def test_independentnormalkernel():
x0 = {'y0': np.array([1, 2]), 'y1': 2.5}
x = {'y0': np.array([0, 0]), 'y1': 7}
# use default var
kernel = IndependentNormalKernel()
kernel.initialize(0, None, x0)
ret = kernel(x, x0)
expected = -0.5 * (3 * np.log(2 * np.pi * 1) + 1**2 + 2**2 + 4.5**2)
assert np.isclose(ret, expected)
# define own var
kernel = IndependentNormalKernel([1, 2, 3])
kernel.initialize(0, None, x0)
ret = kernel(x, x0)
expected = -0.5 * (3 * np.log(2 * np.pi) + np.log(1) + np.log(2) +
np.log(3) + 1**2 / 1 + 2**2 / 2 + 4.5**2 / 3)
assert np.isclose(ret, expected)
# compare to normal kernel
normal_kernel = NormalKernel(cov=np.diag([1, 2, 3]))
normal_kernel.initialize(0, None, x0)
normal_ret = normal_kernel(x, x0)
assert np.isclose(ret, normal_ret)
# function var
def var(p):
if p is None:
return 42
return np.array([p['th0'], p['th1'], 3])
kernel = IndependentNormalKernel(var)
kernel.initialize(0, None, x0)
ret = kernel(x, x0, par={'th0': 1, 'th1': 2})
assert np.isclose(ret, expected)
def test_independentnormalkernel():
x0 = {'y0': np.array([1, 2]), 'y1': 2.5}
x = {'y0': np.array([0, 0]), 'y1': 7}
# use default var
kernel = IndependentNormalKernel()
kernel.initialize(0, None, x0, total_sims=0)
ret = kernel(x, x0)
expected = -0.5 * (3 * np.log(2 * np.pi * 1) + 1**2 + 2**2 + 4.5**2)
sp_expected = np.log(
np.prod([stats.norm.pdf(x=x, loc=0, scale=1) for x in [1, 2, 4.5]]))
assert np.isclose(expected, sp_expected)
assert np.isclose(ret, expected)
# define own var
kernel = IndependentNormalKernel([1, 2, 3])
kernel.initialize(0, None, x0, total_sims=0)
ret = kernel(x, x0)
expected = -0.5 * (3 * np.log(2 * np.pi) + np.log(1) + np.log(2) +
np.log(3) + 1**2 / 1 + 2**2 / 2 + 4.5**2 / 3)
sp_expected = np.log(
np.prod([
stats.norm.pdf(x=x, loc=0, scale=s)
for x, s in zip([1, 2, 4.5], np.sqrt([1, 2, 3]))
]))
assert np.isclose(expected, sp_expected)
assert np.isclose(ret, expected)
# compare to normal kernel
normal_kernel = NormalKernel(cov=np.diag([1, 2, 3]))
normal_kernel.initialize(0, None, x0, total_sims=0)
normal_ret = normal_kernel(x, x0)
assert np.isclose(ret, normal_ret)
# function var
def var(p):
if p is None:
return 42
return np.array([p['th0'], p['th1'], 3])
kernel = IndependentNormalKernel(var)
kernel.initialize(0, None, x, total_sims=0)
ret = kernel(x, x0, par={'th0': 1, 'th1': 2})
assert np.isclose(ret, expected)
def test_normalkernel():
x0 = {'y0': np.array([1, 0]), 'y1': 1}
x = {'y0': np.array([2, 2]), 'y1': 2}
# use default cov
kernel = NormalKernel()
kernel.initialize(0, None, x0, total_sims=0)
ret = kernel(x, x0)
# expected value
logterm = 3 * np.log(2 * np.pi * 1)
quadterm = 1**2 + 2**2 + 1**2
expected = -0.5 * (logterm + quadterm)
assert np.isclose(ret, expected)
# define own cov
cov = np.array([[2, 1, 0], [0, 2, 1], [0, 1, 3]])
kernel = NormalKernel(cov=cov)
kernel.initialize(0, None, x0, total_sims=0)
ret = kernel(x, x0)
expected = stats.multivariate_normal(cov=cov).logpdf([1, 2, 1])
assert np.isclose(ret, expected)
# define own keys, linear output
kernel = NormalKernel(keys=['y0'], ret_scale=SCALE_LIN)
kernel.initialize(0, None, x0, total_sims=0)
ret = kernel(x, x0)
expected = stats.multivariate_normal(cov=np.eye(2)).pdf([1, 2])
assert np.isclose(ret, expected)