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

#*****************************************************************************80
#
## pca_eigen_glass uses an eigenvalue approach for PCA of glass data.
#
#  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_glass:' )
  print ( '  Python version: %s' % ( platform.python_version ( ) ) )
  print ( '  Read data about chemical properties of glass samples.' )
  print ( '  Create matrix A after subtracting averages.' )
  print ( '  Get eigenvalue factorization of A'' A.' )
  print ( '  Plot eigenvalues.' )
  print ( '  Plot cumulative sum of eigenvalues.' )

  data = np.loadtxt ( 'glass_data.txt' )
#
#  Copy all but first and last columns of data into A.
#
  m, n = data.shape
  A = data[:,1:n-1]

  m, n = A.shape
  print ( '' )
  print ( '  Array A has dimensions M = %d, N = %d' % ( m, n ) )
#
#  Subtract off the mean value of each column.
#
  mu = np.mean ( A, axis = 0 )
  for j in range ( 0, n ):
    A[:,j] = A[:,j] - mu[j]
#
#  Compute the NxN symmetric positive semi-definite matrix A'A.
#
  ATA = np.matmul ( A.T, A )
#
#  Get the N eigenvalues LAM and NxN eigenvector matrix V.
#
  lam, v = np.linalg.eig ( ATA )
#
#  Display the eigenvalues.
#
  x = np.arange ( 9 )
  plt.plot ( x, lam, 'ko-', linewidth = 3 )
  plt.grid ( True )
  plt.xlabel ( '<-- Eigenvalue index -->' )
  plt.ylabel ( '<-- Eigenvalue -->' )
  plt.title ( 'Eigenvalues of A\'A ' )
  filename = 'pca_eigen_glass_1.png'
  plt.savefig ( filename )
  print ( '' )
  print ( '  Graphics saved in "%s"' % ( filename ) )
  plt.show ( )
  plt.clf ( )
#
#  Display the relative sum of the first K eigenvalues.
#
  x = np.arange ( 10 )
  y = [ 0.0 ]
  y = np.append ( y, np.cumsum(lam) )
  y = y / np.sum ( lam )
  plt.plot ( x, y, 'ro-', linewidth = 3 )
  plt.grid ( True )
  plt.xlabel ( '<-- K: Number of components-->' )
  plt.ylabel ( '<-- Amount of variance explained-->' )
  plt.title ( 'Information proportion in first K components' )
  filename = 'pca_eigen_glass_2.png'
  plt.savefig ( filename )
  print ( '' )
  print ( '  Graphics saved in "%s"' % ( filename ) )
  plt.show ( )
  plt.clf ( )
#
#  Terminate.
#
  print ( '' )
  print ( 'pca_eigen_glass:' )
  print ( '  Normal end of execution.' )

  return

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