def test_Mean_var(D = 1, kernel = kernel_setups[0]):
N = 4
el = FiniteVec.construct_RKHS_Elem(kernel, np.array([(0.,), (1.,)]), prefactors=np.ones(2)/2)
for pref in [el.prefactors, 2*el.prefactors]:
el.prefactors = pref
m, v = el.normalized().get_mean_var()
#print(m,v)
assert np.allclose(m, 0.5)
assert np.allclose(v, kernel.var + 0.5 - m**2)
el = FiniteVec.construct_RKHS_Elem(kernel, np.array([(0.,), (1.,)]), prefactors=np.array([1./3, 2./3]))
for pref in [el.prefactors, 2*el.prefactors]:
el.prefactors = pref
m, v = el.normalized().get_mean_var()
#print(m,v)
assert np.allclose(m, 2./3)
assert np.allclose(v, kernel.var + 2./3 - m**2)
el = FiniteVec.construct_RKHS_Elem(kernel, np.array([(0.,), (1.,), (2., )]), prefactors=np.array([0.2, 0.5, 0.3]))
for pref in [el.prefactors, 2*el.prefactors]:
el.prefactors = pref
m, v = el.normalized().get_mean_var()
#print(m,v)
assert np.allclose(m, 1.1)
assert np.allclose(v, kernel.var + 0.5 + 0.3*4 - m**2)
vec = FiniteVec(kernel, np.array([(0.,), (1.,), (0.,), (1.,)]), prefactors=np.array([0.5, 0.5, 1./3, 2./3]), points_per_split=2)
m, v = vec.normalized().get_mean_var()
assert np.allclose(m.flatten(), np.array([0.5, 2./3]))
assert np.allclose(v.flatten(), kernel.var + np.array([0.5, 2./3]) - m.flatten()**2)
def test_FiniteVec(D = 1, kernel = kernel_setups[0], N = 10):
X = rng.randn(N, D)
rv = FiniteVec(kernel, X, np.ones(len(X)).astype(np.float32))
rv2 = FiniteVec.construct_RKHS_Elem(kernel, rng.randn(N + 1, D), np.ones(N + 1).astype(np.float32))
assert np.allclose(inner(rv, rv), rv.k(rv.inspace_points, rv.inspace_points)*np.outer(rv.prefactors, rv.prefactors)) , "Simple vector computation not accurate"
assert np.allclose(inner(rv, rv2), (rv.k(rv.inspace_points, rv2.inspace_points)*np.outer(rv.prefactors, rv2.prefactors)).sum(1, keepdims=True)), "Simple vector computation not accurate"
N = 4
X = rng.randn(N, D)
rv = FiniteVec(kernel, X, np.ones(len(X))/2, points_per_split = 2)
el = FiniteVec.construct_RKHS_Elem(kernel, X, prefactors=np.ones(N))
gram = el.k(el.inspace_points)
assert np.allclose(inner(el, el), np.sum(gram))
assert np.allclose(np.squeeze(inner(el, rv)), np.sum(gram, 1).reshape(-1,2).mean(1))
rv = FiniteVec(kernel, X, np.ones(len(X))/2, points_per_split = 2)
assert np.allclose(inner(rv, rv), np.array([[np.mean(rv.k(X[:2,:])), np.mean(rv.k(X[:2,:], X[2:,:]))],
[np.mean(rv.k(X[:2,:], X[2:,:])), np.mean(rv.k(X[2:,:]))]])), "Balanced vector computation not accurate"
vec = FiniteVec(kernel, np.array([(0.,), (1.,), (0.,), (1.,)]), prefactors=np.array([0.5, 0.5, 1./3, 2./3]), points_per_split=2)
m, v = vec.normalized().get_mean_var()
assert np.allclose(m.flatten(), np.array([0.5, 2./3]))
assert np.allclose(v.flatten(), kernel.var + np.array([0.5, 2./3]) - m.flatten()**2)
def test_FiniteVec(D, kernel, N):
X = rng.randn(N, D)
rv = FiniteVec(kernel, X, [Prefactors(np.ones(len(X)).astype(np.float32))])
rv2 = FiniteVec.construct_RKHS_Elem(kernel, rng.randn(N + 1, D),
np.ones(N + 1).astype(np.float32))
assert np.allclose(
inner(rv, rv),
rv.k(rv.inspace_points, rv.inspace_points) *
np.outer(rv.reduce[0].prefactors, rv.reduce[0].prefactors)
), "Simple vector computation not accurate"
assert np.allclose(
inner(rv, rv2),
(rv.k(rv.inspace_points, rv2.inspace_points) *
np.outer(rv.reduce[0].prefactors, rv2.reduce[0].linear_map)).sum(
1, keepdims=True)), "Simple vector computation not accurate"
N = 4
X = rng.randn(N, D)
rv = FiniteVec(kernel, X,
[Prefactors(np.ones(len(X)) / 2),
BalancedSum(2)])
el = FiniteVec.construct_RKHS_Elem(kernel, X, np.ones(N))
gram = el.k(el.inspace_points)
assert np.allclose(inner(el, el), np.sum(gram))
assert np.allclose(np.squeeze(inner(el, rv)),
np.sum(gram, 1).reshape(-1, 2).mean(1))
rv = FiniteVec(kernel, X,
[Prefactors(np.ones(len(X)) / 2),
BalancedSum(2)])
assert np.allclose(
inner(rv, rv),
np.array([[np.mean(rv.k(X[:2, :])),
np.mean(rv.k(X[:2, :], X[2:, :]))],
[np.mean(rv.k(X[:2, :], X[2:, :])),
np.mean(rv.k(X[2:, :]))]
])), "Balanced vector computation not accurate"
vec = FiniteVec(kernel, np.array([(0., ), (1., ), (0., ), (1., )]), [
LinearReduce(
np.array([0.5, 0.5, 0, 0, 0, 0, 1. / 3, 2. / 3]).reshape((2, -1)))
])
m, v = vec.normalized().get_mean_var()
assert np.allclose(m.flatten(), np.array([0.5, 2. / 3]))
assert np.allclose(v.flatten(),
kernel.var + np.array([0.5, 2. / 3]) - m.flatten()**2)
def test_Mean_var(D, kernel):
N = 4
el = FiniteVec.construct_RKHS_Elem(kernel,
np.array([(0., ), (1., )]),
prefactors=np.ones(2) / 2)
for pref in [el.reduce[0].linear_map, 2 * el.reduce[0].linear_map]:
el.reduce[0].linear_map = pref
m, v = el.normalized().get_mean_var()
#print(m,v)
assert np.allclose(m, 0.5)
assert np.allclose(v, kernel.var + 0.5 - m**2)
el = FiniteVec.construct_RKHS_Elem(kernel,
np.array([(0., ), (1., )]),
prefactors=np.array([1. / 3, 2. / 3]))
for pref in [el.reduce[0].linear_map, 2 * el.reduce[0].linear_map]:
el.reduce[0].linear_map = pref
m, v = el.normalized().get_mean_var()
#print(m,v)
assert np.allclose(m, 2. / 3)
assert np.allclose(v, kernel.var + 2. / 3 - m**2)
el = FiniteVec.construct_RKHS_Elem(kernel,
np.array([(0., ), (1., ), (2., )]),
prefactors=np.array([0.2, 0.5, 0.3]))
for pref in [el.reduce[0].linear_map, 2 * el.reduce[0].linear_map]:
el.reduce[0].linear_map = pref
m, v = el.normalized().get_mean_var()
#print(m,v)
assert np.allclose(m, 1.1)
assert np.allclose(v, kernel.var + 0.5 + 0.3 * 4 - m**2)
vec = FiniteVec(kernel, np.array([(0., ), (1., ), (0., ), (1., )]), [
LinearReduce(
np.array([0.5, 0.5, 0, 0, 0, 0, 1. / 3, 2. / 3]).reshape((2, -1)))
])
m, v = vec.normalized().get_mean_var()
assert np.allclose(m.flatten(), np.array([0.5, 2. / 3]))
assert np.allclose(v.flatten(),
kernel.var + np.array([0.5, 2. / 3]) - m.flatten()**2)
