IntGKPData10.h

Go to the documentation of this file.

// -*- lsst-c++ -*-

/* 
 * LSST Data Management System
 * Copyright 2008, 2009, 2010 LSST Corporation.
 * 
 * This product includes software developed by the
 * LSST Project (http://www.lsst.org/).
 *
 * This program is free software: you can redistribute it and/or modify
 * it under the terms of the GNU General Public License as published by
 * the Free Software Foundation, either version 3 of the License, or
 * (at your option) any later version.
 * 
 * This program is distributed in the hope that it will be useful,
 * but WITHOUT ANY WARRANTY; without even the implied warranty of
 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 * GNU General Public License for more details.
 * 
 * You should have received a copy of the LSST License Statement and 
 * the GNU General Public License along with this program.  If not, 
 * see <http://www.lsstcorp.org/LegalNotices/>.
 */
 
#if !defined(LSST_AFW_MATH_INTGKPDATA10_H)
#define LSST_AFW_MATH_INTGKPDATA10_H 1

#include <vector>

namespace lsst { namespace afw { namespace math {

namespace details {            
            
    static const int NGKPLEVELS = 5;
    
    inline int gkp_n(int level) { 
        assert(level >= 0 && level < NGKPLEVELS);
        static const int ngkp[NGKPLEVELS] = {5, 5, 11, 22, 44};
        return ngkp[level]; 
    }
    
    template <class T>
    inline const std::vector<T>& gkp_x(int level) {
        
        // x10, abscissae common to the 10-, 21-, 43- and 87-point rule 
        static const T ax10[5] = {
            0.973906528517171720077964012084452,
            0.865063366688984510732096688423493,
            0.679409568299024406234327365114874,
            0.433395394129247190799265943165784,
            0.148874338981631210884826001129720
        };
        static const std::vector<T> vx10(ax10, ax10 + 5);
        
        // x21, abscissae common to the 21-, 43- and 87-point rule 
        static const T ax21[5] = {
            0.995657163025808080735527280689003,
            0.930157491355708226001207180059508,
            0.780817726586416897063717578345042,
            0.562757134668604683339000099272694,
            0.294392862701460198131126603103866
        };
        static const std::vector<T> vx21(ax21, ax21 + 5);
        
        // x43, abscissae common to the 43- and 87-point rule 
        static const T ax43[11] = {
            0.999333360901932081394099323919911,
            0.987433402908088869795961478381209,
            0.954807934814266299257919200290473,
            0.900148695748328293625099494069092,
            0.825198314983114150847066732588520,
            0.732148388989304982612354848755461,
            0.622847970537725238641159120344323,
            0.499479574071056499952214885499755,
            0.364901661346580768043989548502644,
            0.222254919776601296498260928066212,
            0.074650617461383322043914435796506
        };
        static const std::vector<T> vx43(ax43, ax43 + 11);
        
        // x87, abscissae of the 87-point rule 
        static const T ax87[22] = {
            0.999902977262729234490529830591582,
            0.997989895986678745427496322365960,
            0.992175497860687222808523352251425,
            0.981358163572712773571916941623894,
            0.965057623858384619128284110607926,
            0.943167613133670596816416634507426,
            0.915806414685507209591826430720050,
            0.883221657771316501372117548744163,
            0.845710748462415666605902011504855,
            0.803557658035230982788739474980964,
            0.757005730685495558328942793432020,
            0.706273209787321819824094274740840,
            0.651589466501177922534422205016736,
            0.593223374057961088875273770349144,
            0.531493605970831932285268948562671,
            0.466763623042022844871966781659270,
            0.399424847859218804732101665817923,
            0.329874877106188288265053371824597,
            0.258503559202161551802280975429025,
            0.185695396568346652015917141167606,
            0.111842213179907468172398359241362,
            0.037352123394619870814998165437704
        };
        static const std::vector<T> vx87(ax87, ax87 + 22);
        
        // x175, new abscissae of the 175-point rule
        static const T ax175[44] = {
            0.9999863601049729677997719,
            0.9996988005421428623760900,
            0.9987732473138838303043008,
            0.9969583851613681945576954,
            0.9940679446543307664316419,
            0.9899673391741082769960501,
            0.9845657252243253759726856,
            0.9778061574856414566055911,
            0.9696573134362640567828241,
            0.9601075259508299668299148,
            0.9491605191933640559839528,
            0.9368321320434676982049391,
            0.9231475266471484946315312,
            0.9081385954543932335481458,
            0.8918414554201179766275301,
            0.8742940658668577971868106,
            0.8555341249920432726468181,
            0.8355974653331171075829366,
            0.8145171513255796294567278,
            0.7923233739697216224661771,
            0.7690440708082055924983192,
            0.7447060413364141221086362,
            0.7193362474393392286563226,
            0.6929630148748741413274435,
            0.6656169582351898081906710,
            0.6373315753624730450361940,
            0.6081435407529742253347887,
            0.5780927509986774074337714,
            0.5472221576559162873479056,
            0.5155774001694817879753989,
            0.4832062516695473663839323,
            0.4501579202236101928554315,
            0.4164822936334372150371142,
            0.3822292525735955063074986,
            0.3474481818229070516859048,
            0.3121877718977455143765043,
            0.2764961311348905899785770,
            0.2404211453027010909070665,
            0.2040109589145005126324680,
            0.1673144327616352753945014,
            0.1303814601095591675431696,
            0.09326308333660176874846400,
            0.05601141598806823374241435,
            0.01867941779948308845140053
        };
        static const std::vector<T> vx175(ax175, ax175 + 44);
        
        static const std::vector<T>* x[NGKPLEVELS] = {&vx10, &vx21, &vx43, &vx87, &vx175};
        
        assert(level >= 0 && level < NGKPLEVELS);
        return *x[level];
    }

    template <class T>
    inline const std::vector<T>& gkp_wa(int level) {
        
        // w21a, weights of the 21-point formula for abscissae x10
        static const T aw21a[5] = {
            0.032558162307964727478818972459390,
            0.075039674810919952767043140916190,
            0.109387158802297641899210590325805,
            0.134709217311473325928054001771707,
            0.147739104901338491374841515972068
        };
        static const std::vector<T> vw21a(aw21a, aw21a + 5);

        // w43a, weights of the 43-point formula for abscissae x10,x21
        static const T aw43a[10] = {
            0.016296734289666564924281974617663,
            0.037522876120869501461613795898115,
            0.054694902058255442147212685465005,
            0.067355414609478086075553166302174,
            0.073870199632393953432140695251367,
            0.005768556059769796184184327908655,
            0.027371890593248842081276069289151,
            0.046560826910428830743339154433824,
            0.061744995201442564496240336030883,
            0.071387267268693397768559114425516
        };
        static const std::vector<T> vw43a(aw43a, aw43a + 10);

        // w87a, weights of the 87-point formula for abscissae x10..x43
        static const T aw87a[21] = {
            0.008148377384149172900002878448190,
            0.018761438201562822243935059003794,
            0.027347451050052286161582829741283,
            0.033677707311637930046581056957588,
            0.036935099820427907614589586742499,
            0.002884872430211530501334156248695,
            0.013685946022712701888950035273128,
            0.023280413502888311123409291030404,
            0.030872497611713358675466394126442,
            0.035693633639418770719351355457044,
            0.000915283345202241360843392549948,
            0.005399280219300471367738743391053,
            0.010947679601118931134327826856808,
            0.016298731696787335262665703223280,
            0.021081568889203835112433060188190,
            0.025370969769253827243467999831710,
            0.029189697756475752501446154084920,
            0.032373202467202789685788194889595,
            0.034783098950365142750781997949596,
            0.036412220731351787562801163687577,
            0.037253875503047708539592001191226
        };
        static const std::vector<T> vw87a(aw87a, aw87a + 21);

        // w175a, weights of the 175-point formula for abscissae x10..x87
        static const T aw175a[43] = {
            0.004074188692082600103872341,
            0.009380719100781411819741177,
            0.01367372552502614309257226,
            0.01683885365581896502443513,
            0.01846754991021395380770806,
            0.001442436294030254510518689,
            0.006842973011356375224430623,
            0.01164020675144415562952859,
            0.01543624880585667934076834,
            0.01784681681970938536027839,
            0.0004576754584154192941064591,
            0.002699640110136963534043642,
            0.005473839800559775445647306,
            0.008149365848393670964180954,
            0.01054078444460191775302900,
            0.01268548488462691364854167,
            0.01459484887823787625642303,
            0.01618660123360139484467359,
            0.01739154947518257137619173,
            0.01820611036567589378188459,
            0.01862693775152385427017140,
            0.0001363171844264931156688042,
            0.0009035606060432074452289352,
            0.002048434635928091782250346,
            0.003379145025868061092978424,
            0.004774978836099393880602724,
            0.006164723826122346701274159,
            0.007505223673194467726814647,
            0.008774483993121594091281642,
            0.009969018893220443741650500,
            0.01109746798050614328494604,
            0.01216957356300040269315573,
            0.01318725270741960360319771,
            0.01414345539438560032188640,
            0.01502629056404634765715107,
            0.01582337568571996469999659,
            0.01652520670998925164398162,
            0.01712754985211303089259342,
            0.01763120633007834051620255,
            0.01803849481144435059221422,
            0.01834930224922804724856518,
            0.01856027463491628805666919,
            0.01866711437596752016025132
        };
        static const std::vector<T> vw175a(aw175a, aw175a + 43);

        static const std::vector<T>* wa[NGKPLEVELS] = {0, &vw21a, &vw43a, &vw87a, &vw175a};

        assert(level >= 1 && level < NGKPLEVELS);
        return *wa[level];
    }

  template <class T>
  inline const std::vector<T>& gkp_wb(int level) {
      
      // w10, weights of the 10-point formula 
      static const T aw10b[6] = {
          0.066671344308688137593568809893332,
          0.149451349150580593145776339657697,
          0.219086362515982043995534934228163,
          0.269266719309996355091226921569469,
          0.295524224714752870173892994651338,
          0.0
      };
      static const std::vector<T> vw10b(aw10b, aw10b + 6);

      // w21b, weights of the 21-point formula for abscissae x21
      static const T aw21b[6] = {
          0.011694638867371874278064396062192,
          0.054755896574351996031381300244580,
          0.093125454583697605535065465083366,
          0.123491976262065851077958109831074,
          0.142775938577060080797094273138717,
          0.149445554002916905664936468389821
      };
      static const std::vector<T> vw21b(aw21b, aw21b + 6);

      // w43b, weights of the 43-point formula for abscissae x43
      static const T aw43b[12] = {
          0.001844477640212414100389106552965,
          0.010798689585891651740465406741293,
          0.021895363867795428102523123075149,
          0.032597463975345689443882222526137,
          0.042163137935191811847627924327955,
          0.050741939600184577780189020092084,
          0.058379395542619248375475369330206,
          0.064746404951445885544689259517511,
          0.069566197912356484528633315038405,
          0.072824441471833208150939535192842,
          0.074507751014175118273571813842889,
          0.074722147517403005594425168280423
      };
      static const std::vector<T> vw43b(aw43b, aw43b + 12);

      // w87b, weights of the 87-point formula for abscissae x87
      static const T aw87b[23] = {
          0.000274145563762072350016527092881,
          0.001807124155057942948341311753254,
          0.004096869282759164864458070683480,
          0.006758290051847378699816577897424,
          0.009549957672201646536053581325377,
          0.012329447652244853694626639963780,
          0.015010447346388952376697286041943,
          0.017548967986243191099665352925900,
          0.019938037786440888202278192730714,
          0.022194935961012286796332102959499,
          0.024339147126000805470360647041454,
          0.026374505414839207241503786552615,
          0.028286910788771200659968002987960,
          0.030052581128092695322521110347341,
          0.031646751371439929404586051078883,
          0.033050413419978503290785944862689,
          0.034255099704226061787082821046821,
          0.035262412660156681033782717998428,
          0.036076989622888701185500318003895,
          0.036698604498456094498018047441094,
          0.037120549269832576114119958413599,
          0.037334228751935040321235449094698,
          0.037361073762679023410321241766599
      };
      static const std::vector<T> vw87b(aw87b, aw87b + 23);

      // w175b, weights of the 175-point formula for abscissae x175
      static const T aw175b[45] = {
          0.00003901440664395060055484226,
          0.0002787312407993348139961464,
          0.0006672934146291138823512275,
          0.001163051749910003055308177,
          0.001738533916888715565420637,
          0.002369555040550195269486165,
          0.003036735036032612976379865,
          0.003725394125884235586678819,
          0.004424387541776355951933433,
          0.005125062882078508655875582,
          0.005820601038952832388647054,
          0.006505667785357412495794539,
          0.007176258976795165213169074,
          0.007829642423806550517967042,
          0.008464316525043036555640657,
          0.009079917879101951192512711,
          0.009677029304308397008134699,
          0.01025687419430508685393322,
          0.01082092935368957685380896,
          0.01137052956179654620079332,
          0.01190655150082017425918844,
          0.01242924137407215963971061,
          0.01293819980598456566872951,
          0.01343248644726851711632966,
          0.01391078107864287587682982,
          0.01437154592198526807352501,
          0.01481316256915705351874381,
          0.01523404482122031244940129,
          0.01563274056894636856297717,
          0.01600802989372176552081826,
          0.01635901148521841710605397,
          0.01668515675646806540972517,
          0.01698630892029276765404134,
          0.01726261506199017604299177,
          0.01751439915887340284018269,
          0.01774200489411242260549908,
          0.01794564958245060930824294,
          0.01812532816637054898168673,
          0.01828078919412312732671357,
          0.01841158014800801587767163,
          0.01851713825962505903167768,
          0.01859689376712028821908313,
          0.01865035760791320287947920,
          0.01867717982648033250824110,
          0.01868053688133951170552407
      };
      static const std::vector<T> vw175b(aw175b, aw175b + 45);

      static const std::vector<T>* wb[NGKPLEVELS] = {&vw10b, &vw21b, &vw43b, &vw87b, &vw175b};

      assert(level >= 0 && level < NGKPLEVELS);
      return *wb[level];
  }
    
#ifdef EXTRA_PREC_H

    template<>
    inline const std::vector<Quad>& gkp_x<Quad>(int level) {
        
        // x10, abscissae common to the 10-, 21-, 43- and 87-point rule 
        static const Quad ax10[5] = {
            "0.973906528517171720077964012084452",
            "0.865063366688984510732096688423493",
            "0.679409568299024406234327365114874",
            "0.433395394129247190799265943165784",
            "0.148874338981631210884826001129720"
        };
        static const std::vector<Quad> vx10(ax10, ax10 + 5);

        // x21, abscissae common to the 21-, 43- and 87-point rule 
        static const Quad ax21[5] = {
            "0.995657163025808080735527280689003",
            "0.930157491355708226001207180059508",
            "0.780817726586416897063717578345042",
            "0.562757134668604683339000099272694",
            "0.294392862701460198131126603103866"
        };
        static const std::vector<Quad> vx21(ax21, ax21 + 5);

        // x43, abscissae common to the 43- and 87-point rule 
        static const Quad ax43[11] = {
            "0.999333360901932081394099323919911",
            "0.987433402908088869795961478381209",
            "0.954807934814266299257919200290473",
            "0.900148695748328293625099494069092",
            "0.825198314983114150847066732588520",
            "0.732148388989304982612354848755461",
            "0.622847970537725238641159120344323",
            "0.499479574071056499952214885499755",
            "0.364901661346580768043989548502644",
            "0.222254919776601296498260928066212",
            "0.074650617461383322043914435796506"
        };
        static const std::vector<Quad> vx43(ax43, ax43 + 11);

        // x87, abscissae of the 87-point rule 
        static const Quad ax87[22] = {
            "0.999902977262729234490529830591582",
            "0.997989895986678745427496322365960",
            "0.992175497860687222808523352251425",
            "0.981358163572712773571916941623894",
            "0.965057623858384619128284110607926",
            "0.943167613133670596816416634507426",
            "0.915806414685507209591826430720050",
            "0.883221657771316501372117548744163",
            "0.845710748462415666605902011504855",
            "0.803557658035230982788739474980964",
            "0.757005730685495558328942793432020",
            "0.706273209787321819824094274740840",
            "0.651589466501177922534422205016736",
            "0.593223374057961088875273770349144",
            "0.531493605970831932285268948562671",
            "0.466763623042022844871966781659270",
            "0.399424847859218804732101665817923",
            "0.329874877106188288265053371824597",
            "0.258503559202161551802280975429025",
            "0.185695396568346652015917141167606",
            "0.111842213179907468172398359241362",
            "0.037352123394619870814998165437704"
        };
        static const std::vector<Quad> vx87(ax87, ax87 + 22);

        // x175, new abscissae of the 175-point rule
        static const Quad ax175[44] = {
            "0.9999863601049729677997719",
            "0.9996988005421428623760900",
            "0.9987732473138838303043008",
            "0.9969583851613681945576954",
            "0.9940679446543307664316419",
            "0.9899673391741082769960501",
            "0.9845657252243253759726856",
            "0.9778061574856414566055911",
            "0.9696573134362640567828241",
            "0.9601075259508299668299148",
            "0.9491605191933640559839528",
            "0.9368321320434676982049391",
            "0.9231475266471484946315312",
            "0.9081385954543932335481458",
            "0.8918414554201179766275301",
            "0.8742940658668577971868106",
            "0.8555341249920432726468181",
            "0.8355974653331171075829366",
            "0.8145171513255796294567278",
            "0.7923233739697216224661771",
            "0.7690440708082055924983192",
            "0.7447060413364141221086362",
            "0.7193362474393392286563226",
            "0.6929630148748741413274435",
            "0.6656169582351898081906710",
            "0.6373315753624730450361940",
            "0.6081435407529742253347887",
            "0.5780927509986774074337714",
            "0.5472221576559162873479056",
            "0.5155774001694817879753989",
            "0.4832062516695473663839323",
            "0.4501579202236101928554315",
            "0.4164822936334372150371142",
            "0.3822292525735955063074986",
            "0.3474481818229070516859048",
            "0.3121877718977455143765043",
            "0.2764961311348905899785770",
            "0.2404211453027010909070665",
            "0.2040109589145005126324680",
            "0.1673144327616352753945014",
            "0.1303814601095591675431696",
            "0.09326308333660176874846400",
            "0.05601141598806823374241435",
            "0.01867941779948308845140053"
        };
        static const std::vector<Quad> vx175(ax175, ax175 + 44);

        static const std::vector<Quad>* x[NGKPLEVELS] = {&vx10, &vx21, &vx43, &vx87, &vx175};

        assert(level >= 0 && level < NGKPLEVELS);
        return *x[level];
    }

  template<>
  inline const std::vector<Quad>& gkp_wa<Quad>(int level) {
      
      // w21a, weights of the 21-point formula for abscissae x10
      static const Quad aw21a[5] = {
          "0.032558162307964727478818972459390",
          "0.075039674810919952767043140916190",
          "0.109387158802297641899210590325805",
          "0.134709217311473325928054001771707",
          "0.147739104901338491374841515972068"
      };
      static const std::vector<Quad> vw21a(aw21a, aw21a + 5);

      // w43a, weights of the 43-point formula for abscissae x10,x21
      static const Quad aw43a[10] = {
          "0.016296734289666564924281974617663",
          "0.037522876120869501461613795898115",
          "0.054694902058255442147212685465005",
          "0.067355414609478086075553166302174",
          "0.073870199632393953432140695251367",
          "0.005768556059769796184184327908655",
          "0.027371890593248842081276069289151",
          "0.046560826910428830743339154433824",
          "0.061744995201442564496240336030883",
          "0.071387267268693397768559114425516"
      };
      static const std::vector<Quad> vw43a(aw43a, aw43a + 10);

      // w87a, weights of the 87-point formula for abscissae x10..x43
      static const Quad aw87a[21] = {
          "0.008148377384149172900002878448190",
          "0.018761438201562822243935059003794",
          "0.027347451050052286161582829741283",
          "0.033677707311637930046581056957588",
          "0.036935099820427907614589586742499",
          "0.002884872430211530501334156248695",
          "0.013685946022712701888950035273128",
          "0.023280413502888311123409291030404",
          "0.030872497611713358675466394126442",
          "0.035693633639418770719351355457044",
          "0.000915283345202241360843392549948",
          "0.005399280219300471367738743391053",
          "0.010947679601118931134327826856808",
          "0.016298731696787335262665703223280",
          "0.021081568889203835112433060188190",
          "0.025370969769253827243467999831710",
          "0.029189697756475752501446154084920",
          "0.032373202467202789685788194889595",
          "0.034783098950365142750781997949596",
          "0.036412220731351787562801163687577",
          "0.037253875503047708539592001191226"
      };
      static const std::vector<Quad> vw87a(aw87a, aw87a + 21);

      // w175a, weights of the 175-point formula for abscissae x10..x87
      static const Quad aw175a[43] = {
          "0.004074188692082600103872341",
          "0.009380719100781411819741177",
          "0.01367372552502614309257226",
          "0.01683885365581896502443513",
          "0.01846754991021395380770806",
          "0.001442436294030254510518689",
          "0.006842973011356375224430623",
          "0.01164020675144415562952859",
          "0.01543624880585667934076834",
          "0.01784681681970938536027839",
          "0.0004576754584154192941064591",
          "0.002699640110136963534043642",
          "0.005473839800559775445647306",
          "0.008149365848393670964180954",
          "0.01054078444460191775302900",
          "0.01268548488462691364854167",
          "0.01459484887823787625642303",
          "0.01618660123360139484467359",
          "0.01739154947518257137619173",
          "0.01820611036567589378188459",
          "0.01862693775152385427017140",
          "0.0001363171844264931156688042",
          "0.0009035606060432074452289352",
          "0.002048434635928091782250346",
          "0.003379145025868061092978424",
          "0.004774978836099393880602724",
          "0.006164723826122346701274159",
          "0.007505223673194467726814647",
          "0.008774483993121594091281642",
          "0.009969018893220443741650500",
          "0.01109746798050614328494604",
          "0.01216957356300040269315573",
          "0.01318725270741960360319771",
          "0.01414345539438560032188640",
          "0.01502629056404634765715107",
          "0.01582337568571996469999659",
          "0.01652520670998925164398162",
          "0.01712754985211303089259342",
          "0.01763120633007834051620255",
          "0.01803849481144435059221422",
          "0.01834930224922804724856518",
          "0.01856027463491628805666919",
          "0.01866711437596752016025132"
      };
      static const std::vector<Quad> vw175a(aw175a, aw175a + 43);

      static const std::vector<Quad>* wa[NGKPLEVELS] = {0, &vw21a, &vw43a, &vw87a, &vw175a};

      assert(level >= 1 && level < NGKPLEVELS);
      return *wa[level];
  }

  template<>
  inline const std::vector<Quad>& gkp_wb<Quad>(int level) {
      
      // w10, weights of the 10-point formula 
      static const Quad aw10b[6] = {
          "0.066671344308688137593568809893332",
          "0.149451349150580593145776339657697",
          "0.219086362515982043995534934228163",
          "0.269266719309996355091226921569469",
          "0.295524224714752870173892994651338",
          "0.0"
      };
      static const std::vector<Quad> vw10b(aw10b, aw10b + 6);

      // w21b, weights of the 21-point formula for abscissae x21
      static const Quad aw21b[6] = {
          "0.011694638867371874278064396062192",
          "0.054755896574351996031381300244580",
          "0.093125454583697605535065465083366",
          "0.123491976262065851077958109831074",
          "0.142775938577060080797094273138717",
          "0.149445554002916905664936468389821"
      };
      static const std::vector<Quad> vw21b(aw21b, aw21b + 6);

      // w43b, weights of the 43-point formula for abscissae x43
      static const Quad aw43b[12] = {
          "0.001844477640212414100389106552965",
          "0.010798689585891651740465406741293",
          "0.021895363867795428102523123075149",
          "0.032597463975345689443882222526137",
          "0.042163137935191811847627924327955",
          "0.050741939600184577780189020092084",
          "0.058379395542619248375475369330206",
          "0.064746404951445885544689259517511",
          "0.069566197912356484528633315038405",
          "0.072824441471833208150939535192842",
          "0.074507751014175118273571813842889",
          "0.074722147517403005594425168280423"
      };
      static const std::vector<Quad> vw43b(aw43b, aw43b + 12);

      // w87b, weights of the 87-point formula for abscissae x87
      static const Quad aw87b[23] = {
          "0.000274145563762072350016527092881",
          "0.001807124155057942948341311753254",
          "0.004096869282759164864458070683480",
          "0.006758290051847378699816577897424",
          "0.009549957672201646536053581325377",
          "0.012329447652244853694626639963780",
          "0.015010447346388952376697286041943",
          "0.017548967986243191099665352925900",
          "0.019938037786440888202278192730714",
          "0.022194935961012286796332102959499",
          "0.024339147126000805470360647041454",
          "0.026374505414839207241503786552615",
          "0.028286910788771200659968002987960",
          "0.030052581128092695322521110347341",
          "0.031646751371439929404586051078883",
          "0.033050413419978503290785944862689",
          "0.034255099704226061787082821046821",
          "0.035262412660156681033782717998428",
          "0.036076989622888701185500318003895",
          "0.036698604498456094498018047441094",
          "0.037120549269832576114119958413599",
          "0.037334228751935040321235449094698",
          "0.037361073762679023410321241766599"
      };
      static const std::vector<Quad> vw87b(aw87b, aw87b + 23);

      // w175b, weights of the 175-point formula for abscissae x175
      static const Quad aw175b[45] = {
          "0.00003901440664395060055484226",
          "0.0002787312407993348139961464",
          "0.0006672934146291138823512275",
          "0.001163051749910003055308177",
          "0.001738533916888715565420637",
          "0.002369555040550195269486165",
          "0.003036735036032612976379865",
          "0.003725394125884235586678819",
          "0.004424387541776355951933433",
          "0.005125062882078508655875582",
          "0.005820601038952832388647054",
          "0.006505667785357412495794539",
          "0.007176258976795165213169074",
          "0.007829642423806550517967042",
          "0.008464316525043036555640657",
          "0.009079917879101951192512711",
          "0.009677029304308397008134699",
          "0.01025687419430508685393322",
          "0.01082092935368957685380896",
          "0.01137052956179654620079332",
          "0.01190655150082017425918844",
          "0.01242924137407215963971061",
          "0.01293819980598456566872951",
          "0.01343248644726851711632966",
          "0.01391078107864287587682982",
          "0.01437154592198526807352501",
          "0.01481316256915705351874381",
          "0.01523404482122031244940129",
          "0.01563274056894636856297717",
          "0.01600802989372176552081826",
          "0.01635901148521841710605397",
          "0.01668515675646806540972517",
          "0.01698630892029276765404134",
          "0.01726261506199017604299177",
          "0.01751439915887340284018269",
          "0.01774200489411242260549908",
          "0.01794564958245060930824294",
          "0.01812532816637054898168673",
          "0.01828078919412312732671357",
          "0.01841158014800801587767163",
          "0.01851713825962505903167768",
          "0.01859689376712028821908313",
          "0.01865035760791320287947920",
          "0.01867717982648033250824110",
          "0.01868053688133951170552407"
      };
      static const std::vector<Quad> vw175b(aw175b, aw175b + 45);

      static const std::vector<Quad>* wb[NGKPLEVELS] = {&vw10b, &vw21b, &vw43b, &vw87b, &vw175b};

      assert(level >= 0 && level < NGKPLEVELS);
      return *wb[level];
  }
    
#endif

} // end of namespace details

}}} // of namespaces lsst/afw/math

#endif