class_docstr: DualFormulation is a class that creates the dual objective function
  and access to matrix vector products for the matrix that is constrained
  to be Positive semidefinite
class_docstr_tok: ["DualFormulation","is","a","class","that","creates","the","dual","objective","function","and","access","to","matrix","vector","products","for","the","matrix","that","is","constrained","to","be","Positive","semidefinite"]
docstr: Computes the min eigen value and corresponding vector of matrix M or H
  using the Lanczos algorithm.
  Args:
    compute_m: boolean to determine whether we should compute eig val/vec
      for M or for H. True for M; False for H.
    feed_dict: dictionary mapping from TF placeholders to values (optional)
  Returns:
    min_eig_vec: Corresponding eigen vector to min eig val
    eig_val: Minimum eigen value
docstr_tok: ["Computes","the","min","eigen","value","and","corresponding","vector","of","matrix","M","or","H","using","the","Lanczos","algorithm",".","Args",":","compute_m",":","boolean","to","determine","whether","we","should","compute","eig","val\/vec","for","M","or","for","H.","True","for","M",";","False","for","H.","feed_dict",":","dictionary","mapping","from","TF","placeholders","to","values","(","optional",")","Returns",":","min_eig_vec",":","Corresponding","eigen","vector","to","min","eig","val","eig_val",":","Minimum","eigen","value"]
code: def get_lanczos_eig(self, compute_m=True, feed_dict=None):
      """Computes the min eigen value and corresponding vector of matrix M or H
      using the Lanczos algorithm.
      Args:
        compute_m: boolean to determine whether we should compute eig val/vec
          for M or for H. True for M; False for H.
        feed_dict: dictionary mapping from TF placeholders to values (optional)
      Returns:
        min_eig_vec: Corresponding eigen vector to min eig val
        eig_val: Minimum eigen value
      """
      if compute_m:
          min_eig, min_vec = self.sess.run(
              [self.m_min_eig, self.m_min_vec], feed_dict=feed_dict
          )
  
      else:
          min_eig, min_vec = self.sess.run(
              [self.h_min_eig, self.h_min_vec], feed_dict=feed_dict
          )
  
      return min_vec, min_eig
  
file_path: cleverhans/cleverhans_v3.1.0/cleverhans/experimental/certification/dual_formulation.py
imports: from __future__ import absolute_import
  from __future__ import division
  from __future__ import print_function
  from scipy.sparse.linalg import eigs, LinearOperator
  import tensorflow
  from tensorflow.contrib import autograph
  import numpy
  from cleverhans.experimental.certification import utils
label_desc: Use image node_id 9 for calling the DualFormulation obj's underlying member method code with example usage: obj.get_lanczos_eig(compute_m, feed_dict) and returns: min_vec,  min_eig