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def strang_fix_cowper_03():
weights, points = concat(s3(-frac(9, 16)), s2([frac(25, 48), frac(1, 5)]))
return T2Scheme("Strang-Fix-Cowper 3", weights, points, 3, source)
def lyness_jespersen_09():
weights, points = concat(
s3(frac(81, 320)),
s2(
[frac(1, 90), 0],
[frac(16, 225), frac(1, 2)],
[frac(2401, 14400), frac(1, 7)],
),
)
return T2Scheme("Lyness-Jespersen 9", weights, points, 5, source)
def williams_shunn_jameson_7():
weights, points = concat(
s3(0.083608212215637),
s2(
[0.005272170280495, 0.019977187122193],
[0.044552936679504, 0.131721767529998],
[0.033815712804198, 0.485135346793461],
),
s1(
[0.015710461340183, 0.107951981846011, 0.867911210117951],
[0.028205136280616, 0.270840772921567, 0.700872570380723],
[0.066995957127830, 0.316549598844617, 0.536654684206138],
),
)
return T2Scheme("Williams-Shunn-Jameson 7", weights, points, 10, source, 4.041e-13)
def laursen_gellert_06():
weights, points = concat(
s3(3.0 / 8.0), s1([5.0 / 48.0, 0.736712498968435, 0.237932366472434])
)
return T2Scheme("Laursen-Gellert 6", weights, points, 4, source)
def lyness_jespersen_19():
weights, points = concat(
s3(1.133624844599192e-01),
s2(
[1.062573789846330e-03 / 3, 0],
[4.803411513859279e-02 / 3, 0.5],
[2.524243006337300e-01 / 3, 4.497793381870162e-01],
[7.819254371487040e-02 / 3, 4.694744319909033e-02],
[2.472227459993048e-01 / 3, 1.918719127374489e-01],
),
s1([2.597012362637364e-01 / 6, 3.683841205473626e-02, 7.411985987844980e-01]),
)
return T2Scheme("Lyness-Jespersen 19", weights, points, 9, source)
def lyness_jespersen_15():
weights, points = concat(
s3(1.443156076777862e-01),
s2(
[2.852749028018549e-01 / 3, 4.592925882927229e-01],
[9.737549286959440e-02 / 3, 5.054722831703103e-02],
[3.096521116041552e-01 / 3, 1.705693077517601e-01],
),
s1([1.633818850466092e-01 / 6, 8.394777409957211e-03, 7.284923929554041e-01]),
)
return T2Scheme("Lyness-Jespersen 15", weights, points, 8, source)
def dunavant_11():
weights, points = concat(
s2(
[0.000927006328961, 0.534611048270758],
[0.077149534914813, 0.398969302965855],
[0.059322977380774, 0.203309900431282],
[0.036184540503418, 0.119350912282581],
[0.013659731002678, 0.032364948111276],
),
s1(
[0.052337111962204, 0.050178138310495, 0.356620648261293],
[0.020707659639141, 0.021022016536166, 0.171488980304042],
),
)
return T2Scheme("Dunavant 11", weights, points, 11, source, 1.210e-13)
def laursen_gellert_15b():
weights, points = concat(
s3(0.081743329146286),
s2(
[0.045957963604745, 0.142161101056564],
[0.013352968813150, 0.032055373216944],
),
s1(
[0.063904906396424, 0.148132885783821, 0.321812995288835],
[0.034184648162959, 0.029619889488730, 0.369146781827811],
[0.025297757707288, 0.028367665339938, 0.163701733737182],
),
)
return T2Scheme("Laursen-Gellert 15b", weights, points, 10, source)
def hillion_09():
# ERR the article is missing the minus sign
weights, points = concat(s3(-frac(9, 32)), s2([frac(25, 96), frac(1, 5)]))
weights *= 2
return T2Scheme("Hillion 9", weights, points, 3, source)
def seven_point():
weights, points = concat(
s3(frac(9, 20)), s2([frac(1, 20), 0], [frac(2, 15), frac(1, 2)])
)
return T2Scheme("Seven-point scheme", weights, points, 3)