new_contents: 
  """
  Some code to see if there is any pattern in the SVD of a matrix with fixed 
  sparisty structure. 
  """
  import sys 
  import logging
  import scipy.sparse
  import numpy
  from sparsesvd import sparsesvd
  from exp.util.SparseUtils import SparseUtils 
  
  numpy.random.seed(21)
  logging.basicConfig(stream=sys.stdout, level=logging.DEBUG)
  numpy.set_printoptions(precision=3, suppress=True, linewidth=100)
  
  m = 10 
  n = 10 
  r = 1
  U0, s0, V0 = SparseUtils.generateLowRank((m, n), r)
  
  numInds = 10 
  inds = numpy.unique(numpy.random.randint(0, m*n, numInds)) 
  A = SparseUtils.reconstructLowRank(U0, s0, V0, inds)
  #print(A.todense())
  
  t0 = s0 + numpy.random.rand(s0.shape[0])*0.1
  B = SparseUtils.reconstructLowRank(U0, t0, V0, inds)
  #print(B.todense())
  
  k = 9
  U, s, V = sparsesvd(A, k)
  U2, s2, V2 = sparsesvd(B, k)
  
  print(A.todense())
  
  print(U0)
  print(s0)
  print(V0)
  
  print(U)
  print(s)
  print(V)
  
  
  print(U2)
  print(s2)
  print(V2)
  
  print(U2.T.dot(U))
  #print(s2)
  print(V2.T.dot(V))
  
  #Now try for fixed singular vectors 
subject: Test if there is a pattern in sparsity structure