#! /usr/bin/env python
#
def vandermonde_interp_1d_test ( ):

#*****************************************************************************80
#
## VANDERMONDE_INTERP_1D_TEST tests the VANDERMONDE_INTERP_1D library.
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license. 
#
#  Modified:
#
#    02 July 2015
#
#  Author:
#
#    John Burkardt
#
  import platform
  from vandermonde_coef_1d              import vandermonde_coef_1d_test
  from vandermonde_matrix_1d            import vandermonde_matrix_1d_test
  from vandermonde_value_1d             import vandermonde_value_1d_test
  from p00_data                         import p00_data_test
  from p00_data_num                     import p00_data_num_test
  from p00_dim_num                      import p00_dim_num_test
  from p00_prob_num                     import p00_prob_num
  from p00_prob_num                     import p00_prob_num_test
  from r8mat_print                      import r8mat_print_test
  from r8mat_print_some                 import r8mat_print_some_test
  from r8mat_transpose_print            import r8mat_transpose_print_test
  from r8mat_transpose_print_some       import r8mat_transpose_print_some_test
  from r8poly_print                     import r8poly_print_test
  from r8vec_norm                       import r8vec_norm_test
  from r8vec_norm_affine                import r8vec_norm_affine_test
  from r8vec_print                      import r8vec_print_test
  from r8vec_uniform_ab                 import r8vec_uniform_ab_test
  from r8vec2_print                     import r8vec2_print_test

  print ( '' )
  print ( 'VANDERMONDE_INTERP_1D_TEST' )
  print ( '  Python version: %s' % ( platform.python_version ( ) ) )
  print ( '  Test the VANDERMONDE_INTERP_1D library.' )
#
#  Utility functions.
#
  p00_data_test ( )
  p00_data_num_test ( )
  p00_dim_num_test ( )
  p00_prob_num_test ( )
  r8mat_print_test ( )
  r8mat_print_some_test ( )
  r8mat_transpose_print_test ( )
  r8mat_transpose_print_some_test ( )
  r8poly_print_test ( )
  r8vec_norm_test ( )
  r8vec_norm_affine_test ( )
  r8vec_print_test ( )
  r8vec_uniform_ab_test ( )
  r8vec2_print_test ( )
#
#  Library functions.
#
  vandermonde_coef_1d_test ( )
  vandermonde_matrix_1d_test ( )
  vandermonde_value_1d_test ( )

  prob_num = p00_prob_num ( );
  for prob in range ( 1, prob_num + 1 ):
    vandermonde_interp_1d_test01 ( prob )
#
#  Terminate.
#
  print ( '' )
  print ( 'VANDERMONDE_INTERP_1D_TEST:' )
  print ( '  Normal end of execution.' )
  return

def vandermonde_interp_1d_test01 ( prob ):

#*****************************************************************************80
#
## VANDERMONDE_INTERP_1D_TEST01 tests VANDERMONDE_VALUE_1D.
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    01 July 2015
#
#  Author:
#
#    John Burkardt
#
#  Parameters:
#
#    Input, integer PROB, the problem index.
#
#    Input, integer ND, the number of data points to use.
#
  import matplotlib.pyplot as plt
  import numpy as np
  import platform
  from vandermonde_coef_1d import vandermonde_coef_1d
  from vandermonde_value_1d import vandermonde_value_1d
  from p00_data import p00_data
  from p00_data_num import p00_data_num
  from r8vec_norm_affine import r8vec_norm_affine
  from r8vec2_print import r8vec2_print

  print ( '' )
  print ( 'VANDERMONDE_INTERP_1D_TEST01:' )
  print ( '  Python version: %s' % ( platform.python_version ( ) ) )
  print ( '  Interpolate data from TEST_INTERP problem #%d.' % ( prob ) )

  nd = p00_data_num ( prob )
  print ( '  Number of data points = %d' % ( nd ) )

  xy = p00_data ( prob, 2, nd )
  
  xd = np.zeros ( nd )
  yd = np.zeros ( nd )
  for i in range ( 0, nd ):
    xd[i] = xy[0,i]
    yd[i] = xy[1,i]
 
  if ( nd < 10 ):
    r8vec2_print ( nd, xd, yd, '  Data array:' )
#
#  Get Vandermonde interpolant coefficients.
#
  cd = vandermonde_coef_1d ( nd, xd, yd )
#
#  #1:  Does interpolant match function at interpolation points?
#
  ni = nd
  xi = xd
  yi = vandermonde_value_1d ( nd, cd, ni, xi )

  int_error = r8vec_norm_affine ( ni, yi, yd ) / float ( ni )

  print ( '' )
  print ( '  L2 interpolation error averaged per interpolant node = %g' % ( int_error ) )
#
#  #2: Compare estimated curve length to piecewise linear (minimal) curve length.
#  Assume data is sorted, and normalize X and Y dimensions by (XMAX-XMIN) and
#  (YMAX-YMIN).
#
  xmin = np.min ( xd )
  xmax = np.max ( xd )
  ymin = np.min ( yd )
  ymax = np.max ( yd )

  ni = 501
  xi = np.linspace ( xmin, xmax, ni )
  yi = vandermonde_value_1d ( nd, cd, ni, xi )

  ld = 0.0
  for i in range ( 0, nd - 1 ):
    ld = ld + np.sqrt \
    ( \
        ( ( xd[i+1] - xd[i] ) / ( xmax - xmin ) ) ** 2 \
      + ( ( yd[i+1] - yd[i] ) / ( ymax - ymin ) ) ** 2 \
    )

  li = 0.0
  for i in range ( 0, ni - 1 ):
    li = li + np.sqrt \
    ( \
        ( ( xi[i+1] - xi[i] ) / ( xmax - xmin ) ) ** 2 \
      + ( ( yi[i+1] - yi[i] ) / ( ymax - ymin ) ) ** 2 \
    )
  li = np.sqrt ( li )

  print ( '' )
  print ( '  Normalized length of piecewise linear interpolant = %g' % ( ld ) )
  print ( '  Normalized length of Shepard interpolant          = %g' % ( li ) )
#
#  #3: Plot the data.
#
  plt.plot ( xd, yd, 'b-', linewidth = 3.0 )
  plt.plot ( xd, yd, 'k.', markersize = 10 )
  t = 'p0' + str ( prob ) + ' Piecewise Linear Interpolant'
  plt.title ( t )
  plt.grid ( True )
  plt.xlabel ( '<---X--->' )
  plt.ylabel ( '<---Y--->' )
  filename = 'p0' + str ( prob ) + '_data.png'
  plt.savefig ( filename )
  plt.clf ( )

  print ( '' )
  print ( '  Created plot file "%s"' % ( filename ) )
#
#  #4: Plot the piecewise linear and Vandermonde interpolants.
#
  ni = 501
  xmin = np.min ( xd )
  xmax = np.max ( xd )
  xi = np.linspace ( xmin, xmax, ni )
  yi = vandermonde_value_1d ( nd, cd, ni, xi )

  plt.plot ( xd, yd, 'b-', linewidth = 3.0 )
  plt.plot ( xi, yi, 'r-', linewidth = 4.0 )
  plt.plot ( xd, yd, 'k.', markersize = 10 )
  t = 'p0' + str ( prob ) + ' Vandermonde Interpolant for ' + str ( nd ) + ' nodes.'
  plt.title ( t )
  plt.grid ( True )
  plt.xlabel ( '<---X--->' )
  plt.ylabel ( '<---Y--->' )
  filename = 'p0' + str ( prob ) + '_vandermonde.png'
  plt.savefig ( filename )
  plt.clf ( )

  print ( '  Created plot file "%s".' % ( filename ) )
#
#  Terminate.
#
  print ( '' )
  print ( 'VANDERMONDE_INTERP_1D_TEST01:' )
  print ( '  Normal end of execution.' )
  return

if ( __name__ == '__main__' ):
  from timestamp import timestamp
  timestamp ( )
  vandermonde_interp_1d_test ( )
  timestamp ( )