feat: Add CVXOPT solver infrastructure and VSCode settings

- Add CVXOPT dependency to pyproject.toml and uv.lock
- Create solver module with GLPK-based integer linear programming solver
- Add VSCode Python analysis settings
- Implement matrix and sparse matrix wrappers for CVXOPT
- Add GLPK solver wrapper with type-safe interfaces

app/solver/_wrap/__init__.py

@@ -0,0 +1,184 @@
+"""
+See also:
+    https://github.com/cvxopt/cvxopt/blob/master/src/C/base.c
+"""
+
+from typing import (
+    Any,
+    BinaryIO,
+    Generic,
+    Literal,
+    Optional,
+    Protocol,
+    Sequence,
+    Tuple,
+    TypeVar,
+    Union,
+    overload,
+)
+
+import numpy as np
+from cvxopt import matrix as cvxopt_matrix
+from cvxopt import sparse as cvxopt_sparse
+from cvxopt import spmatrix as cvxopt_spmatrix
+from numpy.typing import NDArray
+from typing_extensions import Self, TypeAlias
+
+Typecode: TypeAlias = Literal["i", "d", "z"]
+# Integer sparse matrices are not implemented.
+SparseTypecode: TypeAlias = Literal["d", "z"]
+DenseT = TypeVar("DenseT", int, float, complex)
+SparseT = TypeVar("SparseT", float, complex)
+IndexType = Union[int, slice, Sequence[int], "Matrix[int]"]
+
+
+class Matrix(Generic[DenseT], Protocol):
+    """
+    cvxopt.matrix interface
+    """
+
+    @property
+    def size(self) -> Tuple[int, int]: ...
+
+    @property
+    def typecode(self) -> Typecode: ...
+
+    def __mul__(self, other): ...
+    def __add__(self, other): ...
+    def __sub__(self, other): ...
+    def __truediv__(self, other): ...
+    def __mod__(self, other): ...
+    def __len__(self) -> int: ...
+
+    def transpose(self) -> Self: ...
+    def ctrans(self) -> Self: ...
+    def real(self) -> "Matrix[float]": ...
+    def imag(self) -> "Matrix[float]": ...
+
+    def tofile(self, f: BinaryIO) -> None: ...
+    def fromfile(self, f: BinaryIO) -> None: ...
+
+    def __getitem__(
+        self, index: Union[IndexType, Tuple[IndexType, IndexType]]
+    ) -> Union[DenseT, Self]: ...
+    def __setitem__(
+        self,
+        index: Union[IndexType, Tuple[IndexType, IndexType]],
+        value: Union[DenseT, "Matrix[Any]"],
+    ) -> None: ...
+
+
+@overload
+def matrix(
+    data: Any, size: Optional[Tuple[int, int]] = None, tc: Typecode = "d"
+) -> Matrix[float]: ...
+
+
+@overload
+def matrix(
+    data: Any, size: Optional[Tuple[int, int]] = None, tc: Typecode = "i"
+) -> Matrix[int]: ...
+
+
+@overload
+def matrix(
+    data: Any, size: Optional[Tuple[int, int]] = None, tc: Typecode = "z"
+) -> Matrix[complex]: ...
+
+
+def matrix(data: Any, size: Optional[Tuple[int, int]] = None, tc: Typecode = "d"):
+    if size is None:
+        return cvxopt_matrix(data, tc=tc)
+    return cvxopt_matrix(data, size=size, tc=tc)
+
+
+class SparseMatrix(Generic[SparseT], Protocol):
+    """
+    cvxopt.spmatrix interface
+    """
+
+    @property
+    def size(self) -> Tuple[int, int]: ...
+
+    @property
+    def typecode(self) -> Typecode: ...
+
+    @property
+    def V(self) -> "Matrix[SparseT]": ...
+
+    @property
+    def I(self) -> "Matrix[int]": ...
+
+    @property
+    def J(self) -> "Matrix[int]": ...
+
+    @property
+    def CCS(self) -> "Matrix[int]": ...
+
+    def __mul__(self, other): ...
+    def __add__(self, other): ...
+    def __sub__(self, other): ...
+    def __truediv__(self, other): ...
+    def __mod__(self, other): ...
+    def __len__(self) -> int: ...
+
+    def transpose(self) -> Self: ...
+    def ctrans(self) -> Self: ...
+    def real(self) -> "Matrix[float]": ...
+    def imag(self) -> "Matrix[float]": ...
+
+    def tofile(self, f: BinaryIO) -> None: ...
+    def fromfile(self, f: BinaryIO) -> None: ...
+
+    def __getitem__(
+        self, index: Union[IndexType, Tuple[IndexType, IndexType]]
+    ) -> Union[DenseT, Self]: ...
+    def __setitem__(
+        self,
+        index: Union[IndexType, Tuple[IndexType, IndexType]],
+        value: Union[DenseT, "Matrix[Any]"],
+    ) -> None: ...
+
+
+@overload
+def spmatrix(
+    x: Union[Sequence[float], float, Matrix[float], NDArray[np.floating[Any]]],
+    I: Union[Sequence[int], NDArray[np.int_]],
+    J: Union[Sequence[int], NDArray[np.int_]],
+    size: Optional[Tuple[int, int]] = None,
+    tc: SparseTypecode = "d",
+) -> SparseMatrix[float]: ...
+
+
+@overload
+def spmatrix(
+    x: Union[
+        Sequence[complex], complex, Matrix[complex], NDArray[np.complexfloating[Any]]
+    ],
+    I: Union[Sequence[int], NDArray[np.int_]],
+    J: Union[Sequence[int], NDArray[np.int_]],
+    size: Optional[Tuple[int, int]] = None,
+    tc: SparseTypecode = "z",
+) -> SparseMatrix[complex]: ...
+
+
+def spmatrix(
+    x: Any,
+    I: Any,
+    J: Any,
+    size: Optional[Tuple[int, int]] = None,
+    tc: SparseTypecode = "d",
+):
+    if size is None:
+        return cvxopt_spmatrix(x, I, J, tc=tc)
+    return cvxopt_spmatrix(x, I, J, size=size, tc=tc)
+
+
+@overload
+def sparse(x: Any, tc: SparseTypecode = "d") -> SparseMatrix[float]: ...
+@overload
+def sparse(x: Any, tc: SparseTypecode = "z") -> SparseMatrix[complex]: ...
+
+
+def sparse(x: Any, tc: SparseTypecode = "d"):
+    return cvxopt_sparse(x, tc=tc)