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lines changed Original file line number Diff line number Diff line change @@ -104,7 +104,7 @@ for (i = 0; i < n; i++)
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2. Parallel Modeling Algorithm Operations on each step:
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* | Stage | Algorithm Operation |
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|-------|---------------------|
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- | 0 | 1. Process <img src="https://tex.s2cms.ru/svg/P_%7Bij%7D" alt="P_{ij}"> has <img src="https://tex.s2cms.ru/svg/%5Cmathbf%7BA_%7Bij%7D%7D" alt="\mathbf{A_{ij}}">, <img src="https://tex.s2cms.ru/svg/%5Cmathbf%7BB_%7Bij%7D%7D" alt="\mathbf{B_{ij}}"> but needs <img src="https://tex.s2cms.ru/svg/%5Cmathbf%7BA_%7Bii%7D%7D" alt="\mathbf{A_{ii}}"> (for each index <img src="https://tex.s2cms.ru/svg/i" alt="i">) <br/> 2. Process <img src="https://tex.s2cms.ru/svg/%5Cmathbf%7BP_%7Bii%7D%7D" alt=\mathbf{P_{ii}}> broadcast <img src="https://tex.s2cms.ru/svg/%5Cmathbf%7BA_%7Bii%7D%7D" alt="\mathbf{A_{ii}}"> across process mesh row <img src="https:https: //tex.s2cms.ru/svg/i" alt="i"> <br/> 3. Process <img src="https://tex.s2cms.ru/svg/P_%7Bij%7D" alt="P_{ij}"> computes <img src="https://tex.s2cms.ru/svg/%5Cmathbf%7BC_%7Bij%7D%3DA_%7Bii%7DB_%7Bij%7D%7D" alt="\mathbf{C_{ij}=A_{ii}B_{ij}}"> |
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+ | 0 | 1. Process <img src="https://tex.s2cms.ru/svg/P_%7Bij%7D" alt="P_{ij}"> has <img src="https://tex.s2cms.ru/svg/%5Cmathbf%7BA_%7Bij%7D%7D" alt="\mathbf{A_{ij}}">, <img src="https://tex.s2cms.ru/svg/%5Cmathbf%7BB_%7Bij%7D%7D" alt="\mathbf{B_{ij}}"> but needs <img src="https://tex.s2cms.ru/svg/%5Cmathbf%7BA_%7Bii%7D%7D" alt="\mathbf{A_{ii}}"> (for each index <img src="https://tex.s2cms.ru/svg/i" alt="i">) <br/> 2. Process <img src="https://tex.s2cms.ru/svg/%5Cmathbf%7BP_%7Bii%7D%7D" alt=\mathbf{P_{ii}}> broadcast <img src="https://tex.s2cms.ru/svg/%5Cmathbf%7BA_%7Bii%7D%7D" alt="\mathbf{A_{ii}}"> across process mesh row <img src="https://tex.s2cms.ru/svg/i" alt="i"> <br/> 3. Process <img src="https://tex.s2cms.ru/svg/P_%7Bij%7D" alt="P_{ij}"> computes <img src="https://tex.s2cms.ru/svg/%5Cmathbf%7BC_%7Bij%7D%3DA_%7Bii%7DB_%7Bij%7D%7D" alt="\mathbf{C_{ij}=A_{ii}B_{ij}}"> |
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| 1 | 1. <img src="https://tex.s2cms.ru/svg/P_%7Bij%7D" alt="P_{ij}"> has <img src="https://tex.s2cms.ru/svg/%5Cmathbf%7BA_%7Bij%7D%7D" alt="\mathbf{A_{ij}}"> and <img src="https://tex.s2cms.ru/svg/%5Cmathbf%7BB_%7Bij%7D%7D" alt="\mathbf{B_{ij}}"> but needs <img src="https://tex.s2cms.ru/svg/%5Cmathbf%7BA_%7Bii%2B1%7D%7D" alt="\mathbf{A_{ii+1}}"> and <img src="https://tex.s2cms.ru/svg/%5Cmathbf%7BB_%7Bi%2B1j%7D%7D" alt="\mathbf{B_{i+1j}}"> <br/> 1.1 Shift the <img src="https://tex.s2cms.ru/svg/j-th" alt="j-th"> block column of <img src="https://tex.s2cms.ru/svg/%5Cmathbf%7BB_%7Bij%7D%7D" alt="\mathbf{B_{ij}}"> by one block up (block <img src="https://tex.s2cms.ru/svg/0" alt="0"> goes to block <img src="https://tex.s2cms.ru/svg/q-1" alt="q-1">) (period) <br/> 1.2 <img src="https://tex.s2cms.ru/svg/P_%7Bii%2B1%7D" alt="P_{ii+1}"> broadcast <img src="https://tex.s2cms.ru/svg/%5Cmathbf%7BA_%7Bii%2B1%7D%7D" alt="\mathbf{A_{ii+1}}"> across process mesh row <img src="https://tex.s2cms.ru/svg/i" alt="i"> <br/> 2. Process <img src="https://tex.s2cms.ru/svg/P_%7Bij%7D" alt="P_{ij}"> Compute <img src="https://tex.s2cms.ru/svg/%5Cmathbf%7BC_%7Bij%7D%3DC_%7Bij%7D%2BA_%7Bii%2B1%7DB_%7Bi%2B1j%7D%7D" alt="\mathbf{C_{ij}=C_{ij}+A_{ii+1}B_{i+1j}}"> |
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| 2 | 1. <img src="https://tex.s2cms.ru/svg/P_%7Bij%7D" alt="P_{ij}"> has <img src="https://tex.s2cms.ru/svg/%5Cmathbf%7BA_%7Bij%7D%7D" alt="\mathbf{A_{ij}}"> and <img src="https://tex.s2cms.ru/svg/%5Cmathbf%7BB_%7Bij%7D%7D" alt="\mathbf{B_{ij}}"> but needs <img src="https://tex.s2cms.ru/svg/%5Cmathbf%7BA_%7Bii%2B2%7D%7D" alt="\mathbf{A_{ii+2}}"> and <img src="https://tex.s2cms.ru/svg/%5Cmathbf%7BB_%7Bi%2B2j%7D%7D" alt="\mathbf{B_{i+2j}}"> <br/> 1.1 Shift the <img src="https://tex.s2cms.ru/svg/j-th" alt="j-th"> block column of <img src="https://tex.s2cms.ru/svg/%5Cmathbf%7BB_%7Bij%7D%7D" alt="\mathbf{B_{ij}}"> by one block up (block <img src="https://tex.s2cms.ru/svg/0" alt="0"> goes to block <img src="https://tex.s2cms.ru/svg/q-1" alt="q−1">) (period) <br/> 1.2 <img src="https://tex.s2cms.ru/svg/P_%7Bii%2B2%7D" alt="P_{ii+2}"> broadcast <img src="https://tex.s2cms.ru/svg/%5Cmathbf%7BA_%7Bii%2B2%7D%7D" alt="\mathbf{A_{ii+2}}"> across process mesh row <img src="https://tex.s2cms.ru/svg/i" alt="i"> <br/> 2. Process <img src="https://tex.s2cms.ru/svg/P_%7Bij%7D" alt="P_{ij}"> Compute <img src="https://tex.s2cms.ru/svg/%5Cmathbf%7BC_%7Bij%7D%3DC_%7Bij%7D%2BA_%7Bii%2B2%7DB_%7Bi%2B2j%7D%7D" alt="\mathbf{C_{ij}=C_{ij}+A_{ii+2}B_{i+2j}}"> |
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