# Imports
import numpy as np
__all__ = ['quadrule_on_flat', 'quadrule_on_simplex']
weights_ps_deg = []
quad_ps_deg = []
[docs]
def quadrule_on_flat(deg):
"""
Quadrature rule
Parameters
----------
deg : int
Algebraic degree of precision of the rule.
Returns
-------
weights_ps : ndarray
n-by-1 array of single or double, weights of quadrature points.
quad_ps : ndarray
n-by-3 array of single or double, natural coordinates of quadrature points.
"""
if deg >= len(weights_ps_deg):
for deg0 in range(len(weights_ps_deg), deg + 1):
weights_ps0, quad_ps0 = quadrule_on_simplex(deg0)
nqp = weights_ps0.shape[0]
quad_ps = np.array([
[(1.0 - quad_ps0[row1, 0] - quad_ps0[row1, 1]), quad_ps0[row1, 0], quad_ps0[row1, 1]]
for row1 in range(nqp)
])
weights_ps_deg.append(weights_ps0)
quad_ps_deg.append(quad_ps)
return weights_ps_deg[deg], quad_ps_deg[deg]
[docs]
def quadrule_on_simplex(deg):
"""
Parameters
----------
deg : int
Algebraic degree of precision of the rule.
CUBATURE RULE ON THE SIMPLEX [0 0; 0 1; 1 0]
Legend
#DEG : algebraic degree of precision.
#CARD : cardinality of the pointset.
#W- : negative weights.
#PT.O : points outside the simplex [0 0; 1 0; 0 1].
#M.E. : maximum moment error in inf norm.
Statistics of quadrature points
# | DEG | CARD | W- | PT.O| M.E.
#------------------------------------
# | 1 | 1 | 0 | 0 | 1.92e-16
# | 2 | 3 | 0 | 0 | 1.18e-16
# | 3 | 4 | 0 | 0 | 2.15e-16
# | 4 | 6 | 0 | 0 | 1.39e-16
# | 5 | 7 | 0 | 0 | 1.60e-16
# | 6 | 11 | 0 | 0 | 1.08e-15
# | 7 | 12 | 0 | 0 | 5.07e-16
# | 8 | 16 | 0 | 0 | 8.05e-16
# | 9 | 19 | 0 | 0 | 3.26e-16
# | 10 | 24 | 0 | 0 | 7.22e-16
# | 11 | 27 | 0 | 0 | 3.64e-15
# | 12 | 32 | 0 | 0 | 1.61e-15
# | 13 | 36 | 0 | 0 | 3.05e-16
# | 14 | 42 | 0 | 0 | 4.37e-16
# | 15 | 46 | 0 | 0 | 5.00e-16
# | 16 | 52 | 0 | 0 | 5.67e-16
# | 17 | 57 | 0 | 0 | 5.83e-16
# | 18 | 66 | 0 | 0 | 6.11e-16
# | 19 | 70 | 0 | 0 | 4.16e-16
# | 20 | 78 | 0 | 0 | 4.89e-16
# | 21 | 85 | 0 | 0 | 4.64e-16
# | 22 | 93 | 0 | 0 | 7.56e-16
# | 23 | 100 | 0 | 0 | 6.66e-16
# | 24 | 109 | 0 | 0 | 7.81e-16
# | 25 | 117 | 0 | 0 | 5.41e-16
CUBATURE RULE ON THE SIMPLEX [0 0; 0 1; 1 0].
--------------------------------------------------------------------
Input:
----------
deg: Algebraic degree of precision of the rule.
Returns
----------
weights_ps: N-by-1 array (single or double), weights of quadrature points
quad_ps: N-by-2 array (single or double),
natural coordinates of quadrature points
"""
# Your function implementation here
if deg <= 1:
quad_ps = np.array([[0.333333333333333314829616256247391, 0.333333333333333314829616256247391]])
weights_ps = np.array([0.500000000000000000000000000000000])
elif deg <= 2:
quad_ps = np.array([ [0.666666666666667, 0.166666666666667,],
[0.166666666666667, 0.666666666666667,],
[0.166666666666667, 0.166666666666667,],])
weights_ps = np.array([0.166666666666667,
0.166666666666667,
0.166666666666667,])
#ALG. DEG.: 3
#PTS CARD.: 4
#NEG. W. : 0
#OUT PTS. : 0
#M.E.INF. : 2.2e-16
elif deg <= 3:
quad_ps = np.array([ [0.644948974278318, 0.280019915499074,],
[0.155051025721682, 0.666390246014701,],
[0.644948974278318, 0.075031110222608,],
[0.155051025721682, 0.178558728263616,],])
weights_ps = np.array([0.090979309128011,
0.159020690871989,
0.090979309128011,
0.159020690871989,])
# ALG. DEG.: 4
# PTS CARD.: 6
# NEG. W. : 0
# OUT PTS. : 0
#M.E.INF. : 1.4e-16
elif deg <= 4:
quad_ps = np.array([[0.445948490915965, 0.445948490915965,],
[0.445948490915965, 0.108103018168070,],
[0.108103018168070, 0.445948490915965,],
[0.091576213509771, 0.091576213509771,],
[0.091576213509771, 0.816847572980459,],
[0.816847572980459, 0.091576213509771,],])
weights_ps = np.array([0.111690794839006,
0.111690794839006,
0.111690794839006,
0.054975871827661,
0.054975871827661,
0.054975871827661,])
# ALG. DEG.: 5
#PTS CARD.: 7
#NEG. W. : 0
#OUT PTS. : 0
#M.E.INF. : 1.6e-16
elif deg <= 5:
quad_ps = np.array([[0.333333333333333, 0.333333333333333,],
[0.797426985353087, 0.101286507323456,],
[0.101286507323456, 0.797426985353087,],
[0.101286507323456, 0.101286507323456,],
[0.059715871789770, 0.470142064105115,],
[0.470142064105115, 0.059715871789770,],
[0.470142064105115, 0.470142064105115,],])
weights_ps = np.array([0.112500000000000,
0.062969590272414,
0.062969590272414,
0.062969590272414,
0.066197076394253,
0.066197076394253,
0.066197076394253,])
#ALG. DEG.: 6
# PTS CARD.: 11
# NEG. W. : 0
#OUT PTS. : 0
#M.E.INF. : 1.1e-15
elif deg <= 6:
quad_ps = np.array([[0.057254986677477, 0.895498146789879,],
[0.895362640024579, 0.061828221250322,],
[0.684475748456514, 0.023343738497683,],
[0.068746255915030, 0.060030275747263,],
[0.615676205575840, 0.333461808341377,],
[0.627946141197789, 0.159189185992151,],
[0.062909138341864, 0.655295093705452,],
[0.068378211920510, 0.309117685428267,],
[0.287529458374392, 0.636426509179620,],
[0.328783556413135, 0.077024005642463,],
[0.312290405013645, 0.352344786445900,],])
weights_ps = np.array([0.019034035926478,
0.019189677653876,
0.023100228372281,
0.026733794722099,
0.041877913482873,
0.050822416512759,
0.050930762230683,
0.055710915830001,
0.056004725131473,
0.062393785718779,
0.094201744418697,])
# ALG. DEG.: 7
# PTS CARD.: 12
# NEG. W. : 0
# OUT PTS. : 0
# M.E.INF. : 5.1e-16
elif deg <= 7:
quad_ps = np.array([[0.062382265094402, 0.067517867073916,],
[0.067517867073916, 0.870099867831682,],
[0.870099867831682, 0.062382265094402,],
[0.055225456656927, 0.321502493851982,],
[0.321502493851982, 0.623272049491092,],
[0.623272049491092, 0.055225456656927,],
[0.034324302945097, 0.660949196186736,],
[0.660949196186736, 0.304726500868167,],
[0.304726500868167, 0.034324302945097,],
[0.515842334353592, 0.277716166976392,],
[0.277716166976392, 0.206441498670016,],
[0.206441498670016, 0.515842334353592,],])
weights_ps = np.array([0.026517028157436,
0.026517028157436,
0.026517028157436,
0.043881408714446,
0.043881408714446,
0.043881408714446,
0.028775042784982,
0.028775042784982,
0.028775042784982,
0.067493187009803,
0.067493187009803,
0.067493187009803,])
#ALG. DEG.: 8
# PTS CARD.: 16
# NEG. W. : 0
# OUT PTS. : 0
# M.E.INF. : 8.0e-16
elif deg <= 8:
quad_ps = np.array([[0.333333333333333, 0.333333333333333,],
[0.459292588292723, 0.459292588292723,],
[0.459292588292723, 0.081414823414554,],
[0.081414823414554, 0.459292588292723,],
[0.170569307751760, 0.170569307751760,],
[0.170569307751760, 0.658861384496480,],
[0.658861384496480, 0.170569307751760,],
[0.050547228317031, 0.050547228317031,],
[0.050547228317031, 0.898905543365938,],
[0.898905543365938, 0.050547228317031,],
[0.008394777409958, 0.263112829634638,],
[0.008394777409958, 0.728492392955404,],
[0.263112829634638, 0.008394777409958,],
[0.263112829634638, 0.728492392955404,],
[0.728492392955404, 0.008394777409958,],
[0.728492392955404, 0.263112829634638,],])
weights_ps = np.array([0.072157803838894,
0.047545817133642,
0.047545817133642,
0.047545817133642,
0.051608685267359,
0.051608685267359,
0.051608685267359,
0.016229248811599,
0.016229248811599,
0.016229248811599,
0.013615157087217,
0.013615157087217,
0.013615157087217,
0.013615157087217,
0.013615157087217,
0.013615157087217,])
# ALG. DEG.: 9
# PTS CARD.: 19
# NEG. W. : 0
# OUT PTS. : 0
# M.E.INF. : 3.3e-16
elif deg <= 9:
quad_ps = np.array([[0.333333333333333, 0.333333333333333,],
[0.437089591492937, 0.437089591492937,],
[0.437089591492937, 0.125820817014127,],
[0.125820817014127, 0.437089591492937,],
[0.188203535619033, 0.188203535619033,],
[0.188203535619033, 0.623592928761935,],
[0.623592928761935, 0.188203535619033,],
[0.489682519198738, 0.489682519198738,],
[0.489682519198738, 0.020634961602525,],
[0.020634961602525, 0.489682519198738,],
[0.044729513394453, 0.044729513394453,],
[0.044729513394453, 0.910540973211095,],
[0.910540973211095, 0.044729513394453,],
[0.036838412054736, 0.221962989160766,],
[0.036838412054736, 0.741198598784498,],
[0.221962989160766, 0.036838412054736,],
[0.221962989160766, 0.741198598784498,],
[0.741198598784498, 0.036838412054736,],
[0.741198598784498, 0.221962989160766,],])
weights_ps = np.array([0.048567898141399,
0.038913770502387,
0.038913770502387,
0.038913770502387,
0.039823869463605,
0.039823869463605,
0.039823869463605,
0.015667350113570,
0.015667350113570,
0.015667350113570,
0.012788837829349,
0.012788837829349,
0.012788837829349,
0.021641769688645,
0.021641769688645,
0.021641769688645,
0.021641769688645,
0.021641769688645,
0.021641769688645,])
# ALG. DEG.: 10
# PTS CARD.: 24
# NEG. W. : 0
# OUT PTS. : 0
# M.E.INF. : 7.2e-16
elif deg <= 10:
quad_ps = np.array([[0.505505073735291, 0.207761165754848,],
[0.275423850244130, 0.481232890624642,],
[0.264815316514968, 0.275863340893160,],
[0.753294027762542, 0.109549598555855,],
[0.524336825589244, 0.364197444303393,],
[0.295304455358511, 0.642033653186627,],
[0.106146429902900, 0.767776801700240,],
[0.634918323792007, 0.036036266787908,],
[0.387296579139604, 0.084198522115544,],
[0.169299274889665, 0.109994390556304,],
[0.080491894656106, 0.579663251054863,],
[0.095379208487722, 0.339472903118006,],
[0.928994869857879, 0.047768381772022,],
[0.747265917288688, 0.223763587742759,],
[0.503658250759440, 0.487984378053975,],
[0.161346504998910, 0.838653495001090,],
[0.029553592846823, 0.930498469002631,],
[0.868543869430765, 0.003810257085464,],
[0.393667744707220, 0,],
[0.176907306255590, 0.010939142057120,],
[0.035319656252586, 0.039099745550423,],
[ 0, 0.777575184294291,],
[ 0, 0.463743838674305,],
[0.030573404093099, 0.193059032242519,],])
weights_ps = np.array([0.043362019313832,
0.047633278635675,
0.042207221279855,
0.026365190704420,
0.037039823668390,
0.027457802196927,
0.026268329551206,
0.021481164696040,
0.031343962650457,
0.028987070299350,
0.033093067237630,
0.030871122933098,
0.007304164611561,
0.016151301011729,
0.009779706108761,
0.005533473391124,
0.007601547013006,
0.005333345637956,
0.005950152407118,
0.007423311823340,
0.008827922296481,
0.006699540392928,
0.007578130958783,
0.015707351180334,])
# ALG. DEG.: 11
# PTS CARD.: 27
# NEG. W. : 0
# OUT PTS. : 0
# M.E.INF. : 3.6e-15
elif deg<=11:
quad_ps = np.array([[0.464945647736940, 0.291338594369424,],
[0.320819579094830, 0.536342281120847,],
[0.513531434334472, 0.124544059105441,],
[0.287903102248196, 0.227899558843475,],
[0.266771680715777, 0.411324991789047,],
[0.116989764133234, 0.319097378146819,],
[0.816262337159688, 0.027719522918619,],
[0.569384861953280, 0.349929143342886,],
[0.372727698616291, 0.598954396299342,],
[0.026807150626773, 0.815629696932682,],
[0.700992679496452, 0.141181197309528,],
[0.327198781575529, 0.081721404855382,],
[0.136670835343905, 0.130354530319427,],
[0.138280002042923, 0.710278681077616,],
[0.022592651051307, 0.389139811133194,],
[0.936148935146756, 0.032899822292186,],
[0.804549747476155, 0.164292867157135,],
[0.619484315331352, 0.378021638913369,],
[0.166556144920606, 0.803648340539039,],
[0.033268560622678, 0.935514342858971,],
[0.619248732321101, 0.026297199713764,],
[0.396597316695865, 0.014354532010931,],
[0.168929709822902, 0.022120535196162,],
[0.032916403879000, 0.034222771841359,],
[0.025660186833052, 0.617588731712772,],
[0.124171485868015, 0.531419601540800,],
[0.025252704638304, 0.174005716730323,],])
weights_ps = np.array([0.034120689978746,
0.031096575055627,
0.028322942561350,
0.033071222942481,
0.029305884203705,
0.027495506358711,
0.011821029782882,
0.027485999004422,
0.016298436572454,
0.011556190176811,
0.026030267669060,
0.021298852449058,
0.022769129560075,
0.024595497454187,
0.013361393587366,
0.006552967426044,
0.013797950075090,
0.005637535607855,
0.013378318081627,
0.006687154643231,
0.014717279053217,
0.009179442195068,
0.010688904048957,
0.007274054340281,
0.014360888683764,
0.027060738237627,
0.012035150250304,])
# ALG. DEG.: 12
# PTS CARD.: 32
# NEG. W. : 0
# OUT PTS. : 0
# M.E.INF. : 1.6e-15
elif deg <= 12:
quad_ps = np.array([[0.379860210934020, 0.210785259391404,],
[0.301417093209093, 0.409786577770025,],
[0.558025289531203, 0.213777432530060,],
[0.125122995058104, 0.619381257362556,],
[0.211179399098049, 0.244982965093490,],
[0.854314749475804, 0.071871496101589,],
[0.717881858980523, 0.203768481077730,],
[0.466317874623231, 0.408963804491245,],
[0.250155003353392, 0.627682615680314,],
[0.079955384841381, 0.826003314017560,],
[0.710081259568365, 0.064413220382261,],
[0.497320633777966, 0.070566724344037,],
[0.260770682565629, 0.095428585810585,],
[0.089602705800587, 0.116386499067277,],
[0.023088148766116, 0.749189739790679,],
[0.129532969004336, 0.422605657433460,],
[0.093448087604441, 0.243458133948800,],
[0.955269193570060, 0.023551733249579,],
[0.845935398373144, 0.154064601626856,],
[0.616009296172675, 0.361181591189672,],
[0.393165103196048, 0.581689214740147,],
[0.189206330617159, 0.788601719223132,],
[0.043010560106405, 0.945475073220971,],
[0.858158884215331, 0,],
[0.627315319232412, 0,],
[0.363846604460775, 0.014566514788347,],
[0.155570668968980, 0.021152223383122,],
[0.029754117496842, 0.027110971356256,],
[ 0, 0.927348974483950,],
[0.025716283623694, 0.544446676271925,],
[0.024506286636990, 0.332129083947645,],
[0.009229690905965, 0.146044961672176,],])
weights_ps = np.array([0.029718916975568,
0.037611031301662,
0.031582273211328,
0.025482462438394,
0.023749787662654,
0.011245373099579,
0.019786802896486,
0.029994853663553,
0.026676041524410,
0.015264586206036,
0.020640943697731,
0.024074402518454,
0.022968921082896,
0.015287638802019,
0.010842542708506,
0.027073436306584,
0.013971867159940,
0.003337950013684,
0.003857246186812,
0.012549586713843,
0.014072779302607,
0.010310002059841,
0.003559875718040,
0.003422767327172,
0.004827354371218,
0.009272740210803,
0.009241842905615,
0.005254663367801,
0.002444024907330,
0.014084827229865,
0.012452036600754,
0.005340421828814,])
# ALG. DEG.: 13
# PTS CARD.: 36
# NEG. W. : 0
# OUT PTS. : 0
# M.E.INF. : 3.1e-16
elif deg <= 13:
quad_ps = np.array([[0.026016788997568, 0.024022226884121,],
[0.024022226605628, 0.949960984299581,],
[0.949960983828827, 0.026016789189575,],
[0.018883630668694, 0.122080867325125,],
[0.122080865615097, 0.859035503703663,],
[0.859035502492874, 0.018883629732181,],
[0.131639216755139, 0.022874709056512,],
[0.022874709316315, 0.845486073780362,],
[0.845486073324166, 0.131639217770325,],
[0.020731531453875, 0.280737807897762,],
[0.280737804477865, 0.698530664767439,],
[0.698530660028288, 0.020731531572896,],
[0.476642854053483, 0.504849500035025,],
[0.504849495463474, 0.018507646297269,],
[0.018507645858560, 0.476642857835612,],
[0.302387014801126, 0.019975751509092,],
[0.019975751174692, 0.677637233570465,],
[0.677637231251634, 0.302387017597125,],
[0.101539777415502, 0.119028238394273,],
[0.119028239511688, 0.779431983178414,],
[0.779431987279475, 0.101539774383865,],
[0.249614419434177, 0.103589969002955,],
[0.103589967812852, 0.646795611281056,],
[0.646795616892277, 0.249614415590636,],
[0.102029245899726, 0.276888289616486,],
[0.276888294228863, 0.621082463846217,],
[0.621082464001206, 0.102029246368156,],
[0.226789276022037, 0.233728374217555,],
[0.233728371859891, 0.539482360682531,],
[0.539482355318466, 0.226789276022037,],
[0.437409498131038, 0.095992085884562,],
[0.095992083695018, 0.466598416159025,],
[0.466598421189779, 0.437409494682125,],
[0.380758577881083, 0.227855355201997,],
[0.227855351201257, 0.391386077299870,],
[0.391386069899954, 0.380758578955005,],])
weights_ps = np.array([0.004039989641807,
0.004039989606522,
0.004039989687279,
0.006446014454400,
0.006446014363749,
0.006446014190778,
0.008280121837020,
0.008280121926735,
0.008280121854134,
0.009511566732096,
0.009511566332444,
0.009511566783975,
0.009679825498283,
0.009679825644521,
0.009679825427656,
0.009791898538588,
0.009791898400449,
0.009791898464615,
0.015140748101228,
0.015140748276015,
0.015140747908421,
0.019082032132037,
0.019082032020072,
0.019082031741448,
0.019099669161417,
0.019099668693700,
0.019099669240405,
0.020423575649243,
0.020423574925769,
0.020423575027017,
0.020542846050484,
0.020542845620860,
0.020542845791993,
0.024628380057602,
0.024628380363337,
0.024628379853901,])
# ALG. DEG.: 14
# PTS CARD.: 42
# NEG. W. : 0
# OUT PTS. : 0
# M.E.INF. : 4.4e-16
elif deg<=14:
quad_ps = np.array([[0.177205532412543 , 0.177205532412543,],
[0.177205532412543 , 0.645588935174913,],
[0.645588935174913 , 0.177205532412543,],
[0.417644719340454 , 0.417644719340454,],
[0.417644719340454 , 0.164710561319092,],
[0.164710561319092 , 0.417644719340454,],
[0.061799883090873 , 0.061799883090873,],
[0.061799883090873 , 0.876400233818255,],
[0.876400233818255 , 0.061799883090873,],
[0.488963910362179 , 0.488963910362179,],
[0.488963910362179 , 0.022072179275643,],
[0.022072179275643 , 0.488963910362179,],
[0.273477528308839 , 0.273477528308839,],
[0.273477528308839 , 0.453044943382323,],
[0.453044943382323 , 0.273477528308839,],
[0.019390961248701 , 0.019390961248701,],
[0.019390961248701 , 0.961218077502598,],
[0.961218077502598 , 0.019390961248701,],
[0.298372882136258 , 0.686980167808088,],
[0.298372882136258 , 0.014646950055654,],
[0.686980167808088 , 0.298372882136258,],
[0.686980167808088 , 0.014646950055654,],
[0.014646950055654 , 0.298372882136258,],
[0.014646950055654 , 0.686980167808088,],
[0.057124757403648 , 0.172266687821356,],
[0.057124757403648 , 0.770608554774996,],
[0.172266687821356 , 0.057124757403648,],
[0.172266687821356 , 0.770608554774996,],
[0.770608554774996 , 0.057124757403648,],
[0.770608554774996 , 0.172266687821356,],
[0.336861459796345 , 0.570222290846683,],
[0.336861459796345 , 0.092916249356972,],
[0.570222290846683 , 0.336861459796345,],
[0.570222290846683 , 0.092916249356972,],
[0.092916249356972 , 0.336861459796345,],
[0.092916249356972 , 0.570222290846683,],
[0.001268330932872 , 0.118974497696957,],
[0.001268330932872 , 0.879757171370171,],
[0.118974497696957 , 0.001268330932872,],
[0.118974497696957 , 0.879757171370171,],
[0.879757171370171 , 0.001268330932872,],
[0.879757171370171 , 0.118974497696957,],
])
weights_ps = np.array([0.021081294368497,
0.021081294368497,
0.021081294368497,
0.016394176772063,
0.016394176772063,
0.016394176772063,
0.007216849834888,
0.007216849834888,
0.007216849834888,
0.010941790684714,
0.010941790684714,
0.010941790684714,
0.025887052253646,
0.025887052253646,
0.025887052253646,
0.002461701801200,
0.002461701801200,
0.002461701801200,
0.007218154056767,
0.007218154056767,
0.007218154056767,
0.007218154056767,
0.007218154056767,
0.007218154056767,
0.012332876606282,
0.012332876606282,
0.012332876606282,
0.012332876606282,
0.012332876606282,
0.012332876606282,
0.019285755393530,
0.019285755393530,
0.019285755393530,
0.019285755393530,
0.019285755393530,
0.019285755393530,
0.002505114419250,
0.002505114419250,
0.002505114419250,
0.002505114419250,
0.002505114419250,
0.002505114419250,])
# ALG. DEG.: 15
# PTS CARD.: 46
# NEG. W. : 0
# OUT PTS. : 0
# M.E.INF. : 5.0e-16
elif deg<=15:
quad_ps = np.array([[0.333333292261712 , 0.333333369225872,],
[0.018434834053485, 0.021020611606486,],
[0.021020619858791, 0.960544553925707,],
[0.960544579872547, 0.018434815403186,],
[0.094469494871460, 0.014008479173568,],
[0.014008449561943, 0.891522111110738,],
[0.891522077853913, 0.094469378400658,],
[0.221059623335565, 0.014600180511535,],
[0.014600162740125, 0.764340360199225,],
[0.764340671414178, 0.221059339300118,],
[0.018316134980082, 0.106831540445692,],
[0.106831572649003, 0.874852289591818,],
[0.874852363873429, 0.018316144510145,],
[0.384111880036756, 0.013506555908128,],
[0.013506550559232, 0.602381757760966,],
[0.602381907561370, 0.384111551382989,],
[0.017609578493398, 0.246869564037977,],
[0.246869635891990, 0.735520785115458,],
[0.735520958397238, 0.017609584738097,],
[0.016211095448872, 0.420027449315563,],
[0.420027557266492, 0.563761341880283,],
[0.563761608884687, 0.016211104648385,],
[0.094583554095873, 0.078193742333583,],
[0.078193645831044, 0.827222782704063,],
[0.827222507563533, 0.094583585587112,],
[0.223020503669574, 0.069024708216097,],
[0.069024590188699, 0.707954806600518,],
[0.707955491881565, 0.223020657547391,],
[0.091368656394297, 0.197441541806722,],
[0.197441432426124, 0.711189907126281,],
[0.711189569389399, 0.091368684008223,],
[0.384530855617108, 0.073097727448546,],
[0.073097710649979, 0.542371300752678,],
[0.542371248933847, 0.384531035703955,],
[0.215038812389832, 0.155893061854053,],
[0.155892843158962, 0.629068363385965,],
[0.629068887420657, 0.215038957479725,],
[0.085318950896480, 0.359007499441052,],
[0.359007386827243, 0.555673632624284,],
[0.555673357289607, 0.085318972494618,],
[0.204230402773116, 0.286157186802204,],
[0.286156970552324, 0.509612567484153,],
[0.509612717585779, 0.204230501683514,],
[0.363891035835017, 0.181085979988353,],
[0.181085896307873, 0.455023141283622,],
[0.455022970575782, 0.363891085598292],])
weights_ps = np.array([0.023374815587576,
0.002513935895072,
0.002513935696375,
0.002513932394528,
0.003799338368173,
0.003799328996728,
0.003799347373062,
0.005366066243257,
0.005366055725637,
0.005365988392369,
0.005415430611740,
0.005415432920521,
0.005415430762611,
0.006124359445576,
0.006124357039502,
0.006124354635641,
0.007198920179902,
0.007198922245045,
0.007198920131792,
0.007491900207990,
0.007491903938849,
0.007491902321217,
0.009616336936211,
0.009616334951196,
0.009616347198282,
0.010417333977873,
0.010417320084083,
0.010417255721889,
0.014288484973080,
0.014288484686990,
0.014288489044840,
0.014515833589325,
0.014515833669194,
0.014515842330252,
0.015120138042124,
0.015120129490667,
0.015120211213143,
0.016255761920007,
0.016255768356984,
0.016255759723645,
0.020093565047808,
0.020093572550897,
0.020093626230188,
0.020657675325257,
0.020657652654019,
0.020657663168879,
])
# ALG. DEG.: 16
# PTS CARD.: 52
# NEG. W. : 0
# OUT PTS. : 0
# M.E.INF. : 5.7e-16
elif deg<=16:
quad_ps = np.array([[0.333333258825058, 0.333333416793498,],
[0.015961002222668, 0.016883133661795,],
[0.016883138683116, 0.967155848242694,],
[0.967155874801574, 0.015961001750531,],
[0.003821752645372, 0.099349798885250,],
[0.099349805946201, 0.896828443482067,],
[0.896828514177594, 0.003821660092936,],
[0.092621638406882, 0.004717676153821,],
[0.004717717821601, 0.902660618534333,],
[0.902660635509004, 0.092621625598950,],
[0.009809782870055, 0.246739276017130,],
[0.246739291498786, 0.743450929200298,],
[0.743450875758368, 0.009809765583970,],
[0.234453465539762, 0.012521206522120,],
[0.012521215962458, 0.753025327539011,],
[0.753025384905626, 0.234453392434268,],
[0.051657112974377, 0.057775750119376,],
[0.057775819366716, 0.890567064125437,],
[0.890567194917750, 0.051656949685233,],
[0.015979112506190, 0.413443247683559,],
[0.413443261309728, 0.570577625472078,],
[0.570577597706887, 0.015979116105793,],
[0.396856249731831, 0.016762648247774,],
[0.016762650225796, 0.586381091244489,],
[0.586381123891194, 0.396856228163050,],
[0.140368578298826, 0.050399889980290,],
[0.050399962289145, 0.809231429420804,],
[0.809231545448009, 0.140368456667959,],
[0.048645802147073, 0.153602435235487,],
[0.153602501486406, 0.797751700040076,],
[0.797751821638013, 0.048645704254426,],
[0.067545529600335, 0.293562763267697,],
[0.293562815361712, 0.638891644704478,],
[0.638891715657272, 0.067545510682958,],
[0.160475924195127, 0.276119726602890,],
[0.276119919814122, 0.563404080925372,],
[0.563404080925372, 0.160475943078973,],
[0.280462494123583, 0.077279816912928,],
[0.077279847608037, 0.642257629182080,],
[0.642257731649287, 0.280462425269745,],
[0.147356656075135, 0.148012282095027,],
[0.148012388896020, 0.704630946772244,],
[0.704630995778555, 0.147356574993520,],
[0.424740426214290, 0.208953868767089,],
[0.208953731775949, 0.366305584744694,],
[0.366305807793043 , 0.424740413497298,],
[0.451724222556604 , 0.087033369844957,],
[0.087033362530209 , 0.461242369666383,],
[0.461242460733382 , 0.451724181218181,],
[0.288318499660714 , 0.190229112412625,],
[0.190229156603659 , 0.521452304852626,],
[0.521452426537516 , 0.288318431951265,],
])
weights_ps = np.array([0.018316135669004,
0.001772150029681,
0.001772151722784,
0.001772148935300,
0.002008767799702,
0.002008767631002,
0.002008754284457,
0.002095346435833,
0.002095353096169,
0.002095355715493,
0.004281371413029,
0.004281370434519,
0.004281365361665,
0.004989495641730,
0.004989499316594,
0.004989502497693,
0.005106272600576,
0.005106275247590,
0.005106269839501,
0.007040733822684,
0.007040734349707,
0.007040733723833,
0.007314960035992,
0.007314961825297,
0.007314962044461,
0.008028237177399,
0.008028241671967,
0.008028247387425,
0.008512172726878,
0.008512171723099,
0.008512168385463,
0.012477872580774,
0.012477876642041,
0.012477872833662,
0.014099575787101,
0.014099594524735,
0.014099588335917,
0.014135293879459,
0.014135298391321,
0.014135299057647,
0.014613064132682,
0.014613072264173,
0.014613073256787,
0.017003482855882,
0.017003487686414,
0.017003475643666,
0.017117829478258,
0.017117827400844,
0.017117828373122,
0.019964633973873,
0.019964640930830,
0.019964633424283,])
# ALG. DEG.: 17
# PTS CARD.: 57
# NEG. W. : 0
# OUT PTS. : 0
# M.E.INF. : 5.8e-16
elif deg<=17:
quad_ps = np.array([[0.014720966195627 , 0.017639984855507,],
[0.017639984855507, 0.967639048948867,],
[0.967639048948867, 0.014720966195627,],
[0.075827872337700, 0.007697475843772,],
[0.007697475843772, 0.916474651818528,],
[0.916474651818528, 0.075827872337700,],
[0.310585516558464, 0.008320091951046,],
[0.008320091951046, 0.681094391490490,],
[0.681094391490490, 0.310585516558464,],
[0.014488314624940, 0.090164039580071,],
[0.090164039580071, 0.895347645794988,],
[0.895347645794988, 0.014488314624940,],
[0.178143852253020, 0.016423858046516,],
[0.016423858046516, 0.805432289700464,],
[0.805432289700464, 0.178143852253020,],
[0.466133550795935, 0.012335581768738,],
[0.012335581768738, 0.521530867435327,],
[0.521530867435327, 0.466133550795935,],
[0.014736566166282, 0.209325171157458,],
[0.209325171157458, 0.775938262676260,],
[0.775938262676260, 0.014736566166282,],
[0.014332535547880, 0.358602315795424,],
[0.358602315795424, 0.627065148656696,],
[0.627065148656696, 0.014332535547880,],
[0.075303349390642, 0.055968132994742,],
[0.055968132994742, 0.868728517614616,],
[0.868728517614616, 0.075303349390642,],
[0.317339393501728, 0.051694878418799,],
[0.051694878418799, 0.630965728079473,],
[0.630965728079473, 0.317339393501728,],
[0.075354265490355, 0.154598211665730,],
[0.154598211665730, 0.770047522843915,],
[0.770047522843915, 0.075354265490355,],
[0.182570774440877 , 0.266530059635147,],
[0.266530059635147, 0.550899165923976,],
[0.550899165923976, 0.182570774440877,],
[0.179710032722075, 0.081586227754906,],
[0.081586227754906, 0.738703739523019,],
[0.738703739523019, 0.179710032722075,],
[0.175807941715677, 0.180353640520786,],
[0.180353640520786, 0.643838417763537,],
[0.643838417763537, 0.175807941715677,],
[0.458731499688784, 0.474126007719327,],
[0.474126007719327 , 0.067142492591890,],
[0.067142492591890 , 0.458731499688784,],
[0.075319692074374 , 0.293754105362968,],
[0.293754105362968 , 0.630926202562658,],
[0.630926202562658 , 0.075319692074374,],
[0.163305177925385 , 0.384251187765942,],
[0.384251187765942 , 0.452443634308674,],
[0.452443634308674 , 0.163305177925385,],
[0.311813568699615 , 0.139501525996608,],
[0.139501525996608 , 0.548684905303777,],
[0.548684905303777 , 0.311813568699615,],
[0.306048259112028 , 0.267720653545962,],
[0.267720653545962 , 0.426231087342010,],
[0.426231087342010 , 0.306048259112028,],
])
weights_ps = np.array([0.001688518004050,
0.001688518004050,
0.001688518004050,
0.001909962835097,
0.001909962835097,
0.001909962835097,
0.003312013040721,
0.003312013040721,
0.003312013040721,
0.003642450367437,
0.003642450367437,
0.003642450367437,
0.004982501236703,
0.004982501236703,
0.004982501236703,
0.005138172549298,
0.005138172549298,
0.005138172549298,
0.005154745651889,
0.005154745651889,
0.005154745651889,
0.005801114568400,
0.005801114568400,
0.005801114568400,
0.006234871893741,
0.006234871893741,
0.006234871893741,
0.009816239757766,
0.009816239757766,
0.009816239757766,
0.010050753537573,
0.010050753537573,
0.010050753537573,
0.010453022784283,
0.010453022784283,
0.010453022784283,
0.010666123835802,
0.010666123835802,
0.010666123835802,
0.011874688594592,
0.011874688594592,
0.011874688594592,
0.012388512004066,
0.012388512004066,
0.012388512004066,
0.012792785121136,
0.012792785121136,
0.012792785121136,
0.015655429401651,
0.015655429401651,
0.015655429401651,
0.015795181274719,
0.015795181274719,
0.015795181274719,
0.019309580207745,
0.019309580207745,
0.019309580207745,])
# ALG. DEG.: 18
# PTS CARD.: 66
# NEG. W. : 0
# OUT PTS. : 0
# M.E.INF. : 6.1e-16
elif deg<=18:
quad_ps = np.array([[0.003697809640551, 0.074357923508124,],
[0.074357923508124 , 0.921944266851325,],
[0.921944266851325 , 0.003697809640551,],
[0.014914399227999 , 0.013690913073363,],
[0.013690913073363 , 0.971394687698638,],
[0.971394687698638 , 0.014914399227999,],
[0.001697399962193 , 0.208913690615461,],
[0.208913690615461 , 0.789388909422346,],
[0.789388909422346 , 0.001697399962193,],
[0.080662083946625 , 0.008243532690291,],
[0.008243532690291 , 0.911094383363083,],
[0.911094383363083 , 0.080662083946625,],
[0.198747901402311 , 0.006976595096183,],
[0.006976595096183 , 0.794275503501506,],
[0.794275503501506 , 0.198747901402311,],
[0.346702719147276 , 0.009059771353480,],
[0.009059771353480 , 0.644237509499244,],
[0.644237509499244 , 0.346702719147276,],
[0.048634633387104 , 0.055791052971747,],
[0.055791052971747 , 0.895574313641149,],
[0.895574313641149 , 0.048634633387104,],
[0.012831862984945 , 0.344692548477970,],
[0.344692548477970 , 0.642475588537085,],
[0.642475588537085 , 0.012831862984945,],
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[0.044707679385502 , 0.816673536554709,],
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[0.709190252000743 , 0.045591174493061,],
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[0.666148899272832 , 0.220575279425483,],
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[0.540756641647415 , 0.071334879410098,],
[0.224126910324972 , 0.213289800009619,],
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[0.137937509976457 , 0.510443440067901,],
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[0.465125819964767 , 0.174111839467500,],
[0.174111839467500 , 0.360762340567732,],
[0.311300128982519 , 0.270073629388671,],
[0.270073629388671 , 0.418626241628809,],
[0.418626241628809 , 0.311300128982519,],])
weights_ps= np.array([0.001318895563441,
0.001318895563441,
0.001318895563441,
0.001337453325498,
0.001337453325498,
0.001337453325498,
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# ALG. DEG.: 19
# PTS CARD.: 70
# NEG. W. : 0
# OUT PTS. : 0
# M.E.INF. : 4.2e-16
elif deg<=19:
quad_ps=np.array([[0.333333333333333, 0.333333333333333,],
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[0.241019074102766, 0.267083117991291,],
[0.267083117991291, 0.491897807905943,],
[0.491897807905943, 0.241019074102766,],
])
weights_ps=np.array([0.015231480880074,
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#ALG. DEG.: 20
# PTS CARD.: 78
# NEG. W. : 0
# OUT PTS. : 0
# M.E.INF. : 4.9e-16
elif deg<=20:
quad_ps=np.array([[0.007903681341623, 0.010892617666330,],
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[0.407445324376853, 0.261691763476095,],
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weights_ps=np.array([0.000569495307449,
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#ALG. DEG.: 21
# PTS CARD.: 85
# NEG. W. : 0
# OUT PTS. : 0
# M.E.INF. : 4.6e-16
elif deg<=21:
quad_ps=np.array([[0.333333333333333, 0.333333333333333,],
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# PTS CARD.: 93
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#ALG. DEG.: 23
#PTS CARD.: 100
#NEG. W. : 0
#OUT PTS. : 0
#M.E.INF. : 6.7e-16
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0.007615697891794,
0.007615697891794,
0.007742936659723,
0.007742936659723,
0.007742936659723,
0.007994478718277,
0.007994478718277,
0.007994478718277,
0.009464517952946,
0.009464517952946,
0.009464517952946,
0.009874040678367,
0.009874040678367,
0.009874040678367,
0.010333890779833,
0.010333890779833,
0.010333890779833,
0.010399171332398,
0.010399171332398,
0.010399171332398,
0.011787787420372,
0.011787787420372,
0.011787787420372,
0.011845927154352,
0.011845927154352,
0.011845927154352,])
#ALG. DEG.: 24
# PTS CARD.: 109
# NEG. W. : 0
#OUT PTS. : 0
#M.E.INF. : 7.8e-16
elif deg<=24:
quad_ps=np.array([[0.333333333333333, 0.333333333333333,],
[0.007277442182286, 0.001871780631611,],
[0.001871780631611 , 0.990850777186103,],
[0.990850777186103, 0.007277442182286,],
[0.093762141740160, 0.002225841776308,],
[0.002225841776308, 0.904012016483533,],
[0.904012016483533, 0.093762141740160,],
[0.027549956725482, 0.964825831627800,],
[0.964825831627800, 0.007624211646718,],
[0.007624211646718, 0.027549956725482,],
[0.038849156576576, 0.009992214684680,],
[0.009992214684680, 0.951158628738743,],
[0.951158628738743, 0.038849156576576,],
[0.084582464342299, 0.907583350374655,],
[0.907583350374655, 0.007834185283046,],
[0.007834185283046, 0.084582464342299,],
[0.169711974261767, 0.008550947694910,],
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[0.821737078043323, 0.169711974261767,],
[0.261114259888929, 0.007355235311152,],
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[0.824005083539038, 0.008075211329878,],
[0.008075211329878, 0.167919705131084,],
[0.366562445874965, 0.007005660169500,],
[0.007005660169500, 0.626431893955535,],
[0.626431893955535, 0.366562445874965,],
[0.271431359408183, 0.720628297746086,],
[0.720628297746086, 0.007940342845731,],
[0.007940342845731, 0.271431359408183,],
[0.483415122297192, 0.007361193566840,],
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[0.509223684135968, 0.483415122297192,],
[0.387957374245692, 0.604329908418651,],
[0.604329908418651, 0.007712717335657,],
[0.007712717335657, 0.387957374245692,],
[0.052053611601208, 0.907672123610023,],
[0.907672123610023, 0.040274264788769,],
[0.040274264788769, 0.052053611601208,],
[0.229018909213726, 0.089345256498108,],
[0.089345256498108, 0.681635834288166,],
[0.681635834288166, 0.229018909213726,],
[0.094914195571636, 0.026796719091792,],
[0.026796719091792, 0.878289085336572,],
[0.878289085336572, 0.094914195571636,],
[0.123228014736413, 0.835184452859200,],
[0.835184452859200, 0.041587532404387,],
[0.041587532404387, 0.123228014736413,],
[0.174126507274860, 0.044130628886304,],
[0.044130628886304, 0.781742863838836,],
[0.781742863838836, 0.174126507274860,],
[0.272180746005687, 0.037468721939443,],
[0.037468721939443, 0.690350532054870,],
[0.690350532054870, 0.272180746005687,],
[0.099006351507515, 0.081968796781302,],
[0.081968796781302, 0.819024851711183,],
[0.819024851711183, 0.099006351507515,],
[0.218932787550637, 0.739314412421514,],
[0.739314412421514, 0.041752800027848,],
[0.041752800027848, 0.218932787550637,],
[0.385457856195294, 0.037011409874506,],
[0.037011409874506, 0.577530733930199,],
[0.577530733930199, 0.385457856195294,],
[0.453931532973698, 0.507124120567042,],
[0.507124120567042, 0.038944346459259,],
[0.038944346459259, 0.453931532973698,],
[0.331414067992492, 0.627872100319266,],
[0.627872100319266, 0.040713831688242,],
[0.040713831688242, 0.331414067992492,],
[0.175418478700221, 0.109788999485381,],
[0.109788999485381, 0.714792521814398,],
[0.714792521814398, 0.175418478700221,],
[0.299424606258227, 0.089517741605651,],
[0.089517741605651, 0.611057652136122,],
[0.611057652136122, 0.299424606258227,],
[0.164438284214270 , 0.735720413124064,],
[0.735720413124064 , 0.099841302661666,],
[0.099841302661666 , 0.164438284214270,],
[0.369724758939287 , 0.463127807453673,],
[0.463127807453673 , 0.167147433607040,],
[0.167147433607040 , 0.369724758939287,],
[0.406369061777283 , 0.090716786111306,],
[0.090716786111306 , 0.502914152111410,],
[0.502914152111410 , 0.406369061777283,],
[0.267420664299268 , 0.632902725169850,],
[0.632902725169850 , 0.099676610530882,],
[0.099676610530882 , 0.267420664299268,],
[0.383204107909751 , 0.521623720050690,],
[0.521623720050690 , 0.095172172039558,],
[0.095172172039558 , 0.383204107909751,],
[0.178724492320245 , 0.192031135757774,],
[0.192031135757774 , 0.629244371921981,],
[0.629244371921981 , 0.178724492320245,],
[0.282829128593355 , 0.537642437490313,],
[0.537642437490313 , 0.179528433916331,],
[0.179528433916331 , 0.282829128593355,],
[0.270606479254229 , 0.161339950052654,],
[0.161339950052654 , 0.568053570693116,],
[0.568053570693116 , 0.270606479254229,],
[0.370874346744923 , 0.164548573538222,],
[0.164548573538222 , 0.464577079716854,],
[0.464577079716854 , 0.370874346744923,],
[0.363840811889283 , 0.383367191770048,],
[0.383367191770048 , 0.252791996340669,],
[0.252791996340669 , 0.363840811889283,],
[0.275735321862771 , 0.252760449512090,],
[0.252760449512090 , 0.471504228625139,],
[0.471504228625139 , 0.275735321862771,],])
weights_ps=np.array([0.005340888466693,
0.000171536069217,
0.000171536069217,
0.000171536069217,
0.000611499851019,
0.000611499851019,
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0.002262440360081,
0.002262440360081,
0.002269801463134,
0.002269801463134,
0.002269801463134,
0.002372847723656,
0.002372847723656,
0.002372847723656,
0.002590268286687,
0.002590268286687,
0.002590268286687,
0.002655961616362,
0.002655961616362,
0.002655961616362,
0.002682097521483,
0.002682097521483,
0.002682097521483,
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0.004349701133107,
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0.004420101816684,
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0.004814566109945,
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0.004901626304942,
0.004901626304942,
0.004971408687914,
0.004971408687914,
0.004971408687914,
0.005374120368350,
0.005374120368350,
0.005374120368350,
0.005387636331802,
0.005387636331802,
0.005387636331802,
0.005891548876413,
0.005891548876413,
0.005891548876413,
0.006078383827052,
0.006078383827052,
0.006078383827052,
0.006472852618066,
0.006472852618066,
0.006472852618066,
0.006777449873740,
0.006777449873740,
0.006777449873740,
0.007337916246535,
0.007337916246535,
0.007337916246535,
0.007710227229200,
0.007710227229200,
0.007710227229200,
0.007757998897078,
0.007757998897078,
0.007757998897078,
0.007831294653005,
0.007831294653005,
0.007831294653005,
0.007963768755424,
0.007963768755424,
0.007963768755424,
0.008051766515040,
0.008051766515040,
0.008051766515040,
0.008329040212866,
0.008329040212866,
0.008329040212866,
0.009676539746181,
0.009676539746181,
0.009676539746181,
0.010229679318868,
0.010229679318868,
0.010229679318868,])
#ALG. DEG.: 25
# PTS CARD.: 117
# NEG. W. : 0
#OUT PTS. : 0
#M.E.INF. : 5.4e-16
else:
quad_ps=np.array([[0.013188177147405, 0.003079563840119,],
[0.003079563840119, 0.983732259012476,],
[0.983732259012476, 0.013188177147405,],
[0.002725962136131, 0.017104304759574,],
[0.017104304759574, 0.980169733104295,],
[0.980169733104295, 0.002725962136131,],
[0.062984002092479, 0.931371984168811,],
[0.931371984168811, 0.005644013738711,],
[0.005644013738711, 0.062984002092479,],
[0.052023800673154, 0.007437914960862,],
[0.007437914960862, 0.940538284365985,],
[0.940538284365985, 0.052023800673154,],
[0.220200206141671, 0.776414334424490,],
[0.776414334424490, 0.003385459433839,],
[0.003385459433839, 0.220200206141671,],
[0.030439556156815, 0.944856451527789,],
[0.944856451527789, 0.024703992315395,],
[0.024703992315395, 0.030439556156815,],
[0.113993174377526, 0.007471029315779,],
[0.007471029315779, 0.878535796306694,],
[0.878535796306694, 0.113993174377526,],
[0.342295210188022, 0.652613563397589,],
[0.652613563397589, 0.005091226414388,],
[0.005091226414388, 0.342295210188022,],
[0.130473991950560, 0.861524966076300,],
[0.861524966076300, 0.008001041973141,],
[0.008001041973141, 0.130473991950560,],
[0.200179308343867, 0.006507818683030,],
[0.006507818683030, 0.793312872973103,],
[0.793312872973103, 0.200179308343867,],
[0.307372363215434, 0.006352407094592,],
[0.006352407094592, 0.686275229689974,],
[0.686275229689974, 0.307372363215434,],
[0.276217326622710, 0.706370557783410,],
[0.706370557783410, 0.017412115593879,],
[0.017412115593879, 0.276217326622710,],
[0.422935483077427, 0.007562754695338,],
[0.007562754695338, 0.569501762227235,],
[0.569501762227235, 0.422935483077427,],
[0.453227003366671, 0.538998045885384,],
[0.538998045885384, 0.007774950747945,],
[0.007774950747945, 0.453227003366671,],
[0.190195202693624, 0.784036511910399,],
[0.784036511910399, 0.025768285395977,],
[0.025768285395977, 0.190195202693624,],
[0.036171829980613, 0.084456400529243,],
[0.084456400529243, 0.879371769490145,],
[0.879371769490145, 0.036171829980613,],
[0.076079438865904, 0.040507632612956,],
[0.040507632612956, 0.883412928521141,],
[0.883412928521141, 0.076079438865904,],
[0.149945977487858, 0.035835058933034,],
[0.035835058933034, 0.814218963579108,],
[0.814218963579108, 0.149945977487858,],
[0.150955341179003, 0.796913702682935,],
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[0.052130956138062, 0.150955341179003,],
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[0.032689779930829, 0.722526909092596,],
[0.722526909092596, 0.244783310976575,],
[0.170674433667943, 0.078755869338189,],
[0.078755869338189, 0.750569696993868,],
[0.750569696993868, 0.170674433667943,],
[0.371942611691943, 0.593428569491770,],
[0.593428569491770, 0.034628818816287,],
[0.034628818816287, 0.371942611691943,],
[0.351792010432224, 0.036352873144138,],
[0.036352873144138, 0.611855116423638,],
[0.611855116423638, 0.351792010432224,],
[0.098440061147215, 0.096959138605558,],
[0.096959138605558, 0.804600800247227,],
[0.804600800247227, 0.098440061147215,],
[0.260865026298108, 0.684089653184229,],
[0.684089653184229, 0.055045320517663,],
[0.055045320517663, 0.260865026298108,],
[0.366582144327067, 0.550781902551757,],
[0.550781902551757, 0.082635953121176,],
[0.082635953121176, 0.366582144327067,],
[0.468735987743839 , 0.041136822171029,],
[0.041136822171029 , 0.490127190085132,],
[0.490127190085132 , 0.468735987743839,],
[0.257617931613541 , 0.082486517285323,],
[0.082486517285323 , 0.659895551101136,],
[0.659895551101136 , 0.257617931613541,],
[0.184517952412834 , 0.712575925803732,],
[0.712575925803732 , 0.102906121783434,],
[0.102906121783434, 0.184517952412834,],
[0.281209118651228, 0.605257308197521,],
[0.605257308197521, 0.113533573151251,],
[0.113533573151251, 0.281209118651228,],
[0.173591491675633, 0.142209318699191,],
[0.142209318699191, 0.684199189625176,],
[0.684199189625176, 0.173591491675633,],
[0.442362027995822, 0.454988327657976,],
[0.454988327657976, 0.102649644346203,],
[0.102649644346203, 0.442362027995822,],
[0.359368226555798, 0.090795315699794,],
[0.090795315699794, 0.549836457744408,],
[0.549836457744408, 0.359368226555798,],
[0.182134268926742, 0.228667042140730,],
[0.228667042140730, 0.589198688932528,],
[0.589198688932528, 0.182134268926742,],
[0.267343042736282, 0.156184413818651,],
[0.156184413818651, 0.576472543445067,],
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[0.482299125389173, 0.172636048009442,],
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[0.265562227862875, 0.256802629703844,],
[0.256802629703844, 0.477635142433280,],
[0.477635142433280, 0.265562227862875,],
[0.362956385501777, 0.371550947373691,],
[0.371550947373691, 0.265492667124532,],
[0.265492667124532, 0.362956385501777
,],])
weights_ps=np.array([0.000263473905486,
0.000263473905486,
0.000263473905486,
0.000269189285624,
0.000269189285624,
0.000269189285624,
0.000856278646941,
0.000856278646941,
0.000856278646941,
0.000956166433485,
0.000956166433485,
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0.000994872257003,
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0.001351500875806,
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0.001411881071032,
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0.001457574586237,
0.001457574586237,
0.001457574586237,
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0.001573114391150,
0.001573114391150,
0.001627198874434,
0.001627198874434,
0.001627198874434,
0.001861532890749,
0.001861532890749,
0.001861532890749,
0.002153157369641,
0.002153157369641,
0.002153157369641,
0.002262567079481,
0.002262567079481,
0.002262567079481,
0.002281249610659,
0.002281249610659,
0.002281249610659,
0.002340138310305,
0.002340138310305,
0.002340138310305,
0.002820277990772,
0.002820277990772,
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0.002889211525387,
0.002889211525387,
0.002889211525387,
0.003289570675358,
0.003289570675358,
0.003289570675358,
0.003364826582921,
0.003364826582921,
0.003364826582921,
0.003787771217934,
0.003787771217934,
0.003787771217934,
0.004072917523167,
0.004072917523167,
0.004072917523167,
0.004540917619813,
0.004540917619813,
0.004540917619813,
0.004700447652154,
0.004700447652154,
0.004700447652154,
0.004762002272035,
0.004762002272035,
0.004762002272035,
0.005053604072634,
0.005053604072634,
0.005053604072634,
0.005429563403857,
0.005429563403857,
0.005429563403857,
0.005584492093144,
0.005584492093144,
0.005584492093144,
0.005886148432616,
0.005886148432616,
0.005886148432616,
0.006071202004239,
0.006071202004239,
0.006071202004239,
0.006276349463350,
0.006276349463350,
0.006276349463350,
0.006390720638049,
0.006390720638049,
0.006390720638049,
0.006623420693812,
0.006623420693812,
0.006623420693812,
0.006914120781756,
0.006914120781756,
0.006914120781756,
0.007964106081075,
0.007964106081075,
0.007964106081075,
0.008372978569252,
0.008372978569252,
0.008372978569252,
0.009387305276897,
0.009387305276897,
0.009387305276897,
0.009869002540093,
0.009869002540093,
0.009869002540093,
0.010143142179343,
0.010143142179343,
0.010143142179343,
0.010812671788974,
0.010812671788974,
0.010812671788974,])
return weights_ps, quad_ps