def test_equality():
# Test `Dense.`
a = Dense(np.random.randn(4, 2))
yield assert_allclose, a == a, dense(a) == dense(a)
# Test `Diagonal`.
d = Diagonal(np.random.randn(4))
yield assert_allclose, d == d, B.diag(d) == B.diag(d)
# Test `LowRank`.
lr = LowRank(left=np.random.randn(4, 2), middle=np.random.randn(2, 2))
yield assert_allclose, lr == lr, (lr.l == lr.l, lr.m == lr.m, lr.r == lr.r)
# Test `Woodbury`.
yield assert_allclose, (lr + d) == (lr + d), (lr == lr, d == d)
# Test `Constant`.
c1 = Constant.from_(1, a)
c1_2 = Constant(1, 4, 3)
c2 = Constant.from_(2, a)
yield eq, c1, c1
yield neq, c1, c1_2
yield neq, c1, c2
# Test `One`.
one1 = One(np.float64, 4, 2)
one2 = One(np.float64, 4, 3)
yield eq, one1, one1
yield neq, one1, one2
# Test `Zero`.
zero1 = Zero(np.float64, 4, 2)
zero2 = Zero(np.float64, 4, 3)
yield eq, zero1, zero1
yield neq, zero1, zero2
def test_dtype():
# Test `Dense`.
yield eq, B.dtype(Dense(np.array([[1]]))), int
yield eq, B.dtype(Dense(np.array([[1.0]]))), float
# Test `Diagonal`.
diag_int = Diagonal(np.array([1]))
diag_float = Diagonal(np.array([1.0]))
yield eq, B.dtype(diag_int), int
yield eq, B.dtype(diag_float), float
# Test `LowRank`.
lr_int = LowRank(left=np.array([[1]]),
right=np.array([[2]]),
middle=np.array([[3]]))
lr_float = LowRank(left=np.array([[1.0]]),
right=np.array([[2.0]]),
middle=np.array([[3.0]]))
yield eq, B.dtype(lr_int), int
yield eq, B.dtype(lr_float), float
# Test `Constant`.
yield eq, B.dtype(Constant(1, rows=1)), int
yield eq, B.dtype(Constant(1.0, rows=1)), float
# Test `Woodbury`.
yield eq, B.dtype(Woodbury(diag_int, lr_int)), int
yield eq, B.dtype(Woodbury(diag_float, lr_float)), float
def test_equality():
# Test `Dense.`
a = Dense(np.random.randn(4, 2))
allclose(a == a, to_np(a) == to_np(a))
# Test `Diagonal`.
d = Diagonal(np.random.randn(4))
allclose(d == d, B.diag(d) == B.diag(d))
# Test `LowRank`.
lr = LowRank(left=np.random.randn(4, 2), middle=np.random.randn(2, 2))
allclose(lr == lr, (lr.l == lr.l, lr.m == lr.m, lr.r == lr.r))
# Test `Woodbury`.
allclose((lr + d) == (lr + d), (lr == lr, d == d))
# Test `Constant`.
c1 = Constant.from_(1, a)
c1_2 = Constant(1, 4, 3)
c2 = Constant.from_(2, a)
assert c1 == c1
assert c1 != c1_2
assert c1 != c2
# Test `One`.
one1 = One(np.float64, 4, 2)
one2 = One(np.float64, 4, 3)
assert one1 == one1
assert one1 != one2
# Test `Zero`.
zero1 = Zero(np.float64, 4, 2)
zero2 = Zero(np.float64, 4, 3)
assert zero1 == zero1
assert zero1 != zero2
def test_dtype():
# Test `Dense`.
assert B.dtype(Dense(np.array([[1]]))) == np.int64
assert B.dtype(Dense(np.array([[1.0]]))) == np.float64
# Test `Diagonal`.
diag_int = Diagonal(np.array([1]))
diag_float = Diagonal(np.array([1.0]))
assert B.dtype(diag_int) == np.int64
assert B.dtype(diag_float) == np.float64
# Test `LowRank`.
lr_int = LowRank(left=np.array([[1]]),
right=np.array([[2]]),
middle=np.array([[3]]))
lr_float = LowRank(left=np.array([[1.0]]),
right=np.array([[2.0]]),
middle=np.array([[3.0]]))
assert B.dtype(lr_int) == np.int64
assert B.dtype(lr_float) == np.float64
# Test `Constant`.
assert B.dtype(Constant(1, rows=1)) == int
assert B.dtype(Constant(1.0, rows=1)) == float
# Test `Woodbury`.
assert B.dtype(Woodbury(diag_int, lr_int)) == np.int64
assert B.dtype(Woodbury(diag_float, lr_float)) == np.float64
def test_constant_zero_one():
a = np.random.randn(4, 2)
b = Dense(a)
yield assert_allclose, Zero.from_(a), np.zeros((4, 2))
yield assert_allclose, Zero.from_(b), np.zeros((4, 2))
yield assert_allclose, One.from_(a), np.ones((4, 2))
yield assert_allclose, One.from_(b), np.ones((4, 2))
yield assert_allclose, Constant.from_(2, a), 2 * np.ones((4, 2))
yield assert_allclose, Constant.from_(2, b), 2 * np.ones((4, 2))
def test_constant_zero_one():
a = np.random.randn(4, 2)
b = Dense(a)
allclose(Zero.from_(a), np.zeros((4, 2)))
allclose(Zero.from_(b), np.zeros((4, 2)))
allclose(One.from_(a), np.ones((4, 2)))
allclose(One.from_(b), np.ones((4, 2)))
allclose(Constant.from_(2, a), 2 * np.ones((4, 2)))
allclose(Constant.from_(2, b), 2 * np.ones((4, 2)))
def test_arithmetic_and_shapes():
a = Dense(np.random.randn(4, 3))
d = Diagonal(np.array([1.0, 2.0, 3.0]), rows=4, cols=3)
lr = LowRank(left=np.random.randn(4, 2),
right=np.random.randn(3, 2),
middle=np.random.randn(2, 2))
zero = Zero.from_(a)
one = One.from_(a)
constant = Constant.from_(2.0, a)
wb = d + lr
# Aggregate all matrices.
candidates = [a, d, lr, wb, constant, one, zero, 2, 1, 0]
# Check division.
yield assert_allclose, a.__div__(5.0), dense(a) / 5.0
yield assert_allclose, a.__truediv__(5.0), dense(a) / 5.0
# Check shapes.
for m in candidates:
yield eq, B.shape(a), (4, 3)
# Check interactions.
for m1, m2 in product(candidates, candidates):
yield assert_allclose, m1 * m2, dense(m1) * dense(m2)
yield assert_allclose, m1 + m2, dense(m1) + dense(m2)
yield assert_allclose, m1 - m2, dense(m1) - dense(m2)
def test_diag():
# Test `Dense`.
a = np.random.randn(5, 3)
yield assert_allclose, B.diag(Dense(a)), np.diag(a)
# Test `Diagonal`.
yield assert_allclose, B.diag(Diagonal([1, 2, 3])), [1, 2, 3]
yield assert_allclose, B.diag(Diagonal([1, 2, 3], 2)), [1, 2]
yield assert_allclose, B.diag(Diagonal([1, 2, 3], 4)), [1, 2, 3, 0]
# Test `LowRank`.
b = np.random.randn(10, 3)
yield assert_allclose, B.diag(LowRank(left=a,
right=a)), np.diag(a.dot(a.T))
yield assert_allclose, B.diag(LowRank(left=a,
right=b)), np.diag(a.dot(b.T))
yield assert_allclose, B.diag(LowRank(left=b,
right=b)), np.diag(b.dot(b.T))
# Test `Constant`.
yield assert_allclose, B.diag(Constant(1, rows=3, cols=5)), np.ones(3)
# Test `Woodbury`.
yield assert_allclose, \
B.diag(Woodbury(Diagonal([1, 2, 3], rows=5, cols=10),
LowRank(left=a, right=b))), \
np.diag(a.dot(b.T) + np.concatenate((np.diag([1, 2, 3, 0, 0]),
np.zeros((5, 5))), axis=1))
def test_arithmetic_and_shapes():
a = Dense(np.random.randn(4, 3))
d = Diagonal(np.array([1.0, 2.0, 3.0]), rows=4, cols=3)
lr = LowRank(left=np.random.randn(4, 2),
right=np.random.randn(3, 2),
middle=np.random.randn(2, 2))
zero = Zero.from_(a)
one = One.from_(a)
constant = Constant.from_(2.0, a)
wb = d + lr
# Aggregate all matrices.
candidates = [a, d, lr, wb, constant, one, zero, 2, 1, 0, 2.0, 1.0, 0.0]
# Check division.
allclose(a.__div__(5.0), to_np(a) / 5.0)
allclose(a.__rdiv__(5.0), 5.0 / to_np(a))
allclose(a.__truediv__(5.0), to_np(a) / 5.0)
allclose(a.__rtruediv__(5.0), 5.0 / to_np(a))
allclose(B.divide(a, 5.0), to_np(a) / 5.0)
allclose(B.divide(a, a), B.ones(to_np(a)))
# Check shapes.
for m in candidates:
assert B.shape(a) == (4, 3)
# Check interactions.
for m1, m2 in product(candidates, candidates):
allclose(m1 * m2, to_np(m1) * to_np(m2))
allclose(m1 + m2, to_np(m1) + to_np(m2))
allclose(m1 - m2, to_np(m1) - to_np(m2))
def test_transposition():
def compare(a):
assert_allclose(B.transpose(a), dense(a).T)
d = Diagonal([1, 2, 3], rows=5, cols=10)
lr = LowRank(left=np.random.randn(5, 3), right=np.random.randn(10, 3))
yield compare, Dense(np.random.randn(5, 5))
yield compare, d
yield compare, lr
yield compare, d + lr
yield compare, Constant(5, rows=4, cols=2)
def test_transposition():
def compare(a):
allclose(B.transpose(a), to_np(a).T)
d = Diagonal(np.array([1, 2, 3]), rows=5, cols=10)
lr = LowRank(left=np.random.randn(5, 3), right=np.random.randn(10, 3))
compare(Dense(np.random.randn(5, 5)))
compare(d)
compare(lr)
compare(d + lr)
compare(Constant(5, rows=4, cols=2))