add collectives slide

lectures/hardware/slides.qmd

@@ -37,14 +37,37 @@ If we want to scale beyond one node, what do we need in our example?
   * Often used for boundary exchange
 * A lot of the details are beyond the scope of this lecture.
 
-## Collectives
-* Acts collectively on all ranks.
-* Can do:
-  * Broadcast
-  * Gather
-  * Scatter
-  * Reductions
-  * All-to-all (why is all-to-all a bad idea for boundary exchange?)
+## Collectives 
+* Collective communication that involves a group of processes (ranks)
+* Examples: broadcast, gather, scatter, reduction ... 
+  * All-to-all is a bad idea for boundary exchange
+* Read more on [mpi-forum.org](https://www.mpi-forum.org/docs/mpi-1.1/mpi-11-html/node64.html)
+
+
+## Collectives - Aggregate results
+
+```C++
+int MPI_Reduce(void* sendbuf, void* recvbuf, int count, 
+               MPI_Datatype datatype, 
+               MPI_Op op,   // MPI_SUM, MPI_MAX, ...
+               int root, 
+               MPI_Comm comm)  
+```
+
+<br>
+
+:::fragment
+![](static/reduce.jpg){.nostretch fig-align="center" width="70%"}
+
+:::{.info .smaller}
+MPI_MAX for 4 ranks and count=2
+:::
+
+:::
+
+
+
+
 
 ## Hands-on Session! {background-color=var(--dark-bg-color) .leftalign}