30 November 2015 11:32:12 AM GEGENBAUER_POLYNOMIAL_TEST: MATLAB version. Test the GEGENBAUER_POLYNOMIAL library. GEGENBAUER_ALPHA_CHECK_TEST GEGENBAUER_ALPHA_CHECK checks that ALPHA is legal; ALPHA Check? -2.81582 0 4.56318 1 3.29509 1 0.616954 1 -0.846929 0 -4.33881 0 -2.42422 0 -3.90043 0 -4.56171 0 1.33966 1 GEGENBAUER_EK_COMPUTE_TEST GEGENBAUER_EK_COMPUTE computes a Gauss-Gegenbauer rule; with ALPHA = 0.5 and integration interval [-1,+1] W X 1.570796326794897 0 0.7853981633974484 -0.4999999999999999 0.7853981633974484 0.4999999999999999 0.3926990816987245 -0.7071067811865475 0.7853981633974486 6.591949208711867e-17 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 5.952490290336006e-17 0.3926990816987242 0.4999999999999998 0.1308996938995747 0.8660254037844388 0.0844886908915887 -0.9009688679024188 0.2743330560697781 -0.6234898018587335 0.4265764164360816 -0.2225209339563142 0.4265764164360817 0.2225209339563143 0.2743330560697784 0.6234898018587332 0.08448869089158853 0.9009688679024188 0.05750944903191328 -0.9238795325112868 0.1963495408493622 -0.7071067811865476 0.3351896326668111 -0.3826834323650896 0.3926990816987249 7.901929723605659e-18 0.335189632666811 0.3826834323650899 0.1963495408493624 0.7071067811865475 0.0575094490319132 0.9238795325112863 0.04083294770910714 -0.9396926207859084 0.144225600795673 -0.7660444431189782 0.2617993877991496 -0.4999999999999999 0.3385402270935193 -0.1736481776669302 0.338540227093519 0.1736481776669302 0.2617993877991501 0.5 0.1442256007956725 0.7660444431189779 0.04083294770910712 0.9396926207859086 0.02999954037160819 -0.9510565162951536 0.1085393567113534 -0.8090169943749472 0.2056199086476264 -0.587785252292473 0.2841597249873707 -0.3090169943749472 0.3141592653589796 5.567534423109432e-17 0.2841597249873716 0.3090169943749471 0.2056199086476266 0.5877852522924728 0.1085393567113536 0.8090169943749472 0.02999954037160805 0.9510565162951536 0.02266894250185894 -0.9594929736144974 0.08347854093418919 -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 0.08347854093418883 0.8412535328311812 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 0.4994395341508804 3 0 4 0.2724215640822983 5 0 6 0.1816143760548657 7 0 8 0.1338211191983219 9 0 10 0.1047295715465129 GEGENBAUER_POLYNOMIAL_VALUE_TEST: GEGENBAUER_POLYNOMIAL_VALUE evaluates the Gegenbauer polynomial. M ALPHA X GPV GEGENBAUER 0 0.5 0.2 1 1 1 0.5 0.2 0.2 0.2 2 0.5 0.2 -0.44 -0.44 3 0.5 0.2 -0.28 -0.28 4 0.5 0.2 0.232 0.232 5 0.5 0.2 0.30752 0.30752 6 0.5 0.2 -0.080576 -0.080576 7 0.5 0.2 -0.293517 -0.293517 8 0.5 0.2 -0.0395648 -0.0395648 9 0.5 0.2 0.245971 0.245957 10 0.5 0.2 0.129072 0.129072 2 0 0.4 0 0 2 1 0.4 -0.36 -0.36 2 2 0.4 -0.08 -0.08 2 3 0.4 0.84 0.84 2 4 0.4 2.4 2.4 2 5 0.4 4.6 4.6 2 6 0.4 7.44 7.44 2 7 0.4 10.92 10.92 2 8 0.4 15.04 15.04 2 9 0.4 19.8 19.8 2 10 0.4 25.2 25.2 5 3 -0.5 -9 9 5 3 -0.4 -0.16128 -0.16128 5 3 -0.3 -6.67296 -6.67296 5 3 -0.2 -8.37504 -8.37504 5 3 -0.1 -5.52672 -5.52672 5 3 0 0 0 5 3 0.1 5.52672 5.52672 5 3 0.2 8.37504 8.37504 5 3 0.3 6.67296 6.67296 5 3 0.4 0.16128 0.16128 5 3 0.5 -9 -9 5 3 0.6 -15.4253 -15.4253 5 3 0.7 -9.69696 -9.69696 5 3 0.8 22.441 22.441 5 3 0.9 100.889 100.889 5 3 1 252 252 GEGENBAUER_SS_COMPUTE_TEST GEGENBAUER_SS_COMPUTE computes a Gauss-Gegenbauer rule; with ALPHA = 0.5 W X 1.570796326794897 0 0.7853981633974484 -0.5 0.7853981633974484 0.5 0.3926990816987239 -0.7071067811865475 0.7853981633974484 0 0.3926990816987245 0.7071067811865476 0.217078713422706 -0.8090169943749475 0.5683194499747424 -0.3090169943749475 0.5683194499747424 0.3090169943749474 0.217078713422706 0.8090169943749475 0.130899693899574 -0.8660254037844387 0.3926990816987242 -0.5 0.5235987755982989 0 0.3926990816987242 0.5 0.1308996938995745 0.8660254037844387 0.08448869089158841 -0.9009688679024191 0.2743330560697777 -0.6234898018587335 0.4265764164360819 -0.2225209339563144 0.4265764164360819 0.2225209339563144 0.2743330560697777 0.6234898018587335 0.08448869089158841 0.9009688679024191 0.05750944903191331 -0.9238795325112867 0.1963495408493619 -0.7071067811865475 0.3351896326668111 -0.3826834323650898 0.3926990816987242 0 0.3351896326668108 0.3826834323650898 0.1963495408493624 0.7071067811865476 0.05750944903191331 0.9238795325112867 0.04083294770910693 -0.9396926207859084 0.1442256007956728 -0.766044443118978 0.2617993877991495 -0.5 0.3385402270935191 -0.1736481776669303 0.3385402270935191 0.1736481776669303 0.2617993877991495 0.5 0.1442256007956728 0.766044443118978 0.04083294770910754 0.9396926207859084 0.02999954037160841 -0.9510565162951536 0.108539356711353 -0.8090169943749475 0.2056199086476264 -0.5877852522924731 0.2841597249873712 -0.3090169943749475 0.3141592653589794 0 0.2841597249873712 0.3090169943749475 0.2056199086476264 0.5877852522924731 0.108539356711353 0.8090169943749475 0.02999954037160841 0.9510565162951536 0.02266894250185901 -0.9594929736144974 0.08347854093418892 -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 0.08347854093418892 0.8412535328311812 0.02266894250185901 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: 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 R8_HYPER_2F1_TEST: R8_HYPER_2F1 evaluates the hypergeometric function 2F1. A B C X 2F1 2F1 DIFF (tabulated) (computed) -2.5 3.3 6.7 0.25 0.7235612934899779 0.7235612934899781 2.22e-16 -0.5 1.1 6.7 0.25 0.9791110934527796 0.9791110934527797 1.11e-16 0.5 1.1 6.7 0.25 1.021657814008856 1.021657814008856 0 2.5 3.3 6.7 0.25 1.405156320011213 1.405156320011212 4.441e-16 -2.5 3.3 6.7 0.55 0.4696143163982161 0.4696143163982162 5.551e-17 -0.5 1.1 6.7 0.55 0.9529619497744632 0.9529619497744636 3.331e-16 0.5 1.1 6.7 0.55 1.051281421394799 1.051281421394798 8.882e-16 2.5 3.3 6.7 0.55 2.399906290477786 2.399906290477784 1.776e-15 -2.5 3.3 6.7 0.85 0.2910609592841472 0.2910609592841471 5.551e-17 -0.5 1.1 6.7 0.85 0.9253696791037318 0.9253696791037308 9.992e-16 0.5 1.1 6.7 0.85 1.0865504094807 1.086550409480699 8.882e-16 2.5 3.3 6.7 0.85 5.738156552618904 5.738156552619273 3.686e-13 3.3 6.7 -5.5 0.25 15090.66974870461 15090.6697487046 1.091e-11 1.1 6.7 -0.5 0.25 -104.3117006736435 -104.3117006736435 2.842e-14 1.1 6.7 0.5 0.25 21.17505070776881 21.1750507077688 1.066e-14 3.3 6.7 4.5 0.25 4.194691581903192 4.194691581903191 8.882e-16 3.3 6.7 -5.5 0.55 10170777974.04881 10170777974.04883 1.144e-05 1.1 6.7 -0.5 0.55 -24708.63532248916 -24708.63532248914 1.819e-11 1.1 6.7 0.5 0.55 1372.230454838499 1372.230454838497 2.274e-12 3.3 6.7 4.5 0.55 58.09272870639465 58.09272870639462 2.842e-14 3.3 6.7 -5.5 0.85 5.868208761512417e+18 5.868208761512401e+18 1.638e+04 1.1 6.7 -0.5 0.85 -446350101.47296 -446350101.4729614 1.431e-06 1.1 6.7 0.5 0.85 5383505.756129573 5383505.756129585 1.211e-08 3.3 6.7 4.5 0.85 20396.91377601966 20396.91377601966 3.638e-12 R8_UNIFORM_AB_TEST R8_UNIFORM_AB produces a random real in a given range. Using range 10 <= A <= 25. I A 0 10 1 13.54 2 22.68 3 21.96 4 10.86 5 20.83 6 22 7 18.11 8 18.22 9 23.35 GEGENBAUER_POLYNOMIAL_TEST: Normal end of execution. 30 November 2015 11:32:12 AM