def test_gen_laguerre_precise():
x, w = gauss_gen_laguerre(3, -S.Half, 40)
assert [str(r) for r in x] ==['0.1901635091934881328718554276203028970878',
'1.784492748543251591186722461957367638500',
'5.525343742263260275941422110422329464413']
assert [str(r) for r in w] == ['1.449259190448785048183829411195134343108',
'0.3141346406457132878326231270167565378246',
'0.009060019811017691281714945129254301865020']
x, w = gauss_gen_laguerre(3, 2, 40)
assert [str(r) for r in x] == ['1.517387080677412495020323111016672547482',
'4.311583133719520302881184669723530562299',
'9.171029785603067202098492219259796890218']
assert [str(r) for r in w] ==['1.037494961490425285817554606541269153041',
'0.9057500047030653669269785048806009945254',
'0.05675503380650934725546688857812985243312']
def test_gen_laguerre_precise():
x, w = gauss_gen_laguerre(3, -S.Half, 40)
assert [str(r) for r in x] == [
'0.1901635091934881328718554276203028970878',
'1.784492748543251591186722461957367638500',
'5.525343742263260275941422110422329464413']
assert [str(r) for r in w] == [
'1.449259190448785048183829411195134343108',
'0.3141346406457132878326231270167565378246',
'0.009060019811017691281714945129254301865020']
x, w = gauss_gen_laguerre(3, 2, 40)
assert [str(r) for r in x] == [
'1.517387080677412495020323111016672547482',
'4.311583133719520302881184669723530562299',
'9.171029785603067202098492219259796890218']
assert [str(r) for r in w] == [
'1.037494961490425285817554606541269153041',
'0.9057500047030653669269785048806009945254',
'0.05675503380650934725546688857812985243312']
def test_gen_laguerre():
x, w = gauss_gen_laguerre(1, Rational(-1, 2), 17)
assert [str(r) for r in x] == ['0.50000000000000000']
assert [str(r) for r in w] == ['1.7724538509055160']
x, w = gauss_gen_laguerre(2, Rational(-1, 2), 17)
assert [str(r) for r in x] == ['0.27525512860841095', '2.7247448713915890']
assert [str(r) for r in w] == ['1.6098281800110257', '0.16262567089449035']
x, w = gauss_gen_laguerre(3, Rational(-1, 2), 17)
assert [str(r) for r in x] == [
'0.19016350919348813', '1.7844927485432516', '5.5253437422632603'
]
assert [str(r) for r in w] == [
'1.4492591904487850', '0.31413464064571329', '0.0090600198110176913'
]
x, w = gauss_gen_laguerre(4, Rational(-1, 2), 17)
assert [str(r) for r in x] == [
'0.14530352150331709', '1.3390972881263614', '3.9269635013582872',
'8.5886356890120343'
]
assert [str(r) for r in w] == [
'1.3222940251164826', '0.41560465162978376', '0.034155966014826951',
'0.00039920814442273524'
]
x, w = gauss_gen_laguerre(5, Rational(-1, 2), 17)
assert [str(r) for r in x] == [
'0.11758132021177814', '1.0745620124369040', '3.0859374437175500',
'6.4147297336620305', '11.807189489971737'
]
assert [str(r) for r in w] == [
'1.2217252674706516', '0.48027722216462937', '0.067748788910962126',
'0.0026872914935624654', '1.5280865710465241e-5'
]
x, w = gauss_gen_laguerre(1, 2, 17)
assert [str(r) for r in x] == ['3.0000000000000000']
assert [str(r) for r in w] == ['2.0000000000000000']
x, w = gauss_gen_laguerre(2, 2, 17)
assert [str(r) for r in x] == ['2.0000000000000000', '6.0000000000000000']
assert [str(r) for r in w] == ['1.5000000000000000', '0.50000000000000000']
x, w = gauss_gen_laguerre(3, 2, 17)
assert [str(r) for r in x] == [
'1.5173870806774125', '4.3115831337195203', '9.1710297856030672'
]
assert [str(r) for r in w] == [
'1.0374949614904253', '0.90575000470306537', '0.056755033806509347'
]
x, w = gauss_gen_laguerre(4, 2, 17)
assert [str(r) for r in x] == [
'1.2267632635003021', '3.4125073586969460', '6.9026926058516134',
'12.458036771951139'
]
assert [str(r) for r in w] == [
'0.72552499769865438', '1.0634242919791946', '0.20669613102835355',
'0.0043545792937974889'
]
x, w = gauss_gen_laguerre(5, 2, 17)
assert [str(r) for r in x] == [
'1.0311091440933816', '2.8372128239538217', '5.6202942725987079',
'9.6829098376640271', '15.828473921690062'
]
assert [str(r) for r in w] == [
'0.52091739683509184', '1.0667059331592211', '0.38354972366693113',
'0.028564233532974658', '0.00026271280578124935'
]
def test_gen_laguerre():
x, w = gauss_gen_laguerre(1, -S.Half, 17)
assert [str(r) for r in x] == ['0.50000000000000000']
assert [str(r) for r in w] == ['1.7724538509055160']
x, w = gauss_gen_laguerre(2, -S.Half, 17)
assert [str(r) for r in x] == ['0.27525512860841095',
'2.7247448713915890']
assert [str(r) for r in w] == ['1.6098281800110257',
'0.16262567089449035']
x, w = gauss_gen_laguerre(3, -S.Half, 17)
assert [str(r) for r in x] == ['0.19016350919348813',
'1.7844927485432516',
'5.5253437422632603']
assert [str(r) for r in w] == ['1.4492591904487850',
'0.31413464064571329',
'0.0090600198110176913']
x, w = gauss_gen_laguerre(4, -S.Half, 17)
assert [str(r) for r in x] == ['0.14530352150331709',
'1.3390972881263614',
'3.9269635013582872',
'8.5886356890120343']
assert [str(r) for r in w] ==['1.3222940251164826',
'0.41560465162978376',
'0.034155966014826951',
'0.00039920814442273524']
x, w = gauss_gen_laguerre(5, -S.Half, 17)
assert [str(r) for r in x] ==['0.11758132021177814',
'1.0745620124369040',
'3.0859374437175500',
'6.4147297336620305',
'11.807189489971737']
assert [str(r) for r in w] ==['1.2217252674706516',
'0.48027722216462937',
'0.067748788910962126',
'0.0026872914935624654',
'1.5280865710465241e-5']
x, w = gauss_gen_laguerre(1, 2, 17)
assert [str(r) for r in x] ==['3.0000000000000000']
assert [str(r) for r in w] == ['2.0000000000000000']
x, w = gauss_gen_laguerre(2, 2, 17)
assert [str(r) for r in x] == ['2.0000000000000000',
'6.0000000000000000']
assert [str(r) for r in w] ==['1.5000000000000000',
'0.50000000000000000']
x, w = gauss_gen_laguerre(3, 2, 17)
assert [str(r) for r in x] ==['1.5173870806774125',
'4.3115831337195203',
'9.1710297856030672']
assert [str(r) for r in w] ==['1.0374949614904253',
'0.90575000470306537',
'0.056755033806509347']
x, w = gauss_gen_laguerre(4, 2, 17)
assert [str(r) for r in x] ==['1.2267632635003021',
'3.4125073586969460',
'6.9026926058516134',
'12.458036771951139']
assert [str(r) for r in w] ==['0.72552499769865438',
'1.0634242919791946',
'0.20669613102835355',
'0.0043545792937974889']
x, w = gauss_gen_laguerre(5, 2, 17)
assert [str(r) for r in x] ==['1.0311091440933816',
'2.8372128239538217',
'5.6202942725987079',
'9.6829098376640271',
'15.828473921690062']
assert [str(r) for r in w] == ['0.52091739683509184',
'1.0667059331592211',
'0.38354972366693113',
'0.028564233532974658',
'0.00026271280578124935']