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.potrs()。
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 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 solve_kkt(U_Q, d, G, A, U_S, rx, rs, rz, ry, dbg=False): """ Solve KKT equations for the affine step""" nineq, nz, neq, _ = get_sizes(G, A) invQ_rx = torch.potrs(rx.view(-1, 1), U_Q).view(-1) if neq > 0: h = torch.cat([torch.mv(A, invQ_rx) - ry, torch.mv(G, invQ_rx) + rs / d - rz], 0) else: h = torch.mv(G, invQ_rx) + rs / d - rz w = -torch.potrs(h.view(-1, 1), U_S).view(-1) g1 = -rx - torch.mv(G.t(), w[neq:]) if neq > 0: g1 -= torch.mv(A.t(), w[:neq]) g2 = -rs - w[neq:] dx = torch.potrs(g1.view(-1, 1), U_Q).view(-1) ds = g2 / d dz = w[neq:] dy = w[:neq] if neq > 0 else None # if np.all(np.array([x.norm() for x in [rx, rs, rz, ry]]) != 0): if dbg: import IPython import sys IPython.embed() sys.exit(-1) # if rs.norm() > 0: import IPython, sys; IPython.embed(); sys.exit(-1) return dx, ds, dz, dy
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_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
