docstr: alpha_t, alpha_t_prev = self._alpha(t), self._alpha(t_prev)
  sigma_t, sigma_t_prev = self._sigma(alpha_t), self._sigma(alpha_t_prev)
  lmbd_t, lmbd_t_prev = self._lmbd(alpha_t, sigma_t), self._lmbd(alpha_t_prev, sigma_t_prev)
docstr_tok: ["alpha_t",",","alpha_t_prev","=","self._alpha","(","t",")",",","self._alpha","(","t_prev",")","sigma_t",",","sigma_t_prev","=","self._sigma","(","alpha_t",")",",","self._sigma","(","alpha_t_prev",")","lmbd_t",",","lmbd_t_prev","=","self._lmbd","(","alpha_t",",","sigma_t",")",",","self._lmbd","(","alpha_t_prev",",","sigma_t_prev",")"]
code: def dpm_solver_2(
      self,
      x_tilde_prev,
      t_prev,
      t,
      text_embeddings,
      guidance_scale=None,
      r1=0.5,
  ):
      # algorithm 4
      # numerically _not_ stable
      """alpha_t, alpha_t_prev = self._alpha(t), self._alpha(t_prev)
      sigma_t, sigma_t_prev = self._sigma(alpha_t), self._sigma(alpha_t_prev)
      lmbd_t, lmbd_t_prev = self._lmbd(alpha_t, sigma_t), self._lmbd(alpha_t_prev, sigma_t_prev)
      """
  
      # numerically stable
      (log_alpha_t, sigma_t, lmbd_t), (
          log_alpha_t_prev,
          sigma_t_prev,
          lmbd_t_prev,
      ) = self.lmbd(t), self.lmbd(t_prev)
      h = lmbd_t - lmbd_t_prev
      s = self.t_lambda(lmbd_t_prev + r1 * h, self.schedule)
      log_alpha_s, sigma_s, lmbd_s = self.lmbd(s)
  
      eps_prev = self.eps_theta(
          x_tilde_prev, t_prev, text_embeddings, guidance_scale
      )
      u = (
          np.exp(log_alpha_s - log_alpha_t_prev) * x_tilde_prev
          - sigma_s * np.expm1(r1 * h) * eps_prev
      )
  
      x_tilde = (
          +np.exp(log_alpha_t - log_alpha_t_prev) * x_tilde_prev
          - sigma_t * np.expm1(h) * eps_prev
          - sigma_t
          / (2 * r1)
          * np.expm1(h)
          * (
              self.eps_theta(u, s, text_embeddings, guidance_scale)
              - eps_prev
          )
      )
      return x_tilde
  
file_path: diffusion-for-beginners/samplers/dpm_solver.py
imports: import torch
  import numpy
label_desc: Use image node_id 9 for calling the DPMSampler obj's underlying member method code with example usage: obj.dpm_solver_2(x_tilde_prev, t_prev, t, text_embeddings, guidance_scale, r1) and returns: x_tilde