def __call__(self, x, y):
f1, f2 = expand(self.fs)
if x is y and f1 is f2:
return LowRank(uprank(f1(uprank(x))))
else:
return LowRank(left=uprank(f1(uprank(x))),
right=uprank(f2(uprank(y))))
def test_dtype_wb_promotion():
wb = LowRank(B.ones(int, 5, 5)) + Diagonal(B.ones(int, 5))
assert B.dtype(wb) == np.int64
wb = LowRank(B.ones(float, 5, 5)) + Diagonal(B.ones(int, 5))
assert B.dtype(wb) == np.float64
wb = LowRank(B.ones(int, 5, 5)) + Diagonal(B.ones(float, 5))
assert B.dtype(wb) == np.float64
def test_dtype_lr_promotion():
lr = LowRank(B.ones(int, 5, 2), B.ones(int, 5, 2), B.ones(int, 2, 2))
assert B.dtype(lr) == np.int64
lr = LowRank(B.ones(float, 5, 2), B.ones(int, 5, 2), B.ones(int, 2, 2))
assert B.dtype(lr) == np.float64
lr = LowRank(B.ones(int, 5, 2), B.ones(float, 5, 2), B.ones(int, 2, 2))
assert B.dtype(lr) == np.float64
lr = LowRank(B.ones(int, 5, 2), B.ones(int, 5, 2), B.ones(float, 2, 2))
assert B.dtype(lr) == np.float64
def test_lowrank_attributes():
# Check default right and middle factor.
left = B.ones(3, 2)
lr = LowRank(left)
assert lr.left is left
assert lr.right is left
approx(lr.middle, B.eye(2))
assert lr.rank == 2
# Check given identical right.
lr = LowRank(left, left)
assert lr.left is left
assert lr.right is left
approx(lr.middle, B.eye(2))
assert lr.rank == 2
# Check given identical right and middle.
middle = B.ones(2, 2)
lr = LowRank(left, left, middle=middle)
assert lr.left is left
assert lr.right is left
approx(lr.middle, B.ones(2, 2))
assert lr.rank == 2
# Check given other right and middle factor.
right = 2 * B.ones(3, 2)
lr = LowRank(left, right, middle=middle)
assert lr.left is left
assert lr.right is right
approx(lr.middle, B.ones(2, 2))
assert lr.rank == 2
# Check rank in non-square case.
assert LowRank(B.ones(3, 2), B.ones(3, 2), B.ones(2, 2)).rank == 2
assert LowRank(B.ones(3, 2), B.ones(3, 1), B.ones(2, 1)).rank == 1
def test_lowrank_formatting():
assert (str(LowRank(B.ones(3, 1), 2 * B.ones(
3, 1))) == "<low-rank matrix: shape=3x3, dtype=float64, rank=1>")
assert (repr(LowRank(B.ones(3, 2), 2 * B.ones(
3, 2))) == "<low-rank matrix: shape=3x3, dtype=float64, rank=2\n"
" left=[[1. 1.]\n"
" [1. 1.]\n"
" [1. 1.]]\n"
" right=[[2. 2.]\n"
" [2. 2.]\n"
" [2. 2.]]>")
assert (repr(LowRank(B.ones(
3, 2))) == "<low-rank matrix: shape=3x3, dtype=float64, rank=2\n"
" left=[[1. 1.]\n"
" [1. 1.]\n"
" [1. 1.]]>")
assert (repr(LowRank(B.ones(3, 2), middle=B.ones(
2, 2))) == "<low-rank matrix: shape=3x3, dtype=float64, rank=2\n"
" left=[[1. 1.]\n"
" [1. 1.]\n"
" [1. 1.]]\n"
" middle=[[1. 1.]\n"
" [1. 1.]]>")
def test_woodbury_formatting():
diag = Diagonal(B.ones(3))
lr = LowRank(B.ones(3, 1), 2 * B.ones(3, 1))
assert str(Woodbury(diag,
lr)) == "<Woodbury matrix: shape=3x3, dtype=float64>"
assert (repr(Woodbury(
diag, lr)) == "<Woodbury matrix: shape=3x3, dtype=float64\n"
" diag=<diagonal matrix: shape=3x3, dtype=float64\n"
" diag=[1. 1. 1.]>\n"
" lr=<low-rank matrix: shape=3x3, dtype=float64, rank=1\n"
" left=[[1.]\n"
" [1.]\n"
" [1.]]\n"
" right=[[2.]\n"
" [2.]\n"
" [2.]]>>")
def compute_K_z(model):
"""Covariance matrix :math:`K_z` of :math:`z_m` for :math:`m=0,\\ldots,2M`.
Args:
model (:class:`.gprv.GPRV`): Model.
Returns:
matrix: :math:`K_z`.
"""
# Compute harmonic frequencies.
m = model.ms - B.cast(model.dtype, model.ms > model.m_max) * model.m_max
omega = 2 * B.pi * m / (model.b - model.a)
# Compute the parameters of the kernel matrix.
lam_t = 1
alpha = 0.5 * (model.b - model.a) / psd_matern_12(omega, model.lam, lam_t)
alpha = alpha + alpha * B.cast(model.dtype, model.ms == 0)
beta = 1 / (lam_t**0.5) * B.cast(model.dtype, model.ms <= model.m_max)
return Diagonal(alpha) + LowRank(left=beta[:, None])
def test_lowrank_shape_checks():
# Check that matrices must be given.
with pytest.raises(AssertionError):
LowRank(B.ones(3))
with pytest.raises(AssertionError):
LowRank(B.ones(3, 1), B.ones(3))
with pytest.raises(AssertionError):
LowRank(B.ones(3, 1), B.ones(3, 1), B.ones(1))
# Check that needs need to be compatible
with pytest.raises(AssertionError):
LowRank(B.ones(3, 1), B.ones(3, 2))
with pytest.raises(AssertionError):
LowRank(B.ones(3, 1), B.ones(3, 2), B.ones(1, 1))
with pytest.raises(AssertionError):
LowRank(B.ones(3, 1), middle=B.ones(2, 1))
def construct(diag, left, right, middle):
return Diagonal(diag) + LowRank(left, right, middle)
def construct(left, right, middle):
return LowRank(left, right, middle)
def test_woodbury_attributes():
diag = Diagonal(B.ones(3))
lr = LowRank(B.ones(3, 1), 2 * B.ones(3, 1))
wb = Woodbury(diag, lr)
assert wb.diag is diag
assert wb.lr is lr
def lr_pd(request):
code_l, code_m = request.param
return LowRank(generate(code_l), middle=generate(code_m))
def lr2(request):
code_lr, code_m = request.param
return LowRank(generate(code_lr),
generate(code_lr),
middle=generate(code_m))
def __call__(self, x, y):
if x is y:
return LowRank(uprank(x))
else:
return LowRank(left=uprank(x), right=uprank(y))