Update README.md in this repository

Author: yangyang14641

README.md

@@ -104,18 +104,20 @@ for (i = 0; i < n; i++)
 2. Parallel Modeling Algorithm Operations on each step:
    * | Stage | Algorithm Operation |
      |-------|---------------------|
-     |   0   | 1. Process P_{ij}  has A_{ij}, B_{ij}  but needs A_{ii}             (for each index i) <br/> 2. Process P_{ii}  broadcast A_{ii}  across process mesh row i <br/> 3. Process P_{ij}  computes C_{ij}=A_{ii}B_{ij}                    |
-     |   1   |                     |
-     |   2   |                     |
-     |  ...  |                     |
-     | q-2-i |                     |
-     | q-1-i |                     |
-     |  ...  |                     |
-     |  ...  |                     |
-     |  ...  |                     |
-     |  q-1  |                     |
+     |   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}}"> |
+     |   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}}"> |
+     |   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}}" |
+     |  ...  |         ...         |
+     | q-2-i | <img src="https://tex.s2cms.ru/svg/%5Cmathbf%7BC_%7Bij%7D%3DC_%7Bij%7D%2BA_%7Biq-2%7DB_%7Bq-2j%7D%7D" alt="\mathbf{C_{ij}=C_{ij}+A_{iq-2}B_{q-2j}}"> |
+     | q-1-i | <img src="https://tex.s2cms.ru/svg/%5Cmathbf%7BC_%7Bij%7D%3DC_%7Bij%7D%2BA_%7Biq-1%7DB_%7Bq-1j%7D%7D" alt="\mathbf{C_{ij}=C_{ij}+A_{iq-1}B_{q-1j}}"> |
+     |  ...  | <img src="https://tex.s2cms.ru/svg/%5Cmathbf%7BC_%7Bij%7D%3DC_%7Bij%7D%2BA_%7Bi1%7DB_%7B1j%7D%7D" alt="\mathbf{C_{ij}=C_{ij}+A_{i1}B_{1j}}"> |
+     |  ...  | <img src="https://tex.s2cms.ru/svg/%5Cmathbf%7BC_%7Bij%7D%3DC_%7Bij%7D%2BA_%7Bi2%7DB_%7B2j%7D%7D" alt="\mathbf{C_{ij}=C_{ij}+A_{i2}B_{2j}}"> |
+     |  ...  |         ...         |
+     |  q-1  | <img src="https://tex.s2cms.ru/svg/%5Cmathbf%7BC_%7Bij%7D%3DC_%7Bij%7D%2BA_%7Bii-1%7DB_%7Bi-1j%7D%7D" alt="\mathbf{C_{ij}=C_{ij}+A_{ii-1}B_{i-1j}}"> |
 
    * *<span style="color: blue">Pipe parallelism: The (0 ~ q−1) Computing Steps for each process P_ij.</span>*
    * <center> <img src="Imagines/FOX.png" width="50%" height="50%" /> </center>
   
-   <img src="https:">
+   <img src="https:">
+
+### **Algorithm Analysis**