multicalc 0.5.0

use crate::utils::error_codes::GAUSSIAN_QUADRATURE_ORDER_OUT_OF_RANGE;

pub const MAX_GH_ORDER: usize = 30;


pub fn get_gh_weights_and_abscissae(order: usize, index: usize) -> Result<(f64, f64), &'static str>
{
    let ref_abs: f64 = match order 
    {
        1 => HERMITE_ABSCISSA_1[index],
        2 => HERMITE_ABSCISSA_2[index],
        3 => HERMITE_ABSCISSA_3[index],
        4 => HERMITE_ABSCISSA_4[index],
        5 => HERMITE_ABSCISSA_5[index],
        6 => HERMITE_ABSCISSA_6[index],
        7 => HERMITE_ABSCISSA_7[index],
        8 => HERMITE_ABSCISSA_8[index],
        9 => HERMITE_ABSCISSA_9[index],
        10 => HERMITE_ABSCISSA_10[index],
        11 => HERMITE_ABSCISSA_11[index],
        12 => HERMITE_ABSCISSA_12[index],
        13 => HERMITE_ABSCISSA_13[index],
        14 => HERMITE_ABSCISSA_14[index],
        15 => HERMITE_ABSCISSA_15[index],
        16 => HERMITE_ABSCISSA_16[index],
        17 => HERMITE_ABSCISSA_17[index],
        18 => HERMITE_ABSCISSA_18[index],
        19 => HERMITE_ABSCISSA_19[index],
        20 => HERMITE_ABSCISSA_20[index],
        21 => HERMITE_ABSCISSA_21[index],
        22 => HERMITE_ABSCISSA_22[index],
        23 => HERMITE_ABSCISSA_23[index],
        24 => HERMITE_ABSCISSA_24[index],
        25 => HERMITE_ABSCISSA_25[index],
        26 => HERMITE_ABSCISSA_26[index],
        27 => HERMITE_ABSCISSA_27[index],
        28 => HERMITE_ABSCISSA_28[index],
        29 => HERMITE_ABSCISSA_29[index],
        30 => HERMITE_ABSCISSA_30[index],
        _ => return Err(GAUSSIAN_QUADRATURE_ORDER_OUT_OF_RANGE),
    };

    let ref_weight: f64 = match order 
    {
        1 => HERMITE_WEIGHT_1[index],
        2 => HERMITE_WEIGHT_2[index],
        3 => HERMITE_WEIGHT_3[index],
        4 => HERMITE_WEIGHT_4[index],
        5 => HERMITE_WEIGHT_5[index],
        6 => HERMITE_WEIGHT_6[index],
        7 => HERMITE_WEIGHT_7[index],
        8 => HERMITE_WEIGHT_8[index],
        9 => HERMITE_WEIGHT_9[index],
        10 => HERMITE_WEIGHT_10[index],
        11 => HERMITE_WEIGHT_11[index],
        12 => HERMITE_WEIGHT_12[index],
        13 => HERMITE_WEIGHT_13[index],
        14 => HERMITE_WEIGHT_14[index],
        15 => HERMITE_WEIGHT_15[index],
        16 => HERMITE_WEIGHT_16[index],
        17 => HERMITE_WEIGHT_17[index],
        18 => HERMITE_WEIGHT_18[index],
        19 => HERMITE_WEIGHT_19[index],
        20 => HERMITE_WEIGHT_20[index],
        21 => HERMITE_WEIGHT_21[index],
        22 => HERMITE_WEIGHT_22[index],
        23 => HERMITE_WEIGHT_23[index],
        24 => HERMITE_WEIGHT_24[index],
        25 => HERMITE_WEIGHT_25[index],
        26 => HERMITE_WEIGHT_26[index],
        27 => HERMITE_WEIGHT_27[index],
        28 => HERMITE_WEIGHT_28[index],
        29 => HERMITE_WEIGHT_29[index],
        30 => HERMITE_WEIGHT_30[index],
        _ => return Err(GAUSSIAN_QUADRATURE_ORDER_OUT_OF_RANGE),
    };

    return Ok((ref_abs, ref_weight));
}

// =============================================================================
// Table generated using Python's numpy.polynomial.hermite
// =============================================================================
const HERMITE_ABSCISSA_1: [f64; 1] = [
0.0];
const HERMITE_ABSCISSA_2: [f64; 2] = [
-0.7071067811865475, 
0.7071067811865475];
const HERMITE_ABSCISSA_3: [f64; 3] = [
-1.224744871391589, 
0.0, 
1.224744871391589];
const HERMITE_ABSCISSA_4: [f64; 4] = [
-1.6506801238857847, 
-0.5246476232752904, 
0.5246476232752904, 
1.6506801238857847];
const HERMITE_ABSCISSA_5: [f64; 5] = [
-2.0201828704560856, 
-0.9585724646138185, 
0.0, 
0.9585724646138185, 
2.0201828704560856];
const HERMITE_ABSCISSA_6: [f64; 6] = [
-2.3506049736744923, 
-1.335849074013697, 
-0.4360774119276165, 
0.4360774119276165, 
1.335849074013697, 
2.3506049736744923];
const HERMITE_ABSCISSA_7: [f64; 7] = [
-2.6519613568352334, 
-1.6735516287674714, 
-0.8162878828589646, 
0.0, 
0.8162878828589646, 
1.6735516287674714, 
2.6519613568352334];
const HERMITE_ABSCISSA_8: [f64; 8] = [
-2.930637420257244, 
-1.981656756695843, 
-1.1571937124467802, 
-0.3811869902073221, 
0.3811869902073221, 
1.1571937124467802, 
1.981656756695843, 
2.930637420257244];
const HERMITE_ABSCISSA_9: [f64; 9] = [
-3.1909932017815277, 
-2.266580584531843, 
-1.468553289216668, 
-0.7235510187528376, 
0.0, 
0.7235510187528376, 
1.468553289216668, 
2.266580584531843, 
3.1909932017815277];
const HERMITE_ABSCISSA_10: [f64; 10] = [
-3.4361591188377374, 
-2.5327316742327897, 
-1.7566836492998816, 
-1.0366108297895136, 
-0.3429013272237046, 
0.3429013272237046, 
1.0366108297895136, 
1.7566836492998816, 
2.5327316742327897, 
3.4361591188377374];
const HERMITE_ABSCISSA_11: [f64; 11] = [
-3.6684708465595826, 
-2.7832900997816514, 
-2.0259480158257555, 
-1.3265570844949328, 
-0.6568095668820998, 
0.0, 
0.6568095668820998, 
1.3265570844949328, 
2.0259480158257555, 
2.7832900997816514, 
3.6684708465595826];
const HERMITE_ABSCISSA_12: [f64; 12] = [
-3.889724897869782, 
-3.0206370251208896, 
-2.2795070805010598, 
-1.5976826351526048, 
-0.9477883912401638, 
-0.31424037625435913, 
0.31424037625435913, 
0.9477883912401638, 
1.5976826351526048, 
2.2795070805010598, 
3.0206370251208896, 
3.889724897869782];
const HERMITE_ABSCISSA_13: [f64; 13] = [
-4.10133759617864, 
-3.24660897837241, 
-2.5197356856782376, 
-1.853107651601512, 
-1.2200550365907483, 
-0.6057638791710601, 
0.0, 
0.6057638791710601, 
1.2200550365907483, 
1.853107651601512, 
2.5197356856782376, 
3.24660897837241, 
4.10133759617864];
const HERMITE_ABSCISSA_14: [f64; 14] = [
-4.304448570473632, 
-3.4626569336022706, 
-2.7484707249854026, 
-2.0951832585077166, 
-1.4766827311411408, 
-0.8787137873293994, 
-0.29174551067256205, 
0.29174551067256205, 
0.8787137873293994, 
1.4766827311411408, 
2.0951832585077166, 
2.7484707249854026, 
3.4626569336022706, 
4.304448570473632];
const HERMITE_ABSCISSA_15: [f64; 15] = [
-4.499990707309392, 
-3.6699503734044527, 
-2.967166927905603, 
-2.325732486173858, 
-1.7199925751864888, 
-1.1361155852109206, 
-0.5650695832555758, 
0.0, 
0.5650695832555758, 
1.1361155852109206, 
1.7199925751864888, 
2.325732486173858, 
2.967166927905603, 
3.6699503734044527, 
4.499990707309392];
const HERMITE_ABSCISSA_16: [f64; 16] = [
-4.688738939305819, 
-3.869447904860123, 
-3.176999161979956, 
-2.5462021578474814, 
-1.9517879909162539, 
-1.3802585391988809, 
-0.8229514491446559, 
-0.27348104613815244, 
0.27348104613815244, 
0.8229514491446559, 
1.3802585391988809, 
1.9517879909162539, 
2.5462021578474814, 
3.176999161979956, 
3.869447904860123, 
4.688738939305819];
const HERMITE_ABSCISSA_17: [f64; 17] = [
-4.871345193674403, 
-4.0619466758754745, 
-3.378932091141494, 
-2.7577629157038888, 
-2.1735028266666205, 
-1.6129243142212313, 
-1.0676487257434506, 
-0.5316330013426548, 
0.0, 
0.5316330013426548, 
1.0676487257434506, 
1.6129243142212313, 
2.1735028266666205, 
2.7577629157038888, 
3.378932091141494, 
4.0619466758754745, 
4.871345193674403];
const HERMITE_ABSCISSA_18: [f64; 18] = [
-5.048364008874467, 
-4.248117873568127, 
-3.573769068486266, 
-2.961377505531607, 
-2.3862990891666858, 
-1.8355316042616288, 
-1.3009208583896175, 
-0.7766829192674116, 
-0.2582677505190968, 
0.2582677505190968, 
0.7766829192674116, 
1.3009208583896175, 
1.8355316042616288, 
2.3862990891666858, 
2.961377505531607, 
3.573769068486266, 
4.248117873568127, 
5.048364008874467];
const HERMITE_ABSCISSA_19: [f64; 19] = [
-5.220271690537482, 
-4.428532806603779, 
-3.76218735196402, 
-3.157848818347602, 
-2.591133789794543, 
-2.049231709850619, 
-1.5241706193935332, 
-1.0103683871343114, 
-0.5035201634238882, 
0.0, 
0.5035201634238882, 
1.0103683871343114, 
1.5241706193935332, 
2.049231709850619, 
2.591133789794543, 
3.157848818347602, 
3.76218735196402, 
4.428532806603779, 
5.220271690537482];
const HERMITE_ABSCISSA_20: [f64; 20] = [
-5.387480890011233, 
-4.603682449550744, 
-3.944764040115625, 
-3.3478545673832163, 
-2.7888060584281305, 
-2.2549740020892757, 
-1.7385377121165861, 
-1.234076215395323, 
-0.7374737285453944, 
-0.24534070830090124, 
0.24534070830090124, 
0.7374737285453944, 
1.234076215395323, 
1.7385377121165861, 
2.2549740020892757, 
2.7888060584281305, 
3.3478545673832163, 
3.944764040115625, 
4.603682449550744, 
5.387480890011233];
const HERMITE_ABSCISSA_21: [f64; 21] = [
-5.550351873264678, 
-4.773992343411219, 
-4.12199554749184, 
-3.5319728771376777, 
-2.979991207704598, 
-2.453552124512838, 
-1.9449629491862537, 
-1.448934250650732, 
-0.961499634418369, 
-0.47945070707910753, 
0.0, 
0.47945070707910753, 
0.961499634418369, 
1.448934250650732, 
1.9449629491862537, 
2.453552124512838, 
2.979991207704598, 
3.5319728771376777, 
4.12199554749184, 
4.773992343411219, 
5.550351873264678];
const HERMITE_ABSCISSA_22: [f64; 22] = [
-5.7092013532052635, 
-4.939834131060176, 
-4.294312480593161, 
-3.710701532877805, 
-3.1652659092021374, 
-2.645637441058173, 
-2.1442335927985345, 
-1.6558743732864225, 
-1.1767139584812445, 
-0.703686097170007, 
-0.2341791399309906, 
0.2341791399309906, 
0.703686097170007, 
1.1767139584812445, 
1.6558743732864225, 
2.1442335927985345, 
2.645637441058173, 
3.1652659092021374, 
3.710701532877805, 
4.294312480593161, 
4.939834131060176, 
5.7092013532052635];
const HERMITE_ABSCISSA_23: [f64; 23] = [
-5.864309498984572, 
-5.101534610476677, 
-4.462091173740006, 
-3.884472708106102, 
-3.3451271599412244, 
-2.831803787126157, 
-2.337016211474456, 
-1.855677037671371, 
-1.3840395856824952, 
-0.9191514654425638, 
-0.4585383500681048, 
0.0, 
0.4585383500681048, 
0.9191514654425638, 
1.3840395856824952, 
1.855677037671371, 
2.337016211474456, 
2.831803787126157, 
3.3451271599412244, 
3.884472708106102, 
4.462091173740006, 
5.101534610476677, 
5.864309498984572];
const HERMITE_ABSCISSA_24: [f64; 24] = [
-6.01592556142574, 
-5.259382927668044, 
-4.625662756423788, 
-4.053664402448149, 
-3.5200068130345246, 
-3.0125461375655647, 
-2.523881017011427, 
-2.049003573661699, 
-1.5842500109616942, 
-1.1267608176112451, 
-0.6741711070372123, 
-0.22441454747251557, 
0.22441454747251557, 
0.6741711070372123, 
1.1267608176112451, 
1.5842500109616942, 
2.049003573661699, 
2.523881017011427, 
3.0125461375655647, 
3.5200068130345246, 
4.053664402448149, 
4.625662756423788, 
5.259382927668044, 
6.01592556142574];
const HERMITE_ABSCISSA_25: [f64; 25] = [
-6.164272434052452, 
-5.413636355280033, 
-4.785320367352224, 
-4.218609444386561, 
-3.690282876998356, 
-3.188294924425105, 
-2.705320237173026, 
-2.236420130267281, 
-1.7780011243371474, 
-1.327280702073084, 
-0.8819827562138213, 
-0.4401472986453083, 
0.0, 
0.4401472986453083, 
0.8819827562138213, 
1.327280702073084, 
1.7780011243371474, 
2.236420130267281, 
2.705320237173026, 
3.188294924425105, 
3.690282876998356, 
4.218609444386561, 
4.785320367352224, 
5.413636355280033, 
6.164272434052452];
const HERMITE_ABSCISSA_26: [f64; 26] = [
-6.309550385625694, 
-5.564524981950103, 
-4.941324957241379, 
-4.379602662983305, 
-3.856288419909149, 
-3.35942718235083, 
-2.881762219543087, 
-2.418415764773779, 
-1.9658547856411366, 
-1.5213615166519214, 
-1.0827330110778832, 
-0.6480952139934484, 
-0.2157778562434634, 
0.2157778562434634, 
0.6480952139934484, 
1.0827330110778832, 
1.5213615166519214, 
1.9658547856411366, 
2.418415764773779, 
2.881762219543087, 
3.35942718235083, 
3.856288419909149, 
4.379602662983305, 
4.941324957241379, 
5.564524981950103, 
6.309550385625694];
const HERMITE_ABSCISSA_27: [f64; 27] = [
-6.4519401407534716, 
-5.712255552816536, 
-5.093910003113184, 
-4.5369066633724415, 
-4.018318670408739, 
-3.526275340134353, 
-3.053582419822255, 
-2.5954163389108182, 
-2.1482966453616275, 
-1.7095607392603371, 
-1.277066817339858, 
-0.849011342060103, 
-0.42380790054385303, 
0.0, 
0.42380790054385303, 
0.849011342060103, 
1.277066817339858, 
1.7095607392603371, 
2.1482966453616275, 
2.5954163389108182, 
3.053582419822255, 
3.526275340134353, 
4.018318670408739, 
4.5369066633724415, 
5.093910003113184, 
5.712255552816536, 
6.4519401407534716];
const HERMITE_ABSCISSA_28: [f64; 28] = [
-6.591605442367743, 
-5.85701464138285, 
-5.243285373202936, 
-4.690756523943118, 
-4.1766367421292685, 
-3.6891342384616794, 
-3.2211120765614556, 
-2.767795352913594, 
-2.3257498426564407, 
-1.8923604968376853, 
-1.465537263457409, 
-1.0435352737542083, 
-0.6248367195052092, 
-0.20806738269073688, 
0.20806738269073688, 
0.6248367195052092, 
1.0435352737542083, 
1.465537263457409, 
1.8923604968376853, 
2.3257498426564407, 
2.767795352913594, 
3.2211120765614556, 
3.6891342384616794, 
4.1766367421292685, 
4.690756523943118, 
5.243285373202936, 
5.85701464138285, 
6.591605442367743];
const HERMITE_ABSCISSA_29: [f64; 29] = [
-6.72869519860885, 
-5.99897128946382, 
-5.389640521966752, 
-4.841363651059164, 
-4.33147829381915, 
-3.8482667922136202, 
-3.3846451410922143, 
-2.9358825042901264, 
-2.498585691019404, 
-2.070181076053428, 
-1.6486229138923163, 
-1.232215755084753, 
-0.8194986812709115, 
-0.4091646363949287, 
0.0, 
0.4091646363949287, 
0.8194986812709115, 
1.232215755084753, 
1.6486229138923163, 
2.070181076053428, 
2.498585691019404, 
2.9358825042901264, 
3.3846451410922143, 
3.8482667922136202, 
4.33147829381915, 
4.841363651059164, 
5.389640521966752, 
5.99897128946382, 
6.72869519860885];
const HERMITE_ABSCISSA_30: [f64; 30] = [
-6.863345293529892, 
-6.138279220123935, 
-5.533147151567496, 
-4.988918968589944, 
-4.4830553570925185, 
-4.003908603861229, 
-3.54444387315535, 
-3.0999705295864417, 
-2.6671321245356174, 
-2.243391467761504, 
-1.826741143603688, 
-1.4155278001981886, 
-1.0083382710467235, 
-0.6039210586255523, 
-0.2011285765488715, 
0.2011285765488715, 
0.6039210586255523, 
1.0083382710467235, 
1.4155278001981886, 
1.826741143603688, 
2.243391467761504, 
2.6671321245356174, 
3.0999705295864417, 
3.54444387315535, 
4.003908603861229, 
4.4830553570925185, 
4.988918968589944, 
5.533147151567496, 
6.138279220123935, 
6.863345293529892];

const HERMITE_WEIGHT_1: [f64; 1] = [
1.7724538509055159];
const HERMITE_WEIGHT_2: [f64; 2] = [
0.8862269254527579, 
0.8862269254527579];
const HERMITE_WEIGHT_3: [f64; 3] = [
0.2954089751509194, 
1.1816359006036772, 
0.2954089751509194];
const HERMITE_WEIGHT_4: [f64; 4] = [
0.08131283544724519, 
0.8049140900055127, 
0.8049140900055127, 
0.08131283544724519];
const HERMITE_WEIGHT_5: [f64; 5] = [
0.019953242059045917, 
0.3936193231522411, 
0.9453087204829418, 
0.3936193231522411, 
0.019953242059045917];
const HERMITE_WEIGHT_6: [f64; 6] = [
0.004530009905508835, 
0.15706732032285647, 
0.7246295952243924, 
0.7246295952243924, 
0.15706732032285647, 
0.004530009905508835];
const HERMITE_WEIGHT_7: [f64; 7] = [
0.0009717812450995199, 
0.05451558281912705, 
0.4256072526101278, 
0.8102646175568072, 
0.4256072526101278, 
0.05451558281912705, 
0.0009717812450995199];
const HERMITE_WEIGHT_8: [f64; 8] = [
0.00019960407221136783, 
0.017077983007413467, 
0.20780232581489183, 
0.6611470125582415, 
0.6611470125582415, 
0.20780232581489183, 
0.017077983007413467, 
0.00019960407221136783];
const HERMITE_WEIGHT_9: [f64; 9] = [
3.9606977263264365e-05, 
0.004943624275536941, 
0.08847452739437664, 
0.43265155900255564, 
0.720235215606051, 
0.43265155900255564, 
0.08847452739437664, 
0.004943624275536941, 
3.9606977263264365e-05];
const HERMITE_WEIGHT_10: [f64; 10] = [
7.640432855232641e-06, 
0.0013436457467812324, 
0.033874394455481106, 
0.2401386110823147, 
0.6108626337353258, 
0.6108626337353258, 
0.2401386110823147, 
0.033874394455481106, 
0.0013436457467812324, 
7.640432855232641e-06];
const HERMITE_WEIGHT_11: [f64; 11] = [
1.4395603937142596e-06, 
0.00034681946632334544, 
0.011911395444911507, 
0.11722787516770851, 
0.42935975235612495, 
0.6547592869145916, 
0.42935975235612495, 
0.11722787516770851, 
0.011911395444911507, 
0.00034681946632334544, 
1.4395603937142596e-06];
const HERMITE_WEIGHT_12: [f64; 12] = [
2.6585516843563044e-07, 
8.573687043587868e-05, 
0.00390539058462906, 
0.05160798561588398, 
0.2604923102641611, 
0.5701352362624795, 
0.5701352362624795, 
0.2604923102641611, 
0.05160798561588398, 
0.00390539058462906, 
8.573687043587868e-05, 
2.6585516843563044e-07];
const HERMITE_WEIGHT_13: [f64; 13] = [
4.825731850073125e-08, 
2.0430360402707087e-05, 
0.001207459992719386, 
0.020862775296169953, 
0.1403233206870235, 
0.4216162968985432, 
0.6043931879211613, 
0.4216162968985432, 
0.1403233206870235, 
0.020862775296169953, 
0.001207459992719386, 
2.0430360402707087e-05, 
4.825731850073125e-08];
const HERMITE_WEIGHT_14: [f64; 14] = [
8.628591168125132e-09, 
4.71648435501891e-06, 
0.00035509261355192297, 
0.007850054726457945, 
0.06850553422346528, 
0.2731056090642464, 
0.5364059097120901, 
0.5364059097120901, 
0.2731056090642464, 
0.06850553422346528, 
0.007850054726457945, 
0.00035509261355192297, 
4.71648435501891e-06, 
8.628591168125132e-09];
const HERMITE_WEIGHT_15: [f64; 15] = [
1.522475804253521e-09, 
1.0591155477110625e-06, 
0.00010000444123249982, 
0.002778068842912775, 
0.0307800338725461, 
0.15848891579593571, 
0.4120286874988987, 
0.5641003087264174, 
0.4120286874988987, 
0.15848891579593571, 
0.0307800338725461, 
0.002778068842912775, 
0.00010000444123249982, 
1.0591155477110625e-06, 
1.522475804253521e-09];
const HERMITE_WEIGHT_16: [f64; 16] = [
2.6548074740111673e-10, 
2.3209808448652032e-07, 
2.7118600925378892e-05, 
0.0009322840086241807, 
0.012880311535509989, 
0.08381004139898583, 
0.2806474585285337, 
0.5079294790166137, 
0.5079294790166137, 
0.2806474585285337, 
0.08381004139898583, 
0.012880311535509989, 
0.0009322840086241807, 
2.7118600925378892e-05, 
2.3209808448652032e-07, 
2.6548074740111673e-10];
const HERMITE_WEIGHT_17: [f64; 17] = [
4.5805789307986096e-11, 
4.97707898163077e-08, 
7.112289140021293e-06, 
0.0002986432866977531, 
0.005067349957627545, 
0.04092003414975629, 
0.17264829767009698, 
0.40182646947041206, 
0.5309179376248635, 
0.40182646947041206, 
0.17264829767009698, 
0.04092003414975629, 
0.005067349957627545, 
0.0002986432866977531, 
7.112289140021293e-06, 
4.97707898163077e-08, 
4.5805789307986096e-11];
const HERMITE_WEIGHT_18: [f64; 18] = [
7.828199772115908e-12, 
1.0467205795792089e-08, 
1.810654481093432e-06, 
9.18112686792939e-05, 
0.001888522630268417, 
0.018640042387544676, 
0.09730174764131541, 
0.2848072856699793, 
0.48349569472545567, 
0.48349569472545567, 
0.2848072856699793, 
0.09730174764131541, 
0.018640042387544676, 
0.001888522630268417, 
9.18112686792939e-05, 
1.810654481093432e-06, 
1.0467205795792089e-08, 
7.828199772115908e-12];
const HERMITE_WEIGHT_19: [f64; 19] = [
1.3262970944985234e-12, 
2.163051009863575e-09, 
4.488243147223115e-07, 
2.7209197763161712e-05, 
0.0006708775214071804, 
0.007988866777723026, 
0.050810386909052006, 
0.1836327013069971, 
0.3916089886130303, 
0.5029748882761865, 
0.3916089886130303, 
0.1836327013069971, 
0.050810386909052006, 
0.007988866777723026, 
0.0006708775214071804, 
2.7209197763161712e-05, 
4.488243147223115e-07, 
2.163051009863575e-09, 
1.3262970944985234e-12];
const HERMITE_WEIGHT_20: [f64; 20] = [
2.2293936455341447e-13, 
4.3993409922731747e-10, 
1.0860693707692782e-07, 
7.80255647853206e-06, 
0.00022833863601635365, 
0.0032437733422378567, 
0.024810520887463643, 
0.1090172060200233, 
0.28667550536283415, 
0.4622436696006101, 
0.4622436696006101, 
0.28667550536283415, 
0.1090172060200233, 
0.024810520887463643, 
0.0032437733422378567, 
0.00022833863601635365, 
7.80255647853206e-06, 
1.0860693707692782e-07, 
4.3993409922731747e-10, 
2.2293936455341447e-13];
const HERMITE_WEIGHT_21: [f64; 21] = [
3.720365070136023e-14, 
8.818611242049933e-11, 
2.5712301800593154e-08, 
2.17188489805667e-06, 
7.478398867310063e-05, 
0.0012549820417264088, 
0.011414065837434397, 
0.0601796466589123, 
0.19212032406699775, 
0.3816690736135022, 
0.47902370312017756, 
0.3816690736135022, 
0.19212032406699775, 
0.0601796466589123, 
0.011414065837434397, 
0.0012549820417264088, 
7.478398867310063e-05, 
2.17188489805667e-06, 
2.5712301800593154e-08, 
8.818611242049933e-11, 
3.720365070136023e-14];
const HERMITE_WEIGHT_22: [f64; 22] = [
6.167183424404064e-15, 
1.744339007547978e-11, 
5.966990986059659e-09, 
5.884287563301018e-07, 
2.36551285525104e-05, 
0.0004648850508842517, 
0.004978399335051638, 
0.03114037088442385, 
0.11910236095878239, 
0.2869714332469073, 
0.44354522643495903, 
0.44354522643495903, 
0.2869714332469073, 
0.11910236095878239, 
0.03114037088442385, 
0.004978399335051638, 
0.0004648850508842517, 
2.36551285525104e-05, 
5.884287563301018e-07, 
5.966990986059659e-09, 
1.744339007547978e-11, 
6.167183424404064e-15];
const HERMITE_WEIGHT_23: [f64; 23] = [
1.0160384620636804e-15, 
3.40831409803052e-12, 
1.3596296504028966e-09, 
1.555339329145767e-07, 
7.249295918002263e-06, 
0.00016556169914187427, 
0.002069567874960639, 
0.01520708400448414, 
0.06889028942908743, 
0.19864489857802245, 
0.372143824877565, 
0.4581965855932132, 
0.372143824877565, 
0.19864489857802245, 
0.06889028942908743, 
0.01520708400448414, 
0.002069567874960639, 
0.00016556169914187427, 
7.249295918002263e-06, 
1.555339329145767e-07, 
1.3596296504028966e-09, 
3.40831409803052e-12, 
1.0160384620636804e-15];
const HERMITE_WEIGHT_24: [f64; 24] = [
1.6643684964891008e-16, 
6.584620243078167e-13, 
3.0462542699875555e-10, 
4.018971174941438e-08, 
2.1582457049023414e-06, 
5.688691636404392e-05, 
0.0008236924826884169, 
0.007048355810072673, 
0.037445470503230736, 
0.12773962178455917, 
0.2861795353464429, 
0.42693116386869934, 
0.42693116386869934, 
0.2861795353464429, 
0.12773962178455917, 
0.037445470503230736, 
0.007048355810072673, 
0.0008236924826884169, 
5.688691636404392e-05, 
2.1582457049023414e-06, 
4.018971174941438e-08, 
3.0462542699875555e-10, 
6.584620243078167e-13, 
1.6643684964891008e-16];
const HERMITE_WEIGHT_25: [f64; 25] = [
2.7119235140383954e-17, 
1.258814987746549e-13, 
6.719638417706253e-11, 
1.017038250301848e-08, 
6.257032499691108e-07, 
1.8915972957340455e-05, 
0.00031508363874548415, 
0.00311570872012563, 
0.019243098965408895, 
0.07688899517580887, 
0.20362113667812404, 
0.36308898927589045, 
0.43986872216948497, 
0.36308898927589045, 
0.20362113667812404, 
0.07688899517580887, 
0.019243098965408895, 
0.00311570872012563, 
0.00031508363874548415, 
1.8915972957340455e-05, 
6.257032499691108e-07, 
1.017038250301848e-08, 
6.719638417706253e-11, 
1.258814987746549e-13, 
2.7119235140383954e-17];
const HERMITE_WEIGHT_26: [f64; 26] = [
4.396916094753858e-18, 
2.3831486593721533e-14, 
1.4609999339815978e-11, 
2.5244940344905305e-09, 
1.7701063373973586e-07, 
6.103291717395996e-06, 
0.00011622970160310945, 
0.0013190647223238565, 
0.009397901291159578, 
0.0435982272172508, 
0.13511332791178782, 
0.2846322411767845, 
0.41204365059036924, 
0.41204365059036924, 
0.2846322411767845, 
0.13511332791178782, 
0.0435982272172508, 
0.009397901291159578, 
0.0013190647223238565, 
0.00011622970160310945, 
6.103291717395996e-06, 
1.7701063373973586e-07, 
2.5244940344905305e-09, 
1.4609999339815978e-11, 
2.3831486593721533e-14, 
4.396916094753858e-18];
const HERMITE_WEIGHT_27: [f64; 27] = [
7.095779297051429e-19, 
4.4707724573931376e-15, 
3.1341176136230647e-12, 
6.155031578231804e-10, 
4.895400409699535e-08, 
1.9152809005952912e-06, 
4.1467580043841464e-05, 
0.0005367696156881122, 
0.004381279835792532, 
0.023415933625341938, 
0.08417308108405192, 
0.20737048075100944, 
0.35451730409975385, 
0.42357728801505956, 
0.35451730409975385, 
0.20737048075100944, 
0.08417308108405192, 
0.023415933625341938, 
0.004381279835792532, 
0.0005367696156881122, 
4.1467580043841464e-05, 
1.9152809005952912e-06, 
4.895400409699535e-08, 
6.155031578231804e-10, 
3.1341176136230647e-12, 
4.4707724573931376e-15, 
7.095779297051429e-19];
const HERMITE_WEIGHT_28: [f64; 28] = [
1.1401393479036659e-19, 
8.315937951206773e-16, 
6.639436714909621e-13, 
1.4758531682776932e-10, 
1.3256825015417047e-08, 
5.857719720992982e-07, 
1.4345504229714393e-05, 
0.0002106181000240319, 
0.0019573312944089908, 
0.01196842321435482, 
0.04951488928989816, 
0.1413946097869548, 
0.28256139125938884, 
0.39860471782645124, 
0.39860471782645124, 
0.28256139125938884, 
0.1413946097869548, 
0.04951488928989816, 
0.01196842321435482, 
0.0019573312944089908, 
0.0002106181000240319, 
1.4345504229714393e-05, 
5.857719720992982e-07, 
1.3256825015417047e-08, 
1.4758531682776932e-10, 
6.639436714909621e-13, 
8.315937951206773e-16, 
1.1401393479036659e-19];
const HERMITE_WEIGHT_29: [f64; 29] = [
1.8244608527672462e-20, 
1.53450044460532e-16, 
1.3901072714495982e-13, 
3.4841301613084254e-11, 
3.5203123276007064e-09, 
1.749229129949943e-07, 
4.823073497647774e-06, 
7.990920354521803e-05, 
0.000840792506140262, 
0.005845503545271507, 
0.02763965559202372, 
0.0907688422155782, 
0.2101426944492106, 
0.34641893907167015, 
0.40897117463522964, 
0.34641893907167015, 
0.2101426944492106, 
0.0907688422155782, 
0.02763965559202372, 
0.005845503545271507, 
0.000840792506140262, 
7.990920354521803e-05, 
4.823073497647774e-06, 
1.749229129949943e-07, 
3.5203123276007064e-09, 
3.4841301613084254e-11, 
1.3901072714495982e-13, 
1.53450044460532e-16, 
1.8244608527672462e-20];
const HERMITE_WEIGHT_30: [f64; 30] = [
2.9082547001312045e-21, 
2.810333602750875e-17, 
2.8786070805487023e-14, 
8.106186297463033e-12, 
9.178580424378485e-10, 
5.108522450775958e-08, 
1.579094887324711e-06, 
2.938725228922988e-05, 
0.00034831012431868485, 
0.0027379224730676565, 
0.014703829704826678, 
0.055144176870234186, 
0.14673584754089003, 
0.28013093083921264, 
0.38639488954181395, 
0.38639488954181395, 
0.28013093083921264, 
0.14673584754089003, 
0.055144176870234186, 
0.014703829704826678, 
0.0027379224730676565, 
0.00034831012431868485, 
2.938725228922988e-05, 
1.579094887324711e-06, 
5.108522450775958e-08, 
9.178580424378485e-10, 
8.106186297463033e-12, 
2.8786070805487023e-14, 
2.810333602750875e-17, 
2.9082547001312045e-21];