1. Collective Communications Self Test with solution

2. Self Test 1.We want to do a simple broadcast of variable abc[7] in processor 0 to the same location in all other processors of the communicator. What is the correct syntax of the call to do this broadcast? a)MPI_Bcast ( &abc[7], 1, MPI_REAL, 0, comm ) b)MPI_Bcast ( &abc, 7, MPI_REAL, 0, comm ) c)MPI_Broadcast ( &abc[7], 1, MPI_REAL, 0, comm )

3. Answer a)Correct! b)Sorry, that's not correct. the first argument should be the location abc[7]. The second argument should be the number of elements to transfer. For this question, we transfer 1 data value. c)Sorry, that's not correct. the correct function name is MPI_Bcast(). Otherwise, the arguments are correct.

4. Self Test 2.Each processor has a local array a with 50 elements. Each local array is a slice of a larger global array. We wish to compute the average (mean) of all elements in the global array. Our preferred approach is to add all of the data element-by-element onto the root processor, sum elements of the resulting array, divide, and broadcast the result to all processes. Which sequence of calls will accomplish this? Assume variables are typed and initialized appropriately.

5. Self Test a) start = 0; final = 49; count = final - start + 1; mysum = 0; for ( i=start; i<=final; ++i ) mysum +=a[i]; MPI_Reduce ( &mysum, &sum, 1, MPI_REAL, MPI_SUM, root, comm ); total_count=nprocs * count; if ( my_rank==root ) average=sum / total_count; MPI_Bcast ( &average, 1, MPI_REAL, root, comm );

6. Self Test b) start = 0; final = 49; count = final - start + 1; MPI_Reduce ( a, sum_array, count, MPI_REAL, MPI_SUM, root, comm ); sum = 0; for ( i=start, i<=final; ++i ) sum +=sum_array[i]; total_count=nprocs * count; if ( my_rank==root ) average=sum / total_count; MPI_Bcast ( &average, 1, MPI_REAL, root, comm );

7. Self Test c) start = 0; final = 49; count = final - start + 1; mysum = 0; for ( i=start; i<=final; ++i ) mysum +=a[i]; my_average=mysum / count; MPI_Reduce ( &my_average, &sum, 1, MPI_REAL, MPI_SUM, root, comm ); if ( my_rank==root ) average=sum / nprocs; MPI_Bcast ( &average, 1, MPI_REAL, root, comm );

8. Answer a)Sorry, that's not correct. -- Well, this is not the way the instructions specified, but it should give the same answer. The instructions were to sum all of the data into the root process, compute the average, and then broadcast the result. This solution computes a partial sum for each process, sums these partial sums onto the root process, then averages and broadcasts. b)That's correct! c)Sorry, that's not correct. -- This is not what the instructions specified. It should produce an answer that is close to the correct one, but numerically these are different calculations The instructions were to sum all of the data into the root process, compute the average, and then broadcast the result. This solution computes an average on each process, sums these averages onto the root process, then averages these partial averages and broadcasts. This is not likely to be the best way to do this calculation.

9. Self Test 3.Consider a communicator with 4 processes. How many total MPI_Send()'s and MPI_Recv()'s would be required to accomplish the following: MPI_Allreduce ( &a, &x, 1, MPI_REAL, MPI_SUM, comm ); a)3 b)4 c)12 d)16

10. Answer a)Sorry, that's not correct. b)Sorry, that's not correct. c)That's correct! You need to do 3 sends of a from the non-root processes and 3 matching receives by the root process. You sum these 3 values with the corresponding data in the root process and store the result in variable x in the root process. Then the root process executes 3 sends to the non-root processes with 3 matching receives. d)Sorry, that's not correct.

11. Course Problem

12. Description –The new problem still implements a parallel search of an integer array. The program should find all occurrences of a certain integer which will be called the target. It should then calculate the average of the target value and its index. Both the target location and the average should be written to an output file. In addition, the program should read both the target value and all the array elements from an input file.

13. Course Problem Exercise –Modify your code from Chapter 5, to change how the master first sends out the target and subarray data to the slaves. –Use the MPI broadcast routines to give each slave the target. –Use the MPI scatter routine to give all processors a section of the array b it will search. –When you use the standard MPI scatter routine you will see that the global array b is now split up into four parts and the master process now has the first fourth of the array to search. –So you should add a search loop (similar to the slaves') in the master section of code to search for the target and calculate the average and then write the result to the output file. –This is actually an improvement in performance since all the processors perform part of the search in parallel.