Python torch 模块，trtrs() 实例源码
我们从Python开源项目中，提取了以下8个代码示例，用于说明如何使用torch.trtrs()。
def _ssor_preconditioner(self, lhs_mat, mat):
if lhs_mat.ndimension() == 2:
DL = lhs_mat.tril()
D = lhs_mat.diag()
upper_part = (1 / D).expand_as(DL).mul(DL.t())
Minv_times_mat = torch.trtrs(torch.trtrs(mat, DL, upper=False)[0], upper_part)[0]
elif lhs_mat.ndimension() == 3:
if mat.size(0) == 1 and lhs_mat.size(0) != 1:
mat = mat.expand(*([lhs_mat.size(0)] + list(mat.size())[1:]))
Minv_times_mat = mat.new(*mat.size())
for i in range(lhs_mat.size(0)):
DL = lhs_mat[i].tril()
D = lhs_mat[i].diag()
upper_part = (1 / D).expand_as(DL).mul(DL.t())
Minv_times_mat[i].copy_(torch.trtrs(torch.trtrs(mat[i], DL, upper=False)[0], upper_part)[0])
else:
raise RuntimeError('Invalid number of dimensions')
return Minv_times_mat
def pre_factor_kkt(Q, G, A):
""" Perform all one-time factorizations and cache relevant matrix products"""
nineq, nz, neq, _ = get_sizes(G, A)
# S = [ A Q^{-1} A^T A Q^{-1} G^T ]
# [ G Q^{-1} A^T G Q^{-1} G^T + D^{-1} ]
U_Q = torch.potrf(Q)
# partial cholesky of S matrix
U_S = torch.zeros(neq + nineq, neq + nineq).type_as(Q)
G_invQ_GT = torch.mm(G, torch.potrs(G.t(), U_Q))
R = G_invQ_GT
if neq > 0:
invQ_AT = torch.potrs(A.t(), U_Q)
A_invQ_AT = torch.mm(A, invQ_AT)
G_invQ_AT = torch.mm(G, invQ_AT)
# TODO: torch.potrf sometimes says the matrix is not PSD but
# numpy does? I filed an issue at
# https://github.com/pytorch/pytorch/issues/199
try:
U11 = torch.potrf(A_invQ_AT)
except:
U11 = torch.Tensor(np.linalg.cholesky(
A_invQ_AT.cpu().numpy())).type_as(A_invQ_AT)
# TODO: torch.trtrs is currently not implemented on the GPU
# and we are using gesv as a workaround.
U12 = torch.gesv(G_invQ_AT.t(), U11.t())[0]
U_S[:neq, :neq] = U11
U_S[:neq, neq:] = U12
R -= torch.mm(U12.t(), U12)
return U_Q, U_S, R
def test_trtrs(self):
def _test_with_size(N, C):
A = Variable(torch.rand(N, N), requires_grad=True)
b = Variable(torch.rand(N, C), requires_grad=True)
for upper, transpose, unitriangular in product((True, False), repeat=3):
def func(A, b):
return torch.trtrs(b, A, upper, transpose, unitriangular)
gradcheck(func, [A, b])
gradgradcheck(func, [A, b])
_test_with_size(S, S + 1)
_test_with_size(S, S - 1)
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)