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fix(mateqn): make _is_symmetric numerically robust and scale-aware #1245

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fix(mateqn): make _is_symmetric numerically robust and scale-aware #1245

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f1f692b
fix(mateqn): make _is_symmetric numerically robust and scale-aware
marko1olo Aug 16, 2026
8f0d749
style(tests): move class docstring before test methods per review
marko1olo Aug 19, 2026
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11 changes: 5 additions & 6 deletions control/mateqn.py
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Original file line number Diff line number Diff line change
Expand Up @@ -14,7 +14,7 @@

import numpy as np
import scipy as sp
from numpy import eye, finfo, inexact
from numpy import eye
from scipy.linalg import eigvals, solve

from .exception import ControlArgument, ControlDimension, ControlSlycot, \
Expand Down Expand Up @@ -69,7 +69,7 @@ def _warn_ill_conditioned_E(E):
not measurably more accurate in that regime.
"""
condE = np.linalg.cond(E)
if condE > 1.0 / np.sqrt(finfo(float).eps):
if condE > 1.0 / np.sqrt(np.finfo(float).eps):
warnings.warn(
f"E is ill-conditioned (cond(E) = {condE:.2g}); the generalized "
"Lyapunov solution may have reduced accuracy. The problem itself "
Expand Down Expand Up @@ -383,7 +383,7 @@ def dlyap(A, Q, C=None, E=None, method=None):
# Solvability requires lam_A * lam_Q != 1 for all pairs of
# eigenvalues (the diagonals of the triangular factors)
if np.min(np.abs(np.outer(np.diag(Tq), np.diag(Ta)) - 1.)) \
< finfo(float).eps * max(
< np.finfo(float).eps * max(
1., np.abs(np.diag(Ta)).max()
* np.abs(np.diag(Tq)).max()):
raise ControlArgument(
Expand Down Expand Up @@ -787,8 +787,7 @@ def _check_shape(M, n, m, square=False, symmetric=False, name="??"):
# Utility function to check if a matrix is symmetric
def _is_symmetric(M):
M = np.atleast_2d(M)
if isinstance(M[0, 0], inexact):
eps = finfo(M.dtype).eps
return ((M - M.T) < eps).all()
if issubclass(M.dtype.type, (np.inexact, float, complex)):
return np.allclose(M, M.conj().T)
else:
return (M == M.T).all()
20 changes: 20 additions & 0 deletions control/tests/mateqn_test.py
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Original file line number Diff line number Diff line change
Expand Up @@ -46,6 +46,26 @@
class TestMatrixEquations:
"""These are tests for the matrix equation solvers in mateqn.py"""

def test_is_symmetric_robustness(self):

@slivingston slivingston Aug 15, 2026

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This test method was put before the docstring, but it should go after the docstring.

"""Test _is_symmetric with scale-aware tolerance and asymmetric matrices (Issue #1174)."""
from control.mateqn import _is_symmetric
# Truly symmetric
M_sym = array([[1.0, 2.0], [2.0, 1.0]])
assert _is_symmetric(M_sym)

# Scale-aware numerical roundoff symmetry
M_roundoff = array([[1e6, 2.0 + 1e-12], [2.0, 1e6]])
assert _is_symmetric(M_roundoff)

# Asymmetric with negative difference (previously failed due to missing abs())
M_asym = array([[1.0, 0.0], [10.0, 1.0]])
assert not _is_symmetric(M_asym)

# Complex Hermitian matrix
M_herm = array([[1.0, 1.0 - 2.0j], [1.0 + 2.0j, 3.0]])
assert _is_symmetric(M_herm)


@pytest.mark.parametrize('method',
['scipy',
pytest.param('slycot', marks=pytest.mark.slycot)])
Expand Down
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