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feat: Add CVXOPT solver infrastructure and VSCode settings

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- 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
This commit is contained in:
crosstyan
2025-03-03 17:27:42 +08:00
parent f0f71f7f81
commit 39da7992d4
6 changed files with 702 additions and 0 deletions
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4
.vscode/settings.json vendored Normal file
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{
"python.analysis.typeCheckingMode": "basic",
"python.analysis.autoImportCompletions": true
}

227
app/solver/__init__.py Normal file
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import itertools
from abc import abstractmethod
from collections import defaultdict
from typing import Tuple, override
import numpy as np
from app._typing import NDArray
from ._wrap import matrix, spmatrix
from ._wrap.glpk import ilp
from ._wrap.glpk import set_global_options as set_glpk_options
set_glpk_options({"msg_lev": "GLP_MSG_ERR"})
FROZEN_POS_EDGE = -1
FROZEN_NEG_EDGE = -2
INVALID_EDGE = -100
class _BIPSolver:
"""
Base class for BIP solvers
"""
min_affinity: float
max_affinity: float
def __init__(self, min_affinity: float = -np.inf, max_affinity: float = np.inf):
self.min_affinity = min_affinity
self.max_affinity = max_affinity
@staticmethod
def _create_bip(affinity_matrix: NDArray, min_affinity: float, max_affinity: float):
n_nodes = affinity_matrix.shape[0]
# mask for selecting pairs of nodes
triu_mask = np.triu(np.ones_like(affinity_matrix, dtype=bool), 1)
affinities = affinity_matrix[triu_mask]
frozen_pos_mask = affinities >= max_affinity
frozen_neg_mask = affinities <= min_affinity
unfrozen_mask = np.logical_not(frozen_pos_mask | frozen_neg_mask)
# generate objective coefficients
objective_coefficients = affinities[unfrozen_mask]
if len(objective_coefficients) == 0: # nio unfrozen edges
objective_coefficients = np.asarray([affinity_matrix[0, -1]])
unfrozen_mask = np.zeros_like(unfrozen_mask, dtype=np.bool)
unfrozen_mask[affinity_matrix.shape[1] - 1] = 1
# create matrix whose rows are the indices of the three edges in a
# constraint x_ij + x_ik - x_jk <= 1
constraints_edges_idx = []
if n_nodes >= 3:
edges_idx = np.empty_like(affinities, dtype=int)
edges_idx[frozen_pos_mask] = FROZEN_POS_EDGE
edges_idx[frozen_neg_mask] = FROZEN_NEG_EDGE
edges_idx[unfrozen_mask] = np.arange(len(objective_coefficients))
nodes_to_edge_matrix = np.empty_like(affinity_matrix, dtype=int)
nodes_to_edge_matrix.fill(INVALID_EDGE)
nodes_to_edge_matrix[triu_mask] = edges_idx
triplets = np.asarray(
tuple(itertools.combinations(range(n_nodes), 3)), dtype=int
)
constraints_edges_idx = np.zeros_like(triplets)
constraints_edges_idx[:, 0] = nodes_to_edge_matrix[
(triplets[:, 0], triplets[:, 1])
]
constraints_edges_idx[:, 1] = nodes_to_edge_matrix[
(triplets[:, 0], triplets[:, 2])
]
constraints_edges_idx[:, 2] = nodes_to_edge_matrix[
(triplets[:, 1], triplets[:, 2])
]
constraints_edges_idx = constraints_edges_idx[
np.any(constraints_edges_idx >= 0, axis=1)
]
if len(constraints_edges_idx) == 0: # no constraints
constraints_edges_idx = np.asarray([0, 0, 0], dtype=int).reshape(-1, 3)
# add remaining constraints by permutation
constraints_edges_idx = np.vstack(
(
constraints_edges_idx,
np.roll(constraints_edges_idx, 1, axis=1),
np.roll(constraints_edges_idx, 2, axis=1),
)
)
# clean redundant constraints
# x1 + x2 <= 2
constraints_edges_idx = constraints_edges_idx[
constraints_edges_idx[:, 2] != FROZEN_POS_EDGE
]
# x1 - x2 <= 1
constraints_edges_idx = constraints_edges_idx[
np.all(constraints_edges_idx[:, 0:2] != FROZEN_NEG_EDGE, axis=1)
]
if len(constraints_edges_idx) == 0: # no constraints
constraints_edges_idx = np.asarray([0, 0, 0], dtype=int).reshape(-1, 3)
# generate constraint coefficients
constraints_coefficients = np.ones_like(constraints_edges_idx)
constraints_coefficients[:, 2] = -1
# generate constraint upper bounds
upper_bounds = np.ones(len(constraints_coefficients), dtype=float)
upper_bounds -= np.sum(
constraints_coefficients * (constraints_edges_idx == FROZEN_POS_EDGE),
axis=1,
)
# flatten constraints data into sparse matrix format
constraints_idx = np.repeat(np.arange(len(constraints_edges_idx)), 3)
constraints_edges_idx = constraints_edges_idx.reshape(-1)
constraints_coefficients = constraints_coefficients.reshape(-1)
unfrozen_edges = constraints_edges_idx >= 0
constraints_idx = constraints_idx[unfrozen_edges]
constraints_edges_idx = constraints_edges_idx[unfrozen_edges]
constraints_coefficients = constraints_coefficients[unfrozen_edges]
return (
objective_coefficients,
unfrozen_mask,
frozen_pos_mask,
frozen_neg_mask,
(constraints_coefficients, constraints_idx, constraints_edges_idx),
upper_bounds,
)
@abstractmethod
def _solve_bip(self, objective_coefficients, sparse_constraints, upper_bounds): ...
@staticmethod
def solution_mat_clusters(solution_mat: NDArray):
n = solution_mat.shape[0]
labels = np.arange(1, n + 1)
for i in range(n):
for j in range(i + 1, n):
if solution_mat[i, j] > 0:
labels[j] = labels[i]
clusters = defaultdict(list)
for i, label in enumerate(labels):
clusters[label].append(i)
return list(clusters.values())
def solve(self, affinity_matrix, rtn_matrix=False):
n_nodes = affinity_matrix.shape[0]
if n_nodes <= 1:
solution_x, sol_matrix = (
np.asarray([], dtype=int),
np.asarray([0] * n_nodes, dtype=int),
)
sol_matrix = sol_matrix[:, None]
elif n_nodes == 2:
solution_matrix = np.zeros_like(affinity_matrix, dtype=int)
solution_matrix[0, 1] = affinity_matrix[0, 1] > 0
solution_matrix += solution_matrix.T
solution_x = (
[solution_matrix[0, 1]]
if self.min_affinity < affinity_matrix[0, 1] < self.max_affinity
else []
)
solution_x, sol_matrix = np.asarray(solution_x), solution_matrix
else:
# create BIP problem
(
objective_coefficients,
unfrozen_mask,
frozen_pos_mask,
frozen_neg_mask,
sparse_constraints,
upper_bounds,
) = self._create_bip(affinity_matrix, self.min_affinity, self.max_affinity)
# solve
solution_x = self._solve_bip(
objective_coefficients, sparse_constraints, upper_bounds
)
# solution to matrix
all_sols = np.zeros_like(unfrozen_mask, dtype=int)
all_sols[unfrozen_mask] = np.array(solution_x, dtype=int).reshape(-1)
all_sols[frozen_neg_mask] = 0
all_sols[frozen_pos_mask] = 1
sol_matrix = np.zeros_like(affinity_matrix, dtype=int)
sol_matrix[np.triu(np.ones([n_nodes, n_nodes], dtype=int), 1) > 0] = (
all_sols
)
sol_matrix += sol_matrix.T
clusters = self.solution_mat_clusters(sol_matrix)
if not rtn_matrix:
return clusters
return clusters, sol_matrix
class GLPKSolver(_BIPSolver):
def __init__(self, min_affinity=-np.inf, max_affinity=np.inf):
super().__init__(min_affinity, max_affinity)
@override
def _solve_bip(
self,
objective_coefficients: NDArray,
sparse_constraints: Tuple[NDArray, NDArray, NDArray],
upper_bounds: NDArray,
):
c = matrix(-objective_coefficients) # max -> min
# G * x <= h
G = spmatrix(
*sparse_constraints, size=(len(upper_bounds), len(objective_coefficients))
)
h = matrix(upper_bounds, tc="d")
status, solution = ilp(c, G, h, B=set(range(len(c))))
assert solution is not None, "Solver error: {}".format(status)
return np.asarray(solution, int).reshape(-1)

184
app/solver/_wrap/__init__.py Normal file
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"""
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)

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app/solver/_wrap/glpk.py Normal file
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"""
See also:
https://github.com/cvxopt/cvxopt/blob/master/src/C/glpk.c
"""
from typing import Tuple, Union, Literal, Optional, Dict, Any, Set, overload, TypedDict
from cvxopt import glpk # type: ignore
from . import Matrix, SparseMatrix
CvxMatLike = Union[Matrix, SparseMatrix]
CvxBool = Literal["GLP_ON", "GLP_OFF"]
class GLPKOptions(TypedDict, total=False):
# Common parameters
msg_lev: Literal["GLP_MSG_OFF", "GLP_MSG_ERR", "GLP_MSG_ON", "GLP_MSG_ALL"]
presolve: CvxBool
tm_lim: int
out_frq: int
out_dly: int
# LP-specific parameters
meth: Literal["GLP_PRIMAL", "GLP_DUAL", "GLP_DUALP"]
pricing: Literal["GLP_PT_STD", "GLP_PT_PSE"]
r_test: Literal["GLP_RT_STD", "GLP_RT_HAR"]
tol_bnd: float
tol_dj: float
tol_piv: float
obj_ll: float
obj_ul: float
it_lim: int
# MILP-specific parameters
br_tech: Literal[
"GLP_BR_FFV", "GLP_BR_LFV", "GLP_BR_MFV", "GLP_BR_DTH", "GLP_BR_PCH"
]
bt_tech: Literal["GLP_BT_DFS", "GLP_BT_BFS", "GLP_BT_BLB", "GLP_BT_BPH"]
pp_tech: Literal["GLP_PP_NONE", "GLP_PP_ROOT", "GLP_PP_ALL"]
fp_heur: CvxBool
gmi_cuts: CvxBool
mir_cuts: CvxBool
cov_cuts: CvxBool
clq_cuts: CvxBool
tol_int: float
tol_obj: float
mip_gap: float
cb_size: int
binarize: CvxBool
StatusLP = Literal["optimal", "primal infeasible", "dual infeasible", "unknown"]
StatusILP = Literal[
"optimal",
"feasible",
"undefined",
"invalid formulation",
"infeasible problem",
"LP relaxation is primal infeasible",
"LP relaxation is dual infeasible",
"unknown",
]
@overload
def lp(
c: Matrix,
G: CvxMatLike,
h: Matrix,
) -> Tuple[StatusLP, Optional[Matrix], Optional[Matrix]]:
"""
(status, x, z) = lp(c, G, h)
PURPOSE
(status, x, z) = lp(c, G, h) solves the pair of primal and dual LPs
minimize c'*x maximize -h'*z
subject to G*x <= h subject to G'*z + c = 0
z >= 0.
ARGUMENTS
c nx1 dense 'd' matrix with n>=1
G mxn dense or sparse 'd' matrix with m>=1
h mx1 dense 'd' matrix
status 'optimal', 'primal infeasible', 'dual infeasible'
or 'unknown'
x if status is 'optimal', a primal optimal solution;
None otherwise
z if status is 'optimal', the dual optimal solution;
None otherwise
"""
@overload
def lp(
c: Matrix,
G: CvxMatLike,
h: Matrix,
A: CvxMatLike,
b: Matrix,
) -> Tuple[StatusLP, Optional[Matrix], Optional[Matrix], Optional[Matrix]]:
"""
(status, x, z, y) = lp(c, G, h, A, b)
PURPOSE
(status, x, z, y) = lp(c, G, h, A, b) solves the pair of primal and
dual LPs
minimize c'*x maximize -h'*z + b'*y
subject to G*x <= h subject to G'*z + A'*y + c = 0
A*x = b z >= 0.
ARGUMENTS
c nx1 dense 'd' matrix with n>=1
G mxn dense or sparse 'd' matrix with m>=1
h mx1 dense 'd' matrix
A pxn dense or sparse 'd' matrix with p>=0
b px1 dense 'd' matrix
status 'optimal', 'primal infeasible', 'dual infeasible'
or 'unknown'
x if status is 'optimal', a primal optimal solution;
None otherwise
z,y if status is 'optimal', the dual optimal solution;
None otherwise
"""
# https://cvxopt.org/userguide/coneprog.html#linear-programming
def lp(
c: Matrix,
G: CvxMatLike,
h: Matrix,
A: Optional[CvxMatLike] = None,
b: Optional[Matrix] = None,
):
"""
(status, x, z, y) = lp(c, G, h, A, b)
(status, x, z) = lp(c, G, h)
PURPOSE
(status, x, z, y) = lp(c, G, h, A, b) solves the pair of primal and
dual LPs
minimize c'*x maximize -h'*z + b'*y
subject to G*x <= h subject to G'*z + A'*y + c = 0
A*x = b z >= 0.
(status, x, z) = lp(c, G, h) solves the pair of primal and dual LPs
minimize c'*x maximize -h'*z
subject to G*x <= h subject to G'*z + c = 0
z >= 0.
ARGUMENTS
c nx1 dense 'd' matrix with n>=1
G mxn dense or sparse 'd' matrix with m>=1
h mx1 dense 'd' matrix
A pxn dense or sparse 'd' matrix with p>=0
b px1 dense 'd' matrix
status 'optimal', 'primal infeasible', 'dual infeasible'
or 'unknown'
x if status is 'optimal', a primal optimal solution;
None otherwise
z,y if status is 'optimal', the dual optimal solution;
None otherwise
"""
if A is None and b is None:
return glpk.lp(c, G, h)
return glpk.lp(c, G, h, A, b)
def ilp(
c: Matrix,
G: CvxMatLike,
h: Matrix,
A: Optional[CvxMatLike] = None,
b: Optional[Matrix] = None,
I: Optional[Set[int]] = None,
B: Optional[Set[int]] = None,
) -> Tuple[StatusILP, Optional[Matrix]]:
"""
Solves a mixed integer linear program using GLPK.
(status, x) = ilp(c, G, h, A, b, I, B)
PURPOSE
Solves the mixed integer linear programming problem
minimize c'*x
subject to G*x <= h
A*x = b
x[k] is integer for k in I
x[k] is binary for k in B
ARGUMENTS
c nx1 dense 'd' matrix with n>=1
G mxn dense or sparse 'd' matrix with m>=1
h mx1 dense 'd' matrix
A pxn dense or sparse 'd' matrix with p>=0
b px1 dense 'd' matrix
I set of indices of integer variables
B set of indices of binary variables
status if status is 'optimal', 'feasible', or 'undefined',
a value of x is returned and the status string
gives the status of x. Other possible values of
status are: 'invalid formulation',
'infeasible problem', 'LP relaxation is primal
infeasible', 'LP relaxation is dual infeasible',
'unknown'.
x a (sub-)optimal solution if status is 'optimal',
'feasible', or 'undefined'. None otherwise
"""
return glpk.ilp(c, G, h, A, b, I, B)
def set_global_options(options: GLPKOptions) -> None:
glpk.options = options
def get_global_options() -> GLPKOptions:
return glpk.options

1
pyproject.toml
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@ -7,6 +7,7 @@ requires-python = ">=3.10"
dependencies = [
"anyio>=4.8.0",
"awkward>=2.7.4",
"cvxopt>=1.3.2",
"jax[cuda12]>=0.5.1",
"jaxtyping>=0.2.38",
"opencv-contrib-python-headless>=4.11.0.86",

37
uv.lock generated
View File

@ -372,6 +372,7 @@ source = { virtual = "." }
dependencies = [
{ name = "anyio" },
{ name = "awkward" },
{ name = "cvxopt" },
{ name = "jax", extra = ["cuda12"] },
{ name = "jaxtyping" },
{ name = "opencv-contrib-python-headless" },
@ -390,6 +391,7 @@ dev = [
requires-dist = [
{ name = "anyio", specifier = ">=4.8.0" },
{ name = "awkward", specifier = ">=2.7.4" },
{ name = "cvxopt", specifier = ">=1.3.2" },
{ name = "jax", extras = ["cuda12"], specifier = ">=0.5.1" },
{ name = "jaxtyping", specifier = ">=0.2.38" },
{ name = "opencv-contrib-python-headless", specifier = ">=4.11.0.86" },
@ -402,6 +404,41 @@ requires-dist = [
[package.metadata.requires-dev]
dev = [{ name = "jupyter", specifier = ">=1.1.1" }]
[[package]]
name = "cvxopt"
version = "1.3.2"
source = { registry = "https://pypi.org/simple" }
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