#! /usr/bin/env python
#
def hermite_poly_phys_values ( n_data ):

#*****************************************************************************80
#
## HERMITE_POLY_PHYS_VALUES returns some values of the physicist's Hermite polynomial.
#
#  Discussion:
#
#    In Mathematica, the function can be evaluated by:
#
#      HermiteH[n,x]
#
#  Differential equation:
#
#    Y'' - 2 X Y' + 2 N Y = 0
#
#  First terms:
#
#      1
#      2 X
#      4 X^2     -  2
#      8 X^3     - 12 X
#     16 X^4     - 48 X^2     + 12
#     32 X^5    - 160 X^3    + 120 X
#     64 X^6    - 480 X^4    + 720 X^2    - 120
#    128 X^7   - 1344 X^5   + 3360 X^3   - 1680 X
#    256 X^8   - 3584 X^6  + 13440 X^4  - 13440 X^2   + 1680
#    512 X^9   - 9216 X^7  + 48384 X^5  - 80640 X^3  + 30240 X
#   1024 X^10 - 23040 X^8 + 161280 X^6 - 403200 X^4 + 302400 X^2 - 30240
#
#  Recursion:
#
#    H(0,X) = 1,
#    H(1,X) = 2*X,
#    H(N,X) = 2*X * H(N-1,X) - 2*(N-1) * H(N-2,X)
#
#  Norm:
#
#    Integral ( -oo < X < +oo ) exp ( - X^2 ) * H(N,X)^2 dX
#    = sqrt ( PI ) * 2^N * N!
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    12 February 2015
#
#  Author:
#
#    John Burkardt
#
#  Reference:
#
#    Milton Abramowitz and Irene Stegun,
#    Handbook of Mathematical Functions,
#    US Department of Commerce, 1964.
#
#    Stephen Wolfram,
#    The Mathematica Book,
#    Fourth Edition,
#    Wolfram Media / Cambridge University Press, 1999.
#
#  Parameters:
#
#    Input/output, integer N_DATA.  The user sets N_DATA to 0 before the
#    first call.  On each call, the routine increments N_DATA by 1, and
#    returns the corresponding data; when there is no more data, the
#    output value of N_DATA will be 0 again.
#
#    Output, integer N, the order of the polynomial.
#
#    Output, real X, the point where the polynomial is evaluated.
#
#    Output, real FX, the value of the function.
#
  import numpy as np

  n_max = 18

  f_vec = np.array ( ( \
      0.1000000000000000E+01, \
      0.1000000000000000E+02, \
      0.9800000000000000E+02, \
      0.9400000000000000E+03, \
      0.8812000000000000E+04, \
      0.8060000000000000E+05, \
      0.7178800000000000E+06, \
      0.6211600000000000E+07, \
      0.5206568000000000E+08, \
      0.4212712000000000E+09, \
      0.3275529760000000E+10, \
      0.2432987360000000E+11, \
      0.1712370812800000E+12, \
      0.0000000000000000E+00, \
      0.4100000000000000E+02, \
     -0.8000000000000000E+01, \
      0.3816000000000000E+04, \
      0.3041200000000000E+07 ))

  n_vec = np.array ( ( \
     0,  1,  2, \
     3,  4,  5, \
     6,  7,  8, \
     9, 10, 11, \
    12,  5,  5, \
     5,  5,  5 ))

  x_vec = np.array ( ( \
     5.0E+00, \
     5.0E+00, \
     5.0E+00, \
     5.0E+00, \
     5.0E+00, \
     5.0E+00, \
     5.0E+00, \
     5.0E+00, \
     5.0E+00, \
     5.0E+00, \
     5.0E+00, \
     5.0E+00, \
     5.0E+00, \
     0.0E+00, \
     0.5E+00, \
     1.0E+00, \
     3.0E+00, \
     1.0E+01 ))

  if ( n_data < 0 ):
    n_data = 0

  if ( n_max <= n_data ):
    n_data = 0
    n = 0
    x = 0.0
    f = 0.0
  else:
    n = n_vec[n_data]
    x = x_vec[n_data]
    f = f_vec[n_data]
    n_data = n_data + 1

  return n_data, n, x, f

def hermite_poly_phys_values_test ( ):

#*****************************************************************************80
#
## HERMITE_POLY_PHYS_VALUES_TEST demonstrates the use of HERMITE_POLY_PHYS_VALUES.
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    12 February 2015
#
#  Author:
#
#    John Burkardt
#
  import platform

  print ( '' )
  print ( 'HERMITE_POLY_PHYS_VALUES_TEST:' )
  print ( '  Python version: %s' % ( platform.python_version ( ) ) )
  print ( '  HERMITE_POLY_PHYS_VALUES stores values of the Hermite physicist polynomials.' )
  print ( '' )
  print ( '      N            X            FX' )
  print ( '' )

  n_data = 0

  while ( True ):

    n_data, n, x, fx = hermite_poly_phys_values ( n_data )

    if ( n_data == 0 ):
      break

    print ( '  %6d  %12f  %24.16g' % ( n, x, fx ) )
#
#  Terminate.
#
  print ( '' )
  print ( 'HERMITE_POLY_PHYS_VALUES_TEST:' )
  print ( '  Normal end of execution.' )
  return

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