def test_construction(x1, x2):
k = EQ()
k(x1)
k(x1, x2)
k.elwise(x1)
k.elwise(x1, x2)
# Test `MultiInput` construction.
approx(
k(MultiInput(x1, x2)),
B.concat2d([k(x1, x1), k(x1, x2)], [k(x2, x1), k(x2, x2)]),
)
approx(k(x1, MultiInput(x1, x2)), B.concat(k(x1, x1), k(x1, x2), axis=1))
approx(k(MultiInput(x1, x2), x2), B.concat(k(x1, x2), k(x2, x2), axis=0))
approx(
k.elwise(MultiInput(x1, x2)),
B.concat(k.elwise(x1, x1), k.elwise(x2, x2), axis=0),
)
with pytest.raises(ValueError):
k.elwise(MultiInput(x1), MultiInput(x1, x2))
with pytest.raises(ValueError):
k.elwise(x1, MultiInput(x1, x2))
with pytest.raises(ValueError):
k.elwise(MultiInput(x1, x2), x2)
def test_momean(x):
prior = Measure()
p1 = GP(lambda x: 2 * x, 1 * EQ(), measure=prior)
p2 = GP(1, 2 * EQ().stretch(2), measure=prior)
m = MultiOutputMean(prior, p1, p2)
ms = prior.means
# Check representation.
assert str(m) == "MultiOutputMean(<lambda>, 1)"
# Check computation.
approx(m(x), B.concat(ms[p1](x), ms[p2](x), axis=0))
approx(m(p1(x)), ms[p1](x))
approx(m(p2(x)), ms[p2](x))
approx(m(MultiInput(p2(x), p1(x))), B.concat(ms[p2](x), ms[p1](x), axis=0))
def test_momean():
m = Graph()
p1 = GP(1 * EQ(), lambda x: 2 * x, graph=m)
p2 = GP(2 * EQ().stretch(2), 1, graph=m)
mom = MultiOutputMean(p1, p2)
ms = m.means
x = np.linspace(0, 1, 10)
assert str(mom) == 'MultiOutputMean(<lambda>, 1)'
allclose(mom(x), np.concatenate([ms[p1](x), ms[p2](x)], axis=0))
allclose(mom(p1(x)), ms[p1](x))
allclose(mom(p2(x)), ms[p2](x))
allclose(mom(MultiInput(p2(x), p1(x))),
np.concatenate([ms[p2](x), ms[p1](x)], axis=0))
def test_mokernel():
m = Graph()
p1 = GP(1 * EQ(), graph=m)
p2 = GP(2 * EQ().stretch(2), graph=m)
mok = MultiOutputKernel(p1, p2)
ks = m.kernels
x1 = np.linspace(0, 1, 10)
x2 = np.linspace(1, 2, 5)
x3 = np.linspace(1, 2, 10)
yield eq, str(mok), 'MultiOutputKernel(EQ(), 2 * (EQ() > 2))'
# `B.Numeric` versus `B.Numeric`:
yield assert_allclose, mok(x1, x2), \
np.concatenate([np.concatenate([dense(ks[p1, p1](x1, x2)),
dense(ks[p1, p2](x1, x2))],
axis=1),
np.concatenate([dense(ks[p2, p1](x1, x2)),
dense(ks[p2, p2](x1, x2))],
axis=1)], axis=0)
yield assert_allclose, mok.elwise(x1, x3), \
np.concatenate([ks[p1, p1].elwise(x1, x3),
ks[p2, p2].elwise(x1, x3)], axis=0)
# `B.Numeric` versus `At`:
yield assert_allclose, mok(p1(x1), x2), \
np.concatenate([dense(ks[p1, p1](x1, x2)),
dense(ks[p1, p2](x1, x2))], axis=1)
yield assert_allclose, mok(p2(x1), x2), \
np.concatenate([dense(ks[p2, p1](x1, x2)),
dense(ks[p2, p2](x1, x2))], axis=1)
yield assert_allclose, mok(x1, p1(x2)), \
np.concatenate([dense(ks[p1, p1](x1, x2)),
dense(ks[p2, p1](x1, x2))], axis=0)
yield assert_allclose, mok(x1, p2(x2)), \
np.concatenate([dense(ks[p1, p2](x1, x2)),
dense(ks[p2, p2](x1, x2))], axis=0)
yield raises, ValueError, lambda: mok.elwise(x1, p2(x3))
yield raises, ValueError, lambda: mok.elwise(p1(x1), x3)
# `At` versus `At`:
yield assert_allclose, mok(p1(x1), p1(x2)), ks[p1](x1, x2)
yield assert_allclose, mok(p1(x1), p2(x2)), ks[p1, p2](x1, x2)
yield assert_allclose, mok.elwise(p1(x1), p1(x3)), ks[p1].elwise(x1, x3)
yield assert_allclose, mok.elwise(p1(x1), p2(x3)), ks[p1,
p2].elwise(x1, x3)
# `MultiInput` versus `MultiInput`:
yield assert_allclose, mok(MultiInput(p2(x1), p1(x2)),
MultiInput(p2(x1))), \
np.concatenate([dense(ks[p2, p2](x1, x1)),
dense(ks[p1, p2](x2, x1))], axis=0)
yield raises, ValueError, \
lambda: mok.elwise(MultiInput(p2(x1), p1(x3)), MultiInput(p2(x1)))
yield assert_allclose, mok.elwise(MultiInput(p2(x1), p1(x3)),
MultiInput(p2(x1), p1(x3))), \
np.concatenate([ks[p2, p2].elwise(x1, x1),
ks[p1, p1].elwise(x3, x3)], axis=0)
# `MultiInput` versus `At`:
yield assert_allclose, mok(MultiInput(p2(x1), p1(x2)),
p2(x1)), \
np.concatenate([dense(ks[p2, p2](x1, x1)),
dense(ks[p1, p2](x2, x1))], axis=0)
yield assert_allclose, mok(p2(x1),
MultiInput(p2(x1), p1(x2))), \
np.concatenate([dense(ks[p2, p2](x1, x1)),
dense(ks[p2, p1](x1, x2))], axis=1)
yield raises, ValueError, \
lambda: mok.elwise(MultiInput(p2(x1), p1(x3)), p2(x1))
yield raises, ValueError, \
lambda: mok.elwise(p2(x1), MultiInput(p2(x1), p1(x3)))
def test_mokernel(x1, x2, x3):
m = Measure()
p1 = GP(1 * EQ(), measure=m)
p2 = GP(2 * EQ().stretch(2), measure=m)
k = MultiOutputKernel(m, p1, p2)
ks = m.kernels
# Check representation.
assert str(k) == "MultiOutputKernel(EQ(), 2 * (EQ() > 2))"
# Input versus input:
approx(
k(x1, x2),
B.concat2d(
[ks[p1, p1](x1, x2), ks[p1, p2](x1, x2)],
[ks[p2, p1](x1, x2), ks[p2, p2](x1, x2)],
),
)
approx(
k.elwise(x1, x3),
B.concat(ks[p1, p1].elwise(x1, x3), ks[p2, p2].elwise(x1, x3), axis=0),
)
# Input versus `FDD`:
approx(k(p1(x1), x2),
B.concat(ks[p1, p1](x1, x2), ks[p1, p2](x1, x2), axis=1))
approx(k(p2(x1), x2),
B.concat(ks[p2, p1](x1, x2), ks[p2, p2](x1, x2), axis=1))
approx(k(x1, p1(x2)),
B.concat(ks[p1, p1](x1, x2), ks[p2, p1](x1, x2), axis=0))
approx(k(x1, p2(x2)),
B.concat(ks[p1, p2](x1, x2), ks[p2, p2](x1, x2), axis=0))
with pytest.raises(ValueError):
k.elwise(x1, p2(x3))
with pytest.raises(ValueError):
k.elwise(p1(x1), x3)
# `FDD` versus `FDD`:
approx(k(p1(x1), p1(x2)), ks[p1](x1, x2))
approx(k(p1(x1), p2(x2)), ks[p1, p2](x1, x2))
approx(k.elwise(p1(x1), p1(x3)), ks[p1].elwise(x1, x3))
approx(k.elwise(p1(x1), p2(x3)), ks[p1, p2].elwise(x1, x3))
# `MultiInput` versus input:
approx(
k(MultiInput(p2(x1), p1(x2)), x1),
B.concat2d(
[ks[p2, p1](x1, x1), ks[p2, p2](x1, x1)],
[ks[p1, p1](x2, x1), ks[p1, p2](x2, x1)],
),
)
approx(
k(x1, MultiInput(p2(x1), p1(x2))),
B.concat2d(
[ks[p1, p2](x1, x1), ks[p1, p1](x1, x2)],
[ks[p2, p2](x1, x1), ks[p2, p1](x1, x2)],
),
)
with pytest.raises(ValueError):
k.elwise(MultiInput(p2(x1), p1(x3)), p2(x1))
with pytest.raises(ValueError):
k.elwise(p2(x1), MultiInput(p2(x1), p1(x3)))
# `MultiInput` versus `FDD`:
approx(
k(MultiInput(p2(x1), p1(x2)), p2(x1)),
B.concat(ks[p2, p2](x1, x1), ks[p1, p2](x2, x1), axis=0),
)
approx(
k(p2(x1), MultiInput(p2(x1), p1(x2))),
B.concat(ks[p2, p2](x1, x1), ks[p2, p1](x1, x2), axis=1),
)
with pytest.raises(ValueError):
k.elwise(MultiInput(p2(x1), p1(x3)), p2(x1))
with pytest.raises(ValueError):
k.elwise(p2(x1), MultiInput(p2(x1), p1(x3)))
# `MultiInput` versus `MultiInput`:
approx(
k(MultiInput(p2(x1), p1(x2)), MultiInput(p2(x1))),
B.concat(ks[p2, p2](x1, x1), ks[p1, p2](x2, x1), axis=0),
)
with pytest.raises(ValueError):
k.elwise(MultiInput(p2(x1), p1(x3)), MultiInput(p2(x1)))
approx(
k.elwise(MultiInput(p2(x1), p1(x3)), MultiInput(p2(x1), p1(x3))),
B.concat(ks[p2, p2].elwise(x1, x1), ks[p1, p1].elwise(x3, x3), axis=0),
)
def test_mokernel():
m = Graph()
p1 = GP(1 * EQ(), graph=m)
p2 = GP(2 * EQ().stretch(2), graph=m)
mok = MultiOutputKernel(p1, p2)
ks = m.kernels
x1 = np.linspace(0, 1, 10)
x2 = np.linspace(1, 2, 5)
x3 = np.linspace(1, 2, 10)
assert str(mok) == 'MultiOutputKernel(EQ(), 2 * (EQ() > 2))'
# `B.Numeric` versus `B.Numeric`:
allclose(
mok(x1, x2),
np.concatenate([
np.concatenate(
[B.dense(ks[p1, p1](x1, x2)),
B.dense(ks[p1, p2](x1, x2))],
axis=1),
np.concatenate(
[B.dense(ks[p2, p1](x1, x2)),
B.dense(ks[p2, p2](x1, x2))],
axis=1)
],
axis=0))
allclose(
mok.elwise(x1, x3),
np.concatenate([ks[p1, p1].elwise(x1, x3), ks[p2, p2].elwise(x1, x3)],
axis=0))
# `B.Numeric` versus `At`:
allclose(
mok(p1(x1), x2),
np.concatenate(
[B.dense(ks[p1, p1](x1, x2)),
B.dense(ks[p1, p2](x1, x2))], axis=1))
allclose(
mok(p2(x1), x2),
np.concatenate(
[B.dense(ks[p2, p1](x1, x2)),
B.dense(ks[p2, p2](x1, x2))], axis=1))
allclose(
mok(x1, p1(x2)),
np.concatenate(
[B.dense(ks[p1, p1](x1, x2)),
B.dense(ks[p2, p1](x1, x2))], axis=0))
allclose(
mok(x1, p2(x2)),
np.concatenate(
[B.dense(ks[p1, p2](x1, x2)),
B.dense(ks[p2, p2](x1, x2))], axis=0))
with pytest.raises(ValueError):
mok.elwise(x1, p2(x3))
with pytest.raises(ValueError):
mok.elwise(p1(x1), x3)
# `At` versus `At`:
allclose(mok(p1(x1), p1(x2)), ks[p1](x1, x2))
allclose(mok(p1(x1), p2(x2)), ks[p1, p2](x1, x2))
allclose(mok.elwise(p1(x1), p1(x3)), ks[p1].elwise(x1, x3))
allclose(mok.elwise(p1(x1), p2(x3)), ks[p1, p2].elwise(x1, x3))
# `MultiInput` versus `MultiInput`:
allclose(
mok(MultiInput(p2(x1), p1(x2)), MultiInput(p2(x1))),
np.concatenate(
[B.dense(ks[p2, p2](x1, x1)),
B.dense(ks[p1, p2](x2, x1))], axis=0))
with pytest.raises(ValueError):
mok.elwise(MultiInput(p2(x1), p1(x3)), MultiInput(p2(x1)))
allclose(
mok.elwise(MultiInput(p2(x1), p1(x3)), MultiInput(p2(x1), p1(x3))),
np.concatenate([ks[p2, p2].elwise(x1, x1), ks[p1, p1].elwise(x3, x3)],
axis=0))
# `MultiInput` versus `At`:
allclose(
mok(MultiInput(p2(x1), p1(x2)), p2(x1)),
np.concatenate(
[B.dense(ks[p2, p2](x1, x1)),
B.dense(ks[p1, p2](x2, x1))], axis=0))
allclose(
mok(p2(x1), MultiInput(p2(x1), p1(x2))),
np.concatenate(
[B.dense(ks[p2, p2](x1, x1)),
B.dense(ks[p2, p1](x1, x2))], axis=1))
with pytest.raises(ValueError):
mok.elwise(MultiInput(p2(x1), p1(x3)), p2(x1))
with pytest.raises(ValueError):
mok.elwise(p2(x1), MultiInput(p2(x1), p1(x3)))
def test_construction(x):
m = TensorProductMean(lambda y: y ** 2)
m(x)
# Test `MultiInput` construction.
approx(m(MultiInput(x, x)), B.concat(m(x), m(x), axis=0))