我们从Python开源项目中，提取了以下22个代码示例，用于说明如何使用torch.potrf()。
def test_cholesky(self): x = torch.rand(10, 10) + 1e-1 A = torch.mm(x, x.t()) # default Case C = torch.potrf(A) B = torch.mm(C.t(), C) self.assertEqual(A, B, 1e-14) # test Upper Triangular U = torch.potrf(A, True) B = torch.mm(U.t(), U) self.assertEqual(A, B, 1e-14, 'potrf (upper) did not allow rebuilding the original matrix') # test Lower Triangular L = torch.potrf(A, False) B = torch.mm(L, L.t()) self.assertEqual(A, B, 1e-14, 'potrf (lower) did not allow rebuilding the original matrix')
def test_potrs(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() # make sure 'a' is symmetric PSD a = torch.mm(a, a.t()) # upper Triangular Test U = torch.potrf(a) x = torch.potrs(b, U) self.assertLessEqual(b.dist(torch.mm(a, x)), 1e-12) # lower Triangular Test L = torch.potrf(a, False) x = torch.potrs(b, L, False) self.assertLessEqual(b.dist(torch.mm(a, x)), 1e-12)
def __init__(self, nFeatures, args): super().__init__() nHidden, neq, nineq = 2*nFeatures-1,0,2*nFeatures-2 assert(neq==0) # self.fc1 = nn.Linear(nFeatures, nHidden) self.M = Variable(torch.tril(torch.ones(nHidden, nHidden)).cuda()) Q = 1e-8*torch.eye(nHidden) Q[:nFeatures,:nFeatures] = torch.eye(nFeatures) self.L = Variable(torch.potrf(Q)) self.D = Parameter(0.3*torch.randn(nFeatures-1, nFeatures)) # self.lam = Parameter(20.*torch.ones(1)) self.h = Variable(torch.zeros(nineq)) self.nFeatures = nFeatures self.nHidden = nHidden self.neq = neq self.nineq = nineq self.args = args
def test_potrs(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() # make sure 'a' is symmetric PSD a = torch.mm(a, a.t()) # upper Triangular Test U = torch.potrf(a) x = torch.potrs(b, U) self.assertLessEqual(b.dist(torch.mm(a, x)), 1e-12) # lower Triangular Test L = torch.potrf(a, False) x = torch.potrs(b, L, False) self.assertLessEqual(b.dist(torch.mm(a, x)), 1e-12)
def tset_potri(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() # make sure 'a' is symmetric PSD a = a * a.t() # compute inverse directly inv0 = torch.inverse(a) # default case chol = torch.potrf(a) inv1 = torch.potri(chol) self.assertLessEqual(inv0.dist(inv1), 1e-12) # upper Triangular Test chol = torch.potrf(a, 'U') inv1 = torch.potri(chol, 'U') self.assertLessEqual(inv0.dist(inv1), 1e-12) # lower Triangular Test chol = torch.potrf(a, 'L') inv1 = torch.potri(chol, 'L') self.assertLessEqual(inv0.dist(inv1), 1e-12)
def tset_potri(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() # make sure 'a' is symmetric PSD a = a * a.t() # compute inverse directly inv0 = torch.inverse(a) # default case chol = torch.potrf(a) inv1 = torch.potri(chol) self.assertLessEqual(inv0.dist(inv1), 1e-12) # upper Triangular Test chol = torch.potrf(a, 'U') inv1 = torch.potri(chol, 'U') self.assertLessEqual(inv0.dist(inv1), 1e-12) # lower Triangular Test chol = torch.potrf(a, 'L') inv1 = torch.potri(chol, 'L') self.assertLessEqual(inv0.dist(inv1), 1e-12)
def forward(ctx, a, upper=True): ctx.upper = upper fact = torch.potrf(a, upper) ctx.save_for_backward(fact) return fact
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 factor_kkt(U_S, R, d): """ Factor the U22 block that we can only do after we know D. """ nineq = R.size(0) U_S[-nineq:, -nineq:] = torch.potrf(R + torch.diag(1 / d.cpu()).type_as(d))
def factor_solve_kkt(Q, D, G, A, rx, rs, rz, ry): nineq, nz, neq, _ = get_sizes(G, A) if neq > 0: H_ = torch.cat([torch.cat([Q, torch.zeros(nz, nineq).type_as(Q)], 1), torch.cat([torch.zeros(nineq, nz).type_as(Q), D], 1)], 0) A_ = torch.cat([torch.cat([G, torch.eye(nineq).type_as(Q)], 1), torch.cat([A, torch.zeros(neq, nineq).type_as(Q)], 1)], 0) g_ = torch.cat([rx, rs], 0) h_ = torch.cat([rz, ry], 0) else: H_ = torch.cat([torch.cat([Q, torch.zeros(nz, nineq).type_as(Q)], 1), torch.cat([torch.zeros(nineq, nz).type_as(Q), D], 1)], 0) A_ = torch.cat([G, torch.eye(nineq).type_as(Q)], 1) g_ = torch.cat([rx, rs], 0) h_ = rz U_H_ = torch.potrf(H_) invH_A_ = torch.potrs(A_.t(), U_H_) invH_g_ = torch.potrs(g_.view(-1, 1), U_H_).view(-1) S_ = torch.mm(A_, invH_A_) U_S_ = torch.potrf(S_) t_ = torch.mv(A_, invH_g_).view(-1, 1) - h_ w_ = -torch.potrs(t_, U_S_).view(-1) v_ = torch.potrs(-g_.view(-1, 1) - torch.mv(A_.t(), w_), U_H_).view(-1) return v_[:nz], v_[nz:], w_[:nineq], w_[nineq:] if neq > 0 else None
def test_potrf(self): root = Variable(torch.tril(torch.rand(S, S)), requires_grad=True) def run_test(upper): def func(root): x = torch.mm(root, root.t()) return torch.potrf(x, upper) gradcheck(func, [root]) gradgradcheck(func, [root]) run_test(upper=True) run_test(upper=False)
def __init__(self, nFeatures, args): super(OptNet, self).__init__() nHidden, neq, nineq = 2*nFeatures-1,0,2*nFeatures-2 assert(neq==0) self.fc1 = nn.Linear(nFeatures, nHidden) self.M = Variable(torch.tril(torch.ones(nHidden, nHidden)).cuda()) if args.tvInit: Q = 1e-8*torch.eye(nHidden) Q[:nFeatures,:nFeatures] = torch.eye(nFeatures) self.L = Parameter(torch.potrf(Q)) D = torch.zeros(nFeatures-1, nFeatures) D[:nFeatures-1,:nFeatures-1] = torch.eye(nFeatures-1) D[:nFeatures-1,1:nFeatures] -= torch.eye(nFeatures-1) G_ = block((( D, -torch.eye(nFeatures-1)), (-D, -torch.eye(nFeatures-1)))) self.G = Parameter(G_) self.s0 = Parameter(torch.ones(2*nFeatures-2)+1e-6*torch.randn(2*nFeatures-2)) G_pinv = (G_.t().mm(G_)+1e-5*torch.eye(nHidden)).inverse().mm(G_.t()) self.z0 = Parameter(-G_pinv.mv(self.s0.data)+1e-6*torch.randn(nHidden)) lam = 21.21 W_fc1, b_fc1 = self.fc1.weight, self.fc1.bias W_fc1.data[:,:] = 1e-3*torch.randn((2*nFeatures-1, nFeatures)) # W_fc1.data[:,:] = 0.0 W_fc1.data[:nFeatures,:nFeatures] += -torch.eye(nFeatures) # b_fc1.data[:] = torch.zeros(2*nFeatures-1) b_fc1.data[:] = 0.0 b_fc1.data[nFeatures:2*nFeatures-1] = lam else: self.L = Parameter(torch.tril(torch.rand(nHidden, nHidden))) self.G = Parameter(torch.Tensor(nineq,nHidden).uniform_(-1,1)) self.z0 = Parameter(torch.zeros(nHidden)) self.s0 = Parameter(torch.ones(nineq)) self.nFeatures = nFeatures self.nHidden = nHidden self.neq = neq self.nineq = nineq self.args = args
