Group 6

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Group 6

Team Members

1. Xiaowei Huang
2. Yihang Yuan
3. Zhijian Zhou

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Progress

Assignment 1 - Select and Assess

Array Processing

Subject: Array Processing

Blaise Barney introduced Parallel Computing https://computing.llnl.gov/tutorials/parallel_comp/ Array processing could become one of the parallel example, which "demonstrates calculations on 2-dimensional array elements; a function is evaluated on each array element."

Standard random method is used to initialize a 2-dimentional array. The purpose of this program is to perform a 2-dimension array calculation, which is a matrix-matrix multiplication in this example.

In this following profile example, n = 1000

Flat profile:
Each sample counts as 0.01 seconds.
  %   cumulative   self              self     total           
 time   seconds   seconds    calls  Ts/call  Ts/call  name    
100.11      1.48     1.48                             multiply(float**, float**, float**, int)
  0.68      1.49     0.01                             init(float**, int)
  0.00      1.49     0.00        1     0.00     0.00  _GLOBAL__sub_I__Z4initPPfi

Call graph

granularity: each sample hit covers 2 byte(s) for 0.67% of 1.49 seconds

index % time    self  children    called     name
                                             <spontaneous>
[1]     99.3    1.48    0.00                 multiply(float**, float**, float**, int) [1]
-----------------------------------------------
                                             <spontaneous>
[2]      0.7    0.01    0.00                 init(float**, int) [2]
-----------------------------------------------
                0.00    0.00       1/1       __libc_csu_init [16]
[10]     0.0    0.00    0.00       1         _GLOBAL__sub_I__Z4initPPfi [10]
-----------------------------------------------
�
Index by function name
  [10] _GLOBAL__sub_I__Z4initPPfi (arrayProcessing.cpp) [2] init(float**, int) [1] multiply(float**, float**, float**, int)

From the call graph, multiply() took major runtime to more than 99%, as it contains 3 for-loop, which T(n) is O(n^3). Besides, init() also became the second busy one, which has a O(n^2).

As the calculation of elements is independent of one another - leads to an embarrassingly parallel solution. Arrays elements are evenly distributed so that each process owns a portion of the array (subarray). It can be solved in less time with multiple compute resources than with a single compute resource.

The Monte Carlo Simulation (PI Calculation)

Subject: The Monte Carlo Simulation (PI Calculation) Got the code from here: https://rosettacode.org/wiki/Monte_Carlo_methods#C.2B.2B A Monte Carlo Simulation is a way of approximating the value of a function where calculating the actual value is difficult or impossible.

It uses random sampling to define constraints on the value and then makes a sort of "best guess."

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Zhijian

Subject: