Sparse interface¶

solve_linear_problem_sparse accepts SciPy sparse matrices for the constraints. It keeps the inequality and equality matrices separate, the way you usually build them, and merges them for you into the single row bounded form the array interface needs. Each code block on this page continues from the previous one.

An inequality only problem¶

You give the inequality matrix as A_ub with its right hand side b_ub. The matrix may be in any SciPy sparse format. Here it is a compressed sparse row matrix. We solve the same problem as on the array interface page, minimizing -x - 2y subject to x + y <= 4 and x + 3y <= 6.

import numpy as np
from scipy.sparse import csr_matrix

from cyhighs import ModelStatus, solve_linear_problem_sparse

inequality = csr_matrix([[1.0, 1.0], [1.0, 3.0]])

solution = solve_linear_problem_sparse(
    objective_coefficients=[-1.0, -2.0],
    inequality_constraint_matrix=inequality,
    inequality_upper_bounds=[4.0, 6.0],
    variable_lower_bounds=[0.0, 0.0],
    variable_upper_bounds=[np.inf, np.inf],
)

assert solution.model_status == ModelStatus.OPTIMAL
np.testing.assert_allclose(solution.column_values, [3.0, 1.0])

Notice that the interface takes plain lists for the vectors. Anything array like is accepted and converted internally.

Adding equality constraints¶

To add equality constraints, pass A_eq and b_eq. When you supply both an inequality and an equality matrix, they must share the same sparse format, so the merge can stay in that format and avoid a conversion. Here both are in coordinate format. The equality row [1, 0] with right hand side 1 pins x to 1.

from scipy.sparse import coo_matrix

solution = solve_linear_problem_sparse(
    objective_coefficients=[-1.0, -2.0],
    inequality_constraint_matrix=coo_matrix([[1.0, 1.0], [1.0, 3.0]]),
    inequality_upper_bounds=[4.0, 6.0],
    equality_constraint_matrix=coo_matrix([[1.0, 0.0]]),
    equality_right_hand_sides=[1.0],
    variable_lower_bounds=[0.0, 0.0],
    variable_upper_bounds=[np.inf, np.inf],
)

assert solution.is_optimal
assert solution.column_values[0] == 1.0

Mixing formats is rejected¶

Because a mixed pairing would force a hidden conversion, it is refused. If you pass one matrix as compressed sparse row and the other as compressed sparse column, the call raises a ValueError, so the layout decision stays in your hands.

from scipy.sparse import csc_matrix

try:
    solve_linear_problem_sparse(
        objective_coefficients=[-1.0, -2.0],
        inequality_constraint_matrix=csr_matrix([[1.0, 1.0]]),
        inequality_upper_bounds=[4.0],
        equality_constraint_matrix=csc_matrix([[1.0, 0.0]]),
        equality_right_hand_sides=[1.0],
    )
except ValueError as error:
    print("rejected:", error)
else:
    raise AssertionError("expected a ValueError for the mixed formats")

For a fully SciPy compatible calling convention, see the linprog interface, which builds on this layer.