23 November 2015 11:19:09.271 PM GEGENBAUER_POLYNOMIAL_PRB FORTRAN90 version Test the GEGENBAUER_POLYNOMIAL library. GEGENBAUER_ALPHA_CHECK_TEST GEGENBAUER_ALPHA_CHECK checks that ALPHA is legal. ALPHA Check? -2.8158 F 4.5632 T 3.2951 T 0.6170 T -0.8469 F -4.3388 F -2.4242 F -3.9004 F -4.5617 F 1.3397 T GEGENBAUER_EK_COMPUTE_TEST GEGENBAUER_EK_COMPUTE computes a Gauss-Gegenbauer rule; Using parameter ALPHA = 0.500000 Integration interval is [-1,+1]. W X 1.570796326794897 0.000000000000000 0.7853981633974484 -0.4999999999999999 0.7853981633974484 0.4999999999999999 0.3926990816987245 -0.7071067811865475 0.7853981633974486 0.6591949208711867E-16 0.3926990816987239 0.7071067811865474 0.2170787134227061 -0.8090169943749475 0.5683194499747424 -0.3090169943749473 0.5683194499747432 0.3090169943749472 0.2170787134227062 0.8090169943749477 0.1308996938995749 -0.8660254037844389 0.3926990816987244 -0.4999999999999998 0.5235987755982987 0.5952490290336006E-16 0.3926990816987242 0.4999999999999998 0.1308996938995747 0.8660254037844388 0.8448869089158870E-01 -0.9009688679024188 0.2743330560697781 -0.6234898018587335 0.4265764164360816 -0.2225209339563142 0.4265764164360817 0.2225209339563143 0.2743330560697784 0.6234898018587332 0.8448869089158853E-01 0.9009688679024188 0.5750944903191328E-01 -0.9238795325112868 0.1963495408493622 -0.7071067811865476 0.3351896326668111 -0.3826834323650896 0.3926990816987249 0.7901929723605659E-17 0.3351896326668110 0.3826834323650899 0.1963495408493624 0.7071067811865475 0.5750944903191320E-01 0.9238795325112863 0.4083294770910714E-01 -0.9396926207859084 0.1442256007956730 -0.7660444431189782 0.2617993877991496 -0.4999999999999999 0.3385402270935193 -0.1736481776669302 0.3385402270935190 0.1736481776669302 0.2617993877991501 0.5000000000000000 0.1442256007956725 0.7660444431189779 0.4083294770910712E-01 0.9396926207859086 0.2999954037160819E-01 -0.9510565162951536 0.1085393567113534 -0.8090169943749472 0.2056199086476264 -0.5877852522924730 0.2841597249873707 -0.3090169943749472 0.3141592653589796 0.5567534423109432E-16 0.2841597249873716 0.3090169943749471 0.2056199086476266 0.5877852522924728 0.1085393567113536 0.8090169943749472 0.2999954037160805E-01 0.9510565162951536 0.2266894250185894E-01 -0.9594929736144974 0.8347854093418919E-01 -0.8412535328311809 0.1631221774548168 -0.6548607339452849 0.2363135602034877 -0.4154150130018863 0.2798149423030964 -0.1423148382732851 0.2798149423030961 0.1423148382732851 0.2363135602034874 0.4154150130018863 0.1631221774548172 0.6548607339452848 0.8347854093418883E-01 0.8412535328311812 0.2266894250185892E-01 0.9594929736144973 GEGENBAUER_INTEGRAL_TEST GEGENBAUER_INTEGRAL evaluates Integral ( -1 < x < +1 ) x^n * (1-x^2)^(alpha-1/2) dx N Value 0 1.570796326794898 1 0.000000000000000 2 0.3926990816987242 3 0.000000000000000 4 0.1963495408493622 5 0.000000000000000 6 0.1227184630308513 7 0.000000000000000 8 0.8590292412159592E-01 9 0.000000000000000 10 0.6442719309119677E-01 GEGENBAUER_POLYNOMIAL_VALUE_TEST: GEGENBAUER_POLYNOMIAL_VALUE evaluates the Gegenbauer polynomial. M ALPHA X GPV GEGENBAUER 0 0.50 0.20 1.0000 1.0000 1 0.50 0.20 0.2000 0.2000 2 0.50 0.20 -0.4400 -0.4400 3 0.50 0.20 -0.2800 -0.2800 4 0.50 0.20 0.2320 0.2320 5 0.50 0.20 0.3075 0.3075 6 0.50 0.20 -0.0806 -0.0806 7 0.50 0.20 -0.2935 -0.2935 8 0.50 0.20 -0.0396 -0.0396 9 0.50 0.20 0.2460 0.2460 10 0.50 0.20 0.1291 0.1291 2 0.00 0.40 0.0000 0.0000 2 1.00 0.40 -0.3600 -0.3600 2 2.00 0.40 -0.0800 -0.0800 2 3.00 0.40 0.8400 0.8400 2 4.00 0.40 2.4000 2.4000 2 5.00 0.40 4.6000 4.6000 2 6.00 0.40 7.4400 7.4400 2 7.00 0.40 10.9200 10.9200 2 8.00 0.40 15.0400 15.0400 2 9.00 0.40 19.8000 19.8000 2 10.00 0.40 25.2000 25.2000 5 3.00 -0.50 -9.0000 9.0000 5 3.00 -0.40 -0.1613 -0.1613 5 3.00 -0.30 -6.6730 -6.6730 5 3.00 -0.20 -8.3750 -8.3750 5 3.00 -0.10 -5.5267 -5.5267 5 3.00 0.00 0.0000 0.0000 5 3.00 0.10 5.5267 5.5267 5 3.00 0.20 8.3750 8.3750 5 3.00 0.30 6.6730 6.6730 5 3.00 0.40 0.1613 0.1613 5 3.00 0.50 -9.0000 -9.0000 5 3.00 0.60 -15.4253 -15.4253 5 3.00 0.70 -9.6970 -9.6970 5 3.00 0.80 22.4410 22.4410 5 3.00 0.90 100.8893 100.8893 5 3.00 1.00 252.0000 252.0000 GEGENBAUER_SS_COMPUTE_TEST GEGENBAUER_SS_COMPUTE computes a Gauss-Gegenbauer rule; Using parameter ALPHA = 0.500000 W X 1.570796326794897 0.000000000000000 0.7853981633974484 -0.5000000000000000 0.7853981633974484 0.5000000000000000 0.3926990816987239 -0.7071067811865475 0.7853981633974484 0.000000000000000 0.3926990816987245 0.7071067811865476 0.2170787134227060 -0.8090169943749475 0.5683194499747424 -0.3090169943749475 0.5683194499747424 0.3090169943749474 0.2170787134227060 0.8090169943749475 0.1308996938995740 -0.8660254037844387 0.3926990816987242 -0.5000000000000000 0.5235987755982989 0.000000000000000 0.3926990816987242 0.5000000000000000 0.1308996938995745 0.8660254037844387 0.8448869089158841E-01 -0.9009688679024191 0.2743330560697777 -0.6234898018587335 0.4265764164360819 -0.2225209339563144 0.4265764164360819 0.2225209339563144 0.2743330560697777 0.6234898018587335 0.8448869089158841E-01 0.9009688679024191 0.5750944903191331E-01 -0.9238795325112867 0.1963495408493619 -0.7071067811865475 0.3351896326668111 -0.3826834323650898 0.3926990816987242 0.000000000000000 0.3351896326668108 0.3826834323650898 0.1963495408493624 0.7071067811865476 0.5750944903191331E-01 0.9238795325112867 0.4083294770910693E-01 -0.9396926207859084 0.1442256007956728 -0.7660444431189780 0.2617993877991495 -0.5000000000000000 0.3385402270935191 -0.1736481776669303 0.3385402270935191 0.1736481776669303 0.2617993877991495 0.5000000000000000 0.1442256007956728 0.7660444431189780 0.4083294770910754E-01 0.9396926207859084 0.2999954037160841E-01 -0.9510565162951536 0.1085393567113530 -0.8090169943749475 0.2056199086476264 -0.5877852522924731 0.2841597249873712 -0.3090169943749475 0.3141592653589794 0.000000000000000 0.2841597249873712 0.3090169943749475 0.2056199086476264 0.5877852522924731 0.1085393567113530 0.8090169943749475 0.2999954037160841E-01 0.9510565162951536 0.2266894250185901E-01 -0.9594929736144974 0.8347854093418892E-01 -0.8412535328311812 0.1631221774548165 -0.6548607339452851 0.2363135602034873 -0.4154150130018864 0.2798149423030965 -0.1423148382732851 0.2798149423030966 0.1423148382732851 0.2363135602034873 0.4154150130018864 0.1631221774548165 0.6548607339452851 0.8347854093418892E-01 0.8412535328311812 0.2266894250185901E-01 0.9594929736144974 IMTQLX_TEST IMTQLX takes a symmetric tridiagonal matrix A and computes its eigenvalues LAM. It also accepts a vector Z and computes Q'*Z, where Q is the matrix that diagonalizes A. Computed eigenvalues: 1: 0.26794919 2: 1.0000000 3: 2.0000000 4: 3.0000000 5: 3.7320508 Exact eigenvalues: 1: 0.26794919 2: 1.0000000 3: 2.0000000 4: 3.0000000 5: 3.7320508 Vector Z: 1: 1.0000000 2: 1.0000000 3: 1.0000000 4: 1.0000000 5: 1.0000000 Vector Q'*Z: 1: -2.1547005 2: 0.17113554E-15 3: 0.57735027 4: 0.68645097E-15 5: -0.15470054 R8_GAMMA_TEST: R8_GAMMA evaluates the Gamma function. X Gamma(X) Gamma(X) DIFF (Tabulated) (R8_GAMMA) -0.5000 -3.544907701811032 -3.544907701811032 0.4441E-15 -0.0100 -100.5871979644108 -100.5871979644108 0.2842E-13 0.0100 99.43258511915060 99.43258511915060 0.000 0.1000 9.513507698668732 9.513507698668731 0.1776E-14 0.2000 4.590843711998803 4.590843711998803 0.000 0.4000 2.218159543757688 2.218159543757688 0.000 0.5000 1.772453850905516 1.772453850905516 0.000 0.6000 1.489192248812817 1.489192248812817 0.000 0.8000 1.164229713725303 1.164229713725303 0.2220E-15 1.0000 1.000000000000000 1.000000000000000 0.000 1.1000 0.9513507698668732 0.9513507698668732 0.000 1.2000 0.9181687423997607 0.9181687423997607 0.000 1.3000 0.8974706963062772 0.8974706963062772 0.000 1.4000 0.8872638175030753 0.8872638175030754 0.1110E-15 1.5000 0.8862269254527581 0.8862269254527581 0.000 1.6000 0.8935153492876903 0.8935153492876903 0.000 1.7000 0.9086387328532904 0.9086387328532904 0.000 1.8000 0.9313837709802427 0.9313837709802427 0.000 1.9000 0.9617658319073874 0.9617658319073874 0.000 2.0000 1.000000000000000 1.000000000000000 0.000 3.0000 2.000000000000000 2.000000000000000 0.000 4.0000 6.000000000000000 6.000000000000000 0.000 10.0000 362880.0000000000 362880.0000000000 0.000 20.0000 0.1216451004088320E+18 0.1216451004088321E+18 80.00 30.0000 0.8841761993739702E+31 0.8841761993739751E+31 0.4954E+17 R8_HYPER_2F1_TEST: R8_HYPER_2F1 evaluates the hypergeometric 2F1 function. A B C X 2F1 2F1 DIFF (tabulated) (computed) -2.50 3.30 6.70 0.25 0.7235612934899779 0.7235612934899781 0.2220E-15 -0.50 1.10 6.70 0.25 0.9791110934527796 0.9791110934527797 0.1110E-15 0.50 1.10 6.70 0.25 1.021657814008856 1.021657814008856 0.000 2.50 3.30 6.70 0.25 1.405156320011213 1.405156320011212 0.4441E-15 -2.50 3.30 6.70 0.55 0.4696143163982161 0.4696143163982162 0.5551E-16 -0.50 1.10 6.70 0.55 0.9529619497744632 0.9529619497744636 0.3331E-15 0.50 1.10 6.70 0.55 1.051281421394799 1.051281421394798 0.8882E-15 2.50 3.30 6.70 0.55 2.399906290477786 2.399906290477784 0.1776E-14 -2.50 3.30 6.70 0.85 0.2910609592841472 0.2910609592841474 0.2220E-15 -0.50 1.10 6.70 0.85 0.9253696791037318 0.9253696791037318 0.000 0.50 1.10 6.70 0.85 1.086550409480700 1.086550409480700 0.000 2.50 3.30 6.70 0.85 5.738156552618904 5.738156552619301 0.3970E-12 3.30 6.70 -5.50 0.25 15090.66974870461 15090.66974870460 0.1091E-10 1.10 6.70 -0.50 0.25 -104.3117006736435 -104.3117006736435 0.2842E-13 1.10 6.70 0.50 0.25 21.17505070776881 21.17505070776880 0.1066E-13 3.30 6.70 4.50 0.25 4.194691581903192 4.194691581903191 0.8882E-15 3.30 6.70 -5.50 0.55 10170777974.04881 10170777974.04883 0.1144E-04 1.10 6.70 -0.50 0.55 -24708.63532248916 -24708.63532248914 0.1819E-10 1.10 6.70 0.50 0.55 1372.230454838499 1372.230454838497 0.2274E-11 3.30 6.70 4.50 0.55 58.09272870639465 58.09272870639462 0.2842E-13 3.30 6.70 -5.50 0.85 0.5868208761512417E+19 0.5868208761512380E+19 0.3686E+05 1.10 6.70 -0.50 0.85 -446350101.4729600 -446350101.4729605 0.4768E-06 1.10 6.70 0.50 0.85 5383505.756129573 5383505.756129581 0.8382E-08 3.30 6.70 4.50 0.85 20396.91377601966 20396.91377601965 0.1455E-10 R8_PSI_TEST: R8_PSI evaluates the Psi function. X Psi(X) Psi(X) DIFF (Tabulated) (R8_PSI) 0.1000 -10.42375494041108 -10.42375494041108 0.000 0.2000 -5.289039896592188 -5.289039896592188 0.000 0.3000 -3.502524222200133 -3.502524222200133 0.000 0.4000 -2.561384544585116 -2.561384544585116 0.000 0.5000 -1.963510026021423 -1.963510026021424 0.6661E-15 0.6000 -1.540619213893190 -1.540619213893191 0.6661E-15 0.7000 -1.220023553697935 -1.220023553697935 0.2220E-15 0.8000 -0.9650085667061385 -0.9650085667061382 0.3331E-15 0.9000 -0.7549269499470515 -0.7549269499470511 0.3331E-15 1.0000 -0.5772156649015329 -0.5772156649015329 0.000 1.1000 -0.4237549404110768 -0.4237549404110768 0.5551E-16 1.2000 -0.2890398965921883 -0.2890398965921884 0.5551E-16 1.3000 -0.1691908888667997 -0.1691908888667995 0.1665E-15 1.4000 -0.6138454458511615E-01 -0.6138454458511624E-01 0.9021E-16 1.5000 0.3648997397857652E-01 0.3648997397857652E-01 0.000 1.6000 0.1260474527734763 0.1260474527734763 0.2776E-16 1.7000 0.2085478748734940 0.2085478748734940 0.2776E-16 1.8000 0.2849914332938615 0.2849914332938615 0.000 1.9000 0.3561841611640597 0.3561841611640596 0.1110E-15 2.0000 0.4227843350984671 0.4227843350984672 0.1110E-15 R8_UNIFORM_AB_TEST R8_UNIFORM returns random values in a given range: [ B, C ] For this problem: B = 10.0000 C = 20.0000 12.1842 19.5632 18.2951 15.6170 14.1531 10.6612 12.5758 11.0996 10.4383 16.3397 GEGENBAUER_POLYNOMIAL_PRB Normal end of execution. 23 November 2015 11:19:09.274 PM