Cholesky decomposition of Matix

To do a Cholesky decomposition the given Matrix Should Be a Symmetric Positive-definite Matrix.

original Matrix

L Matix

Here we have the origianl marix and its cholesky Matrix
A=LLT
LT= Transpose of L Matrix


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#include<stdio.h>
#include<iostream>
#include<conio.h>
#include<malloc.h>
#include<math.h>

using namespace std;

void main()
{

double a[3][3]={{2,-1,0},{-1,2,-1},{0,-1,2}};
double L[3][3]={0};
double LT[3][3]={0};
int i=0,j=0,k=0;
double temp=0;

for(i=0;i<3;i++)
{
for(j=0;j<3;j++)
{
temp=0;
if(i==j)
{
for(k=0;k<j;k++)
{
temp+=((L[j][k])*(L[j][k]));
}

L[i][j]=sqrt((double)(a[i][j]-temp));
}

if(i>j)
{
for(k=1;k<j;k++)
{
temp+=((L[i][k]*L[j][k]));
}
L[i][j]=(1/(L[j][j]))*((a[i][j])-temp);
}

if(i<j)
{
L[i][j]=0;
}
}
}



printf("Given Matrixis\n\n");
for(i=0;i<3;i++)
{
for(j=0;j<3;j++)
{
//printf("%2d\t",a[i][j]);
cout<<a[i][j]<<"\t\t\t";
}
printf("\n");
}
// Cheloskey Transform
printf("\nGiven Matrix cheloskey Transform is\n\n");
for(i=0;i<3;i++)
{
for(j=0;j<3;j++)
{
cout<<L[i][j]<<"\t\t\t";
//printf("%f\t",L[i][j]);
}
printf("\n");
}

for(i=0;i<3;i++)
{
for(j=0;j<3;j++)
{
LT[i][j]=L[j][i];

}
}

printf("\n");
printf("Transpose of L MAtrix is");
printf("\n");
printf("\n");
for(i=0;i<3;i++)
{
for(j=0;j<3;j++)
{
cout<<LT[i][j]<<"\t";
//printf("%2d\t",LT[i][j]);
}
printf("\n");
}

_getch();
}

****************************************************************

The Output will be 

The Input  Matrix Was

The Cheloskey Transform Upper Triangular Matrix is

Its Lower trainguler Matrix is