Manually calculate the gradient of a sparse matrix

Sorry I think I was being unclear
the actual code goes like this

class GCN(nn.Module):
    def __init__(self, nfeat, nhid1, nhid2, nhid3, nclass, dropout, with_relu=True):
        super(GCN, self).__init__()

        self.gc1 = GraphConvolution(nfeat, nhid1)
        self.gc2 = GraphConvolution(nhid1, nclass)
        self.dropout = dropout
        self.with_relu = with_relu

    def forward(self, x, adj):
        axw , w0 = self.gc1(x, adj)
        aaxw0w1, w1 = self.gc2(x, adj)
        return F.log_softmax(aaxw0w1, dim=1)

and

class GraphConvolution(Module):
    """
    Simple GCN layer, similar to https://arxiv.org/abs/1609.02907
    """

    def __init__(self, in_features, out_features, bias=False):
        super(GraphConvolution, self).__init__()
        self.in_features = in_features
        self.out_features = out_features
        self.weight = Parameter(torch.FloatTensor(in_features, out_features))
        if bias:
            self.bias = Parameter(torch.FloatTensor(out_features))
        else:
            self.register_parameter('bias', None)
        self.reset_parameters()

    def reset_parameters(self):
        stdv = 1. / math.sqrt(self.weight.size(1))
        self.weight.data.uniform_(-stdv, stdv)
        if self.bias is not None:
            self.bias.data.uniform_(-stdv, stdv)

    def forward(self, input, adj):
        support = torch.mm(input, self.weight)
        output = torch.spmm(adj, support)
         return output, self.weight

    def __repr__(self):
        return self.__class__.__name__ + ' (' \
               + str(self.in_features) + ' -> ' \
               + str(self.out_features) + ')'

In my neural network X would be the input and adj is used in the hidden layer and output layer and I want to get the gradient w.r.t the adj.

Thank you!