agg-interlock.cs

using System.Threading;
using System.Threading.Tasks;
 
namespace Bronze.Lib
{
  public class ParallelWithInterlock
  {
    public int Sum(int[,] matrix)
    {
      var outerUpperBound = matrix.GetLength(0);
      var commonSum = 0;
 
      var innerUpperBound = matrix.GetLength(1);
      Parallel.For(0, outerUpperBound, i =>
      {
        var localSum = 0;
        for (var j = 0; j < innerUpperBound; j++)
          localSum += matrix[i, j];
        Interlocked.Add(ref commonSum, localSum);
      });
 
      return commonSum;
    }
  }
}

agg-local-sum.cs

using System.Linq;
using System.Threading.Tasks;
 
namespace Bronze.Lib
{
  public class ParallelAggregatorWithLocalSum
  {
    public int Sum(int[,] matrix)
    {
      var outerUpperBound = matrix.GetLength(0);
      var partialSums = new int[outerUpperBound];
 
      var innerUpperBound = matrix.GetLength(1);
      Parallel.For(0, outerUpperBound, i =>
      {
        var localSum = 0;
        for (var j = 0; j < innerUpperBound; j++)
          localSum += matrix[i, j];
        partialSums[i] = localSum;
      });
 
      var result = partialSums.Sum();
      return result;
    }
  }
}

agg-parallel.cs

using System.Linq;
using System.Threading.Tasks;
 
namespace Bronze.Lib
{
  public class ParallelAggregator
  {
    public int Sum(int[,] matrix)
    {
      var outerUpperBound = matrix.GetLength(0);
      var partialSums = new int[outerUpperBound];
 
      var innerUpperBound = matrix.GetLength(1);
      Parallel.For(0, outerUpperBound, i =>
      {
        partialSums[i] = 0;
        for (var j = 0; j < innerUpperBound; j++)
          partialSums[i] += matrix[i, j];
      });
 
      var result = partialSums.Sum();
      return result;
    }
  }
}

agg-simple.cs

namespace Bronze.Lib
{
  public class SimpleAggregator 
  {
    public int Sum(int[,] matrix)
    {
      var result = 0;
      for (var i = 0; i < matrix.GetLength(0); i++)
        for (var j = 0; j < matrix.GetLength(1); j++)
          result += matrix[i, j];
      return result;
    }
  }
}

ps-code.txt

1. common_sum = 0
2. Parallel: for each row in matrix:
  2.1 temp = sum(row)
  2.2 append temp to common_sum