04-Apr-2024 21:59:03 gegenbauer_polynomial_test(): MATLAB/Octave version 6.4.0 Test gegenbauer_polynomial() gegenbauer_alpha_check_test(): gegenbauer_alpha_check() checks that ALPHA is legal; ALPHA Check? 0.2699 1 4.8231 1 2.2556 1 -4.2167 0 0.3062 1 -0.2482 1 -2.6848 0 2.1915 1 3.7676 1 0.9797 1 gegenbauer_ek_compute_test(): gegenbauer_ek_compute() computes Gauss-Gegenbauer rules; Abscissas and weights for a generalized Gauss Gegenbauer rule with ALPHA = 0.500000 Integration interval is [-1,+1] 1 1.570796326794897 0 1 0.7853981633974484 -0.4999999999999999 2 0.7853981633974484 0.4999999999999999 1 0.3926990816987244 -0.7071067811865476 2 0.7853981633974487 4.837676228855989e-17 3 0.3926990816987246 0.7071067811865474 1 0.217078713422706 -0.8090169943749473 2 0.5683194499747422 -0.3090169943749473 3 0.5683194499747424 0.3090169943749473 4 0.217078713422706 0.8090169943749475 1 0.1308996938995748 -0.8660254037844385 2 0.3926990816987244 -0.4999999999999998 3 0.5235987755982987 1.884809048867118e-17 4 0.3926990816987244 0.5 5 0.1308996938995748 0.8660254037844383 1 0.0844886908915886 -0.9009688679024193 2 0.2743330560697776 -0.6234898018587333 3 0.4265764164360817 -0.2225209339563144 4 0.4265764164360816 0.2225209339563145 5 0.2743330560697779 0.6234898018587334 6 0.08448869089158867 0.900968867902419 1 0.05750944903191339 -0.9238795325112866 2 0.1963495408493622 -0.7071067811865474 3 0.3351896326668113 -0.3826834323650896 4 0.3926990816987241 2.455208374201258e-17 5 0.3351896326668114 0.3826834323650897 6 0.1963495408493624 0.7071067811865471 7 0.05750944903191314 0.9238795325112868 1 0.04083294770910707 -0.9396926207859084 2 0.144225600795673 -0.7660444431189782 3 0.2617993877991496 -0.4999999999999999 4 0.3385402270935186 -0.1736481776669303 5 0.3385402270935185 0.1736481776669304 6 0.261799387799149 0.5 7 0.1442256007956726 0.7660444431189781 8 0.04083294770910745 0.9396926207859085 1 0.02999954037160817 -0.9510565162951534 2 0.1085393567113531 -0.8090169943749473 3 0.2056199086476265 -0.587785252292473 4 0.2841597249873712 -0.3090169943749474 5 0.3141592653589791 -8.481943400504541e-17 6 0.2841597249873714 0.3090169943749473 7 0.2056199086476269 0.5877852522924731 8 0.1085393567113536 0.8090169943749473 9 0.02999954037160817 0.9510565162951534 1 0.02266894250185888 -0.9594929736144975 2 0.08347854093418892 -0.8412535328311812 3 0.1631221774548166 -0.654860733945285 4 0.2363135602034876 -0.4154150130018863 5 0.2798149423030963 -0.1423148382732852 6 0.2798149423030966 0.1423148382732851 7 0.2363135602034878 0.4154150130018863 8 0.1631221774548166 0.6548607339452849 9 0.08347854093418941 0.8412535328311812 10 0.02266894250185881 0.9594929736144975 gegenbauer_integral_test(): gegenbauer_integral() evaluates Integral ( -1 < x < +1 ) x^n * (1-x*x)^(alpha-1/2) dx N Value 0 1.570796326794898 1 0 2 0.3926990816987242 3 0 4 0.1963495408493622 5 0 6 0.1227184630308513 7 0 8 0.08590292412159593 9 0 10 0.06442719309119695 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 Gauss-Gegenbauer rules; Abscissas and weights for a generalized Gauss Gegenbauer rule with ALPHA = 0.500000 1 1.570796326794897 0 1 0.7853981633974484 -0.5 2 0.7853981633974484 0.5 1 0.3926990816987239 -0.7071067811865475 2 0.7853981633974484 0 3 0.3926990816987239 0.7071067811865475 1 0.217078713422706 -0.8090169943749475 2 0.5683194499747424 -0.3090169943749475 3 0.5683194499747424 0.3090169943749474 4 0.217078713422706 0.8090169943749475 1 0.130899693899574 -0.8660254037844387 2 0.3926990816987242 -0.5 3 0.5235987755982989 0 4 0.3926990816987242 0.5 5 0.130899693899575 0.8660254037844387 1 0.08448869089158841 -0.9009688679024191 2 0.2743330560697777 -0.6234898018587335 3 0.4265764164360819 -0.2225209339563144 4 0.4265764164360819 0.2225209339563144 5 0.2743330560697777 0.6234898018587335 6 0.08448869089158884 0.900968867902419 1 0.05750944903191331 -0.9238795325112867 2 0.1963495408493619 -0.7071067811865475 3 0.3351896326668111 -0.3826834323650898 4 0.3926990816987242 0 5 0.3351896326668108 0.3826834323650898 6 0.1963495408493624 0.7071067811865476 7 0.05750944903191331 0.9238795325112867 1 0.04083294770910693 -0.9396926207859084 2 0.1442256007956728 -0.766044443118978 3 0.2617993877991495 -0.5 4 0.3385402270935191 -0.1736481776669303 5 0.3385402270935191 0.1736481776669303 6 0.2617993877991495 0.5 7 0.1442256007956728 0.766044443118978 8 0.04083294770910754 0.9396926207859084 1 0.02999954037160841 -0.9510565162951536 2 0.108539356711353 -0.8090169943749475 3 0.2056199086476264 -0.5877852522924731 4 0.2841597249873712 -0.3090169943749475 5 0.3141592653589794 0 6 0.2841597249873712 0.3090169943749475 7 0.2056199086476264 0.5877852522924731 8 0.108539356711353 0.8090169943749475 9 0.02999954037160841 0.9510565162951536 1 0.02266894250185901 -0.9594929736144974 2 0.08347854093418892 -0.8412535328311812 3 0.1631221774548165 -0.6548607339452851 4 0.2363135602034873 -0.4154150130018864 5 0.2798149423030965 -0.1423148382732851 6 0.2798149423030966 0.1423148382732851 7 0.2363135602034873 0.4154150130018864 8 0.1631221774548165 0.6548607339452851 9 0.08347854093418892 0.8412535328311812 10 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: 1.0000 0 -0.5000 0 0.3750 0 1.0000 0 -1.5000 0 0 0 1.5000 0 -3.7500 0 0 0 2.5000 0 0 0 0 0 4.3750 Monomial form of Gegenbauer polynomial #0 = +1.000000 Monomial form of Gegenbauer polynomial #1 = +1.000000 * x Monomial form of Gegenbauer polynomial #2 = +1.500000 * x^2 -0.500000 Monomial form of Gegenbauer polynomial #3 = +2.500000 * x^3 -1.500000 * x Monomial form of Gegenbauer polynomial #4 = +4.375000 * x^4 -3.750000 * 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: 0.267949 2: 1 3: 2 4: 3 5: 3.73205 Exact eigenvalues: 1: 0.267949 2: 1 3: 2 4: 3 5: 3.73205 Vector Z: 1: 1 2: 1 3: 1 4: 1 5: 1 Vector Q'*Z: 1: -2.1547 2: -1.8855e-16 3: 0.57735 4: 1.66533e-16 5: -0.154701 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 7.2356129348997789e-01 7.2356129348997811e-01 2.2204e-16 -0.50 1.10 6.70 0.25 9.7911109345277958e-01 9.7911109345277969e-01 1.1102e-16 0.50 1.10 6.70 0.25 1.0216578140088564e+00 1.0216578140088564e+00 0.0000e+00 2.50 3.30 6.70 0.25 1.4051563200112127e+00 1.4051563200112123e+00 4.4409e-16 -2.50 3.30 6.70 0.55 4.6961431639821610e-01 4.6961431639821616e-01 5.5511e-17 -0.50 1.10 6.70 0.55 9.5296194977446325e-01 9.5296194977446358e-01 3.3307e-16 0.50 1.10 6.70 0.55 1.0512814213947987e+00 1.0512814213947979e+00 8.8818e-16 2.50 3.30 6.70 0.55 2.3999062904777859e+00 2.3999062904777841e+00 1.7764e-15 -2.50 3.30 6.70 0.85 2.9106095928414716e-01 2.9106095928414732e-01 1.6653e-16 -0.50 1.10 6.70 0.85 9.2536967910373180e-01 9.2536967910373136e-01 4.4409e-16 0.50 1.10 6.70 0.85 1.0865504094806997e+00 1.0865504094806995e+00 2.2204e-16 2.50 3.30 6.70 0.85 5.7381565526189044e+00 5.7381565526188183e+00 8.6153e-14 3.30 6.70 -5.50 0.25 1.5090669748704608e+04 1.5090669748704597e+04 1.0914e-11 1.10 6.70 -0.50 0.25 -1.0431170067364350e+02 -1.0431170067364347e+02 2.8422e-14 1.10 6.70 0.50 0.25 2.1175050707768811e+01 2.1175050707768801e+01 1.0658e-14 3.30 6.70 4.50 0.25 4.1946915819031920e+00 4.1946915819031911e+00 8.8818e-16 3.30 6.70 -5.50 0.55 1.0170777974048815e+10 1.0170777974048826e+10 1.1444e-05 1.10 6.70 -0.50 0.55 -2.4708635322489157e+04 -2.4708635322489139e+04 1.8190e-11 1.10 6.70 0.50 0.55 1.3722304548384989e+03 1.3722304548384966e+03 2.2737e-12 3.30 6.70 4.50 0.55 5.8092728706394652e+01 5.8092728706394624e+01 2.8422e-14 3.30 6.70 -5.50 0.85 5.8682087615124173e+18 5.8682087615124050e+18 1.2288e+04 1.10 6.70 -0.50 0.85 -4.4635010147296000e+08 -4.4635010147296035e+08 3.5763e-07 1.10 6.70 0.50 0.85 5.3835057561295731e+06 5.3835057561295796e+06 6.5193e-09 3.30 6.70 4.50 0.85 2.0396913776019661e+04 2.0396913776019646e+04 1.4552e-11 gegenbauer_polynomial_test(): Normal end of execution. 04-Apr-2024 21:59:03