14 September 2012 2:47:34.916 PM QUADRULE_PRB FORTRAN77 version Test the QUADRULE library. TEST0725 CLENSHAW_CURTIS_COMPUTE computes a Clenshaw-Curtis quadrature rule over [-1,1] of given order. Order W X 1 2.000000000000000 0.0000000000000000 2 1.000000000000000 -1.0000000000000000 1.000000000000000 1.0000000000000000 3 0.3333333333333334 -1.0000000000000000 1.333333333333333 0.0000000000000001 0.3333333333333334 1.0000000000000000 4 0.1111111111111111 -1.0000000000000000 0.8888888888888892 -0.4999999999999998 0.8888888888888888 0.5000000000000001 0.1111111111111111 1.0000000000000000 5 0.6666666666666668E-01 -1.0000000000000000 0.5333333333333334 -0.7071067811865475 0.7999999999999999 0.0000000000000001 0.5333333333333333 0.7071067811865476 0.6666666666666668E-01 1.0000000000000000 6 0.4000000000000001E-01 -1.0000000000000000 0.3607430412000113 -0.8090169943749473 0.5992569587999887 -0.3090169943749473 0.5992569587999889 0.3090169943749475 0.3607430412000112 0.8090169943749475 0.4000000000000001E-01 1.0000000000000000 7 0.2857142857142858E-01 -1.0000000000000000 0.2539682539682540 -0.8660254037844387 0.4571428571428573 -0.4999999999999998 0.5206349206349206 0.0000000000000001 0.4571428571428571 0.5000000000000001 0.2539682539682539 0.8660254037844387 0.2857142857142858E-01 1.0000000000000000 8 0.2040816326530613E-01 -1.0000000000000000 0.1901410072182084 -0.9009688679024190 0.3522424237181591 -0.6234898018587334 0.4372084057983264 -0.2225209339563143 0.4372084057983264 0.2225209339563144 0.3522424237181591 0.6234898018587336 0.1901410072182084 0.9009688679024191 0.2040816326530613E-01 1.0000000000000000 9 0.1587301587301588E-01 -1.0000000000000000 0.1462186492160182 -0.9238795325112867 0.2793650793650794 -0.7071067811865475 0.3617178587204898 -0.3826834323650897 0.3936507936507936 0.0000000000000001 0.3617178587204897 0.3826834323650898 0.2793650793650794 0.7071067811865476 0.1462186492160181 0.9238795325112867 0.1587301587301588E-01 1.0000000000000000 10 0.1234567901234569E-01 -1.0000000000000000 0.1165674565720372 -0.9396926207859083 0.2252843233381044 -0.7660444431189779 0.3019400352733687 -0.4999999999999998 0.3438625058041442 -0.1736481776669303 0.3438625058041442 0.1736481776669304 0.3019400352733685 0.5000000000000001 0.2252843233381044 0.7660444431189781 0.1165674565720371 0.9396926207859084 0.1234567901234569E-01 1.0000000000000000 TEST087 HERMITE_EK_COMPUTE computes a Gauss-Hermite rule; Compute the data for ORDER = 31 x( 1) = -6.9956801237185395336837000000000 x( 2) = -6.2750787049428602415446000000000 x( 3) = -5.6739614446185875351603000000000 x( 4) = -5.1335955771123744639794000000000 x( 5) = -4.6315595063128585096024000000000 x( 6) = -4.1562717558181461185995000000000 x( 7) = -3.7007434032314692196053000000000 x( 8) = -3.2603207323135410256043000000000 x( 9) = -2.8316804533902013574220000000000 x( 10) = -2.4123177054804201269178000000000 x( 11) = -2.0002585489356383696702000000000 x( 12) = -1.5938858604721393152914000000000 x( 13) = -1.1918269983500462405601000000000 x( 14) = -0.79287697691530878429944000000000 x( 15) = -0.39594273647142280703193000000000 x( 16) = 0.0000000000000000000000000000000 x( 17) = 0.39594273647142314009884000000000 x( 18) = 0.79287697691530778509872000000000 x( 19) = 1.1918269983500460185155000000000 x( 20) = 1.5938858604721388712022000000000 x( 21) = 2.0002585489356397019378000000000 x( 22) = 2.4123177054804174623825000000000 x( 23) = 2.8316804533902062424033000000000 x( 24) = 3.2603207323135428019611000000000 x( 25) = 3.7007434032314701077837000000000 x( 26) = 4.1562717558181425658859000000000 x( 27) = 4.6315595063128558450671000000000 x( 28) = 5.1335955771123815694068000000000 x( 29) = 5.6739614446185893115171000000000 x( 30) = 6.2750787049428549124741000000000 x( 31) = 6.9956801237185413100406000000000 w( 1) = 0.46189683944640472613159000000000E-21 w( 2) = 0.51106090079271744720309000000000E-17 w( 3) = 0.58995564987538567419078000000000E-14 w( 4) = 0.18603735214521792303326000000000E-11 w( 5) = 0.23524920032086516150128000000000E-09 w( 6) = 0.14611988344910378378437000000000E-07 w( 7) = 0.50437125589398611003142000000000E-06 w( 8) = 0.10498602757675530266330000000000E-04 w( 9) = 0.13952090395047135303400000000000E-03 w( 10) = 0.12336833073068882282025000000000E-02 w( 11) = 0.74827999140351904652779000000000E-02 w( 12) = 0.31847230731300399386718000000000E-01 w( 13) = 0.96717948160870648166565000000000E-01 w( 14) = 0.21213278866876472683600000000000 w( 15) = 0.33877265789410798690895000000000 w( 16) = 0.39577855609861034569263000000000 w( 17) = 0.33877265789410748730859000000000 w( 18) = 0.21213278866876492112503000000000 w( 19) = 0.96717948160870509388687000000000E-01 w( 20) = 0.31847230731300447958976000000000E-01 w( 21) = 0.74827999140351705159580000000000E-02 w( 22) = 0.12336833073068838913938000000000E-02 w( 23) = 0.13952090395046929304987000000000E-03 w( 24) = 0.10498602757675648850942000000000E-04 w( 25) = 0.50437125589398176898757000000000E-06 w( 26) = 0.14611988344910669546012000000000E-07 w( 27) = 0.23524920032086381733278000000000E-09 w( 28) = 0.18603735214521178380215000000000E-11 w( 29) = 0.58995564987538685748213000000000E-14 w( 30) = 0.51106090079273316279143000000000E-17 w( 31) = 0.46189683944640181090560000000000E-21 TEST087 HERMITE_EK_COMPUTE computes a Gauss-Hermite rule; Compute the data for ORDER = 63 x( 1) = -10.435499877854182315673000000000 x( 2) = -9.8028759912975136359137000000000 x( 3) = -9.2792019543050443530774000000000 x( 4) = -8.8118581437284539958910000000000 x( 5) = -8.3807683451863397294801000000000 x( 6) = -7.9755950801420372187067000000000 x( 7) = -7.5901395198641026240693000000000 x( 8) = -7.2203167078889656238516000000000 x( 9) = -6.8632544331795353187431000000000 x( 10) = -6.5168348106821154530621000000000 x( 11) = -6.1794379922705946484029000000000 x( 12) = -5.8497884000810662641356000000000 x( 13) = -5.5268572526403039191223000000000 x( 14) = -5.2097979830408336354708000000000 x( 15) = -4.8979018644975740315317000000000 x( 16) = -4.5905665744435193431627000000000 x( 17) = -4.2872733352824408115112000000000 x( 18) = -3.9875699104197170896668000000000 x( 19) = -3.6910577000963473714990000000000 x( 20) = -3.3973817713303859910923000000000 x( 21) = -3.1062230279282547762421000000000 x( 22) = -2.8172919672837988258607000000000 x( 23) = -2.5303236304711975712678000000000 x( 24) = -2.2450734604812057071399000000000 x( 25) = -1.9613138583081475285752000000000 x( 26) = -1.6788312791720132466367000000000 x( 27) = -1.3974237486049629897167000000000 x( 28) = -1.1168987050996463938901000000000 x( 29) = -0.83707109558947601080092000000000 x( 30) = -0.55776166427908191458584000000000 x( 31) = -0.27879538567115252911677000000000 x( 32) = 0.0000000000000000000000000000000 x( 33) = 0.27879538567115136338259000000000 x( 34) = 0.55776166427908180356354000000000 x( 35) = 0.83707109558947667693474000000000 x( 36) = 1.1168987050996459498009000000000 x( 37) = 1.3974237486049614354044000000000 x( 38) = 1.6788312791720136907259000000000 x( 39) = 1.9613138583081464183522000000000 x( 40) = 2.2450734604812061512291000000000 x( 41) = 2.5303236304712011239815000000000 x( 42) = 2.8172919672837983817715000000000 x( 43) = 3.1062230279282538880636000000000 x( 44) = 3.3973817713303930965196000000000 x( 45) = 3.6910577000963469274097000000000 x( 46) = 3.9875699104197162014884000000000 x( 47) = 4.2872733352824399233327000000000 x( 48) = 4.5905665744435202313412000000000 x( 49) = 4.8979018644975775842454000000000 x( 50) = 5.2097979830408345236492000000000 x( 51) = 5.5268572526403003664086000000000 x( 52) = 5.8497884000810644877788000000000 x( 53) = 6.1794379922705946484029000000000 x( 54) = 6.5168348106821136767053000000000 x( 55) = 6.8632544331795335423863000000000 x( 56) = 7.2203167078889620711379000000000 x( 57) = 7.5901395198641106176751000000000 x( 58) = 7.9755950801420398832420000000000 x( 59) = 8.3807683451863379531233000000000 x( 60) = 8.8118581437284557722478000000000 x( 61) = 9.2792019543050496821479000000000 x( 62) = 9.8028759912975207413410000000000 x( 63) = 10.435499877854171657532000000000 w( 1) = 0.37099206434902337820724000000000E-47 w( 2) = 0.10400778615223436231367000000000E-41 w( 3) = 0.19796804708320132123823000000000E-37 w( 4) = 0.84687478191906799900483000000000E-34 w( 5) = 0.13071305930819457523987000000000E-30 w( 6) = 0.93437837175664140840050000000000E-28 w( 7) = 0.36027426635286631182527000000000E-25 w( 8) = 0.82963863116210472037130000000000E-23 w( 9) = 0.12266629909143528817475000000000E-20 w( 10) = 0.12288435628835350117472000000000E-18 w( 11) = 0.86925536958461996552079000000000E-17 w( 12) = 0.44857058689315770719814000000000E-15 w( 13) = 0.17335817955789411249042000000000E-13 w( 14) = 0.51265062385198185599514000000000E-12 w( 15) = 0.11808921844569651759793000000000E-10 w( 16) = 0.21508698297875722692438000000000E-09 w( 17) = 0.31371929535383214311785000000000E-08 w( 18) = 0.37041625984896954203546000000000E-07 w( 19) = 0.35734732949990455765592000000000E-06 w( 20) = 0.28393114498469816954474000000000E-05 w( 21) = 0.18709113003788956975694000000000E-04 w( 22) = 0.10284880800685642558787000000000E-03 w( 23) = 0.47411702610320431575466000000000E-03 w( 24) = 0.18409222622442040443597000000000E-02 w( 25) = 0.60436044551375545444416000000000E-02 w( 26) = 0.16829299199652036911345000000000E-01 w( 27) = 0.39858264027817079389049000000000E-01 w( 28) = 0.80467087994200908740439000000000E-01 w( 29) = 0.13871950817658507126851000000000 w( 30) = 0.20448695346897388658292000000000 w( 31) = 0.25799889943138243353360000000000 w( 32) = 0.27876694884925218298477000000000 w( 33) = 0.25799889943138337722317000000000 w( 34) = 0.20448695346897496905036000000000 w( 35) = 0.13871950817658493249063000000000 w( 36) = 0.80467087994200506284592000000000E-01 w( 37) = 0.39858264027817259800290000000000E-01 w( 38) = 0.16829299199651922419596000000000E-01 w( 39) = 0.60436044551375823000172000000000E-02 w( 40) = 0.18409222622442023096362000000000E-02 w( 41) = 0.47411702610320523732651000000000E-03 w( 42) = 0.10284880800685772663048000000000E-03 w( 43) = 0.18709113003788807897895000000000E-04 w( 44) = 0.28393114498469168974269000000000E-05 w( 45) = 0.35734732949990704581520000000000E-06 w( 46) = 0.37041625984896921116322000000000E-07 w( 47) = 0.31371929535383723027862000000000E-08 w( 48) = 0.21508698297874781774491000000000E-09 w( 49) = 0.11808921844569267250055000000000E-10 w( 50) = 0.51265062385197337416269000000000E-12 w( 51) = 0.17335817955789035751251000000000E-13 w( 52) = 0.44857058689317821758168000000000E-15 w( 53) = 0.86925536958458098469871000000000E-17 w( 54) = 0.12288435628834984190783000000000E-18 w( 55) = 0.12266629909143194036684000000000E-20 w( 56) = 0.82963863116215085852457000000000E-23 w( 57) = 0.36027426635283709665805000000000E-25 w( 58) = 0.93437837175658255386500000000000E-28 w( 59) = 0.13071305930819028376332000000000E-30 w( 60) = 0.84687478191904725835068000000000E-34 w( 61) = 0.19796804708317172245716000000000E-37 w( 62) = 0.10400778615223136730088000000000E-41 w( 63) = 0.37099206434904999618275000000000E-47 TEST095 HERMITE_GENZ_KEISTER_SET sets up a nested rule for the Hermite integration problem. The integration interval is ( -oo, +oo ). The weight function is exp ( - x * x ) HERMITE_INTEGRAL determines the exact value of the integal when f(x) = x^m. M N Estimate Exact Error 0 1 1.77245 1.77245 0.00000 2 1 0.00000 0.886227 0.886227 0 3 1.77245 1.77245 0.222045E-15 2 3 0.886227 0.886227 0.222045E-15 4 3 1.32934 1.32934 0.444089E-15 6 3 1.99401 3.32335 1.32934 0 7 1.77245 1.77245 0.222045E-15 2 7 0.886227 0.886227 0.444089E-15 4 7 1.32934 1.32934 0.888178E-15 6 7 3.32335 3.32335 0.133227E-14 8 7 16.9910 11.6317 5.35929 0 9 1.77245 1.77245 0.222045E-15 2 9 0.886227 0.886227 0.111022E-15 4 9 1.32934 1.32934 0.222045E-15 6 9 3.32335 3.32335 0.00000 8 9 11.6317 11.6317 0.177636E-14 10 9 52.3428 52.3428 0.142109E-13 12 9 287.885 287.885 0.568434E-13 14 9 1871.25 1871.25 0.909495E-12 16 9 13798.9 14034.4 235.543 0 17 1.77245 1.77245 0.222045E-15 2 17 0.886227 0.886227 0.444089E-15 4 17 1.32934 1.32934 0.666134E-15 6 17 3.32335 3.32335 0.177636E-14 8 17 11.6317 11.6317 0.532907E-14 10 17 52.3428 52.3428 0.213163E-13 12 17 287.885 287.885 0.113687E-12 14 17 1871.25 1871.25 0.227374E-12 16 17 14034.4 14034.4 0.00000 18 17 122706. 119292. 3413.58 0 19 1.77245 1.77245 0.888178E-15 2 19 0.886227 0.886227 0.00000 4 19 1.32934 1.32934 0.888178E-15 6 19 3.32335 3.32335 0.222045E-14 8 19 11.6317 11.6317 0.106581E-13 10 19 52.3428 52.3428 0.426326E-13 12 19 287.885 287.885 0.113687E-12 14 19 1871.25 1871.25 0.136424E-11 16 19 14034.4 14034.4 0.200089E-10 18 19 119292. 119292. 0.247383E-09 20 19 0.113328E+07 0.113328E+07 0.186265E-08 0 31 1.77245 1.77245 0.222045E-15 2 31 0.886227 0.886227 0.333067E-15 4 31 1.32934 1.32934 0.222045E-15 6 31 3.32335 3.32335 0.444089E-15 8 31 11.6317 11.6317 0.355271E-14 10 31 52.3428 52.3428 0.213163E-13 12 31 287.885 287.885 0.341061E-12 14 31 1871.25 1871.25 0.409273E-11 16 31 14034.4 14034.4 0.418368E-10 18 31 119292. 119292. 0.378350E-09 20 31 0.113328E+07 0.113328E+07 0.349246E-08 0 33 1.77245 1.77245 0.888178E-15 2 33 0.886227 0.886227 0.111022E-15 4 33 1.32934 1.32934 0.888178E-15 6 33 3.32335 3.32335 0.177636E-14 8 33 11.6317 11.6317 0.355271E-14 10 33 52.3428 52.3428 0.284217E-13 12 33 287.885 287.885 0.284217E-12 14 33 1871.25 1871.25 0.272848E-11 16 33 14034.4 14034.4 0.236469E-10 18 33 119292. 119292. 0.247383E-09 20 33 0.113328E+07 0.113328E+07 0.209548E-08 0 35 1.77245 1.77245 0.888178E-15 2 35 0.886227 0.886227 0.888178E-15 4 35 1.32934 1.32934 0.133227E-14 6 35 3.32335 3.32335 0.177636E-14 8 35 11.6317 11.6317 0.177636E-14 10 35 52.3428 52.3428 0.213163E-13 12 35 287.885 287.885 0.284217E-12 14 35 1871.25 1871.25 0.318323E-11 16 35 14034.4 14034.4 0.272848E-10 18 35 119292. 119292. 0.261934E-09 20 35 0.113328E+07 0.113328E+07 0.209548E-08 QUADRULE_PRB Normal end of execution. 14 September 2012 2:47:34.919 PM