# Group 6

## 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."

Here is my source code

arrayProcessing.cpp
```
// arrayProcessing.cpp
// Array processing implement parallel solution
#include <iostream>
#include <iomanip>
#include <cstdlib>
#include <ctime>

void init(float** randomValue, int n) {
//std::srand(std::time(nullptr));
float f = 1.0f / RAND_MAX;
for (int i = 0; i < n; i++)
for (int j = 0; j < n; j++)
randomValue[i][j] = std::rand() * f;
}

void multiply(float** a, float** b, float** c, int n) {
for (int i = 0; i < n; i++)
for (int j = 0; j < n; j++) {
float sum = 0.0f;
for (int k = 0; k < n; k++)
sum += a[i][k] * b[k][j];

c[i][j] = sum;
if(n <= 10){
std::cout << "array c[" << i << "," << j << "]: " << c[i][j] << std::endl;
}
}
}

int main(int argc, char* argv[]) {
// interpret command-line argument
if (argc != 2) {
std::cerr << argv[0] << ": invalid number of arguments\n";
std::cerr << "Usage: " << argv[0] << "  size_of_matrices\n";
return 1;
}
int n  = std::atoi(argv[1]);   // size of matrices

float** a = new float*[n];
for (int i = 0; i < n; i++)
a[i] = new float[n];
float** b = new float*[n];
for (int i = 0; i < n; i++)
b[i] = new float[n];
float** c = new float*[n];
for (int i = 0; i < n; i++)
c[i] = new float[n];

std::srand(std::time(nullptr));
init(a, n);
init(b, n);

multiply(a, b, c, n);

for (int i = 0; i < n; i++)
delete [] a[i];
delete [] a;
for (int i = 0; i < n; i++)
delete [] b[i];
delete [] b;
for (int i = 0; i < n; i++)
delete [] c[i];
delete [] c;
}
```

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."

Subject: