Python mxnet.nd.dot() Examples

def forward(self,x):
        """
        return shape:(batch_size,2000,2)
        """
        # Encode layer
        question = x[:,0:30]
        question = self.Embed(question)
        question = self.gru(question)

        #interaction layer
        interaction = nd.dot(question,self.topic_embedding.data())
        interaction = nd.transpose(interaction,axes=(0,2,1))
        interaction = interaction.reshape((batch_size*2000,-1))
        # interaction = interaction.expand_dims(axis=1)
        # print("interaction done")

        #agg layer
        # interaction = self.pooling(self.conv_2(self.conv_1(interaction)))
        # print("agg done")
        res = self.mlp_2(self.mlp_1(interaction))
        res = res.reshape((batch_size,2000))

        return res

#Train Model 

def basis_message_func(self, edges):
        """Message function for basis regularizer"""
        ctx = edges.src['h'].context
        if self.num_bases < self.num_rels:
            # generate all weights from bases
            weight = self.weight.data(ctx).reshape(
                self.num_bases, self.in_feat * self.out_feat)
            weight = nd.dot(self.w_comp.data(ctx), weight).reshape(
                self.num_rels, self.in_feat, self.out_feat)
        else:
            weight = self.weight.data(ctx)

        msg = utils.bmm_maybe_select(edges.src['h'], weight, edges.data['type'])
        if 'norm' in edges.data:
            msg = msg * edges.data['norm']
        return {'msg': msg} 

def global_norm(arrays: Union[Generator[NDArray, NDArray, NDArray], List[NDArray], Tuple[NDArray]]) -> NDArray:
    """
    Calculate global norm on list or tuple of NDArrays using this formula:
        `global_norm = sqrt(sum([l2norm(p)**2 for p in parameters]))`

    :param arrays: list or tuple of parameters to calculate global norm on
    :return: single-value NDArray
    """
    def _norm(array):
        if array.stype == 'default':
            x = array.reshape((-1,))
            return nd.dot(x, x)
        return array.norm().square()

    total_norm = nd.add_n(*[_norm(arr) for arr in arrays])
    total_norm = nd.sqrt(total_norm)
    return total_norm 

def get_distance_matrix(x):
    """Get distance matrix given a matrix. Used in testing."""
    square = nd.sum(x ** 2.0, axis=1, keepdims=True)
    distance_square = square + square.transpose() - (2.0 * nd.dot(x, x.transpose()))
    return nd.sqrt(distance_square) 

def matmul_maybe_select(A, B):
    """Perform Matrix multiplication C = A * B but A could be an integer id vector.

    If A is an integer vector, we treat it as multiplying a one-hot encoded tensor.
    In this case, the expensive dense matrix multiply can be replaced by a much
    cheaper index lookup.

    For example,
    ::

        A = [2, 0, 1],
        B = [[0.1, 0.2],
             [0.3, 0.4],
             [0.5, 0.6]]

    then matmul_maybe_select(A, B) is equivalent to
    ::

        [[0, 0, 1],     [[0.1, 0.2],
         [1, 0, 0],  *   [0.3, 0.4],
         [0, 1, 0]]      [0.5, 0.6]]

    In all other cases, perform a normal matmul.

    Parameters
    ----------
    A : mxnet.NDArray
        lhs tensor
    B : mxnet.NDArray
        rhs tensor

    Returns
    -------
    C : mxnet.NDArray
        result tensor
    """
    if A.dtype in (np.int32, np.int64) and len(A.shape) == 1:
        return nd.take(B, A, axis=0)
    else:
        return nd.dot(A, B) 

def forward(self, x, cheb_polys):
        '''
        Parameters
        ----------
        x: nd.array, shape is (batch_size * time_step, num_of_vertices, c_in)

        cheb_polys: nd.array,
                shape is (num_of_vertices, order_of_cheb * num_of_vertices)

        Returns
        ----------
        shape is (batch_size * time_step, num_of_vertices, c_out)

        '''

        _, num_of_vertices, c_in = x.shape

        # (batch_size * c_in, num_of_vertices)
        x_tmp = x.transpose((0, 2, 1)).reshape((-1, num_of_vertices))

        # (batch_size, c_in, order_of_cheb, num_of_vertices)
        x_mul = nd.dot(x_tmp, cheb_polys).reshape((-1,
                                                   c_in,
                                                   self.order_of_cheb,
                                                   num_of_vertices))

        # (batch_size, num_of_vertices, c_in * order_of_cheb)
        x_ker = x_mul.transpose((0, 3, 1, 2)) \
                     .reshape((-1, num_of_vertices, c_in * self.order_of_cheb))

        return self.theta(x_ker) 

def get_distance_matrix(x):
    """Get distance matrix given a matrix. Used in testing."""
    square = nd.sum(x ** 2.0, axis=1, keepdims=True)
    distance_square = square + square.transpose() - (2.0 * nd.dot(x, x.transpose()))
    return nd.sqrt(distance_square) 

def linreg(X, w, b):
    """Linear regression."""
    return nd.dot(X, w) + b 

def linreg(X, w, b):
    """Linear regression."""
    return nd.dot(X, w) + b 

def get_distance_matrix(x):
    """Get distance matrix given a matrix. Used in testing."""
    square = nd.sum(x ** 2.0, axis=1, keepdims=True)
    distance_square = square + square.transpose() - (2.0 * nd.dot(x, x.transpose()))
    return nd.sqrt(distance_square) 

def forward(self, adj, feat):
        r"""Compute (Dense) Graph SAGE layer.

        Parameters
        ----------
        adj : mxnet.NDArray
            The adjacency matrix of the graph to apply SAGE Convolution on, when
            applied to a unidirectional bipartite graph, ``adj`` should be of shape
            should be of shape :math:`(N_{out}, N_{in})`; when applied to a homo
            graph, ``adj`` should be of shape :math:`(N, N)`. In both cases,
            a row represents a destination node while a column represents a source
            node.
        feat : mxnet.NDArray or a pair of mxnet.NDArray
            If a mxnet.NDArray is given, the input feature of shape :math:`(N, D_{in})`
            where :math:`D_{in}` is size of input feature, :math:`N` is the number of
            nodes.
            If a pair of torch.Tensor is given, the pair must contain two tensors of
            shape :math:`(N_{in}, D_{in})` and :math:`(N_{out}, D_{in})`.

        Returns
        -------
        mxnet.NDArray
            The output feature of shape :math:`(N, D_{out})` where :math:`D_{out}`
            is size of output feature.
        """
        check_eq_shape(feat)
        if isinstance(feat, tuple):
            feat_src = self.feat_drop(feat[0])
            feat_dst = self.feat_drop(feat[1])
        else:
            feat_src = feat_dst = self.feat_drop(feat)
        adj = adj.astype(feat_src.dtype).as_in_context(feat_src.context)
        in_degrees = adj.sum(axis=1, keepdims=True)
        h_neigh = (nd.dot(adj, feat_src) + feat_dst) / (in_degrees + 1)
        rst = self.fc(h_neigh)
        # activation
        if self.activation is not None:
            rst = self.activation(rst)
        # normalization
        if self._norm is not None:
            rst = self._norm(rst)

        return rst 

def forward(self, adj, feat, lambda_max=None):
        r"""Compute (Dense) Chebyshev Spectral Graph Convolution layer.

        Parameters
        ----------
        adj : mxnet.NDArray
            The adjacency matrix of the graph to apply Graph Convolution on,
            should be of shape :math:`(N, N)`, where a row represents the destination
            and a column represents the source.
        feat : mxnet.NDArray
            The input feature of shape :math:`(N, D_{in})` where :math:`D_{in}`
            is size of input feature, :math:`N` is the number of nodes.
        lambda_max : float or None, optional
            A float value indicates the largest eigenvalue of given graph.
            Default: None.

        Returns
        -------
        mxnet.NDArray
            The output feature of shape :math:`(N, D_{out})` where :math:`D_{out}`
            is size of output feature.
        """
        A = adj.astype(feat.dtype).as_in_context(feat.context)
        num_nodes = A.shape[0]

        in_degree = 1. / nd.clip(A.sum(axis=1), 1, float('inf')).sqrt()
        D_invsqrt = nd.diag(in_degree)
        I = nd.eye(num_nodes, ctx=A.context)
        L = I - nd.dot(D_invsqrt, nd.dot(A, D_invsqrt))

        if lambda_max is None:
            # NOTE(zihao): this only works for directed graph.
            lambda_max = (nd.linalg.syevd(L)[1]).max()

        L_hat = 2 * L / lambda_max - I
        Z = [nd.eye(num_nodes, ctx=A.context)]
        Zh = self.fc[0](feat)
        for i in range(1, self._k):
            if i == 1:
                Z.append(L_hat)
            else:
                Z.append(2 * nd.dot(L_hat, Z[-1]) - Z[-2])
            Zh = Zh + nd.dot(Z[i], self.fc[i](feat))

        if self.bias is not None:
            Zh = Zh + self.bias.data(feat.context)
        return Zh 

def forward(self, adj, feat):
        r"""Compute (Dense) Graph Convolution layer.

        Parameters
        ----------
        adj : mxnet.NDArray
            The adjacency matrix of the graph to apply Graph Convolution on, when
            applied to a unidirectional bipartite graph, ``adj`` should be of shape
            should be of shape :math:`(N_{out}, N_{in})`; when applied to a homo
            graph, ``adj`` should be of shape :math:`(N, N)`. In both cases,
            a row represents a destination node while a column represents a source
            node.
        feat : torch.Tensor
            The input feature.

        Returns
        -------
        mxnet.NDArray
            The output feature of shape :math:`(N, D_{out})` where :math:`D_{out}`
            is size of output feature.
        """
        adj = adj.astype(feat.dtype).as_in_context(feat.context)
        src_degrees = nd.clip(adj.sum(axis=0), a_min=1, a_max=float('inf'))
        dst_degrees = nd.clip(adj.sum(axis=1), a_min=1, a_max=float('inf'))
        feat_src = feat

        if self._norm == 'both':
            norm_src = nd.power(src_degrees, -0.5)
            shp_src = norm_src.shape + (1,) * (feat.ndim - 1)
            norm_src = norm_src.reshape(shp_src).as_in_context(feat.context)
            feat_src = feat_src * norm_src

        if self._in_feats > self._out_feats:
            # mult W first to reduce the feature size for aggregation.
            feat_src = nd.dot(feat_src, self.weight.data(feat_src.context))
            rst = nd.dot(adj, feat_src)
        else:
            # aggregate first then mult W
            rst = nd.dot(adj, feat_src)
            rst = nd.dot(rst, self.weight.data(feat_src.context))

        if self._norm != 'none':
            if self._norm == 'both':
                norm_dst = nd.power(dst_degrees, -0.5)
            else: # right
                norm_dst = 1.0 / dst_degrees
            shp_dst = norm_dst.shape + (1,) * (feat.ndim - 1)
            norm_dst = norm_dst.reshape(shp_dst).as_in_context(feat.context)
            rst = rst * norm_dst

        if self.bias is not None:
            rst = rst + self.bias.data(feat.context)

        if self._activation is not None:
            rst = self._activation(rst)

        return rst