24 April 2024 08:39:27 PM gegenbauer_polynomial_test(): C version. Test gegenbauer_polynomial(). gegenbauer_alpha_check_test(): gegenbauer_alpha_check() checks that ALPHA is legal; ALPHA Check? -2.8158 0 4.5632 1 3.2951 1 0.6170 1 -0.8469 0 -4.3388 0 -2.4242 0 -3.9004 0 -4.5617 0 1.3397 1 gegenbauer_ek_compute_test(): gegenbauer_ek_compute() computes a Gauss-Gegenbauer rule; Abscissas X and weights W for a Gauss Gegenbauer rule with ALPHA = 0.500000 Integration interval = [-1,+1] W X 0 1.570796326794897 0 0 0.7853981633974484 -0.4999999999999999 1 0.7853981633974484 0.4999999999999999 0 0.3926990816987245 -0.7071067811865475 1 0.7853981633974486 6.591949208711867e-17 2 0.3926990816987239 0.7071067811865474 0 0.2170787134227061 -0.8090169943749475 1 0.5683194499747424 -0.3090169943749473 2 0.5683194499747432 0.3090169943749472 3 0.2170787134227062 0.8090169943749477 0 0.1308996938995749 -0.8660254037844389 1 0.3926990816987244 -0.4999999999999998 2 0.5235987755982987 5.952490290336006e-17 3 0.3926990816987242 0.4999999999999998 4 0.1308996938995747 0.8660254037844388 0 0.0844886908915887 -0.9009688679024188 1 0.2743330560697781 -0.6234898018587335 2 0.4265764164360816 -0.2225209339563142 3 0.4265764164360817 0.2225209339563143 4 0.2743330560697784 0.6234898018587332 5 0.08448869089158853 0.9009688679024188 0 0.05750944903191328 -0.9238795325112868 1 0.1963495408493622 -0.7071067811865476 2 0.3351896326668111 -0.3826834323650896 3 0.3926990816987249 7.901929723605659e-18 4 0.335189632666811 0.3826834323650899 5 0.1963495408493624 0.7071067811865475 6 0.0575094490319132 0.9238795325112863 0 0.04083294770910714 -0.9396926207859084 1 0.144225600795673 -0.7660444431189782 2 0.2617993877991496 -0.4999999999999999 3 0.3385402270935193 -0.1736481776669302 4 0.338540227093519 0.1736481776669302 5 0.2617993877991501 0.5 6 0.1442256007956725 0.7660444431189779 7 0.04083294770910712 0.9396926207859086 0 0.02999954037160819 -0.9510565162951536 1 0.1085393567113534 -0.8090169943749472 2 0.2056199086476264 -0.587785252292473 3 0.2841597249873707 -0.3090169943749472 4 0.3141592653589796 5.567534423109432e-17 5 0.2841597249873716 0.3090169943749471 6 0.2056199086476266 0.5877852522924728 7 0.1085393567113536 0.8090169943749472 8 0.02999954037160805 0.9510565162951536 0 0.02266894250185894 -0.9594929736144974 1 0.08347854093418919 -0.8412535328311809 2 0.1631221774548168 -0.6548607339452849 3 0.2363135602034877 -0.4154150130018863 4 0.2798149423030964 -0.1423148382732851 5 0.2798149423030961 0.1423148382732851 6 0.2363135602034874 0.4154150130018863 7 0.1631221774548172 0.6548607339452848 8 0.08347854093418883 0.8412535328311812 9 0.02266894250185892 0.9594929736144973 GEGENBAUER_INTEGRAL_TEST GEGENBAUER_INTEGRAL evaluates Integral ( -1 < x < +1 ) x^n * (1-x*x)^alpha dx N Value 0 1.748038369528081 1 0 2 0.4994395341508805 3 0 4 0.2724215640822983 5 0 6 0.1816143760548655 7 0 8 0.133821119198322 9 0 10 0.1047295715465128 GEGENBAUER_POLYNOMIAL_VALUE_TEST: GEGENBAUER_POLYNOMIAL_VALUE evaluates the Gegenbauer polynomial. M ALPHA X GPV GEGENBAUER 0 0.50 0.20 1.000000 1.000000 1 0.50 0.20 0.200000 0.200000 2 0.50 0.20 -0.440000 -0.440000 3 0.50 0.20 -0.280000 -0.280000 4 0.50 0.20 0.232000 0.232000 5 0.50 0.20 0.307520 0.307520 6 0.50 0.20 -0.080576 -0.080576 7 0.50 0.20 -0.293517 -0.293517 8 0.50 0.20 -0.039565 -0.039565 9 0.50 0.20 0.245971 0.245957 10 0.50 0.20 0.129072 0.129072 2 0.00 0.40 0.000000 0.000000 2 1.00 0.40 -0.360000 -0.360000 2 2.00 0.40 -0.080000 -0.080000 2 3.00 0.40 0.840000 0.840000 2 4.00 0.40 2.400000 2.400000 2 5.00 0.40 4.600000 4.600000 2 6.00 0.40 7.440000 7.440000 2 7.00 0.40 10.920000 10.920000 2 8.00 0.40 15.040000 15.040000 2 9.00 0.40 19.800000 19.800000 2 10.00 0.40 25.200000 25.200000 5 3.00 -0.50 -9.000000 9.000000 5 3.00 -0.40 -0.161280 -0.161280 5 3.00 -0.30 -6.672960 -6.672960 5 3.00 -0.20 -8.375040 -8.375040 5 3.00 -0.10 -5.526720 -5.526720 5 3.00 0.00 0.000000 0.000000 5 3.00 0.10 5.526720 5.526720 5 3.00 0.20 8.375040 8.375040 5 3.00 0.30 6.672960 6.672960 5 3.00 0.40 0.161280 0.161280 5 3.00 0.50 -9.000000 -9.000000 5 3.00 0.60 -15.425280 -15.425280 5 3.00 0.70 -9.696960 -9.696960 5 3.00 0.80 22.440960 22.440960 5 3.00 0.90 100.889280 100.889280 5 3.00 1.00 252.000000 252.000000 GEGENBAUER_SS_COMPUTE_TEST GEGENBAUER_SS_COMPUTE computes a Gauss-Gegenbauer rule; Abscissas X and weights W for a Gauss Gegenbauer rule with ALPHA = 0.500000 W X 0 1.570796326794897 0 0 0.7853981633974484 -0.5 1 0.7853981633974484 0.5 0 0.3926990816987239 -0.7071067811865475 1 0.7853981633974484 0 2 0.3926990816987245 0.7071067811865476 0 0.217078713422706 -0.8090169943749475 1 0.5683194499747424 -0.3090169943749475 2 0.5683194499747424 0.3090169943749474 3 0.217078713422706 0.8090169943749475 0 0.130899693899574 -0.8660254037844387 1 0.3926990816987242 -0.5 2 0.5235987755982989 0 3 0.3926990816987242 0.5 4 0.1308996938995745 0.8660254037844387 0 0.08448869089158841 -0.9009688679024191 1 0.2743330560697777 -0.6234898018587335 2 0.4265764164360819 -0.2225209339563144 3 0.4265764164360819 0.2225209339563144 4 0.2743330560697777 0.6234898018587335 5 0.08448869089158841 0.9009688679024191 0 0.05750944903191331 -0.9238795325112867 1 0.1963495408493619 -0.7071067811865475 2 0.3351896326668111 -0.3826834323650898 3 0.3926990816987242 0 4 0.3351896326668108 0.3826834323650898 5 0.1963495408493624 0.7071067811865476 6 0.05750944903191331 0.9238795325112867 0 0.04083294770910693 -0.9396926207859084 1 0.1442256007956728 -0.766044443118978 2 0.2617993877991495 -0.5 3 0.3385402270935191 -0.1736481776669303 4 0.3385402270935191 0.1736481776669303 5 0.2617993877991495 0.5 6 0.1442256007956728 0.766044443118978 7 0.04083294770910754 0.9396926207859084 0 0.02999954037160841 -0.9510565162951536 1 0.108539356711353 -0.8090169943749475 2 0.2056199086476264 -0.5877852522924731 3 0.2841597249873712 -0.3090169943749475 4 0.3141592653589794 0 5 0.2841597249873712 0.3090169943749475 6 0.2056199086476264 0.5877852522924731 7 0.108539356711353 0.8090169943749475 8 0.02999954037160841 0.9510565162951536 0 0.02266894250185901 -0.9594929736144974 1 0.08347854093418892 -0.8412535328311812 2 0.1631221774548165 -0.6548607339452851 3 0.2363135602034873 -0.4154150130018864 4 0.2798149423030965 -0.1423148382732851 5 0.2798149423030966 0.1423148382732851 6 0.2363135602034873 0.4154150130018864 7 0.1631221774548165 0.6548607339452851 8 0.08347854093418892 0.8412535328311812 9 0.02266894250185901 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: 0 1 2 3 4 Row 0: 1 0 -0.5 0 0.375 1: 0 1 0 -1.5 0 2: 0 0 1.5 0 -3.75 3: 0 0 0 2.5 0 4: 0 0 0 0 4.375 Monomial form of Gegenbauer polynomial 0 p(x) = 1 Monomial form of Gegenbauer polynomial 1 p(x) = 1 * x Monomial form of Gegenbauer polynomial 2 p(x) = 1.5 * x^2 -0.5 Monomial form of Gegenbauer polynomial 3 p(x) = 2.5 * x^3 -1.5 * x Monomial form of Gegenbauer polynomial 4 p(x) = 4.375 * x^4 -3.75 * x^2 +0.375 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: 0: 0.267949 1: 1 2: 2 3: 3 4: 3.73205 Exact eigenvalues: 0: 0.267949 1: 1 2: 2 3: 3 4: 3.73205 Vector Z: 0: 1 1: 1 2: 1 3: 1 4: 1 Vector Q'*Z: 0: 2.1547 1: -3.33067e-16 2: -0.57735 3: 1.66533e-16 4: 0.154701 monomial_to_gegenbauer_matrix_test(): monomial_to_gegenbauer_matrix() evaluates the matrix which converts monomial polynomial coefficients to Gegenbauer coefficients. Using parameter alpha = 0.5 Gegenbauer to Monomial matrix G: Col: 0 1 2 3 4 Row 0: 1 0 -0.5 0 0.375 1: 0 1 0 -1.5 0 2: 0 0 1.5 0 -3.75 3: 0 0 0 2.5 0 4: 0 0 0 0 4.375 Monomial to Gegenbauer matrix Ginv: Col: 0 1 2 3 4 Row 0: 1 0 0.333333 0 0.2 1: 0 1 0 0.6 0 2: 0 0 0.666667 0 0.571429 3: 0 0 0 0.4 0 4: 0 0 0 0 0.228571 I = G * Ginv: Col: 0 1 2 3 4 Row 0: 1 0 0 0 2.77556e-17 1: 0 1 0 0 0 2: 0 0 1 0 0 3: 0 0 0 1 0 4: 0 0 0 0 1 R8_HYPER_2F1_TEST: R8_HYPER_2F1 evaluates the hypergeometric function 2F1. A B C X 2F1 2F1 DIFF (tabulated) (computed) -2.500000 3.300000 6.700000 0.250000 0.7235612934899779 0.7235612934899781 2.22e-16 -0.500000 1.100000 6.700000 0.250000 0.9791110934527796 0.9791110934527797 1.11e-16 0.500000 1.100000 6.700000 0.250000 1.021657814008856 1.021657814008856 0 2.500000 3.300000 6.700000 0.250000 1.405156320011213 1.405156320011212 4.441e-16 -2.500000 3.300000 6.700000 0.550000 0.4696143163982161 0.4696143163982162 5.551e-17 -0.500000 1.100000 6.700000 0.550000 0.9529619497744632 0.9529619497744636 3.331e-16 0.500000 1.100000 6.700000 0.550000 1.051281421394799 1.051281421394798 8.882e-16 2.500000 3.300000 6.700000 0.550000 2.399906290477786 2.399906290477784 1.776e-15 -2.500000 3.300000 6.700000 0.850000 0.2910609592841472 0.2910609592841473 1.665e-16 -0.500000 1.100000 6.700000 0.850000 0.9253696791037318 0.9253696791037314 4.441e-16 0.500000 1.100000 6.700000 0.850000 1.0865504094807 1.086550409480699 2.22e-16 2.500000 3.300000 6.700000 0.850000 5.738156552618904 5.738156552618818 8.615e-14 3.300000 6.700000 -5.500000 0.250000 15090.66974870461 15090.6697487046 1.091e-11 1.100000 6.700000 -0.500000 0.250000 -104.3117006736435 -104.3117006736435 2.842e-14 1.100000 6.700000 0.500000 0.250000 21.17505070776881 21.1750507077688 1.066e-14 3.300000 6.700000 4.500000 0.250000 4.194691581903192 4.194691581903191 8.882e-16 3.300000 6.700000 -5.500000 0.550000 10170777974.04881 10170777974.04883 1.144e-05 1.100000 6.700000 -0.500000 0.550000 -24708.63532248916 -24708.63532248914 1.819e-11 1.100000 6.700000 0.500000 0.550000 1372.230454838499 1372.230454838497 2.274e-12 3.300000 6.700000 4.500000 0.550000 58.09272870639465 58.09272870639462 2.842e-14 3.300000 6.700000 -5.500000 0.850000 5.868208761512417e+18 5.868208761512405e+18 1.229e+04 1.100000 6.700000 -0.500000 0.850000 -446350101.47296 -446350101.4729604 3.576e-07 1.100000 6.700000 0.500000 0.850000 5383505.756129573 5383505.75612958 6.519e-09 3.300000 6.700000 4.500000 0.850000 20396.91377601966 20396.91377601965 1.455e-11 R8_UNIFORM_AB_TEST R8_UNIFORM_AB produces a random real in a given range. Using range 10.000000 <= A <= 25.000000. I A 0 10.001996 1 13.542136 2 22.679357 3 21.955784 4 10.855646 5 20.834593 6 21.996377 7 18.110503 8 18.220583 9 23.346688 gegenbauer_polynomial_test(): Normal end of execution. 24 April 2024 08:39:27 PM