17 September 2013 5:10:45.077 PM TOMS655_ORIGINAL_PRB FORTRAN77 version Test the TOMS655_ORIGINAL library. ---------------------------------------- BEGINNING TEST OF CIQFS 1 INTERPOLATORY QUADRATURE FORMULA TYPE INTERVAL WEIGHT FUNCTION NAME 1 (-1,1) ONE LEGENDRE MACHINE PRECISION 0.2D-15 KNOTS MULT WEIGHTS 1 0.95105651629515353D+00 2 0.22240110861588505D+00 -0.73134471884532138D-02 2 0.58778525229247314D+00 2 0.48363063741586088D+00 -0.17871860197559895D-01 3 0.61232339957367660D-16 2 0.58793650793650787D+00 -0.76050277186823266D-16 4 -0.58778525229247303D+00 2 0.48363063741586082D+00 0.17871860197559951D-01 5 -0.95105651629515353D+00 2 0.22240110861588536D+00 0.73134471884532008D-02 COMPARISON OF MOMENTS ORDER OF PRECISION 10 ERRORS : ABSOLUTE RELATIVE ---------+------------------------- MINIMUM : 0.000D+00 0.000D+00 MAXIMUM : 0.250D-15 0.250D-15 WEIGHTS RATIO 0.667D+00 ERROR FOR 10-TH POWER 0.387D-02 ERROR CONSTANT 0.107D-08 MOMENTS: TRUE FROM Q.F. ERROR RELATIVE 1 0.2000000000D+01 0.2000000000D+01 0.000D+00 0.000D+00 2 0.0000000000D+00 -0.2220446049D-15 0.222D-15 0.222D-15 3 0.6666666667D+00 0.6666666667D+00 0.222D-15 0.133D-15 4 0.0000000000D+00 -0.2220446049D-15 0.222D-15 0.222D-15 5 0.4000000000D+00 0.4000000000D+00 0.111D-15 0.793D-16 6 0.0000000000D+00 -0.2220446049D-15 0.222D-15 0.222D-15 7 0.2857142857D+00 0.2857142857D+00 0.111D-15 0.864D-16 8 0.0000000000D+00 -0.1942890293D-15 0.194D-15 0.194D-15 9 0.2222222222D+00 0.2222222222D+00 0.139D-15 0.114D-15 10 0.0000000000D+00 -0.2498001805D-15 0.250D-15 0.250D-15 11 0.1818181818D+00 0.1779513889D+00 0.387D-02 0.327D-02 12 0.0000000000D+00 -0.2498001805D-15 0.250D-15 0.250D-15 13 0.1538461538D+00 0.1429191468D+00 0.109D-01 0.947D-02 RETURN FROM CIQFS: ERROR INDICATOR IER= 0 ---------------------------------------- BEGINNING TEST OF CIQF,CIQFS,CGQF AND CGQFS WITH ALL CLASSICAL WEIGHT FUNCTIONS KNOTS AND WEIGHTS OF GAUSS QF COMPUTED BY CGQF(S) 1 INTERPOLATORY QUADRATURE FORMULA TYPE INTERVAL WEIGHT FUNCTION NAME 1 (A,B) ONE LEGENDRE PARAMETERS A -0.50000 B 2.00000 MACHINE PRECISION 0.2D-15 KNOTS MULT WEIGHTS 1 -0.38272480742333004D+00 1 0.29615860632023655D+00 2 0.76913362367896254D-01 1 0.59828583812420855D+00 3 0.74999999999999989D+00 1 0.71111111111111125D+00 4 0.14230866376321039D+01 1 0.59828583812420899D+00 5 0.18827248074233298D+01 1 0.29615860632023638D+00 COMPARISON OF MOMENTS ORDER OF PRECISION 10 ERRORS : ABSOLUTE RELATIVE ---------+------------------------- MINIMUM : 0.000D+00 0.000D+00 MAXIMUM : 0.200D-14 0.200D-14 WEIGHTS RATIO 0.714D+00 ERROR FOR 10-TH POWER 0.341D-01 ERROR CONSTANT 0.941D-08 MOMENTS: TRUE FROM Q.F. ERROR RELATIVE 1 0.2500000000D+01 0.2500000000D+01 -0.178D-14 -0.508D-15 2 0.0000000000D+00 -0.5551115123D-16 0.555D-16 0.555D-16 3 0.1302083333D+01 0.1302083333D+01 -0.666D-15 -0.289D-15 4 0.0000000000D+00 -0.2775557562D-15 0.278D-15 0.278D-15 5 0.1220703125D+01 0.1220703125D+01 -0.444D-15 -0.200D-15 6 0.0000000000D+00 -0.7771561172D-15 0.777D-15 0.777D-15 7 0.1362391881D+01 0.1362391881D+01 -0.222D-15 -0.940D-16 8 0.0000000000D+00 -0.1554312234D-14 0.155D-14 0.155D-14 9 0.1655684577D+01 0.1655684577D+01 0.000D+00 0.000D+00 10 0.0000000000D+00 -0.1998401444D-14 0.200D-14 0.200D-14 11 0.2116642215D+01 0.2082511426D+01 0.341D-01 0.110D-01 12 0.0000000000D+00 -0.3108624469D-14 0.311D-14 0.311D-14 13 0.2798445236D+01 0.2653042970D+01 0.145D+00 0.383D-01 RETURN FROM CGQF(S): ERROR INDICATOR IER= 0 WEIGHTS OF GAUSS QF COMPUTED FROM THE KNOTS BY CIQF(S) 1 INTERPOLATORY QUADRATURE FORMULA TYPE INTERVAL WEIGHT FUNCTION NAME 1 (A,B) ONE LEGENDRE PARAMETERS A -0.50000 B 2.00000 MACHINE PRECISION 0.2D-15 KNOTS MULT WEIGHTS 1 -0.38272480742333004D+00 2 0.29615860632023622D+00 0.33728379694473035D-32 2 0.76913362367896254D-01 2 0.59828583812420810D+00 0.36876231259379350D-31 3 0.74999999999999989D+00 2 0.71111111111111114D+00 -0.96164787288126241D-16 4 0.14230866376321039D+01 2 0.59828583812420855D+00 0.87989865281877796D-31 5 0.18827248074233298D+01 2 0.29615860632023616D+00 -0.41100262959702906D-16 COMPARISON OF MOMENTS ORDER OF PRECISION 10 ERRORS : ABSOLUTE RELATIVE ---------+------------------------- MINIMUM : 0.000D+00 0.000D+00 MAXIMUM : 0.266D-14 0.266D-14 WEIGHTS RATIO 0.714D+00 ERROR FOR 10-TH POWER 0.341D-01 ERROR CONSTANT 0.941D-08 MOMENTS: TRUE FROM Q.F. ERROR RELATIVE 1 0.2500000000D+01 0.2500000000D+01 0.000D+00 0.000D+00 2 0.0000000000D+00 -0.1110223025D-15 0.111D-15 0.111D-15 3 0.1302083333D+01 0.1302083333D+01 0.444D-15 0.193D-15 4 0.0000000000D+00 -0.3885780586D-15 0.389D-15 0.389D-15 5 0.1220703125D+01 0.1220703125D+01 0.888D-15 0.400D-15 6 0.0000000000D+00 -0.9992007222D-15 0.999D-15 0.999D-15 7 0.1362391881D+01 0.1362391881D+01 0.155D-14 0.658D-15 8 0.0000000000D+00 -0.1665334537D-14 0.167D-14 0.167D-14 9 0.1655684577D+01 0.1655684577D+01 0.222D-14 0.836D-15 10 0.0000000000D+00 -0.2664535259D-14 0.266D-14 0.266D-14 11 0.2116642215D+01 0.2082511426D+01 0.341D-01 0.110D-01 12 0.0000000000D+00 -0.4440892099D-14 0.444D-14 0.444D-14 13 0.2798445236D+01 0.2653042970D+01 0.145D+00 0.383D-01 RETURN FROM CIQF(S): ERROR INDICATOR IER= 0 KNOTS AND WEIGHTS OF GAUSS QF COMPUTED BY CGQF(S) 1 INTERPOLATORY QUADRATURE FORMULA TYPE INTERVAL WEIGHT FUNCTION NAME 2 (A,B) ((B-X)*(X-A))**(-HALF) CHEBYSHEV PARAMETERS A -0.50000 B 2.00000 MACHINE PRECISION 0.2D-15 KNOTS MULT WEIGHTS 1 -0.43882064536894183D+00 1 0.62831853071795774D+00 2 0.15268434634408190D-01 1 0.62831853071795873D+00 3 0.75000000000000000D+00 1 0.62831853071795929D+00 4 0.14847315653655919D+01 1 0.62831853071795962D+00 5 0.19388206453689418D+01 1 0.62831853071795862D+00 COMPARISON OF MOMENTS ORDER OF PRECISION 10 ERRORS : ABSOLUTE RELATIVE ---------+------------------------- MINIMUM : 0.444D-15 0.129D-15 MAXIMUM : 0.711D-14 0.400D-14 WEIGHTS RATIO 0.759D+00 ERROR FOR 10-TH POWER 0.571D-01 ERROR CONSTANT 0.157D-07 MOMENTS: TRUE FROM Q.F. ERROR RELATIVE 1 0.3141592654D+01 0.3141592654D+01 -0.888D-15 -0.214D-15 2 0.0000000000D+00 0.1776356839D-14 -0.178D-14 -0.178D-14 3 0.2454369261D+01 0.2454369261D+01 0.444D-15 0.129D-15 4 0.0000000000D+00 0.1998401444D-14 -0.200D-14 -0.200D-14 5 0.2876213977D+01 0.2876213977D+01 0.178D-14 0.458D-15 6 0.0000000000D+00 0.2664535259D-14 -0.266D-14 -0.266D-14 7 0.3745070283D+01 0.3745070283D+01 0.400D-14 0.842D-15 8 0.0000000000D+00 0.3552713679D-14 -0.355D-14 -0.355D-14 9 0.5120213277D+01 0.5120213277D+01 0.711D-14 0.116D-14 10 0.0000000000D+00 0.3996802889D-14 -0.400D-14 -0.400D-14 11 0.7200299921D+01 0.7143154684D+01 0.571D-01 0.697D-02 12 0.0000000000D+00 0.6217248938D-14 -0.622D-14 -0.622D-14 13 0.1031292957D+02 0.1004506127D+02 0.268D+00 0.237D-01 RETURN FROM CGQF(S): ERROR INDICATOR IER= 0 WEIGHTS OF GAUSS QF COMPUTED FROM THE KNOTS BY CIQF(S) 1 INTERPOLATORY QUADRATURE FORMULA TYPE INTERVAL WEIGHT FUNCTION NAME 2 (A,B) ((B-X)*(X-A))**(-HALF) CHEBYSHEV PARAMETERS A -0.50000 B 2.00000 MACHINE PRECISION 0.2D-15 KNOTS MULT WEIGHTS 1 -0.43882064536894183D+00 2 0.62831853071795774D+00 -0.87196712450215769D-16 2 0.15268434634408190D-01 2 0.62831853071795907D+00 -0.16407443524653312D-30 3 0.75000000000000000D+00 2 0.62831853071795951D+00 -0.85419973901991823D-16 4 0.14847315653655919D+01 2 0.62831853071795962D+00 -0.87196712450215979D-16 5 0.19388206453689418D+01 2 0.62831853071795907D+00 -0.99103068477365931D-32 COMPARISON OF MOMENTS ORDER OF PRECISION 10 ERRORS : ABSOLUTE RELATIVE ---------+------------------------- MINIMUM : 0.444D-15 0.115D-15 MAXIMUM : 0.355D-14 0.311D-14 WEIGHTS RATIO 0.759D+00 ERROR FOR 10-TH POWER 0.571D-01 ERROR CONSTANT 0.157D-07 MOMENTS: TRUE FROM Q.F. ERROR RELATIVE 1 0.3141592654D+01 0.3141592654D+01 -0.178D-14 -0.429D-15 2 0.0000000000D+00 0.2109423747D-14 -0.211D-14 -0.211D-14 3 0.2454369261D+01 0.2454369261D+01 -0.444D-15 -0.129D-15 4 0.0000000000D+00 0.1776356839D-14 -0.178D-14 -0.178D-14 5 0.2876213977D+01 0.2876213977D+01 0.444D-15 0.115D-15 6 0.0000000000D+00 0.2442490654D-14 -0.244D-14 -0.244D-14 7 0.3745070283D+01 0.3745070283D+01 0.133D-14 0.281D-15 8 0.0000000000D+00 0.2664535259D-14 -0.266D-14 -0.266D-14 9 0.5120213277D+01 0.5120213277D+01 0.355D-14 0.580D-15 10 0.0000000000D+00 0.3108624469D-14 -0.311D-14 -0.311D-14 11 0.7200299921D+01 0.7143154684D+01 0.571D-01 0.697D-02 12 0.0000000000D+00 0.3552713679D-14 -0.355D-14 -0.355D-14 13 0.1031292957D+02 0.1004506127D+02 0.268D+00 0.237D-01 RETURN FROM CIQF(S): ERROR INDICATOR IER= 0 KNOTS AND WEIGHTS OF GAUSS QF COMPUTED BY CGQF(S) 1 INTERPOLATORY QUADRATURE FORMULA TYPE INTERVAL WEIGHT FUNCTION NAME 3 (A,B) ((B-X)*(X-A))**ALPHA GEGENBAUER PARAMETERS A -0.50000 B 2.00000 ALPHA 0.50000 MACHINE PRECISION 0.2D-15 KNOTS MULT WEIGHTS 1 -0.33253175473054863D+00 1 0.20453077171808579D+00 2 0.12500000000000022D+00 1 0.61359231515425683D+00 3 0.75000000000000011D+00 1 0.81812308687234170D+00 4 0.13749999999999998D+01 1 0.61359231515425661D+00 5 0.18325317547305486D+01 1 0.20453077171808542D+00 COMPARISON OF MOMENTS ORDER OF PRECISION 10 ERRORS : ABSOLUTE RELATIVE ---------+------------------------- MINIMUM : 0.416D-15 0.129D-15 MAXIMUM : 0.200D-14 0.111D-14 WEIGHTS RATIO 0.711D+00 ERROR FOR 10-TH POWER 0.223D-01 ERROR CONSTANT 0.615D-08 MOMENTS: TRUE FROM Q.F. ERROR RELATIVE 1 0.2454369261D+01 0.2454369261D+01 -0.444D-15 -0.129D-15 2 0.0000000000D+00 -0.4163336342D-15 0.416D-15 0.416D-15 3 0.9587379924D+00 0.9587379924D+00 -0.444D-15 -0.227D-15 4 0.0000000000D+00 -0.4996003611D-15 0.500D-15 0.500D-15 5 0.7490140566D+00 0.7490140566D+00 -0.777D-15 -0.444D-15 6 0.0000000000D+00 -0.6106226635D-15 0.611D-15 0.611D-15 7 0.7314590396D+00 0.7314590396D+00 -0.133D-14 -0.769D-15 8 0.0000000000D+00 -0.6661338148D-15 0.666D-15 0.666D-15 9 0.8000333246D+00 0.8000333246D+00 -0.200D-14 -0.111D-14 10 0.0000000000D+00 -0.7216449660D-15 0.722D-15 0.722D-15 11 0.9375390523D+00 0.9152166939D+00 0.223D-01 0.115D-01 12 0.0000000000D+00 -0.8326672685D-15 0.833D-15 0.833D-15 13 0.1150996604D+01 0.1063799892D+01 0.872D-01 0.405D-01 RETURN FROM CGQF(S): ERROR INDICATOR IER= 0 WEIGHTS OF GAUSS QF COMPUTED FROM THE KNOTS BY CIQF(S) 1 INTERPOLATORY QUADRATURE FORMULA TYPE INTERVAL WEIGHT FUNCTION NAME 3 (A,B) ((B-X)*(X-A))**ALPHA GEGENBAUER PARAMETERS A -0.50000 B 2.00000 ALPHA 0.50000 MACHINE PRECISION 0.2D-15 KNOTS MULT WEIGHTS 1 -0.33253175473054863D+00 2 0.20453077171808590D+00 -0.28384346500721374D-16 2 0.12500000000000022D+00 2 0.61359231515425661D+00 -0.42576519751081996D-16 3 0.75000000000000011D+00 2 0.81812308687234192D+00 -0.52664014366543454D-16 4 0.13749999999999998D+01 2 0.61359231515425627D+00 -0.42576519751081866D-16 5 0.18325317547305486D+01 2 0.20453077171808540D+00 -0.28384346500721250D-16 COMPARISON OF MOMENTS ORDER OF PRECISION 10 ERRORS : ABSOLUTE RELATIVE ---------+------------------------- MINIMUM : 0.000D+00 0.000D+00 MAXIMUM : 0.222D-14 0.200D-14 WEIGHTS RATIO 0.711D+00 ERROR FOR 10-TH POWER 0.223D-01 ERROR CONSTANT 0.615D-08 MOMENTS: TRUE FROM Q.F. ERROR RELATIVE 1 0.2454369261D+01 0.2454369261D+01 0.000D+00 0.000D+00 2 0.0000000000D+00 -0.6938893904D-15 0.694D-15 0.694D-15 3 0.9587379924D+00 0.9587379924D+00 -0.222D-15 -0.113D-15 4 0.0000000000D+00 -0.9992007222D-15 0.999D-15 0.999D-15 5 0.7490140566D+00 0.7490140566D+00 -0.777D-15 -0.444D-15 6 0.0000000000D+00 -0.1332267630D-14 0.133D-14 0.133D-14 7 0.7314590396D+00 0.7314590396D+00 -0.144D-14 -0.834D-15 8 0.0000000000D+00 -0.1554312234D-14 0.155D-14 0.155D-14 9 0.8000333246D+00 0.8000333246D+00 -0.222D-14 -0.123D-14 10 0.0000000000D+00 -0.1998401444D-14 0.200D-14 0.200D-14 11 0.9375390523D+00 0.9152166939D+00 0.223D-01 0.115D-01 12 0.0000000000D+00 -0.2553512957D-14 0.255D-14 0.255D-14 13 0.1150996604D+01 0.1063799892D+01 0.872D-01 0.405D-01 RETURN FROM CIQF(S): ERROR INDICATOR IER= 0 KNOTS AND WEIGHTS OF GAUSS QF COMPUTED BY CGQF(S) 1 INTERPOLATORY QUADRATURE FORMULA TYPE INTERVAL WEIGHT FUNCTION NAME 4 (A,B) (B-X)**ALPHA*(X-A)**BETA JACOBI PARAMETERS A -0.50000 B 2.00000 ALPHA 0.50000 BETA 2.00000 MACHINE PRECISION 0.2D-15 KNOTS MULT WEIGHTS 1 -0.15303633066793587D+00 1 0.76617129890421465D-01 2 0.35753707671627766D+00 1 0.53659067985975850D+00 3 0.94535638653559406D+00 1 0.12551248538055733D+01 4 0.14858880884829690D+01 1 0.13472898724319176D+01 5 0.18642547789330952D+01 1 0.54899372611754638D+00 COMPARISON OF MOMENTS ORDER OF PRECISION 10 ERRORS : ABSOLUTE RELATIVE ---------+------------------------- MINIMUM : 0.888D-15 0.407D-15 MAXIMUM : 0.355D-14 0.797D-15 WEIGHTS RATIO 0.790D+00 ERROR FOR 10-TH POWER 0.146D-01 ERROR CONSTANT 0.402D-08 MOMENTS: TRUE FROM Q.F. ERROR RELATIVE 1 0.3764616262D+01 0.3764616262D+01 -0.355D-14 -0.746D-15 2 0.1568590109D+01 0.1568590109D+01 -0.111D-14 -0.432D-15 3 0.1604239884D+01 0.1604239884D+01 -0.133D-14 -0.512D-15 4 0.1216891365D+01 0.1216891365D+01 -0.133D-14 -0.601D-15 5 0.1306872769D+01 0.1306872769D+01 -0.133D-14 -0.578D-15 6 0.1183053821D+01 0.1183053821D+01 -0.888D-15 -0.407D-15 7 0.1308228360D+01 0.1308228360D+01 -0.111D-14 -0.481D-15 8 0.1289910261D+01 0.1289910261D+01 -0.178D-14 -0.776D-15 9 0.1454550385D+01 0.1454550385D+01 -0.178D-14 -0.724D-15 10 0.1508092819D+01 0.1508092819D+01 -0.200D-14 -0.797D-15 11 0.1724613987D+01 0.1710038800D+01 0.146D-01 0.535D-02 12 0.1848110450D+01 0.1825870725D+01 0.222D-01 0.781D-02 13 0.2135936129D+01 0.2067375141D+01 0.686D-01 0.219D-01 RETURN FROM CGQF(S): ERROR INDICATOR IER= 0 WEIGHTS OF GAUSS QF COMPUTED FROM THE KNOTS BY CIQF(S) 1 INTERPOLATORY QUADRATURE FORMULA TYPE INTERVAL WEIGHT FUNCTION NAME 4 (A,B) (B-X)**ALPHA*(X-A)**BETA JACOBI PARAMETERS A -0.50000 B 2.00000 ALPHA 0.50000 BETA 2.00000 MACHINE PRECISION 0.2D-15 KNOTS MULT WEIGHTS 1 -0.15303633066793587D+00 2 0.76617129890421368D-01 0.80169897973760331D-32 2 0.35753707671627766D+00 2 0.53659067985975828D+00 -0.37233457973722994D-16 3 0.94535638653559406D+00 2 0.12551248538055706D+01 -0.87091781967138696D-16 4 0.14858880884829690D+01 2 0.13472898724319171D+01 -0.18697402965227462D-15 5 0.18642547789330952D+01 2 0.54899372611754571D+00 -0.15237636877761369D-15 COMPARISON OF MOMENTS ORDER OF PRECISION 10 ERRORS : ABSOLUTE RELATIVE ---------+------------------------- MINIMUM : 0.444D-15 0.932D-16 MAXIMUM : 0.311D-14 0.124D-14 WEIGHTS RATIO 0.790D+00 ERROR FOR 10-TH POWER 0.146D-01 ERROR CONSTANT 0.402D-08 MOMENTS: TRUE FROM Q.F. ERROR RELATIVE 1 0.3764616262D+01 0.3764616262D+01 0.444D-15 0.932D-16 2 0.1568590109D+01 0.1568590109D+01 0.666D-15 0.259D-15 3 0.1604239884D+01 0.1604239884D+01 0.666D-15 0.256D-15 4 0.1216891365D+01 0.1216891365D+01 0.666D-15 0.300D-15 5 0.1306872769D+01 0.1306872769D+01 0.133D-14 0.578D-15 6 0.1183053821D+01 0.1183053821D+01 0.155D-14 0.712D-15 7 0.1308228360D+01 0.1308228360D+01 0.200D-14 0.866D-15 8 0.1289910261D+01 0.1289910261D+01 0.200D-14 0.873D-15 9 0.1454550385D+01 0.1454550385D+01 0.266D-14 0.109D-14 10 0.1508092819D+01 0.1508092819D+01 0.311D-14 0.124D-14 11 0.1724613987D+01 0.1710038800D+01 0.146D-01 0.535D-02 12 0.1848110450D+01 0.1825870725D+01 0.222D-01 0.781D-02 13 0.2135936129D+01 0.2067375141D+01 0.686D-01 0.219D-01 RETURN FROM CIQF(S): ERROR INDICATOR IER= 0 KNOTS AND WEIGHTS OF GAUSS QF COMPUTED BY CGQF(S) 1 INTERPOLATORY QUADRATURE FORMULA TYPE INTERVAL WEIGHT FUNCTION NAME 5 (A,INF) (X-A)**ALPHA*EXP(-B*(X-A)) GEN LAGUERRE PARAMETERS A -0.50000 B 2.00000 ALPHA 0.50000 MACHINE PRECISION 0.2D-15 KNOTS MULT WEIGHTS 1 -0.28430059642607391D+00 1 0.13097405507334794D+00 2 0.37987684921184894D+00 1 0.14587060425199255D+00 3 0.15522326814141580D+01 1 0.34570386911402198D-01 4 0.33733518897712789D+01 1 0.18997892129372692D-02 5 0.62288391760287887D+01 1 0.13698879195062412D-04 COMPARISON OF MOMENTS ORDER OF PRECISION 10 ERRORS : ABSOLUTE RELATIVE ---------+------------------------- MINIMUM : 0.278D-16 0.225D-16 MAXIMUM : 0.341D-12 0.536D-15 WEIGHTS RATIO 0.239D+00 ERROR FOR 10-TH POWER 0.119D+02 ERROR CONSTANT 0.329D-05 MOMENTS: TRUE FROM Q.F. ERROR RELATIVE 1 0.3133285343D+00 0.3133285343D+00 0.555D-16 0.423D-16 2 0.2349964007D+00 0.2349964007D+00 -0.278D-16 -0.225D-16 3 0.2937455009D+00 0.2937455009D+00 -0.167D-15 -0.129D-15 4 0.5140546266D+00 0.5140546266D+00 -0.222D-15 -0.147D-15 5 0.1156622910D+01 0.1156622910D+01 -0.444D-15 -0.206D-15 6 0.3180713002D+01 0.3180713002D+01 -0.178D-14 -0.425D-15 7 0.1033731726D+02 0.1033731726D+02 -0.533D-14 -0.470D-15 8 0.3876493972D+02 0.3876493972D+02 -0.213D-13 -0.536D-15 9 0.1647509938D+03 0.1647509938D+03 -0.853D-13 -0.514D-15 10 0.7825672205D+03 0.7825672205D+03 -0.341D-12 -0.435D-15 11 0.4108477908D+04 0.4096550234D+04 0.119D+02 0.290D-02 12 0.2362374797D+05 0.2322715282D+05 0.397D+03 0.168D-01 13 0.1476484248D+06 0.1398805273D+06 0.777D+04 0.526D-01 RETURN FROM CGQF(S): ERROR INDICATOR IER= 0 WEIGHTS OF GAUSS QF COMPUTED FROM THE KNOTS BY CIQF(S) 1 INTERPOLATORY QUADRATURE FORMULA TYPE INTERVAL WEIGHT FUNCTION NAME 5 (A,INF) (X-A)**ALPHA*EXP(-B*(X-A)) GEN LAGUERRE PARAMETERS A -0.50000 B 2.00000 ALPHA 0.50000 MACHINE PRECISION 0.2D-15 KNOTS MULT WEIGHTS 1 -0.28430059642607391D+00 2 0.13097405507334794D+00 0.00000000000000000D+00 2 0.37987684921184894D+00 2 0.14587060425199269D+00 0.00000000000000000D+00 3 0.15522326814141580D+01 2 0.34570386911402178D-01 0.00000000000000000D+00 4 0.33733518897712789D+01 2 0.18997892129372711D-02 0.00000000000000000D+00 5 0.62288391760287887D+01 2 0.13698879195062407D-04 0.00000000000000000D+00 COMPARISON OF MOMENTS ORDER OF PRECISION 10 ERRORS : ABSOLUTE RELATIVE ---------+------------------------- MINIMUM : 0.555D-16 0.423D-16 MAXIMUM : 0.568D-12 0.110D-14 WEIGHTS RATIO 0.239D+00 ERROR FOR 10-TH POWER 0.119D+02 ERROR CONSTANT 0.329D-05 MOMENTS: TRUE FROM Q.F. ERROR RELATIVE 1 0.3133285343D+00 0.3133285343D+00 -0.555D-16 -0.423D-16 2 0.2349964007D+00 0.2349964007D+00 -0.139D-15 -0.112D-15 3 0.2937455009D+00 0.2937455009D+00 -0.167D-15 -0.129D-15 4 0.5140546266D+00 0.5140546266D+00 -0.222D-15 -0.147D-15 5 0.1156622910D+01 0.1156622910D+01 -0.888D-15 -0.412D-15 6 0.3180713002D+01 0.3180713002D+01 -0.266D-14 -0.637D-15 7 0.1033731726D+02 0.1033731726D+02 -0.124D-13 -0.110D-14 8 0.3876493972D+02 0.3876493972D+02 -0.426D-13 -0.107D-14 9 0.1647509938D+03 0.1647509938D+03 -0.171D-12 -0.103D-14 10 0.7825672205D+03 0.7825672205D+03 -0.568D-12 -0.725D-15 11 0.4108477908D+04 0.4096550234D+04 0.119D+02 0.290D-02 12 0.2362374797D+05 0.2322715282D+05 0.397D+03 0.168D-01 13 0.1476484248D+06 0.1398805273D+06 0.777D+04 0.526D-01 RETURN FROM CIQF(S): ERROR INDICATOR IER= 0 KNOTS AND WEIGHTS OF GAUSS QF COMPUTED BY CGQF(S) 1 INTERPOLATORY QUADRATURE FORMULA TYPE INTERVAL WEIGHT FUNCTION NAME 6 (-INF,INF) ABS(X-A)**ALFA*EXP(-B*(X-A)**2) GEN HERMITE PARAMETERS A -0.50000 B 2.00000 ALPHA 0.50000 MACHINE PRECISION 0.2D-15 KNOTS MULT WEIGHTS 1 -0.19846400902538133D+01 1 0.12302854647083833D-01 2 -0.12388124270822396D+01 1 0.20061059263754044D+00 3 -0.50000000000000022D+00 1 0.30281023613813191D+00 4 0.23881242708224004D+00 1 0.20061059263754014D+00 5 0.98464009025381238D+00 1 0.12302854647083803D-01 COMPARISON OF MOMENTS ORDER OF PRECISION 10 ERRORS : ABSOLUTE RELATIVE ---------+------------------------- MINIMUM : 0.278D-16 0.224D-16 MAXIMUM : 0.333D-14 0.333D-14 WEIGHTS RATIO 0.422D+00 ERROR FOR 10-TH POWER 0.164D+00 ERROR CONSTANT 0.453D-07 MOMENTS: TRUE FROM Q.F. ERROR RELATIVE 1 0.7286371307D+00 0.7286371307D+00 0.555D-15 0.321D-15 2 0.0000000000D+00 -0.2567390744D-15 0.257D-15 0.257D-15 3 0.2732389240D+00 0.2732389240D+00 0.111D-15 0.872D-16 4 0.0000000000D+00 -0.1457167720D-15 0.146D-15 0.146D-15 5 0.2390840585D+00 0.2390840585D+00 -0.278D-16 -0.224D-16 6 0.0000000000D+00 -0.4163336342D-15 0.416D-15 0.416D-15 7 0.3287405805D+00 0.3287405805D+00 -0.167D-15 -0.125D-15 8 0.0000000000D+00 -0.1221245327D-14 0.122D-14 0.122D-14 9 0.6163885884D+00 0.6163885884D+00 -0.333D-15 -0.206D-15 10 0.0000000000D+00 -0.3330669074D-14 0.333D-14 0.333D-14 11 0.1463922897D+01 0.1299552607D+01 0.164D+00 0.667D-01 12 0.0000000000D+00 -0.8659739592D-14 0.866D-14 0.866D-14 13 0.4208778330D+01 0.2832177149D+01 0.138D+01 0.264D+00 RETURN FROM CGQF(S): ERROR INDICATOR IER= 0 WEIGHTS OF GAUSS QF COMPUTED FROM THE KNOTS BY CIQF(S) 1 INTERPOLATORY QUADRATURE FORMULA TYPE INTERVAL WEIGHT FUNCTION NAME 6 (-INF,INF) ABS(X-A)**ALFA*EXP(-B*(X-A)**2) GEN HERMITE PARAMETERS A -0.50000 B 2.00000 ALPHA 0.50000 MACHINE PRECISION 0.2D-15 KNOTS MULT WEIGHTS 1 -0.19846400902538133D+01 2 0.12302854647083838D-01 0.16245898753159158D-34 2 -0.12388124270822396D+01 2 0.20061059263754036D+00 0.53232725458077471D-33 3 -0.50000000000000022D+00 2 0.30281023613813207D+00 0.16420852419561420D-16 4 0.23881242708224004D+00 2 0.20061059263754016D+00 -0.53232725458077411D-33 5 0.98464009025381238D+00 2 0.12302854647083803D-01 -0.16245898753159249D-34 COMPARISON OF MOMENTS ORDER OF PRECISION 10 ERRORS : ABSOLUTE RELATIVE ---------+------------------------- MINIMUM : 0.278D-16 0.224D-16 MAXIMUM : 0.350D-14 0.350D-14 WEIGHTS RATIO 0.422D+00 ERROR FOR 10-TH POWER 0.164D+00 ERROR CONSTANT 0.453D-07 MOMENTS: TRUE FROM Q.F. ERROR RELATIVE 1 0.7286371307D+00 0.7286371307D+00 0.444D-15 0.257D-15 2 0.0000000000D+00 -0.1457167720D-15 0.146D-15 0.146D-15 3 0.2732389240D+00 0.2732389240D+00 0.167D-15 0.131D-15 4 0.0000000000D+00 -0.1179611964D-15 0.118D-15 0.118D-15 5 0.2390840585D+00 0.2390840585D+00 -0.278D-16 -0.224D-16 6 0.0000000000D+00 -0.4440892099D-15 0.444D-15 0.444D-15 7 0.3287405805D+00 0.3287405805D+00 -0.222D-15 -0.167D-15 8 0.0000000000D+00 -0.1304512054D-14 0.130D-14 0.130D-14 9 0.6163885884D+00 0.6163885884D+00 -0.333D-15 -0.206D-15 10 0.0000000000D+00 -0.3497202528D-14 0.350D-14 0.350D-14 11 0.1463922897D+01 0.1299552607D+01 0.164D+00 0.667D-01 12 0.0000000000D+00 -0.9103828802D-14 0.910D-14 0.910D-14 13 0.4208778330D+01 0.2832177149D+01 0.138D+01 0.264D+00 RETURN FROM CIQF(S): ERROR INDICATOR IER= 0 KNOTS AND WEIGHTS OF GAUSS QF COMPUTED BY CGQF(S) 1 INTERPOLATORY QUADRATURE FORMULA TYPE INTERVAL WEIGHT FUNCTION NAME 7 (A,B) ABS(X-(A+B)/TWO)**ALFA EXPONENTIAL PARAMETERS A -0.50000 B 2.00000 ALPHA 0.50000 MACHINE PRECISION 0.2D-15 KNOTS MULT WEIGHTS 1 -0.39148162917747831D+00 1 0.29332908318369361D+00 2 0.38501428978160779D-01 1 0.47745248689814068D+00 3 0.75000000000000022D+00 1 0.32182684108615661D+00 4 0.14614985710218396D+01 1 0.47745248689814029D+00 5 0.18914816291774779D+01 1 0.29332908318369405D+00 COMPARISON OF MOMENTS ORDER OF PRECISION 10 ERRORS : ABSOLUTE RELATIVE ---------+------------------------- MINIMUM : 0.167D-15 0.917D-16 MAXIMUM : 0.200D-14 0.200D-14 WEIGHTS RATIO 0.651D+00 ERROR FOR 10-TH POWER 0.285D-01 ERROR CONSTANT 0.786D-08 MOMENTS: TRUE FROM Q.F. ERROR RELATIVE 1 0.1863389981D+01 0.1863389981D+01 -0.666D-15 -0.233D-15 2 0.0000000000D+00 0.3330669074D-15 -0.333D-15 -0.333D-15 3 0.1247805791D+01 0.1247805791D+01 -0.222D-15 -0.988D-16 4 0.0000000000D+00 0.1665334537D-15 -0.167D-15 -0.167D-15 5 0.1240715985D+01 0.1240715985D+01 -0.222D-15 -0.991D-16 6 0.0000000000D+00 -0.2220446049D-15 0.222D-15 0.222D-15 7 0.1421653733D+01 0.1421653733D+01 0.222D-15 0.917D-16 8 0.0000000000D+00 -0.8881784197D-15 0.888D-15 0.888D-15 9 0.1753684704D+01 0.1753684704D+01 0.666D-15 0.242D-15 10 0.0000000000D+00 -0.1998401444D-14 0.200D-14 0.200D-14 11 0.2263587593D+01 0.2235050644D+01 0.285D-01 0.874D-02 12 0.0000000000D+00 -0.3552713679D-14 0.355D-14 0.355D-14 13 0.3012877005D+01 0.2886932684D+01 0.126D+00 0.314D-01 RETURN FROM CGQF(S): ERROR INDICATOR IER= 0 WEIGHTS OF GAUSS QF COMPUTED FROM THE KNOTS BY CIQF(S) 1 INTERPOLATORY QUADRATURE FORMULA TYPE INTERVAL WEIGHT FUNCTION NAME 7 (A,B) ABS(X-(A+B)/TWO)**ALFA EXPONENTIAL PARAMETERS A -0.50000 B 2.00000 ALPHA 0.50000 MACHINE PRECISION 0.2D-15 KNOTS MULT WEIGHTS 1 -0.39148162917747831D+00 2 0.29332908318369372D+00 0.40707587742840522D-16 2 0.38501428978160779D-01 2 0.47745248689814052D+00 -0.64202040326854086D-31 3 0.75000000000000022D+00 2 0.32182684108615639D+00 -0.30075161219879185D-16 4 0.14614985710218396D+01 2 0.47745248689813979D+00 0.64202040326853987D-31 5 0.18914816291774779D+01 2 0.29332908318369399D+00 -0.40707587742840565D-16 COMPARISON OF MOMENTS ORDER OF PRECISION 10 ERRORS : ABSOLUTE RELATIVE ---------+------------------------- MINIMUM : 0.111D-15 0.988D-16 MAXIMUM : 0.244D-14 0.244D-14 WEIGHTS RATIO 0.651D+00 ERROR FOR 10-TH POWER 0.285D-01 ERROR CONSTANT 0.786D-08 MOMENTS: TRUE FROM Q.F. ERROR RELATIVE 1 0.1863389981D+01 0.1863389981D+01 0.444D-15 0.155D-15 2 0.0000000000D+00 -0.1110223025D-15 0.111D-15 0.111D-15 3 0.1247805791D+01 0.1247805791D+01 0.222D-15 0.988D-16 4 0.0000000000D+00 -0.2220446049D-15 0.222D-15 0.222D-15 5 0.1240715985D+01 0.1240715985D+01 0.222D-15 0.991D-16 6 0.0000000000D+00 -0.6661338148D-15 0.666D-15 0.666D-15 7 0.1421653733D+01 0.1421653733D+01 0.133D-14 0.550D-15 8 0.0000000000D+00 -0.1221245327D-14 0.122D-14 0.122D-14 9 0.1753684704D+01 0.1753684704D+01 0.222D-14 0.806D-15 10 0.0000000000D+00 -0.2442490654D-14 0.244D-14 0.244D-14 11 0.2263587593D+01 0.2235050644D+01 0.285D-01 0.874D-02 12 0.0000000000D+00 -0.4218847494D-14 0.422D-14 0.422D-14 13 0.3012877005D+01 0.2886932684D+01 0.126D+00 0.314D-01 RETURN FROM CIQF(S): ERROR INDICATOR IER= 0 KNOTS AND WEIGHTS OF GAUSS QF COMPUTED BY CGQF(S) 1 INTERPOLATORY QUADRATURE FORMULA TYPE INTERVAL WEIGHT FUNCTION NAME 8 (A,INF) (X-A)**ALFA*(B+X)**BETA RATIONAL PARAMETERS A -0.50000 B 2.00000 ALPHA 0.50000 BETA -16.00000 MACHINE PRECISION 0.2D-15 KNOTS MULT WEIGHTS 1 -0.43541078852037896D+00 1 0.26216877717069240D-04 2 -0.21664377601574747D+00 1 0.16250543349707118D-04 3 0.25596297684363967D+00 1 0.12927396984510179D-05 4 0.12864478502358694D+01 1 0.11152074844159677D-07 5 0.41096437374566168D+01 1 0.28799054822892571D-11 COMPARISON OF MOMENTS ORDER OF PRECISION 10 ERRORS : ABSOLUTE RELATIVE ---------+------------------------- MINIMUM : 0.000D+00 0.000D+00 MAXIMUM : 0.169D-20 0.169D-20 WEIGHTS RATIO 0.438D-04 ERROR FOR 10-TH POWER 0.825D-06 ERROR CONSTANT 0.227D-12 MOMENTS: TRUE FROM Q.F. ERROR RELATIVE 1 0.4377131572D-04 0.4377131572D-04 0.000D+00 0.000D+00 2 0.7295219287D-05 0.7295219287D-05 0.169D-20 0.169D-20 3 0.2188565786D-05 0.2188565786D-05 -0.424D-21 -0.424D-21 4 0.9991278588D-06 0.9991278588D-06 -0.847D-21 -0.847D-21 5 0.6422964807D-06 0.6422964807D-06 -0.741D-21 -0.741D-21 6 0.5577837858D-06 0.5577837858D-06 -0.741D-21 -0.741D-21 7 0.6398108132D-06 0.6398108132D-06 -0.635D-21 -0.635D-21 8 0.9597162198D-06 0.9597162198D-06 -0.847D-21 -0.847D-21 9 0.1882520277D-05 0.1882520277D-05 -0.106D-20 -0.106D-20 10 0.4877438900D-05 0.4877438900D-05 0.000D+00 0.000D+00 11 0.1707103615D-04 0.1624615493D-04 0.825D-06 0.825D-06 12 0.8413582103D-04 0.6416191151D-04 0.200D-04 0.200D-04 13 0.6310186577D-03 0.2769134667D-03 0.354D-03 0.354D-03 RETURN FROM CGQF(S): ERROR INDICATOR IER= 0 WEIGHTS OF GAUSS QF COMPUTED FROM THE KNOTS BY CIQF(S) 1 INTERPOLATORY QUADRATURE FORMULA TYPE INTERVAL WEIGHT FUNCTION NAME 8 (A,INF) (X-A)**ALFA*(B+X)**BETA RATIONAL PARAMETERS A -0.50000 B 2.00000 ALPHA 0.50000 BETA -16.00000 MACHINE PRECISION 0.2D-15 KNOTS MULT WEIGHTS 1 -0.43541078852037896D+00 2 0.26216877717069250D-04 -0.81862259836703927D-21 2 -0.21664377601574747D+00 2 0.16250543349707135D-04 0.67656477710677773D-21 3 0.25596297684363967D+00 2 0.12927396984510196D-05 -0.46767663452359208D-37 4 0.12864478502358694D+01 2 0.11152074844159682D-07 -0.51629379760698428D-39 5 0.41096437374566168D+01 2 0.28799054822892583D-11 -0.23648100824274140D-42 COMPARISON OF MOMENTS ORDER OF PRECISION 10 ERRORS : ABSOLUTE RELATIVE ---------+------------------------- MINIMUM : 0.127D-20 0.127D-20 MAXIMUM : 0.271D-19 0.271D-19 WEIGHTS RATIO 0.438D-04 ERROR FOR 10-TH POWER 0.825D-06 ERROR CONSTANT 0.227D-12 MOMENTS: TRUE FROM Q.F. ERROR RELATIVE 1 0.4377131572D-04 0.4377131572D-04 -0.271D-19 -0.271D-19 2 0.7295219287D-05 0.7295219287D-05 -0.424D-20 -0.424D-20 3 0.2188565786D-05 0.2188565786D-05 -0.296D-20 -0.296D-20 4 0.9991278588D-06 0.9991278588D-06 -0.212D-20 -0.212D-20 5 0.6422964807D-06 0.6422964807D-06 -0.159D-20 -0.159D-20 6 0.5577837858D-06 0.5577837858D-06 -0.127D-20 -0.127D-20 7 0.6398108132D-06 0.6398108132D-06 -0.127D-20 -0.127D-20 8 0.9597162198D-06 0.9597162198D-06 -0.127D-20 -0.127D-20 9 0.1882520277D-05 0.1882520277D-05 -0.212D-20 -0.212D-20 10 0.4877438900D-05 0.4877438900D-05 -0.169D-20 -0.169D-20 11 0.1707103615D-04 0.1624615493D-04 0.825D-06 0.825D-06 12 0.8413582103D-04 0.6416191151D-04 0.200D-04 0.200D-04 13 0.6310186577D-03 0.2769134667D-03 0.354D-03 0.354D-03 RETURN FROM CIQF(S): ERROR INDICATOR IER= 0 ---------------------------------------- BEGINNING TEST OF CEIQFS RETURN FROM CEIQFS: ERROR INDICATOR IER= 0 INTEGRAL OF SIN(X) ON [-1,1] BY FEJER TYPE RULE WITH 5 POINTS OF MULTIPLICITY 2 QUADRATURE FORMULA: -1.18828558104411286E-016 EXACT VALUE : 0.0000000000000000 ERROR : 1.18828558104411286E-016 ---------------------------------------- BEGINNING TEST OF CEIQF RETURN FROM CEIQF: ERROR INDICATOR IER= 0 INTEGRAL OF SIN(X) FROM -0.50000000000000000 TO 2.0000000000000000 BY FEJER TYPE RULE WITH 5 POINTS OF MULTIPLICITY 2 QUADRATURE FORMULA: 1.2937294066147371 EXACT VALUE : 1.2937293984375151 ERROR : 8.17722201063020293E-009 ---------------------------------------- BEGINNING TEST OF CLIQFS 1 INTERPOLATORY QUADRATURE FORMULA TYPE INTERVAL WEIGHT FUNCTION NAME 1 (-1,1) ONE LEGENDRE MACHINE PRECISION 0.2D-15 KNOTS MULT WEIGHTS 1 0.95105651629515353D+00 1 0.16778122846668317D+00 2 0.58778525229247314D+00 1 0.52555210486664983D+00 3 0.61232339957367660D-16 1 0.61333333333333362D+00 4 -0.58778525229247303D+00 1 0.52555210486664961D+00 5 -0.95105651629515353D+00 1 0.16778122846668339D+00 COMPARISON OF MOMENTS ORDER OF PRECISION 5 ERRORS : ABSOLUTE RELATIVE ---------+------------------------- MINIMUM : 0.000D+00 0.000D+00 MAXIMUM : 0.555D-15 0.333D-15 WEIGHTS RATIO 0.667D+00 ERROR FOR 5-TH POWER 0.139D-15 ERROR CONSTANT 0.116D-17 MOMENTS: TRUE FROM Q.F. ERROR RELATIVE 1 0.2000000000D+01 0.2000000000D+01 0.444D-15 0.148D-15 2 0.0000000000D+00 0.0000000000D+00 0.000D+00 0.000D+00 3 0.6666666667D+00 0.6666666667D+00 0.555D-15 0.333D-15 4 0.0000000000D+00 -0.8326672685D-16 0.833D-16 0.833D-16 5 0.4000000000D+00 0.4000000000D+00 0.444D-15 0.317D-15 6 0.0000000000D+00 -0.1387778781D-15 0.139D-15 0.139D-15 7 0.2857142857D+00 0.2916666667D+00 -0.595D-02 -0.463D-02 8 0.0000000000D+00 -0.1387778781D-15 0.139D-15 0.139D-15 RETURN FROM CLIQFS. IER= 0 ---------------------------------------- BEGINNING TEST OF CLIQF AND EIQFS 1 INTERPOLATORY QUADRATURE FORMULA TYPE INTERVAL WEIGHT FUNCTION NAME 1 (A,B) ONE LEGENDRE PARAMETERS A -0.50000 B 2.00000 MACHINE PRECISION 0.2D-15 KNOTS MULT WEIGHTS 1 0.19388206453689418D+01 1 0.20972653558335388D+00 2 0.14847315653655915D+01 1 0.65694013108331240D+00 3 0.75000000000000011D+00 1 0.76666666666666683D+00 4 0.15268434634408745D-01 1 0.65694013108331206D+00 5 -0.43882064536894183D+00 1 0.20972653558335438D+00 COMPARISON OF MOMENTS ORDER OF PRECISION 5 ERRORS : ABSOLUTE RELATIVE ---------+------------------------- MINIMUM : 0.833D-16 0.833D-16 MAXIMUM : 0.155D-14 0.700D-15 WEIGHTS RATIO 0.714D+00 ERROR FOR 5-TH POWER 0.833D-15 ERROR CONSTANT 0.694D-17 MOMENTS: TRUE FROM Q.F. ERROR RELATIVE 1 0.2500000000D+01 0.2500000000D+01 0.444D-15 0.127D-15 2 0.0000000000D+00 -0.8326672685D-16 0.833D-16 0.833D-16 3 0.1302083333D+01 0.1302083333D+01 0.888D-15 0.386D-15 4 0.0000000000D+00 -0.5551115123D-15 0.555D-15 0.555D-15 5 0.1220703125D+01 0.1220703125D+01 0.155D-14 0.700D-15 6 0.0000000000D+00 -0.8326672685D-15 0.833D-15 0.833D-15 7 0.1362391881D+01 0.1390775045D+01 -0.284D-01 -0.120D-01 8 0.0000000000D+00 -0.1554312234D-14 0.155D-14 0.155D-14 RETURN FROM CLIQF: ERROR INDICATOR IER= 0 RETURN FROM EIQFS: ERROR INDICATOR IER= 0 INTEGRAL OF SIN(X) FROM -0.50000000000000000 TO 2.0000000000000000 BY FEJER TYPE RULE WITH 5 POINTS OF MULTIPLICITY ONE QUADRATURE FORMULA: 1.2937046571063417 EXACT VALUE : 1.2937293984375151 ERROR : 2.47413311733613028E-005 ---------------------------------------- TEST08 BEGINNING TEST OF CEGQF RETURN FROM CEGQF: ERROR INDICATOR IER= 0 INTEGRAL OF X*SIN(X) FROM 1.0000000000000000 TO 4.0000000000000000 BY GAUSS-EXPONENTIAL RULE WITH 12 POINTS QUADRATURE FORMULA: 0.67864309138968260 EXACT VALUE : 0.67864309138968260 ERROR : 0.0000000000000000 BEGINNING TEST OF CEGQFS RETURN FROM CEGQFS: ERROR INDICATOR IER= 0 INTEGRAL OF X*SIN(X) FROM -1.0000000000000000 TO 1.0000000000000000 BY GAUSS-EXPONENTIAL RULE WITH 12 POINTS QUADRATURE FORMULA: 2.08166817117216851E-017 EXACT VALUE : 0.0000000000000000 ERROR : 2.08166817117216851E-017 TEST09 Call CGQFS for generalized Hermite rules. NT = 15 ALPHA = 1.00000 1 INTERPOLATORY QUADRATURE FORMULA TYPE INTERVAL WEIGHT FUNCTION NAME 6 (-INF,INF) ABS(X)**ALFA*EXP(-X**2) GEN HERMITE PARAMETER(S) ALPHA 1.00000 MACHINE PRECISION 0.2D-15 KNOTS MULT WEIGHTS 1 -0.45926220079551996D+01 1 0.29948067642554377D-08 2 -0.37675145053479846D+01 1 0.19192628375770240D-05 3 -0.30693157841808327D+01 1 0.16455571024870811D-03 4 -0.24323439824622972D+01 1 0.40399515839194084D-02 5 -0.18308605906886350D+01 1 0.37756369726656018D-01 6 -0.12504344003802288D+01 1 0.15020237158948324D+00 7 -0.67898764333748718D+00 1 0.24533482913204793D+00 8 -0.44954222270085497D-16 1 0.12500000000000008D+00 9 0.67898764333748785D+00 1 0.24533482913204810D+00 10 0.12504344003802290D+01 1 0.15020237158948338D+00 11 0.18308605906886348D+01 1 0.37756369726656254D-01 12 0.24323439824622946D+01 1 0.40399515839194284D-02 13 0.30693157841808332D+01 1 0.16455571024870882D-03 14 0.37675145053479873D+01 1 0.19192628375770181D-05 15 0.45926220079551960D+01 1 0.29948067642554397D-08 IER = 0 TEST10 Call CDGQF to compute a quadrature formula. KIND = 1 ALPHA = 0.00000 BETA = 0.00000 Index Abscissas Weights 1 -0.9879925180204860 0.3075324199611693E-01 2 -0.9372733924007061 0.7036604748810849E-01 3 -0.8482065834104269 0.1071592204671715 4 -0.7244177313601700 0.1395706779261550 5 -0.5709721726085385 0.1662692058169941 6 -0.3941513470775634 0.1861610000155613 7 -0.2011940939974347 0.1984314853271120 8 -0.1675838770760716E-15 0.2025782419255613 9 0.2011940939974347 0.1984314853271111 10 0.3941513470775637 0.1861610000155626 11 0.5709721726085392 0.1662692058169944 12 0.7244177313601701 0.1395706779261534 13 0.8482065834104270 0.1071592204671729 14 0.9372733924007057 0.7036604748810786E-01 15 0.9879925180204853 0.3075324199611744E-01 TEST10 Call CDGQF to compute a quadrature formula. KIND = 2 ALPHA = 0.00000 BETA = 0.00000 Index Abscissas Weights 1 -0.9945218953682731 0.2094395102393206 2 -0.9510565162951536 0.2094395102393177 3 -0.8660254037844385 0.2094395102393196 4 -0.7431448254773944 0.2094395102393191 5 -0.5877852522924731 0.2094395102393199 6 -0.4067366430758003 0.2094395102393200 7 -0.2079116908177589 0.2094395102393191 8 0.4333930988356310E-16 0.2094395102393193 9 0.2079116908177593 0.2094395102393198 10 0.4067366430758002 0.2094395102393194 11 0.5877852522924731 0.2094395102393196 12 0.7431448254773940 0.2094395102393204 13 0.8660254037844384 0.2094395102393211 14 0.9510565162951534 0.2094395102393198 15 0.9945218953682728 0.2094395102393178 TEST10 Call CDGQF to compute a quadrature formula. KIND = 3 ALPHA = 0.00000 BETA = 0.00000 Index Abscissas Weights 1 -0.9879925180204860 0.3075324199611693E-01 2 -0.9372733924007061 0.7036604748810849E-01 3 -0.8482065834104269 0.1071592204671715 4 -0.7244177313601700 0.1395706779261550 5 -0.5709721726085385 0.1662692058169941 6 -0.3941513470775634 0.1861610000155613 7 -0.2011940939974347 0.1984314853271120 8 -0.1675838770760716E-15 0.2025782419255613 9 0.2011940939974347 0.1984314853271111 10 0.3941513470775637 0.1861610000155626 11 0.5709721726085392 0.1662692058169944 12 0.7244177313601701 0.1395706779261534 13 0.8482065834104270 0.1071592204671729 14 0.9372733924007057 0.7036604748810786E-01 15 0.9879925180204853 0.3075324199611744E-01 TEST10 Call CDGQF to compute a quadrature formula. KIND = 4 ALPHA = 0.00000 BETA = 0.00000 Index Abscissas Weights 1 -0.9879925180204860 0.3075324199611693E-01 2 -0.9372733924007061 0.7036604748810849E-01 3 -0.8482065834104269 0.1071592204671715 4 -0.7244177313601700 0.1395706779261550 5 -0.5709721726085385 0.1662692058169941 6 -0.3941513470775634 0.1861610000155613 7 -0.2011940939974347 0.1984314853271120 8 -0.1675838770760716E-15 0.2025782419255613 9 0.2011940939974347 0.1984314853271111 10 0.3941513470775637 0.1861610000155626 11 0.5709721726085392 0.1662692058169944 12 0.7244177313601701 0.1395706779261534 13 0.8482065834104270 0.1071592204671729 14 0.9372733924007057 0.7036604748810786E-01 15 0.9879925180204853 0.3075324199611744E-01 TEST10 Call CDGQF to compute a quadrature formula. KIND = 5 ALPHA = 0.00000 BETA = 0.00000 Index Abscissas Weights 1 0.9330781201728104E-01 0.2182348859400854 2 0.4926917403018810 0.3422101779228836 3 1.215595412070946 0.2630275779416809 4 2.269949526203739 0.1264258181059313 5 3.667622721751437 0.4020686492100100E-01 6 5.425336627413552 0.8563877803611831E-02 7 7.565916226613070 0.1212436147214254E-02 8 10.12022856801912 0.1116743923442514E-03 9 13.13028248217572 0.6459926762022903E-05 10 16.65440770832996 0.2226316907096256E-06 11 20.77647889944877 0.4227430384979374E-08 12 25.62389422672879 0.3921897267041077E-10 13 31.40751916975393 0.1456515264073139E-12 14 38.53068330648603 0.1483027051113284E-15 15 48.02608557268580 0.1600594906211132E-19 TEST10 Call CDGQF to compute a quadrature formula. KIND = 6 ALPHA = 0.00000 BETA = 0.00000 Index Abscissas Weights 1 -4.499990707309390 0.1522475804253516E-08 2 -3.669950373404451 0.1059115547711071E-05 3 -2.967166927905604 0.1000044412324996E-03 4 -2.325732486173856 0.2778068842912774E-02 5 -1.719992575186489 0.3078003387254618E-01 6 -1.136115585210921 0.1584889157959359 7 -0.5650695832555758 0.4120286874988984 8 -0.1638469319558613E-15 0.5641003087264176 9 0.5650695832555758 0.4120286874988981 10 1.136115585210921 0.1584889157959361 11 1.719992575186488 0.3078003387254607E-01 12 2.325732486173858 0.2778068842912767E-02 13 2.967166927905603 0.1000044412325003E-03 14 3.669950373404451 0.1059115547711071E-05 15 4.499990707309388 0.1522475804253535E-08 TEST10 Call CDGQF to compute a quadrature formula. KIND = 7 ALPHA = 0.00000 BETA = 0.00000 Index Abscissas Weights 1 -0.9879925180204860 0.3075324199611693E-01 2 -0.9372733924007061 0.7036604748810849E-01 3 -0.8482065834104269 0.1071592204671715 4 -0.7244177313601700 0.1395706779261550 5 -0.5709721726085385 0.1662692058169941 6 -0.3941513470775634 0.1861610000155613 7 -0.2011940939974347 0.1984314853271120 8 -0.1675838770760716E-15 0.2025782419255613 9 0.2011940939974347 0.1984314853271111 10 0.3941513470775637 0.1861610000155626 11 0.5709721726085392 0.1662692058169944 12 0.7244177313601701 0.1395706779261534 13 0.8482065834104270 0.1071592204671729 14 0.9372733924007057 0.7036604748810786E-01 15 0.9879925180204853 0.3075324199611744E-01 TEST10 Call CDGQF to compute a quadrature formula. KIND = 8 ALPHA = 1.00000 BETA = -33.0000 Index Abscissas Weights 1 0.1361683909815457E-01 0.2011020498189999E-03 2 0.4663820034482355E-01 0.4495038907551715E-03 3 0.1015058265688505 0.2802834772408015E-03 4 0.1827118416726538 0.6939527832882334E-04 5 0.2975340241767022 0.7430450609904248E-05 6 0.4575406384763867 0.3428803023873920E-06 7 0.6813618059551224 0.6444586110015433E-08 8 0.9999999999999997 0.4439192701910469E-10 9 1.467649039408975 0.9487478523343415E-13 10 2.185598209002824 0.4870831200746219E-16 11 3.360960154950583 0.4014002150239493E-20 12 5.473099011237577 0.2707472673069550E-25 13 9.851651218481582 0.4323502217203962E-32 14 21.44165067705037 0.1112359536745308E-41 15 73.43848251357539 0.1554638299716086E-57 TOMS655_ORIGINAL_PRB Normal end of execution. 17 September 2013 5:10:45.105 PM