# dgl.function¶

This subpackage hosts all the built-in functions provided by DGL. Built-in functions are DGL’s recommended way to express different types of ref:guide-message-passing computation (i.e., via update_all()) or computing edge-wise features from node-wise features (i.e., via apply_edges()). Built-in functions describe the node-wise and edge-wise computation in a symbolic way without any actual computation, so DGL can analyze and map them to efficient low-level kernels. Here are some examples:

import dgl
import dgl.function as fn
import torch as th
g = ... # create a DGLGraph
g.ndata['h'] = th.randn((g.num_nodes(), 10)) # each node has feature size 10
g.edata['w'] = th.randn((g.num_edges(), 1))  # each edge has feature size 1
# collect features from source nodes and aggregate them in destination nodes
g.update_all(fn.copy_u('h', 'm'), fn.sum('m', 'h_sum'))
# multiply source node features with edge weights and aggregate them in destination nodes
g.update_all(fn.u_mul_e('h', 'w', 'm'), fn.max('m', 'h_max'))
# compute edge embedding by multiplying source and destination node embeddings
g.apply_edges(fn.u_mul_v('h', 'h', 'w_new'))


fn.copy_u, fn.u_mul_e, fn.u_mul_v are built-in message functions, while fn.sum and fn.max are built-in reduce functions. DGL’s convention is to use u, v and e to represent source nodes, destination nodes, and edges, respectively. For example, copy_u tells DGL to copy the source node data as the messages; u_mul_e tells DGL to multiply source node features with edge features.

To define a unary message function (e.g. copy_u), specify one input feature name and one output message name. To define a binary message function (e.g. u_mul_e), specify two input feature names and one output message name. During the computation, the message function will read the data under the given names, perform computation, and return the output using the output name. For example, the above fn.u_mul_e('h', 'w', 'm') is the same as the following user-defined function:

def udf_u_mul_e(edges):
return {'m' : edges.src['h'] * edges.data['w']}


To define a reduce function, one input message name and one output node feature name need to be specified. For example, the above fn.max('m', 'h_max') is the same as the following user-defined function:

def udf_max(nodes):
return {'h_max' : th.max(nodes.mailbox['m'], 1)[0]}


All binary message function supports broadcasting, a mechansim for extending element-wise operations to tensor inputs with different shapes. DGL generally follows the standard broadcasting semantic by NumPy and PyTorch. Below are some examples:

import dgl
import dgl.function as fn
import torch as th
g = ... # create a DGLGraph

# case 1
g.ndata['h'] = th.randn((g.num_nodes(), 10))
g.edata['w'] = th.randn((g.num_edges(), 1))
# OK, valid broadcasting between feature shapes (10,) and (1,)
g.update_all(fn.u_mul_e('h', 'w', 'm'), fn.sum('m', 'h_new'))
g.ndata['h_new']  # shape: (g.num_nodes(), 10)

# case 2
g.ndata['h'] = th.randn((g.num_nodes(), 5, 10))
g.edata['w'] = th.randn((g.num_edges(), 10))
# OK, valid broadcasting between feature shapes (5, 10) and (10,)
g.update_all(fn.u_mul_e('h', 'w', 'm'), fn.sum('m', 'h_new'))
g.ndata['h_new']  # shape: (g.num_nodes(), 5, 10)

# case 3
g.ndata['h'] = th.randn((g.num_nodes(), 5, 10))
g.edata['w'] = th.randn((g.num_edges(), 5))
# NOT OK, invalid broadcasting between feature shapes (5, 10) and (5,)
# shapes are aligned from right
g.update_all(fn.u_mul_e('h', 'w', 'm'), fn.sum('m', 'h_new'))

# case 3
g.ndata['h1'] = th.randn((g.num_nodes(), 1, 10))
g.ndata['h2'] = th.randn((g.num_nodes(), 5, 1))
# OK, valid broadcasting between feature shapes (1, 10) and (5, 1)
g.edata['x']  # shape: (g.num_edges(), 5, 10)

# case 4
g.ndata['h1'] = th.randn((g.num_nodes(), 1, 10, 128))
g.ndata['h2'] = th.randn((g.num_nodes(), 5, 1, 128))
# OK, u_dot_v supports broadcasting but requires the last dimension to match
g.apply_edges(fn.u_dot_v('h1', 'h2', 'x'))
g.edata['x']  # shape: (g.num_edges(), 5, 10, 1)


## DGL Built-in Function¶

Here is a cheatsheet of all the DGL built-in functions.

Category

Functions

Memo

Unary message function

copy_u

copy_e

copy_src

alias of copy_u

copy_edge

alias of copy_e

Binary message function

u_add_v, u_sub_v, u_mul_v, u_div_v, u_dot_v

u_add_e, u_sub_e, u_mul_e, u_div_e, u_dot_e

v_add_u, v_sub_u, v_mul_u, v_div_u, v_dot_u

v_add_e, v_sub_e, v_mul_e, v_div_e, v_dot_e

e_add_u, e_sub_u, e_mul_u, e_div_u, e_dot_u

e_add_v, e_sub_v, e_mul_v, e_div_v, e_dot_v

src_mul_edge

alias of u_mul_e

Reduce function

max

min

sum

mean

## Message functions¶

 copy_src(src, out) Builtin message function that computes message using source node feature. copy_edge(edge, out) Builtin message function that computes message using edge feature. src_mul_edge(src, edge, out) Builtin message function that computes message by performing binary operation mul between src feature and edge feature. copy_u(u, out) Builtin message function that computes message using source node feature. copy_e(e, out) Builtin message function that computes message using edge feature. u_add_v(lhs_field, rhs_field, out) Builtin message function that computes a message on an edge by performing element-wise add between features of u and v if the features have the same shape; otherwise, it first broadcasts the features to a new shape and performs the element-wise operation. u_sub_v(lhs_field, rhs_field, out) Builtin message function that computes a message on an edge by performing element-wise sub between features of u and v if the features have the same shape; otherwise, it first broadcasts the features to a new shape and performs the element-wise operation. u_mul_v(lhs_field, rhs_field, out) Builtin message function that computes a message on an edge by performing element-wise mul between features of u and v if the features have the same shape; otherwise, it first broadcasts the features to a new shape and performs the element-wise operation. u_div_v(lhs_field, rhs_field, out) Builtin message function that computes a message on an edge by performing element-wise div between features of u and v if the features have the same shape; otherwise, it first broadcasts the features to a new shape and performs the element-wise operation. u_add_e(lhs_field, rhs_field, out) Builtin message function that computes a message on an edge by performing element-wise add between features of u and e if the features have the same shape; otherwise, it first broadcasts the features to a new shape and performs the element-wise operation. u_sub_e(lhs_field, rhs_field, out) Builtin message function that computes a message on an edge by performing element-wise sub between features of u and e if the features have the same shape; otherwise, it first broadcasts the features to a new shape and performs the element-wise operation. u_mul_e(lhs_field, rhs_field, out) Builtin message function that computes a message on an edge by performing element-wise mul between features of u and e if the features have the same shape; otherwise, it first broadcasts the features to a new shape and performs the element-wise operation. u_div_e(lhs_field, rhs_field, out) Builtin message function that computes a message on an edge by performing element-wise div between features of u and e if the features have the same shape; otherwise, it first broadcasts the features to a new shape and performs the element-wise operation. v_add_u(lhs_field, rhs_field, out) Builtin message function that computes a message on an edge by performing element-wise add between features of v and u if the features have the same shape; otherwise, it first broadcasts the features to a new shape and performs the element-wise operation. v_sub_u(lhs_field, rhs_field, out) Builtin message function that computes a message on an edge by performing element-wise sub between features of v and u if the features have the same shape; otherwise, it first broadcasts the features to a new shape and performs the element-wise operation. v_mul_u(lhs_field, rhs_field, out) Builtin message function that computes a message on an edge by performing element-wise mul between features of v and u if the features have the same shape; otherwise, it first broadcasts the features to a new shape and performs the element-wise operation. v_div_u(lhs_field, rhs_field, out) Builtin message function that computes a message on an edge by performing element-wise div between features of v and u if the features have the same shape; otherwise, it first broadcasts the features to a new shape and performs the element-wise operation. v_add_e(lhs_field, rhs_field, out) Builtin message function that computes a message on an edge by performing element-wise add between features of v and e if the features have the same shape; otherwise, it first broadcasts the features to a new shape and performs the element-wise operation. v_sub_e(lhs_field, rhs_field, out) Builtin message function that computes a message on an edge by performing element-wise sub between features of v and e if the features have the same shape; otherwise, it first broadcasts the features to a new shape and performs the element-wise operation. v_mul_e(lhs_field, rhs_field, out) Builtin message function that computes a message on an edge by performing element-wise mul between features of v and e if the features have the same shape; otherwise, it first broadcasts the features to a new shape and performs the element-wise operation. v_div_e(lhs_field, rhs_field, out) Builtin message function that computes a message on an edge by performing element-wise div between features of v and e if the features have the same shape; otherwise, it first broadcasts the features to a new shape and performs the element-wise operation. e_add_u(lhs_field, rhs_field, out) Builtin message function that computes a message on an edge by performing element-wise add between features of e and u if the features have the same shape; otherwise, it first broadcasts the features to a new shape and performs the element-wise operation. e_sub_u(lhs_field, rhs_field, out) Builtin message function that computes a message on an edge by performing element-wise sub between features of e and u if the features have the same shape; otherwise, it first broadcasts the features to a new shape and performs the element-wise operation. e_mul_u(lhs_field, rhs_field, out) Builtin message function that computes a message on an edge by performing element-wise mul between features of e and u if the features have the same shape; otherwise, it first broadcasts the features to a new shape and performs the element-wise operation. e_div_u(lhs_field, rhs_field, out) Builtin message function that computes a message on an edge by performing element-wise div between features of e and u if the features have the same shape; otherwise, it first broadcasts the features to a new shape and performs the element-wise operation. e_add_v(lhs_field, rhs_field, out) Builtin message function that computes a message on an edge by performing element-wise add between features of e and v if the features have the same shape; otherwise, it first broadcasts the features to a new shape and performs the element-wise operation. e_sub_v(lhs_field, rhs_field, out) Builtin message function that computes a message on an edge by performing element-wise sub between features of e and v if the features have the same shape; otherwise, it first broadcasts the features to a new shape and performs the element-wise operation. e_mul_v(lhs_field, rhs_field, out) Builtin message function that computes a message on an edge by performing element-wise mul between features of e and v if the features have the same shape; otherwise, it first broadcasts the features to a new shape and performs the element-wise operation. e_div_v(lhs_field, rhs_field, out) Builtin message function that computes a message on an edge by performing element-wise div between features of e and v if the features have the same shape; otherwise, it first broadcasts the features to a new shape and performs the element-wise operation. u_dot_v(lhs_field, rhs_field, out) Builtin message function that computes a message on an edge by performing element-wise dot between features of u and v if the features have the same shape; otherwise, it first broadcasts the features to a new shape and performs the element-wise operation. u_dot_e(lhs_field, rhs_field, out) Builtin message function that computes a message on an edge by performing element-wise dot between features of u and e if the features have the same shape; otherwise, it first broadcasts the features to a new shape and performs the element-wise operation. v_dot_e(lhs_field, rhs_field, out) Builtin message function that computes a message on an edge by performing element-wise dot between features of v and e if the features have the same shape; otherwise, it first broadcasts the features to a new shape and performs the element-wise operation. v_dot_u(lhs_field, rhs_field, out) Builtin message function that computes a message on an edge by performing element-wise dot between features of v and u if the features have the same shape; otherwise, it first broadcasts the features to a new shape and performs the element-wise operation. e_dot_u(lhs_field, rhs_field, out) Builtin message function that computes a message on an edge by performing element-wise dot between features of e and u if the features have the same shape; otherwise, it first broadcasts the features to a new shape and performs the element-wise operation. e_dot_v(lhs_field, rhs_field, out) Builtin message function that computes a message on an edge by performing element-wise dot between features of e and v if the features have the same shape; otherwise, it first broadcasts the features to a new shape and performs the element-wise operation.

## Reduce functions¶

 sum(msg, out) Builtin reduce function that aggregates messages by sum. max(msg, out) Builtin reduce function that aggregates messages by max. min(msg, out) Builtin reduce function that aggregates messages by min. mean(msg, out) Builtin reduce function that aggregates messages by mean.