#! /usr/bin/env python
#
def rule_adjust ( a, b, c, d, norder, x, w ):

#*****************************************************************************80
#
## RULE_ADJUST maps a quadrature rule from [A,B] to [C,D].
#
#  Discussion:
#
#    Most quadrature rules are defined on a special interval, like
#    [-1,1] or [0,1].  To integrate over an interval, the abscissas
#    and weights must be adjusted.  This can be done on the fly,
#    or by calling this routine.
#
#    If the weight function W(X) is not 1, then the W vector will
#    require further adjustment by the user.
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license. 
#
#  Modified:
#
#    08 July 2018
#
#  Author:
#
#    John Burkardt
#
#  Parameters:
#
#    Input, real A, B, the endpoints of the definition interval.
#
#    Input, real C, D, the endpoints of the integration interval.
#
#    Input, integer NORDER, the number of abscissas and weights.
#
#    Input, real X(NORDER), W(NORDER), the abscissas
#    and weights defined on [A,B].
#
#    Output, real X_NEW(NORDER), W_NEW(NORDER), the abscissas
#    and weights, redefined on [C,D].
#
  x_new = \
    ( ( b - x[:]     ) * c   \
    + (     x[:] - a ) * d ) \
    / ( b        - a )

  w_new = ( ( d - c ) / ( b - a ) ) * w[:]

  return x_new, w_new

def rule_adjust_test ( ):

#*****************************************************************************80
#
## RULE_ADJUST_TEST tests RULE_ADJUST.
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    08 July 2018
#
#  Author:
#
#    John Burkardt
#
  import numpy as np
  import platform
  from r8vec2_print import r8vec2_print

  print ( '' )
  print ( 'RULE_ADJUST_TEST' )
  print ( '  Python version: %s' % ( platform.python_version ( ) ) )
  print ( '  RULE_ADJUST adjusts a quadrature rule from [A,B] to [C,D].' )

  n = 7

  x = np.zeros ( n )
  w = np.zeros ( n )

  for i in range ( 0, n ):
    angle = np.pi * float ( n - i ) / float ( n + 1 )
    w[i] = np.pi / float ( n + 1 ) * ( np.sin ( angle ) ) ** 2
    x[i] = np.cos ( angle )

  r8vec2_print ( n, w, x, '  W, X defined on [-1,+1]' )

  a = - 1.0;
  b = + 1.0;

  c = 0.0;
  d = +1.0;
  [ x_new, w_new ] = rule_adjust ( a, b, c, d, n, x, w )

  r8vec2_print ( n, w_new, x_new, '  W, X adjusted to [0,1]' )
#
#  Terminate.
#
  print ( '' )
  print ( 'RULE_ADJUST_TEST' )
  print ( '  Normal end of execution.' )
  return

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