def test_makecovblock_checks():
a = np.random.randn(10, 10)
b = np.copy(a)
b[0, 0] = np.inf
m = b.T @ b
gp = lgp.GP(checksym=False)
gp.addcov(a, 0)
gp._checksym = True
with pytest.raises(RuntimeError):
gp.prior(raw=True)
gp = lgp.GP(checkfinite=False)
gp.addcov(m, 0)
gp._checkfinite = True
with pytest.raises(RuntimeError):
gp.prior(raw=True)
gp = lgp.GP(checksym=False, checkpos=False)
gp.addcov(a, 0)
gp.prior(raw=True)
gp = lgp.GP(checkfinite=False, checkpos=False)
gp.addcov(m, 0)
gp.prior(raw=True)
def test_incompatible_dtypes():
gp = lgp.GP(lgp.ExpQuad())
gp.addx(0, 0)
with pytest.raises(TypeError):
gp.addx(np.zeros(1, 'd,d'), 1)
gp = lgp.GP(lgp.ExpQuad())
gp.addx(np.zeros(1, 'd,d'), 0)
# gp.addx(np.zeros(1, 'i,i'), 1) # succeeds only if numpy >= 1.23
with pytest.raises(TypeError):
gp.addx(np.zeros(1, 'd,d,d'), 2)
def test_partial_derivative():
gp = lgp.GP(lgp.ExpQuad())
x = np.arange(20)
y = np.zeros(len(x), 'f8,f8')
y['f0'] = x
gp.addx(y, 0, deriv='f0')
cov1 = gp.prior(0, raw=True)
gp = lgp.GP(lgp.ExpQuad())
gp.addx(x, 0, deriv=1)
cov2 = gp.prior(0, raw=True)
util.assert_equal(cov1, cov2)
def test_none_key():
gp = lgp.GP(lgp.ExpQuad())
with pytest.raises(ValueError):
gp.addx({None: 0})
gp = lgp.GP(lgp.ExpQuad())
gp.addx(0, 0)
with pytest.raises(ValueError):
gp.addtransf({0: 1}, None)
gp = lgp.GP(lgp.ExpQuad())
with pytest.raises(ValueError):
gp.addcov({None: 1})
def test_key_already_used():
gp = lgp.GP(lgp.ExpQuad())
gp.addx(0, 0)
with pytest.raises(KeyError):
gp.addx(0, 0)
gp = lgp.GP(lgp.ExpQuad())
gp.addx(0, 0)
with pytest.raises(KeyError):
gp.addtransf({0: 1}, 0)
gp = lgp.GP(lgp.ExpQuad())
gp.addx(0, 0)
with pytest.raises(KeyError):
gp.addcov(1, 0)
def makegp(params):
kernel_time = lgp.ExpQuad(scale=params['time_scale'], dim='time')
kernel_label = lgp.ExpQuad(scale=label_scale, dim='label')
gp = lgp.GP(kernel_time * kernel_label)
gp.addx(x, 'data', deriv=(data_deriv, 'time'))
gp.addx(np.array([(0, 0)], dtype=x.dtype), 'fixed_point')
return gp
def makegp(hp):
gp = lgp.GP()
kernel = makekernel(hp)
gp.addproc(kernel, 'h')
gp.addproctransf({'h': 1}, 'primitive', deriv='x' )
gp.addproctransf({'h': 1}, 'f' , deriv=(2, 'x'))
gp.addproctransf({
'primitive': lambda x: x['x'],
'h' : -1,
}, 'primitive of xf(x)')
# data
gp.addx(xdata, 'xdata', proc='f')
gp.addtransf({'xdata': M}, 'data', axes=2)
# total momentum rule
gp.addx(xinteg, 'xmomrule', proc='primitive of xf(x)')
gp.addtransf({'xmomrule': suminteg}, 'momrule', axes=2)
# quark sum rules
for quark in 'ducs':
idx = indices[quark]
label = f'{quark}{quark}bar' # the one appearing in `constraints`
xlabel = f'x{label}'
gp.addx(xinteg[idx], xlabel, proc='primitive')
gp.addtransf({xlabel: suminteg[idx] * qdiff}, label, axes=2)
return gp
def makegp(x):
gp = lgp.GP(lgp.ExpQuad(),
checkfinite=False,
checksym=False,
checkpos=False)
gp.addx(np.nan, 0)
return gp
def makegp(params):
kernel = lgp.Cauchy(scale=params['time_scale'], dim='time', beta=2)
kernel *= lgp.ExpQuad(scale=params['label_scale'], dim='label')
gp = lgp.GP(kernel)
x['time'] = jnp.array([time, time - params['delay']])
gp.addx(x, 'A')
return gp
def test_addcov_checks():
gp = lgp.GP()
a = np.random.randn(10, 10)
b = np.copy(a)
b[0, 0] = np.inf
m = b.T @ b
with pytest.raises(ValueError):
gp.addcov(a, 0)
with pytest.raises(ValueError):
gp.addcov(m, 0)
gp = lgp.GP(checksym=False)
gp.addcov(a, 0)
gp = lgp.GP(checkfinite=False)
gp.addcov(m, 0)
def test_cov():
A = np.random.randn(20, 20)
M1 = A.T @ A
gp = lgp.GP()
gp.addcov(M1, 'M')
M2 = gp.prior('M', raw=True)
util.assert_equal(M1, M2)
def test_addcov_wrong_blocks():
gp = lgp.GP(lgp.ExpQuad())
with pytest.raises(ValueError):
gp.addcov(np.zeros((1, 1, 1)), 0)
with pytest.raises(ValueError):
gp.addcov(np.zeros((1, 2, 2, 1)), 0)
with pytest.raises(ValueError):
gp.addcov(np.random.randn(10, 10), 0)
with pytest.raises(KeyError):
gp.addcov({
(0, 0): 1,
(0, 1): 0,
})
with pytest.raises(ValueError):
gp.addcov({
(0, 0): np.ones((2, 2)),
(1, 1): np.ones((3, 3)),
(0, 1): np.ones((3, 2)),
})
with pytest.raises(ValueError):
gp.addcov({
(0, 0): np.ones((2, 2)),
(1, 1): np.ones((3, 3)),
(0, 1): np.ones((2, 3)),
(1, 0): np.zeros((3, 2)),
})
def test_fourier(self):
for kw in self.kwargs_list:
kernel = self.kernel_class(**kw)
try:
kernel.fourier(True, True)
except NotImplementedError:
pytest.skip()
if isinstance(kernel, _kernels.Zeta) and kw['nu'] == 0:
continue
x = np.linspace(0, 1, 100)
gp = lgp.GP(kernel, posepsfac=200)
gp.addkernelop('fourier', True, 'F')
gp.addx(x, 'x')
gp.addx(1, 's1', proc='F')
gp.addx(2, 'c1', proc='F')
ms, cs = gp.predfromdata(dict(s1=1, c1=0), 'x', raw=True)
mc, cc = gp.predfromdata(dict(c1=1, s1=0), 'x', raw=True)
np.testing.assert_allclose(ms,
np.sin(2 * np.pi * x),
equal_nan=False)
np.testing.assert_allclose(mc,
np.cos(2 * np.pi * x),
equal_nan=False)
eps = np.finfo(cs.dtype).eps
np.testing.assert_allclose(np.diag(cs),
cs[0, 0],
atol=eps,
equal_nan=False)
np.testing.assert_allclose(np.diag(cc),
cc[0, 0],
atol=eps,
equal_nan=False)
def preparegp():
gp = lgp.GP()
gp.addproc(lgp.ExpQuad(), 'a')
gp.addproc(lgp.Cauchy(), 'b')
gp.addx(x, 'ax', proc='a')
gp.addx(x, 'bx', proc='b')
return gp
def test_no_checksym():
covs = []
for checksym in [False, True]:
gp = lgp.GP(lgp.ExpQuad(), checksym=checksym)
gp.addx({'x': np.arange(20)})
covs.append(gp.prior('x', raw=True))
util.assert_equal(*covs)
def test_marginal_likelihood_separate():
gp = lgp.GP(lgp.ExpQuad())
x, y = np.random.randn(2, 20)
gp.addx(x, 0)
ml1 = gp.marginal_likelihood({0: y})
l, r = gp.marginal_likelihood({0: y}, separate=True)
ml2 = -1 / 2 * (l + r @ r)
np.testing.assert_allclose(ml2, ml1, rtol=1e-15)
def test_transf_vector():
gp = lgp.GP(lgp.ExpQuad())
gp.addx([0, 1], 'x')
gp.addtransf({'x': [-1, 1]}, 'y')
prior = gp.prior()
y1 = prior['y']
y2 = prior['x'][1] - prior['x'][0]
util.assert_same_gvars(y1, y2, atol=1e-12)
def test_zero_covblock():
gp = lgp.GP()
a = np.random.randn(10, 10)
m = a.T @ a
gp.addcov(m, 0)
gp.addcov(m, 1)
prior = gp.prior(raw=True)
util.assert_equal(prior[0, 1], np.zeros_like(m))
def test_addcov_no_checksym():
gp = lgp.GP(lgp.ExpQuad(), checksym=False)
gp.addcov({
(0, 0): np.ones((2, 2)),
(1, 1): np.ones((3, 3)),
(0, 1): np.ones((2, 3)),
(1, 0): np.zeros((3, 2)),
})
def test_prior_raw_shape():
gp = lgp.GP(lgp.ExpQuad())
gp.addx(np.arange(20).reshape(2, 10), 'x')
cov = gp.prior(raw=True)
assert cov['x', 'x'].shape == (2, 10, 2, 10)
cov = gp.prior('x', raw=True)
assert cov.shape == (2, 10, 2, 10)
def test_priorpoints_cache():
gp = lgp.GP(lgp.ExpQuad())
x = np.arange(20)
gp.addx(x, 0)
gp.addx(x, 1)
prior = gp.prior()
cov = gvar.evalcov(prior)
util.assert_equal(cov[0, 0], cov[1, 1])
util.assert_equal(cov[0, 0], cov[0, 1])
def test_addprocderiv():
gp = lgp.GP(lgp.ExpQuad())
gp.addprocderiv(1, 'a')
x = np.arange(20)
gp.addx(x, 0, proc='a')
gp.addx(x, 1, deriv=1)
prior = gp.prior(raw=True)
util.assert_equal(prior[0, 0], prior[1, 1])
util.assert_equal(prior[0, 0], prior[0, 1])
def test_pred_all():
gp = lgp.GP(lgp.ExpQuad())
x, y, z = np.random.randn(3, 20)
gp.addx(x, 0)
gp.addx(y, 1)
m1, c1 = gp.predfromdata({0: z}, raw=True)
m2, c2 = gp.predfromdata({0: z}, [0, 1], raw=True)
util.assert_equal(m1, m2)
util.assert_equal(c1, c2)
def test_addcov_missing_block():
gp = lgp.GP(lgp.ExpQuad())
gp.addcov({
(0, 0): np.ones((2, 2)),
(1, 1): np.ones((3, 3)),
(0, 1): np.ones((2, 3)),
})
prior = gp.prior(raw=True)
util.assert_equal(prior[0, 1], prior[1, 0].T)
def test_default_kernel():
gp = lgp.GP(lgp.ExpQuad())
gp.addproc(key='a')
x = np.arange(20)
gp.addx(x, 'x1')
gp.addx(x, 'x2', proc='a')
prior = gp.prior(raw=True)
util.assert_equal(prior['x1', 'x1'], prior['x2', 'x2'])
util.assert_equal(prior['x1', 'x2'], np.zeros(2 * x.shape))
def test_marginal_likelihood_gvar():
gp = lgp.GP(lgp.ExpQuad())
x, y = np.random.randn(2, 20)
gp.addx(x, 0)
a = np.random.randn(20, 20)
m = a.T @ a
ml1 = gp.marginal_likelihood({0: gvar.gvar(y, m)})
ml2 = gp.marginal_likelihood({0: y}, {(0, 0): m})
np.testing.assert_allclose(ml2, ml1, rtol=1e-15)
def test_nonsense_tensors():
gp = lgp.GP(lgp.ExpQuad())
gp.addx(0, 0)
with pytest.raises(TypeError):
gp.addtransf({0: 'a'}, 1)
with pytest.raises(ValueError):
gp.addtransf({0: np.inf}, 1)
gp.addx([0, 1], 1)
with pytest.raises(ValueError):
gp.addtransf({1: [1, 2, 3]}, 2)
def test_empty_proc():
gp = lgp.GP()
gp.addproctransf({}, 'a')
gp.addproclintransf(lambda: lambda x: 0, [], 'b')
x = np.arange(20)
gp.addx(x, 'ax', proc='a')
gp.addx(x, 'bx', proc='b')
cov = gp.prior(raw=True)
util.assert_equal(cov['ax', 'ax'], np.zeros(2 * x.shape))
util.assert_equal(cov['bx', 'bx'], np.zeros(2 * x.shape))
def test_priortransf():
gp = lgp.GP(lgp.ExpQuad())
x, y = np.arange(40).reshape(2, -1)
gp.addx(x, 0)
gp.addx(y, 1)
gp.addtransf({0: x, 1: y}, 2)
cov1 = gp.prior(2, raw=True)
u = gp.prior(2)
cov2 = gvar.evalcov(u)
np.testing.assert_allclose(cov1, cov2, rtol=1e-15)
def test_zero_givencov():
gp = lgp.GP(lgp.ExpQuad())
x, y, z = np.random.randn(3, 20)
gp.addx(x, 0)
gp.addx(y, 1)
cov = np.zeros(2 * x.shape)
m1, c1 = gp.predfromdata({0: z}, 1, {(0, 0): cov}, raw=True)
m2, c2 = gp.predfromdata({0: z}, 1, raw=True)
util.assert_equal(m1, m2)
util.assert_equal(c1, c2)
