Sat Apr 18 12:26:44 2015 QUADRULE_TEST Python version: Test the QUADRULE library. BASHFORTH_SET_TEST BASHFORTH_SET sets the abscissas and weights for an Adams-Bashforth quadrature rule. Order W X 1 1 -0 2 1.5 -0 -0.5 -1 3 1.91667 -0 -1.33333 -1 0.416667 -2 4 2.29167 -0 -2.45833 -1 1.54167 -2 -0.375 -3 5 2.64028 -0 -3.85278 -1 3.63333 -2 -1.76944 -3 0.348611 -4 6 2.97014 -0 -5.50208 -1 6.93194 -2 -5.06806 -3 1.99792 -4 -0.329861 -5 7 3.28573 -0 -7.39563 -1 11.6658 -2 -11.3799 -3 6.7318 -4 -2.22341 -5 0.315592 -6 8 3.58996 -0 -9.52521 -1 18.0545 -2 -22.0278 -3 17.3797 -4 -8.61213 -5 2.44516 -6 -0.304225 -7 9 3.88482 -0 -11.8842 -1 26.3108 -2 -38.5404 -3 38.0204 -4 -25.1247 -5 10.7015 -6 -2.66317 -7 0.294868 -8 10 4.1718 -0 -14.4669 -1 36.642 -2 -62.6463 -3 74.1793 -4 -61.2836 -5 34.8074 -6 -12.9943 -7 2.87765 -8 -0.286975 -9 BASHFORTH_SET_TEST: Normal end of execution. CHEBYSHEV1_COMPUTE_TEST CHEBYSHEV1_COMPUTE computes a Chebyshev Type 1 quadrature rule over [-1,1]. Index X W 0 6.123233995736766e-17 3.141592653589793 0 -0.7071067811865475 1.570796326794897 1 0.7071067811865476 1.570796326794897 0 -0.8660254037844387 1.047197551196598 1 6.123233995736766e-17 1.047197551196598 2 0.8660254037844387 1.047197551196598 0 -0.9238795325112867 0.7853981633974483 1 -0.3826834323650897 0.7853981633974483 2 0.3826834323650898 0.7853981633974483 3 0.9238795325112867 0.7853981633974483 0 -0.9510565162951535 0.6283185307179586 1 -0.587785252292473 0.6283185307179586 2 6.123233995736766e-17 0.6283185307179586 3 0.5877852522924731 0.6283185307179586 4 0.9510565162951535 0.6283185307179586 0 -0.9659258262890682 0.5235987755982988 1 -0.7071067811865475 0.5235987755982988 2 -0.2588190451025206 0.5235987755982988 3 0.2588190451025207 0.5235987755982988 4 0.7071067811865476 0.5235987755982988 5 0.9659258262890683 0.5235987755982988 0 -0.9749279121818237 0.4487989505128276 1 -0.7818314824680295 0.4487989505128276 2 -0.4338837391175581 0.4487989505128276 3 6.123233995736766e-17 0.4487989505128276 4 0.4338837391175582 0.4487989505128276 5 0.7818314824680298 0.4487989505128276 6 0.9749279121818236 0.4487989505128276 0 -0.9807852804032304 0.3926990816987241 1 -0.8314696123025453 0.3926990816987241 2 -0.555570233019602 0.3926990816987241 3 -0.1950903220161282 0.3926990816987241 4 0.1950903220161283 0.3926990816987241 5 0.5555702330196023 0.3926990816987241 6 0.8314696123025452 0.3926990816987241 7 0.9807852804032304 0.3926990816987241 0 -0.984807753012208 0.3490658503988659 1 -0.8660254037844385 0.3490658503988659 2 -0.6427876096865394 0.3490658503988659 3 -0.3420201433256685 0.3490658503988659 4 6.123233995736766e-17 0.3490658503988659 5 0.3420201433256688 0.3490658503988659 6 0.6427876096865394 0.3490658503988659 7 0.8660254037844387 0.3490658503988659 8 0.984807753012208 0.3490658503988659 0 -0.9876883405951377 0.3141592653589793 1 -0.8910065241883678 0.3141592653589793 2 -0.7071067811865475 0.3141592653589793 3 -0.4539904997395467 0.3141592653589793 4 -0.1564344650402306 0.3141592653589793 5 0.1564344650402309 0.3141592653589793 6 0.4539904997395468 0.3141592653589793 7 0.7071067811865476 0.3141592653589793 8 0.8910065241883679 0.3141592653589793 9 0.9876883405951378 0.3141592653589793 CHEBYSHEV1_COMPUTE_TEST: Normal end of execution. CHEBYSHEV3_COMPUTE_TEST CHEBYSHEV3_COMPUTE computes a Chebyshev Type 3 quadrature rule over [-1,1]. Index X W 0 0 3.141592653589793 0 1 1.570796326794897 1 -1 1.570796326794897 0 1 0.7853981633974483 1 6.123233995736766e-17 1.570796326794897 2 -1 0.7853981633974483 0 1 0.5235987755982988 1 0.5000000000000001 1.047197551196598 2 -0.4999999999999998 1.047197551196598 3 -1 0.5235987755982988 0 1 0.3926990816987241 1 0.7071067811865476 0.7853981633974483 2 6.123233995736766e-17 0.7853981633974483 3 -0.7071067811865475 0.7853981633974483 4 -1 0.3926990816987241 0 1 0.3141592653589793 1 0.8090169943749475 0.6283185307179586 2 0.3090169943749475 0.6283185307179586 3 -0.3090169943749473 0.6283185307179586 4 -0.8090169943749473 0.6283185307179586 5 -1 0.3141592653589793 0 1 0.2617993877991494 1 0.8660254037844387 0.5235987755982988 2 0.5000000000000001 0.5235987755982988 3 6.123233995736766e-17 0.5235987755982988 4 -0.4999999999999998 0.5235987755982988 5 -0.8660254037844387 0.5235987755982988 6 -1 0.2617993877991494 0 1 0.2243994752564138 1 0.9009688679024191 0.4487989505128276 2 0.6234898018587336 0.4487989505128276 3 0.2225209339563144 0.4487989505128276 4 -0.2225209339563143 0.4487989505128276 5 -0.6234898018587335 0.4487989505128276 6 -0.900968867902419 0.4487989505128276 7 -1 0.2243994752564138 0 1 0.1963495408493621 1 0.9238795325112867 0.3926990816987241 2 0.7071067811865476 0.3926990816987241 3 0.3826834323650898 0.3926990816987241 4 6.123233995736766e-17 0.3926990816987241 5 -0.3826834323650897 0.3926990816987241 6 -0.7071067811865475 0.3926990816987241 7 -0.9238795325112867 0.3926990816987241 8 -1 0.1963495408493621 0 1 0.1745329251994329 1 0.9396926207859084 0.3490658503988659 2 0.766044443118978 0.3490658503988659 3 0.5000000000000001 0.3490658503988659 4 0.1736481776669304 0.3490658503988659 5 -0.1736481776669303 0.3490658503988659 6 -0.4999999999999998 0.3490658503988659 7 -0.7660444431189779 0.3490658503988659 8 -0.9396926207859083 0.3490658503988659 9 -1 0.1745329251994329 CHEBYSHEV3_COMPUTE_TEST: Normal end of execution. CLENSHAW_CURTIS_COMPUTE_TEST CLENSHAW_CURTIS_COMPUTE computes a Clenshaw-Curtis quadrature rule over [-1,1]. Index X W 0 0 2 0 -1 1 1 1 1 0 -1 0.3333333333333334 1 6.123233995736766e-17 1.333333333333333 2 1 0.3333333333333334 0 -1 0.1111111111111111 1 -0.4999999999999998 0.8888888888888892 2 0.5000000000000001 0.8888888888888888 3 1 0.1111111111111111 0 -1 0.06666666666666668 1 -0.7071067811865475 0.5333333333333334 2 6.123233995736766e-17 0.7999999999999999 3 0.7071067811865476 0.5333333333333333 4 1 0.06666666666666668 0 -1 0.04000000000000001 1 -0.8090169943749473 0.3607430412000113 2 -0.3090169943749473 0.5992569587999887 3 0.3090169943749475 0.5992569587999889 4 0.8090169943749475 0.3607430412000112 5 1 0.04000000000000001 0 -1 0.02857142857142858 1 -0.8660254037844387 0.2539682539682539 2 -0.4999999999999998 0.4571428571428573 3 6.123233995736766e-17 0.5206349206349206 4 0.5000000000000001 0.4571428571428571 5 0.8660254037844387 0.2539682539682539 6 1 0.02857142857142858 0 -1 0.02040816326530613 1 -0.900968867902419 0.1901410072182084 2 -0.6234898018587335 0.3522424237181591 3 -0.2225209339563143 0.4372084057983264 4 0.2225209339563144 0.4372084057983264 5 0.6234898018587336 0.3522424237181591 6 0.9009688679024191 0.1901410072182084 7 1 0.02040816326530613 0 -1 0.01587301587301588 1 -0.9238795325112867 0.1462186492160182 2 -0.7071067811865475 0.2793650793650794 3 -0.3826834323650897 0.3617178587204898 4 6.123233995736766e-17 0.3936507936507936 5 0.3826834323650898 0.3617178587204897 6 0.7071067811865476 0.2793650793650794 7 0.9238795325112867 0.1462186492160181 8 1 0.01587301587301588 0 -1 0.01234567901234569 1 -0.9396926207859083 0.1165674565720372 2 -0.7660444431189779 0.2252843233381044 3 -0.4999999999999998 0.3019400352733687 4 -0.1736481776669303 0.3438625058041442 5 0.1736481776669304 0.3438625058041442 6 0.5000000000000001 0.3019400352733685 7 0.766044443118978 0.2252843233381044 8 0.9396926207859084 0.1165674565720371 9 1 0.01234567901234569 CLENSHAW_CURTIS_COMPUTE_TEST: Normal end of execution. CLENSHAW_CURTIS_SET_TEST CLENSHAW_CURTIS_SET sets up a Clenshaw Curtis quadrature rule over [-1,1]. Estimate the integral of sqrt(abs(x)) over [-1,+1]. N Estimate Error 1 0 1.333333e+00 2 2 6.666667e-01 3 0.6666666666666666 6.666667e-01 4 1.47930094433164 1.459676e-01 5 1.030289509603962 3.030438e-01 6 1.395188802266437 6.185547e-02 7 1.176328668057338 1.570047e-01 8 1.370529534325666 3.719620e-02 9 1.230194560888044 1.031388e-01 10 1.358632996768151 2.529966e-02 CLENSHAW_CURTIS_SET_TEST: Normal end of execution. FEJER1_COMPUTE_TEST FEJER1_COMPUTE computes the abscissas and weights of a Fejer type 1 quadrature rule. Order W X 1 2 6.12323e-17 2 1 -0.707107 1 0.707107 3 0.444444 -0.866025 1.11111 6.12323e-17 0.444444 0.866025 4 0.264298 -0.92388 0.735702 -0.382683 0.735702 0.382683 0.264298 0.92388 5 0.167781 -0.951057 0.525552 -0.587785 0.613333 6.12323e-17 0.525552 0.587785 0.167781 0.951057 6 0.118661 -0.965926 0.377778 -0.707107 0.503561 -0.258819 0.503561 0.258819 0.377778 0.707107 0.118661 0.965926 7 0.0867162 -0.974928 0.287831 -0.781831 0.398242 -0.433884 0.454422 6.12323e-17 0.398242 0.433884 0.287831 0.781831 0.0867162 0.974928 8 0.0669829 -0.980785 0.222988 -0.83147 0.324153 -0.55557 0.385877 -0.19509 0.385877 0.19509 0.324153 0.55557 0.222988 0.83147 0.0669829 0.980785 9 0.0527366 -0.984808 0.179189 -0.866025 0.264037 -0.642788 0.330845 -0.34202 0.346384 6.12323e-17 0.330845 0.34202 0.264037 0.642788 0.179189 0.866025 0.0527366 0.984808 10 0.0429391 -0.987688 0.145875 -0.891007 0.220317 -0.707107 0.280879 -0.45399 0.309989 -0.156434 0.309989 0.156434 0.280879 0.45399 0.220317 0.707107 0.145875 0.891007 0.0429391 0.987688 FEJER1_COMPUTE_TEST: Normal end of execution. FEJER1_SET_TEST FEJER1_SET sets the abscissas and weights of a Fejer type 1 quadrature rule. Order W X 1 2 0 2 1 -0.707107 1 0.707107 3 0.444444 -0.866025 1.11111 0 0.444444 0.866025 4 0.264298 -0.92388 0.735702 -0.382683 0.735702 0.382683 0.264298 0.92388 5 0.167781 -0.951057 0.525552 -0.587785 0.613333 0 0.525552 0.587785 0.167781 0.951057 6 0.118661 -0.965926 0.377778 -0.707107 0.503561 -0.258819 0.503561 0.258819 0.377778 0.707107 0.118661 0.965926 7 0.0867162 -0.974928 0.287831 -0.781831 0.398242 -0.433884 0.454422 0 0.398242 0.433884 0.287831 0.781831 0.0867162 0.974928 8 0.0669829 -0.980785 0.222988 -0.83147 0.324153 -0.55557 0.385877 -0.19509 0.385877 0.19509 0.324153 0.55557 0.222988 0.83147 0.0669829 0.980785 9 0.0527366 -0.984808 0.179189 -0.866025 0.264037 -0.642788 0.330845 -0.34202 0.346384 0 0.330845 0.34202 0.264037 0.642788 0.179189 0.866025 0.0527366 0.984808 10 0.0429391 -0.987688 0.145875 -0.891007 0.220317 -0.707107 0.280879 -0.45399 0.309989 -0.156434 0.309989 0.156434 0.280879 0.45399 0.220317 0.707107 0.145875 0.891007 0.0429391 0.987688 FEJER1_SET_TEST: Normal end of execution. FEJER2_COMPUTE_TEST FEJER2_COMPUTE computes the abscissas and weights of a Fejer type 2 quadrature rule. Order W X 1 2 0 2 1 -0.5 1 0.5 3 0.666667 -0.707107 0.666667 6.12323e-17 0.666667 0.707107 4 0.425464 -0.809017 0.574536 -0.309017 0.574536 0.309017 0.425464 0.809017 5 0.311111 -0.866025 0.4 -0.5 0.577778 6.12323e-17 0.4 0.5 0.311111 0.866025 6 0.226915 -0.900969 0.326794 -0.62349 0.446291 -0.222521 0.446291 0.222521 0.326794 0.62349 0.226915 0.900969 7 0.177965 -0.92388 0.247619 -0.707107 0.393464 -0.382683 0.361905 6.12323e-17 0.393464 0.382683 0.247619 0.707107 0.177965 0.92388 8 0.13977 -0.939693 0.20637 -0.766044 0.314286 -0.5 0.339575 -0.173648 0.339575 0.173648 0.314286 0.5 0.20637 0.766044 0.13977 0.939693 9 0.114781 -0.951057 0.165433 -0.809017 0.27379 -0.587785 0.279011 -0.309017 0.333968 6.12323e-17 0.279011 0.309017 0.27379 0.587785 0.165433 0.809017 0.114781 0.951057 10 0.0944195 -0.959493 0.141135 -0.841254 0.226387 -0.654861 0.253051 -0.415415 0.285007 -0.142315 0.285007 0.142315 0.253051 0.415415 0.226387 0.654861 0.141135 0.841254 0.0944195 0.959493 FEJER2_COMPUTE_TEST: Normal end of execution. FEJER2_SET_TEST FEJER2_SET sets the abscissas and weights of a Fejer type 2 quadrature rule. Order W X 1 2 0 2 1 -0.5 1 0.5 3 0.666667 -0.707107 0.666667 0 0.666667 0.707107 4 0.425464 -0.809017 0.574536 -0.309017 0.574536 0.309017 0.425464 0.809017 5 0.311111 -0.866025 0.4 -0.5 0.577778 0 0.4 0.5 0.311111 0.866025 6 0.226915 -0.900969 0.326794 -0.62349 0.446291 -0.222521 0.446291 0.222521 0.326794 0.62349 0.226915 0.900969 7 0.177965 -0.92388 0.247619 -0.707107 0.393464 -0.382683 0.361905 0 0.393464 0.382683 0.247619 0.707107 0.177965 0.92388 8 0.13977 -0.939693 0.20637 -0.766044 0.314286 -0.5 0.339575 -0.173648 0.339575 0.173648 0.314286 0.5 0.20637 0.766044 0.13977 0.939693 9 0.114781 -0.951057 0.165433 -0.809017 0.27379 -0.587785 0.279011 -0.309017 0.333968 0 0.279011 0.309017 0.27379 0.587785 0.165433 0.809017 0.114781 0.951057 10 0.0944195 -0.959493 0.141135 -0.841254 0.226387 -0.654861 0.253051 -0.415415 0.285007 -0.142315 0.285007 0.142315 0.253051 0.415415 0.226387 0.654861 0.141135 0.841254 0.0944195 0.959493 FEJER2_SET_TEST: Normal end of execution. LEGENDRE_SET_TEST01: LEGENDRE_SET returns points and weights of a Gauss-Legendre quadrature rule. Gauss-Legendre rule of order 3: Index X W 0 -0.7745966692414834 0.5555555555555556 1 0.0000000000000000 0.8888888888888888 2 0.7745966692414834 0.5555555555555556 Gauss-Legendre rule of order 6: Index X W 0 -0.9324695142031521 0.1713244923791704 1 -0.6612093864662645 0.3607615730481386 2 -0.2386191860831969 0.4679139345726910 3 0.2386191860831969 0.4679139345726910 4 0.6612093864662645 0.3607615730481386 5 0.9324695142031521 0.1713244923791704 Gauss-Legendre rule of order 11: Index X W 0 -0.9782286581460570 0.0556685671161737 1 -0.8870625997680953 0.1255803694649046 2 -0.7301520055740494 0.1862902109277343 3 -0.5190961292068118 0.2331937645919905 4 -0.2695431559523450 0.2628045445102467 5 0.0000000000000000 0.2729250867779006 6 0.2695431559523450 0.2628045445102467 7 0.5190961292068118 0.2331937645919905 8 0.7301520055740494 0.1862902109277343 9 0.8870625997680953 0.1255803694649046 10 0.9782286581460570 0.0556685671161737 LEGENDRE_SET_TEST01: Normal end of execution. MOULTON_SET_TEST MOULTON_SET sets the abscissas and weights for an Adams-Moulton quadrature rule. Order W X 1 1 1 2 0.5 1 0.5 0 3 0.416667 1 0.666667 0 -0.0833333 -1 4 0.375 1 0.791667 0 -0.208333 -1 0.0416667 -2 5 0.348611 1 0.897222 0 -0.366667 -1 0.147222 -2 -0.0263889 -3 6 0.329861 1 0.990972 0 -0.554167 -1 0.334722 -2 -0.120139 -3 0.01875 -4 7 0.315592 1 1.07659 0 -0.768204 -1 0.620106 -2 -0.334177 -3 0.104365 -4 -0.0142692 -5 8 0.304225 1 1.15616 0 -1.00692 -1 1.01796 -2 -0.732035 -3 0.34308 -4 -0.0938409 -5 0.0113674 -6 9 0.294868 1 1.23101 0 -1.2689 -1 1.54193 -2 -1.38699 -3 0.867046 -4 -0.355824 -5 0.0862197 -6 -0.00935654 -7 10 0.286975 1 1.30204 0 -1.55303 -1 2.20491 -2 -2.38145 -3 1.86151 -4 -1.0188 -5 0.370352 -6 -0.0803895 -7 0.00789255 -8 MOULTON_SET_TEST: Normal end of execution. TIMESTAMP_TEST: Python version: TIMESTAMP prints a timestamp of the current date and time. Sat Apr 18 12:26:44 2015 TIMESTAMP_TEST: Normal end of execution. QUADRULE_TEST: Normal end of execution. Sat Apr 18 12:26:44 2015