def test_triu(self):
x = torch.rand(SIZE, SIZE)
res1 = torch.triu(x)
res2 = torch.Tensor()
torch.triu(res2, x)
self.assertEqual(res1, res2, 0)
python类triu()的实例源码
def btriunpack(LU_data, LU_pivots, unpack_data=True, unpack_pivots=True):
"""Unpacks the data and pivots from a batched LU factorization (btrifact) of a tensor.
Returns a tuple indexed by:
0: The pivots.
1: The L tensor.
2: The U tensor.
Arguments:
LU_data (Tensor): The packed LU factorization data.
LU_pivots (Tensor): The packed LU factorization pivots.
unpack_data (bool): Flag indicating if the data should be unpacked.
unpack_pivots (bool): Flag indicating if the pivots should be unpacked.
"""
nBatch, sz, _ = LU_data.size()
if unpack_data:
I_U = torch.triu(torch.ones(sz, sz)).type_as(LU_data).byte().unsqueeze(0).expand(nBatch, sz, sz)
I_L = 1 - I_U
L = LU_data.new(LU_data.size()).zero_()
U = LU_data.new(LU_data.size()).zero_()
I_diag = torch.eye(sz).type_as(LU_data).byte().unsqueeze(0).expand(nBatch, sz, sz)
L[I_diag] = 1.0
L[I_L] = LU_data[I_L]
U[I_U] = LU_data[I_U]
else:
L = U = None
if unpack_pivots:
P = torch.eye(sz).type_as(LU_data).unsqueeze(0).repeat(nBatch, 1, 1)
for i in range(nBatch):
for j in range(sz):
k = LU_pivots[i, j] - 1
t = P[i, :, j].clone()
P[i, :, j] = P[i, :, k]
P[i, :, k] = t
else:
P = None
return P, L, U
def test_triu(self):
x = torch.rand(SIZE, SIZE)
res1 = torch.triu(x)
res2 = torch.Tensor()
torch.triu(x, out=res2)
self.assertEqual(res1, res2, 0)
def btriunpack(LU_data, LU_pivots, unpack_data=True, unpack_pivots=True):
"""Unpacks the data and pivots from a batched LU factorization (btrifact) of a tensor.
Returns a tuple indexed by:
0: The pivots.
1: The L tensor.
2: The U tensor.
Arguments:
LU_data (Tensor): The packed LU factorization data.
LU_pivots (Tensor): The packed LU factorization pivots.
unpack_data (bool): Flag indicating if the data should be unpacked.
unpack_pivots (bool): Flag indicating if the pivots should be unpacked.
"""
nBatch, sz, _ = LU_data.size()
if unpack_data:
I_U = torch.triu(torch.ones(sz, sz)).type_as(LU_data).byte().unsqueeze(0).expand(nBatch, sz, sz)
I_L = 1 - I_U
L = LU_data.new(LU_data.size()).zero_()
U = LU_data.new(LU_data.size()).zero_()
I_diag = torch.eye(sz).type_as(LU_data).byte().unsqueeze(0).expand(nBatch, sz, sz)
L[I_diag] = 1.0
L[I_L] = LU_data[I_L]
U[I_U] = LU_data[I_U]
else:
L = U = None
if unpack_pivots:
P = torch.eye(sz).type_as(LU_data).unsqueeze(0).repeat(nBatch, 1, 1)
for i in range(nBatch):
for j in range(sz):
k = LU_pivots[i, j] - 1
t = P[i, :, j].clone()
P[i, :, j] = P[i, :, k]
P[i, :, k] = t
else:
P = None
return P, L, U
def test_triu(self):
x = torch.rand(SIZE, SIZE)
res1 = torch.triu(x)
res2 = torch.Tensor()
torch.triu(x, out=res2)
self.assertEqual(res1, res2, 0)
def btriunpack(LU_data, LU_pivots, unpack_data=True, unpack_pivots=True):
"""Unpacks the data and pivots from a batched LU factorization (btrifact) of a tensor.
Returns a tuple indexed by:
0: The pivots.
1: The L tensor.
2: The U tensor.
Arguments:
LU_data (Tensor): The packed LU factorization data.
LU_pivots (Tensor): The packed LU factorization pivots.
unpack_data (bool): Flag indicating if the data should be unpacked.
unpack_pivots (bool): Flag indicating if the pivots should be unpacked.
"""
nBatch, sz, _ = LU_data.size()
if unpack_data:
I_U = torch.triu(torch.ones(sz, sz)).type_as(LU_data).byte().unsqueeze(0).expand(nBatch, sz, sz)
I_L = 1 - I_U
L = LU_data.new(LU_data.size()).zero_()
U = LU_data.new(LU_data.size()).zero_()
I_diag = torch.eye(sz).type_as(LU_data).byte().unsqueeze(0).expand(nBatch, sz, sz)
L[I_diag] = 1.0
L[I_L] = LU_data[I_L]
U[I_U] = LU_data[I_U]
else:
L = U = None
if unpack_pivots:
P = torch.eye(sz).type_as(LU_data).unsqueeze(0).repeat(nBatch, 1, 1)
for i in range(nBatch):
for j in range(sz):
k = LU_pivots[i, j] - 1
t = P[i, :, j].clone()
P[i, :, j] = P[i, :, k]
P[i, :, k] = t
else:
P = None
return P, L, U
def test_triu(self):
x = torch.rand(SIZE, SIZE)
res1 = torch.triu(x)
res2 = torch.Tensor()
torch.triu(x, out=res2)
self.assertEqual(res1, res2, 0)
def btriunpack(LU_data, LU_pivots, unpack_data=True, unpack_pivots=True):
r"""Unpacks the data and pivots from a batched LU factorization (btrifact) of a tensor.
Returns a tuple indexed by:
0: The pivots.
1: The L tensor.
2: The U tensor.
Arguments:
LU_data (Tensor): the packed LU factorization data
LU_pivots (Tensor): the packed LU factorization pivots
unpack_data (bool): flag indicating if the data should be unpacked
unpack_pivots (bool): tlag indicating if the pivots should be unpacked
"""
nBatch, sz, _ = LU_data.size()
if unpack_data:
I_U = torch.triu(torch.ones(sz, sz)).type_as(LU_data).byte().unsqueeze(0).expand(nBatch, sz, sz)
I_L = 1 - I_U
L = LU_data.new(LU_data.size()).zero_()
U = LU_data.new(LU_data.size()).zero_()
I_diag = torch.eye(sz).type_as(LU_data).byte().unsqueeze(0).expand(nBatch, sz, sz)
L[I_diag] = 1.0
L[I_L] = LU_data[I_L]
U[I_U] = LU_data[I_U]
else:
L = U = None
if unpack_pivots:
P = torch.eye(sz).type_as(LU_data).unsqueeze(0).repeat(nBatch, 1, 1)
for i in range(nBatch):
for j in range(sz):
k = LU_pivots[i, j] - 1
t = P[i, :, j].clone()
P[i, :, j] = P[i, :, k]
P[i, :, k] = t
else:
P = None
return P, L, U
def test_triu(self):
x = torch.rand(SIZE, SIZE)
res1 = torch.triu(x)
res2 = torch.Tensor()
torch.triu(x, out=res2)
self.assertEqual(res1, res2, 0)
def test_trtrs(self):
a = torch.Tensor(((6.80, -2.11, 5.66, 5.97, 8.23),
(-6.05, -3.30, 5.36, -4.44, 1.08),
(-0.45, 2.58, -2.70, 0.27, 9.04),
(8.32, 2.71, 4.35, -7.17, 2.14),
(-9.67, -5.14, -7.26, 6.08, -6.87))).t()
b = torch.Tensor(((4.02, 6.19, -8.22, -7.57, -3.03),
(-1.56, 4.00, -8.67, 1.75, 2.86),
(9.81, -4.09, -4.57, -8.61, 8.99))).t()
U = torch.triu(a)
L = torch.tril(a)
# solve Ux = b
x = torch.trtrs(b, U)[0]
self.assertLessEqual(b.dist(torch.mm(U, x)), 1e-12)
x = torch.trtrs(b, U, True, False, False)[0]
self.assertLessEqual(b.dist(torch.mm(U, x)), 1e-12)
# solve Lx = b
x = torch.trtrs(b, L, False)[0]
self.assertLessEqual(b.dist(torch.mm(L, x)), 1e-12)
x = torch.trtrs(b, L, False, False, False)[0]
self.assertLessEqual(b.dist(torch.mm(L, x)), 1e-12)
# solve U'x = b
x = torch.trtrs(b, U, True, True)[0]
self.assertLessEqual(b.dist(torch.mm(U.t(), x)), 1e-12)
x = torch.trtrs(b, U, True, True, False)[0]
self.assertLessEqual(b.dist(torch.mm(U.t(), x)), 1e-12)
# solve U'x = b by manual transposition
y = torch.trtrs(b, U.t(), False, False)[0]
self.assertLessEqual(x.dist(y), 1e-12)
# solve L'x = b
x = torch.trtrs(b, L, False, True)[0]
self.assertLessEqual(b.dist(torch.mm(L.t(), x)), 1e-12)
x = torch.trtrs(b, L, False, True, False)[0]
self.assertLessEqual(b.dist(torch.mm(L.t(), x)), 1e-12)
# solve L'x = b by manual transposition
y = torch.trtrs(b, L.t(), True, False)[0]
self.assertLessEqual(x.dist(y), 1e-12)
# test reuse
res1 = torch.trtrs(b,a)[0]
ta = torch.Tensor()
tb = torch.Tensor()
torch.trtrs(tb,ta,b,a)
self.assertEqual(res1, tb, 0)
tb.zero_()
torch.trtrs(tb,ta,b,a)
self.assertEqual(res1, tb, 0)
def test_trtrs(self):
a = torch.Tensor(((6.80, -2.11, 5.66, 5.97, 8.23),
(-6.05, -3.30, 5.36, -4.44, 1.08),
(-0.45, 2.58, -2.70, 0.27, 9.04),
(8.32, 2.71, 4.35, -7.17, 2.14),
(-9.67, -5.14, -7.26, 6.08, -6.87))).t()
b = torch.Tensor(((4.02, 6.19, -8.22, -7.57, -3.03),
(-1.56, 4.00, -8.67, 1.75, 2.86),
(9.81, -4.09, -4.57, -8.61, 8.99))).t()
U = torch.triu(a)
L = torch.tril(a)
# solve Ux = b
x = torch.trtrs(b, U)[0]
self.assertLessEqual(b.dist(torch.mm(U, x)), 1e-12)
x = torch.trtrs(b, U, True, False, False)[0]
self.assertLessEqual(b.dist(torch.mm(U, x)), 1e-12)
# solve Lx = b
x = torch.trtrs(b, L, False)[0]
self.assertLessEqual(b.dist(torch.mm(L, x)), 1e-12)
x = torch.trtrs(b, L, False, False, False)[0]
self.assertLessEqual(b.dist(torch.mm(L, x)), 1e-12)
# solve U'x = b
x = torch.trtrs(b, U, True, True)[0]
self.assertLessEqual(b.dist(torch.mm(U.t(), x)), 1e-12)
x = torch.trtrs(b, U, True, True, False)[0]
self.assertLessEqual(b.dist(torch.mm(U.t(), x)), 1e-12)
# solve U'x = b by manual transposition
y = torch.trtrs(b, U.t(), False, False)[0]
self.assertLessEqual(x.dist(y), 1e-12)
# solve L'x = b
x = torch.trtrs(b, L, False, True)[0]
self.assertLessEqual(b.dist(torch.mm(L.t(), x)), 1e-12)
x = torch.trtrs(b, L, False, True, False)[0]
self.assertLessEqual(b.dist(torch.mm(L.t(), x)), 1e-12)
# solve L'x = b by manual transposition
y = torch.trtrs(b, L.t(), True, False)[0]
self.assertLessEqual(x.dist(y), 1e-12)
# test reuse
res1 = torch.trtrs(b, a)[0]
ta = torch.Tensor()
tb = torch.Tensor()
torch.trtrs(b, a, out=(tb, ta))
self.assertEqual(res1, tb, 0)
tb.zero_()
torch.trtrs(b, a, out=(tb, ta))
self.assertEqual(res1, tb, 0)
def test_trtrs(self):
a = torch.Tensor(((6.80, -2.11, 5.66, 5.97, 8.23),
(-6.05, -3.30, 5.36, -4.44, 1.08),
(-0.45, 2.58, -2.70, 0.27, 9.04),
(8.32, 2.71, 4.35, -7.17, 2.14),
(-9.67, -5.14, -7.26, 6.08, -6.87))).t()
b = torch.Tensor(((4.02, 6.19, -8.22, -7.57, -3.03),
(-1.56, 4.00, -8.67, 1.75, 2.86),
(9.81, -4.09, -4.57, -8.61, 8.99))).t()
U = torch.triu(a)
L = torch.tril(a)
# solve Ux = b
x = torch.trtrs(b, U)[0]
self.assertLessEqual(b.dist(torch.mm(U, x)), 1e-12)
x = torch.trtrs(b, U, True, False, False)[0]
self.assertLessEqual(b.dist(torch.mm(U, x)), 1e-12)
# solve Lx = b
x = torch.trtrs(b, L, False)[0]
self.assertLessEqual(b.dist(torch.mm(L, x)), 1e-12)
x = torch.trtrs(b, L, False, False, False)[0]
self.assertLessEqual(b.dist(torch.mm(L, x)), 1e-12)
# solve U'x = b
x = torch.trtrs(b, U, True, True)[0]
self.assertLessEqual(b.dist(torch.mm(U.t(), x)), 1e-12)
x = torch.trtrs(b, U, True, True, False)[0]
self.assertLessEqual(b.dist(torch.mm(U.t(), x)), 1e-12)
# solve U'x = b by manual transposition
y = torch.trtrs(b, U.t(), False, False)[0]
self.assertLessEqual(x.dist(y), 1e-12)
# solve L'x = b
x = torch.trtrs(b, L, False, True)[0]
self.assertLessEqual(b.dist(torch.mm(L.t(), x)), 1e-12)
x = torch.trtrs(b, L, False, True, False)[0]
self.assertLessEqual(b.dist(torch.mm(L.t(), x)), 1e-12)
# solve L'x = b by manual transposition
y = torch.trtrs(b, L.t(), True, False)[0]
self.assertLessEqual(x.dist(y), 1e-12)
# test reuse
res1 = torch.trtrs(b, a)[0]
ta = torch.Tensor()
tb = torch.Tensor()
torch.trtrs(b, a, out=(tb, ta))
self.assertEqual(res1, tb, 0)
tb.zero_()
torch.trtrs(b, a, out=(tb, ta))
self.assertEqual(res1, tb, 0)
def test_trtrs(self):
a = torch.Tensor(((6.80, -2.11, 5.66, 5.97, 8.23),
(-6.05, -3.30, 5.36, -4.44, 1.08),
(-0.45, 2.58, -2.70, 0.27, 9.04),
(8.32, 2.71, 4.35, -7.17, 2.14),
(-9.67, -5.14, -7.26, 6.08, -6.87))).t()
b = torch.Tensor(((4.02, 6.19, -8.22, -7.57, -3.03),
(-1.56, 4.00, -8.67, 1.75, 2.86),
(9.81, -4.09, -4.57, -8.61, 8.99))).t()
U = torch.triu(a)
L = torch.tril(a)
# solve Ux = b
x = torch.trtrs(b, U)[0]
self.assertLessEqual(b.dist(torch.mm(U, x)), 1e-12)
x = torch.trtrs(b, U, True, False, False)[0]
self.assertLessEqual(b.dist(torch.mm(U, x)), 1e-12)
# solve Lx = b
x = torch.trtrs(b, L, False)[0]
self.assertLessEqual(b.dist(torch.mm(L, x)), 1e-12)
x = torch.trtrs(b, L, False, False, False)[0]
self.assertLessEqual(b.dist(torch.mm(L, x)), 1e-12)
# solve U'x = b
x = torch.trtrs(b, U, True, True)[0]
self.assertLessEqual(b.dist(torch.mm(U.t(), x)), 1e-12)
x = torch.trtrs(b, U, True, True, False)[0]
self.assertLessEqual(b.dist(torch.mm(U.t(), x)), 1e-12)
# solve U'x = b by manual transposition
y = torch.trtrs(b, U.t(), False, False)[0]
self.assertLessEqual(x.dist(y), 1e-12)
# solve L'x = b
x = torch.trtrs(b, L, False, True)[0]
self.assertLessEqual(b.dist(torch.mm(L.t(), x)), 1e-12)
x = torch.trtrs(b, L, False, True, False)[0]
self.assertLessEqual(b.dist(torch.mm(L.t(), x)), 1e-12)
# solve L'x = b by manual transposition
y = torch.trtrs(b, L.t(), True, False)[0]
self.assertLessEqual(x.dist(y), 1e-12)
# test reuse
res1 = torch.trtrs(b, a)[0]
ta = torch.Tensor()
tb = torch.Tensor()
torch.trtrs(b, a, out=(tb, ta))
self.assertEqual(res1, tb, 0)
tb.zero_()
torch.trtrs(b, a, out=(tb, ta))
self.assertEqual(res1, tb, 0)
def test_trtrs(self):
a = torch.Tensor(((6.80, -2.11, 5.66, 5.97, 8.23),
(-6.05, -3.30, 5.36, -4.44, 1.08),
(-0.45, 2.58, -2.70, 0.27, 9.04),
(8.32, 2.71, 4.35, -7.17, 2.14),
(-9.67, -5.14, -7.26, 6.08, -6.87))).t()
b = torch.Tensor(((4.02, 6.19, -8.22, -7.57, -3.03),
(-1.56, 4.00, -8.67, 1.75, 2.86),
(9.81, -4.09, -4.57, -8.61, 8.99))).t()
U = torch.triu(a)
L = torch.tril(a)
# solve Ux = b
x = torch.trtrs(b, U)[0]
self.assertLessEqual(b.dist(torch.mm(U, x)), 1e-12)
x = torch.trtrs(b, U, True, False, False)[0]
self.assertLessEqual(b.dist(torch.mm(U, x)), 1e-12)
# solve Lx = b
x = torch.trtrs(b, L, False)[0]
self.assertLessEqual(b.dist(torch.mm(L, x)), 1e-12)
x = torch.trtrs(b, L, False, False, False)[0]
self.assertLessEqual(b.dist(torch.mm(L, x)), 1e-12)
# solve U'x = b
x = torch.trtrs(b, U, True, True)[0]
self.assertLessEqual(b.dist(torch.mm(U.t(), x)), 1e-12)
x = torch.trtrs(b, U, True, True, False)[0]
self.assertLessEqual(b.dist(torch.mm(U.t(), x)), 1e-12)
# solve U'x = b by manual transposition
y = torch.trtrs(b, U.t(), False, False)[0]
self.assertLessEqual(x.dist(y), 1e-12)
# solve L'x = b
x = torch.trtrs(b, L, False, True)[0]
self.assertLessEqual(b.dist(torch.mm(L.t(), x)), 1e-12)
x = torch.trtrs(b, L, False, True, False)[0]
self.assertLessEqual(b.dist(torch.mm(L.t(), x)), 1e-12)
# solve L'x = b by manual transposition
y = torch.trtrs(b, L.t(), True, False)[0]
self.assertLessEqual(x.dist(y), 1e-12)
# test reuse
res1 = torch.trtrs(b, a)[0]
ta = torch.Tensor()
tb = torch.Tensor()
torch.trtrs(b, a, out=(tb, ta))
self.assertEqual(res1, tb, 0)
tb.zero_()
torch.trtrs(b, a, out=(tb, ta))
self.assertEqual(res1, tb, 0)
