#! /usr/bin/env python
#
def laguerre_1_set ( n ):

#*****************************************************************************80
#
## LAGUERRE_1_SET sets abscissas and weights for Laguerre quadrature.
#
#  Discussion:
#
#    This routine is specialized for the case where the density function is 1.
#
#    The integral is:
#      I(f) = integral ( 0 <= x < +oo ) f(x) dx
#    The quadrature rule is
#      Q(f) = sum ( 1 <= i <= n ) w(i) * f ( x(i) )
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    17 June 2015
#
#  Author:
#
#    John Burkardt
#
#  Parameters:
#
#    Input, integer N, the order.
#    N must be between 1 and 10.
#
#    Output, real X(N), the abscissas.
#
#    Output, real W(N), the weights.
#
  import numpy as np
  from sys import exit

  if ( n == 1 ):

    x = np.array ( [ \
            1.00000000000000000000000000000 ] )

    w = np.array ( [ \
            2.7182818284590451 ] )

  elif ( n == 2 ):

    x = np.array ( [ \
           0.585786437626904951198311275790, \
           3.41421356237309504880168872421 ] )

    w = np.array ( [ \
           1.5333260331194167, \
           4.4509573350545928 ] )

  elif ( n == 3 ):

    x = np.array ( [ \
           0.415774556783479083311533873128, \
           2.29428036027904171982205036136, \
           6.28994508293747919686641576551 ] )

    w = np.array ( [ \
           1.0776928592709207, \
           2.7621429619015876, \
           5.6010946254344267 ] )

  elif ( n == 4 ):

    x = np.array ( [ \
           0.322547689619392311800361459104, \
           1.74576110115834657568681671252, \
           4.53662029692112798327928538496, \
           9.39507091230113312923353644342 ] )

    w = np.array ( [ \
           0.83273912383788917, \
           2.0481024384542965, \
           3.6311463058215168, \
           6.4871450844076604 ] )

  elif ( n == 5 ):

    x = np.array ( [ \
           0.263560319718140910203061943361, \
           1.41340305910651679221840798019, \
           3.59642577104072208122318658878, \
           7.08581000585883755692212418111, \
           12.6408008442757826594332193066 ] )

    w = np.array ( [ \
           0.67909404220775038, \
           1.6384878736027471, \
           2.7694432423708375, \
           4.3156569009208940, \
           7.2191863543544450 ] )

  elif ( n == 6 ):

    x = np.array ( [ \
           0.222846604179260689464354826787, \
           1.18893210167262303074315092194, \
           2.99273632605931407769132528451, \
           5.77514356910451050183983036943, \
           9.83746741838258991771554702994, \
           15.9828739806017017825457915674 ] )

    w = np.array ( [ \
           0.57353550742273818, \
           1.3692525907123045, \
           2.2606845933826722, \
           3.3505245823554555, \
           4.8868268002108213, \
           7.8490159455958279 ] )

  elif ( n == 7 ):

    x = np.array ( [ \
           0.193043676560362413838247885004, \
           1.02666489533919195034519944317, \
           2.56787674495074620690778622666, \
           4.90035308452648456810171437810, \
           8.18215344456286079108182755123, \
           12.7341802917978137580126424582, \
           19.3957278622625403117125820576 ] )

    w = np.array ( [ \
           0.49647759753997234, \
           1.1776430608611976, \
           1.9182497816598063, \
           2.7718486362321113, \
           3.8412491224885148, \
           5.3806782079215330, \
           8.4054324868283103 ] )

  elif ( n == 8 ):

    x = np.array ( [ \
           0.170279632305100999788861856608, \
           0.903701776799379912186020223555, \
           2.25108662986613068930711836697, \
           4.26670017028765879364942182690, \
           7.04590540239346569727932548212, \
           10.7585160101809952240599567880, \
           15.7406786412780045780287611584, \
           22.8631317368892641057005342974 ] )

    w = np.array ( [ \
           0.43772341049291136, \
           1.0338693476655976, \
           1.6697097656587756, \
           2.3769247017585995, \
           3.2085409133479259, \
           4.2685755108251344, \
           5.8180833686719184, \
           8.9062262152922216 ] )

  elif ( n == 9 ):

    x = np.array ( [ \
           0.152322227731808247428107073127, \
           0.807220022742255847741419210952, \
           2.00513515561934712298303324701, \
           3.78347397333123299167540609364, \
           6.20495677787661260697353521006, \
           9.37298525168757620180971073215, \
           13.4662369110920935710978818397, \
           18.8335977889916966141498992996, \
           26.3740718909273767961410072937 ] )

    w = np.array ( [ \
           0.39143112431563987, \
           0.92180502852896307, \
           1.4801279099429154, \
           2.0867708075492613, \
           2.7729213897119713, \
           3.5916260680922663, \
           4.6487660021402037, \
           6.2122754197471348, \
           9.3632182377057980 ] )

  elif ( n == 10 ):

    x = np.array ( [ \
           0.137793470540492430830772505653, \
           0.729454549503170498160373121676, \
           1.80834290174031604823292007575, \
           3.40143369785489951448253222141, \
           5.55249614006380363241755848687, \
           8.33015274676449670023876719727, \
           11.8437858379000655649185389191, \
           16.2792578313781020995326539358, \
           21.9965858119807619512770901956, \
           29.9206970122738915599087933408 ] )

    w = np.array ( [ \
           0.35400973860699630, \
           0.83190230104358065, \
           1.3302885617493283, \
           1.8630639031111309, \
           2.4502555580830108, \
           3.1227641551351848, \
           3.9341526955615240, \
           4.9924148721930299, \
           6.5722024851307994, \
           9.7846958403746243 ] )

  else:

    print ( '' )
    print ( 'LAGUERRE_1_SET - Fatal error!' )
    print ( '  Illegal value of N = %d' % ( n ) )
    print ( '  Legal values are 1 to 10.' )
    exit ( 'LAGUERRE_1_SET - Fatal error!' )

  return x, w

def laguerre_1_set_test ( ):

#*****************************************************************************80
#
## LAGUERRE_1_SET_TEST tests LAGUERRE_1_SET.
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license. 
#
#  Modified:
#
#    17 June 2015
#
#  Author:
#
#    John Burkardt
#
  import platform

  print ( '' )
  print ( 'LAGUERRE_1_SET_TEST' )
  print ( '  Python version: %s' % ( platform.python_version ( ) ) )
  print ( '  LAGUERRE_1_SET sets a Laguerre rule.' )
  print ( '  The density function is rho(x)=1.' )
  print ( '' )
  print ( '         I            X                  W' )

  for n in range ( 1, 11 ):

    x, w = laguerre_1_set ( n )

    print ( '' )
    for i in range ( 0, n ):
      print ( '  %8d  %24.16g  %24.16g' % ( i, x[i], w[i] ) )
#
#  Terminate.
#
  print ( '' )
  print ( 'LAGUERRE_1_SET_TEST:' )
  print ( '  Normal end of execution.' )
  return

if ( __name__ == '__main__' ):
  from timestamp import timestamp
  timestamp ( )
  laguerre_1_set_test ( )
  timestamp ( )