-l(g, x)</code></pre><p>See also <a href="#GNNlib.apply_edges"><code>apply_edges</code></a> and <a href="#GNNlib.aggregate_neighbors"><code>aggregate_neighbors</code></a>.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/CarloLucibello/GraphNeuralNetworks.jl/blob/v0.2.2/src/msgpass.jl#L1-L68">source</a></section></article><h2 id="Built-in-message-functions"><a class="docs-heading-anchor" href="#Built-in-message-functions">Built-in message functions</a><a id="Built-in-message-functions-1"></a><a class="docs-heading-anchor-permalink" href="#Built-in-message-functions" title="Permalink"></a></h2><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="GNNlib.copy_xi" href="#GNNlib.copy_xi"><code>GNNlib.copy_xi</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">copy_xi(xi, xj, e) = xi</code></pre></div><a class="docs-sourcelink" target="_blank" href="https://github.com/CarloLucibello/GraphNeuralNetworks.jl/blob/v0.2.2/src/msgpass.jl#L164-L166">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="GNNlib.copy_xj" href="#GNNlib.copy_xj"><code>GNNlib.copy_xj</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">copy_xj(xi, xj, e) = xj</code></pre></div><a class="docs-sourcelink" target="_blank" href="https://github.com/CarloLucibello/GraphNeuralNetworks.jl/blob/v0.2.2/src/msgpass.jl#L159-L161">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="GNNlib.xi_dot_xj" href="#GNNlib.xi_dot_xj"><code>GNNlib.xi_dot_xj</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">xi_dot_xj(xi, xj, e) = sum(xi .* xj, dims=1)</code></pre></div><a class="docs-sourcelink" target="_blank" href="https://github.com/CarloLucibello/GraphNeuralNetworks.jl/blob/v0.2.2/src/msgpass.jl#L169-L171">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="GNNlib.xi_sub_xj" href="#GNNlib.xi_sub_xj"><code>GNNlib.xi_sub_xj</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">xi_sub_xj(xi, xj, e) = xi .- xj</code></pre></div><a class="docs-sourcelink" target="_blank" href="https://github.com/CarloLucibello/GraphNeuralNetworks.jl/blob/v0.2.2/src/msgpass.jl#L174-L176">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="GNNlib.xj_sub_xi" href="#GNNlib.xj_sub_xi"><code>GNNlib.xj_sub_xi</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">xj_sub_xi(xi, xj, e) = xj .- xi</code></pre></div><a class="docs-sourcelink" target="_blank" href="https://github.com/CarloLucibello/GraphNeuralNetworks.jl/blob/v0.2.2/src/msgpass.jl#L179-L181">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="GNNlib.e_mul_xj" href="#GNNlib.e_mul_xj"><code>GNNlib.e_mul_xj</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">e_mul_xj(xi, xj, e) = reshape(e, (...)) .* xj</code></pre><p>Reshape <code>e</code> into broadcast compatible shape with <code>xj</code> (by prepending singleton dimensions) then perform broadcasted multiplication.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/CarloLucibello/GraphNeuralNetworks.jl/blob/v0.2.2/src/msgpass.jl#L184-L190">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="GNNlib.w_mul_xj" href="#GNNlib.w_mul_xj"><code>GNNlib.w_mul_xj</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">w_mul_xj(xi, xj, w) = reshape(w, (...)) .* xj</code></pre><p>Similar to <a href="#GNNlib.e_mul_xj"><code>e_mul_xj</code></a> but specialized on scalar edge features (weights).</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/CarloLucibello/GraphNeuralNetworks.jl/blob/v0.2.2/src/msgpass.jl#L198-L202">source</a></section></article></article><nav class="docs-footer"><a 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