict(gen_terms())) + sum_of_squares = self._get_equality_equations_from_terms(dict(gen_terms())) - equality_constraints = self.get_equality_constraints() + equality_constraints = self._get_equality_equations_from_terms(self.equality_constraints) n_equality_constraints = len(equality_constraints) @@ -323,7 +324,7 @@ class OptimizationMixin(abc.ABC): used_param_indices = set(param_idx for monomial_value_pairs in itertools.chain(equality_constraints.values(), self.inequality_constraints.values(), self.auxillary_equality.values()) for monomial, _ in monomial_value_pairs for param_idx in monomial) param_update = {monom: idx for idx, monom in enumerate(sorted(used_param_indices))} - assert max(used_param_indices) == state.n_param - 1, f'{max(used_param_indices)=} is not {state.n_param - 1=}' + assert max(used_param_indices) == state[0].n_param - 1, f'{max(used_param_indices)=} is not {state[0].n_param - 1=}' # param_indices = tuple(start + idx for start, end in state.offset_dict.values() for idx in range(end - start)) # print(tuple(m for m in monom_update_reverse if m not in param_indices)) @@ -331,11 +332,12 @@ class OptimizationMixin(abc.ABC): # the variables x are assumed to be the parameters of all registered polynomial matrices # todo: this would later come from a specific polynomial matrices - param_indices = tuple(param_update[start + idx] for start, end in state.offset_dict.values() for idx in range(end - start) if start + idx in used_param_indices) + param_indices = tuple(param_update[start + idx] for start, end in state[0].offset_dict.values() for idx in range(end - start) if start + idx in used_param_indices) equality_constraints = tuple((eq_index, tuple((tuple(param_update[m] for m in monom), val) for monom, val in monomial_value_pair)) for eq_index, monomial_value_pair in equality_constraints.items()) inequality_constraints = tuple((key, tuple((tuple(param_update[m] for m in monom), val) for monom, val in monom_val)) for key, monom_val in self.inequality_constraints.items()) auxillary_equality = tuple((key, tuple((tuple(param_update[m] for m in monom), val) for monom, val in monom_val)) for key, monom_val in self.auxillary_equality.items()) + sum_of_squares = tuple((key, tuple((tuple(param_update[m] for m in monom), val) for monom, val in monom_val)) for key, monom_val in sum_of_squares.items()) # introduce variable nu for each equality/inequality idx_nu = len(used_param_indices) @@ -357,7 +359,7 @@ class OptimizationMixin(abc.ABC): # > inequality constraints - r1^2 for eq, monom_val_list in inequality_constraints: - eq_buffer[current_eq_offset + eq] += monom_val_list + ((2 * (idx_r1 + eq,), -1),) + eq_buffer[current_eq_offset + eq] += monom_val_list + ((2 * (idx_r1 + eq,), -1),) # (tuple(), -0.1)) current_eq_offset += n_inequality_constraints # assert max(eq_buffer.keys()) < current_eq_offset @@ -372,25 +374,16 @@ class OptimizationMixin(abc.ABC): aux_variables = set(var for p_monomial, _ in aux_eq_data for var in p_monomial if var not in param_indices) variables = set(var for p_monomial, _ in aux_eq_data for var in p_monomial if var in param_indices) - # def gen_equation(): # eq1 = (x, a d_a x) # eq2 = (-1, a d_b x) for var in variables: - - # print(f'{var=}') # a x - b # ((a, x), (-b,)) for p_monomial, val in aux_eq_data: - - # print(f'{p_monomial=}') p_monomial_grp = dict(collections.Counter(p_monomial)) - # d_a, d_b - # for var, counter in p_monomial_grp.items(): - # if var in param_indices: - if var in p_monomial_grp: def generate_monom(): # for each variable in the monomial @@ -432,7 +425,6 @@ class OptimizationMixin(abc.ABC): yield dx_dict[var][aux_var] der_monomial_2 = tuple(generate_monom_2()) - # print(f'{der_monomial_2=}') if len(der_monomial_2): eq_buffer[current_eq_offset] += ((der_monomial_2, val * p_monomial_grp[aux_var]),) @@ -440,25 +432,14 @@ class OptimizationMixin(abc.ABC): # print(dx_dict) - # @dataclasses.dataclass - # class VariableIndexingState: - # index: int - - # def increment(self): - # return dataclasses.replace(self, index=self.index + 1), self.index - def differentiate(data, var, dx_dict): eq_buffer = tuple() - - # print(f'{var=}') for p_monomial, val in data: # count powers for each variable p_monomial_grp = dict(collections.Counter(p_monomial)) - # print(f'{p_monomial=}') - # for var, counter in p_monomial_grp.items(): if var in p_monomial_grp: def generate_monom(): @@ -473,7 +454,7 @@ class OptimizationMixin(abc.ABC): eq_buffer += (( tuple(generate_monom()), - -val * p_monomial_grp[var], + val * p_monomial_grp[var], ),) if var in dx_dict: @@ -490,24 +471,12 @@ class OptimizationMixin(abc.ABC): yield i_var yield dx_dict[var][aux_var] - - # der_monomial = tuple(generate_monom()) - - # if 1 < len(der_monomial): - # aux_eq_buffer += (( - # (der_monomial, 1), ((index_buffer[0],), -1) - # ),) - # variable_indices = (index_buffer[0],) - # else: - # variable_indices = der_monomial eq_buffer += (( tuple(generate_monom()), - -val * p_monomial_grp[aux_var], + val * p_monomial_grp[aux_var], ),) - # index_buffer[0] += 1 - return eq_buffer def reduce_to_quadratic_equation(eq, index): @@ -518,9 +487,6 @@ class OptimizationMixin(abc.ABC): for monomial, val in eq: n_aux = len(monomial) - 2 - # print(f'{monomial=}') - # print(f'{n_aux=}') - if 0 < n_aux: eq_buffer += ((monomial[0:1] + (index_buffer[0],), val),) @@ -544,62 +510,43 @@ class OptimizationMixin(abc.ABC): # > x + nu * equality constraint + lambda * inequality constraint # --------------------------------------------------------------- + # print(sum_of_squares) + for index, param in enumerate(param_indices): - eq_buffer[current_eq_offset + index] += (((param,), 1),) + # print(param) + def gen_cost_terms(): + for _, data in sum_of_squares: + equation = differentiate(data, param, {}) + for d_monomials, d_val in equation: + for monomials, val in data: + yield monomials + d_monomials, val * d_val + + eq_buffer[current_eq_offset + index] += tuple(gen_cost_terms()) + + # eq_buffer[current_eq_offset + index] += (((param,), 1),) # differentiate equality constraints for each variable x for eq_constr_idx, eq_data in equality_constraints: for var in param_indices: - equation = differentiate(eq_data, var, dx_dict) + equation = differentiate(eq_data, var, dx_dict) equation = tuple((monomials + (idx_nu + eq_constr_idx,), val) for monomials, val in equation) - equation, aux_equations, idx_dx[0] = reduce_to_quadratic_equation(equation, idx_dx[0]) if len(equation): eq_idx = param_indices.index(var) - # print(f'{equation=}') - eq_buffer[current_eq_offset + eq_idx] += equation - - # # print(f'{aux_equations=}') - # for aux_eq in aux_equations: - # eq_buffer[next_current_eq_offset] = aux_eq - # next_current_eq_offset += 1 - - # for p_monomial, val in ineq_data: - - # p_monomial_grp = dict(collections.Counter(p_monomial)) - - # for var, counter in p_monomial_grp.items(): - # if var in param_indices: - # def generate_monom(): - # for i_m, i_counter in p_monomial_grp.items(): - # if var is i_m: - # sel_counter = i_counter - 1 - # else: - # sel_counter = i_counter - - # for _ in range(sel_counter): - # yield i_m - - # eq_idx = param_indices.index(var) - # der_monomial = tuple(generate_monom()) + (idx_nu + eq_constr_idx,) - # eq_buffer[current_eq_offset + eq_idx] += ((der_monomial, val * counter),) + eq_buffer[current_eq_offset + eq_idx] += equation next_current_eq_offset = current_eq_offset + len(param_indices) # differentiate inequality constraints for each variable x for ineq_constr_idx, ineq_data in inequality_constraints: - # aux_variables = set(var for p_monomial, _ in ineq_data for var in p_monomial if var not in param_indices) - # variables = set(var for p_monomial, _ in ineq_data for var in p_monomial if var in param_indices) for var in param_indices: - equation = differentiate(ineq_data, var, dx_dict) - - equation = tuple((monomials + (idx_lambda + ineq_constr_idx,), val) for monomials, val in equation) + equation = differentiate(ineq_data, var, dx_dict) + equation = tuple((monomials + (idx_lambda + ineq_constr_idx,), -val) for monomials, val in equation) equation, aux_equations, idx_dx[0] = reduce_to_quadratic_equation(equation, idx_dx[0]) - # idx_dx[0] = index if len(equation): eq_idx = param_indices.index(var) @@ -611,50 +558,6 @@ class OptimizationMixin(abc.ABC): eq_buffer[next_current_eq_offset] = aux_eq next_current_eq_offset += 1 - # for p_monomial, val in ineq_data: - - # # count powers for each variable - # p_monomial_grp = dict(collections.Counter(p_monomial)) - - # # for var, counter in p_monomial_grp.items(): - # if var in p_monomial_grp: - # def generate_monom(): - # for i_var, i_counter in p_monomial_grp.items(): - # if var is i_var: - # sel_counter = i_counter - 1 - # else: - # sel_counter = i_counter - - # for _ in range(sel_counter): - # yield i_var - - # eq_idx = param_indices.index(var) - # der_monomial = tuple(generate_monom()) + (idx_lambda + ineq_constr_idx,) - # eq_buffer[current_eq_offset + eq_idx] += ((der_monomial, -val * counter),) - - # if var in dx_dict: - # for aux_var in dx_dict[var]: - # if aux_var in p_monomial_grp: - # def generate_monom(): - # for i_var, i_counter in p_monomial_grp.items(): - # if i_var is aux_var: - # sel_counter = i_counter - 1 - # else: - # sel_counter = i_counter - - # for _ in range(sel_counter): - # yield i_var - - # yield dx_dict[var][aux_var] - - # eq_idx = param_indices.index(var) - # der_monomial_2 = tuple(generate_monom()) - # eq_buffer[next_current_eq_offset] = ((der_monomial_2, 1), ((idx_dx[0],), -1)) - # next_current_eq_offset += 1 - - # eq_buffer[current_eq_offset + eq_idx] += (((idx_lambda + ineq_constr_idx, idx_dx[0]), -val * p_monomial_grp[aux_var]),) - # idx_dx[0] += 1 - # current_eq_offset += len(param_indices) current_eq_offset = next_current_eq_offset @@ -669,11 +572,22 @@ class OptimizationMixin(abc.ABC): # assert max(eq_buffer.keys()) < current_eq_offset assert max(eq_buffer.keys()) == current_eq_offset - 1 - # > r1 * r2 + next_current_eq_offset = current_eq_offset + n_inequality_constraints + # # > r1 * r2 + # for idx in range(n_inequality_constraints): + # eq_buffer[current_eq_offset + idx] += (((idx_r1 + idx, idx_r2 + idx), 1),) + + # > r1^2 * lambda for idx in range(n_inequality_constraints): - eq_buffer[current_eq_offset + idx] += (((idx_r1 + idx, idx_r2 + idx), 1),) + eq_buffer[next_current_eq_offset] += (((idx_dx[0],), 1), (2 * (idx_r1 + idx,), -1)) + next_current_eq_offset += 1 + + eq_buffer[current_eq_offset + idx] += (((idx_lambda + idx, idx_dx[0]), 1), (tuple(), -1/t)) + idx_dx[0] += 1 + + # current_eq_offset += n_inequality_constraints + current_eq_offset = next_current_eq_offset - current_eq_offset += n_inequality_constraints # assert max(eq_buffer.keys()) < current_eq_offset assert max(eq_buffer.keys()) == current_eq_offset - 1 diff --git a/polymatrix/mixins/optimizationpipeopmixin.py b/polymatrix/mixins/optimizationpipeopmixin.py deleted file mode 100644 index a90c193..0000000 --- a/polymatrix/mixins/optimizationpipeopmixin.py +++ /dev/null @@ -1,12 +0,0 @@ -import abc -import typing - - -class OptimizationPipeOpMixin(abc.ABC): - @property - @abc.abstractmethod - def func(self) -> typing.Callable[[typing.Any], typing.Any]: - ... - - def __call__(self, source: typing.Any): - return self.func(source) diff --git a/polymatrix/mixins/scalarmultexprmixin.py b/polymatrix/mixins/scalarmultexprmixin.py new file mode 100644 index 0000000..ec98722 --- /dev/null +++ b/polymatrix/mixins/scalarmultexprmixin.py @@ -0,0 +1,14 @@ +import abc +from polymatrix.expression.mixins.expressionbasemixin import ExpressionBaseMixin + + +class ScalarMultExprMixin(ExpressionBaseMixin, abc.ABC): + @property + @abc.abstractmethod + def left(self) -> float: + ... + + @property + @abc.abstractmethod + def right(self) -> ExpressionBaseMixin: + ... diff --git a/polymatrix/mixins/statemonadmixin.py b/polymatrix/mixins/statemonadmixin.py new file mode 100644 index 0000000..c90ebc8 --- /dev/null +++ b/polymatrix/mixins/statemonadmixin.py @@ -0,0 +1,18 @@ +import abc +import typing + + +StateType = typing.TypeVar('StateType') +ValueType = typing.TypeVar('ValueType') + +class StateMonadMixin( + # typing.Generic[StateType, ValueType], + abc.ABC, +): + @abc.abstractmethod + def apply(self, state: StateType) -> tuple[StateType, ValueType]: + ... + + # def __apply__(self, state: StateType) -> ValueType: + # _, value = self.state_func(state) + # return value diff --git a/polymatrix/multexpr.py b/polymatrix/multexpr.py new file mode 100644 index 0000000..568bbf8 --- /dev/null +++ b/polymatrix/multexpr.py @@ -0,0 +1,4 @@ +from polymatrix.mixins.multexprmixin import MultExprMixin + +class MultExpr(MultExprMixin): + pass diff --git a/polymatrix/oldpolymatrix.py b/polymatrix/oldpolymatrix.py new file mode 100644 index 0000000..409680d --- /dev/null +++ b/polymatrix/oldpolymatrix.py @@ -0,0 +1,6 @@ +from polymatrix.expression.mixins.expressionbasemixin import ExpressionBaseMixin +from polymatrix.mixins.oldpolymatrixmixin import OldPolyMatrixMixin + + +class OldPolyMatrix(OldPolyMatrixMixin): + pass diff --git a/polymatrix/oldpolymatrixexprstate.py b/polymatrix/oldpolymatrixexprstate.py new file mode 100644 index 0000000..1397f9e --- /dev/null +++ b/polymatrix/oldpolymatrixexprstate.py @@ -0,0 +1,5 @@ +from polymatrix.mixins.oldpolymatrixexprstatemixin import OldPolyMatrixExprStateMixin + + +class OldPolyMatrixExprState(OldPolyMatrixExprStateMixin): + pass diff --git a/polymatrix/optimizationstate.py b/polymatrix/optimizationstate.py deleted file mode 100644 index 775e976..0000000 --- a/polymatrix/optimizationstate.py +++ /dev/null @@ -1,5 +0,0 @@ -from polymatrix.mixins.optimizationstatemixin import OptimizationStateMixin - - -class OptimizationState(OptimizationStateMixin): - pass diff --git a/polymatrix/polymatrix.py b/polymatrix/polymatrix.py deleted file mode 100644 index ff43af5..0000000 --- a/polymatrix/polymatrix.py +++ /dev/null @@ -1,5 +0,0 @@ -from polymatrix.mixins.polymatrixmixin import PolyMatrixMixin - - -class PolyMatrix(PolyMatrixMixin): - pass diff --git a/polymatrix/polymatrixaddexpr.py b/polymatrix/polymatrixaddexpr.py new file mode 100644 index 0000000..5d4f567 --- /dev/null +++ b/polymatrix/polymatrixaddexpr.py @@ -0,0 +1,4 @@ +from polymatrix.expression.mixins.additionexprmixin import AddExprMixin + +class PolyMatrixAddExpr(AddExprMixin): + pass diff --git a/polymatrix/polymatrixarrayexpr.py b/polymatrix/polymatrixarrayexpr.py new file mode 100644 index 0000000..c9b572d --- /dev/null +++ b/polymatrix/polymatrixarrayexpr.py @@ -0,0 +1,4 @@ +from polymatrix.expression.mixins.fromarrayexprmixin import FromArrayExprMixin + +class PolyMatrixArrayExpr(FromArrayExprMixin): + pass diff --git a/polymatrix/polymatrixexpr.py b/polymatrix/polymatrixexpr.py new file mode 100644 index 0000000..74e8757 --- /dev/null +++ b/polymatrix/polymatrixexpr.py @@ -0,0 +1,4 @@ +from polymatrix.expression.mixins.expressionmixin import ExpressionMixin + +class PolyMatrixExpr(ExpressionMixin): + pass diff --git a/polymatrix/polymatrixexprstate.py b/polymatrix/polymatrixexprstate.py new file mode 100644 index 0000000..11419cb --- /dev/null +++ b/polymatrix/polymatrixexprstate.py @@ -0,0 +1,4 @@ +from polymatrix.expression.mixins.expressionstatemixin import ExpressionStateMixin + +class PolyMatrixExprState(ExpressionStateMixin): + pass diff --git a/polymatrix/polymatrixmultexpr.py b/polymatrix/polymatrixmultexpr.py new file mode 100644 index 0000000..6b7f997 --- /dev/null +++ b/polymatrix/polymatrixmultexpr.py @@ -0,0 +1,4 @@ +from polymatrix.expression.mixins.matrixmultexprmixin import MatrixMultExprMixin + +class PolyMatrixMultExpr(MatrixMultExprMixin): + pass diff --git a/polymatrix/polymatrixparamexpr.py b/polymatrix/polymatrixparamexpr.py new file mode 100644 index 0000000..f396bc9 --- /dev/null +++ b/polymatrix/polymatrixparamexpr.py @@ -0,0 +1,4 @@ +from polymatrix.expression.mixins.parametrizetermsexprmixin import ParametrizeTermsExprMixin + +class PolyMatrixParamExpr(ParametrizeTermsExprMixin): + pass diff --git a/polymatrix/polysolver.py b/polymatrix/polysolver.py index 1f7bc8e..2cb9b7b 100644 --- a/polymatrix/polysolver.py +++ b/polymatrix/polysolver.py @@ -276,7 +276,9 @@ def outer_smart_solve(data, n_iter=10, a_max=1.0, irange=None, idegree=None): subs_data = substitude_x_add_a(data, a[-1]) sol = solve_poly_system(subs_data, 6) - error_index = np.max(np.abs(eval_solution(subs_data, sol))) + max(a[-1]) + + error_index = np.max(np.abs(eval_solution(data, a[-1] + sol))) + max(a[-1]) + # error_index = np.max(np.abs(eval_solution(subs_data, sol))) + max(a[-1]) # error_index = np.max(np.abs(eval_solution(subs_data, sol))) except: diff --git a/polymatrix/polystruct.py b/polymatrix/polystruct.py deleted file mode 100644 index 808b7ab..0000000 --- a/polymatrix/polystruct.py +++ /dev/null @@ -1,480 +0,0 @@ -import abc -import collections -import typing -import numpy as np -import dataclasses -import dataclass_abc -import scipy.sparse -import itertools -import functools -import more_itertools - -import polymatrix.utils - -DegreeType = int -# CoordType = tuple[int, int] -# SubsDictType = dict[DegreeType, dict[CoordType, float]] - -######################################## -# Mixins -######################################## - -class PolyMatrixMixin(abc.ABC): - @property - @abc.abstractmethod - def degrees(self) -> list[int]: - ... - - @property - @abc.abstractmethod - def subs(self) -> dict[DegreeType, dict[int, int, float]]: - ... - - @property - @abc.abstractmethod - def re_index(self) -> typing.Callable[[int, int, int, tuple[int, ...]], tuple[int, int, int, tuple[int, ...], float]]: - ... - - @property - @abc.abstractmethod - def is_constant(self) -> int: - ... - - @property - @abc.abstractmethod - def shape(self) -> tuple[int, int]: - ... - - -class State(abc.ABC): - @property - @abc.abstractmethod - def n_param(self) -> int: - ... - - @property - @abc.abstractmethod - def offset_dict(self) -> dict[tuple[PolyMatrixMixin, int], int]: - ... - - @property - @abc.abstractmethod - def local_index_dict(self) -> dict[tuple[PolyMatrixMixin, int], dict[int, int]]: - ... - - @property - @abc.abstractmethod - def eq_constraints(self) -> dict[int, dict[tuple[int, int], float]]: - ... - - @property - @abc.abstractmethod - def ineq_constraints(self) -> dict[int, dict[tuple[int, int], float]]: - ... - - - -class PolyExpressionMixin(abc.ABC): - @property - @abc.abstractmethod - def data(self) -> dict[int, dict[tuple[int, int], float]]: - ... - - @property - @abc.abstractmethod - def n_var(self) -> int: - ... - - @property - @abc.abstractmethod - def n_eq(self): - ... - - # @property - # @abc.abstractmethod - # def n_param(self) -> int: - # ... - - # @property - # @abc.abstractmethod - # def offset_dict(self) -> dict[tuple[PolyMatrixMixin, int], int]: - # ... - - -class OptimizationMixin(abc.ABC): - @property - @abc.abstractmethod - def cost_function(self) -> dict[int, dict[int, float]]: - ... - - @property - @abc.abstractmethod - def eq_constraints(self) -> dict[int, dict[tuple[int, int], float]]: - ... - - @property - @abc.abstractmethod - def ineq_constraints(self) -> dict[int, dict[tuple[int, int], float]]: - ... - - @property - @abc.abstractmethod - def n_var(self) -> int: - ... - - # @property - # @abc.abstractmethod - # def n_param(self) -> int: - # ... - - @property - @abc.abstractmethod - def n_eq_constraints(self): - ... - - @property - @abc.abstractmethod - def n_ineq_constraints(self): - ... - - # @property - # @abc.abstractmethod - # def offset_dict(self) -> dict[tuple[PolyMatrixMixin, int], int]: - # ... - - def create(self) -> PolyExpressionMixin: - """ - - adds nu and lambda for each equality and inequality - - lambda - r_lambda = 0 for each inequality - - lambda r_ineq = 0 for each inequality - - add vanishing gradient - """ - - pass - - def add_positive_definiteness_condition(self, key): - pass - - -class PolyMatrixEquationMixin(abc.ABC): - @property - @abc.abstractmethod - def terms(self) -> list[tuple[PolyMatrixMixin, PolyMatrixMixin]]: - """ - the terms the polynomial matrix equation consists of - """ - - ... - - @property - @abc.abstractmethod - def n_var(self) -> int: - """ - number of variables defining the polynomials - - for example n_var=3: x1, x2 and x3 - """ - - ... - - @property - @abc.abstractmethod - def monom_to_index(self) -> typing.Callable[[int, tuple[int, ...]], int]: - ... - - def create( - self, - subs: dict[PolyMatrixMixin, dict[DegreeType, dict[int, int, float]]] = None, - ) -> PolyExpressionMixin: - if subs is None: - added_subs = {} - else: - added_subs = subs - - # create parameter offset - all_structs = set(indexed_poly_mat for term in self.terms for indexed_poly_mat in term) - - def gen_n_param_per_struct(): - - for struct in all_structs: - - if struct.is_constant: - continue - - for degree in struct.degrees: - number_of_terms = int(struct.shape[0] * struct.shape[1] * (self.monom_to_index(self.n_var, degree*(self.n_var-1,)) + 1)) - yield (struct, degree), number_of_terms - - # param_list = list(gen_n_param_per_struct()) - param_key, param_value = list(zip(*gen_n_param_per_struct())) - cum_sum = list(itertools.accumulate(param_value)) - offset_dict = dict(zip(param_key, [0] + cum_sum[:-1])) - - # # create parameter offset - # all_structs = set(indexed_poly_mat for term in self.terms for indexed_poly_mat in term) - - def gen_substitutions(): - for struct in all_structs: - added_struct_subs = added_subs.get(struct, None) - - if added_struct_subs is not None: - if struct.subs is not None: - def gen_merged_subs(): - for degree in struct.degrees: - all_subs = struct.subs.get(degree, {}) | added_struct_subs.get(degree, {}) - yield degree, all_subs - - all_subs = dict(gen_merged_subs()) - - else: - all_subs = added_struct_subs - - else: - if struct.subs is not None: - all_subs = struct.subs - - else: - all_subs = None - - yield struct, all_subs - - subs_dict = dict(gen_substitutions()) - - eq_constr_buffer = collections.defaultdict(lambda: collections.defaultdict(float)) - - def gen_re_indexing(term, degrees, curr_rows_col, monoms, col_defaults, d_subs, d_offsets, perm): - for m, degree, (poly_row, poly_col), monom, col_default, subs, offset in zip( - term, degrees, itertools.pairwise(curr_rows_col), monoms, col_defaults, d_subs, d_offsets): - - if m.re_index is not None: - re_index = m.re_index(degree, poly_row, poly_col, monom) - else: - re_index = None - - if re_index is None: - col = col_default - new_poly_row = poly_row - new_poly_col = poly_col - factor = 1.0 - - else: - new_poly_row, new_poly_col, new_monom, factor = re_index - col = self.monom_to_index(self.n_var, new_monom) - - if subs is not None: - try: - subs_val = subs[(new_poly_row, new_poly_col, col)] - except KeyError: - subs_val = None - else: - subs_val = None - - if subs_val is None: - # the coefficient is selected after the reindexing - - row = new_poly_row + new_poly_col * m.shape[0] - - # linearize parameter matrix - param_idx = int(offset + row + col * m.shape[0] * m.shape[1]) - - else: - param_idx = None - - yield poly_row, poly_col, param_idx, factor, subs_val - - for term in self.terms: - - term_subs = [subs_dict[m] for m in term] - # n_matrices = len(term) - - for degrees in itertools.product(*(m.degrees for m in term)): - total_degree = sum(degrees) - d_subs = [subs[degree] if subs is not None and degree in subs else None for degree, subs in zip(degrees, term_subs)] - d_offsets = [offset_dict.get((m, degree), 0) for m, degree in zip(term, degrees)] - - for combination in itertools.combinations_with_replacement(range(self.n_var), total_degree): - # n_var = 2, degree = 3 - # cominations = [(0, 0, 0), (0, 0, 1), (0, 1, 1), (1, 1, 1)] - - for monom in more_itertools.distinct_permutations(combination): - - def acc_func(acc, v): - last, _ = acc - new = last + v - - return new, monom[last:new] - - # monom=(1, 0, 1) -> monom1=(x2, x1), monom2=(x2) - monoms = list(monom for _, monom in itertools.accumulate(degrees, acc_func, initial=(0, None)))[1:] - - def non_increasing(seq): - return all(y <= x for x, y in zip(seq, seq[1:])) - - # (1,0) -> x2*x1 instead of (0,1)->x1*x2 - if all(non_increasing(monom) for monom in monoms): - - col_defaults = [self.monom_to_index(self.n_var, monom) for monom in monoms] - - n_rows_col = itertools.chain((m.shape[0] for m in term), (term[-1].shape[1],)) - - for curr_rows_col in itertools.product(*[range(e) for e in n_rows_col]): - - data = tuple(gen_re_indexing(term, degrees, curr_rows_col, monoms, col_defaults, d_subs, d_offsets, monom)) - - total_factor = functools.reduce(lambda x, y: x*y, (d[3] for d in data)) - - if total_factor == 0: - continue - - value = functools.reduce(lambda x, y: x*y, (d[4] for d in data if d[4] is not None), 1) * total_factor - - if value == 0: - continue - - poly_row = data[0][0] - param_idx = tuple(d[2] for d in data if d[4] is None) - degree = len(param_idx) - - eq_constr_buffer[degree][poly_row, monom, param_idx] += value - - # assign equations - rows_perm_set = set((eq_idx, perm) for eq_tuple_degree in eq_constr_buffer.values() for (eq_idx, perm, _) in eq_tuple_degree.keys()) - eq_to_rows = {eq: idx for idx, eq in enumerate(rows_perm_set)} - - # # calculate offset - # monom_update_reverse = sorted(set(m for eq_tuple_degree in eq_constr_buffer.values() for (_, _, monoms) in eq_tuple_degree.keys() for m in monoms)) - # monom_update = {monom: idx for idx, monom in enumerate(monom_update_reverse)} - - # def gen_n_cum_sum(): - # groups = itertools.groupby(monom_update_reverse, lambda v: next((i for i, g in enumerate(cum_sum) if v < g))) - # for _, group in groups: - # yield sum(1 for _ in group) - - # n_cum_sum = list(itertools.accumulate(gen_n_cum_sum())) - # n_offset_dict = dict(zip(param_key, [0] + n_cum_sum[:-1])) - # n_param = n_cum_sum[-1] - - # def gen_eq_data(): - # for degree, d_data in eq_constr_buffer.items(): - # def gen_eq_degree_data(): - # for (eq_idx, perm, monoms), val in d_data.items(): - # row = eq_to_rows[(eq_idx, perm)] - # monoms_updated = tuple(monom_update[m] for m in monoms) - # # print(f'{n_param=}') - # col = self.monom_to_index(n_param, monoms_updated) - # yield (row, col), val - - # yield degree, dict(gen_eq_degree_data()) - - # eq_data = dict(gen_eq_data()) - - def gen_eq_data(): - for degree, d_data in eq_constr_buffer.items(): - def gen_eq_degree_data(): - for (eq_idx, perm, monoms), val in d_data.items(): - row = eq_to_rows[(eq_idx, perm)] - # monoms_updated = tuple(monom_update[m] for m in monoms) - # col = self.monom_to_index(n_param, monoms_updated) - yield (row, monoms), val - - yield degree, dict(gen_eq_degree_data()) - - eq_data = dict(gen_eq_data()) - - return PolyEquationImpl( - data=eq_data, - n_param=cum_sum[-1], - n_eq=len(eq_to_rows), - n_var=self.n_var, - offset_dict=offset_dict, - ) - -######################################## -# Classes -######################################## - -class PolyMatrix(PolyMatrixMixin): - pass - - -class PolyEquation(PolyExpressionMixin): - pass - - -class PolyMatrixEquation(PolyMatrixEquationMixin): - pass - - -######################################## -# Implementations -######################################## - -@dataclass_abc.dataclass_abc(frozen=True, eq=False) -class PolyMatrixImpl(PolyMatrix): - degrees: list[int] - subs: dict[int, dict[tuple[int, int], float]] - re_index: typing.Callable[[int, int, int, tuple[int, ...]], tuple[int, int, int, tuple[int, ...], float]] - is_constant: bool - shape: tuple[int, int] - - -@dataclass_abc.dataclass_abc(frozen=True) -class PolyEquationImpl(PolyEquation): - data: dict[int, dict[tuple[int, tuple, int], float]] - offset_dict: dict[tuple[PolyMatrixMixin, int], int] - n_param: int - n_eq: int - n_var: int - - -@dataclass_abc.dataclass_abc(frozen=True) -class PolyMatrixEquationImpl(PolyMatrixEquation): - terms: list[tuple[PolyMatrix, PolyMatrix]] - monom_to_index: typing.Callable[[int, tuple[int, ...]], int] - n_var: int - -######################################## -# init functions -######################################## - -def init_poly_matrix( - shape: tuple[int, int], - degrees: list[int] = None, - subs: dict[int, dict[tuple[int, int], float]] = None, - re_index: typing.Callable[[int, int, int, tuple[int, ...]], tuple[int, int, int, tuple[int, ...], float]] = None, - is_constant: bool = None, -): - if degrees is None: - assert isinstance(subs, dict) - degrees = list(subs.keys()) - - if is_constant is None: - if subs is None: - is_constant = False - else: - is_constant = True - - return PolyMatrixImpl( - degrees=degrees, - subs=subs, - re_index=re_index, - is_constant=is_constant, - shape=shape, - ) - - -def init_equation( - n_var: int, - terms: list[tuple[PolyMatrix, PolyMatrix]], - monom_to_index: typing.Callable[[int, tuple[int, ...]], int] = None, -): - # assert all(not left.is_vector and right.is_vector for left, right in terms) - - if monom_to_index is None: - monom_to_index = polymatrix.utils.variable_to_index - - return PolyMatrixEquationImpl( - n_var=n_var, - terms=terms, - monom_to_index=monom_to_index, - ) diff --git a/polymatrix/scalarmultexpr.py b/polymatrix/scalarmultexpr.py new file mode 100644 index 0000000..3d9a075 --- /dev/null +++ b/polymatrix/scalarmultexpr.py @@ -0,0 +1,4 @@ +from polymatrix.mixins.scalarmultexprmixin import ScalarMultExprMixin + +class ScalarMultExpr(ScalarMultExprMixin): + pass diff --git a/polymatrix/statemonad.py b/polymatrix/statemonad.py index 9be3b61..3054160 100644 --- a/polymatrix/statemonad.py +++ b/polymatrix/statemonad.py @@ -14,6 +14,7 @@ class StateMonad(Generic[U, State]): return cls(lambda state: (value, state)) def map(self, fn: Callable[[U], V]) -> 'StateMonad[V, State]': + def internal_map(state: State) -> Tuple[U, State]: val, n_state = self._fn(state) return fn(val), n_state @@ -24,7 +25,6 @@ class StateMonad(Generic[U, State]): def internal_map(state: State) -> Tuple[V, State]: val, n_state = self._fn(state) - return fn(val).run(n_state) return StateMonad(internal_map) |