def block(*rows):
"""Construct a matrix from its blocks, preserving structure when possible.
Assumes that every row has an equal number of blocks and that the sizes
of the blocks align to form a grid.
Args:
*rows (list): Rows of the block matrix.
Returns:
matrix: Assembled matrix with as much structured as possible.
"""
if len(rows) == 1 and len(rows[0]) == 1:
# There is just one block. Return it.
return rows[0][0]
res = _attempt_zero(rows)
if res is not None:
return res
res = _attempt_diagonal(rows)
if res is not None:
return res
# Could not preserve any structure. Simply concatenate them all densely.
warn_upmodule(
"Could not preserve structure in block matrix: converting to dense.",
category=ToDenseWarning,
)
return Dense(B.concat2d(*[[B.dense(x) for x in row] for row in rows]))
def test_diag_block_diag(diag1, diag2):
approx(
B.diag(diag1, diag2),
B.concat2d(
[B.dense(diag1), B.zeros(B.dense(diag2))],
[B.zeros(B.dense(diag2)), B.dense(diag2)],
),
)
assert isinstance(B.diag(diag1, diag2), Diagonal)
def test_diag_block_dense(dense1, dense2):
with AssertDenseWarning(concat_warnings):
res = B.diag(dense1, dense2)
approx(
res,
B.concat2d(
[B.dense(dense1), B.zeros(B.dense(dense1))],
[B.zeros(B.dense(dense2)),
B.dense(dense2)],
),
)
assert isinstance(res, Dense)
def test_block_diag():
rows = [
[generate("diag:6"),
generate("zero:6,6"),
generate("zero:6,3")],
[generate("zero:6,6"),
generate("zero:6,6"),
generate("zero:6,3")],
[generate("zero:3,6"),
generate("zero:3,6"),
generate("diag:3")],
]
res = B.block(*rows)
approx(res, B.concat2d(*_dense(rows)))
assert isinstance(res, Diagonal)
def diag(a, b):
# We could merge this with `block`, but `block` has a lot of overhead. It
# seems advantageous to optimise this common case.
warn_upmodule(
f"Constructing a dense block-diagonal matrix from "
f"{a} and {b}: converting to dense.",
category=ToDenseWarning,
)
a = B.dense(a)
b = B.dense(b)
dtype = B.dtype(a)
ar, ac = B.shape(a)
br, bc = B.shape(b)
return Dense(
B.concat2d([a, B.zeros(dtype, ar, bc)], [B.zeros(dtype, br, ac), b]))
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_block_zero():
rows = [[generate("zero:6,6") for _ in range(3)] for _ in range(3)]
res = B.block(*rows)
approx(res, B.concat2d(*_dense(rows)))
assert isinstance(res, Zero)
def test_block_dense():
rows = [[generate("dense:6,6") for _ in range(3)] for _ in range(3)]
with AssertDenseWarning("could not preserve structure"):
res = B.block(*rows)
approx(res, B.concat2d(*_dense(rows)))
def test_mok():
x1 = B.linspace(0, 1, 10)
x2 = B.linspace(1, 2, 5)
x3 = B.linspace(1, 2, 10)
m = Measure()
p1 = GP(EQ(), measure=m)
p2 = GP(2 * EQ().stretch(2), measure=m)
k = MultiOutputKernel(m, p1, p2)
ks = m.kernels
# Check dimensionality.
assert dimensionality(k) == 2
# 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))
# Multiple inputs versus input:
approx(
k((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, (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((p2(x1), p1(x3)), p2(x1))
with pytest.raises(ValueError):
k.elwise(p2(x1), (p2(x1), p1(x3)))
# Multiple inputs versus `FDD`:
approx(
k((p2(x1), p1(x2)), p2(x1)),
B.concat(ks[p2, p2](x1, x1), ks[p1, p2](x2, x1), axis=0),
)
approx(
k(p2(x1), (p2(x1), p1(x2))),
B.concat(ks[p2, p2](x1, x1), ks[p2, p1](x1, x2), axis=1),
)
with pytest.raises(ValueError):
k.elwise((p2(x1), p1(x3)), p2(x1))
with pytest.raises(ValueError):
k.elwise(p2(x1), (p2(x1), p1(x3)))
# Multiple inputs versus multiple inputs:
approx(
k((p2(x1), p1(x2)), (p2(x1))),
B.concat(ks[p2, p2](x1, x1), ks[p1, p2](x2, x1), axis=0),
)
with pytest.raises(ValueError):
k.elwise((p2(x1), p1(x3)), (p2(x1),))
approx(
k.elwise((p2(x1), p1(x3)), (p2(x1), p1(x3))),
B.concat(ks[p2, p2].elwise(x1, x1), ks[p1, p1].elwise(x3, x3), axis=0),
)