R/GQU.R

In SparseGrid: Sparse grid integration in R

# Copyright (C) 2011 Jelmer Ypma. All Rights Reserved.
# This code is published under the GPL.
#
# File:   GQU.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: 

GQU <- function( level ) {
  switch( level,
          { # case 1
            n = c(5.0000000000000000e-001)
            w = c(1.0000000000000000e+000)
          },
          { # case 2
            n = c(7.8867513459481287e-001)
            w = c(5.0000000000000000e-001)
          },
          { # case 3
            n = c(5.0000000000000000e-001, 8.8729833462074170e-001)
            w = c(4.4444444444444570e-001, 2.7777777777777712e-001)
          },
          { # case 4
            n = c(6.6999052179242813e-001, 9.3056815579702623e-001)
            w = c(3.2607257743127516e-001, 1.7392742256872484e-001)
          },
          { # case 5
            n = c(5.0000000000000000e-001, 7.6923465505284150e-001, 9.5308992296933193e-001)
            w = c(2.8444444444444655e-001, 2.3931433524968501e-001, 1.1846344252809174e-001)
          },
          { # case 6
            n = c(6.1930959304159849e-001, 8.3060469323313235e-001, 9.6623475710157603e-001)
            w = c(2.3395696728634746e-001, 1.8038078652407072e-001, 8.5662246189581834e-002)
          },
          { # case 7
            n = c(5.0000000000000000e-001, 7.0292257568869854e-001, 8.7076559279969723e-001, 9.7455395617137919e-001)
            w = c(2.0897959183673620e-001, 1.9091502525256090e-001, 1.3985269574463935e-001, 6.4742483084431701e-002)
          },
          { # case 8
            n = c(5.9171732124782495e-001, 7.6276620495816450e-001, 8.9833323870681348e-001, 9.8014492824876809e-001)
            w = c(1.8134189168918213e-001, 1.5685332293894469e-001, 1.1119051722668793e-001, 5.0614268145185180e-002)
          },
          { # case 9
            n = c(5.0000000000000000e-001, 6.6212671170190451e-001, 8.0668571635029518e-001, 9.1801555366331788e-001, 9.8408011975381304e-001)
            w = c(1.6511967750063075e-001, 1.5617353852000226e-001, 1.3030534820146844e-001, 9.0324080347429253e-002, 4.0637194180784583e-002)
          },
          { # case 10
            n = c(5.7443716949081558e-001, 7.1669769706462361e-001, 8.3970478414951222e-001, 9.3253168334449232e-001, 9.8695326425858587e-001)
            w = c(1.4776211235737713e-001, 1.3463335965499873e-001, 1.0954318125799158e-001, 7.4725674575290599e-002, 3.3335672154342001e-002)
          },
          { # case 11
            n = c(5.0000000000000000e-001, 6.3477157797617245e-001, 7.5954806460340585e-001, 8.6507600278702468e-001, 9.4353129988404771e-001, 9.8911432907302843e-001)
            w = c(1.3646254338895086e-001, 1.3140227225512388e-001, 1.1659688229599563e-001, 9.3145105463867520e-002, 6.2790184732452625e-002, 2.7834283558084916e-002)
          },
          { # case 12
            n = c(5.6261670425573451e-001, 6.8391574949909006e-001, 7.9365897714330869e-001, 8.8495133709715235e-001, 9.5205862818523745e-001, 9.9078031712335957e-001)
            w = c(1.2457352290670189e-001, 1.1674626826917781e-001, 1.0158371336153328e-001, 8.0039164271673444e-002, 5.3469662997659276e-002, 2.3587668193254314e-002)
          },
          { # case 13
            n = c(5.0000000000000000e-001, 6.1522915797756739e-001, 7.2424637551822335e-001, 8.2117466972017006e-001, 9.0078904536665494e-001, 9.5879919961148907e-001, 9.9209152735929407e-001)
            w = c(1.1627577661543741e-001, 1.1314159013144903e-001, 1.0390802376844462e-001, 8.9072990380973202e-002, 6.9436755109893875e-002, 4.6060749918864378e-002, 2.0242002382656228e-002)
          },
          { # case 14
            n = c(5.5402747435367183e-001, 6.5955618446394482e-001, 7.5762431817907705e-001, 8.4364645240584268e-001, 9.1360065753488251e-001, 9.6421744183178681e-001, 9.9314190434840621e-001)
            w = c(1.0763192673157916e-001, 1.0259923186064811e-001, 9.2769198738969161e-002, 7.8601583579096995e-002, 6.0759285343951711e-002, 4.0079043579880291e-002, 1.7559730165874574e-002)
          },
          { # case 15
            n = c(5.0000000000000000e-001, 6.0059704699871730e-001, 6.9707567353878175e-001, 7.8548608630426942e-001, 8.6220886568008503e-001, 9.2410329170521366e-001, 9.6863669620035298e-001, 9.9399625901024269e-001)
            w = c(1.0128912096278091e-001, 9.9215742663556039e-002, 9.3080500007781286e-002, 8.3134602908497196e-002, 6.9785338963077315e-002, 5.3579610233586157e-002, 3.5183023744054159e-002, 1.5376620998057434e-002)
          },
          { # case 16
            n = c(5.4750625491881877e-001, 6.4080177538962946e-001, 7.2900838882861363e-001, 8.0893812220132189e-001, 8.7770220417750155e-001, 9.3281560119391593e-001, 9.7228751153661630e-001, 9.9470046749582497e-001)
            w = c(9.4725305227534431e-002, 9.1301707522462000e-002, 8.4578259697501462e-002, 7.4797994408288562e-002, 6.2314485627767105e-002, 4.7579255841246545e-002, 3.1126761969323954e-002, 1.3576229705875955e-002)
          },
          { # case 17
            n = c(5.0000000000000000e-001, 5.8924209074792389e-001, 6.7561588172693821e-001, 7.5634526854323847e-001, 8.2883557960834531e-001, 8.9075700194840068e-001, 9.4011957686349290e-001, 9.7533776088438384e-001, 9.9528773765720868e-001)
            w = c(8.9723235178103419e-002, 8.8281352683496447e-002, 8.4002051078225143e-002, 7.7022880538405308e-002, 6.7568184234262890e-002, 5.5941923596702053e-002, 4.2518074158589644e-002, 2.7729764686993612e-002, 1.2074151434273140e-002)
          },
          { # case 18
            n = c(5.4238750652086765e-001, 6.2594311284575277e-001, 7.0587558073142131e-001, 7.7988541553697377e-001, 8.4584352153017661e-001, 9.0185247948626157e-001, 9.4630123324877791e-001, 9.7791197478569880e-001, 9.9578258421046550e-001)
            w = c(8.4571191481571939e-002, 8.2138241872916504e-002, 7.7342337563132801e-002, 7.0321457335325452e-002, 6.1277603355739306e-002, 5.0471022053143716e-002, 3.8212865127444665e-002, 2.4857274447484968e-002, 1.0808006763240719e-002)
          },
          { # case 19
            n = c(5.0000000000000000e-001, 5.8017932282011264e-001, 6.5828204998181494e-001, 7.3228537068798050e-001, 8.0027265233084055e-001, 8.6048308866761469e-001, 9.1135732826857141e-001, 9.5157795180740901e-001, 9.8010407606741501e-001, 9.9620342192179212e-001)
            w = c(8.0527224924391946e-002, 7.9484421696977337e-002, 7.6383021032929960e-002, 7.1303351086803413e-002, 6.4376981269668232e-002, 5.5783322773667113e-002, 4.5745010811225124e-002, 3.4522271368820669e-002, 2.2407113382849821e-002, 9.7308941148624341e-003)
          },
          { # case 20
            n = c(5.3826326056674867e-001, 6.1389292557082253e-001, 6.8685304435770977e-001, 7.5543350097541362e-001, 8.1802684036325757e-001, 8.7316595323007540e-001, 9.1955848591110945e-001, 9.5611721412566297e-001, 9.8198596363895696e-001, 9.9656429959254744e-001)
            w = c(7.6376693565363113e-002, 7.4586493236301996e-002, 7.1048054659191187e-002, 6.5844319224588346e-002, 5.9097265980759248e-002, 5.0965059908620318e-002, 4.1638370788352433e-002, 3.1336024167054569e-002, 2.0300714900193556e-002, 8.8070035695753026e-003)
          },
          { # case 21
            n = c(5.0000000000000000e-001, 5.7278092708044759e-001, 6.4401065840120053e-001, 7.1217106010371944e-001, 7.7580941794360991e-001, 8.3356940209870611e-001, 8.8421998173783889e-001, 9.2668168229165859e-001, 9.6004966707520034e-001, 9.8361341928315316e-001, 9.9687608531019478e-001)
            w = c(7.3040566824845346e-002, 7.2262201994985134e-002, 6.9943697395536658e-002, 6.6134469316668845e-002, 6.0915708026864350e-002, 5.4398649583574356e-002, 4.6722211728016994e-002, 3.8050056814189707e-002, 2.8567212713428641e-002, 1.8476894885426285e-002, 8.0086141288864491e-003)
          },
          { # case 22
            n = c(5.3486963665986109e-001, 6.0393021334411068e-001, 6.7096791044604209e-001, 7.3467791899337853e-001, 7.9382020175345580e-001, 8.4724363159334137e-001, 8.9390840298960406e-001, 9.3290628886015003e-001, 9.6347838609358694e-001, 9.8503024891771429e-001, 9.9714729274119962e-001)
            w = c(6.9625936427816129e-002, 6.8270749173007697e-002, 6.5586752393531317e-002, 6.1626188405256251e-002, 5.6466148040269712e-002, 5.0207072221440600e-002, 4.2970803108533975e-002, 3.4898234212260300e-002, 2.6146667576341692e-002, 1.6887450792407110e-002, 7.3139976491353280e-003)
          },
          { # case 23
            n = c(5.0000000000000000e-001, 5.6662841214923310e-001, 6.3206784048517251e-001, 6.9515051901514546e-001, 7.5475073892300371e-001, 8.0980493788182306e-001, 8.5933068156597514e-001, 9.0244420080942001e-001, 9.3837617913522076e-001, 9.6648554341300807e-001, 9.8627123560905761e-001, 9.9738466749877608e-001)
            w = c(6.6827286093053176e-002, 6.6231019702348404e-002, 6.4452861094041150e-002, 6.1524542153364815e-002, 5.7498320111205814e-002, 5.2446045732270824e-002, 4.6457883030017563e-002, 3.9640705888359551e-002, 3.2116210704262994e-002, 2.4018835865542369e-002, 1.5494002928489686e-002, 6.7059297435702412e-003)
          },
          { # case 24
            n = c(5.3202844643130276e-001, 5.9555943373680820e-001, 6.5752133984808170e-001, 7.1689675381302254e-001, 7.7271073569441984e-001, 8.2404682596848777e-001, 8.7006209578927718e-001, 9.1000099298695147e-001, 9.4320776350220048e-001, 9.6913727600136634e-001, 9.8736427798565474e-001, 9.9759360999851066e-001)
            w = c(6.3969097673376246e-002, 6.2918728173414318e-002, 6.0835236463901793e-002, 5.7752834026862883e-002, 5.3722135057982914e-002, 4.8809326052057039e-002, 4.3095080765976693e-002, 3.6673240705540205e-002, 2.9649292457718385e-002, 2.2138719408709880e-002, 1.4265694314466934e-002, 6.1706148999928351e-003)
          },
          { # case 25
            n = c(5.0000000000000000e-001, 5.6143234630535521e-001, 6.2193344186049426e-001, 6.8058615290469393e-001, 7.3650136572285752e-001, 7.8883146512061142e-001, 8.3678318423673415e-001, 8.7962963151867890e-001, 9.1672131438041693e-001, 9.4749599893913761e-001, 9.7148728561448716e-001, 9.8833196072975871e-001, 9.9777848489524912e-001)
            w = c(6.1588026863357799e-002, 6.1121221495155122e-002, 5.9727881767892461e-002, 5.7429129572855862e-002, 5.4259812237131867e-002, 5.0267974533525363e-002, 4.5514130991481903e-002, 4.0070350167500532e-002, 3.4019166906178545e-002, 2.7452347987917691e-002, 2.0469578350653148e-002, 1.3177493307516108e-002, 5.6968992505125535e-003)
        }
    )   # end switch
  
    return( list( "nodes"     = n,
                  "weights"   = w ) )
}