#! /usr/bin/env python3
#
def pca_eigen_6x4 ( ):

#*****************************************************************************80
#
## pca_eigen_6x4 uses an eigenvalue approach for PCA of a random 6x4 matrix.
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    24 June 2019
#
#  Author:
#
#    John Burkardt
#
  import matplotlib.pyplot as plt
  import numpy as np
  import platform

  print ( '' )
  print ( 'pca_eigen_6x4:' )
  print ( '  Python version: %s' % ( platform.python_version ( ) ) )
  print ( '  Create a random 6x4 matrix.' )
  print ( '  Get the eigenvalue factorization of A\' A' )
  print ( '  Get the SVD factorization of A.' )

  m = 6
  n = 4
  A = np.random.randn ( 6, 4 )
  print ( '' )
  print ( '  Matrix A:' )
  print ( A )
#
#  Compute A'A.
#
  ATA = np.matmul ( A.T, A )
  print ( '  Matrix ATA:' )
  print ( ATA )
#
#  Get the eigenvalue decomposition of A' A.
#
  L, X = np.linalg.eig ( ATA )
#
#  Check that A' A * X1 = L1 * X1.
#
  prod = np.matmul ( ATA, X[:,0] ) - L[0] * X[:,0]
  diff = np.linalg.norm ( prod )
  print ( '  Norm of A\'*A*X1 - L1 * X1 = %g' % ( diff ) )
#
#  Check that A' A * X = X * L.
#
  prod = np.matmul ( ATA, X ) - np.matmul ( X, np.diag ( L ) ) 
  diff = np.linalg.norm ( prod )
  print ( '  Norm of A\'*A*X - L * X = %g' % ( diff ) )
#
#  Terminate.
#
  print ( '' )
  print ( 'pca_eigen_6x4:' )
  print ( '  Normal end of execution.' )

  return

if ( __name__ == '__main__' ):
  pca_eigen_6x4 ( )