batch.py 文件源码

def pre_factor_kkt(Q, G, A):
    """ Perform all one-time factorizations and cache relevant matrix products"""
    nineq, nz, neq, nBatch = get_sizes(G, A)

    try:
        Q_LU = btrifact_hack(Q)
    except:
        raise RuntimeError("""
qpth Error: Cannot perform LU factorization on Q.
Please make sure that your Q matrix is PSD and has
a non-zero diagonal.
""")

    # S = [ A Q^{-1} A^T        A Q^{-1} G^T          ]
    #     [ G Q^{-1} A^T        G Q^{-1} G^T + D^{-1} ]
    #
    # We compute a partial LU decomposition of the S matrix
    # that can be completed once D^{-1} is known.
    # See the 'Block LU factorization' part of our website
    # for more details.

    G_invQ_GT = torch.bmm(G, G.transpose(1, 2).btrisolve(*Q_LU))
    R = G_invQ_GT.clone()
    S_LU_pivots = torch.IntTensor(range(1, 1 + neq + nineq)).unsqueeze(0) \
        .repeat(nBatch, 1).type_as(Q).int()
    if neq > 0:
        invQ_AT = A.transpose(1, 2).btrisolve(*Q_LU)
        A_invQ_AT = torch.bmm(A, invQ_AT)
        G_invQ_AT = torch.bmm(G, invQ_AT)

        LU_A_invQ_AT = btrifact_hack(A_invQ_AT)
        P_A_invQ_AT, L_A_invQ_AT, U_A_invQ_AT = torch.btriunpack(*LU_A_invQ_AT)
        P_A_invQ_AT = P_A_invQ_AT.type_as(A_invQ_AT)

        S_LU_11 = LU_A_invQ_AT[0]
        U_A_invQ_AT_inv = (P_A_invQ_AT.bmm(L_A_invQ_AT)
                           ).btrisolve(*LU_A_invQ_AT)
        S_LU_21 = G_invQ_AT.bmm(U_A_invQ_AT_inv)
        T = G_invQ_AT.transpose(1, 2).btrisolve(*LU_A_invQ_AT)
        S_LU_12 = U_A_invQ_AT.bmm(T)
        S_LU_22 = torch.zeros(nBatch, nineq, nineq).type_as(Q)
        S_LU_data = torch.cat((torch.cat((S_LU_11, S_LU_12), 2),
                               torch.cat((S_LU_21, S_LU_22), 2)),
                              1)
        S_LU_pivots[:, :neq] = LU_A_invQ_AT[1]

        R -= G_invQ_AT.bmm(T)
    else:
        S_LU_data = torch.zeros(nBatch, nineq, nineq).type_as(Q)

    S_LU = [S_LU_data, S_LU_pivots]
    return Q_LU, S_LU, R