Solves for C given an LDL decomposition in the form LDL^T C = X^T Y.

basicLDLsolve.java

public double[] solvesystem(double L[][], double D[], double XTY[]){
  //back substitution with L
  double p[] = new double[XTY.length] ;
  for (int j = 0; j < inputs; j++){
    p[j] = XTY[j] ;
    for (int i = 0; i < j; i++){
      p[j] -= L[j][i] * p[i];
    }
  }
  //Multiply by inverse of D matrix
  double q[] = new double[p.length] ;
  for (int k = 0; k < inputs; k++){//inverse of diagonal
    q[k] = p[k]/D[k];//is 1 / each element
  }
  // forward substitution with L^T
  double c[] = new double[q.length];
  for (int j = inputs - 1; j >= 0; j--){
    c[j] = q[j] ;
    for (int i = j + 1; i < inputs; i++){
      c[j] -= L[i][j] * c[i];
    }
  }
  return c ;
}