R/KPN.R

In SparseGrid: Sparse grid integration in R

# Copyright (C) 2011 Jelmer Ypma. All Rights Reserved.
# This code is published under the GPL.
#
# File:   KPN.R
# Author: Jelmer Ypma
# Date:   31 March 2011
#
# This code is based on code from www.sparse-grids.de
# with permission from the authors.
#
# Input: 
# Output: 

KPN <- function( level ) {
  switch( level,
          { # case 1
            n = c(0.0000000000000000e+000)
            w = c(1.0000000000000000e+000)
          },
          { # case 2
            n = c(0.0000000000000000e+000, 1.7320508075688772e+000)
            w = c(6.6666666666666663e-001, 1.6666666666666666e-001)
          },
          { # case 3
            n = c(0.0000000000000000e+000, 1.7320508075688772e+000)
            w = c(6.6666666666666674e-001, 1.6666666666666666e-001)
          },
          { # case 4
            n = c(0.0000000000000000e+000, 7.4109534999454085e-001, 1.7320508075688772e+000, 4.1849560176727323e+000)
            w = c(4.5874486825749189e-001, 1.3137860698313561e-001, 1.3855327472974924e-001, 6.9568415836913987e-004)
          },
          { # case 5
            n = c(0.0000000000000000e+000, 7.4109534999454085e-001, 1.7320508075688772e+000, 2.8612795760570582e+000, 4.1849560176727323e+000)
            w = c(2.5396825396825407e-001, 2.7007432957793776e-001, 9.4850948509485125e-002, 7.9963254708935293e-003, 9.4269457556517470e-005)
          },
          { # case 6
            n = c(0.0000000000000000e+000, 7.4109534999454085e-001, 1.7320508075688772e+000, 2.8612795760570582e+000, 4.1849560176727323e+000)
            w = c(2.5396825396825429e-001, 2.7007432957793776e-001, 9.4850948509485070e-002, 7.9963254708935293e-003, 9.4269457556517551e-005)
          },
          { # case 7
            n = c(0.0000000000000000e+000, 7.4109534999454085e-001, 1.7320508075688772e+000, 2.8612795760570582e+000, 4.1849560176727323e+000)
            w = c(2.5396825396825418e-001, 2.7007432957793781e-001, 9.4850948509485014e-002, 7.9963254708935311e-003, 9.4269457556517592e-005)
          },
          { # case 8
            n = c(0.0000000000000000e+000, 7.4109534999454085e-001, 1.7320508075688772e+000, 2.8612795760570582e+000, 4.1849560176727323e+000)
            w = c(2.5396825396825418e-001, 2.7007432957793781e-001, 9.4850948509485042e-002, 7.9963254708935276e-003, 9.4269457556517375e-005)
          },
          { # case 9
            n = c(0.0000000000000000e+000, 7.4109534999454085e-001, 1.2304236340273060e+000, 1.7320508075688772e+000, 2.5960831150492023e+000, 2.8612795760570582e+000, 4.1849560176727323e+000, 5.1870160399136562e+000, 6.3633944943363696e+000)
            w = c(2.6692223033505302e-001, 2.5456123204171222e-001, 1.4192654826449365e-002, 8.8681002152028010e-002, 1.9656770938777492e-003, 7.0334802378279075e-003, 1.0563783615416941e-004, -8.2049207541509217e-007, 2.1136499505424257e-008)
          },
          { # case 10
            n = c(0.0000000000000000e+000, 7.4109534999454085e-001, 1.2304236340273060e+000, 1.7320508075688772e+000, 2.5960831150492023e+000, 2.8612795760570582e+000, 3.2053337944991944e+000, 4.1849560176727323e+000, 5.1870160399136562e+000, 6.3633944943363696e+000)
            w = c(3.0346719985420623e-001, 2.0832499164960877e-001, 6.1151730125247716e-002, 6.4096054686807610e-002, 1.8085234254798462e-002, -6.3372247933737571e-003, 2.8848804365067559e-003, 6.0123369459847997e-005, 6.0948087314689840e-007, 8.6296846022298632e-010)
          },
          { # case 11
            n = c(0.0000000000000000e+000, 7.4109534999454085e-001, 1.2304236340273060e+000, 1.7320508075688772e+000, 2.5960831150492023e+000, 2.8612795760570582e+000, 3.2053337944991944e+000, 4.1849560176727323e+000, 5.1870160399136562e+000, 6.3633944943363696e+000)
            w = c(3.0346719985420623e-001, 2.0832499164960872e-001, 6.1151730125247709e-002, 6.4096054686807541e-002, 1.8085234254798459e-002, -6.3372247933737545e-003, 2.8848804365067555e-003, 6.0123369459847922e-005, 6.0948087314689830e-007, 8.6296846022298839e-010)
          },
          { # case 12
            n = c(0.0000000000000000e+000, 7.4109534999454085e-001, 1.2304236340273060e+000, 1.7320508075688772e+000, 2.5960831150492023e+000, 2.8612795760570582e+000, 3.2053337944991944e+000, 4.1849560176727323e+000, 5.1870160399136562e+000, 6.3633944943363696e+000)
            w = c(3.0346719985420623e-001, 2.0832499164960872e-001, 6.1151730125247716e-002, 6.4096054686807624e-002, 1.8085234254798466e-002, -6.3372247933737545e-003, 2.8848804365067559e-003, 6.0123369459847841e-005, 6.0948087314689830e-007, 8.6296846022298963e-010)
          },
          { # case 13
            n = c(0.0000000000000000e+000, 7.4109534999454085e-001, 1.2304236340273060e+000, 1.7320508075688772e+000, 2.5960831150492023e+000, 2.8612795760570582e+000, 3.2053337944991944e+000, 4.1849560176727323e+000, 5.1870160399136562e+000, 6.3633944943363696e+000)
            w = c(3.0346719985420600e-001, 2.0832499164960883e-001, 6.1151730125247730e-002, 6.4096054686807638e-002, 1.8085234254798459e-002, -6.3372247933737580e-003, 2.8848804365067555e-003, 6.0123369459847868e-005, 6.0948087314689830e-007, 8.6296846022298756e-010)
          },
          { # case 14
            n = c(0.0000000000000000e+000, 7.4109534999454085e-001, 1.2304236340273060e+000, 1.7320508075688772e+000, 2.5960831150492023e+000, 2.8612795760570582e+000, 3.2053337944991944e+000, 4.1849560176727323e+000, 5.1870160399136562e+000, 6.3633944943363696e+000)
            w = c(3.0346719985420617e-001, 2.0832499164960874e-001, 6.1151730125247702e-002, 6.4096054686807596e-002, 1.8085234254798459e-002, -6.3372247933737563e-003, 2.8848804365067555e-003, 6.0123369459847936e-005, 6.0948087314689851e-007, 8.6296846022298322e-010)
          },
          { # case 15
            n = c(0.0000000000000000e+000, 7.4109534999454085e-001, 1.2304236340273060e+000, 1.7320508075688772e+000, 2.5960831150492023e+000, 2.8612795760570582e+000, 3.2053337944991944e+000, 4.1849560176727323e+000, 5.1870160399136562e+000, 6.3633944943363696e+000)
            w = c(3.0346719985420612e-001, 2.0832499164960874e-001, 6.1151730125247723e-002, 6.4096054686807652e-002, 1.8085234254798459e-002, -6.3372247933737597e-003, 2.8848804365067563e-003, 6.0123369459848091e-005, 6.0948087314689851e-007, 8.6296846022298983e-010)
          },
          { # case 16
            n = c(0.0000000000000000e+000, 2.4899229757996061e-001, 7.4109534999454085e-001, 1.2304236340273060e+000, 1.7320508075688772e+000, 2.2336260616769419e+000, 2.5960831150492023e+000, 2.8612795760570582e+000, 3.2053337944991944e+000, 3.6353185190372783e+000, 4.1849560176727323e+000, 5.1870160399136562e+000, 6.3633944943363696e+000, 7.1221067008046166e+000, 7.9807717985905606e+000, 9.0169397898903032e+000)
            w = c(2.5890005324151566e-001, 2.8128101540033167e-002, 1.9968863511734550e-001, 6.5417392836092561e-002, 6.1718532565867179e-002, 1.7608475581318002e-003, 1.6592492698936010e-002, -5.5610063068358157e-003, 2.7298430467334002e-003, 1.5044205390914219e-005, 5.9474961163931621e-005, 6.1435843232617913e-007, 7.9298267864869338e-010, 5.1158053105504208e-012, -1.4840835740298868e-013, 1.2618464280815118e-015)
          },
          { # case 17
            n = c(0.0000000000000000e+000, 2.4899229757996061e-001, 7.4109534999454085e-001, 1.2304236340273060e+000, 1.7320508075688772e+000, 2.2336260616769419e+000, 2.5960831150492023e+000, 2.8612795760570582e+000, 3.2053337944991944e+000, 3.6353185190372783e+000, 4.1849560176727323e+000, 5.1870160399136562e+000, 5.6981777684881099e+000, 6.3633944943363696e+000, 7.1221067008046166e+000, 7.9807717985905606e+000, 9.0169397898903032e+000)
            w = c(1.3911022236338039e-001, 1.0387687125574284e-001, 1.7607598741571459e-001, 7.7443602746299481e-002, 5.4677556143463042e-002, 7.3530110204955076e-003, 1.1529247065398790e-002, -2.7712189007789243e-003, 2.1202259559596325e-003, 8.3236045295766745e-005, 5.5691158981081479e-005, 6.9086261179113738e-007, -1.3486017348542930e-008, 1.5542195992782658e-009, -1.9341305000880955e-011, 2.6640625166231651e-013, -9.9313913286822465e-016)
          },
          { # case 18
            n = c(0.0000000000000000e+000, 2.4899229757996061e-001, 7.4109534999454085e-001, 1.2304236340273060e+000, 1.7320508075688772e+000, 2.2336260616769419e+000, 2.5960831150492023e+000, 2.8612795760570582e+000, 3.2053337944991944e+000, 3.6353185190372783e+000, 4.1849560176727323e+000, 4.7364330859522967e+000, 5.1870160399136562e+000, 5.6981777684881099e+000, 6.3633944943363696e+000, 7.1221067008046166e+000, 7.9807717985905606e+000, 9.0169397898903032e+000)
            w = c(5.1489450806921377e-004, 1.9176011588804434e-001, 1.4807083115521585e-001, 9.2364726716986353e-002, 4.5273685465150391e-002, 1.5673473751851151e-002, 3.1554462691875513e-003, 2.3113452403522071e-003, 8.1895392750226735e-004, 2.7524214116785131e-004, 3.5729348198975332e-005, 2.7342206801187888e-006, 2.4676421345798140e-007, 2.1394194479561062e-008, 4.6011760348655917e-010, 3.0972223576062995e-012, 5.4500412650638128e-015, 1.0541326582334014e-018)
          },
          { # case 19
            n = c(0.0000000000000000e+000, 2.4899229757996061e-001, 7.4109534999454085e-001, 1.2304236340273060e+000, 1.7320508075688772e+000, 2.2336260616769419e+000, 2.5960831150492023e+000, 2.8612795760570582e+000, 3.2053337944991944e+000, 3.6353185190372783e+000, 4.1849560176727323e+000, 4.7364330859522967e+000, 5.1870160399136562e+000, 5.6981777684881099e+000, 6.3633944943363696e+000, 7.1221067008046166e+000, 7.9807717985905606e+000, 9.0169397898903032e+000)
            w = c(5.1489450806921377e-004, 1.9176011588804437e-001, 1.4807083115521585e-001, 9.2364726716986353e-002, 4.5273685465150523e-002, 1.5673473751851151e-002, 3.1554462691875604e-003, 2.3113452403522050e-003, 8.1895392750226670e-004, 2.7524214116785131e-004, 3.5729348198975447e-005, 2.7342206801187884e-006, 2.4676421345798140e-007, 2.1394194479561056e-008, 4.6011760348656077e-010, 3.0972223576063011e-012, 5.4500412650637663e-015, 1.0541326582337958e-018)
          },
          { # case 20
            n = c(0.0000000000000000e+000, 2.4899229757996061e-001, 7.4109534999454085e-001, 1.2304236340273060e+000, 1.7320508075688772e+000, 2.2336260616769419e+000, 2.5960831150492023e+000, 2.8612795760570582e+000, 3.2053337944991944e+000, 3.6353185190372783e+000, 4.1849560176727323e+000, 4.7364330859522967e+000, 5.1870160399136562e+000, 5.6981777684881099e+000, 6.3633944943363696e+000, 7.1221067008046166e+000, 7.9807717985905606e+000, 9.0169397898903032e+000)
            w = c(5.1489450806925551e-004, 1.9176011588804440e-001, 1.4807083115521585e-001, 9.2364726716986298e-002, 4.5273685465150537e-002, 1.5673473751851155e-002, 3.1554462691875573e-003, 2.3113452403522080e-003, 8.1895392750226724e-004, 2.7524214116785137e-004, 3.5729348198975352e-005, 2.7342206801187888e-006, 2.4676421345798124e-007, 2.1394194479561056e-008, 4.6011760348656144e-010, 3.0972223576062963e-012, 5.4500412650638365e-015, 1.0541326582335402e-018)
          },
          { # case 21
            n = c(0.0000000000000000e+000, 2.4899229757996061e-001, 7.4109534999454085e-001, 1.2304236340273060e+000, 1.7320508075688772e+000, 2.2336260616769419e+000, 2.5960831150492023e+000, 2.8612795760570582e+000, 3.2053337944991944e+000, 3.6353185190372783e+000, 4.1849560176727323e+000, 4.7364330859522967e+000, 5.1870160399136562e+000, 5.6981777684881099e+000, 6.3633944943363696e+000, 7.1221067008046166e+000, 7.9807717985905606e+000, 9.0169397898903032e+000)
            w = c(5.1489450806913744e-004, 1.9176011588804429e-001, 1.4807083115521594e-001, 9.2364726716986312e-002, 4.5273685465150391e-002, 1.5673473751851151e-002, 3.1554462691875565e-003, 2.3113452403522089e-003, 8.1895392750226670e-004, 2.7524214116785142e-004, 3.5729348198975285e-005, 2.7342206801187888e-006, 2.4676421345798119e-007, 2.1394194479561059e-008, 4.6011760348656594e-010, 3.0972223576062950e-012, 5.4500412650638696e-015, 1.0541326582332041e-018)
          },
          { # case 22
            n = c(0.0000000000000000e+000, 2.4899229757996061e-001, 7.4109534999454085e-001, 1.2304236340273060e+000, 1.7320508075688772e+000, 2.2336260616769419e+000, 2.5960831150492023e+000, 2.8612795760570582e+000, 3.2053337944991944e+000, 3.6353185190372783e+000, 4.1849560176727323e+000, 4.7364330859522967e+000, 5.1870160399136562e+000, 5.6981777684881099e+000, 6.3633944943363696e+000, 7.1221067008046166e+000, 7.9807717985905606e+000, 9.0169397898903032e+000)
            w = c(5.1489450806903368e-004, 1.9176011588804448e-001, 1.4807083115521574e-001, 9.2364726716986423e-002, 4.5273685465150516e-002, 1.5673473751851161e-002, 3.1554462691875543e-003, 2.3113452403522063e-003, 8.1895392750226713e-004, 2.7524214116785164e-004, 3.5729348198975319e-005, 2.7342206801187905e-006, 2.4676421345798151e-007, 2.1394194479561082e-008, 4.6011760348656005e-010, 3.0972223576063043e-012, 5.4500412650637592e-015, 1.0541326582339926e-018)
          },
          { # case 23
            n = c(0.0000000000000000e+000, 2.4899229757996061e-001, 7.4109534999454085e-001, 1.2304236340273060e+000, 1.7320508075688772e+000, 2.2336260616769419e+000, 2.5960831150492023e+000, 2.8612795760570582e+000, 3.2053337944991944e+000, 3.6353185190372783e+000, 4.1849560176727323e+000, 4.7364330859522967e+000, 5.1870160399136562e+000, 5.6981777684881099e+000, 6.3633944943363696e+000, 7.1221067008046166e+000, 7.9807717985905606e+000, 9.0169397898903032e+000)
            w = c(5.1489450806913755e-004, 1.9176011588804442e-001, 1.4807083115521577e-001, 9.2364726716986381e-002, 4.5273685465150468e-002, 1.5673473751851155e-002, 3.1554462691875560e-003, 2.3113452403522045e-003, 8.1895392750226572e-004, 2.7524214116785158e-004, 3.5729348198975298e-005, 2.7342206801187892e-006, 2.4676421345798129e-007, 2.1394194479561072e-008, 4.6011760348656103e-010, 3.0972223576062963e-012, 5.4500412650638207e-015, 1.0541326582338368e-018)
          },
          { # case 24
            n = c(0.0000000000000000e+000, 2.4899229757996061e-001, 7.4109534999454085e-001, 1.2304236340273060e+000, 1.7320508075688772e+000, 2.2336260616769419e+000, 2.5960831150492023e+000, 2.8612795760570582e+000, 3.2053337944991944e+000, 3.6353185190372783e+000, 4.1849560176727323e+000, 4.7364330859522967e+000, 5.1870160399136562e+000, 5.6981777684881099e+000, 6.3633944943363696e+000, 7.1221067008046166e+000, 7.9807717985905606e+000, 9.0169397898903032e+000)
            w = c(5.1489450806914438e-004, 1.9176011588804442e-001, 1.4807083115521577e-001, 9.2364726716986340e-002, 4.5273685465150509e-002, 1.5673473751851155e-002, 3.1554462691875586e-003, 2.3113452403522058e-003, 8.1895392750226551e-004, 2.7524214116785142e-004, 3.5729348198975386e-005, 2.7342206801187884e-006, 2.4676421345798082e-007, 2.1394194479561059e-008, 4.6011760348656382e-010, 3.0972223576062942e-012, 5.4500412650638381e-015, 1.0541326582336941e-018)
          },
          { # case 25
            n = c(0.0000000000000000e+000, 2.4899229757996061e-001, 7.4109534999454085e-001, 1.2304236340273060e+000, 1.7320508075688772e+000, 2.2336260616769419e+000, 2.5960831150492023e+000, 2.8612795760570582e+000, 3.2053337944991944e+000, 3.6353185190372783e+000, 4.1849560176727323e+000, 4.7364330859522967e+000, 5.1870160399136562e+000, 5.6981777684881099e+000, 6.3633944943363696e+000, 7.1221067008046166e+000, 7.9807717985905606e+000, 9.0169397898903032e+000)
            w = c(5.1489450806919989e-004, 1.9176011588804437e-001, 1.4807083115521580e-001, 9.2364726716986395e-002, 4.5273685465150426e-002, 1.5673473751851158e-002, 3.1554462691875539e-003, 2.3113452403522054e-003, 8.1895392750226681e-004, 2.7524214116785142e-004, 3.5729348198975292e-005, 2.7342206801187884e-006, 2.4676421345798108e-007, 2.1394194479561056e-008, 4.6011760348655901e-010, 3.0972223576062975e-012, 5.4500412650638412e-015, 1.0541326582337527e-018)
        }
    )   # end switch
  
    return( list( "nodes"     = n,
                  "weights"   = w ) )
}