---------------------------------------- TESTING CIQFS 1 INTERPOLATORY QUADRATURE FORMULA TYPE INTERVAL WEIGHT FUNCTION NAME 1 (-1,1) ONE LEGENDRE MACHINE PRECISION 0.1D-16 KNOTS MULT WEIGHTS 1 0.95105651629515357D+00 2 0.22240110861588534D+00 -0.73134471884532099D-02 2 0.58778525229247312D+00 2 0.48363063741586058D+00 -0.17871860197559908D-01 3 -0.22034386889519082D-16 2 0.58793650793650781D+00 0.86736173798840349D-17 4 -0.58778525229247315D+00 2 0.48363063741586064D+00 0.17871860197559929D-01 5 -0.95105651629515357D+00 2 0.22240110861588531D+00 0.73134471884532081D-02 COMPARISON OF MOMENTS ORDER OF PRECISION 10 ERRORS : ABSOLUTE RELATIVE ---------+------------------------- MINIMUM : 0.104D-16 0.104D-16 MAXIMUM : 0.305D-15 0.102D-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 0.305D-15 0.102D-15 2 0.0000000000D+00 -0.1387778781D-16 0.139D-16 0.139D-16 3 0.6666666667D+00 0.6666666667D+00 0.278D-16 0.167D-16 4 0.0000000000D+00 0.2081668171D-16 -0.208D-16 -0.208D-16 5 0.4000000000D+00 0.4000000000D+00 -0.347D-16 -0.248D-16 6 0.0000000000D+00 0.1734723476D-16 -0.173D-16 -0.173D-16 7 0.2857142857D+00 0.2857142857D+00 -0.555D-16 -0.432D-16 8 0.0000000000D+00 0.1387778781D-16 -0.139D-16 -0.139D-16 9 0.2222222222D+00 0.2222222222D+00 -0.590D-16 -0.483D-16 10 0.0000000000D+00 0.1040834086D-16 -0.104D-16 -0.104D-16 11 0.1818181818D+00 0.1779513889D+00 0.387D-02 0.327D-02 12 0.0000000000D+00 0.3469446952D-17 -0.347D-17 -0.347D-17 13 0.1538461538D+00 0.1429191468D+00 0.109D-01 0.947D-02 RETURN FROM CIQFS: ERROR INDICATOR IER= 0 ---------------------------------------- TESTING 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 0.1D-16 KNOTS MULT WEIGHTS 1 -0.38272480742333004D+00 1 0.29615860632023627D+00 2 0.76913362367896129D-01 1 0.59828583812420807D+00 3 0.74999999999999999D+00 1 0.71111111111111097D+00 4 0.14230866376321039D+01 1 0.59828583812420795D+00 5 0.18827248074233300D+01 1 0.29615860632023639D+00 COMPARISON OF MOMENTS ORDER OF PRECISION 10 ERRORS : ABSOLUTE RELATIVE ---------+------------------------- MINIMUM : 0.416D-16 0.241D-16 MAXIMUM : 0.389D-15 0.375D-15 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 0.333D-15 0.952D-16 2 0.0000000000D+00 0.4163336342D-16 -0.416D-16 -0.416D-16 3 0.1302083333D+01 0.1302083333D+01 0.555D-16 0.241D-16 4 0.0000000000D+00 0.1457167720D-15 -0.146D-15 -0.146D-15 5 0.1220703125D+01 0.1220703125D+01 -0.555D-16 -0.250D-16 6 0.0000000000D+00 0.2081668171D-15 -0.208D-15 -0.208D-15 7 0.1362391881D+01 0.1362391881D+01 -0.222D-15 -0.940D-16 8 0.0000000000D+00 0.2636779683D-15 -0.264D-15 -0.264D-15 9 0.1655684577D+01 0.1655684577D+01 -0.389D-15 -0.146D-15 10 0.0000000000D+00 0.3747002708D-15 -0.375D-15 -0.375D-15 11 0.2116642215D+01 0.2082511426D+01 0.341D-01 0.110D-01 12 0.0000000000D+00 0.4440892099D-15 -0.444D-15 -0.444D-15 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 0.1D-16 KNOTS MULT WEIGHTS 1 -0.38272480742333004D+00 2 0.29615860632023633D+00 0.51375328699628709D-17 2 0.76913362367896129D-01 2 0.59828583812420802D+00 0.10378604887385233D-16 3 0.74999999999999999D+00 2 0.71111111111111097D+00 0.70271193197689065D-17 4 0.14230866376321039D+01 2 0.59828583812420796D+00 -0.10378604887385234D-16 5 0.18827248074233300D+01 2 0.29615860632023636D+00 -0.10517194876048111D-33 COMPARISON OF MOMENTS ORDER OF PRECISION 10 ERRORS : ABSOLUTE RELATIVE ---------+------------------------- MINIMUM : 0.694D-17 0.694D-17 MAXIMUM : 0.361D-15 0.222D-15 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 0.333D-15 0.952D-16 2 0.0000000000D+00 0.6938893904D-17 -0.694D-17 -0.694D-17 3 0.1302083333D+01 0.1302083333D+01 0.833D-16 0.362D-16 4 0.0000000000D+00 0.6938893904D-16 -0.694D-16 -0.694D-16 5 0.1220703125D+01 0.1220703125D+01 -0.278D-16 -0.125D-16 6 0.0000000000D+00 0.1110223025D-15 -0.111D-15 -0.111D-15 7 0.1362391881D+01 0.1362391881D+01 -0.194D-15 -0.822D-16 8 0.0000000000D+00 0.1526556659D-15 -0.153D-15 -0.153D-15 9 0.1655684577D+01 0.1655684577D+01 -0.361D-15 -0.136D-15 10 0.0000000000D+00 0.2220446049D-15 -0.222D-15 -0.222D-15 11 0.2116642215D+01 0.2082511426D+01 0.341D-01 0.110D-01 12 0.0000000000D+00 0.3330669074D-15 -0.333D-15 -0.333D-15 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 0.1D-16 KNOTS MULT WEIGHTS 1 -0.43882064536894194D+00 1 0.62831853071795850D+00 2 0.15268434634408592D-01 1 0.62831853071795866D+00 3 0.75000000000000000D+00 1 0.62831853071795835D+00 4 0.14847315653655914D+01 1 0.62831853071795842D+00 5 0.19388206453689420D+01 1 0.62831853071795848D+00 COMPARISON OF MOMENTS ORDER OF PRECISION 10 ERRORS : ABSOLUTE RELATIVE ---------+------------------------- MINIMUM : 0.278D-16 0.278D-16 MAXIMUM : 0.167D-14 0.444D-15 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 0.777D-15 0.188D-15 2 0.0000000000D+00 -0.1804112415D-15 0.180D-15 0.180D-15 3 0.2454369261D+01 0.2454369261D+01 0.555D-15 0.161D-15 4 0.0000000000D+00 -0.2775557562D-16 0.278D-16 0.278D-16 5 0.2876213977D+01 0.2876213977D+01 0.722D-15 0.186D-15 6 0.0000000000D+00 0.1110223025D-15 -0.111D-15 -0.111D-15 7 0.3745070283D+01 0.3745070283D+01 0.111D-14 0.234D-15 8 0.0000000000D+00 0.2775557562D-15 -0.278D-15 -0.278D-15 9 0.5120213277D+01 0.5120213277D+01 0.167D-14 0.272D-15 10 0.0000000000D+00 0.4440892099D-15 -0.444D-15 -0.444D-15 11 0.7200299921D+01 0.7143154684D+01 0.571D-01 0.697D-02 12 0.0000000000D+00 0.7771561172D-15 -0.777D-15 -0.777D-15 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 0.1D-16 KNOTS MULT WEIGHTS 1 -0.43882064536894194D+00 2 0.62831853071795850D+00 0.15624107072989836D-33 2 0.15268434634408592D-01 2 0.62831853071795868D+00 0.10899589056276976D-16 3 0.75000000000000000D+00 2 0.62831853071795843D+00 -0.35666697511613738D-17 4 0.14847315653655914D+01 2 0.62831853071795848D+00 -0.10899589056276969D-16 5 0.19388206453689420D+01 2 0.62831853071795851D+00 -0.10899589056276971D-16 COMPARISON OF MOMENTS ORDER OF PRECISION 10 ERRORS : ABSOLUTE RELATIVE ---------+------------------------- MINIMUM : 0.000D+00 0.000D+00 MAXIMUM : 0.189D-14 0.308D-15 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 0.611D-15 0.147D-15 2 0.0000000000D+00 -0.1110223025D-15 0.111D-15 0.111D-15 3 0.2454369261D+01 0.2454369261D+01 0.555D-15 0.161D-15 4 0.0000000000D+00 0.0000000000D+00 0.000D+00 0.000D+00 5 0.2876213977D+01 0.2876213977D+01 0.777D-15 0.200D-15 6 0.0000000000D+00 0.5551115123D-16 -0.555D-16 -0.555D-16 7 0.3745070283D+01 0.3745070283D+01 0.122D-14 0.257D-15 8 0.0000000000D+00 0.1110223025D-15 -0.111D-15 -0.111D-15 9 0.5120213277D+01 0.5120213277D+01 0.189D-14 0.308D-15 10 0.0000000000D+00 0.2220446049D-15 -0.222D-15 -0.222D-15 11 0.7200299921D+01 0.7143154684D+01 0.571D-01 0.697D-02 12 0.0000000000D+00 0.3330669074D-15 -0.333D-15 -0.333D-15 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 0.1D-16 KNOTS MULT WEIGHTS 1 -0.33253175473054836D+00 1 0.20453077171808547D+00 2 0.12500000000000004D+00 1 0.61359231515425650D+00 3 0.75000000000000000D+00 1 0.81812308687234188D+00 4 0.13750000000000000D+01 1 0.61359231515425636D+00 5 0.18325317547305483D+01 1 0.20453077171808545D+00 COMPARISON OF MOMENTS ORDER OF PRECISION 10 ERRORS : ABSOLUTE RELATIVE ---------+------------------------- MINIMUM : 0.139D-16 0.771D-17 MAXIMUM : 0.333D-15 0.146D-15 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 0.333D-15 0.964D-16 2 0.0000000000D+00 -0.8673617380D-16 0.867D-16 0.867D-16 3 0.9587379924D+00 0.9587379924D+00 0.125D-15 0.638D-16 4 0.0000000000D+00 -0.5551115123D-16 0.555D-16 0.555D-16 5 0.7490140566D+00 0.7490140566D+00 0.833D-16 0.476D-16 6 0.0000000000D+00 -0.6245004514D-16 0.625D-16 0.625D-16 7 0.7314590396D+00 0.7314590396D+00 0.139D-16 0.802D-17 8 0.0000000000D+00 -0.1040834086D-15 0.104D-15 0.104D-15 9 0.8000333246D+00 0.8000333246D+00 -0.139D-16 -0.771D-17 10 0.0000000000D+00 -0.1457167720D-15 0.146D-15 0.146D-15 11 0.9375390523D+00 0.9152166939D+00 0.223D-01 0.115D-01 12 0.0000000000D+00 -0.2012279232D-15 0.201D-15 0.201D-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 0.1D-16 KNOTS MULT WEIGHTS 1 -0.33253175473054836D+00 2 0.20453077171808549D+00 0.51690110349341779D-34 2 0.12500000000000004D+00 2 0.61359231515425650D+00 0.53220649688852420D-17 3 0.75000000000000000D+00 2 0.81812308687234199D+00 0.71948497126933839D-18 4 0.13750000000000000D+01 2 0.61359231515425630D+00 -0.10644129937770478D-16 5 0.18325317547305483D+01 2 0.20453077171808546D+00 0.35480433125901607D-17 COMPARISON OF MOMENTS ORDER OF PRECISION 10 ERRORS : ABSOLUTE RELATIVE ---------+------------------------- MINIMUM : 0.416D-16 0.238D-16 MAXIMUM : 0.222D-15 0.135D-15 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 0.222D-15 0.643D-16 2 0.0000000000D+00 -0.1353084311D-15 0.135D-15 0.135D-15 3 0.9587379924D+00 0.9587379924D+00 0.125D-15 0.638D-16 4 0.0000000000D+00 -0.6938893904D-16 0.694D-16 0.694D-16 5 0.7490140566D+00 0.7490140566D+00 0.416D-16 0.238D-16 6 0.0000000000D+00 -0.5551115123D-16 0.555D-16 0.555D-16 7 0.7314590396D+00 0.7314590396D+00 -0.416D-16 -0.240D-16 8 0.0000000000D+00 -0.8326672685D-16 0.833D-16 0.833D-16 9 0.8000333246D+00 0.8000333246D+00 -0.125D-15 -0.694D-16 10 0.0000000000D+00 -0.9714451465D-16 0.971D-16 0.971D-16 11 0.9375390523D+00 0.9152166939D+00 0.223D-01 0.115D-01 12 0.0000000000D+00 -0.1318389842D-15 0.132D-15 0.132D-15 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 0.1D-16 KNOTS MULT WEIGHTS 1 -0.15303633066793587D+00 1 0.76617129890421453D-01 2 0.35753707671627774D+00 1 0.53659067985975822D+00 3 0.94535638653559417D+00 1 0.12551248538055703D+01 4 0.14858880884829689D+01 1 0.13472898724319172D+01 5 0.18642547789330951D+01 1 0.54899372611754609D+00 COMPARISON OF MOMENTS ORDER OF PRECISION 10 ERRORS : ABSOLUTE RELATIVE ---------+------------------------- MINIMUM : 0.000D+00 0.000D+00 MAXIMUM : 0.333D-15 0.775D-16 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 0.333D-15 0.699D-16 2 0.1568590109D+01 0.1568590109D+01 0.000D+00 0.000D+00 3 0.1604239884D+01 0.1604239884D+01 0.278D-16 0.107D-16 4 0.1216891365D+01 0.1216891365D+01 0.278D-16 0.125D-16 5 0.1306872769D+01 0.1306872769D+01 0.555D-16 0.241D-16 6 0.1183053821D+01 0.1183053821D+01 0.278D-16 0.127D-16 7 0.1308228360D+01 0.1308228360D+01 0.555D-16 0.240D-16 8 0.1289910261D+01 0.1289910261D+01 0.111D-15 0.485D-16 9 0.1454550385D+01 0.1454550385D+01 0.111D-15 0.452D-16 10 0.1508092819D+01 0.1508092819D+01 0.194D-15 0.775D-16 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 0.1D-16 KNOTS MULT WEIGHTS 1 -0.15303633066793587D+00 2 0.76617129890421451D-01 0.32590860751743046D-34 2 0.35753707671627774D+00 2 0.53659067985975821D+00 0.46541822467153897D-17 3 0.94535638653559417D+00 2 0.12551248538055703D+01 0.17784281776530149D-32 4 0.14858880884829689D+01 2 0.13472898724319171D+01 0.33436908629561223D-32 5 0.18642547789330951D+01 2 0.54899372611754609D+00 -0.95235230486008862D-17 COMPARISON OF MOMENTS ORDER OF PRECISION 10 ERRORS : ABSOLUTE RELATIVE ---------+------------------------- MINIMUM : 0.278D-16 0.108D-16 MAXIMUM : 0.389D-15 0.155D-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 0.389D-15 0.816D-16 2 0.1568590109D+01 0.1568590109D+01 0.278D-16 0.108D-16 3 0.1604239884D+01 0.1604239884D+01 0.833D-16 0.320D-16 4 0.1216891365D+01 0.1216891365D+01 0.833D-16 0.376D-16 5 0.1306872769D+01 0.1306872769D+01 0.111D-15 0.481D-16 6 0.1183053821D+01 0.1183053821D+01 0.111D-15 0.509D-16 7 0.1308228360D+01 0.1308228360D+01 0.139D-15 0.601D-16 8 0.1289910261D+01 0.1289910261D+01 0.250D-15 0.109D-15 9 0.1454550385D+01 0.1454550385D+01 0.278D-15 0.113D-15 10 0.1508092819D+01 0.1508092819D+01 0.389D-15 0.155D-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 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 0.1D-16 KNOTS MULT WEIGHTS 1 -0.28430059642607425D+00 1 0.13097405507334787D+00 2 0.37987684921184824D+00 1 0.14587060425199263D+00 3 0.15522326814141575D+01 1 0.34570386911402214D-01 4 0.33733518897712785D+01 1 0.18997892129372685D-02 5 0.62288391760287902D+01 1 0.13698879195062384D-04 COMPARISON OF MOMENTS ORDER OF PRECISION 10 ERRORS : ABSOLUTE RELATIVE ---------+------------------------- MINIMUM : 0.104D-16 0.843D-17 MAXIMUM : 0.995D-13 0.156D-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 0.139D-16 0.106D-16 2 0.2349964007D+00 0.2349964007D+00 0.104D-16 0.843D-17 3 0.2937455009D+00 0.2937455009D+00 0.208D-16 0.161D-16 4 0.5140546266D+00 0.5140546266D+00 0.555D-16 0.367D-16 5 0.1156622910D+01 0.1156622910D+01 0.167D-15 0.772D-16 6 0.3180713002D+01 0.3180713002D+01 0.500D-15 0.120D-15 7 0.1033731726D+02 0.1033731726D+02 0.155D-14 0.137D-15 8 0.3876493972D+02 0.3876493972D+02 0.622D-14 0.156D-15 9 0.1647509938D+03 0.1647509938D+03 0.249D-13 0.150D-15 10 0.7825672205D+03 0.7825672205D+03 0.995D-13 0.127D-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 0.1D-16 KNOTS MULT WEIGHTS 1 -0.28430059642607425D+00 2 0.13097405507334787D+00 0.45440753615923155D-18 2 0.37987684921184824D+00 2 0.14587060425199263D+00 -0.10783931190249757D-34 3 0.15522326814141575D+01 2 0.34570386911402215D-01 -0.21557758188527963D-35 4 0.33733518897712785D+01 2 0.18997892129372686D-02 -0.11226942266757488D-36 5 0.62288391760287902D+01 2 0.13698879195062384D-04 0.00000000000000000D+00 COMPARISON OF MOMENTS ORDER OF PRECISION 10 ERRORS : ABSOLUTE RELATIVE ---------+------------------------- MINIMUM : 0.173D-16 0.140D-16 MAXIMUM : 0.853D-13 0.118D-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 0.208D-16 0.159D-16 2 0.2349964007D+00 0.2349964007D+00 0.173D-16 0.140D-16 3 0.2937455009D+00 0.2937455009D+00 0.208D-16 0.161D-16 4 0.5140546266D+00 0.5140546266D+00 0.555D-16 0.367D-16 5 0.1156622910D+01 0.1156622910D+01 0.139D-15 0.643D-16 6 0.3180713002D+01 0.3180713002D+01 0.389D-15 0.929D-16 7 0.1033731726D+02 0.1033731726D+02 0.133D-14 0.118D-15 8 0.3876493972D+02 0.3876493972D+02 0.444D-14 0.112D-15 9 0.1647509938D+03 0.1647509938D+03 0.178D-13 0.107D-15 10 0.7825672205D+03 0.7825672205D+03 0.853D-13 0.109D-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 0.1D-16 KNOTS MULT WEIGHTS 1 -0.19846400902538129D+01 1 0.12302854647083805D-01 2 -0.12388124270822399D+01 1 0.20061059263754047D+00 3 -0.49999999999999999D+00 1 0.30281023613813227D+00 4 0.23881242708223986D+00 1 0.20061059263754044D+00 5 0.98464009025381294D+00 1 0.12302854647083807D-01 COMPARISON OF MOMENTS ORDER OF PRECISION 10 ERRORS : ABSOLUTE RELATIVE ---------+------------------------- MINIMUM : 0.347D-17 0.347D-17 MAXIMUM : 0.236D-15 0.146D-15 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 0.694D-16 0.401D-16 2 0.0000000000D+00 -0.1431146868D-16 0.143D-16 0.143D-16 3 0.2732389240D+00 0.2732389240D+00 0.347D-16 0.272D-16 4 0.0000000000D+00 -0.1214306433D-16 0.121D-16 0.121D-16 5 0.2390840585D+00 0.2390840585D+00 0.520D-16 0.420D-16 6 0.0000000000D+00 -0.3469446952D-17 0.347D-17 0.347D-17 7 0.3287405805D+00 0.3287405805D+00 0.104D-15 0.783D-16 8 0.0000000000D+00 0.1387778781D-16 -0.139D-16 -0.139D-16 9 0.6163885884D+00 0.6163885884D+00 0.236D-15 0.146D-15 10 0.0000000000D+00 0.4857225733D-16 -0.486D-16 -0.486D-16 11 0.1463922897D+01 0.1299552607D+01 0.164D+00 0.667D-01 12 0.0000000000D+00 0.9714451465D-16 -0.971D-16 -0.971D-16 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 0.1D-16 KNOTS MULT WEIGHTS 1 -0.19846400902538129D+01 2 0.12302854647083803D-01 0.48291548254172280D-18 2 -0.12388124270822399D+01 2 0.20061059263754046D+00 0.39372147329035634D-17 3 -0.49999999999999999D+00 2 0.30281023613813223D+00 0.63813859671973973D-18 4 0.23881242708223986D+00 2 0.20061059263754042D+00 -0.19211226557309852D-33 5 0.98464009025381294D+00 2 0.12302854647083805D-01 -0.85397410072820073D-35 COMPARISON OF MOMENTS ORDER OF PRECISION 10 ERRORS : ABSOLUTE RELATIVE ---------+------------------------- MINIMUM : 0.260D-17 0.260D-17 MAXIMUM : 0.389D-15 0.240D-15 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 0.125D-15 0.723D-16 2 0.0000000000D+00 -0.1951563910D-16 0.195D-16 0.195D-16 3 0.2732389240D+00 0.2732389240D+00 0.694D-16 0.545D-16 4 0.0000000000D+00 -0.2602085214D-17 0.260D-17 0.260D-17 5 0.2390840585D+00 0.2390840585D+00 0.937D-16 0.756D-16 6 0.0000000000D+00 0.2255140519D-16 -0.226D-16 -0.226D-16 7 0.3287405805D+00 0.3287405805D+00 0.173D-15 0.131D-15 8 0.0000000000D+00 0.6938893904D-16 -0.694D-16 -0.694D-16 9 0.6163885884D+00 0.6163885884D+00 0.389D-15 0.240D-15 10 0.0000000000D+00 0.1873501354D-15 -0.187D-15 -0.187D-15 11 0.1463922897D+01 0.1299552607D+01 0.164D+00 0.667D-01 12 0.0000000000D+00 0.4857225733D-15 -0.486D-15 -0.486D-15 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 0.1D-16 KNOTS MULT WEIGHTS 1 -0.39148162917747822D+00 1 0.29332908318369346D+00 2 0.38501428978160557D-01 1 0.47745248689814077D+00 3 0.75000000000000006D+00 1 0.32182684108615619D+00 4 0.14614985710218395D+01 1 0.47745248689814066D+00 5 0.18914816291774782D+01 1 0.29332908318369348D+00 COMPARISON OF MOMENTS ORDER OF PRECISION 10 ERRORS : ABSOLUTE RELATIVE ---------+------------------------- MINIMUM : 0.416D-16 0.416D-16 MAXIMUM : 0.103D-14 0.375D-15 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 0.194D-15 0.679D-16 2 0.0000000000D+00 -0.4163336342D-16 0.416D-16 0.416D-16 3 0.1247805791D+01 0.1247805791D+01 0.222D-15 0.988D-16 4 0.0000000000D+00 -0.5551115123D-16 0.555D-16 0.555D-16 5 0.1240715985D+01 0.1240715985D+01 0.416D-15 0.186D-15 6 0.0000000000D+00 -0.9714451465D-16 0.971D-16 0.971D-16 7 0.1421653733D+01 0.1421653733D+01 0.694D-15 0.287D-15 8 0.0000000000D+00 -0.1942890293D-15 0.194D-15 0.194D-15 9 0.1753684704D+01 0.1753684704D+01 0.103D-14 0.373D-15 10 0.0000000000D+00 -0.3747002708D-15 0.375D-15 0.375D-15 11 0.2263587593D+01 0.2235050644D+01 0.285D-01 0.874D-02 12 0.0000000000D+00 -0.5828670879D-15 0.583D-15 0.583D-15 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 0.1D-16 KNOTS MULT WEIGHTS 1 -0.39148162917747822D+00 2 0.29332908318369348D+00 0.50529291023025702D-34 2 0.38501428978160557D-01 2 0.47745248689814078D+00 0.82824803768571371D-17 3 0.75000000000000006D+00 2 0.32182684108615620D+00 0.57575818627259635D-18 4 0.14614985710218395D+01 2 0.47745248689814064D+00 -0.10193662741455050D-33 5 0.18914816291774782D+01 2 0.29332908318369348D+00 -0.11795232945122243D-34 COMPARISON OF MOMENTS ORDER OF PRECISION 10 ERRORS : ABSOLUTE RELATIVE ---------+------------------------- MINIMUM : 0.902D-16 0.582D-16 MAXIMUM : 0.971D-15 0.444D-15 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 0.167D-15 0.582D-16 2 0.0000000000D+00 -0.9020562075D-16 0.902D-16 0.902D-16 3 0.1247805791D+01 0.1247805791D+01 0.222D-15 0.988D-16 4 0.0000000000D+00 -0.9020562075D-16 0.902D-16 0.902D-16 5 0.1240715985D+01 0.1240715985D+01 0.389D-15 0.173D-15 6 0.0000000000D+00 -0.1387778781D-15 0.139D-15 0.139D-15 7 0.1421653733D+01 0.1421653733D+01 0.638D-15 0.264D-15 8 0.0000000000D+00 -0.2498001805D-15 0.250D-15 0.250D-15 9 0.1753684704D+01 0.1753684704D+01 0.971D-15 0.353D-15 10 0.0000000000D+00 -0.4440892099D-15 0.444D-15 0.444D-15 11 0.2263587593D+01 0.2235050644D+01 0.285D-01 0.874D-02 12 0.0000000000D+00 -0.6661338148D-15 0.666D-15 0.666D-15 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 0.1D-16 KNOTS MULT WEIGHTS 1 -0.43541078852037897D+00 1 0.26216877717069183D-04 2 -0.21664377601574750D+00 1 0.16250543349707103D-04 3 0.25596297684363936D+00 1 0.12927396984510148D-05 4 0.12864478502358691D+01 1 0.11152074844159659D-07 5 0.41096437374566179D+01 1 0.28799054822892455D-11 COMPARISON OF MOMENTS ORDER OF PRECISION 10 ERRORS : ABSOLUTE RELATIVE ---------+------------------------- MINIMUM : 0.265D-22 0.265D-22 MAXIMUM : 0.254D-20 0.254D-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 0.254D-20 0.254D-20 2 0.7295219287D-05 0.7295219287D-05 0.318D-21 0.318D-21 3 0.2188565786D-05 0.2188565786D-05 0.529D-22 0.529D-22 4 0.9991278588D-06 0.9991278588D-06 0.265D-22 0.265D-22 5 0.6422964807D-06 0.6422964807D-06 0.397D-22 0.397D-22 6 0.5577837858D-06 0.5577837858D-06 0.662D-22 0.662D-22 7 0.6398108132D-06 0.6398108132D-06 0.159D-21 0.159D-21 8 0.9597162198D-06 0.9597162198D-06 0.371D-21 0.371D-21 9 0.1882520277D-05 0.1882520277D-05 0.900D-21 0.900D-21 10 0.4877438900D-05 0.4877438900D-05 0.244D-20 0.244D-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 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 0.1D-16 KNOTS MULT WEIGHTS 1 -0.43541078852037897D+00 2 0.26216877717069183D-04 0.68218549863919726D-22 2 -0.21664377601574750D+00 2 0.16250543349707102D-04 0.35129201900358245D-38 3 0.25596297684363936D+00 2 0.12927396984510146D-05 -0.26910550838761838D-22 4 0.12864478502358691D+01 2 0.11152074844159657D-07 -0.46429838491233957D-24 5 0.41096437374566179D+01 2 0.28799054822892453D-11 0.00000000000000000D+00 COMPARISON OF MOMENTS ORDER OF PRECISION 10 ERRORS : ABSOLUTE RELATIVE ---------+------------------------- MINIMUM : 0.185D-21 0.185D-21 MAXIMUM : 0.424D-20 0.423D-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 0.424D-20 0.423D-20 2 0.7295219287D-05 0.7295219287D-05 0.741D-21 0.741D-21 3 0.2188565786D-05 0.2188565786D-05 0.318D-21 0.318D-21 4 0.9991278588D-06 0.9991278588D-06 0.212D-21 0.212D-21 5 0.6422964807D-06 0.6422964807D-06 0.185D-21 0.185D-21 6 0.5577837858D-06 0.5577837858D-06 0.212D-21 0.212D-21 7 0.6398108132D-06 0.6398108132D-06 0.344D-21 0.344D-21 8 0.9597162198D-06 0.9597162198D-06 0.635D-21 0.635D-21 9 0.1882520277D-05 0.1882520277D-05 0.132D-20 0.132D-20 10 0.4877438900D-05 0.4877438900D-05 0.339D-20 0.339D-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 ---------------------------------------- TESTING CEIQFS RETURN FROM CEIQFS: ERROR INDICATOR IER= 0 INTERGRAL OF SIN(X) ON [-1,1] BY FEJER TYPE RULE WITH 5 POINTS OF MULTIPLICITY 2 QUADRATURE FORMULA: -1.7564075194265172E-17 EXACT VALUE : 0.0000000000000000E+00 ---------------------------------------- TESTING CEIQF RETURN FROM CEIQF: ERROR INDICATOR IER= 0 INTERGRAL OF SIN(X) FROM -0.5000000000000000 TO 2.000000000000000 BY FEJER TYPE RULE WITH 5 POINTS OF MULTIPLICITY 2 QUADRATURE FORMULA: 1.293729406614736 EXACT VALUE : 1.293729398437515 ---------------------------------------- TESTING CLIQFS 1 INTERPOLATORY QUADRATURE FORMULA TYPE INTERVAL WEIGHT FUNCTION NAME 1 (-1,1) ONE LEGENDRE MACHINE PRECISION 0.1D-16 KNOTS MULT WEIGHTS 1 0.95105651629515357D+00 1 0.16778122846668345D+00 2 0.58778525229247312D+00 1 0.52555210486664980D+00 3 -0.22034386889519082D-16 1 0.61333333333333317D+00 4 -0.58778525229247315D+00 1 0.52555210486664973D+00 5 -0.95105651629515357D+00 1 0.16778122846668345D+00 COMPARISON OF MOMENTS ORDER OF PRECISION 5 ERRORS : ABSOLUTE RELATIVE ---------+------------------------- MINIMUM : 0.347D-17 0.347D-17 MAXIMUM : 0.361D-15 0.120D-15 WEIGHTS RATIO 0.667D+00 ERROR FOR 5-TH POWER -0.347D-17 ERROR CONSTANT -0.289D-19 MOMENTS: TRUE FROM Q.F. ERROR RELATIVE 1 0.2000000000D+01 0.2000000000D+01 0.361D-15 0.120D-15 2 0.0000000000D+00 0.1734723476D-16 -0.173D-16 -0.173D-16 3 0.6666666667D+00 0.6666666667D+00 0.111D-15 0.666D-16 4 0.0000000000D+00 0.3469446952D-17 -0.347D-17 -0.347D-17 5 0.4000000000D+00 0.4000000000D+00 0.763D-16 0.545D-16 6 0.0000000000D+00 0.3469446952D-17 -0.347D-17 -0.347D-17 7 0.2857142857D+00 0.2916666667D+00 -0.595D-02 -0.463D-02 8 0.0000000000D+00 0.0000000000D+00 0.000D+00 0.000D+00 RETURN FROM CLIQFS. IER= 0 ---------------------------------------- TESTING 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 0.1D-16 KNOTS MULT WEIGHTS 1 0.19388206453689420D+01 1 0.20972653558335429D+00 2 0.14847315653655914D+01 1 0.65694013108331227D+00 3 0.74999999999999997D+00 1 0.76666666666666645D+00 4 0.15268434634408565D-01 1 0.65694013108331215D+00 5 -0.43882064536894197D+00 1 0.20972653558335429D+00 COMPARISON OF MOMENTS ORDER OF PRECISION 5 ERRORS : ABSOLUTE RELATIVE ---------+------------------------- MINIMUM : 0.486D-16 0.486D-16 MAXIMUM : 0.500D-15 0.143D-15 WEIGHTS RATIO 0.714D+00 ERROR FOR 5-TH POWER -0.694D-17 ERROR CONSTANT -0.578D-19 MOMENTS: TRUE FROM Q.F. ERROR RELATIVE 1 0.2500000000D+01 0.2500000000D+01 0.500D-15 0.143D-15 2 0.0000000000D+00 0.5204170428D-16 -0.520D-16 -0.520D-16 3 0.1302083333D+01 0.1302083333D+01 0.278D-15 0.121D-15 4 0.0000000000D+00 0.4857225733D-16 -0.486D-16 -0.486D-16 5 0.1220703125D+01 0.1220703125D+01 0.278D-15 0.125D-15 6 0.0000000000D+00 0.6938893904D-17 -0.694D-17 -0.694D-17 7 0.1362391881D+01 0.1390775045D+01 -0.284D-01 -0.120D-01 8 0.0000000000D+00 -0.1387778781D-16 0.139D-16 0.139D-16 RETURN FROM CLIQF: ERROR INDICATOR IER= 0 RETURN FROM EIQFS: ERROR INDICATOR IER= 0 INTERGRAL OF SIN(X) FROM -0.5000000000000000 TO 2.000000000000000 BY FEJER TYPE RULE WITH 5 POINTS OF MULTIPLICITY ONE QUADRATURE FORMULA: 1.293704657106341 EXACT VALUE : 1.293729398437515 ---------------------------------------- TESTING CEGQF RETURN FROM CEGQF: ERROR INDICATOR IER= 0 INTERGRAL OF X*SIN(X) FROM 1.000000000000000 TO 4.000000000000000 BY GAUSS-EXPONENTIAL RULE WITH 12 POINTS QUADRATURE FORMULA: 0.6786430913896829 EXACT VALUE : 0.6786430913896827 TESTING CEGQFS RETURN FROM CEGQFS: ERROR INDICATOR IER= 0 INTERGRAL OF X*SIN(X) FROM -1.000000000000000 TO 1.000000000000000 BY GAUSS-EXPONENTIAL RULE WITH 12 POINTS QUADRATURE FORMULA: -1.7694179454963432E-16 EXACT VALUE : 0.0000000000000000E+00