06 April 2023 8:12:32.782 PM toms672_test(): FORTRAN90 version Test toms672(). Choose ICASE, the initial rule to extend: 1, 3 point Gauss-Legendre in [-1,1]; 2, 2 point Gauss-Lobatto in [-1,1]; 3, 6 point Radau in [-1,1]; 4, 2 point Gauss-Laguerre in [0,+oo); 5, 3 point Gauss-Hermite in (-oo,+oo); 6, 3 point Gauss-Jacobi in [0,1]. Enter ICASE, between 1 and 6, or -1 to stop: ICASE = 1 Enter NSEQ, the number of nested rules to compute: NSEQ = 7 TEST01 Extension of a 3 point Gauss-Legendre rule. N = 0 M = 3 M0 = 0 SYMMET = T START = F Iteration 1 Coefficients of expansion whose roots are the new nodes: 0.0000000000000000D+00 * P( 0,X) 0.0000000000000000D+00 * P( 1,X) 0.0000000000000000D+00 * P( 2,X) 0.1000000000000000D+01 * P( 3,X) New nodes real Imaginary Flag Err 0.0000000000000000D+00 0.0000000000000000D+00 0 0.0D+00 -0.7745966692414834D+00 0.0000000000000000D+00 0 0.0D+00 0.7745966692414833D+00 0.0000000000000000D+00 0 0.0D+00 New full extended expansion 0.1000000000000000D+01 * P( 3,X)/HI Complete extended rule: STEP = 1 POINTS = 3 IFLAG = 0 Nodes added = 3 No. Node Weight 1 0.7745966692414833D+00 0.5555555555555559D+00 2 0.0000000000000000D+00 0.8888888888888888D+00 Test( 0) = 0.1000000000000000D+01 Test( 1) = 0.1000000000000001D+01 Test( 2) = 0.1000000000000000D+01 Iteration 2 Coefficients of expansion whose roots are the new nodes: 0.1571268237934878D-01 * P( 0,X) 0.0000000000000000D+00 * P( 1,X) -0.7407407407407408D+00 * P( 2,X) 0.0000000000000000D+00 * P( 3,X) 0.1000000000000000D+01 * P( 4,X) New nodes real Imaginary Flag Err 0.4342437493468025D+00 0.0000000000000000D+00 0 0.1D-16 -0.4342437493468025D+00 0.0000000000000000D+00 0 0.1D-16 -0.9604912687080204D+00 0.0000000000000000D+00 0 0.1D-16 0.9604912687080203D+00 0.0000000000000000D+00 0 0.1D-16 New full extended expansion 0.0000000000000000D+00 * P( 4,X)/HI -0.4444444444444440D+00 * P( 5,X)/HI 0.0000000000000000D+00 * P( 6,X)/HI 0.1000000000000000D+01 * P( 7,X)/HI Complete extended rule: STEP = 2 POINTS = 7 IFLAG = 0 Nodes added = 4 No. Node Weight 1 0.9604912687080203D+00 0.1046562260264672D+00 2 0.7745966692414833D+00 0.2684880898683333D+00 3 0.4342437493468025D+00 0.4013974147759621D+00 4 0.0000000000000000D+00 0.4509165386584741D+00 Test( 0) = 0.9999999999999997D+00 Test( 1) = 0.9999999999999996D+00 Test( 2) = 0.9999999999999998D+00 Test( 3) = 0.1000000000000000D+01 Test( 4) = 0.1000000000000000D+01 Iteration 3 Coefficients of expansion whose roots are the new nodes: 0.5772349298068201D-03 * P( 0,X) 0.0000000000000000D+00 * P( 1,X) 0.1407910917434216D-02 * P( 2,X) 0.0000000000000000D+00 * P( 3,X) 0.2790650691523969D+00 * P( 4,X) 0.0000000000000000D+00 * P( 5,X) -0.1205049839843540D+01 * P( 6,X) 0.0000000000000000D+00 * P( 7,X) 0.1000000000000000D+01 * P( 8,X) New nodes real Imaginary Flag Err 0.2233866864289669D+00 0.0000000000000000D+00 0 0.0D+00 -0.2233866864289669D+00 0.0000000000000000D+00 0 0.0D+00 0.6211029467372263D+00 0.0000000000000000D+00 0 0.3D-17 -0.6211029467372264D+00 0.0000000000000000D+00 0 0.3D-17 0.8884592328722570D+00 0.0000000000000000D+00 0 0.0D+00 -0.8884592328722569D+00 0.0000000000000000D+00 0 0.0D+00 -0.9938319632127550D+00 0.0000000000000000D+00 0 0.2D-16 0.9938319632127551D+00 0.0000000000000000D+00 0 0.2D-16 New full extended expansion 0.0000000000000000D+00 * P( 8,X)/HI -0.2896464423067137D-01 * P( 9,X)/HI 0.0000000000000000D+00 * P( 10,X)/HI 0.3461310330856245D+00 * P( 11,X)/HI 0.0000000000000000D+00 * P( 12,X)/HI -0.1000000000000000D+01 * P( 13,X)/HI 0.0000000000000000D+00 * P( 14,X)/HI 0.7705426896934804D+00 * P( 15,X)/HI Complete extended rule: STEP = 3 POINTS = 15 IFLAG = 0 Nodes added = 8 No. Node Weight 1 0.9938319632127551D+00 0.1700171962994060D-01 2 0.9604912687080203D+00 0.5160328299707961D-01 3 0.8884592328722570D+00 0.9292719531512468D-01 4 0.7745966692414833D+00 0.1344152552437841D+00 5 0.6211029467372263D+00 0.1715119091363912D+00 6 0.4342437493468025D+00 0.2006285293769889D+00 7 0.2233866864289669D+00 0.2191568584015875D+00 8 0.0000000000000000D+00 0.2255104997982067D+00 Test( 0) = 0.1000000000000000D+01 Test( 1) = 0.1000000000000000D+01 Test( 2) = 0.1000000000000001D+01 Test( 3) = 0.1000000000000002D+01 Test( 4) = 0.1000000000000002D+01 Iteration 4 Coefficients of expansion whose roots are the new nodes: 0.4594336614924235D-05 * P( 0,X) 0.0000000000000000D+00 * P( 1,X) 0.2102213998818682D-04 * P( 2,X) 0.0000000000000000D+00 * P( 3,X) 0.3284239361934402D-04 * P( 4,X) 0.0000000000000000D+00 * P( 5,X) 0.3983737163135045D-04 * P( 6,X) 0.0000000000000000D+00 * P( 7,X) 0.2118704776054677D-01 * P( 8,X) 0.0000000000000000D+00 * P( 9,X) -0.3321835300554099D+00 * P( 10,X) 0.0000000000000000D+00 * P( 11,X) 0.1390617734655774D+01 * P( 12,X) 0.0000000000000000D+00 * P( 13,X) -0.2071847272743303D+01 * P( 14,X) 0.0000000000000000D+00 * P( 15,X) 0.1000000000000000D+01 * P( 16,X) New nodes real Imaginary Flag Err 0.1124889431331867D+00 0.0000000000000000D+00 0 0.1D-16 -0.1124889431331867D+00 0.0000000000000000D+00 0 0.1D-16 0.3311353932579769D+00 0.0000000000000000D+00 0 0.4D-17 -0.3311353932579769D+00 0.0000000000000000D+00 0 0.4D-17 0.5313197436443756D+00 0.0000000000000000D+00 0 0.1D-16 -0.5313197436443756D+00 0.0000000000000000D+00 0 0.1D-16 0.7024962064915270D+00 0.0000000000000000D+00 0 0.6D-17 -0.7024962064915271D+00 0.0000000000000000D+00 0 0.6D-17 0.8367259381688688D+00 0.0000000000000000D+00 0 0.5D-17 -0.8367259381688688D+00 0.0000000000000000D+00 0 0.5D-17 0.9296548574297400D+00 0.0000000000000000D+00 0 0.8D-17 -0.9296548574297401D+00 0.0000000000000000D+00 0 0.8D-17 0.9815311495537394D+00 0.0000000000000000D+00 0 0.1D-16 -0.9815311495537397D+00 0.0000000000000000D+00 0 0.1D-16 0.9990981249676684D+00 0.0000000000000000D+00 0 0.2D-16 -0.9990981249676685D+00 0.0000000000000000D+00 0 0.2D-16 New full extended expansion 0.0000000000000000D+00 * P( 16,X)/HI -0.3511346182465012D-04 * P( 17,X)/HI 0.0000000000000000D+00 * P( 18,X)/HI 0.1821511633710668D-02 * P( 19,X)/HI 0.0000000000000000D+00 * P( 20,X)/HI -0.2732224288321012D-01 * P( 21,X)/HI 0.0000000000000000D+00 * P( 22,X)/HI 0.1776094066225408D+00 * P( 23,X)/HI 0.0000000000000000D+00 * P( 24,X)/HI -0.5826038173584090D+00 * P( 25,X)/HI 0.0000000000000000D+00 * P( 26,X)/HI 0.1000000000000000D+01 * P( 27,X)/HI 0.0000000000000000D+00 * P( 28,X)/HI -0.8533770765897805D+00 * P( 29,X)/HI 0.0000000000000000D+00 * P( 30,X)/HI 0.2848623286437712D+00 * P( 31,X)/HI Complete extended rule: STEP = 4 POINTS = 31 IFLAG = 0 Nodes added = 16 No. Node Weight 1 0.9990981249676684D+00 0.2544780791562395D-02 2 0.9938319632127551D+00 0.8434565739322653D-02 3 0.9815311495537394D+00 0.1644604985438693D-01 4 0.9604912687080203D+00 0.2580759809617683D-01 5 0.9296548574297400D+00 0.3595710330712853D-01 6 0.8884592328722570D+00 0.4646289326175795D-01 7 0.8367259381688688D+00 0.5697950949412346D-01 8 0.7745966692414833D+00 0.6720775429599059D-01 9 0.7024962064915270D+00 0.7687962049900343D-01 10 0.6211029467372263D+00 0.8575592004999016D-01 11 0.5313197436443756D+00 0.9362710998126446D-01 12 0.4342437493468025D+00 0.1003142786117955D+00 13 0.3311353932579769D+00 0.1056698935802349D+00 14 0.2233866864289669D+00 0.1095784210559247D+00 15 0.1124889431331867D+00 0.1119568730209535D+00 16 0.0000000000000000D+00 0.1127552567207687D+00 Test( 0) = 0.1000000000000000D+01 Test( 1) = 0.1000000000000001D+01 Test( 2) = 0.1000000000000004D+01 Test( 3) = 0.1000000000000007D+01 Test( 4) = 0.1000000000000010D+01 Iteration 5 Coefficients of expansion whose roots are the new nodes: 0.7116088478528588D-08 * P( 0,X) 0.0000000000000000D+00 * P( 1,X) 0.3532911993571470D-07 * P( 2,X) 0.0000000000000000D+00 * P( 3,X) 0.6257040032105011D-07 * P( 4,X) 0.0000000000000000D+00 * P( 5,X) 0.8817862113447986D-07 * P( 6,X) 0.0000000000000000D+00 * P( 7,X) 0.1116456776178847D-06 * P( 8,X) 0.0000000000000000D+00 * P( 9,X) 0.1326231271428104D-06 * P( 10,X) 0.0000000000000000D+00 * P( 11,X) 0.1509058848218026D-06 * P( 12,X) 0.0000000000000000D+00 * P( 13,X) 0.1664059795023336D-06 * P( 14,X) 0.0000000000000000D+00 * P( 15,X) 0.6566348222612201D-04 * P( 16,X) 0.0000000000000000D+00 * P( 17,X) -0.3865699006967617D-02 * P( 18,X) 0.0000000000000000D+00 * P( 19,X) 0.6693574111003317D-01 * P( 20,X) 0.0000000000000000D+00 * P( 21,X) -0.5140199299838704D+00 * P( 22,X) 0.0000000000000000D+00 * P( 23,X) 0.2065147195919813D+01 * P( 24,X) 0.0000000000000000D+00 * P( 25,X) -0.4622952217984019D+01 * P( 26,X) 0.0000000000000000D+00 * P( 27,X) 0.5785693203195086D+01 * P( 28,X) 0.0000000000000000D+00 * P( 29,X) -0.3776887826861610D+01 * P( 30,X) 0.0000000000000000D+00 * P( 31,X) 0.1000000000000000D+01 * P( 32,X) New nodes real Imaginary Flag Err 0.5634431304659279D-01 0.0000000000000000D+00 0 0.1D-16 -0.5634431304659279D-01 0.0000000000000000D+00 0 0.1D-16 0.1682352515522074D+00 0.0000000000000000D+00 0 0.3D-17 -0.1682352515522074D+00 0.0000000000000000D+00 0 0.3D-17 0.2777498220218243D+00 0.0000000000000000D+00 0 0.3D-17 -0.2777498220218243D+00 0.0000000000000000D+00 0 0.3D-17 0.3833593241987304D+00 0.0000000000000000D+00 0 0.1D-16 -0.3833593241987303D+00 0.0000000000000000D+00 0 0.1D-16 0.4836180269458411D+00 0.0000000000000000D+00 0 0.2D-16 -0.4836180269458410D+00 0.0000000000000000D+00 0 0.2D-16 0.5771957100520458D+00 0.0000000000000000D+00 0 0.7D-17 -0.5771957100520457D+00 0.0000000000000000D+00 0 0.7D-17 0.6629096600247807D+00 0.0000000000000000D+00 0 0.6D-17 -0.6629096600247806D+00 0.0000000000000000D+00 0 0.6D-17 0.7397560443526947D+00 0.0000000000000000D+00 0 0.2D-17 -0.7397560443526949D+00 0.0000000000000000D+00 0 0.2D-17 0.8069405319502176D+00 0.0000000000000000D+00 0 0.1D-16 -0.8069405319502176D+00 0.0000000000000000D+00 0 0.1D-16 0.8639079381936914D+00 0.0000000000000000D+00 0 0.2D-16 -0.8639079381936915D+00 0.0000000000000000D+00 0 0.2D-16 0.9103711569570022D+00 0.0000000000000000D+00 0 0.1D-16 -0.9103711569570022D+00 0.0000000000000000D+00 0 0.1D-16 0.9463428583734306D+00 0.0000000000000000D+00 0 0.4D-16 -0.9463428583734306D+00 0.0000000000000000D+00 0 0.4D-16 0.9721828747483419D+00 0.0000000000000000D+00 0 0.8D-16 -0.9721828747483421D+00 0.0000000000000000D+00 0 0.8D-16 0.9886847575496512D+00 0.0000000000000000D+00 0 0.5D-15 -0.9886847575496512D+00 0.0000000000000000D+00 0 0.5D-15 0.9972062593519975D+00 0.0000000000000000D+00 0 0.2D-15 -0.9972062593519975D+00 0.0000000000000000D+00 0 0.2D-15 -0.9998728881624622D+00 0.0000000000000000D+00 0 0.5D-15 0.9998728881624621D+00 0.0000000000000000D+00 0 0.5D-15 New full extended expansion 0.0000000000000000D+00 * P( 32,X)/HI -0.1969658036411059D-10 * P( 33,X)/HI 0.0000000000000000D+00 * P( 34,X)/HI 0.3910708908139239D-08 * P( 35,X)/HI 0.0000000000000000D+00 * P( 36,X)/HI -0.2507443416299357D-06 * P( 37,X)/HI 0.0000000000000000D+00 * P( 38,X)/HI 0.7504947976344545D-05 * P( 39,X)/HI 0.0000000000000000D+00 * P( 40,X)/HI -0.1272930729584675D-03 * P( 41,X)/HI 0.0000000000000000D+00 * P( 42,X)/HI 0.1355468374334545D-02 * P( 43,X)/HI 0.0000000000000000D+00 * P( 44,X)/HI -0.9644301042308694D-02 * P( 45,X)/HI 0.0000000000000000D+00 * P( 46,X)/HI 0.4767465225958541D-01 * P( 47,X)/HI 0.0000000000000000D+00 * P( 48,X)/HI -0.1676018046835677D+00 * P( 49,X)/HI 0.0000000000000000D+00 * P( 50,X)/HI 0.4238271464611814D+00 * P( 51,X)/HI 0.0000000000000000D+00 * P( 52,X)/HI -0.7714935146989157D+00 * P( 53,X)/HI 0.0000000000000000D+00 * P( 54,X)/HI 0.1000000000000000D+01 * P( 55,X)/HI 0.0000000000000000D+00 * P( 56,X)/HI -0.8989323767258427D+00 * P( 57,X)/HI 0.0000000000000000D+00 * P( 58,X)/HI 0.5318583303989894D+00 * P( 59,X)/HI 0.0000000000000000D+00 * P( 60,X)/HI -0.1860455273010188D+00 * P( 61,X)/HI 0.0000000000000000D+00 * P( 62,X)/HI 0.2912202192754925D-01 * P( 63,X)/HI Complete extended rule: STEP = 5 POINTS = 63 IFLAG = 0 Nodes added = 32 No. Node Weight 1 0.9998728881624621D+00 0.3632214353548940D-03 2 0.9990981249676684D+00 0.1265156629062565D-02 3 0.9972062593519975D+00 0.2579049776280808D-02 4 0.9938319632127551D+00 0.4217630431178584D-02 5 0.9886847575496512D+00 0.6115506824605626D-02 6 0.9815311495537394D+00 0.8223007958269015D-02 7 0.9721828747483419D+00 0.1049824690924750D-01 8 0.9604912687080203D+00 0.1290380010020241D-01 9 0.9463428583734306D+00 0.1540675046657413D-01 10 0.9296548574297400D+00 0.1797855156813466D-01 11 0.9103711569570022D+00 0.2059423391591271D-01 12 0.8884592328722570D+00 0.2323144663990674D-01 13 0.8639079381936914D+00 0.2586967932721557D-01 14 0.8367259381688688D+00 0.2848975474583409D-01 15 0.8069405319502176D+00 0.3107355111168843D-01 16 0.7745966692414833D+00 0.3360387714820731D-01 17 0.7397560443526947D+00 0.3606443278078231D-01 18 0.7024962064915270D+00 0.3843981024945529D-01 19 0.6629096600247807D+00 0.4071551011694457D-01 20 0.6211029467372263D+00 0.4287796002500757D-01 21 0.5771957100520458D+00 0.4491453165363227D-01 22 0.5313197436443756D+00 0.4681355499062800D-01 23 0.4836180269458411D+00 0.4856433040667326D-01 24 0.4342437493468025D+00 0.5015713930589947D-01 25 0.3833593241987304D+00 0.5158325395204848D-01 26 0.3311353932579769D+00 0.5283494679011655D-01 27 0.2777498220218243D+00 0.5390549933526607D-01 28 0.2233866864289669D+00 0.5478921052796289D-01 29 0.1682352515522074D+00 0.5548140435655936D-01 30 0.1124889431331867D+00 0.5597843651047632D-01 31 0.5634431304659279D-01 0.5627769983125428D-01 32 0.0000000000000000D+00 0.5637762836038470D-01 Test( 0) = 0.1000000000000574D+01 Test( 1) = 0.1000000000001712D+01 Test( 2) = 0.1000000000002809D+01 Test( 3) = 0.1000000000003811D+01 Test( 4) = 0.1000000000004636D+01 Iteration 6 Coefficients of expansion whose roots are the new nodes: 0.4334576111581531D-06 * P( 0,X) 0.0000000000000000D+00 * P( 1,X) 0.2163092931545225D-05 * P( 2,X) 0.0000000000000000D+00 * P( 3,X) 0.3876065861349511D-05 * P( 4,X) 0.0000000000000000D+00 * P( 5,X) 0.5559510344788366D-05 * P( 6,X) 0.0000000000000000D+00 * P( 7,X) 0.7201322660422004D-05 * P( 8,X) 0.0000000000000000D+00 * P( 9,X) 0.8790432372519419D-05 * P( 10,X) 0.0000000000000000D+00 * P( 11,X) 0.1031701071304755D-04 * P( 12,X) 0.0000000000000000D+00 * P( 13,X) 0.1177261128919885D-04 * P( 14,X) 0.0000000000000000D+00 * P( 15,X) 0.1315024449274791D-04 * P( 16,X) 0.0000000000000000D+00 * P( 17,X) 0.1444439193284604D-04 * P( 18,X) 0.0000000000000000D+00 * P( 19,X) 0.1565097017684540D-04 * P( 20,X) 0.0000000000000000D+00 * P( 21,X) 0.1676725460731948D-04 * P( 22,X) 0.0000000000000000D+00 * P( 23,X) 0.1779177418616185D-04 * P( 24,X) 0.0000000000000000D+00 * P( 25,X) 0.1872418709945868D-04 * P( 26,X) 0.0000000000000000D+00 * P( 27,X) 0.1956514600429026D-04 * P( 28,X) 0.0000000000000000D+00 * P( 29,X) 0.2031615995564612D-04 * P( 30,X) 0.0000000000000000D+00 * P( 31,X) 0.2097980730561345D-04 * P( 32,X) 0.0000000000000000D+00 * P( 33,X) 0.2148536442843617D-04 * P( 34,X) 0.0000000000000000D+00 * P( 35,X) 0.2683607809632266D-04 * P( 36,X) 0.0000000000000000D+00 * P( 37,X) -0.1214689005728997D-03 * P( 38,X) 0.0000000000000000D+00 * P( 39,X) 0.2420231891595355D-02 * P( 40,X) 0.0000000000000000D+00 * P( 41,X) -0.2432094257155350D-01 * P( 42,X) 0.0000000000000000D+00 * P( 43,X) 0.1591742352955007D+00 * P( 44,X) 0.0000000000000000D+00 * P( 45,X) -0.6874683464844179D+00 * P( 46,X) 0.0000000000000000D+00 * P( 47,X) 0.1962791845850270D+01 * P( 48,X) 0.0000000000000000D+00 * P( 49,X) -0.3580614805651047D+01 * P( 50,X) 0.0000000000000000D+00 * P( 51,X) 0.3762586371279657D+01 * P( 52,X) 0.0000000000000000D+00 * P( 53,X) -0.1603245431026113D+01 * P( 54,X) 0.0000000000000000D+00 * P( 55,X) 0.6728301612733349D-01 * P( 56,X) 0.0000000000000000D+00 * P( 57,X) -0.2138405562922082D+01 * P( 58,X) 0.0000000000000000D+00 * P( 59,X) 0.4693926653116400D+01 * P( 60,X) 0.0000000000000000D+00 * P( 61,X) -0.3612868602590880D+01 * P( 62,X) 0.0000000000000000D+00 * P( 63,X) 0.1000000000000000D+01 * P( 64,X) New nodes real Imaginary Flag Err 0.2818464894974543D-01 0.0000000000000000D+00 0 0.1D-16 -0.2818464894974544D-01 0.0000000000000000D+00 0 0.1D-16 0.8445404008371089D-01 0.0000000000000000D+00 0 0.4D-17 -0.8445404008371091D-01 0.0000000000000000D+00 0 0.4D-17 0.1404242331525601D+00 0.0000000000000000D+00 0 0.2D-17 -0.1404242331525601D+00 0.0000000000000000D+00 0 0.2D-17 0.1958975027111002D+00 0.0000000000000000D+00 0 0.3D-16 -0.1958975027111001D+00 0.0000000000000000D+00 0 0.3D-16 0.2506787303034833D+00 0.0000000000000000D+00 0 0.3D-16 -0.2506787303034832D+00 0.0000000000000000D+00 0 0.3D-16 0.3045764415567139D+00 0.0000000000000000D+00 0 0.6D-16 -0.3045764415567140D+00 0.0000000000000000D+00 0 0.6D-16 0.3098990805289147D+00 0.0000000000000000D+00 0 0.3D-16 -0.3098990805289147D+00 0.0000000000000000D+00 0 0.3D-16 0.3574038378315321D+00 0.0000000000000000D+00 0 0.3D-17 -0.3574038378315321D+00 0.0000000000000000D+00 0 0.3D-17 0.4089798212298887D+00 0.0000000000000000D+00 0 0.1D-16 -0.4089798212298886D+00 0.0000000000000000D+00 0 0.1D-16 0.4591300119898323D+00 0.0000000000000000D+00 0 0.2D-17 -0.4591300119898323D+00 0.0000000000000000D+00 0 0.2D-17 0.5076877575337166D+00 0.0000000000000000D+00 0 0.2D-16 -0.5076877575337166D+00 0.0000000000000000D+00 0 0.2D-16 0.5544951326319326D+00 0.0000000000000000D+00 0 0.2D-16 -0.5544951326319325D+00 0.0000000000000000D+00 0 0.2D-16 0.5994039302422429D+00 0.0000000000000000D+00 0 0.3D-17 -0.5994039302422429D+00 0.0000000000000000D+00 0 0.3D-17 0.6422766425097596D+00 0.0000000000000000D+00 0 0.2D-16 -0.6422766425097595D+00 0.0000000000000000D+00 0 0.2D-16 0.6829874310910792D+00 0.0000000000000000D+00 0 0.2D-17 -0.6829874310910793D+00 0.0000000000000000D+00 0 0.2D-17 0.7214230853700990D+00 0.0000000000000000D+00 0 0.1D-16 -0.7214230853700990D+00 0.0000000000000000D+00 0 0.1D-16 0.7574839663805136D+00 0.0000000000000000D+00 0 0.4D-17 -0.7574839663805139D+00 0.0000000000000000D+00 0 0.4D-17 0.7910849337998478D+00 0.0000000000000000D+00 0 0.5D-17 -0.7910849337998478D+00 0.0000000000000000D+00 0 0.5D-17 0.8221562543649820D+00 0.0000000000000000D+00 0 0.2D-16 -0.8221562543649820D+00 0.0000000000000000D+00 0 0.2D-16 0.8506444947683428D+00 0.0000000000000000D+00 0 0.2D-16 -0.8506444947683430D+00 0.0000000000000000D+00 0 0.2D-16 0.8765134144847476D+00 0.0000000000000000D+00 0 0.2D-16 -0.8765134144847476D+00 0.0000000000000000D+00 0 0.2D-16 0.8997448997767079D+00 0.0000000000000000D+00 0 0.0D+00 -0.8997448997767078D+00 0.0000000000000000D+00 0 0.0D+00 0.9203400254715381D+00 0.0000000000000000D+00 0 0.3D-16 -0.9203400254715383D+00 0.0000000000000000D+00 0 0.3D-16 0.9383203977686887D+00 0.0000000000000000D+00 0 0.1D-15 -0.9383203977686888D+00 0.0000000000000000D+00 0 0.1D-15 0.9537300065144182D+00 0.0000000000000000D+00 0 0.7D-16 -0.9537300065144181D+00 0.0000000000000000D+00 0 0.7D-16 0.9666378507595709D+00 0.0000000000000000D+00 0 0.4D-16 -0.9666378507595709D+00 0.0000000000000000D+00 0 0.4D-16 0.9771415224797756D+00 0.0000000000000000D+00 0 0.3D-15 -0.9771415224797758D+00 0.0000000000000000D+00 0 0.3D-15 0.9853714172836795D+00 0.0000000000000000D+00 0 0.8D-16 -0.9853714172836795D+00 0.0000000000000000D+00 0 0.8D-16 0.9914966039134901D+00 0.0000000000000000D+00 0 0.6D-15 -0.9914966039134901D+00 0.0000000000000000D+00 0 0.6D-15 0.9957152446419197D+00 0.0000000000000000D+00 0 0.2D-15 -0.9957152446419198D+00 0.0000000000000000D+00 0 0.2D-15 0.9983957632275292D+00 0.0000000000000000D+00 0 0.6D-15 -0.9983957632275291D+00 0.0000000000000000D+00 0 0.6D-15 0.9993687148939459D+00 0.0000000000000000D+00 0 0.6D-16 -0.9993687148939457D+00 0.0000000000000000D+00 0 0.6D-16 New full extended expansion 0.0000000000000000D+00 * P( 64,X)/HI 0.5003868880569939D-14 * P( 65,X)/HI 0.0000000000000000D+00 * P( 66,X)/HI 0.2165296117408135D-13 * P( 67,X)/HI 0.0000000000000000D+00 * P( 68,X)/HI 0.6465549991701755D-13 * P( 69,X)/HI 0.0000000000000000D+00 * P( 70,X)/HI 0.1406521282833675D-12 * P( 71,X)/HI 0.0000000000000000D+00 * P( 72,X)/HI 0.2073147060701107D-12 * P( 73,X)/HI 0.0000000000000000D+00 * P( 74,X)/HI 0.2895531536685530D-11 * P( 75,X)/HI 0.0000000000000000D+00 * P( 76,X)/HI -0.7696657698996768D-10 * P( 77,X)/HI 0.0000000000000000D+00 * P( 78,X)/HI 0.1779584839218193D-08 * P( 79,X)/HI 0.0000000000000000D+00 * P( 80,X)/HI -0.3070872574353036D-07 * P( 81,X)/HI 0.0000000000000000D+00 * P( 82,X)/HI 0.4099520255409629D-06 * P( 83,X)/HI 0.0000000000000000D+00 * P( 84,X)/HI -0.4314936557177205D-05 * P( 85,X)/HI 0.0000000000000000D+00 * P( 86,X)/HI 0.3634982329728776D-04 * P( 87,X)/HI 0.0000000000000000D+00 * P( 88,X)/HI -0.2478665931980241D-03 * P( 89,X)/HI 0.0000000000000000D+00 * P( 90,X)/HI 0.1379464230283251D-02 * P( 91,X)/HI 0.0000000000000000D+00 * P( 92,X)/HI -0.6301120798052684D-02 * P( 93,X)/HI 0.0000000000000000D+00 * P( 94,X)/HI 0.2369791395578046D-01 * P( 95,X)/HI 0.0000000000000000D+00 * P( 96,X)/HI -0.7343520280396312D-01 * P( 97,X)/HI 0.0000000000000000D+00 * P( 98,X)/HI 0.1871649439900920D+00 * P( 99,X)/HI 0.0000000000000000D+00 * P(100,X)/HI -0.3906079902734594D+00 * P(101,X)/HI 0.0000000000000000D+00 * P(102,X)/HI 0.6628549245265236D+00 * P(103,X)/HI 0.0000000000000000D+00 * P(104,X)/HI -0.9073465583981467D+00 * P(105,X)/HI 0.0000000000000000D+00 * P(106,X)/HI 0.1000000000000000D+01 * P(107,X)/HI 0.0000000000000000D+00 * P(108,X)/HI -0.9151528513429209D+00 * P(109,X)/HI 0.0000000000000000D+00 * P(110,X)/HI 0.7890948216980128D+00 * P(111,X)/HI 0.0000000000000000D+00 * P(112,X)/HI -0.7850343836330265D+00 * P(113,X)/HI 0.0000000000000000D+00 * P(114,X)/HI 0.8838703368792266D+00 * P(115,X)/HI 0.0000000000000000D+00 * P(116,X)/HI -0.8941878731010805D+00 * P(117,X)/HI 0.0000000000000000D+00 * P(118,X)/HI 0.6975456370973014D+00 * P(119,X)/HI 0.0000000000000000D+00 * P(120,X)/HI -0.3908265571826735D+00 * P(121,X)/HI 0.0000000000000000D+00 * P(122,X)/HI 0.1477867911986695D+00 * P(123,X)/HI 0.0000000000000000D+00 * P(124,X)/HI -0.3383879243343160D-01 * P(125,X)/HI 0.0000000000000000D+00 * P(126,X)/HI 0.3551947402437924D-02 * P(127,X)/HI Complete extended rule: STEP = 6 POINTS = 127 IFLAG = 0 Nodes added = 64 No. Node Weight 1 0.9998728881624621D+00 0.3236167685534062D-03 2 0.9993687148939459D+00 0.6090402816815537D-03 3 0.9990981249676684D+00 0.1779303763664910D-03 4 0.9983957632275292D+00 0.1042010061850228D-02 5 0.9972062593519975D+00 0.1329808017888389D-02 6 0.9957152446419197D+00 0.1671408976532943D-02 7 0.9938319632127551D+00 0.2104331274942691D-02 8 0.9914966039134901D+00 0.2569808240865058D-02 9 0.9886847575496512D+00 0.3058176756546499D-02 10 0.9853714172836795D+00 0.3572795391028807D-02 11 0.9815311495537394D+00 0.4111464511528377D-02 12 0.9771415224797756D+00 0.4671059449707099D-02 13 0.9721828747483419D+00 0.5249127334564408D-02 14 0.9666378507595709D+00 0.5843448986621006D-02 15 0.9604912687080203D+00 0.6451899637197071D-02 16 0.9537300065144182D+00 0.7072490087856192D-02 17 0.9463428583734306D+00 0.7703375282769579D-02 18 0.9383203977686887D+00 0.8342838743282134D-02 19 0.9296548574297400D+00 0.8989275776689344D-02 20 0.9203400254715381D+00 0.9641177730572985D-02 21 0.9103711569570022D+00 0.1029711695891056D-01 22 0.8997448997767079D+00 0.1095573338777317D-01 23 0.8884592328722570D+00 0.1161572331982810D-01 24 0.8765134144847476D+00 0.1227583056010316D-01 25 0.8639079381936914D+00 0.1293483966362576D-01 26 0.8506444947683428D+00 0.1359157100975411D-01 27 0.8367259381688688D+00 0.1424487737290513D-01 28 0.8221562543649820D+00 0.1489364166481153D-01 29 0.8069405319502176D+00 0.1553677555584463D-01 30 0.7910849337998478D+00 0.1617321872957747D-01 31 0.7745966692414833D+00 0.1680193857410342D-01 32 0.7574839663805136D+00 0.1742193015946372D-01 33 0.7397560443526947D+00 0.1803221639039098D-01 34 0.7214230853700990D+00 0.1863184825613894D-01 35 0.7024962064915270D+00 0.1921990512472742D-01 36 0.6829874310910792D+00 0.1979549504809729D-01 37 0.6629096600247807D+00 0.2035775505847229D-01 38 0.6422766425097596D+00 0.2090585144581211D-01 39 0.6211029467372263D+00 0.2143898001250364D-01 40 0.5994039302422429D+00 0.2195636630531778D-01 41 0.5771957100520458D+00 0.2245726582681611D-01 42 0.5544951326319326D+00 0.2294096422938786D-01 43 0.5313197436443756D+00 0.2340677749531401D-01 44 0.5076877575337166D+00 0.2385405210603862D-01 45 0.4836180269458411D+00 0.2428216520333664D-01 46 0.4591300119898323D+00 0.2469052474448762D-01 47 0.4342437493468025D+00 0.2507856965294973D-01 48 0.4089798212298887D+00 0.2544576996546478D-01 49 0.3833593241987304D+00 0.2579162697602426D-01 50 0.3574038378315321D+00 0.2611567337670609D-01 51 0.3311353932579769D+00 0.2641747339505825D-01 52 0.3098990805289147D+00 0.9955804320592319D-16 53 0.3045764415567139D+00 0.2669662292744961D-01 54 0.2777498220218243D+00 0.2695274966763299D-01 55 0.2506787303034833D+00 0.2718551322962489D-01 56 0.2233866864289669D+00 0.2739460526398145D-01 57 0.1958975027111002D+00 0.2757974956648188D-01 58 0.1682352515522074D+00 0.2774070217827967D-01 59 0.1404242331525601D+00 0.2787725147661368D-01 60 0.1124889431331867D+00 0.2798921825523815D-01 61 0.8445404008371089D-01 0.2807645579381726D-01 62 0.5634431304659279D-01 0.2813884991562716D-01 63 0.2818464894974543D-01 0.2817631903301657D-01 64 0.0000000000000000D+00 0.2818881418019235D-01 Test( 0) = 0.1000000005654649D+01 Test( 1) = 0.1000000016959396D+01 Test( 2) = 0.1000000028249521D+01 Test( 3) = 0.1000000039512130D+01 Test( 4) = 0.1000000050729775D+01 SOLVE - Warning: Poor convergence for some roots. EXTEND - Fatal error! SOLVE returns IFLAG = 3 Iteration 7 Coefficients of expansion whose roots are the new nodes: -0.2580307132569334D-05 * P( 0,X) 0.0000000000000000D+00 * P( 1,X) -0.1270488216156726D-04 * P( 2,X) 0.0000000000000000D+00 * P( 3,X) -0.2205749039263837D-04 * P( 4,X) 0.0000000000000000D+00 * P( 5,X) -0.3007776535116582D-04 * P( 6,X) 0.0000000000000000D+00 * P( 7,X) -0.3629806423368887D-04 * P( 8,X) 0.0000000000000000D+00 * P( 9,X) -0.4037349264391787D-04 * P( 10,X) 0.0000000000000000D+00 * P( 11,X) -0.4210136092460498D-04 * P( 12,X) 0.0000000000000000D+00 * P( 13,X) -0.4142901149700837D-04 * P( 14,X) 0.0000000000000000D+00 * P( 15,X) -0.3845019596654649D-04 * P( 16,X) 0.0000000000000000D+00 * P( 17,X) -0.3339126347394148D-04 * P( 18,X) 0.0000000000000000D+00 * P( 19,X) -0.2658922886817990D-04 * P( 20,X) 0.0000000000000000D+00 * P( 21,X) -0.1846426540587949D-04 * P( 22,X) 0.0000000000000000D+00 * P( 23,X) -0.9489312209600707D-05 * P( 24,X) 0.0000000000000000D+00 * P( 25,X) -0.1593450231364667D-06 * P( 26,X) 0.0000000000000000D+00 * P( 27,X) 0.9037497844730667D-05 * P( 28,X) 0.0000000000000000D+00 * P( 29,X) 0.1764523355165478D-04 * P( 30,X) 0.0000000000000000D+00 * P( 31,X) 0.2526064286573970D-04 * P( 32,X) 0.0000000000000000D+00 * P( 33,X) 0.3154855112301063D-04 * P( 34,X) 0.0000000000000000D+00 * P( 35,X) 0.3625164448486388D-04 * P( 36,X) 0.0000000000000000D+00 * P( 37,X) 0.3919507527916312D-04 * P( 38,X) 0.0000000000000000D+00 * P( 39,X) 0.4028640147001533D-04 * P( 40,X) 0.0000000000000000D+00 * P( 41,X) 0.3951159596076911D-04 * P( 42,X) 0.0000000000000000D+00 * P( 43,X) 0.3692795973151690D-04 * P( 44,X) 0.0000000000000000D+00 * P( 45,X) 0.3265479471627631D-04 * P( 46,X) 0.0000000000000000D+00 * P( 47,X) 0.2686265427445052D-04 * P( 48,X) 0.0000000000000000D+00 * P( 49,X) 0.1976190878562915D-04 * P( 50,X) 0.0000000000000000D+00 * P( 51,X) 0.1159125789081208D-04 * P( 52,X) 0.0000000000000000D+00 * P( 53,X) 0.2606701477501469D-05 * P( 54,X) 0.0000000000000000D+00 * P( 55,X) -0.6928639348876158D-05 * P( 56,X) 0.0000000000000000D+00 * P( 57,X) -0.1675357624742866D-04 * P( 58,X) 0.0000000000000000D+00 * P( 59,X) -0.2661661160470647D-04 * P( 60,X) 0.0000000000000000D+00 * P( 61,X) -0.3628231929618645D-04 * P( 62,X) 0.0000000000000000D+00 * P( 63,X) -0.4553634165138149D-04 * P( 64,X) 0.0000000000000000D+00 * P( 65,X) -0.5418905422707506D-04 * P( 66,X) 0.0000000000000000D+00 * P( 67,X) -0.6207799456454264D-04 * P( 68,X) 0.0000000000000000D+00 * P( 69,X) -0.6906918036107572D-04 * P( 70,X) 0.0000000000000000D+00 * P( 71,X) -0.7505744970218468D-04 * P( 72,X) 0.0000000000000000D+00 * P( 73,X) -0.7996639127066295D-04 * P( 74,X) 0.0000000000000000D+00 * P( 75,X) -0.8373422493125932D-04 * P( 76,X) 0.0000000000000000D+00 * P( 77,X) -0.8661541215891325D-04 * P( 78,X) 0.0000000000000000D+00 * P( 79,X) -0.8384535848925232D-04 * P( 80,X) 0.0000000000000000D+00 * P( 81,X) -0.1379781715721291D-03 * P( 82,X) 0.0000000000000000D+00 * P( 83,X) 0.3927179850922222D-03 * P( 84,X) 0.0000000000000000D+00 * P( 85,X) -0.3711431642911460D-02 * P( 86,X) 0.0000000000000000D+00 * P( 87,X) 0.2150892326405985D-01 * P( 88,X) 0.0000000000000000D+00 * P( 89,X) -0.1016809490108177D+00 * P( 90,X) 0.0000000000000000D+00 * P( 91,X) 0.3763361114793951D+00 * P( 92,X) 0.0000000000000000D+00 * P( 93,X) -0.1085417441020777D+01 * P( 94,X) 0.0000000000000000D+00 * P( 95,X) 0.2375537425429683D+01 * P( 96,X) 0.0000000000000000D+00 * P( 97,X) -0.3736779997954924D+01 * P( 98,X) 0.0000000000000000D+00 * P( 99,X) 0.3622481669022352D+01 * P(100,X) 0.0000000000000000D+00 * P(101,X) -0.6187618930469512D+00 * P(102,X) 0.0000000000000000D+00 * P(103,X) -0.4011035270510712D+01 * P(104,X) 0.0000000000000000D+00 * P(105,X) 0.6300019104576946D+01 * P(106,X) 0.0000000000000000D+00 * P(107,X) -0.4469911127035225D+01 * P(108,X) 0.0000000000000000D+00 * P(109,X) 0.1995108475994128D+01 * P(110,X) 0.0000000000000000D+00 * P(111,X) -0.2255186961203005D+01 * P(112,X) 0.0000000000000000D+00 * P(113,X) 0.3725721541746456D+01 * P(114,X) 0.0000000000000000D+00 * P(115,X) -0.4461767929835689D+01 * P(116,X) 0.0000000000000000D+00 * P(117,X) 0.4626873922499746D+01 * P(118,X) 0.0000000000000000D+00 * P(119,X) -0.2376277464109862D+01 * P(120,X) 0.0000000000000000D+00 * P(121,X) -0.2952854466650706D+01 * P(122,X) 0.0000000000000000D+00 * P(123,X) 0.6107717520204258D+01 * P(124,X) 0.0000000000000000D+00 * P(125,X) -0.4077876915209710D+01 * P(126,X) 0.0000000000000000D+00 * P(127,X) 0.1000000000000000D+01 * P(128,X) New nodes real Imaginary Flag Err 0.1409388641078189D-01 0.0000000000000000D+00 0 0.1D-16 -0.1409388641078189D-01 0.0000000000000000D+00 0 0.1D-16 0.4226916476536349D-01 0.0000000000000000D+00 0 0.1D-16 -0.4226916476536349D-01 0.0000000000000000D+00 0 0.1D-16 0.7040697604285520D-01 0.0000000000000000D+00 0 0.1D-17 -0.7040697604285520D-01 0.0000000000000000D+00 0 0.1D-17 0.9848239659811915D-01 0.0000000000000000D+00 0 0.7D-17 -0.9848239659811915D-01 0.0000000000000000D+00 0 0.7D-17 0.1264705843723020D+00 0.0000000000000000D+00 0 0.5D-17 -0.1264705843723020D+00 0.0000000000000000D+00 0 0.5D-17 0.1543468114813780D+00 0.0000000000000000D+00 0 0.1D-16 -0.1543468114813780D+00 0.0000000000000000D+00 0 0.1D-16 0.1820864967592521D+00 0.0000000000000000D+00 0 0.2D-16 -0.1820864967592521D+00 0.0000000000000000D+00 0 0.2D-16 0.2096652382431812D+00 0.0000000000000000D+00 0 0.2D-16 -0.2096652382431811D+00 0.0000000000000000D+00 0 0.2D-16 0.2370588455898297D+00 0.0000000000000000D+00 0 0.1D-16 -0.2370588455898298D+00 0.0000000000000000D+00 0 0.1D-16 0.2642433724109268D+00 0.0000000000000000D+00 0 0.1D-17 -0.2642433724109267D+00 0.0000000000000000D+00 0 0.1D-17 0.2911951485182467D+00 0.0000000000000000D+00 0 0.1D-16 -0.2911951485182467D+00 0.0000000000000000D+00 0 0.1D-16 0.3178908120684766D+00 0.0000000000000000D+00 0 0.1D-16 -0.3178908120684766D+00 0.0000000000000000D+00 0 0.1D-16 0.3398606040578615D+00 0.0000000000000000D+00 0 0.2D-17 -0.3398606040578615D+00 0.0000000000000000D+00 0 0.2D-17 0.3443073415994378D+00 0.0000000000000000D+00 0 0.4D-16 -0.3443073415994378D+00 0.0000000000000000D+00 0 0.4D-16 0.3704220879500782D+00 0.0000000000000000D+00 0 0.4D-16 -0.3704220879500782D+00 0.0000000000000000D+00 0 0.4D-16 0.3962128060576159D+00 0.0000000000000000D+00 0 0.8D-15 -0.3962128060576159D+00 0.0000000000000000D+00 0 0.8D-15 0.4216576866261633D+00 0.0000000000000000D+00 0 0.4D-17 -0.4216576866261633D+00 0.0000000000000000D+00 0 0.4D-17 0.4467353876620285D+00 0.0000000000000000D+00 0 0.6D-17 -0.4467353876620284D+00 0.0000000000000000D+00 0 0.6D-17 0.4714250658716589D+00 0.0000000000000000D+00 0 0.8D-18 -0.4714250658716588D+00 0.0000000000000000D+00 0 0.8D-18 0.4957064079187614D+00 0.0000000000000000D+00 0 0.9D-18 -0.4957064079187614D+00 0.0000000000000000D+00 0 0.9D-18 0.5195596615374570D+00 0.0000000000000000D+00 0 0.1D-16 -0.5195596615374570D+00 0.0000000000000000D+00 0 0.1D-16 0.5429656664983115D+00 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0.6190590357823814D+00 1 0.1D-01 -0.7114605496035055D+00 -0.5717274020495896D+00 1 0.2D-01 -0.7114605496035055D+00 0.5717274020495896D+00 1 0.2D-01 -0.4706355996374432D+00 -0.5099952459464036D+00 1 0.1D-01 -0.4706355996374432D+00 0.5099952459464036D+00 1 0.1D-01 0.6142985857856117D+02 0.0000000000000000D+00 1 0.4D+00 -0.1158055379511748D+00 0.0000000000000000D+00 1 0.4D+00 0.1517483773311097D+01 -0.4118617856549458D+02 1 0.2D+02 0.1517483773311097D+01 0.4118617856549458D+02 1 0.2D+02 -0.1564437629886350D+01 -0.4026971440968532D+02 1 0.2D+02 -0.1564437629886350D+01 0.4026971440968532D+02 1 0.2D+02 0.8251453720294290D+01 -0.3860655152417073D+02 1 0.2D+02 0.8251453720294290D+01 0.3860655152417073D+02 1 0.2D+02 0.4847989239210336D+01 -0.3813991465195169D+02 1 0.2D+02 0.4847989239210336D+01 0.3813991465195169D+02 1 0.2D+02 0.9739990170249014D+00 -0.3721376162418424D+02 1 0.2D+02 0.9739990170249014D+00 0.3721376162418424D+02 1 0.2D+02 0.5480192168186195D+01 -0.3530521376437455D+02 1 0.2D+02 0.5480192168186195D+01 0.3530521376437455D+02 1 0.2D+02 -0.8588622838604534D+01 -0.3550548584201808D+02 1 0.2D+02 -0.8588622838604534D+01 0.3550548584201808D+02 1 0.2D+02 -0.2049446786257225D+02 -0.3223478174219792D+02 1 0.2D+02 -0.2049446786257225D+02 0.3223478174219792D+02 1 0.2D+02 0.2157646420786845D+02 -0.3037022380165719D+02 1 0.2D+02 0.2157646420786845D+02 0.3037022380165719D+02 1 0.2D+02 -0.3026180056460393D+02 -0.2522283397375342D+02 1 0.2D+02 -0.3026180056460393D+02 0.2522283397375342D+02 1 0.2D+02 0.6320496579237715D+02 0.0000000000000000D+00 1 0.5D+01 -0.1226497814783316D+02 0.0000000000000000D+00 1 0.5D+01 -0.4917567215118617D+01 -0.3512750939253156D+02 1 0.2D+02 -0.4917567215118617D+01 0.3512750939253156D+02 1 0.2D+02 0.1964422625977344D+02 -0.3400685107883386D+02 1 0.2D+02 0.1964422625977344D+02 0.3400685107883386D+02 1 0.2D+02 0.4288911541223624D+02 -0.1298611637163242D+02 1 0.2D+02 0.4288911541223624D+02 0.1298611637163242D+02 1 0.2D+02 0.2066623386288757D+02 -0.3605139440753968D+02 1 0.2D+02 0.2066623386288757D+02 0.3605139440753968D+02 1 0.2D+02 0.9830631849597431D+01 -0.3252171770736040D+02 1 0.1D+02 0.9830631849597431D+01 0.3252171770736040D+02 1 0.1D+02 -0.5819249344144195D+02 -0.9923760587829888D+01 1 0.4D+02 -0.5819249344144195D+02 0.9923760587829888D+01 1 0.4D+02 -0.5094360782412482D+02 -0.1261379850724425D+02 1 0.3D+02 -0.5094360782412482D+02 0.1261379850724425D+02 1 0.3D+02 -0.4076628871029118D+02 -0.1954942303084562D+02 1 0.3D+02 -0.4076628871029118D+02 0.1954942303084562D+02 1 0.3D+02 0.2580122163189354D+02 0.0000000000000000D+00 1 0.1D+01 -0.6463242721401898D+01 0.0000000000000000D+00 1 0.1D+01 -0.2946716766610052D+02 -0.3276714096371409D+02 1 0.2D+02 -0.2946716766610052D+02 0.3276714096371409D+02 1 0.2D+02 0.3112709618849416D+02 -0.1250207555917080D+02 1 0.1D+02 0.3112709618849416D+02 0.1250207555917080D+02 1 0.1D+02 New full extended expansion 0.0000000000000000D+00 * P(128,X)/HI -0.4962072252508144D-14 * P(129,X)/HI 0.0000000000000000D+00 * P(130,X)/HI -0.1076243889967590D-13 * P(131,X)/HI 0.0000000000000000D+00 * P(132,X)/HI -0.2057313304496479D-13 * P(133,X)/HI 0.0000000000000000D+00 * P(134,X)/HI -0.2948530106214013D-13 * P(135,X)/HI 0.0000000000000000D+00 * P(136,X)/HI -0.3754186745449104D-13 * P(137,X)/HI 0.0000000000000000D+00 * P(138,X)/HI -0.4138885555025451D-13 * P(139,X)/HI 0.0000000000000000D+00 * P(140,X)/HI -0.4053911314367540D-13 * P(141,X)/HI 0.0000000000000000D+00 * P(142,X)/HI -0.3449562176776439D-13 * P(143,X)/HI 0.0000000000000000D+00 * P(144,X)/HI -0.2643022307259670D-13 * P(145,X)/HI 0.0000000000000000D+00 * P(146,X)/HI -0.1330306773419125D-13 * P(147,X)/HI 0.0000000000000000D+00 * P(148,X)/HI -0.1269028884924023D-14 * P(149,X)/HI 0.0000000000000000D+00 * P(150,X)/HI 0.1212302309911380D-13 * P(151,X)/HI 0.0000000000000000D+00 * P(152,X)/HI 0.2187869240799009D-13 * P(153,X)/HI 0.0000000000000000D+00 * P(154,X)/HI 0.3037523476293116D-13 * P(155,X)/HI 0.0000000000000000D+00 * P(156,X)/HI 0.3416267548378544D-13 * P(157,X)/HI 0.0000000000000000D+00 * P(158,X)/HI 0.3664963971721163D-13 * P(159,X)/HI 0.0000000000000000D+00 * P(160,X)/HI 0.2682075136027513D-13 * P(161,X)/HI 0.0000000000000000D+00 * P(162,X)/HI 0.1278069286700070D-12 * P(163,X)/HI 0.0000000000000000D+00 * P(164,X)/HI -0.1252130508280231D-11 * P(165,X)/HI 0.0000000000000000D+00 * P(166,X)/HI 0.1462695178375512D-10 * P(167,X)/HI 0.0000000000000000D+00 * P(168,X)/HI -0.1479517932120430D-09 * P(169,X)/HI 0.0000000000000000D+00 * P(170,X)/HI 0.1329014025073030D-08 * P(171,X)/HI 0.0000000000000000D+00 * P(172,X)/HI -0.1061859988569617D-07 * P(173,X)/HI 0.0000000000000000D+00 * P(174,X)/HI 0.7564344524187773D-07 * P(175,X)/HI 0.0000000000000000D+00 * P(176,X)/HI -0.4813268018021467D-06 * P(177,X)/HI 0.0000000000000000D+00 * P(178,X)/HI 0.2739434138482447D-05 * P(179,X)/HI 0.0000000000000000D+00 * P(180,X)/HI -0.1395759693249851D-04 * P(181,X)/HI 0.0000000000000000D+00 * P(182,X)/HI 0.6368645484301090D-04 * P(183,X)/HI 0.0000000000000000D+00 * P(184,X)/HI -0.2601911847741672D-03 * P(185,X)/HI 0.0000000000000000D+00 * P(186,X)/HI 0.9510593929026752D-03 * P(187,X)/HI 0.0000000000000000D+00 * P(188,X)/HI -0.3105627823587974D-02 * P(189,X)/HI 0.0000000000000000D+00 * P(190,X)/HI 0.9038761070434293D-02 * P(191,X)/HI 0.0000000000000000D+00 * P(192,X)/HI -0.2336763963070269D-01 * P(193,X)/HI 0.0000000000000000D+00 * P(194,X)/HI 0.5340505732287978D-01 * P(195,X)/HI 0.0000000000000000D+00 * P(196,X)/HI -0.1071678068301593D+00 * P(197,X)/HI 0.0000000000000000D+00 * P(198,X)/HI 0.1869882878012319D+00 * P(199,X)/HI 0.0000000000000000D+00 * P(200,X)/HI -0.2795410712330007D+00 * P(201,X)/HI 0.0000000000000000D+00 * P(202,X)/HI 0.3496043317918647D+00 * P(203,X)/HI 0.0000000000000000D+00 * P(204,X)/HI -0.3498097019518254D+00 * P(205,X)/HI 0.0000000000000000D+00 * P(206,X)/HI 0.2511187196295779D+00 * P(207,X)/HI 0.0000000000000000D+00 * P(208,X)/HI -0.7522321364031687D-01 * P(209,X)/HI 0.0000000000000000D+00 * P(210,X)/HI -0.1087480735770800D+00 * P(211,X)/HI 0.0000000000000000D+00 * P(212,X)/HI 0.2397342634148028D+00 * P(213,X)/HI 0.0000000000000000D+00 * P(214,X)/HI -0.3282020168585482D+00 * P(215,X)/HI 0.0000000000000000D+00 * P(216,X)/HI 0.4501152104063689D+00 * P(217,X)/HI 0.0000000000000000D+00 * P(218,X)/HI -0.6556324643910839D+00 * P(219,X)/HI 0.0000000000000000D+00 * P(220,X)/HI 0.8852945073223238D+00 * P(221,X)/HI 0.0000000000000000D+00 * P(222,X)/HI -0.1000000000000000D+01 * P(223,X)/HI 0.0000000000000000D+00 * P(224,X)/HI 0.9065054932346233D+00 * P(225,X)/HI 0.0000000000000000D+00 * P(226,X)/HI -0.6463891812780058D+00 * P(227,X)/HI 0.0000000000000000D+00 * P(228,X)/HI 0.3591931222266041D+00 * P(229,X)/HI 0.0000000000000000D+00 * P(230,X)/HI -0.1656939985085564D+00 * P(231,X)/HI 0.0000000000000000D+00 * P(232,X)/HI 0.8155251345267542D-01 * P(233,X)/HI 0.0000000000000000D+00 * P(234,X)/HI -0.2767457496198599D-01 * P(235,X)/HI 0.0000000000000000D+00 * P(236,X)/HI -0.7811330411595731D-01 * P(237,X)/HI 0.0000000000000000D+00 * P(238,X)/HI 0.2319926296444720D+00 * P(239,X)/HI 0.0000000000000000D+00 * P(240,X)/HI -0.3483001392661862D+00 * P(241,X)/HI 0.0000000000000000D+00 * P(242,X)/HI 0.3531696107438190D+00 * P(243,X)/HI 0.0000000000000000D+00 * P(244,X)/HI -0.2587110013262305D+00 * P(245,X)/HI 0.0000000000000000D+00 * P(246,X)/HI 0.1387732450607733D+00 * P(247,X)/HI 0.0000000000000000D+00 * P(248,X)/HI -0.5361361767916559D-01 * P(249,X)/HI 0.0000000000000000D+00 * P(250,X)/HI 0.1421086182740145D-01 * P(251,X)/HI 0.0000000000000000D+00 * P(252,X)/HI -0.2323314591012385D-02 * P(253,X)/HI 0.0000000000000000D+00 * P(254,X)/HI 0.1772113206924611D-03 * P(255,X)/HI Complete extended rule: STEP = 7 POINTS = 255 IFLAG = 3 Nodes added = 128 IFLAG = 3 Computation terminated prematurely. Choose ICASE, the initial rule to extend: 1, 3 point Gauss-Legendre in [-1,1]; 2, 2 point Gauss-Lobatto in [-1,1]; 3, 6 point Radau in [-1,1]; 4, 2 point Gauss-Laguerre in [0,+oo); 5, 3 point Gauss-Hermite in (-oo,+oo); 6, 3 point Gauss-Jacobi in [0,1]. Enter ICASE, between 1 and 6, or -1 to stop: ICASE = 2 Enter NSEQ, the number of nested rules to compute: NSEQ = 3 TEST02 Extension of a Lobatto 2 point rule. N = 2 M = 1 M0 = 0 SYMMET = T START = T Iteration 1 Coefficients of expansion whose roots are the new nodes: 0.0000000000000000D+00 * P( 0,X) 0.1000000000000000D+01 * P( 1,X) New nodes real Imaginary Flag Err 0.0000000000000000D+00 0.0000000000000000D+00 0 0.0D+00 New full extended expansion -0.1000000000000000D+01 * P( 1,X)/HI 0.0000000000000000D+00 * P( 2,X)/HI 0.4285714285714284D+00 * P( 3,X)/HI Complete extended rule: STEP = 1 POINTS = 3 IFLAG = 0 Nodes added = 1 No. Node Weight 1 0.1000000000000000D+01 0.3333333333333333D+00 2 0.0000000000000000D+00 0.1333333333333333D+01 Test( 0) = 0.1000000000000000D+01 Test( 1) = 0.1000000000000000D+01 Iteration 2 Coefficients of expansion whose roots are the new nodes: -0.1428571428571429D+00 * P( 0,X) 0.0000000000000000D+00 * P( 1,X) 0.1000000000000000D+01 * P( 2,X) New nodes real Imaginary Flag Err -0.6546536707079772D+00 0.0000000000000000D+00 0 0.3-320 0.6546536707079771D+00 0.0000000000000000D+00 0 0.3-320 New full extended expansion 0.0000000000000000D+00 * P( 2,X)/HI -0.1000000000000000D+01 * P( 3,X)/HI 0.0000000000000000D+00 * P( 4,X)/HI 0.6363636363636362D+00 * P( 5,X)/HI Complete extended rule: STEP = 2 POINTS = 5 IFLAG = 0 Nodes added = 2 No. Node Weight 1 0.1000000000000000D+01 0.1000000000000001D+00 2 0.6546536707079771D+00 0.5444444444444444D+00 3 0.0000000000000000D+00 0.7111111111111112D+00 Test( 0) = 0.1000000000000000D+01 Test( 1) = 0.1000000000000000D+01 Test( 2) = 0.1000000000000000D+01 Test( 3) = 0.1000000000000000D+01 Iteration 3 Coefficients of expansion whose roots are the new nodes: -0.4746768383132036D-01 * P( 0,X) 0.0000000000000000D+00 * P( 1,X) -0.1515151515151517D+00 * P( 2,X) 0.0000000000000000D+00 * P( 3,X) 0.1000000000000000D+01 * P( 4,X) New nodes real Imaginary Flag Err 0.3409822659109928D+00 0.0000000000000000D+00 0 0.1D-16 -0.3409822659109928D+00 0.0000000000000000D+00 0 0.1D-16 -0.8904055275126689D+00 0.0000000000000000D+00 0 0.1D-16 0.8904055275126688D+00 0.0000000000000000D+00 0 0.1D-16 New full extended expansion 0.0000000000000000D+00 * P( 4,X)/HI -0.3813459268004732D+00 * P( 5,X)/HI 0.0000000000000000D+00 * P( 6,X)/HI -0.9870129870129877D+00 * P( 7,X)/HI 0.0000000000000000D+00 * P( 8,X)/HI 0.1000000000000000D+01 * P( 9,X)/HI Complete extended rule: STEP = 3 POINTS = 9 IFLAG = 0 Nodes added = 4 No. Node Weight 1 0.1000000000000000D+01 0.3064373897707198D-01 2 0.8904055275126688D+00 0.1792626995532073D+00 3 0.6546536707079771D+00 0.2839787780481211D+00 4 0.3409822659109928D+00 0.3342337398164176D+00 5 0.0000000000000000D+00 0.3437620872103630D+00 Test( 0) = 0.9999999999999996D+00 Test( 1) = 0.9999999999999988D+00 Test( 2) = 0.9999999999999984D+00 Test( 3) = 0.9999999999999976D+00 Test( 4) = 0.9999999999999972D+00 Choose ICASE, the initial rule to extend: 1, 3 point Gauss-Legendre in [-1,1]; 2, 2 point Gauss-Lobatto in [-1,1]; 3, 6 point Radau in [-1,1]; 4, 2 point Gauss-Laguerre in [0,+oo); 5, 3 point Gauss-Hermite in (-oo,+oo); 6, 3 point Gauss-Jacobi in [0,1]. Enter ICASE, between 1 and 6, or -1 to stop: ICASE = 3 Enter NSEQ, the number of nested rules to compute: NSEQ = 3 TEST03 Extension of a 6 point Radau rule. N = 1 M = 5 M0 = 0 SYMMET = F START = T Iteration 1 Coefficients of expansion whose roots are the new nodes: -0.9090909090909083D-01 * P( 0,X) 0.2727272727272725D+00 * P( 1,X) -0.4545454545454543D+00 * P( 2,X) 0.6363636363636364D+00 * P( 3,X) -0.8181818181818183D+00 * P( 4,X) 0.1000000000000000D+01 * P( 5,X) New nodes real Imaginary Flag Err 0.1240503795052278D+00 0.0000000000000000D+00 0 0.5D-17 0.6039731642527837D+00 0.0000000000000000D+00 0 0.2D-16 -0.3909285467072722D+00 0.0000000000000000D+00 0 0.2D-16 0.9203802858970626D+00 0.0000000000000000D+00 0 0.3D-16 -0.8029298284023469D+00 0.0000000000000000D+00 0 0.3D-16 New full extended expansion 0.1000000000000000D+01 * P( 5,X)/HI 0.8461538461538459D+00 * P( 6,X)/HI Complete extended rule: STEP = 1 POINTS = 6 IFLAG = 0 Nodes added = 5 No. Node Weight 1 0.9203802858970626D+00 0.2015883852534809D+00 2 0.6039731642527837D+00 0.4169013343119077D+00 3 0.1240503795052278D+00 0.5209267831895750D+00 4 -0.3909285467072722D+00 0.4853871884689699D+00 5 -0.8029298284023469D+00 0.3196407532205105D+00 6 -0.1000000000000000D+01 0.5555555555555560D-01 Test( 0) = 0.9999999999999999D+00 Test( 1) = 0.9999999999999996D+00 Test( 2) = 0.9999999999999997D+00 Test( 3) = 0.1000000000000000D+01 Test( 4) = 0.1000000000000001D+01 Iteration 2 Coefficients of expansion whose roots are the new nodes: 0.1238920331102948D-01 * P( 0,X) -0.1115360783931154D-01 * P( 1,X) 0.2930949908491550D-01 * P( 2,X) -0.2573880815370944D-01 * P( 3,X) -0.8051048473617496D+00 * P( 4,X) -0.6245367209597321D+00 * P( 5,X) 0.7380888520433200D+00 * P( 6,X) 0.1000000000000000D+01 * P( 7,X) New nodes real Imaginary Flag Err -0.1366416372713494D+00 0.0000000000000000D+00 0 0.7D-17 -0.6212165636007759D+00 0.0000000000000000D+00 0 0.6D-16 0.3761018966748717D+00 0.0000000000000000D+00 0 0.6D-16 -0.8487727816552596D+00 0.0000000000000000D+00 0 0.6D-16 0.7905296024586544D+00 0.0000000000000000D+00 0 0.6D-16 0.9865012767506532D+00 0.0000000000000000D+00 0 0.8D-16 -0.9439342521493513D+00 0.0000000000000000D+00 0 0.8D-16 New full extended expansion -0.8815438503554278D-01 * P( 7,X)/HI -0.8472981649988011D-01 * P( 8,X)/HI -0.3768076078706985D+00 * P( 9,X)/HI -0.4473580103536869D+00 * P( 10,X)/HI 0.3851866566831172D+00 * P( 11,X)/HI 0.1000000000000000D+01 * P( 12,X)/HI 0.5106460045718261D+00 * P( 13,X)/HI Complete extended rule: STEP = 2 POINTS = 13 IFLAG = 0 Nodes added = 7 No. Node Weight 1 0.9865012767506532D+00 0.3610633344712032D-01 2 0.9203802858970626D+00 0.9797463317823503D-01 3 0.7905296024586544D+00 0.1603549149394082D+00 4 0.6039731642527837D+00 0.2100921244820766D+00 5 0.3761018966748717D+00 0.2427304474580506D+00 6 0.1240503795052278D+00 0.2588076132975782D+00 7 -0.1366416372713494D+00 0.2601366692626690D+00 8 -0.3909285467072722D+00 0.2455064597946104D+00 9 -0.6212165636007759D+00 0.2115512241336129D+00 10 -0.8029298284023469D+00 0.1329820397038963D+00 11 -0.8487727816552596D+00 0.3616137156650032D-01 12 -0.9439342521493513D+00 0.9202712852123043D-01 13 -0.1000000000000000D+01 0.1556904021500854D-01 Test( 0) = 0.9999999999999984D+00 Test( 1) = 0.9999999999999961D+00 Test( 2) = 0.9999999999999954D+00 Test( 3) = 0.9999999999999954D+00 Test( 4) = 0.9999999999999949D+00 EXTEND - Warning! Error test not passed. CHECK returns IFLAG = 6. Iteration 3 Coefficients of expansion whose roots are the new nodes: -0.2568241533598138D+00 * P( 0,X) 0.6273882318501727D+00 * P( 1,X) -0.6950114612478444D+00 * P( 2,X) 0.3514310704829928D+00 * P( 3,X) 0.2414864785762013D+00 * P( 4,X) -0.9310510552262480D+00 * P( 5,X) 0.1469801497275483D+01 * P( 6,X) -0.5792538945781199D+01 * P( 7,X) 0.4360460897293910D+01 * P( 8,X) -0.1885604119802034D+02 * P( 9,X) 0.1887338563559287D+01 * P( 10,X) 0.6992128566615199D+02 * P( 11,X) -0.1072921826817461D+02 * P( 12,X) -0.4426841333551039D+02 * P( 13,X) 0.1000000000000000D+01 * P( 14,X) New nodes real Imaginary Flag Err 0.9979162551518678D+00 0.0000000000000000D+00 0 0.4D-16 -0.6134267604635526D-02 0.0000000000000000D+00 0 0.4D-16 0.9613067296650284D+00 0.0000000000000000D+00 0 0.6D-16 -0.2655914229442032D+00 0.0000000000000000D+00 0 0.6D-16 0.8632649380482538D+00 0.0000000000000000D+00 0 0.3D-15 0.7034887989758215D+00 0.0000000000000000D+00 0 0.3D-15 0.4941080138619340D+00 0.0000000000000000D+00 0 0.4D-16 0.2520863057103870D+00 0.0000000000000000D+00 0 0.4D-16 -0.7205766157140706D+00 0.0000000000000000D+00 0 0.2D-15 -0.5103354152259294D+00 0.0000000000000000D+00 0 0.2D-15 -0.9812660421998122D+00 0.0000000000000000D+00 0 0.6D-15 -0.8923964308975324D+00 0.0000000000000000D+00 0 0.6D-15 0.2307179086987864D+02 0.0000000000000000D+00 0 0.4D-14 -0.1013669616811473D+01 0.0000000000000000D+00 0 0.4D-14 New full extended expansion 0.5454360425671964D-02 * P( 14,X)/HI 0.1275790889142930D-02 * P( 15,X)/HI 0.1362458441982813D-01 * P( 16,X)/HI 0.1061409558174561D-01 * P( 17,X)/HI -0.7800045804653981D-01 * P( 18,X)/HI -0.6147544605703550D-01 * P( 19,X)/HI -0.2027665031851316D+00 * P( 20,X)/HI -0.2559758659656056D+00 * P( 21,X)/HI 0.5447045628625399D+00 * P( 22,X)/HI 0.1000000000000000D+01 * P( 23,X)/HI 0.5759468453180573D-02 * P( 24,X)/HI -0.7380381496936699D+00 * P( 25,X)/HI -0.3289096723205033D+00 * P( 26,X)/HI 0.7335603893054691D-02 * P( 27,X)/HI Complete extended rule: STEP = 3 POINTS = 27 IFLAG = 6 Nodes added = 14 No. Node Weight 1 0.2307179086987864D+02 0.8410877949033471D-15 2 0.9979162551518678D+00 0.5761238214206084D-02 3 0.9865012767506532D+00 0.1781397602627029D-01 4 0.9613067296650284D+00 0.3288145280959059D-01 5 0.9203802858970626D+00 0.4904105110221105D-01 6 0.8632649380482538D+00 0.6509033800352287D-01 7 0.7905296024586544D+00 0.8015752890516900D-01 8 0.7034887989758215D+00 0.9361527599467599D-01 9 0.6039731642527837D+00 0.1050581380411569D+00 10 0.4941080138619340D+00 0.1143012662323622D+00 11 0.3761018966748717D+00 0.1213546454148586D+00 12 0.2520863057103870D+00 0.1263455706105022D+00 13 0.1240503795052278D+00 0.1294155830050473D+00 14 -0.6134267604635526D-02 0.1306510180165526D+00 15 -0.1366416372713494D+00 0.1300525005145075D+00 16 -0.2655914229442032D+00 0.1275061882372416D+00 17 -0.3909285467072722D+00 0.1227817936161397D+00 18 -0.5103354152259294D+00 0.1155996181401652D+00 19 -0.6212165636007759D+00 0.1056775942146707D+00 20 -0.7205766157140706D+00 0.9232499519844747D-01 21 -0.8029298284023469D+00 0.6879140063252921D-01 22 -0.8487727816552596D+00 0.3092904062992966D-01 23 -0.8923964308975324D+00 0.5477880738382557D-01 24 -0.9439342521493513D+00 0.4546365767395871D-01 25 -0.9812660421998122D+00 0.2876294640770519D-01 26 -0.1000000000000000D+01 0.5992084797066201D-02 27 -0.1013669616811473D+01 -0.1477098223025303D-03 Test( 0) = 0.1000000000000006D+01 Test( 1) = 0.1000000000000687D+01 Test( 2) = 0.1000000001338920D+01 Test( 3) = 0.1000002768838603D+01 Test( 4) = 0.1005797769035385D+01 IFLAG = 6, The rule test is unsatisfactory. Choose ICASE, the initial rule to extend: 1, 3 point Gauss-Legendre in [-1,1]; 2, 2 point Gauss-Lobatto in [-1,1]; 3, 6 point Radau in [-1,1]; 4, 2 point Gauss-Laguerre in [0,+oo); 5, 3 point Gauss-Hermite in (-oo,+oo); 6, 3 point Gauss-Jacobi in [0,1]. Enter ICASE, between 1 and 6, or -1 to stop: ICASE = 4 Enter NSEQ, the number of nested rules to compute: NSEQ = 2 TEST04 Extension of 2 point Gauss-Laguerre rule. N = 0 M = 2 M0 = 0 SYMMET = F START = F Iteration 1 Coefficients of expansion whose roots are the new nodes: 0.0000000000000000D+00 * P( 0,X) 0.0000000000000000D+00 * P( 1,X) 0.1000000000000000D+01 * P( 2,X) New nodes real Imaginary Flag Err 0.3414213562373095D+01 0.0000000000000000D+00 0 0.7-309 0.5857864376269050D+00 0.0000000000000000D+00 0 0.7-309 New full extended expansion 0.1000000000000000D+01 * P( 2,X)/HI Complete extended rule: STEP = 1 POINTS = 2 IFLAG = 0 Nodes added = 2 No. Node Weight 1 0.3414213562373095D+01 0.1464466094067263D+00 2 0.5857864376269050D+00 0.8535533905932738D+00 Test( 0) = 0.1000000000000000D+01 Test( 1) = 0.1000000000000000D+01 QI(J) /= 0 QI(J) = -1.9593892764699326 EXTEND - Fatal error! SOLVE returns IFLAG = 4 Iteration 2 Coefficients of expansion whose roots are the new nodes: 0.6000000000000000D+01 * P( 0,X) -0.1500000000000000D+01 * P( 1,X) -0.0000000000000000D+00 * P( 2,X) 0.1000000000000000D+01 * P( 3,X) New nodes real Imaginary Flag Err 0.8396196974011156D+01 0.0000000000000000D+00 0 0.4D-15 0.3019015129944225D+00 -0.1959389276469933D+01 0 0.2D-16 0.3019015129944225D+00 0.1959389276469933D+01 0 0.2D-16 New full extended expansion 0.8125000000000000D+00 * P( 3,X)/HI -0.1000000000000000D+01 * P( 4,X)/HI 0.4166666666666667D+00 * P( 5,X)/HI Complete extended rule: STEP = 2 POINTS = 5 IFLAG = 4 Nodes added = 3 IFLAG = 4 Computation terminated prematurely. Choose ICASE, the initial rule to extend: 1, 3 point Gauss-Legendre in [-1,1]; 2, 2 point Gauss-Lobatto in [-1,1]; 3, 6 point Radau in [-1,1]; 4, 2 point Gauss-Laguerre in [0,+oo); 5, 3 point Gauss-Hermite in (-oo,+oo); 6, 3 point Gauss-Jacobi in [0,1]. Enter ICASE, between 1 and 6, or -1 to stop: ICASE = 5 Enter NSEQ, the number of nested rules to compute: NSEQ = 2 TEST05 Extension of a 3 point Gauss-Hermite rule. N = 0 M = 3 M0 = 0 SYMMET = T START = F Iteration 1 Coefficients of expansion whose roots are the new nodes: 0.0000000000000000D+00 * P( 0,X) 0.0000000000000000D+00 * P( 1,X) 0.0000000000000000D+00 * P( 2,X) 0.1000000000000000D+01 * P( 3,X) New nodes real Imaginary Flag Err 0.0000000000000000D+00 0.0000000000000000D+00 0 0.0D+00 -0.1224744871391589D+01 0.0000000000000000D+00 0 0.0D+00 0.1224744871391589D+01 0.0000000000000000D+00 0 0.0D+00 New full extended expansion 0.1000000000000000D+01 * P( 3,X)/HI Complete extended rule: STEP = 1 POINTS = 3 IFLAG = 0 Nodes added = 3 No. Node Weight 1 0.1224744871391589D+01 0.2954089751509192D+00 2 0.0000000000000000D+00 0.1181635900603677D+01 Test( 0) = 0.9999999999999999D+00 Test( 1) = 0.9999999999999998D+00 Test( 2) = 0.9999999999999999D+00 QI(J) /= 0 QI(J) = -0.48848007894471041 EXTEND - Fatal error! SOLVE returns IFLAG = 4 Iteration 2 Coefficients of expansion whose roots are the new nodes: -0.3000000000000000D+01 * P( 0,X) 0.0000000000000000D+00 * P( 1,X) -0.2000000000000000D+01 * P( 2,X) 0.0000000000000000D+00 * P( 3,X) 0.1000000000000000D+01 * P( 4,X) New nodes real Imaginary Flag Err 0.0000000000000000D+00 -0.4884800789447104D+00 0 0.0D+00 0.0000000000000000D+00 0.4884800789447104D+00 0 0.0D+00 0.2288801605103822D+01 0.0000000000000000D+00 0 0.2D-15 -0.2288801605103822D+01 0.0000000000000000D+00 0 0.2D-15 New full extended expansion 0.0000000000000000D+00 * P( 4,X)/HI 0.3809523809523809D+00 * P( 5,X)/HI 0.0000000000000000D+00 * P( 6,X)/HI 0.1000000000000000D+01 * P( 7,X)/HI Complete extended rule: STEP = 2 POINTS = 7 IFLAG = 4 Nodes added = 4 IFLAG = 4 Computation terminated prematurely. Choose ICASE, the initial rule to extend: 1, 3 point Gauss-Legendre in [-1,1]; 2, 2 point Gauss-Lobatto in [-1,1]; 3, 6 point Radau in [-1,1]; 4, 2 point Gauss-Laguerre in [0,+oo); 5, 3 point Gauss-Hermite in (-oo,+oo); 6, 3 point Gauss-Jacobi in [0,1]. Enter ICASE, between 1 and 6, or -1 to stop: ICASE = 6 Enter NSEQ, the number of nested rules to compute: NSEQ = 3 TEST06 Extension of a 3 point Gauss-Jacobi rule. N = 0 M = 3 M0 = 0 SYMMET = F START = F Iteration 1 Coefficients of expansion whose roots are the new nodes: 0.0000000000000000D+00 * P( 0,X) 0.0000000000000000D+00 * P( 1,X) 0.0000000000000000D+00 * P( 2,X) 0.1000000000000000D+01 * P( 3,X) New nodes real Imaginary Flag Err 0.1647102868965424D+00 0.0000000000000000D+00 0 0.1D-16 0.9008058292716294D+00 0.0000000000000000D+00 0 0.0D+00 0.5498684992164435D+00 0.0000000000000000D+00 0 0.0D+00 New full extended expansion 0.1000000000000000D+01 * P( 3,X)/HI Complete extended rule: STEP = 1 POINTS = 3 IFLAG = 0 Nodes added = 3 No. Node Weight 1 0.9008058292716294D+00 0.2332816246559147D+00 2 0.5498684992164435D+00 0.3076023676819127D+00 3 0.1647102868965424D+00 0.1257826743288388D+00 Test( 0) = 0.9999999999999994D+00 Test( 1) = 0.9999999999999996D+00 Test( 2) = 0.1000000000000000D+01 Iteration 2 Coefficients of expansion whose roots are the new nodes: 0.8302544967323905D-04 * P( 0,X) 0.1808212463080845D-03 * P( 1,X) -0.6293935530868694D-01 * P( 2,X) -0.0000000000000000D+00 * P( 3,X) 0.1000000000000000D+01 * P( 4,X) New nodes real Imaginary Flag Err 0.3434982475781609D+00 0.0000000000000000D+00 0 0.6D-16 0.4317458752763434D-01 0.0000000000000000D+00 0 0.6D-16 0.9829837529243093D+00 0.0000000000000000D+00 0 0.2D-16 0.7479904707934251D+00 0.0000000000000000D+00 0 0.2D-16 New full extended expansion -0.1000000000000000D+01 * P( 4,X)/HI -0.7540286168214388D+00 * P( 5,X)/HI -0.9004851826770348D+00 * P( 6,X)/HI 0.5021708298937922D+00 * P( 7,X)/HI Complete extended rule: STEP = 2 POINTS = 7 IFLAG = 0 Nodes added = 4 No. Node Weight 1 0.9829837529243093D+00 0.4509009780887673D-01 2 0.9008058292716294D+00 0.1136674496440606D+00 3 0.7479904707934251D+00 0.1567638583107755D+00 4 0.5498684992164435D+00 0.1546815936593538D+00 5 0.3434982475781609D+00 0.1161056548660292D+00 6 0.1647102868965424D+00 0.6270539664794701D-01 7 0.4317458752763434D-01 0.1765261572962527D-01 Test( 0) = 0.1000000000000002D+01 Test( 1) = 0.1000000000000005D+01 Test( 2) = 0.1000000000000012D+01 Test( 3) = 0.1000000000000014D+01 Test( 4) = 0.1000000000000015D+01 Iteration 3 Coefficients of expansion whose roots are the new nodes: 0.1246085068899699D-07 * P( 0,X) 0.5106502089851601D-07 * P( 1,X) 0.1857830431069533D-06 * P( 2,X) 0.3154953497851395D-04 * P( 3,X) 0.3729410486893076D-03 * P( 4,X) 0.6566133154308322D-02 * P( 5,X) -0.6845782043616046D-01 * P( 6,X) -0.1121555778222753D+00 * P( 7,X) 0.1000000000000000D+01 * P( 8,X) New nodes real Imaginary Flag Err 0.9522115224106353D-01 0.0000000000000000D+00 0 0.4D-16 0.1092616002586211D-01 0.0000000000000000D+00 0 0.4D-16 0.4453534840434268D+00 0.0000000000000000D+00 0 0.8D-17 0.2486386449037344D+00 0.0000000000000000D+00 0 0.8D-17 0.8321177481736280D+00 0.0000000000000000D+00 0 0.0D+00 0.6523614224614962D+00 0.0000000000000000D+00 0 0.0D+00 0.9973759430379301D+00 0.0000000000000000D+00 0 0.1D-15 0.9513731441472559D+00 0.0000000000000000D+00 0 0.1D-15 New full extended expansion -0.1000000000000000D+01 * P( 8,X)/HI -0.7219216410505802D+00 * P( 9,X)/HI -0.4137098497953547D+00 * P( 10,X)/HI 0.6243456378892446D+00 * P( 11,X)/HI 0.2379858019591277D+00 * P( 12,X)/HI 0.3071737360112755D+00 * P( 13,X)/HI -0.3226631546878036D+00 * P( 14,X)/HI 0.5874911786041682D-01 * P( 15,X)/HI Complete extended rule: STEP = 3 POINTS = 15 IFLAG = 0 Nodes added = 8 No. Node Weight 1 0.9973759430379301D+00 0.7250785857080798D-02 2 0.9829837529243093D+00 0.2225370714572952D-01 3 0.9513731441472559D+00 0.4003272827656491D-01 4 0.9008058292716294D+00 0.5689076367068385D-01 5 0.8321177481736280D+00 0.7021992138795241D-01 6 0.7479904707934251D+00 0.7836602038520812D-01 7 0.6523614224614962D+00 0.8066055699011999D-01 8 0.5498684992164435D+00 0.7734675361301652D-01 9 0.4453534840434268D+00 0.6936411431773185D-01 10 0.3434982475781609D+00 0.5805035560699042D-01 11 0.2486386449037344D+00 0.4488514434457877D-01 12 0.1647102868965424D+00 0.3135360123263906D-01 13 0.9522115224106353D-01 0.1889127817157218D-01 14 0.4317458752763434D-01 0.8826110122443246D-02 15 0.1092616002586211D-01 0.2274825544358582D-02 Test( 0) = 0.1000000000000006D+01 Test( 1) = 0.1000000000000008D+01 Test( 2) = 0.1000000000000003D+01 Test( 3) = 0.9999999999999848D+00 Test( 4) = 0.9999999999999758D+00 Choose ICASE, the initial rule to extend: 1, 3 point Gauss-Legendre in [-1,1]; 2, 2 point Gauss-Lobatto in [-1,1]; 3, 6 point Radau in [-1,1]; 4, 2 point Gauss-Laguerre in [0,+oo); 5, 3 point Gauss-Hermite in (-oo,+oo); 6, 3 point Gauss-Jacobi in [0,1]. Enter ICASE, between 1 and 6, or -1 to stop: ICASE = -1 ICASE out of bounds. TOMS672_TEST: Normal end of execution. 06 April 2023 8:12:32.870 PM