code: def cg(
      A,
      b,
      x0=None,
      tol=1e-5,
      maxiter=None,
      M=None,
      callback=None,
      atol=None,
  ):
      """Uses Conjugate Gradient iteration to solve ``Ax = b``.
  
      Args:
          A (ndarray, spmatrix or LinearOperator): The real or complex matrix of
              the linear system with shape ``(n, n)``. ``A`` must be a hermitian,
              positive definitive matrix with type of :class:`cupy.ndarray`,
              :class:`cupyx.scipy.sparse.spmatrix` or
              :class:`cupyx.scipy.sparse.linalg.LinearOperator`.
          b (cupy.ndarray): Right hand side of the linear system with shape
              ``(n,)`` or ``(n, 1)``.
          x0 (cupy.ndarray): Starting guess for the solution.
          tol (float): Tolerance for convergence.
          maxiter (int): Maximum number of iterations.
          M (ndarray, spmatrix or LinearOperator): Preconditioner for ``A``.
              The preconditioner should approximate the inverse of ``A``.
              ``M`` must be :class:`cupy.ndarray`,
              :class:`cupyx.scipy.sparse.spmatrix` or
              :class:`cupyx.scipy.sparse.linalg.LinearOperator`.
          callback (function): User-specified function to call after each
              iteration. It is called as ``callback(xk)``, where ``xk`` is the
              current solution vector.
          atol (float): Tolerance for convergence.
  
      Returns:
          tuple:
              It returns ``x`` (cupy.ndarray) and ``info`` (int) where ``x`` is
              the converged solution and ``info`` provides convergence
              information.
  
      .. seealso:: :func:`scipy.sparse.linalg.cg`
      """
      A, M, x, b = _make_system(A, M, x0, b)
      matvec = A.matvec
      psolve = M.matvec
  
      n = A.shape[0]
      if maxiter is None:
          maxiter = n * 10
      if n == 0:
          return cupy.empty_like(b), 0
      b_norm = cupy.linalg.norm(b)
      if b_norm == 0:
          return b, 0
      if atol is None:
          atol = tol * float(b_norm)
      else:
          atol = max(float(atol), tol * float(b_norm))
  
      r = b - matvec(x)
      iters = 0
      rho = 0
      while iters < maxiter:
          z = psolve(r)
          rho1 = rho
          rho = cublas.dotc(r, z)
          if iters == 0:
              p = z
          else:
              beta = rho / rho1
              p = z + beta * p
          q = matvec(p)
          alpha = rho / cublas.dotc(p, q)
          x = x + alpha * p
          r = r - alpha * q
          iters += 1
          if callback is not None:
              callback(x)
          resid = cublas.nrm2(r)
          if resid <= atol:
              break
  
      info = 0
      if iters == maxiter and not (resid <= atol):
          info = iters
  
      return x, info
  
file_path: cupy/cupyx/scipy/sparse/linalg/_iterative.py
imports: import numpy
  import cupy
  from cupy import cublas
  from cupy._core import _dtype
  from cupy.cuda import device
  from cupy_backends.cuda.libs import cublas
  from cupyx.scipy.sparse import _csr
  from cupyx.scipy.sparse.linalg import _interface
label_desc: Use image node_id 1 for calling a global function with example usage: cg(A, b, x0, tol, maxiter, M, callback, atol) and returns: x,  info, cupy,  int, b,  int