#! /usr/bin/env python
#
def monomial_value ( m, n, e, x ):

#*****************************************************************************80
#
## MONOMIAL_VALUE evaluates a monomial.
#
#  Discussion:
#
#    This routine evaluates a monomial of the form
#
#      product ( 1 <= i <= m ) x(i)^e(i)
#
#    The combination 0.0^0, if encountered, is treated as 1.0.
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license. 
#
#  Modified:
#
#    07 April 2015
#
#  Author:
#
#    John Burkardt
#
#  Parameters:
#
#    Input, integer M, the spatial dimension.
#
#    Input, integer N, the number of evaluation points.
#
#    Input, integer E(M), the exponents.
#
#    Input, real X(M,N), the point coordinates.
#
#    Output, real V(N), the monomial values.
#
  import numpy as np

  v = np.ones ( n )

  for i in range ( 0, m ):
    if ( 0 != e[i] ):
      for j in range ( 0, n ):
        v[j] = v[j] * x[i,j] ** e[i]

  return v

def monomial_value_test ( ):

#*****************************************************************************80
#
## MONOMIAL_VALUE_TEST tests MONOMIAL_VALUE on sets of data in various dimensions.
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    07 April 2015
#
#  Author:
#
#    John Burkardt
#
  import platform
  from i4vec_transpose_print import i4vec_transpose_print
  from i4vec_uniform_ab import i4vec_uniform_ab
  from monomial_value import monomial_value
  from r8mat_uniform_ab import r8mat_uniform_ab

  print ( '' )
  print ( 'MONOMIAL_VALUE_TEST' )
  print ( '  Python version: %s' % ( platform.python_version ( ) ) )
  print ( '  Use monomial_value() to evaluate some monomials' )
  print ( '  in dimensions 1 through 3.' )

  e_min = -3
  e_max = 6
  n = 5
  seed = 123456789
  x_min = -2.0
  x_max = +10.0

  for m in range ( 1, 4 ):

    print ( '' )
    print ( '  Spatial dimension M =  %d' % ( m ) )

    e, seed = i4vec_uniform_ab ( m, e_min, e_max, seed )
    i4vec_transpose_print ( m, e, '  Exponents:' )
    x, seed = r8mat_uniform_ab ( m, n, x_min, x_max, seed )
#
#  To make checking easier, make the X values integers.
#
    for i in range ( 0, m ):
      for j in range ( 0, n ):
        x[i,j] = round ( x[i,j] )

    v = monomial_value ( m, n, e, x )

    print ( '' )
    print ( '   V(X)         ', end = '' )
    for i in range ( 0, m ):
      print ( '      X(%d)' % ( i ), end = '' )
    print ( '' )
    print ( '' )
    for j in range ( 0, n ):
      print ( '%14.6g  ' % ( v[j] ), end = '' )
      for i in range ( 0, m ):
        print ( '%10.4f' % ( x[i,j] ), end = '' )
      print ( '' )
#
#  Terminate.
#
  print ( '' )
  print ( 'MONOMIAL_VALUE_TEST' )
  print ( '  Normal end of execution.' )
  return

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