gauss.h

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#ifndef THEORETICA_GAUSS_H
#define THEORETICA_GAUSS_H
 
#include "../core/constants.h"
 
 
namespace theoretica {
 
    namespace tables {
 
 
        // Legendre
 
        static real legendre_roots_2[2] = {
            -0.577350269189625764506505,
            0.577350269189625764506505
        };
 
        static real legendre_weights_2[2] = {
            1, 1
        };
 
        static real legendre_roots_4[4] = {
            -0.861136311594052575194101,
            -0.339981043584856264846549,
            0.339981043584856264738129,
            0.861136311594052575194101
        };
 
        static real legendre_weights_4[4] = {
            0.347854845137453857491878,
            0.652145154862546142535227,
            0.652145154862546142643647,
            0.347854845137453857491878
        };
 
        static real legendre_roots_8[8] = {
            -0.960289856497536231715127,
            -0.796666477413626739621007,
            -0.525532409916328985884527,
            -0.183434642495649804990214,
            0.183434642495649804936004,
            0.525532409916328985884527,
            0.796666477413626739621007,
            0.960289856497536231715127
        };
 
        static real legendre_weights_8[8] = {
            0.101228536290376258828787,
            0.222381034453374470260959,
            0.313706645877887287419484,
            0.362683783378361982948669,
            0.362683783378361982948669,
            0.313706645877887287419484,
            0.222381034453374470260959,
            0.101228536290376258828787
        };
 
        static real legendre_roots_16[16] = {
            -0.989400934991649929186111,
            -0.944575023073232580589787,
            -0.865631202387831746901999,
            -0.755404408355003026897482,
            -0.617876244402643747097217,
            -0.458016777657227386105678,
            -0.281603550779258913257935,
            -0.0950125098376374401876535,
            0.0950125098376374401605484,
            0.281603550779258913203725,
            0.458016777657227386701989,
            0.617876244402643747097217,
            0.755404408355003026897482,
            0.865631202387831746901999,
            0.944575023073232565953058,
            0.989400934991649929186111
        };
 
        static real legendre_weights_16[16] = {
            0.0271524594117540951122847,
            0.0622535239386478849447004,
            0.0951585116824928647197876,
            0.124628971255533850669866,
            0.149595988816576744480109,
            0.169156519395002539321907,
            0.182603415044923588682552,
            0.189450610455068496273891,
            0.189450610455068496300996,
            0.182603415044923588967155,
            0.169156519395002538020865,
            0.149595988816576744480109,
            0.124628971255533850669866,
            0.0951585116824928647197876,
            0.0622535239386479161324535,
            0.0271524594117540951122847
        };
 
 
        // Laguerre
 
        static real laguerre_roots_2[2] = {
            0.58578643762690546732,
            3.4142135623730945322
        };
 
        static real laguerre_weights_2[2] = {
            0.85355339059327000202,
            0.14644660940672634871
        };
 
 
        static real laguerre_roots_4[4] = {
            0.32254768961939191742,
            1.7457611011583463777,
            4.5366202969211275316,
            9.3950709123011330332
        };
 
        static real laguerre_weights_4[4] = {
            0.60315410434164023839,
            0.35741869243780005017,
            0.03888790851500541948,
            0.00053929470556132749637
        };
 
 
        static real laguerre_roots_8[8] = {
            0.17027963230510124502,
            0.90370177679937967218,
            2.2510866298661306928,
            4.2667001702876592626,
            7.0459054023934658056,
            10.758516010180995295,
            15.740678641278004193,
            22.863131736889263833
        };
 
        static real laguerre_weights_8[8] = {
            0.36918858934162849121,
            0.41878678081434484077,
            0.17579498663717180432,
            0.033343492261215595242,
            0.0027945362352256706928,
            9.0765087733582173847e-005,
            8.4857467162725295329e-007,
            1.0480011748715107818e-009
        };
 
 
        static real laguerre_roots_16[16] = {
            0.087649410478928189153,
            0.46269632891508138072,
            1.1410577748312272208,
            2.1292836450983810438,
            3.4370866338932063403,
            5.0780186145497663115,
            7.0703385350482545854,
            9.4383143363918924219,
            12.214223368866159374,
            15.441527368781641486,
            19.180156856752924456,
            23.51590569399238859,
            28.578729742881671998,
            34.583398702286930866,
            41.940452647688152288,
            51.701160339543346826
        };
 
        static real laguerre_weights_16[16] = {
            0.20615171495777392289,
            0.33105785495087120126,
            0.26579577764421131011,
            0.13629693429637680541,
            0.047328928694125499268,
            0.011299900080339313299,
            0.0018490709435266595795,
            0.00020427191530818007586,
            1.4844586873978733152e-005,
            6.8283193308651186878e-007,
            1.8810248410831411265e-008,
            2.8623502429707047297e-010,
            2.1270790332192899185e-012,
            6.2979670025300090354e-015,
            5.050473700032298015e-018,
            4.1614623703730629937e-022
        };
 
 
        // Hermite
 
 
        static real hermite_roots_2[2] = {
            -0.707106781186547524,
            0.707106781186547524
        };
 
        static real hermite_weights_2[2] = {
            0.886226925452757941,
            0.886226925452757941
        };
 
 
        static real hermite_roots_4[4] = {
            -1.65068012388578456,
            -0.52464762327529032,
            0.52464762327529032,
            1.65068012388578456
        };
 
        static real hermite_weights_4[4] = {
            0.08131283544724517,
            0.80491409000551277,
            0.80491409000551277,
            0.08131283544724517
        };
 
 
        static real hermite_roots_8[8] = {
            -2.93063742025724402,
            -1.98165675669584293,
            -1.15719371244678019,
            -0.381186990207322117,
            0.381186990207322117,
            1.15719371244678019,
            1.98165675669584293,
            2.93063742025724402,
        };
 
        static real hermite_weights_8[8] = {
            0.0001996040722113676,
            0.0170779830074134741,
            0.207802325814891863,
            0.66114701255824124,
            0.66114701255824124,
            0.207802325814891863,
            0.0170779830074134741,
            0.0001996040722113676
        };
 
 
        static real hermite_roots_16[16] = {
            -4.68873893930581836,
            -3.86944790486012269,
            -3.17699916197995602,
            -2.54620215784748137,
            -1.95178799091625398,
            -1.3802585391988808,
            -0.822951449144655892,
            -0.273481046138152452,
            0.273481046138152453,
            0.822951449144655892,
            1.3802585391988808,
            1.95178799091625398,
            2.54620215784748136,
            3.17699916197995602,
            3.86944790486012269,
            4.68873893930581836
        };
 
        static real hermite_weights_16[16] = {
            2.65480747401118205e-010,
            2.32098084486521081e-007,
            2.71186009253788177e-005,
            0.000932284008624180443,
            0.0128803115355099723,
            0.0838100413989858226,
            0.280647458528533652,
            0.5079294790166137,
            0.5079294790166137,
            0.280647458528533652,
            0.0838100413989858228,
            0.0128803115355099723,
            0.000932284008624180486,
            2.71186009253788177e-005,
            2.32098084486521081e-007,
            2.65480747401118205e-010
        };
 
    }
 
}
 
#endif