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Miscellaneous typos fixed

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VictorianHues
2024-09-30 23:14:53 +02:00
parent 024429bceb
commit 82cfa1d44b
8 changed files with 32 additions and 32 deletions
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20
notebooks/jacobi_method.ipynb
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@@ -27,7 +27,7 @@
"\n",
"In this notebook, we will learn\n",
"\n",
"- How to paralleize the Jacobi method\n",
"- How to parallelize the Jacobi method\n",
"- How the data partition can impact the performance of a distributed algorithm\n",
"- How to use latency hiding to improve parallel performance\n",
"\n"
@@ -452,7 +452,7 @@
"- We need to get remote entries from 2 neighbors (2 messages per iteration)\n",
"- We need to communicate 1 entry per message\n",
"- Thus, communication complexity is $O(1)$\n",
"- Communication/computation ration is $O(P/N)$, making the algorithm potentially scalable if $P<<N$.\n"
"- Communication/computation ratio is $O(P/N)$, making the algorithm potentially scalable if $P<<N$.\n"
]
},
{
@@ -655,7 +655,7 @@
"end\n",
"```\n",
"\n",
"- The outer loop cannot be parallelized (like in the 1d case). \n",
"- The outer loop cannot be parallelized (like in the 1D case). \n",
"- The two inner loops are trivially parallel\n"
]
},
@@ -666,7 +666,7 @@
"source": [
"### Parallelization strategies\n",
"\n",
"In 2d one has more flexibility in order to distribute the data over the processes. We consider these three alternatives:\n",
"In 2D, one has more flexibility in order to distribute the data over the processes. We consider these three alternatives:\n",
"\n",
"- 1D block row partition (each worker handles a subset of consecutive rows and all columns)\n",
"- 2D block partition (each worker handles a subset of consecutive rows and columns)\n",
@@ -848,9 +848,9 @@
"\n",
"|Partition | Messages <br> per iteration | Communication <br>per worker | Computation <br>per worker | Ratio communication/<br>computation |\n",
"|---|---|---|---|---|\n",
"| 1d block | 2 | O(N) | N²/P | O(P/N) |\n",
"| 2d block | 4 | O(N/√P) | N²/P | O(√P/N) |\n",
"| 2d cyclic | 4 |O(N²/P) | N²/P | O(1) |"
"| 1D block | 2 | O(N) | N²/P | O(P/N) |\n",
"| 2D block | 4 | O(N/√P) | N²/P | O(√P/N) |\n",
"| 2D cyclic | 4 |O(N²/P) | N²/P | O(1) |"
]
},
{
@@ -862,9 +862,9 @@
"\n",
"\n",
"\n",
"- Both 1d and 2d block partitions are potentially scalable if $P<<N$\n",
"- The 2d block partition has the lowest communication complexity\n",
"- The 1d block partition requires to send less messages (It can be useful if the fixed cost of sending a message is high)\n",
"- Both 1D and 2D block partitions are potentially scalable if $P<<N$\n",
"- The 2D block partition has the lowest communication complexity\n",
"- The 1D block partition requires to send less messages (It can be useful if the fixed cost of sending a message is high)\n",
"- The best strategy for a given problem size will thus depend on the machine.\n",
"- Cyclic partitions are impractical for this application (but they are useful in others) \n",
"\n"