def test_spectral_radius_bound():
tol = 10**(-6)
rng = np.random.RandomState(utt.fetch_seed())
x = theano.tensor.matrix()
radius_bound = spectral_radius_bound(x, 5)
f = theano.function([x], radius_bound)
shp = (3, 4)
m = rng.rand(*shp)
m = np.cov(m).astype(config.floatX)
radius_bound_theano = f(m)
# test the approximation
mm = m
for i in range(5):
mm = np.dot(mm, mm)
radius_bound_numpy = np.trace(mm)**(2**(-5))
assert abs(radius_bound_numpy - radius_bound_theano) < tol
# test the bound
eigen_val = numpy.linalg.eig(m)
assert (eigen_val[0].max() - radius_bound_theano) < tol
# test type errors
xx = theano.tensor.vector()
ok = False
try:
spectral_radius_bound(xx, 5)
except TypeError:
ok = True
assert ok
ok = False
try:
spectral_radius_bound(x, 5.0)
except TypeError:
ok = True
assert ok
# test value error
ok = False
try:
spectral_radius_bound(x, -5)
except ValueError:
ok = True
assert ok
def test_spectral_radius_bound():
tol = 10 ** (-6)
rng = numpy.random.RandomState(utt.fetch_seed())
x = theano.tensor.matrix()
radius_bound = spectral_radius_bound(x, 5)
f = theano.function([x], radius_bound)
shp = (3, 4)
m = rng.rand(*shp)
m = numpy.cov(m).astype(config.floatX)
radius_bound_theano = f(m)
# test the approximation
mm = m
for i in range(5):
mm = numpy.dot(mm, mm)
radius_bound_numpy = numpy.trace(mm) ** (2 ** (-5))
assert abs(radius_bound_numpy - radius_bound_theano) < tol
# test the bound
eigen_val = numpy.linalg.eig(m)
assert (eigen_val[0].max() - radius_bound_theano) < tol
# test type errors
xx = theano.tensor.vector()
ok = False
try:
spectral_radius_bound(xx, 5)
except TypeError:
ok = True
assert ok
ok = False
try:
spectral_radius_bound(x, 5.)
except TypeError:
ok = True
assert ok
# test value error
ok = False
try:
spectral_radius_bound(x, -5)
except ValueError:
ok = True
assert ok
