docstr: ivy.Container instance method variant of ivy.cholesky. This method
  simply wraps the function, and so the docstring for ivy.cholesky also
  applies to this method with minimal changes.
  
  Parameters
  ----------
  self
      input container having shape (..., M, M) and whose innermost two dimensions
      form square symmetric positive-definite matrices. Should have a
      floating-point data type.
  upper
      If True, the result must be the upper-triangular Cholesky factor U. If
      False, the result must be the lower-triangular Cholesky factor L.
      Default: ``False``.
  key_chains
      The key-chains to apply or not apply the method to. Default is ``None``.
  to_apply
      If True, the method will be applied to key_chains, otherwise key_chains
      will be skipped. Default is ``True``.
  prune_unapplied
      Whether to prune key_chains for which the function was not applied.
      Default is ``False``.
  map_sequences
      Whether to also map method to sequences (lists, tuples).
      Default is ``False``.
  out
      optional output container, for writing the result to. It must have a shape
      that the inputs broadcast to.
  
  Returns
  -------
  ret
      a container containing the Cholesky factors for each square matrix. If upper
      is False, the returned container must contain lower-triangular matrices;
      otherwise, the returned container must contain upper-triangular matrices.
      The returned container must have a floating-point data type determined by
      Type Promotion Rules and must have the same shape as self.
  
  Examples
  --------
  >>> x = ivy.Container(a=ivy.array([[3., -1],[-1., 3.]]),
  ...                      b=ivy.array([[2., 1.],[1., 1.]]))
  >>> y = x.cholesky(upper='false')
  >>> print(y)
  {
      a: ivy.array([[1.73, -0.577],
                      [0., 1.63]]),
      b: ivy.array([[1.41, 0.707],
                      [0., 0.707]])
  }
code: def cholesky(
      self: ivy.Container,
      /,
      *,
      upper: Union[bool, ivy.Container] = False,
      key_chains: Optional[
          Union[List[str], Dict[str, str], ivy.Container]
      ] = None,
      to_apply: Union[bool, ivy.Container] = True,
      prune_unapplied: Union[bool, ivy.Container] = False,
      map_sequences: Union[bool, ivy.Container] = False,
      out: Optional[ivy.Container] = None,
  ) -> ivy.Container:
      """ivy.Container instance method variant of ivy.cholesky. This method
      simply wraps the function, and so the docstring for ivy.cholesky also
      applies to this method with minimal changes.
  
      Parameters
      ----------
      self
          input container having shape (..., M, M) and whose innermost two dimensions
          form square symmetric positive-definite matrices. Should have a
          floating-point data type.
      upper
          If True, the result must be the upper-triangular Cholesky factor U. If
          False, the result must be the lower-triangular Cholesky factor L.
          Default: ``False``.
      key_chains
          The key-chains to apply or not apply the method to. Default is ``None``.
      to_apply
          If True, the method will be applied to key_chains, otherwise key_chains
          will be skipped. Default is ``True``.
      prune_unapplied
          Whether to prune key_chains for which the function was not applied.
          Default is ``False``.
      map_sequences
          Whether to also map method to sequences (lists, tuples).
          Default is ``False``.
      out
          optional output container, for writing the result to. It must have a shape
          that the inputs broadcast to.
  
      Returns
      -------
      ret
          a container containing the Cholesky factors for each square matrix. If upper
          is False, the returned container must contain lower-triangular matrices;
          otherwise, the returned container must contain upper-triangular matrices.
          The returned container must have a floating-point data type determined by
          Type Promotion Rules and must have the same shape as self.
  
      Examples
      --------
      >>> x = ivy.Container(a=ivy.array([[3., -1],[-1., 3.]]),
      ...                      b=ivy.array([[2., 1.],[1., 1.]]))
      >>> y = x.cholesky(upper='false')
      >>> print(y)
      {
          a: ivy.array([[1.73, -0.577],
                          [0., 1.63]]),
          b: ivy.array([[1.41, 0.707],
                          [0., 0.707]])
      }
      """
      return self._static_cholesky(
          self,
          upper=upper,
          key_chains=key_chains,
          to_apply=to_apply,
          prune_unapplied=prune_unapplied,
          map_sequences=map_sequences,
          out=out,
      )
  
imports: from typing import Union, Optional, Tuple, Literal, List, Dict, Sequence
  from ivy.data_classes.container.base import ContainerBase
  import ivy
label_desc: Use image node_id 4 for calling the _ContainerWithLinearAlgebra obj's underlying member method code with example usage: obj.cholesky() and returns: self