19 September 2013 10:12:38 AM TANH_QUAD_PRB C++ version Test the TANH_QUAD library. TEST01 TANH_M_TO_H determines the spacing H from level M TANH_H_TO_N determines the quadrature order N from the spacing H and tolerance TOL. All tests use TOL = 2.22045e-16 M H N -2 4 10 -1 2 19 0 1 37 1 0.5 73 2 0.25 142 3 0.125 278 4 0.0625 544 5 0.03125 1065 6 0.015625 2085 7 0.0078125 4082 8 0.00390625 7986 TEST012 Determine nested midpoint quadrature rules W, X by choosing N = 0, 1, 3, 7. M = 1 ORDER = 1 N = 0 H = 1 I Wi Xi 0 2 0 M = 2 ORDER = 3 N = 1 H = 0.5 I Wi Xi -1 0.75 -0.5 0 0.5 0 1 0.75 0.5 M = 3 ORDER = 7 N = 3 H = 0.25 I Wi Xi -3 0.375 -0.75 -2 0.25 -0.5 -1 0.25 -0.25 0 0.25 0 1 0.25 0.25 2 0.25 0.5 3 0.375 0.75 M = 4 ORDER = 15 N = 7 H = 0.125 I Wi Xi -7 0.1875 -0.875 -6 0.125 -0.75 -5 0.125 -0.625 -4 0.125 -0.5 -3 0.125 -0.375 -2 0.125 -0.25 -1 0.125 -0.125 0 0.125 0 1 0.125 0.125 2 0.125 0.25 3 0.125 0.375 4 0.125 0.5 5 0.125 0.625 6 0.125 0.75 7 0.1875 0.875 TEST02 Determine tanh quadrature rules W, X by choosing N = 5, 10, 20. The rule for N = 5 appears in the reference Kahaner, Moler and Nash. Also note that the rule for H(N) means that rules for doubled N do not nest. Quadrature order N = 5 I Wi Xi -5 0.000470736 -0.999737 -4 0.0028071 -0.998428 -3 0.016631 -0.990649 -2 0.0948442 -0.945434 -1 0.439127 -0.713098 0 0.893459 0 1 0.439127 0.713098 2 0.0948442 0.945434 3 0.016631 0.990649 4 0.0028071 0.998428 5 0.000470736 0.999737 Quadrature order N = 10 I Wi Xi -10 5.61364e-06 -0.999996 -9 2.07003e-05 -0.999984 -8 7.63303e-05 -0.999942 -7 0.000281428 -0.999784 -6 0.00103718 -0.999205 -5 0.00381649 -0.997071 -4 0.0139634 -0.989242 -3 0.0500336 -0.960894 -2 0.166539 -0.862995 -1 0.438 -0.573338 0 0.652481 0 1 0.438 0.573338 2 0.166539 0.862995 3 0.0500336 0.960894 4 0.0139634 0.989242 5 0.00381649 0.997071 6 0.00103718 0.999205 7 0.000281428 0.999784 8 7.63303e-05 0.999942 9 2.07003e-05 0.999984 10 5.61364e-06 0.999996 Quadrature order N = 20 I Wi Xi -20 1.20496e-08 -1 -19 3.09537e-08 -1 -18 7.95155e-08 -1 -17 2.04263e-07 -1 -16 5.24722e-07 -0.999999 -15 1.34793e-06 -0.999999 -14 3.46263e-06 -0.999996 -13 8.89493e-06 -0.999991 -12 2.28494e-05 -0.999976 -11 5.86945e-05 -0.999938 -10 0.000150763 -0.99984 -9 0.00038719 -0.99959 -8 0.000993993 -0.998946 -7 0.0025492 -0.997294 -6 0.00652081 -0.993064 -5 0.0165702 -0.98228 -4 0.0414073 -0.955103 -3 0.0992549 -0.888591 -2 0.215635 -0.736807 -1 0.38057 -0.439596 0 0.471729 0 1 0.38057 0.439596 2 0.215635 0.736807 3 0.0992549 0.888591 4 0.0414073 0.955103 5 0.0165702 0.98228 6 0.00652081 0.993064 7 0.0025492 0.997294 8 0.000993993 0.998946 9 0.00038719 0.99959 10 0.000150763 0.99984 11 5.86945e-05 0.999938 12 2.28494e-05 0.999976 13 8.89493e-06 0.999991 14 3.46263e-06 0.999996 15 1.34793e-06 0.999999 16 5.24722e-07 0.999999 17 2.04263e-07 1 18 7.95155e-08 1 19 3.09537e-08 1 20 1.20496e-08 1 Note that the weights do not sum to 2! N sum(W) 5 2.00122 10 2.00003 20 2 40 2 80 2 TEST025 Determine tanh-sinh quadrature rules W, X for N = 1, 3, 7, 15, 31, 63. M = -3 ORDER = 1 N = 0 H = 2 I Wi Xi 0 3.14159 0 M = -2 ORDER = 3 N = 1 H = 1 I Wi Xi -1 0.230022 -0.951368 0 1.5708 0 1 0.230022 0.951368 M = -1 ORDER = 7 N = 3 H = 0.5 I Wi Xi -3 0.00917158 -0.997515 -2 0.115011 -0.951368 -1 0.482988 -0.674271 0 0.785398 0 1 0.482988 0.674271 2 0.115011 0.951368 3 0.00917158 0.997515 M = 0 ORDER = 15 N = 7 H = 0.25 I Wi Xi -7 0.000725629 -0.999688 -6 0.00458579 -0.997515 -5 0.0190964 -0.987041 -4 0.0575056 -0.951368 -3 0.13277 -0.859569 -2 0.241494 -0.674271 -1 0.347404 -0.37721 0 0.392699 0 1 0.347404 0.37721 2 0.241494 0.674271 3 0.13277 0.859569 4 0.0575056 0.951368 5 0.0190964 0.987041 6 0.00458579 0.997515 7 0.000725629 0.999688 M = 1 ORDER = 31 N = 15 H = 0.125 I Wi Xi -15 0.000118743 -0.999909 -14 0.000362815 -0.999688 -13 0.000967825 -0.999065 -12 0.0022929 -0.997515 -11 0.00489688 -0.994056 -10 0.00954822 -0.987041 -9 0.0171778 -0.973967 -8 0.0287528 -0.951368 -7 0.0450577 -0.914879 -6 0.0663848 -0.859569 -5 0.0921797 -0.780607 -4 0.120747 -0.674271 -3 0.149183 -0.539147 -2 0.173702 -0.37721 -1 0.19041 -0.194357 0 0.19635 0 1 0.19041 0.194357 2 0.173702 0.37721 3 0.149183 0.539147 4 0.120747 0.674271 5 0.0921797 0.780607 6 0.0663848 0.859569 7 0.0450577 0.914879 8 0.0287528 0.951368 9 0.0171778 0.973967 10 0.00954822 0.987041 11 0.00489688 0.994056 12 0.0022929 0.997515 13 0.000967825 0.999065 14 0.000362815 0.999688 15 0.000118743 0.999909 M = 2 ORDER = 63 N = 31 H = 0.0625 I Wi Xi -31 3.20871e-05 -0.999954 -30 5.93717e-05 -0.999909 -29 0.00010568 -0.999829 -28 0.000181407 -0.999688 -27 0.000301019 -0.999451 -26 0.000483913 -0.999065 -25 0.000755221 -0.998454 -24 0.00114645 -0.997515 -23 0.00169584 -0.996109 -22 0.00244844 -0.994056 -21 0.00345561 -0.991127 -20 0.00477411 -0.987041 -19 0.00646451 -0.981455 -18 0.00858888 -0.973967 -17 0.0112078 -0.964112 -16 0.0143764 -0.951368 -15 0.01814 -0.935161 -14 0.0225288 -0.914879 -13 0.0275521 -0.889891 -12 0.0331924 -0.859569 -11 0.0394003 -0.823317 -10 0.0460899 -0.780607 -9 0.0531358 -0.731018 -8 0.0603735 -0.674271 -7 0.0676022 -0.610274 -6 0.0745914 -0.539147 -5 0.0810922 -0.461254 -4 0.0868509 -0.37721 -3 0.0916259 -0.28788 -2 0.0952052 -0.194357 -1 0.0974233 -0.0979239 0 0.0981748 0 1 0.0974233 0.0979239 2 0.0952052 0.194357 3 0.0916259 0.28788 4 0.0868509 0.37721 5 0.0810922 0.461254 6 0.0745914 0.539147 7 0.0676022 0.610274 8 0.0603735 0.674271 9 0.0531358 0.731018 10 0.0460899 0.780607 11 0.0394003 0.823317 12 0.0331924 0.859569 13 0.0275521 0.889891 14 0.0225288 0.914879 15 0.01814 0.935161 16 0.0143764 0.951368 17 0.0112078 0.964112 18 0.00858888 0.973967 19 0.00646451 0.981455 20 0.00477411 0.987041 21 0.00345561 0.991127 22 0.00244844 0.994056 23 0.00169584 0.996109 24 0.00114645 0.997515 25 0.000755221 0.998454 26 0.000483913 0.999065 27 0.000301019 0.999451 28 0.000181407 0.999688 29 0.00010568 0.999829 30 5.93717e-05 0.999909 31 3.20871e-05 0.999954 M = 3 ORDER = 127 N = 63 H = 0.03125 I Wi Xi -63 1.16146e-05 -0.999968 -62 1.60436e-05 -0.999954 -61 2.19331e-05 -0.999935 -60 2.96858e-05 -0.999909 -59 3.97915e-05 -0.999875 -58 5.28398e-05 -0.999829 -57 6.95338e-05 -0.999768 -56 9.07037e-05 -0.999688 -55 0.00011732 -0.999585 -54 0.000150509 -0.999451 -53 0.000191564 -0.999281 -52 0.000241956 -0.999065 -51 0.000303351 -0.998794 -50 0.000377611 -0.998454 -49 0.000466807 -0.998033 -48 0.000573224 -0.997515 -47 0.000699358 -0.99688 -46 0.000847922 -0.996109 -45 0.00102184 -0.995176 -44 0.00122422 -0.994056 -43 0.00145838 -0.992717 -42 0.0017278 -0.991127 -41 0.00203611 -0.989248 -40 0.00238705 -0.987041 -39 0.00278447 -0.984459 -38 0.00323225 -0.981455 -37 0.00373429 -0.977976 -36 0.00429444 -0.973967 -35 0.00491644 -0.969367 -34 0.00560389 -0.964112 -33 0.00636012 -0.958136 -32 0.0071882 -0.951368 -31 0.00809077 -0.943735 -30 0.00907002 -0.935161 -29 0.0101276 -0.925569 -28 0.0112644 -0.914879 -27 0.0124808 -0.903013 -26 0.013776 -0.889891 -25 0.0151487 -0.875435 -24 0.0165962 -0.859569 -23 0.0181149 -0.842219 -22 0.0197002 -0.823317 -21 0.0213459 -0.802799 -20 0.0230449 -0.780607 -19 0.0247888 -0.756694 -18 0.0265679 -0.731018 -17 0.0283712 -0.70355 -16 0.0301868 -0.674271 -15 0.0320014 -0.643177 -14 0.0338011 -0.610274 -13 0.035571 -0.575584 -12 0.0372957 -0.539147 -11 0.0389594 -0.501013 -10 0.0405461 -0.461254 -9 0.04204 -0.419952 -8 0.0434255 -0.37721 -7 0.0446878 -0.333142 -6 0.045813 -0.28788 -5 0.0467883 -0.241566 -4 0.0476026 -0.194357 -3 0.0482463 -0.146418 -2 0.0487117 -0.0979239 -1 0.0489932 -0.049056 0 0.0490874 0 1 0.0489932 0.049056 2 0.0487117 0.0979239 3 0.0482463 0.146418 4 0.0476026 0.194357 5 0.0467883 0.241566 6 0.045813 0.28788 7 0.0446878 0.333142 8 0.0434255 0.37721 9 0.04204 0.419952 10 0.0405461 0.461254 11 0.0389594 0.501013 12 0.0372957 0.539147 13 0.035571 0.575584 14 0.0338011 0.610274 15 0.0320014 0.643177 16 0.0301868 0.674271 17 0.0283712 0.70355 18 0.0265679 0.731018 19 0.0247888 0.756694 20 0.0230449 0.780607 21 0.0213459 0.802799 22 0.0197002 0.823317 23 0.0181149 0.842219 24 0.0165962 0.859569 25 0.0151487 0.875435 26 0.013776 0.889891 27 0.0124808 0.903013 28 0.0112644 0.914879 29 0.0101276 0.925569 30 0.00907002 0.935161 31 0.00809077 0.943735 32 0.0071882 0.951368 33 0.00636012 0.958136 34 0.00560389 0.964112 35 0.00491644 0.969367 36 0.00429444 0.973967 37 0.00373429 0.977976 38 0.00323225 0.981455 39 0.00278447 0.984459 40 0.00238705 0.987041 41 0.00203611 0.989248 42 0.0017278 0.991127 43 0.00145838 0.992717 44 0.00122422 0.994056 45 0.00102184 0.995176 46 0.000847922 0.996109 47 0.000699358 0.99688 48 0.000573224 0.997515 49 0.000466807 0.998033 50 0.000377611 0.998454 51 0.000303351 0.998794 52 0.000241956 0.999065 53 0.000191564 0.999281 54 0.000150509 0.999451 55 0.00011732 0.999585 56 9.07037e-05 0.999688 57 6.95338e-05 0.999768 58 5.28398e-05 0.999829 59 3.97915e-05 0.999875 60 2.96858e-05 0.999909 61 2.19331e-05 0.999935 62 1.60436e-05 0.999954 63 1.16146e-05 0.999968 Note that, especially for low N, the weights need not sum to 2! N H sum(W) 0 12.5664 1 6.28319 3 3.14266 7 2.03137 15 2.00001 31 2 63 2 127 2 255 2 511 2 1023 2 2047 2 4095 2 8191 2 TEST03 Determine a quadrature rule W, X by specifying a tolerance. Tolerance TOL = 2.22045e-16 Level M = -1 Spacing H = 2 Quadrature order N = 19 I Wi Xi -19 1.25565e-16 -1 -18 9.27809e-16 -1 -17 6.85563e-15 -1 -16 5.06567e-14 -1 -15 3.74305e-13 -1 -14 2.76576e-12 -1 -13 2.04364e-11 -1 -12 1.51005e-10 -1 -11 1.11579e-09 -1 -10 8.24461e-09 -1 -9 6.09199e-08 -1 -8 4.50141e-07 -1 -7 3.32611e-06 -0.999998 -6 2.45765e-05 -0.999988 -5 0.000181583 -0.999909 -4 0.00134095 -0.999329 -3 0.00986604 -0.995055 -2 0.0706508 -0.964028 -1 0.419974 -0.761594 0 1 0 1 0.419974 0.761594 2 0.0706508 0.964028 3 0.00986604 0.995055 4 0.00134095 0.999329 5 0.000181583 0.999909 6 2.45765e-05 0.999988 7 3.32611e-06 0.999998 8 4.50141e-07 1 9 6.09199e-08 1 10 8.24461e-09 1 11 1.11579e-09 1 12 1.51005e-10 1 13 2.04364e-11 1 14 2.76576e-12 1 15 3.74305e-13 1 16 5.06567e-14 1 17 6.85563e-15 1 18 9.27809e-16 1 19 1.25565e-16 1 Level M = 0 Spacing H = 1 Quadrature order N = 37 I Wi Xi -37 1.70661e-16 -1 -36 4.63905e-16 -1 -35 1.26102e-15 -1 -34 3.42782e-15 -1 -33 9.31777e-15 -1 -32 2.53283e-14 -1 -31 6.88495e-14 -1 -30 1.87152e-13 -1 -29 5.08733e-13 -1 -28 1.38288e-12 -1 -27 3.75906e-12 -1 -26 1.02182e-11 -1 -25 2.77759e-11 -1 -24 7.55027e-11 -1 -23 2.05238e-10 -1 -22 5.57894e-10 -1 -21 1.51651e-09 -1 -20 4.12231e-09 -1 -19 1.12056e-08 -1 -18 3.046e-08 -1 -17 8.27987e-08 -1 -16 2.2507e-07 -1 -15 6.11804e-07 -0.999999 -14 1.66305e-06 -0.999998 -13 4.52064e-06 -0.999995 -12 1.22883e-05 -0.999988 -11 3.34023e-05 -0.999967 -10 9.07916e-05 -0.999909 -9 0.000246759 -0.999753 -8 0.000670475 -0.999329 -7 0.00182044 -0.998178 -6 0.00493302 -0.995055 -5 0.0132961 -0.986614 -4 0.0353254 -0.964028 -3 0.0903533 -0.905148 -2 0.209987 -0.761594 -1 0.393224 -0.462117 0 0.5 0 1 0.393224 0.462117 2 0.209987 0.761594 3 0.0903533 0.905148 4 0.0353254 0.964028 5 0.0132961 0.986614 6 0.00493302 0.995055 7 0.00182044 0.998178 8 0.000670475 0.999329 9 0.000246759 0.999753 10 9.07916e-05 0.999909 11 3.34023e-05 0.999967 12 1.22883e-05 0.999988 13 4.52064e-06 0.999995 14 1.66305e-06 0.999998 15 6.11804e-07 0.999999 16 2.2507e-07 1 17 8.27987e-08 1 18 3.046e-08 1 19 1.12056e-08 1 20 4.12231e-09 1 21 1.51651e-09 1 22 5.57894e-10 1 23 2.05238e-10 1 24 7.55027e-11 1 25 2.77759e-11 1 26 1.02182e-11 1 27 3.75906e-12 1 28 1.38288e-12 1 29 5.08733e-13 1 30 1.87152e-13 1 31 6.88495e-14 1 32 2.53283e-14 1 33 9.31777e-15 1 34 3.42782e-15 1 35 1.26102e-15 1 36 4.63905e-16 1 37 1.70661e-16 1 Level M = 1 Spacing H = 0.5 Quadrature order N = 73 I Wi Xi -73 1.40686e-16 -1 -72 2.31952e-16 -1 -71 3.82425e-16 -1 -70 6.30512e-16 -1 -69 1.03954e-15 -1 -68 1.71391e-15 -1 -67 2.82576e-15 -1 -66 4.65889e-15 -1 -65 7.6812e-15 -1 -64 1.26642e-14 -1 -63 2.08797e-14 -1 -62 3.44248e-14 -1 -61 5.67569e-14 -1 -60 9.35762e-14 -1 -59 1.54281e-13 -1 -58 2.54367e-13 -1 -57 4.1938e-13 -1 -56 6.9144e-13 -1 -55 1.13999e-12 -1 -54 1.87953e-12 -1 -53 3.09882e-12 -1 -52 5.10909e-12 -1 -51 8.42346e-12 -1 -50 1.38879e-11 -1 -49 2.28973e-11 -1 -48 3.77513e-11 -1 -47 6.22414e-11 -1 -46 1.02619e-10 -1 -45 1.6919e-10 -1 -44 2.78947e-10 -1 -43 4.59906e-10 -1 -42 7.58256e-10 -1 -41 1.25015e-09 -1 -40 2.06115e-09 -1 -39 3.39827e-09 -1 -38 5.6028e-09 -1 -37 9.23745e-09 -1 -36 1.523e-08 -1 -35 2.511e-08 -1 -34 4.13994e-08 -1 -33 6.8256e-08 -1 -32 1.12535e-07 -1 -31 1.85539e-07 -1 -30 3.05902e-07 -0.999999 -29 5.04347e-07 -0.999999 -28 8.31527e-07 -0.999998 -27 1.37096e-06 -0.999997 -26 2.26032e-06 -0.999995 -25 3.72663e-06 -0.999993 -24 6.14414e-06 -0.999988 -23 1.01299e-05 -0.99998 -22 1.67011e-05 -0.999967 -21 2.75349e-05 -0.999945 -20 4.53958e-05 -0.999909 -19 7.48406e-05 -0.99985 -18 0.000123379 -0.999753 -17 0.000203386 -0.999593 -16 0.000335238 -0.999329 -15 0.000552473 -0.998894 -14 0.000910221 -0.998178 -13 0.00149893 -0.996998 -12 0.00246651 -0.995055 -11 0.00405357 -0.99186 -10 0.00664806 -0.986614 -9 0.0108662 -0.978026 -8 0.0176627 -0.964028 -7 0.028453 -0.941376 -6 0.0451767 -0.905148 -5 0.0701037 -0.848284 -4 0.104994 -0.761594 -3 0.149146 -0.635149 -2 0.196612 -0.462117 -1 0.235004 -0.244919 0 0.25 0 1 0.235004 0.244919 2 0.196612 0.462117 3 0.149146 0.635149 4 0.104994 0.761594 5 0.0701037 0.848284 6 0.0451767 0.905148 7 0.028453 0.941376 8 0.0176627 0.964028 9 0.0108662 0.978026 10 0.00664806 0.986614 11 0.00405357 0.99186 12 0.00246651 0.995055 13 0.00149893 0.996998 14 0.000910221 0.998178 15 0.000552473 0.998894 16 0.000335238 0.999329 17 0.000203386 0.999593 18 0.000123379 0.999753 19 7.48406e-05 0.99985 20 4.53958e-05 0.999909 21 2.75349e-05 0.999945 22 1.67011e-05 0.999967 23 1.01299e-05 0.99998 24 6.14414e-06 0.999988 25 3.72663e-06 0.999993 26 2.26032e-06 0.999995 27 1.37096e-06 0.999997 28 8.31527e-07 0.999998 29 5.04347e-07 0.999999 30 3.05902e-07 0.999999 31 1.85539e-07 1 32 1.12535e-07 1 33 6.8256e-08 1 34 4.13994e-08 1 35 2.511e-08 1 36 1.523e-08 1 37 9.23745e-09 1 38 5.6028e-09 1 39 3.39827e-09 1 40 2.06115e-09 1 41 1.25015e-09 1 42 7.58256e-10 1 43 4.59906e-10 1 44 2.78947e-10 1 45 1.6919e-10 1 46 1.02619e-10 1 47 6.22414e-11 1 48 3.77513e-11 1 49 2.28973e-11 1 50 1.38879e-11 1 51 8.42346e-12 1 52 5.10909e-12 1 53 3.09882e-12 1 54 1.87953e-12 1 55 1.13999e-12 1 56 6.9144e-13 1 57 4.1938e-13 1 58 2.54367e-13 1 59 1.54281e-13 1 60 9.35762e-14 1 61 5.67569e-14 1 62 3.44248e-14 1 63 2.08797e-14 1 64 1.26642e-14 1 65 7.6812e-15 1 66 4.65889e-15 1 67 2.82576e-15 1 68 1.71391e-15 1 69 1.03954e-15 1 70 6.30512e-16 1 71 3.82425e-16 1 72 2.31952e-16 1 73 1.40686e-16 1 Level M = 2 Spacing H = 0.25 Quadrature order N = 142 I Wi Xi -142 1.91212e-16 -1 -141 2.45521e-16 -1 -140 3.15256e-16 -1 -139 4.04797e-16 -1 -138 5.19769e-16 -1 -137 6.67397e-16 -1 -136 8.56954e-16 -1 -135 1.10035e-15 -1 -134 1.41288e-15 -1 -133 1.81417e-15 -1 -132 2.32944e-15 -1 -131 2.99106e-15 -1 -130 3.8406e-15 -1 -129 4.93143e-15 -1 -128 6.33208e-15 -1 -127 8.13056e-15 -1 -126 1.04398e-14 -1 -125 1.3405e-14 -1 -124 1.72124e-14 -1 -123 2.21011e-14 -1 -122 2.83784e-14 -1 -121 3.64386e-14 -1 -120 4.67881e-14 -1 -119 6.00771e-14 -1 -118 7.71406e-14 -1 -117 9.90504e-14 -1 -116 1.27183e-13 -1 -115 1.63307e-13 -1 -114 2.0969e-13 -1 -113 2.69247e-13 -1 -112 3.4572e-13 -1 -111 4.43913e-13 -1 -110 5.69996e-13 -1 -109 7.31889e-13 -1 -108 9.39764e-13 -1 -107 1.20668e-12 -1 -106 1.54941e-12 -1 -105 1.98948e-12 -1 -104 2.55454e-12 -1 -103 3.2801e-12 -1 -102 4.21173e-12 -1 -101 5.40797e-12 -1 -100 6.94397e-12 -1 -99 8.91624e-12 -1 -98 1.14487e-11 -1 -97 1.47004e-11 -1 -96 1.88757e-11 -1 -95 2.42368e-11 -1 -94 3.11207e-11 -1 -93 3.99598e-11 -1 -92 5.13094e-11 -1 -91 6.58826e-11 -1 -90 8.45949e-11 -1 -89 1.08622e-10 -1 -88 1.39473e-10 -1 -87 1.79087e-10 -1 -86 2.29953e-10 -1 -85 2.95265e-10 -1 -84 3.79128e-10 -1 -83 4.8681e-10 -1 -82 6.25076e-10 -1 -81 8.02614e-10 -1 -80 1.03058e-09 -1 -79 1.32329e-09 -1 -78 1.69913e-09 -1 -77 2.18173e-09 -1 -76 2.8014e-09 -1 -75 3.59707e-09 -1 -74 4.61872e-09 -1 -73 5.93056e-09 -1 -72 7.61499e-09 -1 -71 9.77784e-09 -1 -70 1.2555e-08 -1 -69 1.61209e-08 -1 -68 2.06997e-08 -1 -67 2.65789e-08 -1 -66 3.4128e-08 -1 -65 4.38212e-08 -1 -64 5.62676e-08 -1 -63 7.2249e-08 -1 -62 9.27695e-08 -1 -61 1.19118e-07 -1 -60 1.52951e-07 -0.999999 -59 1.96393e-07 -0.999999 -58 2.52174e-07 -0.999999 -57 3.23797e-07 -0.999999 -56 4.15764e-07 -0.999998 -55 5.33851e-07 -0.999998 -54 6.85478e-07 -0.999997 -53 8.8017e-07 -0.999996 -52 1.13016e-06 -0.999995 -51 1.45115e-06 -0.999994 -50 1.86331e-06 -0.999993 -49 2.39254e-06 -0.99999 -48 3.07207e-06 -0.999988 -47 3.9446e-06 -0.999984 -46 5.06494e-06 -0.99998 -45 6.50348e-06 -0.999974 -44 8.35057e-06 -0.999967 -43 1.07222e-05 -0.999957 -42 1.37675e-05 -0.999945 -41 1.76775e-05 -0.999929 -40 2.26979e-05 -0.999909 -39 2.91439e-05 -0.999883 -38 3.74203e-05 -0.99985 -37 4.80466e-05 -0.999808 -36 6.16897e-05 -0.999753 -35 7.92056e-05 -0.999683 -34 0.000101693 -0.999593 -33 0.000130561 -0.999478 -32 0.000167619 -0.999329 -31 0.000215186 -0.999139 -30 0.000276237 -0.998894 -29 0.000354583 -0.998581 -28 0.000455111 -0.998178 -27 0.000584071 -0.997661 -26 0.000749464 -0.996998 -25 0.000961511 -0.996147 -24 0.00123325 -0.995055 -23 0.00158131 -0.993655 -22 0.00202679 -0.99186 -21 0.00259644 -0.98956 -20 0.00332403 -0.986614 -19 0.00425196 -0.982845 -18 0.00543311 -0.978026 -17 0.00693292 -0.971873 -16 0.00883135 -0.964028 -15 0.0112247 -0.954045 -14 0.0142265 -0.941376 -13 0.0179668 -0.925346 -12 0.0225883 -0.905148 -11 0.0282381 -0.879827 -10 0.0350519 -0.848284 -9 0.043129 -0.809301 -8 0.0524968 -0.761594 -7 0.0630646 -0.703906 -6 0.0745732 -0.635149 -5 0.0865524 -0.5546 -4 0.098306 -0.462117 -3 0.108947 -0.358357 -2 0.117502 -0.244919 -1 0.123067 -0.124353 0 0.125 0 1 0.123067 0.124353 2 0.117502 0.244919 3 0.108947 0.358357 4 0.098306 0.462117 5 0.0865524 0.5546 6 0.0745732 0.635149 7 0.0630646 0.703906 8 0.0524968 0.761594 9 0.043129 0.809301 10 0.0350519 0.848284 11 0.0282381 0.879827 12 0.0225883 0.905148 13 0.0179668 0.925346 14 0.0142265 0.941376 15 0.0112247 0.954045 16 0.00883135 0.964028 17 0.00693292 0.971873 18 0.00543311 0.978026 19 0.00425196 0.982845 20 0.00332403 0.986614 21 0.00259644 0.98956 22 0.00202679 0.99186 23 0.00158131 0.993655 24 0.00123325 0.995055 25 0.000961511 0.996147 26 0.000749464 0.996998 27 0.000584071 0.997661 28 0.000455111 0.998178 29 0.000354583 0.998581 30 0.000276237 0.998894 31 0.000215186 0.999139 32 0.000167619 0.999329 33 0.000130561 0.999478 34 0.000101693 0.999593 35 7.92056e-05 0.999683 36 6.16897e-05 0.999753 37 4.80466e-05 0.999808 38 3.74203e-05 0.99985 39 2.91439e-05 0.999883 40 2.26979e-05 0.999909 41 1.76775e-05 0.999929 42 1.37675e-05 0.999945 43 1.07222e-05 0.999957 44 8.35057e-06 0.999967 45 6.50348e-06 0.999974 46 5.06494e-06 0.99998 47 3.9446e-06 0.999984 48 3.07207e-06 0.999988 49 2.39254e-06 0.99999 50 1.86331e-06 0.999993 51 1.45115e-06 0.999994 52 1.13016e-06 0.999995 53 8.8017e-07 0.999996 54 6.85478e-07 0.999997 55 5.33851e-07 0.999998 56 4.15764e-07 0.999998 57 3.23797e-07 0.999999 58 2.52174e-07 0.999999 59 1.96393e-07 0.999999 60 1.52951e-07 0.999999 61 1.19118e-07 1 62 9.27695e-08 1 63 7.2249e-08 1 64 5.62676e-08 1 65 4.38212e-08 1 66 3.4128e-08 1 67 2.65789e-08 1 68 2.06997e-08 1 69 1.61209e-08 1 70 1.2555e-08 1 71 9.77784e-09 1 72 7.61499e-09 1 73 5.93056e-09 1 74 4.61872e-09 1 75 3.59707e-09 1 76 2.8014e-09 1 77 2.18173e-09 1 78 1.69913e-09 1 79 1.32329e-09 1 80 1.03058e-09 1 81 8.02614e-10 1 82 6.25076e-10 1 83 4.8681e-10 1 84 3.79128e-10 1 85 2.95265e-10 1 86 2.29953e-10 1 87 1.79087e-10 1 88 1.39473e-10 1 89 1.08622e-10 1 90 8.45949e-11 1 91 6.58826e-11 1 92 5.13094e-11 1 93 3.99598e-11 1 94 3.11207e-11 1 95 2.42368e-11 1 96 1.88757e-11 1 97 1.47004e-11 1 98 1.14487e-11 1 99 8.91624e-12 1 100 6.94397e-12 1 101 5.40797e-12 1 102 4.21173e-12 1 103 3.2801e-12 1 104 2.55454e-12 1 105 1.98948e-12 1 106 1.54941e-12 1 107 1.20668e-12 1 108 9.39764e-13 1 109 7.31889e-13 1 110 5.69996e-13 1 111 4.43913e-13 1 112 3.4572e-13 1 113 2.69247e-13 1 114 2.0969e-13 1 115 1.63307e-13 1 116 1.27183e-13 1 117 9.90504e-14 1 118 7.71406e-14 1 119 6.00771e-14 1 120 4.67881e-14 1 121 3.64386e-14 1 122 2.83784e-14 1 123 2.21011e-14 1 124 1.72124e-14 1 125 1.3405e-14 1 126 1.04398e-14 1 127 8.13056e-15 1 128 6.33208e-15 1 129 4.93143e-15 1 130 3.8406e-15 1 131 2.99106e-15 1 132 2.32944e-15 1 133 1.81417e-15 1 134 1.41288e-15 1 135 1.10035e-15 1 136 8.56954e-16 1 137 6.67397e-16 1 138 5.19769e-16 1 139 4.04797e-16 1 140 3.15256e-16 1 141 2.45521e-16 1 142 1.91212e-16 1 TEST032 Apply a sequence of midpoint rules to a test integral. Problem index P = 1 Tolerance TOL = 2.22045e-16 M H_MIDPOINT N Exact Quad Error 1 0.0135135 73 1 1 2.22045e-15 2 0.00699301 142 1 1 6.21725e-15 3 0.00358423 278 1 1 8.99281e-15 4 0.00183486 544 1 1 2.26485e-14 5 0.000938086 1065 1 1 3.4639e-14 6 0.000479386 2085 1 1 1.35447e-14 7 0.000244918 4082 1 1 5.973e-14 8 0.000125203 7986 1 1 1.48992e-13 TEST032 Apply a sequence of midpoint rules to a test integral. Problem index P = 2 Tolerance TOL = 2.22045e-16 M H_MIDPOINT N Exact Quad Error 1 0.0135135 73 1 1 0 2 0.00699301 142 1 1 2.22045e-16 3 0.00358423 278 1 1 0 4 0.00183486 544 1 1 1.11022e-16 5 0.000938086 1065 1 1 5.55112e-16 6 0.000479386 2085 1 1 2.22045e-16 7 0.000244918 4082 1 1 1.11022e-16 8 0.000125203 7986 1 1 1.11022e-16 TEST032 Apply a sequence of midpoint rules to a test integral. Problem index P = 3 Tolerance TOL = 2.22045e-16 M H_MIDPOINT N Exact Quad Error 1 0.0135135 73 1 0.999887 0.000113209 2 0.00699301 142 1 0.99997 3.04356e-05 3 0.00358423 278 1 0.999992 8.01192e-06 4 0.00183486 544 1 0.999998 2.10188e-06 5 0.000938086 1065 1 0.999999 5.49694e-07 6 0.000479386 2085 1 1 1.43591e-07 7 0.000244918 4082 1 1 3.7485e-08 8 0.000125203 7986 1 1 9.7967e-09 TEST032 Apply a sequence of midpoint rules to a test integral. Problem index P = 4 Tolerance TOL = 2.22045e-16 M H_MIDPOINT N Exact Quad Error 1 0.0135135 73 -0.316714 -0.312342 0.00437233 2 0.00699301 142 -0.316714 -0.314412 0.00230191 3 0.00358423 278 -0.316714 -0.315521 0.00119276 4 0.00183486 544 -0.316714 -0.3161 0.000614647 5 0.000938086 1065 -0.316714 -0.316399 0.000315473 6 0.000479386 2085 -0.316714 -0.316553 0.000161581 7 0.000244918 4082 -0.316714 -0.316632 8.26591e-05 8 0.000125203 7986 -0.316714 -0.316672 4.2287e-05 TEST032 Apply a sequence of midpoint rules to a test integral. Problem index P = 5 Tolerance TOL = 2.22045e-16 M H_MIDPOINT N Exact Quad Error 1 0.0135135 73 0.25 0.249978 2.24849e-05 2 0.00699301 142 0.25 0.249994 6.0485e-06 3 0.00358423 278 0.25 0.249998 1.59271e-06 4 0.00183486 544 0.25 0.25 4.17906e-07 5 0.000938086 1065 0.25 0.25 1.09302e-07 6 0.000479386 2085 0.25 0.25 2.85529e-08 7 0.000244918 4082 0.25 0.25 7.45402e-09 8 0.000125203 7986 0.25 0.25 1.94813e-09 TEST032 Apply a sequence of midpoint rules to a test integral. Problem index P = 6 Tolerance TOL = 2.22045e-16 M H_MIDPOINT N Exact Quad Error 1 0.0135135 73 0.210657 0.210618 3.91537e-05 2 0.00699301 142 0.210657 0.210647 1.05157e-05 3 0.00358423 278 0.210657 0.210654 2.76671e-06 4 0.00183486 544 0.210657 0.210657 7.25635e-07 5 0.000938086 1065 0.210657 0.210657 1.89745e-07 6 0.000479386 2085 0.210657 0.210657 4.95616e-08 7 0.000244918 4082 0.210657 0.210657 1.29378e-08 8 0.000125203 7986 0.210657 0.210657 3.38123e-09 TEST032 Apply a sequence of midpoint rules to a test integral. Problem index P = 7 Tolerance TOL = 2.22045e-16 M H_MIDPOINT N Exact Quad Error 1 0.0135135 73 1.90524 1.90551 0.000269852 2 0.00699301 142 1.90524 1.90531 7.26333e-05 3 0.00358423 278 1.90524 1.90526 1.91318e-05 4 0.00183486 544 1.90524 1.90524 5.02071e-06 5 0.000938086 1065 1.90524 1.90524 1.31325e-06 6 0.000479386 2085 1.90524 1.90524 3.43075e-07 7 0.000244918 4082 1.90524 1.90524 8.9565e-08 8 0.000125203 7986 1.90524 1.90524 2.34083e-08 TEST032 Apply a sequence of midpoint rules to a test integral. Problem index P = 8 Tolerance TOL = 2.22045e-16 M H_MIDPOINT N Exact Quad Error 1 0.0135135 73 0.514042 0.514049 6.78814e-06 2 0.00699301 142 0.514042 0.514044 1.82897e-06 3 0.00358423 278 0.514042 0.514042 4.82009e-07 4 0.00183486 544 0.514042 0.514042 1.26526e-07 5 0.000938086 1065 0.514042 0.514042 3.30996e-08 6 0.000479386 2085 0.514042 0.514042 8.64757e-09 7 0.000244918 4082 0.514042 0.514042 2.25766e-09 8 0.000125203 7986 0.514042 0.514042 5.90057e-10 TEST032 Apply a sequence of midpoint rules to a test integral. Problem index P = 9 Tolerance TOL = 2.22045e-16 M H_MIDPOINT N Exact Quad Error 1 0.0135135 73 -0.444444 -0.445074 0.000629354 2 0.00699301 142 -0.444444 -0.444717 0.000272082 3 0.00358423 278 -0.444444 -0.444559 0.000114119 4 0.00183486 544 -0.444444 -0.444492 4.70952e-05 5 0.000938086 1065 -0.444444 -0.444464 1.91703e-05 6 0.000479386 2085 -0.444444 -0.444452 7.72135e-06 7 0.000244918 4082 -0.444444 -0.444448 3.08301e-06 8 0.000125203 7986 -0.444444 -0.444446 1.22329e-06 TEST032 Apply a sequence of midpoint rules to a test integral. Problem index P = 10 Tolerance TOL = 2.22045e-16 M H_MIDPOINT N Exact Quad Error 1 0.0135135 73 0.785398 0.785627 0.000228736 2 0.00699301 142 0.785398 0.785483 8.52798e-05 3 0.00358423 278 0.785398 0.785429 3.1317e-05 4 0.00183486 544 0.785398 0.78541 1.14751e-05 5 0.000938086 1065 0.785398 0.785402 4.19567e-06 6 0.000479386 2085 0.785398 0.7854 1.53288e-06 7 0.000244918 4082 0.785398 0.785399 5.59798e-07 8 0.000125203 7986 0.785398 0.785398 2.04614e-07 TEST032 Apply a sequence of midpoint rules to a test integral. Problem index P = 11 Tolerance TOL = 2.22045e-16 M H_MIDPOINT N Exact Quad Error 1 0.0135135 73 3.3726 1.14245 2.23015 2 0.00699301 142 3.3726 1.15804 2.21457 3 0.00358423 278 3.3726 1.16941 2.20319 4 0.00183486 544 3.3726 1.17758 2.19502 5 0.000938086 1065 3.3726 1.18344 2.18917 6 0.000479386 2085 3.3726 1.18763 2.18498 7 0.000244918 4082 3.3726 1.19063 2.18198 8 0.000125203 7986 3.3726 1.19277 2.17984 TEST032 Apply a sequence of midpoint rules to a test integral. Problem index P = 12 Tolerance TOL = 2.22045e-16 M H_MIDPOINT N Exact Quad Error 1 0.0135135 73 2 1.92439 0.0756121 2 0.00699301 142 2 1.95664 0.0433614 3 0.00358423 278 2 1.97557 0.0244261 4 0.00183486 544 2 1.98637 0.0136333 5 0.000938086 1065 2 1.99245 0.00754847 6 0.000479386 2085 2 1.99585 0.00415321 7 0.000244918 4082 2 1.99773 0.00227302 8 0.000125203 7986 2 1.99876 0.00123918 TEST032 Apply a sequence of midpoint rules to a test integral. Problem index P = 13 Tolerance TOL = 2.22045e-16 M H_MIDPOINT N Exact Quad Error 1 0.0135135 73 -1.08879 -1.07904 0.00975275 2 0.00699301 142 -1.08879 -1.08375 0.00504703 3 0.00358423 278 -1.08879 -1.08621 0.00258685 4 0.00183486 544 -1.08879 -1.08747 0.00132428 5 0.000938086 1065 -1.08879 -1.08812 0.000677047 6 0.000479386 2085 -1.08879 -1.08845 0.000345989 7 0.000244918 4082 -1.08879 -1.08862 0.000176765 8 0.000125203 7986 -1.08879 -1.0887 9.03634e-05 TEST032 Apply a sequence of midpoint rules to a test integral. Problem index P = 14 Tolerance TOL = 2.22045e-16 M H_MIDPOINT N Exact Quad Error 1 0.0135135 73 2.22144 2.12282 0.0986189 2 0.00699301 142 2.22144 2.15039 0.0710532 3 0.00358423 278 2.22144 2.17053 0.05091 4 0.00183486 544 2.22144 2.185 0.0364408 5 0.000938086 1065 2.22144 2.19538 0.0260616 6 0.000479386 2085 2.22144 2.20281 0.0186324 7 0.000244918 4082 2.22144 2.20812 0.0133187 8 0.000125203 7986 2.22144 2.21192 0.00952295 TEST04 Apply a sequence of trapezoid rules to a test integral. Problem index P = 1 Tolerance TOL = 2.22045e-16 M H N Exact Quad Error 1 0.5 73 1 1 2.88658e-15 2 0.25 142 1 1 1.11022e-15 3 0.125 278 1 1 5.32907e-15 4 0.0625 544 1 1 2.66454e-14 5 0.03125 1065 1 1 3.27516e-14 6 0.015625 2085 1 1 6.28386e-14 7 0.0078125 4082 1 1 1.67422e-13 8 0.00390625 7986 1 1 2.59348e-13 TEST04 Apply a sequence of trapezoid rules to a test integral. Problem index P = 2 Tolerance TOL = 2.22045e-16 M H N Exact Quad Error 1 0.5 73 1 1 0 2 0.25 142 1 1 2.22045e-16 3 0.125 278 1 1 0 4 0.0625 544 1 1 0 5 0.03125 1065 1 1 0 6 0.015625 2085 1 1 0 7 0.0078125 4082 1 1 1.11022e-16 8 0.00390625 7986 1 1 3.33067e-16 TEST04 Apply a sequence of trapezoid rules to a test integral. Problem index P = 3 Tolerance TOL = 2.22045e-16 M H N Exact Quad Error 1 0.5 73 1 1.00002 2.34566e-05 2 0.25 142 1 1.00001 6.19917e-06 3 0.125 278 1 1 1.61741e-06 4 0.0625 544 1 1 4.22389e-07 5 0.03125 1065 1 1 1.10207e-07 6 0.015625 2085 1 1 2.8754e-08 7 0.0078125 4082 1 1 7.50177e-09 8 0.00390625 7986 1 1 1.95998e-09 TEST04 Apply a sequence of trapezoid rules to a test integral. Problem index P = 4 Tolerance TOL = 2.22045e-16 M H N Exact Quad Error 1 0.5 73 -0.316714 -inf inf 2 0.25 142 -0.316714 -inf inf 3 0.125 278 -0.316714 -inf inf 4 0.0625 544 -0.316714 -inf inf 5 0.03125 1065 -0.316714 -inf inf 6 0.015625 2085 -0.316714 -inf inf 7 0.0078125 4082 -0.316714 -inf inf 8 0.00390625 7986 -0.316714 -inf inf TEST04 Apply a sequence of trapezoid rules to a test integral. Problem index P = 5 Tolerance TOL = 2.22045e-16 M H N Exact Quad Error 1 0.5 73 0.25 0.250005 4.66451e-06 2 0.25 142 0.25 0.250001 1.23275e-06 3 0.125 278 0.25 0.25 3.21635e-07 4 0.0625 544 0.25 0.25 8.39953e-08 5 0.03125 1065 0.25 0.25 2.19156e-08 6 0.015625 2085 0.25 0.25 5.71795e-09 7 0.0078125 4082 0.25 0.25 1.49179e-09 8 0.00390625 7986 0.25 0.25 3.89757e-10 TEST04 Apply a sequence of trapezoid rules to a test integral. Problem index P = 6 Tolerance TOL = 2.22045e-16 M H N Exact Quad Error 1 0.5 73 0.210657 0.210665 8.09564e-06 2 0.25 142 0.210657 0.210659 2.13954e-06 3 0.125 278 0.210657 0.210658 5.58222e-07 4 0.0625 544 0.210657 0.210657 1.4578e-07 5 0.03125 1065 0.210657 0.210657 3.80362e-08 6 0.015625 2085 0.210657 0.210657 9.92394e-09 7 0.0078125 4082 0.210657 0.210657 2.58911e-09 8 0.00390625 7986 0.210657 0.210657 6.76453e-10 TEST04 Apply a sequence of trapezoid rules to a test integral. Problem index P = 7 Tolerance TOL = 2.22045e-16 M H N Exact Quad Error 1 0.5 73 1.90524 1.90518 5.60484e-05 2 0.25 142 1.90524 1.90522 1.48127e-05 3 0.125 278 1.90524 1.90523 3.86474e-06 4 0.0625 544 1.90524 1.90524 1.00928e-06 5 0.03125 1065 1.90524 1.90524 2.63337e-07 6 0.015625 2085 1.90524 1.90524 6.87066e-08 7 0.0078125 4082 1.90524 1.90524 1.79252e-08 8 0.00390625 7986 1.90524 1.90524 4.6833e-09 TEST04 Apply a sequence of trapezoid rules to a test integral. Problem index P = 8 Tolerance TOL = 2.22045e-16 M H N Exact Quad Error 1 0.5 73 0.514042 0.51404 1.41287e-06 2 0.25 142 0.514042 0.514042 3.73396e-07 3 0.125 278 0.514042 0.514042 9.7422e-08 4 0.0625 544 0.514042 0.514042 2.54419e-08 5 0.03125 1065 0.514042 0.514042 6.63816e-09 6 0.015625 2085 0.514042 0.514042 1.73195e-09 7 0.0078125 4082 0.514042 0.514042 4.51856e-10 8 0.00390625 7986 0.514042 0.514042 1.18053e-10 TEST04 Apply a sequence of trapezoid rules to a test integral. Problem index P = 9 Tolerance TOL = 2.22045e-16 M H N Exact Quad Error 1 0.5 73 -0.444444 -nan nan 2 0.25 142 -0.444444 -nan nan 3 0.125 278 -0.444444 -nan nan 4 0.0625 544 -0.444444 -nan nan 5 0.03125 1065 -0.444444 -nan nan 6 0.015625 2085 -0.444444 -nan nan 7 0.0078125 4082 -0.444444 -nan nan 8 0.00390625 7986 -0.444444 -nan nan TEST04 Apply a sequence of trapezoid rules to a test integral. Problem index P = 10 Tolerance TOL = 2.22045e-16 M H N Exact Quad Error 1 0.5 73 0.785398 0.785232 0.000166617 2 0.25 142 0.785398 0.785337 6.14209e-05 3 0.125 278 0.785398 0.785376 2.24236e-05 4 0.0625 544 0.785398 0.78539 8.19191e-06 5 0.03125 1065 0.785398 0.785395 2.99065e-06 6 0.015625 2085 0.785398 0.785397 1.09178e-06 7 0.0078125 4082 0.785398 0.785398 3.98552e-07 8 0.00390625 7986 0.785398 0.785398 1.45647e-07 TEST04 Apply a sequence of trapezoid rules to a test integral. Problem index P = 11 Tolerance TOL = 2.22045e-16 M H N Exact Quad Error 1 0.5 73 3.3726 inf inf 2 0.25 142 3.3726 inf inf 3 0.125 278 3.3726 inf inf 4 0.0625 544 3.3726 inf inf 5 0.03125 1065 3.3726 inf inf 6 0.015625 2085 3.3726 inf inf 7 0.0078125 4082 3.3726 inf inf 8 0.00390625 7986 3.3726 inf inf TEST04 Apply a sequence of trapezoid rules to a test integral. Problem index P = 12 Tolerance TOL = 2.22045e-16 M H N Exact Quad Error 1 0.5 73 2 inf inf 2 0.25 142 2 inf inf 3 0.125 278 2 inf inf 4 0.0625 544 2 inf inf 5 0.03125 1065 2 inf inf 6 0.015625 2085 2 inf inf 7 0.0078125 4082 2 inf inf 8 0.00390625 7986 2 inf inf TEST04 Apply a sequence of trapezoid rules to a test integral. Problem index P = 13 Tolerance TOL = 2.22045e-16 M H N Exact Quad Error 1 0.5 73 -1.08879 -1.25535 0.166558 2 0.25 142 -1.08879 -1.17258 0.0837848 3 0.125 278 -1.08879 -1.13064 0.0418476 4 0.0625 544 -1.08879 -1.10969 0.0209007 5 0.03125 1065 -1.08879 -1.09922 0.0104283 6 0.015625 2085 -1.08879 -1.09399 0.00520018 7 0.0078125 4082 -1.08879 -1.09138 0.00259151 8 0.00390625 7986 -1.08879 -1.09008 0.00129164 TEST04 Apply a sequence of trapezoid rules to a test integral. Problem index P = 14 Tolerance TOL = 2.22045e-16 M H N Exact Quad Error 1 0.5 73 2.22144 687461 687459 2 0.25 142 2.22144 353414 353412 3 0.125 278 2.22144 180522 180520 4 0.0625 544 2.22144 92253.1 92250.8 5 0.03125 1065 2.22144 47123.8 47121.5 6 0.015625 2085 2.22144 24071.5 24069.3 7 0.0078125 4082 2.22144 12296.3 12294.1 8 0.00390625 7986 2.22144 6286.26 6284.04 TEST05 Apply a sequence of tanh rules to a test integral. Problem index P = 1 Tolerance TOL = 2.22045e-16 M H N Exact Quad Error -2 4 10 1 1.14403 0.144034 -1 2 19 1 1.00204 0.00204216 0 1 37 1 1 2.11232e-07 1 0.5 73 1 1 1.11022e-15 2 0.25 142 1 1 1.22125e-15 3 0.125 278 1 1 1.22125e-15 4 0.0625 544 1 1 3.44169e-15 5 0.03125 1065 1 1 7.10543e-15 6 0.015625 2085 1 1 1.44329e-14 7 0.0078125 4082 1 1 2.95319e-14 8 0.00390625 7986 1 1 5.76206e-14 TEST05 Apply a sequence of tanh rules to a test integral. Problem index P = 2 Tolerance TOL = 2.22045e-16 M H N Exact Quad Error -2 4 10 1 1.14403 0.144034 -1 2 19 1 1.00204 0.00204216 0 1 37 1 1 2.11232e-07 1 0.5 73 1 1 1.11022e-15 2 0.25 142 1 1 5.55112e-16 3 0.125 278 1 1 7.77156e-16 4 0.0625 544 1 1 4.88498e-15 5 0.03125 1065 1 1 7.77156e-15 6 0.015625 2085 1 1 1.53211e-14 7 0.0078125 4082 1 1 2.63123e-14 8 0.00390625 7986 1 1 5.77316e-14 TEST05 Apply a sequence of tanh rules to a test integral. Problem index P = 3 Tolerance TOL = 2.22045e-16 M H N Exact Quad Error -2 4 10 1 0.95856 0.0414396 -1 2 19 1 0.991961 0.00803863 0 1 37 1 0.999996 3.95833e-06 1 0.5 73 1 1 8.85958e-14 2 0.25 142 1 1 9.99201e-16 3 0.125 278 1 1 2.22045e-15 4 0.0625 544 1 1 5.66214e-15 5 0.03125 1065 1 1 1.03251e-14 6 0.015625 2085 1 1 2.08722e-14 7 0.0078125 4082 1 1 4.13003e-14 8 0.00390625 7986 1 1 8.50431e-14 TEST05 Apply a sequence of tanh rules to a test integral. Problem index P = 4 Tolerance TOL = 2.22045e-16 M H N Exact Quad Error -2 4 10 -0.316714 -inf inf -1 2 19 -0.316714 -inf inf 0 1 37 -0.316714 -0.316658 5.58619e-05 1 0.5 73 -0.316714 -0.316714 7.72425e-11 2 0.25 142 -0.316714 -0.316714 8.99281e-15 3 0.125 278 -0.316714 -0.316714 1.95954e-14 4 0.0625 544 -0.316714 -0.316714 4.10227e-14 5 0.03125 1065 -0.316714 -0.316714 8.4599e-14 6 0.015625 2085 -0.316714 -0.316714 1.66533e-13 7 0.0078125 4082 -0.316714 -0.316714 3.25628e-13 8 0.00390625 7986 -0.316714 -0.316714 6.41376e-13 TEST05 Apply a sequence of tanh rules to a test integral. Problem index P = 5 Tolerance TOL = 2.22045e-16 M H N Exact Quad Error -2 4 10 0.25 0.251165 0.00116534 -1 2 19 0.25 0.248706 0.00129355 0 1 37 0.25 0.249999 5.69104e-07 1 0.5 73 0.25 0.25 8.27116e-15 2 0.25 142 0.25 0.25 3.33067e-16 3 0.125 278 0.25 0.25 4.996e-16 4 0.0625 544 0.25 0.25 1.19349e-15 5 0.03125 1065 0.25 0.25 2.16493e-15 6 0.015625 2085 0.25 0.25 5.44009e-15 7 0.0078125 4082 0.25 0.25 9.40914e-15 8 0.00390625 7986 0.25 0.25 1.94289e-14 TEST05 Apply a sequence of tanh rules to a test integral. Problem index P = 6 Tolerance TOL = 2.22045e-16 M H N Exact Quad Error -2 4 10 0.210657 0.169877 0.0407804 -1 2 19 0.210657 0.206851 0.00380595 0 1 37 0.210657 0.210655 2.47604e-06 1 0.5 73 0.210657 0.210657 4.36873e-14 2 0.25 142 0.210657 0.210657 2.22045e-16 3 0.125 278 0.210657 0.210657 4.996e-16 4 0.0625 544 0.210657 0.210657 1.16573e-15 5 0.03125 1065 0.210657 0.210657 2.85882e-15 6 0.015625 2085 0.210657 0.210657 5.77316e-15 7 0.0078125 4082 0.210657 0.210657 1.10745e-14 8 0.00390625 7986 0.210657 0.210657 2.21212e-14 TEST05 Apply a sequence of tanh rules to a test integral. Problem index P = 7 Tolerance TOL = 2.22045e-16 M H N Exact Quad Error -2 4 10 1.90524 2.56705 0.661808 -1 2 19 1.90524 1.92734 0.0221036 0 1 37 1.90524 1.90524 2.22634e-06 1 0.5 73 1.90524 1.90524 6.47038e-13 2 0.25 142 1.90524 1.90524 1.11022e-15 3 0.125 278 1.90524 1.90524 6.66134e-16 4 0.0625 544 1.90524 1.90524 3.9968e-15 5 0.03125 1065 1.90524 1.90524 6.21725e-15 6 0.015625 2085 1.90524 1.90524 7.32747e-15 7 0.0078125 4082 1.90524 1.90524 2.84217e-14 8 0.00390625 7986 1.90524 1.90524 5.52891e-14 TEST05 Apply a sequence of tanh rules to a test integral. Problem index P = 8 Tolerance TOL = 2.22045e-16 M H N Exact Quad Error -2 4 10 0.514042 0.595022 0.0809802 -1 2 19 0.514042 0.515159 0.00111742 0 1 37 0.514042 0.514041 1.09466e-06 1 0.5 73 0.514042 0.514042 2.39697e-13 2 0.25 142 0.514042 0.514042 3.33067e-16 3 0.125 278 0.514042 0.514042 9.99201e-16 4 0.0625 544 0.514042 0.514042 1.11022e-15 5 0.03125 1065 0.514042 0.514042 3.21965e-15 6 0.015625 2085 0.514042 0.514042 4.88498e-15 7 0.0078125 4082 0.514042 0.514042 1.75415e-14 8 0.00390625 7986 0.514042 0.514042 2.78666e-14 TEST05 Apply a sequence of tanh rules to a test integral. Problem index P = 9 Tolerance TOL = 2.22045e-16 M H N Exact Quad Error -2 4 10 -0.444444 -nan nan -1 2 19 -0.444444 -0.445542 0.00109726 0 1 37 -0.444444 -0.444444 3.21454e-08 1 0.5 73 -0.444444 -0.444444 8.88178e-16 2 0.25 142 -0.444444 -0.444444 1.66533e-16 3 0.125 278 -0.444444 -0.444444 1.66533e-16 4 0.0625 544 -0.444444 -0.444444 0 5 0.03125 1065 -0.444444 -0.444444 3.88578e-16 6 0.015625 2085 -0.444444 -0.444444 5.55112e-17 7 0.0078125 4082 -0.444444 -0.444444 4.996e-16 8 0.00390625 7986 -0.444444 -0.444444 3.05311e-15 TEST05 Apply a sequence of tanh rules to a test integral. Problem index P = 10 Tolerance TOL = 2.22045e-16 M H N Exact Quad Error -2 4 10 0.785398 0.951405 0.166007 -1 2 19 0.785398 0.788993 0.00359504 0 1 37 0.785398 0.785399 6.78767e-07 1 0.5 73 0.785398 0.785398 7.43849e-15 2 0.25 142 0.785398 0.785398 2.22045e-16 3 0.125 278 0.785398 0.785398 1.77636e-15 4 0.0625 544 0.785398 0.785398 2.9976e-15 5 0.03125 1065 0.785398 0.785398 3.9968e-15 6 0.015625 2085 0.785398 0.785398 8.54872e-15 7 0.0078125 4082 0.785398 0.785398 1.95399e-14 8 0.00390625 7986 0.785398 0.785398 3.41949e-14 TEST05 Apply a sequence of tanh rules to a test integral. Problem index P = 11 Tolerance TOL = 2.22045e-16 M H N Exact Quad Error -2 4 10 3.3726 inf inf -1 2 19 3.3726 inf inf 0 1 37 3.3726 1.19814 2.17446 1 0.5 73 3.3726 1.19814 2.17446 2 0.25 142 3.3726 1.19814 2.17446 3 0.125 278 3.3726 1.19814 2.17446 4 0.0625 544 3.3726 1.19814 2.17446 5 0.03125 1065 3.3726 1.19814 2.17446 6 0.015625 2085 3.3726 1.19814 2.17446 7 0.0078125 4082 3.3726 1.19814 2.17446 8 0.00390625 7986 3.3726 1.19814 2.17446 TEST05 Apply a sequence of tanh rules to a test integral. Problem index P = 12 Tolerance TOL = 2.22045e-16 M H N Exact Quad Error -2 4 10 2 inf inf -1 2 19 2 1.99581 0.00419313 0 1 37 2 2 1.79024e-07 1 0.5 73 2 2 1.56097e-13 2 0.25 142 2 2 4.56302e-13 3 0.125 278 2 2 9.76774e-13 4 0.0625 544 2 2 2.04103e-12 5 0.03125 1065 2 2 4.07274e-12 6 0.015625 2085 2 2 7.96185e-12 7 0.0078125 4082 2 2 1.52438e-11 8 0.00390625 7986 2 2 2.93379e-11 TEST05 Apply a sequence of tanh rules to a test integral. Problem index P = 13 Tolerance TOL = 2.22045e-16 M H N Exact Quad Error -2 4 10 -1.08879 -0.956624 0.132169 -1 2 19 -1.08879 -1.08308 0.00571673 0 1 37 -1.08879 -1.08879 1.40616e-06 1 0.5 73 -1.08879 -1.08879 2.4869e-14 2 0.25 142 -1.08879 -1.08879 2.17604e-14 3 0.125 278 -1.08879 -1.08879 4.44089e-14 4 0.0625 544 -1.08879 -1.08879 9.41469e-14 5 0.03125 1065 -1.08879 -1.08879 1.84741e-13 6 0.015625 2085 -1.08879 -1.08879 3.66596e-13 7 0.0078125 4082 -1.08879 -1.08879 7.16316e-13 8 0.00390625 7986 -1.08879 -1.08879 1.40976e-12 TEST05 Apply a sequence of tanh rules to a test integral. Problem index P = 14 Tolerance TOL = 2.22045e-16 M H N Exact Quad Error -2 4 10 2.22144 2.35581 0.134366 -1 2 19 2.22144 2.22362 0.00217982 0 1 37 2.22144 2.22144 2.17635e-07 1 0.5 73 2.22144 2.22144 3.57702e-08 2 0.25 142 2.22144 2.22144 4.94493e-08 3 0.125 278 2.22144 2.22144 7.10129e-08 4 0.0625 544 2.22144 2.22144 1.03297e-07 5 0.03125 1065 2.22144 2.22144 1.4837e-07 6 0.015625 2085 2.22144 2.22144 2.1114e-07 7 0.0078125 4082 2.22144 2.22144 2.97825e-07 8 0.00390625 7986 2.22144 2.22144 4.21691e-07 TEST06 Apply a sequence of tanh-sinh rules to a test integral. Problem index P = 1 Tolerance TOL = 2.22045e-16 M H N Exact Quad Error -2 4 1 1 3.14159 2.14159 -1 2 2 1 1.57133 0.571329 0 1 4 1 1.01569 0.0156868 1 0.5 7 1 1 3.35957e-06 2 0.25 13 1 1 3.66374e-14 3 0.125 26 1 1 0 4 0.0625 51 1 1 2.22045e-16 5 0.03125 102 1 1 2.22045e-16 6 0.015625 201 1 1 5.55112e-16 7 0.0078125 400 1 1 1.11022e-15 8 0.00390625 794 1 1 0 TEST06 Apply a sequence of tanh-sinh rules to a test integral. Problem index P = 2 Tolerance TOL = 2.22045e-16 M H N Exact Quad Error -2 4 1 1 3.14159 2.14159 -1 2 2 1 1.57133 0.571329 0 1 4 1 1.01569 0.0156868 1 0.5 7 1 1 3.35957e-06 2 0.25 13 1 1 3.66374e-14 3 0.125 26 1 1 2.22045e-16 4 0.0625 51 1 1 3.33067e-16 5 0.03125 102 1 1 4.44089e-16 6 0.015625 201 1 1 0 7 0.0078125 400 1 1 1.77636e-15 8 0.00390625 794 1 1 5.55112e-16 TEST06 Apply a sequence of tanh-sinh rules to a test integral. Problem index P = 3 Tolerance TOL = 2.22045e-16 M H N Exact Quad Error -2 4 1 1 2.35619 1.35619 -1 2 2 1 1.1789 0.178896 0 1 4 1 0.91811 0.0818902 1 0.5 7 1 0.99971 0.000290388 2 0.25 13 1 1 4.90843e-11 3 0.125 26 1 1 2.22045e-16 4 0.0625 51 1 1 3.33067e-16 5 0.03125 102 1 1 4.44089e-16 6 0.015625 201 1 1 0 7 0.0078125 400 1 1 1.9984e-15 8 0.00390625 794 1 1 2.22045e-15 TEST06 Apply a sequence of tanh-sinh rules to a test integral. Problem index P = 4 Tolerance TOL = 2.22045e-16 M H N Exact Quad Error -2 4 1 -0.316714 -inf inf -1 2 2 -0.316714 -inf inf 0 1 4 -0.316714 -inf inf 1 0.5 7 -0.316714 -inf inf 2 0.25 13 -0.316714 -inf inf 3 0.125 26 -0.316714 -inf inf 4 0.0625 51 -0.316714 -inf inf 5 0.03125 102 -0.316714 -inf inf 6 0.015625 201 -0.316714 -0.316714 3.44169e-15 7 0.0078125 400 -0.316714 -0.316714 7.27196e-15 8 0.00390625 794 -0.316714 -0.316714 1.74305e-14 TEST06 Apply a sequence of tanh-sinh rules to a test integral. Problem index P = 5 Tolerance TOL = 2.22045e-16 M H N Exact Quad Error -2 4 1 0.25 0.636903 0.386903 -1 2 2 0.25 0.318636 0.0686361 0 1 4 0.25 0.235794 0.0142062 1 0.5 7 0.25 0.249961 3.94434e-05 2 0.25 13 0.25 0.25 3.71378e-12 3 0.125 26 0.25 0.25 0 4 0.0625 51 0.25 0.25 5.55112e-17 5 0.03125 102 0.25 0.25 5.55112e-17 6 0.015625 201 0.25 0.25 1.11022e-16 7 0.0078125 400 0.25 0.25 5.27356e-16 8 0.00390625 794 0.25 0.25 6.66134e-16 TEST06 Apply a sequence of tanh-sinh rules to a test integral. Problem index P = 6 Tolerance TOL = 2.22045e-16 M H N Exact Quad Error -2 4 1 0.210657 0.364148 0.153491 -1 2 2 0.210657 0.182283 0.0283742 0 1 4 0.210657 0.175786 0.0348714 1 0.5 7 0.210657 0.210472 0.000184939 2 0.25 13 0.210657 0.210657 1.20203e-11 3 0.125 26 0.210657 0.210657 2.77556e-17 4 0.0625 51 0.210657 0.210657 2.77556e-17 5 0.03125 102 0.210657 0.210657 5.55112e-17 6 0.015625 201 0.210657 0.210657 2.77556e-17 7 0.0078125 400 0.210657 0.210657 2.77556e-16 8 0.00390625 794 0.210657 0.210657 3.33067e-16 TEST06 Apply a sequence of tanh-sinh rules to a test integral. Problem index P = 7 Tolerance TOL = 2.22045e-16 M H N Exact Quad Error -2 4 1 1.90524 7.6533 5.74806 -1 2 2 1.90524 3.82707 1.92183 0 1 4 1.90524 2.13303 0.227794 1 0.5 7 1.90524 1.90531 7.07982e-05 2 0.25 13 1.90524 1.90524 2.48501e-09 3 0.125 26 1.90524 1.90524 2.22045e-16 4 0.0625 51 1.90524 1.90524 6.66134e-16 5 0.03125 102 1.90524 1.90524 4.44089e-16 6 0.015625 201 1.90524 1.90524 6.66134e-16 7 0.0078125 400 1.90524 1.90524 8.88178e-16 8 0.00390625 794 1.90524 1.90524 2.22045e-15 TEST06 Apply a sequence of tanh-sinh rules to a test integral. Problem index P = 8 Tolerance TOL = 2.22045e-16 M H N Exact Quad Error -2 4 1 0.514042 1.64669 1.13264 -1 2 2 0.514042 0.823604 0.309562 0 1 4 0.514042 0.525234 0.0111917 1 0.5 7 0.514042 0.513975 6.70175e-05 2 0.25 13 0.514042 0.514042 2.26336e-09 3 0.125 26 0.514042 0.514042 1.11022e-16 4 0.0625 51 0.514042 0.514042 2.22045e-16 5 0.03125 102 0.514042 0.514042 2.22045e-16 6 0.015625 201 0.514042 0.514042 0 7 0.0078125 400 0.514042 0.514042 2.22045e-16 8 0.00390625 794 0.514042 0.514042 0 TEST06 Apply a sequence of tanh-sinh rules to a test integral. Problem index P = 9 Tolerance TOL = 2.22045e-16 M H N Exact Quad Error -2 4 1 -0.444444 -nan nan -1 2 2 -0.444444 -nan nan 0 1 4 -0.444444 -nan nan 1 0.5 7 -0.444444 -nan nan 2 0.25 13 -0.444444 -nan nan 3 0.125 26 -0.444444 -nan nan 4 0.0625 51 -0.444444 -0.444444 2.77556e-16 5 0.03125 102 -0.444444 -0.444444 1.11022e-16 6 0.015625 201 -0.444444 -0.444444 1.66533e-16 7 0.0078125 400 -0.444444 -0.444444 6.66134e-16 8 0.00390625 794 -0.444444 -0.444444 3.33067e-16 TEST06 Apply a sequence of tanh-sinh rules to a test integral. Problem index P = 10 Tolerance TOL = 2.22045e-16 M H N Exact Quad Error -2 4 1 0.785398 2.7207 1.9353 -1 2 2 0.785398 1.36062 0.575219 0 1 4 0.785398 0.820494 0.0350959 1 0.5 7 0.785398 0.785427 2.92204e-05 2 0.25 13 0.785398 0.785398 1.47993e-12 3 0.125 26 0.785398 0.785398 0 4 0.0625 51 0.785398 0.785398 0 5 0.03125 102 0.785398 0.785398 1.11022e-16 6 0.015625 201 0.785398 0.785398 2.22045e-16 7 0.0078125 400 0.785398 0.785398 9.99201e-16 8 0.00390625 794 0.785398 0.785398 5.55112e-16 TEST06 Apply a sequence of tanh-sinh rules to a test integral. Problem index P = 11 Tolerance TOL = 2.22045e-16 M H N Exact Quad Error -2 4 1 3.3726 inf inf -1 2 2 3.3726 inf inf 0 1 4 3.3726 inf inf 1 0.5 7 3.3726 inf inf 2 0.25 13 3.3726 inf inf 3 0.125 26 3.3726 inf inf 4 0.0625 51 3.3726 inf inf 5 0.03125 102 3.3726 inf inf 6 0.015625 201 3.3726 1.19814 2.17446 7 0.0078125 400 3.3726 1.19814 2.17446 8 0.00390625 794 3.3726 1.19814 2.17446 TEST06 Apply a sequence of tanh-sinh rules to a test integral. Problem index P = 12 Tolerance TOL = 2.22045e-16 M H N Exact Quad Error -2 4 1 2 inf inf -1 2 2 2 inf inf 0 1 4 2 inf inf 1 0.5 7 2 inf inf 2 0.25 13 2 inf inf 3 0.125 26 2 inf inf 4 0.0625 51 2 2 1.5099e-14 5 0.03125 102 2 2 3.15303e-14 6 0.015625 201 2 2 1.93401e-13 7 0.0078125 400 2 2 3.80584e-13 8 0.00390625 794 2 2 8.88178e-13 TEST06 Apply a sequence of tanh-sinh rules to a test integral. Problem index P = 13 Tolerance TOL = 2.22045e-16 M H N Exact Quad Error -2 4 1 -1.08879 -1.71027 0.621479 -1 2 2 -1.08879 -0.859712 0.229081 0 1 4 -1.08879 -1.01989 0.0689026 1 0.5 7 -1.08879 -1.08872 7.18899e-05 2 0.25 13 -1.08879 -1.08879 5.43232e-12 3 0.125 26 -1.08879 -1.08879 1.9984e-15 4 0.0625 51 -1.08879 -1.08879 3.10862e-15 5 0.03125 102 -1.08879 -1.08879 3.10862e-15 6 0.015625 201 -1.08879 -1.08879 1.11022e-14 7 0.0078125 400 -1.08879 -1.08879 1.93179e-14 8 0.00390625 794 -1.08879 -1.08879 4.06342e-14 TEST06 Apply a sequence of tanh-sinh rules to a test integral. Problem index P = 14 Tolerance TOL = 2.22045e-16 M H N Exact Quad Error -2 4 1 2.22144 4.9348 2.71336 -1 2 2 2.22144 2.56682 0.345381 0 1 4 2.22144 2.2429 0.0214538 1 0.5 7 2.22144 2.22144 4.47087e-07 2 0.25 13 2.22144 2.22144 1.74414e-08 3 0.125 26 2.22144 2.22144 1.00584e-08 4 0.0625 51 2.22144 2.22144 1.14089e-08 5 0.03125 102 2.22144 2.22144 1.515e-08 6 0.015625 201 2.22144 2.22144 3.37554e-08 7 0.0078125 400 2.22144 2.22144 4.44574e-08 8 0.00390625 794 2.22144 2.22144 6.71828e-08 TANH_QUAD_PRB Normal end of execution. 19 September 2013 10:12:40 AM