24 April 2024 9:36:01.974 PM gegenbauer_polynomial_test(): Fortran90 version Test gegenbauer_polynomial(). gegenbauer_alpha_check_test(): gegenbauer_alpha_check() checks that ALPHA is legal. ALPHA Check? 3.7866 T 4.9905 T -0.6687 F 3.0195 T -1.6001 F 0.0081 T 3.4214 T -3.4600 F 2.9282 T -3.6992 F 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 0.8590292412159593E-01 9 0.000000000000000 10 0.6442719309119695E-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 gegenbauer_to_monomial_matrix_test(): gegenbauer_to_monomial_matrix() evaluates the matrix which converts Gegenbauer polyjomial coefficients to monomial coefficients. Gegenbauer to Monomial matrix G: Col 1 2 3 4 5 Row 1: 1.00000 0.00000 -0.500000 0.00000 0.375000 2: 0.00000 1.00000 0.00000 -1.50000 0.00000 3: 0.00000 0.00000 1.50000 0.00000 -3.75000 4: 0.00000 0.00000 0.00000 2.50000 0.00000 5: 0.00000 0.00000 0.00000 0.00000 4.37500 Monomial form of Gegenbauer polynomial 0 p(x) = 1.00000 Monomial form of Gegenbauer polynomial 1 p(x) = 1.00000 * x Monomial form of Gegenbauer polynomial 2 p(x) = 1.50000 * x ^ 2 - 0.500000 Monomial form of Gegenbauer polynomial 3 p(x) = 2.50000 * x ^ 3 - 1.50000 * x Monomial form of Gegenbauer polynomial 4 p(x) = 4.37500 * x ^ 4 - 3.75000 * x ^ 2 + 0.375000 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 monomial_to_gegenbauer_matrix_test(): monomial_to_gegenbauer_matrix() evaluates the matrix which converts monomial polynomial coefficients to Gegenbauer coefficients. Gegenbauer to Monomial matrix G: Col 1 2 3 4 5 Row 1: 1.00000 0.00000 -0.500000 0.00000 0.375000 2: 0.00000 1.00000 0.00000 -1.50000 0.00000 3: 0.00000 0.00000 1.50000 0.00000 -3.75000 4: 0.00000 0.00000 0.00000 2.50000 0.00000 5: 0.00000 0.00000 0.00000 0.00000 4.37500 Monomial to Gegenbauer matrix Ginv: Col 1 2 3 4 5 Row 1: 1.00000 0.00000 0.333333 0.00000 0.200000 2: 0.00000 1.00000 0.00000 0.600000 0.00000 3: 0.00000 0.00000 0.666667 0.00000 0.571429 4: 0.00000 0.00000 0.00000 0.400000 0.00000 5: 0.00000 0.00000 0.00000 0.00000 0.228571 I = G * Ginv: Col 1 2 3 4 5 Row 1: 1.00000 0.00000 0.00000 0.00000 0.277556E-16 2: 0.00000 1.00000 0.00000 0.00000 0.00000 3: 0.00000 0.00000 1.00000 0.00000 0.00000 4: 0.00000 0.00000 0.00000 1.00000 0.00000 5: 0.00000 0.00000 0.00000 0.00000 1.00000 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 0.2910609592841473 0.1665E-15 -0.50 1.10 6.70 0.85 0.9253696791037318 0.9253696791037314 0.4441E-15 0.50 1.10 6.70 0.85 1.086550409480700 1.086550409480699 0.2220E-15 2.50 3.30 6.70 0.85 5.738156552618904 5.738156552618818 0.8615E-13 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 0.5868208761512405E+19 0.1229E+05 1.10 6.70 -0.50 0.85 -446350101.4729600 -446350101.4729604 0.3576E-06 1.10 6.70 0.50 0.85 5383505.756129573 5383505.756129580 0.6519E-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 gegenbauer_polynomial_test(): Normal end of execution. 24 April 2024 9:36:01.975 PM