I have made a program of LU Decomposition using Gauss Elimination method in Intel Array Building Block but it is running quite slow.

For a 512 x 512 matrix time for my serial and parallel programs are

Serial execution : 76 ms

Parallel Execution using Arbb : 230 ms

My Arbb code is

#include<arbb.hpp>
#include<stdio.h>
using namespace arbb;

void decompose(arbb::dense<arbb::f32, 2>& source, const arbb::i32 dim)
{
    _for(i32 k=0, k<dim-1, k++)
    {    
        arbb::dense<f32, 2> pivot_col = section(source, k, 1, k+1, dim-k-1);
        pivot_col = pivot_col / source(k, k);
        source = replace(source, k, 1, k+1, dim-k-1, pivot_col);

        arbb::dense<f32, 2> pivot_col_tmp(dim-k-1, dim-k-1);
        _for(i32 col=0, col<dim-k-1, col++)
        {
            pivot_col_tmp = replace(pivot_col_tmp, col, 1, 0, dim-k-1, pivot_col);         
        }_end_for;    

        arbb::dense<f32, 2> pivot_row(dim-k-1, dim-k-1);

        _for(i32 row=0, row<dim-k-1, row++)
        {
            pivot_row = replace(pivot_row, 0, dim-k-1, row, 1, section(source, k+1, dim-k-1, k, 1));
        }_end_for;

        arbb::dense<f32, 2> sum(dim-k-1, dim-k-1);
        sum = pivot_col_tmp * pivot_row;        

        arbb::dense<f32, 2> temp_source(dim-k-1, dim-k-1);
        temp_source = section(source, k+1, dim-k-1, k+1, dim-k-1);
        temp_source = temp_source - sum;
        
        source = replace(source, k+1, dim-k-1, k+1, dim-k-1, temp_source);        
    }_end_for;    
}

If some one finds mistake in it, Please figure it out