cg.cpp

r_0 = b
p_0 = b
||r0||_2 = r.r
x_0 = 0

for i = 1 to N
{
  // upate alpha
  alpha_i = ||r_(i-1)||_2 / p_(i-1).(A * p_(i-1))
  
  // update vectors
  x_i = x_(i-1) + alpha_i * p_(i-1)
  r_i = r_(i-1) - alpha_i * (A * p_(i-1))
  
  // update beta
  beta_i = ||r_i||_2 / ||r_(i-1)||_2
  
  // update vector
  p_i = r_i + beta_i * p_(i-1)
}

preconditioned_cg.cpp

r_0 = b
p_0 = b
||r0||_2 = r.r
x_0 = 0

//extra
z_0 = M * r_0
r_0.z_0

for i = 1 to N
{
  // upate alpha
  alpha_i = ||r_(i-1)||_2 / p_(i-1).(A * p_(i-1))
  
  // update vectors
  x_i = x_(i-1) + alpha_i * p_(i-1)
  r_i = r_(i-1) - alpha_i * (A * p_(i-1))
  
  // preconditioning
  z_i = M * r_(i-1)
  
  // update beta
  beta_i = r_i.z_i / r_(i-1).z_(i-1)
  
  // update vector
  p_i = z_i + beta_i * p_(i-1)
}