A basic LDL decomposition of a matrix X times its transpose.

basicLDL.java

double[][] L = new double[inputs][ inputs];
double D[] = new double[inputs] ;
//for each column j
for (int j = 0; j < inputs; j++){
  D[j] = XTX[j][j];//calculate Dj
  for (int k = 0; k < j; k++){
    D[j] -= L[j][k] * L[j][k] * D[k];
  }
  //calculate jth column of L
  L[j][j] = 1 ; // don't really need to save this but its a 1
  for (int i = j + 1; i < inputs; i++){
    L[i][j] = XTX[i][j];
    for (int k = 0; k < j; k++){
      L[i][j] -= L[i][k] * L[j][k] * D[k];
    }
    L[i][j] /= D[j];
  }
}