def spectral_radius_bound(X, log2_exponent):
"""
Returns upper bound on the largest eigenvalue of square symmetrix matrix X.
log2_exponent must be a positive-valued integer. The larger it is, the
slower and tighter the bound. Values up to 5 should usually suffice. The
algorithm works by multiplying X by itself this many times.
From V.Pan, 1990. "Estimating the Extremal Eigenvalues of a Symmetric
Matrix", Computers Math Applic. Vol 20 n. 2 pp 17-22.
Rq: an efficient algorithm, not used here, is defined in this paper.
"""
if X.type.ndim != 2:
raise TypeError("spectral_radius_bound requires a matrix argument", X)
if not isinstance(log2_exponent, int):
raise TypeError("spectral_radius_bound requires an integer exponent",
log2_exponent)
if log2_exponent <= 0:
raise ValueError(
"spectral_radius_bound requires a strictly positive "
"exponent",
log2_exponent,
)
XX = X
for i in range(log2_exponent):
XX = dot(XX, XX)
return aet_pow(trace(XX), 2**(-log2_exponent))
def test_trace():
rng = np.random.RandomState(utt.fetch_seed())
x = matrix()
g = trace(x)
f = aesara.function([x], g)
for shp in [(2, 3), (3, 2), (3, 3)]:
m = rng.rand(*shp).astype(config.floatX)
v = np.trace(m)
assert v == f(m)
xx = vector()
ok = False
try:
trace(xx)
except TypeError:
ok = True
except ValueError:
ok = True
assert ok