1956   // tril(L^H gL) = tril(L^H (triu(gL, 1) + tril(gL)))  in cholesky_backward()
1957   //              = tril(L^H tril(gL)) + tril(L^H triu(gL, 1))  in cholesky_backward()
1959   // since tril(L^H triu(gL, 1)) = 0, as L^H triu(gL, 1) is upper triangular  in cholesky_backward()
3917   // and define syminv(X) = triu(X) - 0.5 * diag(X) the inverse of  in linalg_qr_jvp()
3918   // sym : Triu(k, diag \in \mathbb{R}) -> Her(k) to give  in linalg_qr_jvp()
3952       auto ret = X.triu();  in linalg_qr_jvp()
4009   // need are syminv*(R) = 0.5 * (R.triu() + R.triu()^H - Re diag(R)) sym*(X) =  in linalg_qr_backward()
4011   // syminvadj(triu(gR R^H - Q^H gQ)))R^{-H}  in linalg_qr_backward()
4065     gA = Q.matmul(syminvadj(gA.triu()));  in linalg_qr_backward()
4378           grad_a = grad_a.triu((int)unitriangular);  in triangular_solve_backward()
4428   const Tensor proj_A_t = upper ? A_t.triu(static_cast<int>(unitriangular))  in linalg_solve_triangular_forward_AD()
4466   // triangular matrices of the formula above, i.e. simply taking triu (resp.  in linalg_solve_triangular_backward()
4485     G_A = upper ? G_A.triu(static_cast<int>(unitriangular))  in linalg_solve_triangular_backward()
5655 // 1_U = 1.triu(),
5720   //   gU = gR.triu()  in linalg_lu_solve_LU()
5725   //   gU = (L^H gR U^{-H}).triu()  in linalg_lu_solve_LU()
5750     return gL + gR.triu();  in linalg_lu_solve_LU()
5758     // gU = (L^H gR U^{-H}).triu()  in linalg_lu_solve_LU()
5761                   .triu();  in linalg_lu_solve_LU()
5802     auto U = LU.triu();  in linalg_lu_solve_jvp()
5804         U, dLU.triu() + R.matmul(U), /*upper*/ true);  in linalg_lu_solve_jvp()
5819                  U, L.matmul(dLU.triu()), /*upper*/ true, /*left*/ false) +  in linalg_lu_solve_jvp()
5950     return n == k ? U.triu() : U.narrow_symint(-1, 0, k).triu();  in lu_unpack_backward()
5959         return L_grad.tril(-1) + U_grad.triu();  in lu_unpack_backward()
5979       return U_grad.triu();  in lu_unpack_backward()
5984           {U_grad.triu(), at::zeros_symint(size, U_grad.options())},  in lu_unpack_backward()
6475       A_grad = A_grad.defined() ? A_grad + U_grad.matmul(U.mH()).triu()  in linalg_lu_backward()
6476                                 : U_grad.matmul(U.mH()).triu();  in linalg_lu_backward()
6504       A_grad = A_grad.defined() ? A_grad - U_grad.triu().matmul(U.mH())  in linalg_lu_backward()
6505                                 : -U_grad.triu().matmul(U.mH());  in linalg_lu_backward()
6515           at::cat({A_grad + get_U1(U_grad).triu(), get_U2(U_grad)}, /*dim=*/-1);  in linalg_lu_backward()
6551         A_grad.triu(),  in linalg_lu_backward()
6635   auto dU1 = dK.triu().matmul(U1);  in linalg_lu_jvp()
6652     // dL2 := PdA2 U^{-1} - L2 dK.triu()  in linalg_lu_jvp()
6657         L2.matmul(dK.triu());  in linalg_lu_jvp()