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Force positive definite Gramiam matrices when balancing #119

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Force positive definite Gramiam matrices when balancing #119

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20 changes: 19 additions & 1 deletion nengolib/signal/lyapunov.py
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Original file line number Diff line number Diff line change
@@ -1,6 +1,8 @@
import warnings

import numpy as np
from scipy.linalg import (solve_lyapunov, solve_discrete_lyapunov, eig,
cholesky, svd)
cholesky, svd, eigvalsh)
from scipy.optimize import fminbound

from nengolib.signal.discrete import cont2discrete
Expand Down Expand Up @@ -176,6 +178,22 @@ def balanced_transformation(sys):
R = control_gram(sys)
O = observe_gram(sys)

def force_positive_definite(M, neg_tol=1e-9, eps=1e-19):
eig = np.min(eigvalsh(M))
if -neg_tol < eig < 0:
cond = eps - eig
warnings.warn("Conditioning matrix by adding %s to diagonal due "
"to rounding errors" % cond)
M += np.eye(len(M)) * cond
return M

# Mathematically R and O should be positive definite.
# However, due to possible rounding errors in control_gram
# and observe_gram this will not always be the case.
# Also see https://github.com/scikit-learn/scikit-learn/issues/8252
R = force_positive_definite(R)
O = force_positive_definite(O)

LR = cholesky(R, lower=True)
LO = cholesky(O, lower=True)

Expand Down