def backward(ctx, grad_output):
L, = ctx.saved_variables
if ctx.upper:
L = L.t()
grad_output = grad_output.t()
# make sure not to double-count variation, since
# only half of output matrix is unique
Lbar = grad_output.tril()
P = Potrf.phi(torch.mm(L.t(), Lbar))
S = torch.gesv(P + P.t(), L.t())[0]
S = torch.gesv(S.t(), L.t())[0]
S = Potrf.phi(S)
return S, None
python类gesv()的实例源码
def test_gesv(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()
res1 = torch.gesv(b,a)[0]
self.assertLessEqual(b.dist(torch.mm(a, res1)), 1e-12)
ta = torch.Tensor()
tb = torch.Tensor()
res2 = torch.gesv(tb, ta, b, a)[0]
res3 = torch.gesv(b, a, b, a)[0]
self.assertEqual(res1, tb)
self.assertEqual(res1, b)
self.assertEqual(res1, res2)
self.assertEqual(res1, res3)
# test reuse
res1 = torch.gesv(b, a)[0]
ta = torch.Tensor()
tb = torch.Tensor()
torch.gesv(tb, ta, b, a)[0]
self.assertEqual(res1, tb)
torch.gesv(tb, ta, b, a)[0]
self.assertEqual(res1, tb)
def test_gesv(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()
res1 = torch.gesv(b, a)[0]
self.assertLessEqual(b.dist(torch.mm(a, res1)), 1e-12)
ta = torch.Tensor()
tb = torch.Tensor()
res2 = torch.gesv(b, a, out=(tb, ta))[0]
res3 = torch.gesv(b, a, out=(b, a))[0]
self.assertEqual(res1, tb)
self.assertEqual(res1, b)
self.assertEqual(res1, res2)
self.assertEqual(res1, res3)
# test reuse
res1 = torch.gesv(b, a)[0]
ta = torch.Tensor()
tb = torch.Tensor()
torch.gesv(b, a, out=(tb, ta))[0]
self.assertEqual(res1, tb)
torch.gesv(b, a, out=(tb, ta))[0]
self.assertEqual(res1, tb)
def test_gesv(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()
res1 = torch.gesv(b, a)[0]
self.assertLessEqual(b.dist(torch.mm(a, res1)), 1e-12)
ta = torch.Tensor()
tb = torch.Tensor()
res2 = torch.gesv(b, a, out=(tb, ta))[0]
res3 = torch.gesv(b, a, out=(b, a))[0]
self.assertEqual(res1, tb)
self.assertEqual(res1, b)
self.assertEqual(res1, res2)
self.assertEqual(res1, res3)
# test reuse
res1 = torch.gesv(b, a)[0]
ta = torch.Tensor()
tb = torch.Tensor()
torch.gesv(b, a, out=(tb, ta))[0]
self.assertEqual(res1, tb)
torch.gesv(b, a, out=(tb, ta))[0]
self.assertEqual(res1, tb)
def forward(ctx, b, a):
# TODO see if one can backprop through LU
X, LU = torch.gesv(b, a)
ctx.save_for_backward(X, a)
ctx.mark_non_differentiable(LU)
return X, LU
def backward(ctx, grad_output, grad_LU=None):
X, a = ctx.saved_variables
grad_b, _ = torch.gesv(grad_output, a.t())
grad_a = -torch.mm(grad_b, X.t())
return grad_b, grad_a
def test_gesv(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()
res1 = torch.gesv(b, a)[0]
self.assertLessEqual(b.dist(torch.mm(a, res1)), 1e-12)
ta = torch.Tensor()
tb = torch.Tensor()
res2 = torch.gesv(b, a, out=(tb, ta))[0]
res3 = torch.gesv(b, a, out=(b, a))[0]
self.assertEqual(res1, tb)
self.assertEqual(res1, b)
self.assertEqual(res1, res2)
self.assertEqual(res1, res3)
# test reuse
res1 = torch.gesv(b, a)[0]
ta = torch.Tensor()
tb = torch.Tensor()
torch.gesv(b, a, out=(tb, ta))[0]
self.assertEqual(res1, tb)
torch.gesv(b, a, out=(tb, ta))[0]
self.assertEqual(res1, tb)
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 solve(matrix1, matrix2):
solution, _ = torch.gesv(matrix2, matrix1)
return solution
def test_gesv(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()
res1 = torch.gesv(b, a)[0]
self.assertLessEqual(b.dist(torch.mm(a, res1)), 1e-12)
ta = torch.Tensor()
tb = torch.Tensor()
res2 = torch.gesv(b, a, out=(tb, ta))[0]
res3 = torch.gesv(b, a, out=(b, a))[0]
self.assertEqual(res1, tb)
self.assertEqual(res1, b)
self.assertEqual(res1, res2)
self.assertEqual(res1, res3)
# test reuse
res1 = torch.gesv(b, a)[0]
ta = torch.Tensor()
tb = torch.Tensor()
torch.gesv(b, a, out=(tb, ta))[0]
self.assertEqual(res1, tb)
torch.gesv(b, a, out=(tb, ta))[0]
self.assertEqual(res1, tb)
