19 November 2015 12:31:04.670 PM QUADRULE_PRB FORTRAN90 version Test the QUADRULE library. CHEBYSHEV_SET_TEST CHEBYSHEV_SET sets a Chebyshev rule over [-1,1]. Index X W 1 0.000000000000000 2.000000000000000 1 -0.5773502691896258 1.000000000000000 2 0.5773502691896258 1.000000000000000 1 -0.7071067811865475 0.6666666666666666 2 0.000000000000000 0.6666666666666666 3 0.7071067811865475 0.6666666666666666 1 -0.7946544722917661 0.5000000000000000 2 -0.1875924740850799 0.5000000000000000 3 0.1875924740850799 0.5000000000000000 4 0.7946544722917661 0.5000000000000000 1 -0.8324974870009819 0.4000000000000000 2 -0.3745414095535811 0.4000000000000000 3 0.000000000000000 0.4000000000000000 4 0.3745414095535811 0.4000000000000000 5 0.8324974870009819 0.4000000000000000 1 -0.8662468181078206 0.3333333333333333 2 -0.4225186537611115 0.3333333333333333 3 -0.2666354015167047 0.3333333333333333 4 0.2666354015167047 0.3333333333333333 5 0.4225186537611115 0.3333333333333333 6 0.8662468181078206 0.3333333333333333 1 -0.8838617007580490 0.2857142857142857 2 -0.5296567752851569 0.2857142857142857 3 -0.3239118105199076 0.2857142857142857 4 0.000000000000000 0.2857142857142857 5 0.3239118105199076 0.2857142857142857 6 0.5296567752851569 0.2857142857142857 7 0.8838617007580490 0.2857142857142857 1 -0.9115893077284345 0.2222222222222222 2 -0.6010186553802380 0.2222222222222222 3 -0.5287617830578800 0.2222222222222222 4 -0.1679061842148039 0.2222222222222222 5 0.000000000000000 0.2222222222222222 6 0.1679061842148039 0.2222222222222222 7 0.5287617830578800 0.2222222222222222 8 0.6010186553802380 0.2222222222222222 9 0.9115893077284345 0.2222222222222222 CHEBYSHEV1_COMPUTE_TEST CHEBYSHEV1_COMPUTE computes a Chebyshev Type 1 quadrature rule over [-1,1]. Index X W 1 0.6123233995736766E-16 3.141592653589793 1 -0.7071067811865475 1.570796326794897 2 0.7071067811865476 1.570796326794897 1 -0.8660254037844387 1.047197551196598 2 0.6123233995736766E-16 1.047197551196598 3 0.8660254037844387 1.047197551196598 1 -0.9238795325112867 0.7853981633974483 2 -0.3826834323650897 0.7853981633974483 3 0.3826834323650898 0.7853981633974483 4 0.9238795325112867 0.7853981633974483 1 -0.9510565162951535 0.6283185307179586 2 -0.5877852522924730 0.6283185307179586 3 0.6123233995736766E-16 0.6283185307179586 4 0.5877852522924731 0.6283185307179586 5 0.9510565162951535 0.6283185307179586 1 -0.9659258262890682 0.5235987755982988 2 -0.7071067811865475 0.5235987755982988 3 -0.2588190451025206 0.5235987755982988 4 0.2588190451025207 0.5235987755982988 5 0.7071067811865476 0.5235987755982988 6 0.9659258262890683 0.5235987755982988 1 -0.9749279121818237 0.4487989505128276 2 -0.7818314824680295 0.4487989505128276 3 -0.4338837391175581 0.4487989505128276 4 0.6123233995736766E-16 0.4487989505128276 5 0.4338837391175582 0.4487989505128276 6 0.7818314824680298 0.4487989505128276 7 0.9749279121818236 0.4487989505128276 1 -0.9807852804032304 0.3926990816987241 2 -0.8314696123025453 0.3926990816987241 3 -0.5555702330196020 0.3926990816987241 4 -0.1950903220161282 0.3926990816987241 5 0.1950903220161283 0.3926990816987241 6 0.5555702330196023 0.3926990816987241 7 0.8314696123025452 0.3926990816987241 8 0.9807852804032304 0.3926990816987241 1 -0.9848077530122080 0.3490658503988659 2 -0.8660254037844385 0.3490658503988659 3 -0.6427876096865394 0.3490658503988659 4 -0.3420201433256685 0.3490658503988659 5 0.6123233995736766E-16 0.3490658503988659 6 0.3420201433256688 0.3490658503988659 7 0.6427876096865394 0.3490658503988659 8 0.8660254037844387 0.3490658503988659 9 0.9848077530122080 0.3490658503988659 1 -0.9876883405951377 0.3141592653589793 2 -0.8910065241883678 0.3141592653589793 3 -0.7071067811865475 0.3141592653589793 4 -0.4539904997395467 0.3141592653589793 5 -0.1564344650402306 0.3141592653589793 6 0.1564344650402309 0.3141592653589793 7 0.4539904997395468 0.3141592653589793 8 0.7071067811865476 0.3141592653589793 9 0.8910065241883679 0.3141592653589793 10 0.9876883405951378 0.3141592653589793 CHEBYSHEV1_INTEGRAL_TEST CHEBYSHEV1_INTEGRAL evaluates Integral ( -1 < x < +1 ) x^n / sqrt(1-x^2) dx N Value 0 3.141592653589793 1 0.000000000000000 2 1.570796326794897 3 0.000000000000000 4 1.178097245096172 5 0.000000000000000 6 0.9817477042468102 7 0.000000000000000 8 0.8590292412159591 9 0.000000000000000 10 0.7731263170943631 CHEBYSHEV1_SET_TEST CHEBYSHEV1_SET sets a Chebyshev Type 1 quadrature rule over [-1,1]. Index X W 1 0.000000000000000 3.141592653589793 1 -0.7071067811865475 1.570796326794897 2 0.7071067811865476 1.570796326794897 1 -0.8660254037844387 1.047197551196598 2 0.000000000000000 1.047197551196598 3 0.8660254037844387 1.047197551196598 1 -0.9238795325112867 0.7853981633974483 2 -0.3826834323650897 0.7853981633974483 3 0.3826834323650898 0.7853981633974483 4 0.9238795325112867 0.7853981633974483 1 -0.9510565162951535 0.6283185307179586 2 -0.5877852522924730 0.6283185307179586 3 0.000000000000000 0.6283185307179586 4 0.5877852522924731 0.6283185307179586 5 0.9510565162951535 0.6283185307179586 1 -0.9659258262890682 0.5235987755982988 2 -0.7071067811865475 0.5235987755982988 3 -0.2588190451025206 0.5235987755982988 4 0.2588190451025207 0.5235987755982988 5 0.7071067811865476 0.5235987755982988 6 0.9659258262890683 0.5235987755982988 1 -0.9749279121818237 0.4487989505128276 2 -0.7818314824680295 0.4487989505128276 3 -0.4338837391175581 0.4487989505128276 4 0.000000000000000 0.4487989505128276 5 0.4338837391175582 0.4487989505128276 6 0.7818314824680298 0.4487989505128276 7 0.9749279121818236 0.4487989505128276 1 -0.9807852804032304 0.3926990816987241 2 -0.8314696123025453 0.3926990816987241 3 -0.5555702330196020 0.3926990816987241 4 -0.1950903220161282 0.3926990816987241 5 0.1950903220161283 0.3926990816987241 6 0.5555702330196023 0.3926990816987241 7 0.8314696123025452 0.3926990816987241 8 0.9807852804032304 0.3926990816987241 1 -0.9848077530122080 0.3490658503988659 2 -0.8660254037844385 0.3490658503988659 3 -0.6427876096865394 0.3490658503988659 4 -0.3420201433256685 0.3490658503988659 5 0.000000000000000 0.3490658503988659 6 0.3420201433256688 0.3490658503988659 7 0.6427876096865394 0.3490658503988659 8 0.8660254037844387 0.3490658503988659 9 0.9848077530122080 0.3490658503988659 1 -0.9876883405951377 0.3141592653589793 2 -0.8910065241883678 0.3141592653589793 3 -0.7071067811865475 0.3141592653589793 4 -0.4539904997395467 0.3141592653589793 5 -0.1564344650402306 0.3141592653589793 6 0.1564344650402309 0.3141592653589793 7 0.4539904997395468 0.3141592653589793 8 0.7071067811865476 0.3141592653589793 9 0.8910065241883679 0.3141592653589793 10 0.9876883405951378 0.3141592653589793 CHEBYSHEV2_COMPUTE_TEST CHEBYSHEV2_COMPUTE computes a Gauss-Chebyshev type 2 rule; Index X W 1 0.6123233995736766E-16 1.570796326794897 1 -0.4999999999999998 0.7853981633974484 2 0.5000000000000001 0.7853981633974481 1 -0.7071067811865475 0.3926990816987243 2 0.6123233995736766E-16 0.7853981633974483 3 0.7071067811865476 0.3926990816987240 1 -0.8090169943749473 0.2170787134227061 2 -0.3090169943749473 0.5683194499747424 3 0.3090169943749475 0.5683194499747423 4 0.8090169943749475 0.2170787134227060 1 -0.8660254037844387 0.1308996938995747 2 -0.4999999999999998 0.3926990816987242 3 0.6123233995736766E-16 0.5235987755982988 4 0.5000000000000001 0.3926990816987240 5 0.8660254037844387 0.1308996938995747 1 -0.9009688679024190 0.8448869089158863E-01 2 -0.6234898018587335 0.2743330560697779 3 -0.2225209339563143 0.4265764164360819 4 0.2225209339563144 0.4265764164360819 5 0.6234898018587336 0.2743330560697778 6 0.9009688679024191 0.8448869089158857E-01 1 -0.9238795325112867 0.5750944903191316E-01 2 -0.7071067811865475 0.1963495408493621 3 -0.3826834323650897 0.3351896326668110 4 0.6123233995736766E-16 0.3926990816987241 5 0.3826834323650898 0.3351896326668110 6 0.7071067811865476 0.1963495408493620 7 0.9238795325112867 0.5750944903191313E-01 1 -0.9396926207859083 0.4083294770910712E-01 2 -0.7660444431189779 0.1442256007956728 3 -0.4999999999999998 0.2617993877991495 4 -0.1736481776669303 0.3385402270935190 5 0.1736481776669304 0.3385402270935190 6 0.5000000000000001 0.2617993877991494 7 0.7660444431189780 0.1442256007956727 8 0.9396926207859084 0.4083294770910708E-01 1 -0.9510565162951535 0.2999954037160818E-01 2 -0.8090169943749473 0.1085393567113530 3 -0.5877852522924730 0.2056199086476263 4 -0.3090169943749473 0.2841597249873712 5 0.6123233995736766E-16 0.3141592653589793 6 0.3090169943749475 0.2841597249873711 7 0.5877852522924731 0.2056199086476263 8 0.8090169943749475 0.1085393567113530 9 0.9510565162951535 0.2999954037160816E-01 1 -0.9594929736144974 0.2266894250185884E-01 2 -0.8412535328311811 0.8347854093418908E-01 3 -0.6548607339452850 0.1631221774548166 4 -0.4154150130018863 0.2363135602034873 5 -0.1423148382732850 0.2798149423030966 6 0.1423148382732851 0.2798149423030965 7 0.4154150130018864 0.2363135602034873 8 0.6548607339452851 0.1631221774548166 9 0.8412535328311812 0.8347854093418902E-01 10 0.9594929736144974 0.2266894250185884E-01 CHEBYSHEV2_COMPUTE_TEST2 Approximate the integral of f(x,y) over the semicircle -1 <= x <= 1, y = sqrt ( 1 - x^2 ) using N Chebyshev points. If p(x,y) involves any term of odd degree in y, the estimate will only be approximate. Polynomial N Integral Estimate Error 1 10 1.57080 1.57080 0.222045E-15 x 10 0.00000 -0.104083E-16 0.104083E-16 y 10 0.666667 0.666723 0.565402E-04 x^2 10 0.392699 0.392699 0.555112E-16 x y 10 0.00000 -0.221177E-16 0.221177E-16 y^2 10 0.392699 0.392699 0.00000 x^3 10 0.00000 0.242861E-16 0.242861E-16 x^2y 10 0.133333 0.133392 0.588566E-04 x y^2 10 0.00000 0.477049E-17 0.477049E-17 y^3 10 0.266667 0.266666 0.115821E-05 x^4 10 0.196350 0.196350 0.546392E-08 x^2y^2 10 0.654498E-01 0.654498E-01 0.138778E-16 y^4 10 0.196350 0.196350 0.555112E-16 x^4y 10 0.571429E-01 0.572043E-01 0.613939E-04 x^2y^3 10 0.380952E-01 0.380940E-01 0.126862E-05 y^5 10 0.152381 0.152381 0.736100E-07 x^6 10 0.122718 0.122718 0.138778E-16 x^4y^2 10 0.245437E-01 0.245437E-01 0.00000 x^2y^4 10 0.245437E-01 0.245437E-01 0.346945E-17 y^6 10 0.122718 0.122718 0.277556E-16 CHEBYSHEV2_INTEGRAL_TEST CHEBYSHEV2_INTEGRAL evaluates Integral ( -1 < x < +1 ) x^n * sqrt(1-x^2) dx N Value 0 1.570796326794897 1 0.000000000000000 2 0.3926990816987241 3 0.000000000000000 4 0.1963495408493621 5 0.000000000000000 6 0.1227184630308513 7 0.000000000000000 8 0.8590292412159591E-01 9 0.000000000000000 10 0.6442719309119692E-01 CHEBYSHEV2_SET_TEST CHEBYSHEV2_SET sets a Chebyshev Type 2 quadrature rule over [-1,1]. Index X W 1 0.000000000000000 1.570796326794897 1 -0.5000000000000000 0.7853981633974484 2 0.5000000000000000 0.7853981633974481 1 -0.7071067811865475 0.3926990816987243 2 0.000000000000000 0.7853981633974483 3 0.7071067811865476 0.3926990816987240 1 -0.8090169943749473 0.2170787134227061 2 -0.3090169943749473 0.5683194499747424 3 0.3090169943749475 0.5683194499747423 4 0.8090169943749475 0.2170787134227060 1 -0.8660254037844387 0.1308996938995747 2 -0.5000000000000000 0.3926990816987242 3 0.000000000000000 0.5235987755982988 4 0.5000000000000000 0.3926990816987240 5 0.8660254037844387 0.1308996938995747 1 -0.9009688679024190 0.8448869089158863E-01 2 -0.6234898018587335 0.2743330560697779 3 -0.2225209339563143 0.4265764164360819 4 0.2225209339563144 0.4265764164360819 5 0.6234898018587336 0.2743330560697778 6 0.9009688679024191 0.8448869089158857E-01 1 -0.9238795325112867 0.5750944903191316E-01 2 -0.7071067811865475 0.1963495408493621 3 -0.3826834323650897 0.3351896326668110 4 0.000000000000000 0.3926990816987241 5 0.3826834323650898 0.3351896326668110 6 0.7071067811865476 0.1963495408493620 7 0.9238795325112867 0.5750944903191313E-01 1 -0.9396926207859083 0.4083294770910712E-01 2 -0.7660444431189779 0.1442256007956728 3 -0.5000000000000000 0.2617993877991495 4 -0.1736481776669303 0.3385402270935190 5 0.1736481776669304 0.3385402270935190 6 0.5000000000000000 0.2617993877991494 7 0.7660444431189780 0.1442256007956727 8 0.9396926207859084 0.4083294770910708E-01 1 -0.9510565162951535 0.2999954037160818E-01 2 -0.8090169943749473 0.1085393567113530 3 -0.5877852522924730 0.2056199086476263 4 -0.3090169943749473 0.2841597249873712 5 0.000000000000000 0.3141592653589793 6 0.3090169943749475 0.2841597249873711 7 0.5877852522924731 0.2056199086476263 8 0.8090169943749475 0.1085393567113530 9 0.9510565162951535 0.2999954037160816E-01 1 -0.9594929736144974 0.2266894250185884E-01 2 -0.8412535328311811 0.8347854093418908E-01 3 -0.6548607339452850 0.1631221774548166 4 -0.4154150130018863 0.2363135602034873 5 -0.1423148382732850 0.2798149423030966 6 0.1423148382732851 0.2798149423030965 7 0.4154150130018864 0.2363135602034873 8 0.6548607339452851 0.1631221774548166 9 0.8412535328311812 0.8347854093418902E-01 10 0.9594929736144974 0.2266894250185884E-01 CHEBYSHEV3_COMPUTE_TEST CHEBYSHEV3_COMPUTE computes a Chebyshev Type 3 quadrature rule over [-1,1]. Index X W 1 0.000000000000000 3.141592653589793 1 -1.000000000000000 1.570796326794897 2 1.000000000000000 1.570796326794897 1 -1.000000000000000 0.7853981633974483 2 0.6123233995736766E-16 1.570796326794897 3 1.000000000000000 0.7853981633974483 1 -1.000000000000000 0.5235987755982988 2 -0.4999999999999998 1.047197551196598 3 0.5000000000000001 1.047197551196598 4 1.000000000000000 0.5235987755982988 1 -1.000000000000000 0.3926990816987241 2 -0.7071067811865475 0.7853981633974483 3 0.6123233995736766E-16 0.7853981633974483 4 0.7071067811865476 0.7853981633974483 5 1.000000000000000 0.3926990816987241 1 -1.000000000000000 0.3141592653589793 2 -0.8090169943749473 0.6283185307179586 3 -0.3090169943749473 0.6283185307179586 4 0.3090169943749475 0.6283185307179586 5 0.8090169943749475 0.6283185307179586 6 1.000000000000000 0.3141592653589793 1 -1.000000000000000 0.2617993877991494 2 -0.8660254037844387 0.5235987755982988 3 -0.4999999999999998 0.5235987755982988 4 0.6123233995736766E-16 0.5235987755982988 5 0.5000000000000001 0.5235987755982988 6 0.8660254037844387 0.5235987755982988 7 1.000000000000000 0.2617993877991494 1 -1.000000000000000 0.2243994752564138 2 -0.9009688679024190 0.4487989505128276 3 -0.6234898018587335 0.4487989505128276 4 -0.2225209339563143 0.4487989505128276 5 0.2225209339563144 0.4487989505128276 6 0.6234898018587336 0.4487989505128276 7 0.9009688679024191 0.4487989505128276 8 1.000000000000000 0.2243994752564138 1 -1.000000000000000 0.1963495408493621 2 -0.9238795325112867 0.3926990816987241 3 -0.7071067811865475 0.3926990816987241 4 -0.3826834323650897 0.3926990816987241 5 0.6123233995736766E-16 0.3926990816987241 6 0.3826834323650898 0.3926990816987241 7 0.7071067811865476 0.3926990816987241 8 0.9238795325112867 0.3926990816987241 9 1.000000000000000 0.1963495408493621 1 -1.000000000000000 0.1745329251994329 2 -0.9396926207859083 0.3490658503988659 3 -0.7660444431189779 0.3490658503988659 4 -0.4999999999999998 0.3490658503988659 5 -0.1736481776669303 0.3490658503988659 6 0.1736481776669304 0.3490658503988659 7 0.5000000000000001 0.3490658503988659 8 0.7660444431189780 0.3490658503988659 9 0.9396926207859084 0.3490658503988659 10 1.000000000000000 0.1745329251994329 CHEBYSHEV3_INTEGRAL_TEST CHEBYSHEV3_INTEGRAL evaluates Integral ( -1 < x < +1 ) x^n / sqrt(1-x^2) dx N Value 0 3.141592653589793 1 0.000000000000000 2 1.570796326794897 3 0.000000000000000 4 1.178097245096172 5 0.000000000000000 6 0.9817477042468102 7 0.000000000000000 8 0.8590292412159591 9 0.000000000000000 10 0.7731263170943631 CHEBYSHEV3_SET_TEST CHEBYSHEV3_SET sets a Chebyshev Type 3 quadrature rule over [-1,1]. Index X W 1 0.000000000000000 3.141592653589793 1 -1.000000000000000 1.570796326794897 2 1.000000000000000 1.570796326794897 1 -1.000000000000000 0.7853981633974483 2 0.000000000000000 1.570796326794897 3 1.000000000000000 0.7853981633974483 1 -1.000000000000000 0.5235987755982988 2 -0.5000000000000000 1.047197551196598 3 0.5000000000000000 1.047197551196598 4 1.000000000000000 0.5235987755982988 1 -1.000000000000000 0.3926990816987241 2 -0.7071067811865475 0.7853981633974483 3 0.000000000000000 0.7853981633974483 4 0.7071067811865476 0.7853981633974483 5 1.000000000000000 0.3926990816987241 1 -1.000000000000000 0.3141592653589793 2 -0.8090169943749473 0.6283185307179586 3 -0.3090169943749473 0.6283185307179586 4 0.3090169943749475 0.6283185307179586 5 0.8090169943749475 0.6283185307179586 6 1.000000000000000 0.3141592653589793 1 -1.000000000000000 0.2617993877991494 2 -0.8660254037844387 0.5235987755982988 3 -0.5000000000000000 0.5235987755982988 4 0.000000000000000 0.5235987755982988 5 0.5000000000000001 0.5235987755982988 6 0.8660254037844387 0.5235987755982988 7 1.000000000000000 0.2617993877991494 1 -1.000000000000000 0.2243994752564138 2 -0.9009688679024190 0.4487989505128276 3 -0.6234898018587335 0.4487989505128276 4 -0.2225209339563143 0.4487989505128276 5 0.2225209339563144 0.4487989505128276 6 0.6234898018587336 0.4487989505128276 7 0.9009688679024191 0.4487989505128276 8 1.000000000000000 0.2243994752564138 1 -1.000000000000000 0.1963495408493621 2 -0.9238795325112867 0.3926990816987241 3 -0.7071067811865475 0.3926990816987241 4 -0.3826834323650897 0.3926990816987241 5 0.000000000000000 0.3926990816987241 6 0.3826834323650898 0.3926990816987241 7 0.7071067811865476 0.3926990816987241 8 0.9238795325112867 0.3926990816987241 9 1.000000000000000 0.1963495408493621 1 -1.000000000000000 0.1745329251994329 2 -0.9396926207859083 0.3490658503988659 3 -0.7660444431189779 0.3490658503988659 4 -0.5000000000000000 0.3490658503988659 5 -0.1736481776669303 0.3490658503988659 6 0.1736481776669304 0.3490658503988659 7 0.5000000000000001 0.3490658503988659 8 0.7660444431189780 0.3490658503988659 9 0.9396926207859084 0.3490658503988659 10 1.000000000000000 0.1745329251994329 CLENSHAW_CURTIS_COMPUTE_TEST CLENSHAW_CURTIS_COMPUTE computes a Clenshaw-Curtis quadrature rule over [-1,1]. Index X W 1 0.000000000000000 2.000000000000000 1 -1.000000000000000 1.000000000000000 2 1.000000000000000 1.000000000000000 1 -1.000000000000000 0.3333333333333334 2 0.6123233995736766E-16 1.333333333333333 3 1.000000000000000 0.3333333333333334 1 -1.000000000000000 0.1111111111111111 2 -0.4999999999999998 0.8888888888888892 3 0.5000000000000001 0.8888888888888888 4 1.000000000000000 0.1111111111111111 1 -1.000000000000000 0.6666666666666668E-01 2 -0.7071067811865475 0.5333333333333334 3 0.6123233995736766E-16 0.7999999999999999 4 0.7071067811865476 0.5333333333333333 5 1.000000000000000 0.6666666666666668E-01 1 -1.000000000000000 0.4000000000000001E-01 2 -0.8090169943749473 0.3607430412000113 3 -0.3090169943749473 0.5992569587999887 4 0.3090169943749475 0.5992569587999889 5 0.8090169943749475 0.3607430412000112 6 1.000000000000000 0.4000000000000001E-01 1 -1.000000000000000 0.2857142857142858E-01 2 -0.8660254037844387 0.2539682539682539 3 -0.4999999999999998 0.4571428571428573 4 0.6123233995736766E-16 0.5206349206349206 5 0.5000000000000001 0.4571428571428571 6 0.8660254037844387 0.2539682539682539 7 1.000000000000000 0.2857142857142858E-01 1 -1.000000000000000 0.2040816326530613E-01 2 -0.9009688679024190 0.1901410072182084 3 -0.6234898018587335 0.3522424237181591 4 -0.2225209339563143 0.4372084057983264 5 0.2225209339563144 0.4372084057983264 6 0.6234898018587336 0.3522424237181591 7 0.9009688679024191 0.1901410072182084 8 1.000000000000000 0.2040816326530613E-01 1 -1.000000000000000 0.1587301587301588E-01 2 -0.9238795325112867 0.1462186492160182 3 -0.7071067811865475 0.2793650793650794 4 -0.3826834323650897 0.3617178587204898 5 0.6123233995736766E-16 0.3936507936507936 6 0.3826834323650898 0.3617178587204897 7 0.7071067811865476 0.2793650793650794 8 0.9238795325112867 0.1462186492160181 9 1.000000000000000 0.1587301587301588E-01 1 -1.000000000000000 0.1234567901234569E-01 2 -0.9396926207859083 0.1165674565720372 3 -0.7660444431189779 0.2252843233381044 4 -0.4999999999999998 0.3019400352733687 5 -0.1736481776669303 0.3438625058041442 6 0.1736481776669304 0.3438625058041442 7 0.5000000000000001 0.3019400352733685 8 0.7660444431189780 0.2252843233381044 9 0.9396926207859084 0.1165674565720371 10 1.000000000000000 0.1234567901234569E-01 CLENSHAW_CURTIS_SET_TEST CLENSHAW_CURTIS_SET sets a Clenshaw-Curtis quadrature rule over [-1,1]. Index X W 1 0.000000000000000 2.000000000000000 1 -1.000000000000000 1.000000000000000 2 1.000000000000000 1.000000000000000 1 -1.000000000000000 0.3333333333333333 2 0.000000000000000 1.333333333333333 3 1.000000000000000 0.3333333333333333 1 -1.000000000000000 0.1111111111111111 2 -0.5000000000000000 0.8888888888888888 3 0.5000000000000000 0.8888888888888888 4 1.000000000000000 0.1111111111111111 1 -1.000000000000000 0.6666666666666667E-01 2 -0.7071067811865476 0.5333333333333333 3 0.000000000000000 0.8000000000000000 4 0.7071067811865476 0.5333333333333333 5 1.000000000000000 0.6666666666666667E-01 1 -1.000000000000000 0.4000000000000000E-01 2 -0.8090169943749475 0.3607430412000112 3 -0.3090169943749475 0.5992569587999887 4 0.3090169943749475 0.5992569587999887 5 0.8090169943749373 0.3607430412000112 6 1.000000000000000 0.4000000000000000E-01 1 -1.000000000000000 0.2857142857142857E-01 2 -0.8660254037844386 0.2539682539682540 3 -0.5000000000000000 0.4571428571428571 4 0.000000000000000 0.5206349206349207 5 0.5000000000000000 0.4571428571428571 6 0.8660254037844386 0.2539682539682540 7 1.000000000000000 0.2857142857142857E-01 1 -1.000000000000000 0.2040816326530612E-01 2 -0.9009688679024191 0.1901410072182083 3 -0.6234898018587335 0.3522424237181591 4 -0.2225209339563144 0.4372084057983264 5 0.2225209339563144 0.4372084057983264 6 0.6234898018587335 0.3522424237181591 7 0.9009688679024191 0.1901410072182083 8 1.000000000000000 0.2040816326530612E-01 1 -1.000000000000000 0.1587301587301587E-01 2 -0.9238795325112867 0.1462186492160182 3 -0.7071067811865476 0.2793650793650794 4 -0.3826834323650898 0.3617178587204898 5 0.000000000000000 0.3936507936507936 6 0.3826834323650898 0.3617178587204898 7 0.7071067811865476 0.2793650793650794 8 0.9238795325112867 0.1462186492160182 9 1.000000000000000 0.1587301587301587E-01 1 -1.000000000000000 0.1234567901234568E-01 2 -0.9396926207859084 0.1165674565720371 3 -0.7660444431189790 0.2252843233381044 4 -0.5000000000000000 0.3019400352733686 5 -0.1736481776669304 0.3438625058041442 6 0.1736481776669304 0.3438625058041442 7 0.5000000000000000 0.3019400352733686 8 0.7660444431189790 0.2252843233381044 9 0.9396926207859084 0.1165674565720371 10 1.000000000000000 0.1234567901234568E-01 FEJER1_COMPUTE_TEST FEJER1_COMPUTE computes a Fejer type 1 rule. Order W X 1 2.000000000000000 0.000000000000000 2 1.000000000000000 -0.7071067811865475 1.000000000000000 0.7071067811865476 3 0.4444444444444444 -0.8660254037844387 1.111111111111111 0.6123233995736766E-16 0.4444444444444444 0.8660254037844387 4 0.2642977396044843 -0.9238795325112867 0.7357022603955159 -0.3826834323650897 0.7357022603955158 0.3826834323650898 0.2642977396044841 0.9238795325112867 5 0.1677812284666836 -0.9510565162951535 0.5255521048666498 -0.5877852522924730 0.6133333333333333 0.6123233995736766E-16 0.5255521048666498 0.5877852522924731 0.1677812284666835 0.9510565162951535 6 0.1186610213812360 -0.9659258262890682 0.3777777777777778 -0.7071067811865475 0.5035612008409863 -0.2588190451025206 0.5035612008409863 0.2588190451025207 0.3777777777777778 0.7071067811865476 0.1186610213812358 0.9659258262890683 7 0.8671618072672234E-01 -0.9749279121818237 0.2878313947886921 -0.7818314824680295 0.3982415401308442 -0.4338837391175581 0.4544217687074830 0.6123233995736766E-16 0.3982415401308441 0.4338837391175582 0.2878313947886919 0.7818314824680298 0.8671618072672246E-01 0.9749279121818236 8 0.6698294569858997E-01 -0.9807852804032304 0.2229879330145788 -0.8314696123025453 0.3241525190645244 -0.5555702330196020 0.3858766022223070 -0.1950903220161282 0.3858766022223071 0.1950903220161283 0.3241525190645244 0.5555702330196023 0.2229879330145788 0.8314696123025452 0.6698294569858981E-01 0.9807852804032304 9 0.5273664990990675E-01 -0.9848077530122080 0.1791887125220460 -0.8660254037844385 0.2640372225410044 -0.6427876096865394 0.3308451751681365 -0.3420201433256685 0.3463844797178130 0.6123233995736766E-16 0.3308451751681364 0.3420201433256688 0.2640372225410044 0.6427876096865394 0.1791887125220458 0.8660254037844387 0.5273664990990676E-01 0.9848077530122080 10 0.4293911957413079E-01 -0.9876883405951377 0.1458749193773909 -0.8910065241883678 0.2203174603174603 -0.7071067811865475 0.2808792186638755 -0.4539904997395467 0.3099892820671425 -0.1564344650402306 0.3099892820671425 0.1564344650402309 0.2808792186638755 0.4539904997395468 0.2203174603174603 0.7071067811865476 0.1458749193773909 0.8910065241883679 0.4293911957413078E-01 0.9876883405951378 FEJER1_SET_TEST FEJER1_SET sets a Fejer type 1 rule. Order W X 1 2.000000000000000 0.000000000000000 2 1.000000000000000 -0.7071067811865475 1.000000000000000 0.7071067811865475 3 0.4444444444444444 -0.8660254037844387 1.111111111111111 0.000000000000000 0.4444444444444444 0.8660254037844387 4 0.2642977396044841 -0.9238795325112867 0.7357022603955158 -0.3826834323650897 0.7357022603955158 0.3826834323650898 0.2642977396044841 0.9238795325112867 5 0.1677812284666835 -0.9510565162951535 0.5255521048666498 -0.5877852522924730 0.6133333333333333 0.000000000000000 0.5255521048666498 0.5877852522924731 0.1677812284666835 0.9510565162951535 6 0.1186610213812358 -0.9659258262890682 0.3777777777777778 -0.7071067811865475 0.5035612008409863 -0.2588190451025206 0.5035612008409863 0.2588190451025207 0.3777777777777778 0.7071067811865476 0.1186610213812358 0.9659258262890683 7 0.8671618072672234E-01 -0.9749279121818237 0.2878313947886919 -0.7818314824680295 0.3982415401308441 -0.4338837391175581 0.4544217687074830 0.000000000000000 0.3982415401308441 0.4338837391175582 0.2878313947886919 0.7818314824680298 0.8671618072672234E-01 0.9749279121818236 8 0.6698294569858981E-01 -0.9807852804032304 0.2229879330145788 -0.8314696123025453 0.3241525190645244 -0.5555702330196020 0.3858766022223071 -0.1950903220161282 0.3858766022223071 0.1950903220161283 0.3241525190645244 0.5555702330196023 0.2229879330145788 0.8314696123025452 0.6698294569858981E-01 0.9807852804032304 9 0.5273664990990676E-01 -0.9848077530122080 0.1791887125220458 -0.8660254037844385 0.2640372225410044 -0.6427876096865394 0.3308451751681364 -0.3420201433256685 0.3463844797178130 0.000000000000000 0.3308451751681364 0.3420201433256688 0.2640372225410044 0.6427876096865394 0.1791887125220458 0.8660254037844387 0.5273664990990676E-01 0.9848077530122080 10 0.4293911957413078E-01 -0.9876883405951377 0.1458749193773909 -0.8910065241883678 0.2203174603174603 -0.7071067811865475 0.2808792186638755 -0.4539904997395467 0.3099892820671425 -0.1564344650402306 0.3099892820671425 0.1564344650402309 0.2808792186638755 0.4539904997395468 0.2203174603174603 0.7071067811865476 0.1458749193773909 0.8910065241883679 0.4293911957413078E-01 0.9876883405951378 FEJER2_COMPUTE_TEST FEJER2_COMPUTE computes a Fejer type 2 rule. Order W X 1 2.000000000000000 0.000000000000000 2 1.000000000000000 -0.5000000000000000 1.000000000000000 0.5000000000000000 3 0.6666666666666667 -0.7071067811865475 0.6666666666666666 0.6123233995736766E-16 0.6666666666666666 0.7071067811865476 4 0.4254644007500071 -0.8090169943749473 0.5745355992499930 -0.3090169943749473 0.5745355992499930 0.3090169943749475 0.4254644007500070 0.8090169943749475 5 0.3111111111111111 -0.8660254037844387 0.4000000000000001 -0.4999999999999998 0.5777777777777777 0.6123233995736766E-16 0.4000000000000000 0.5000000000000001 0.3111111111111111 0.8660254037844387 6 0.2269152467244296 -0.9009688679024190 0.3267938603769863 -0.6234898018587335 0.4462908928985842 -0.2225209339563143 0.4462908928985841 0.2225209339563144 0.3267938603769863 0.6234898018587336 0.2269152467244296 0.9009688679024191 7 0.1779646809620499 -0.9238795325112867 0.2476190476190477 -0.7071067811865475 0.3934638904665215 -0.3826834323650897 0.3619047619047619 0.6123233995736766E-16 0.3934638904665215 0.3826834323650898 0.2476190476190476 0.7071067811865476 0.1779646809620499 0.9238795325112867 8 0.1397697435050226 -0.9396926207859083 0.2063696457302284 -0.7660444431189779 0.3142857142857144 -0.4999999999999998 0.3395748964790348 -0.1736481776669303 0.3395748964790348 0.1736481776669304 0.3142857142857143 0.5000000000000001 0.2063696457302284 0.7660444431189780 0.1397697435050225 0.9396926207859084 9 0.1147810750857218 -0.9510565162951535 0.1654331942222276 -0.8090169943749473 0.2737903534857068 -0.5877852522924730 0.2790112502222169 -0.3090169943749473 0.3339682539682539 0.6123233995736766E-16 0.2790112502222170 0.3090169943749475 0.2737903534857068 0.5877852522924731 0.1654331942222276 0.8090169943749475 0.1147810750857217 0.9510565162951535 10 0.9441954173982806E-01 -0.9594929736144974 0.1411354380109716 -0.8412535328311811 0.2263866903636005 -0.6548607339452850 0.2530509772156453 -0.4154150130018863 0.2850073526699546 -0.1423148382732850 0.2850073526699544 0.1423148382732851 0.2530509772156453 0.4154150130018864 0.2263866903636005 0.6548607339452851 0.1411354380109716 0.8412535328311812 0.9441954173982806E-01 0.9594929736144974 FEJER2_SET_TEST FEJER2_SET sets a Fejer type 2 rule. Order W X 1 2.000000000000000 0.000000000000000 2 1.000000000000000 -0.5000000000000000 1.000000000000000 0.5000000000000000 3 0.6666666666666666 -0.7071067811865476 0.6666666666666666 0.000000000000000 0.6666666666666666 0.7071067811865476 4 0.4254644007500070 -0.8090169943749475 0.5745355992499930 -0.3090169943749475 0.5745355992499930 0.3090169943749475 0.4254644007500070 0.8090169943749475 5 0.3111111111111111 -0.8660254037844387 0.4000000000000000 -0.5000000000000000 0.5777777777777777 0.000000000000000 0.4000000000000000 0.5000000000000000 0.3111111111111111 0.8660254037844387 6 0.2269152467244296 -0.9009688679024191 0.3267938603769863 -0.6234898018587336 0.4462908928985841 -0.2225209339563144 0.4462908928985841 0.2225209339563144 0.3267938603769863 0.6234898018587336 0.2269152467244296 0.9009688679024191 7 0.1779646809620499 -0.9238795325112867 0.2476190476190476 -0.7071067811865476 0.3934638904665215 -0.3826834323650898 0.3619047619047619 0.000000000000000 0.3934638904665215 0.3826834323650898 0.2476190476190476 0.7071067811865476 0.1779646809620499 0.9238795325112867 8 0.1397697435050225 -0.9396926207859084 0.2063696457302284 -0.7660444431189780 0.3142857142857143 -0.5000000000000000 0.3395748964790348 -0.1736481776669304 0.3395748964790348 0.1736481776669304 0.3142857142857143 0.5000000000000000 0.2063696457302284 0.7660444431189780 0.1397697435050225 0.9396926207859084 9 0.1147810750857217 -0.9510565162951535 0.1654331942222276 -0.8090169943749475 0.2737903534857068 -0.5877852522924731 0.2790112502222170 -0.3090169943749475 0.3339682539682539 0.000000000000000 0.2790112502222170 0.3090169943749475 0.2737903534857068 0.5877852522924731 0.1654331942222276 0.8090169943749475 0.1147810750857217 0.9510565162951535 10 0.9441954173982806E-01 -0.9594929736144974 0.1411354380109716 -0.8412535328311812 0.2263866903636005 -0.6548607339452851 0.2530509772156453 -0.4154150130018864 0.2850073526699544 -0.1423148382732851 0.2850073526699544 0.1423148382732851 0.2530509772156453 0.4154150130018864 0.2263866903636005 0.6548607339452851 0.1411354380109716 0.8412535328311812 0.9441954173982806E-01 0.9594929736144974 GEGENBAUER_INTEGRAL_TEST GEGENBAUER_INTEGRAL evaluates Integral ( -1 < x < +1 ) x^n * (1-x^2)^alpha dx N Value 0 1.748038369528081 1 0.000000000000000 2 0.4994395341508805 3 0.000000000000000 4 0.2724215640822983 5 0.000000000000000 6 0.1816143760548655 7 0.000000000000000 8 0.1338211191983220 9 0.000000000000000 10 0.1047295715465127 GEGENBAUER_EK_COMPUTE_TEST GEGENBAUER_EK_COMPUTE computes a Gauss-Gegenbauer rule; Using parameter ALPHA = 0.500000 Integration interval from -1.00000 to 1.00000 W X 1.570796326794897 0.000000000000000 0.7853981633974484 -0.4999999999999999 0.7853981633974484 0.4999999999999999 0.3926990816987245 -0.7071067811865475 0.7853981633974486 0.6591949208711867E-16 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 0.5952490290336006E-16 0.3926990816987242 0.4999999999999998 0.1308996938995747 0.8660254037844388 0.8448869089158870E-01 -0.9009688679024188 0.2743330560697781 -0.6234898018587335 0.4265764164360816 -0.2225209339563142 0.4265764164360817 0.2225209339563143 0.2743330560697784 0.6234898018587332 0.8448869089158853E-01 0.9009688679024188 0.5750944903191328E-01 -0.9238795325112868 0.1963495408493622 -0.7071067811865476 0.3351896326668111 -0.3826834323650896 0.3926990816987249 0.7901929723605659E-17 0.3351896326668110 0.3826834323650899 0.1963495408493624 0.7071067811865475 0.5750944903191320E-01 0.9238795325112863 0.4083294770910714E-01 -0.9396926207859084 0.1442256007956730 -0.7660444431189782 0.2617993877991496 -0.4999999999999999 0.3385402270935193 -0.1736481776669302 0.3385402270935190 0.1736481776669302 0.2617993877991501 0.5000000000000000 0.1442256007956725 0.7660444431189779 0.4083294770910712E-01 0.9396926207859086 0.2999954037160819E-01 -0.9510565162951536 0.1085393567113534 -0.8090169943749472 0.2056199086476264 -0.5877852522924730 0.2841597249873707 -0.3090169943749472 0.3141592653589796 0.5567534423109432E-16 0.2841597249873716 0.3090169943749471 0.2056199086476266 0.5877852522924728 0.1085393567113536 0.8090169943749472 0.2999954037160805E-01 0.9510565162951536 0.2266894250185894E-01 -0.9594929736144974 0.8347854093418919E-01 -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 0.8347854093418883E-01 0.8412535328311812 0.2266894250185892E-01 0.9594929736144973 GEGENBAUER_SS_COMPUTE_TEST GEGENBAUER_SS_COMPUTE computes a Gauss-Gegenbauer rule; Using parameter ALPHA = 0.500000 W X 1.570796326794897 0.000000000000000 0.7853981633974484 -0.5000000000000000 0.7853981633974484 0.5000000000000000 0.3926990816987239 -0.7071067811865475 0.7853981633974484 0.000000000000000 0.3926990816987245 0.7071067811865476 0.2170787134227060 -0.8090169943749475 0.5683194499747424 -0.3090169943749475 0.5683194499747424 0.3090169943749474 0.2170787134227060 0.8090169943749475 0.1308996938995740 -0.8660254037844387 0.3926990816987242 -0.5000000000000000 0.5235987755982989 0.000000000000000 0.3926990816987242 0.5000000000000000 0.1308996938995745 0.8660254037844387 0.8448869089158841E-01 -0.9009688679024191 0.2743330560697777 -0.6234898018587335 0.4265764164360819 -0.2225209339563144 0.4265764164360819 0.2225209339563144 0.2743330560697777 0.6234898018587335 0.8448869089158841E-01 0.9009688679024191 0.5750944903191331E-01 -0.9238795325112867 0.1963495408493619 -0.7071067811865475 0.3351896326668111 -0.3826834323650898 0.3926990816987242 0.000000000000000 0.3351896326668108 0.3826834323650898 0.1963495408493624 0.7071067811865476 0.5750944903191331E-01 0.9238795325112867 0.4083294770910693E-01 -0.9396926207859084 0.1442256007956728 -0.7660444431189780 0.2617993877991495 -0.5000000000000000 0.3385402270935191 -0.1736481776669303 0.3385402270935191 0.1736481776669303 0.2617993877991495 0.5000000000000000 0.1442256007956728 0.7660444431189780 0.4083294770910754E-01 0.9396926207859084 0.2999954037160841E-01 -0.9510565162951536 0.1085393567113530 -0.8090169943749475 0.2056199086476264 -0.5877852522924731 0.2841597249873712 -0.3090169943749475 0.3141592653589794 0.000000000000000 0.2841597249873712 0.3090169943749475 0.2056199086476264 0.5877852522924731 0.1085393567113530 0.8090169943749475 0.2999954037160841E-01 0.9510565162951536 0.2266894250185901E-01 -0.9594929736144974 0.8347854093418892E-01 -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 0.8347854093418892E-01 0.8412535328311812 0.2266894250185901E-01 0.9594929736144974 GEN_HERMITE_EK_COMPUTE_TEST GEN_HERMITE_EK_COMPUTE computes a generalized Hermite quadrature rule using the Elhay-Kautsky algorithm. Using ALPHA = 0.500000 Order W X 1 1.225416702465178 0.000000000000000 2 0.6127083512325888 -0.8660254037844385 0.6127083512325888 0.8660254037844385 3 0.2625892933853953 -1.322875655532295 0.7002381156943873 0.9974659986866641E-16 0.2625892933853950 1.322875655532295 4 0.7477218653431637E-01 -1.752961966367866 0.5379361646982722 -0.6535475074298001 0.5379361646982725 0.6535475074298001 0.7477218653431640E-01 1.752961966367866 5 0.2069085274024060E-01 -2.099598150879759 0.3373854564216620 -1.044838554429487 0.5092640841413719 -0.2563766590867021E-15 0.3373854564216615 1.044838554429487 0.2069085274024055E-01 2.099598150879757 6 0.4758432285876815E-02 -2.431196006814871 0.1432946705182553 -1.428264330850235 0.4646552484284568 -0.5471261076464521 0.4646552484284568 0.5471261076464523 0.1432946705182556 1.428264330850235 0.4758432285876798E-02 2.431196006814872 7 0.1106289401968460E-02 -2.719880088556291 0.5564733125066088E-01 -1.747360778896522 0.3522490969234104 -0.8938582730216025 0.4074112673130981 0.1730010352426829E-15 0.3522490969234107 0.8938582730216027 0.5564733125066092E-01 1.747360778896522 0.1106289401968460E-02 2.719880088556291 8 0.2288084584739132E-03 -2.999078968343317 0.1787577463926715E-01 -2.057439418477469 0.1866121206001916 -1.241738340943189 0.4079916475346554 -0.4801606747408061 0.4079916475346549 0.4801606747408064 0.1866121206001921 1.241738340943189 0.1787577463926723E-01 2.057439418477470 0.2288084584739144E-03 2.999078968343317 9 0.4824428349517051E-04 -3.251152326134132 0.5575754103643749E-02 -2.331322119300713 0.8875797489986070E-01 -1.537416408684744 0.3467847917084952 -0.7945417010067838 0.3430831724741884 0.2193238645380863E-15 0.3467847917084951 0.7945417010067843 0.8875797489986054E-01 1.537416408684744 0.5575754103643714E-02 2.331322119300712 0.4824428349517031E-04 3.251152326134132 10 0.9347334083394694E-05 -3.496605880747678 0.1536356442402549E-02 -2.598397149544625 0.3517634314374581E-01 -1.827991812365275 0.2117439807373518 -1.114905370566644 0.3642423235750056 -0.4330259998733385 0.3642423235750059 0.4330259998733390 0.2117439807373522 1.114905370566644 0.3517634314374581E-01 1.827991812365276 0.1536356442402550E-02 2.598397149544625 0.9347334083394745E-05 3.496605880747678 GEN_HERMITE_INTEGRAL_TEST GEN_HERMITE_INTEGRAL evaluates Integral ( -oo < x < +oo ) exp(-x^2) x^n |x|^alpha dx Using ALPHA = 0.500000 N Value 0 1.225416702465178 1 0.000000000000000 2 0.9190625268488832 3 0.000000000000000 4 1.608359421985546 5 0.000000000000000 6 4.422988410460251 7 0.000000000000000 8 16.58620653922594 9 0.000000000000000 10 78.78448106132322 GEN_LAGUERRE_EK_COMPUTE_TEST GEN_LAGUERRE_EK_COMPUTE computes a generalized Laguerre quadrature rule using the Elhay-Kautsky algorithm. Using ALPHA = 0.500000 Order W X 1 0.8862269254527581 1.500000000000000 2 0.7233630235462752 0.9188611699158105 0.1628639019064825 4.081138830084189 3 0.5671862778403116 0.6663259077023710 0.3053717688445466 2.800775054150256 0.1366887876790012E-01 7.032899038147372 4 0.4530087465586073 0.5235260767382686 0.3816169601718006 2.156648763269094 0.5079462757224074E-01 5.137387546176712 0.8065911501100318E-03 10.18243761381593 5 0.3704505700074587 0.4313988071478522 0.4125843737694527 1.759753698423698 0.9777982005318063E-01 4.104465362828316 0.5373415341171988E-02 7.746703779542558 0.3874628149393578E-04 13.45767835205758 6 0.3094240968362603 0.3669498773083705 0.4177521497070222 1.488534292310453 0.1432858732209771 3.434007968424071 0.1533249102263385E-01 6.349067925680379 0.4306911960439409E-03 10.54046985844834 0.1623469821074067E-05 16.82097007782838 7 0.2631245143958913 0.3193036339206293 0.4091418694141027 1.290758622959152 0.1821177320927163 2.958374458696651 0.3005332430127098E-01 5.409031597244436 0.1760894117540066E-02 8.804079578056774 0.2852947122115974E-04 13.46853574325148 0.6166001541039146E-07 20.24991636587088 8 0.2271393619524710 0.2826336481165983 0.3935945428036152 1.139873801581612 0.2129089708672288 2.601524843406029 0.4787748320313817E-01 4.724114537527790 0.4542517474762631E-02 7.605256299231614 0.1624046001853252E-03 11.41718207654583 0.1642377413806097E-05 16.49941079765581 0.2173943126630911E-08 23.73000399593471 9 0.1985712548680196 0.2535325549744193 0.3749207846631705 1.020844277720390 0.2360748210008252 2.323096077022465 0.6709610500320433E-01 4.199350600657293 0.9008508896644308E-02 6.713974316615030 0.5426607386359281E-03 9.972009159539351 0.1270536687910834E-04 14.15405367127805 0.8484309239668581E-07 19.61190281916595 0.7228647164396506E-10 27.25123652302706 10 0.1754708150466599 0.2298729805186566 0.3552233888020720 0.9244815469866562 0.2526835596756785 2.099410462708798 0.8635610269533257E-01 3.782880873707289 0.1510977803486079E-01 6.019918027701461 0.1328215628363565E-02 8.880347597996709 0.5418780021170343E-04 12.47483240483621 0.8737475869187116E-06 16.99084729354256 0.4019699886939779E-08 22.79100289494895 0.2292221530204704E-11 30.80640591705272 GEN_LAGUERRE_INTEGRAL_TEST GEN_LAGUERRE_INTEGRAL evaluates Integral ( 0 < x < +oo ) exp(-x) x^n x^alpha dx Using ALPHA = 0.500000 N Value 0 0.8862269254527581 1 1.329340388179137 2 3.323350970447843 3 11.63172839656745 4 52.34277778455353 5 287.8852778150444 6 1871.254305797788 7 14034.40729348341 8 119292.4619946090 9 1133278.388948786 10 11899423.08396225 GEN_LAGUERRE_SS_COMPUTE_TEST GEN_LAGUERRE_SS_COMPUTE computes a generalized Laguerre quadrature rule using the Stroud-Secrest algorithm. Using ALPHA = 0.500000 Order W X 1 0.8862269254527581 1.500000000000000 2 0.7233630235462755 0.9188611699158102 0.1628639019064825 4.081138830084190 3 0.5671862778403113 0.6663259077023709 0.3053717688445466 2.800775054150257 0.1366887876790012E-01 7.032899038147373 4 0.4530087465586076 0.5235260767382691 0.3816169601717996 2.156648763269094 0.5079462757224078E-01 5.137387546176711 0.8065911501100311E-03 10.18243761381592 5 0.3704505700074590 0.4313988071478514 0.4125843737694528 1.759753698423696 0.9777982005318073E-01 4.104465362828315 0.5373415341171988E-02 7.746703779542557 0.3874628149393578E-04 13.45767835205758 6 0.3094240968362596 0.3669498773083708 0.4177521497070224 1.488534292310452 0.1432858732209768 3.434007968424071 0.1533249102263384E-01 6.349067925680379 0.4306911960439413E-03 10.54046985844834 0.1623469821074075E-05 16.82097007782838 7 0.2631245143958917 0.3193036339206299 0.4091418694141027 1.290758622959153 0.1821177320927161 2.958374458696650 0.3005332430127097E-01 5.409031597244433 0.1760894117540062E-02 8.804079578056776 0.2852947122115974E-04 13.46853574325148 0.6166001541039151E-07 20.24991636587088 8 0.2271393619524718 0.2826336481165991 0.3935945428036146 1.139873801581614 0.2129089708672283 2.601524843406029 0.4787748320313819E-01 4.724114537527790 0.4542517474762639E-02 7.605256299231614 0.1624046001853258E-03 11.41718207654583 0.1642377413806097E-05 16.49941079765582 0.2173943126630915E-08 23.73000399593471 9 0.1985712548680168 0.2535325549744192 0.3749207846631697 1.020844277720390 0.2360748210008255 2.323096077022466 0.6709610500320429E-01 4.199350600657293 0.9008508896644332E-02 6.713974316615029 0.5426607386359305E-03 9.972009159539349 0.1270536687910839E-04 14.15405367127805 0.8484309239668552E-07 19.61190281916595 0.7228647164396543E-10 27.25123652302706 10 0.1754708150466581 0.2298729805186563 0.3552233888020710 0.9244815469866572 0.2526835596756779 2.099410462708798 0.8635610269533264E-01 3.782880873707290 0.1510977803486081E-01 6.019918027701461 0.1328215628363563E-02 8.880347597996709 0.5418780021170349E-04 12.47483240483620 0.8737475869187144E-06 16.99084729354255 0.4019699886939800E-08 22.79100289494895 0.2292221530204716E-11 30.80640591705272 HERMITE_EK_COMPUTE_TEST HERMITE_EK_COMPUTE computes a Hermite quadrature rule using the Elhay-Kautsky algorithm. Order W X 1 1.772453850905516 0.000000000000000 2 0.8862269254527578 -0.7071067811865475 0.8862269254527578 0.7071067811865475 3 0.2954089751509195 -1.224744871391589 1.181635900603677 0.000000000000000 0.2954089751509196 1.224744871391589 4 0.8131283544724513E-01 -1.650680123885784 0.8049140900055129 -0.5246476232752904 0.8049140900055121 0.5246476232752902 0.8131283544724525E-01 1.650680123885784 5 0.1995324205904597E-01 -2.020182870456086 0.3936193231522413 -0.9585724646138184 0.9453087204829430 0.000000000000000 0.3936193231522411 0.9585724646138187 0.1995324205904589E-01 2.020182870456086 6 0.4530009905508857E-02 -2.350604973674493 0.1570673203228569 -1.335849074013696 0.7246295952243929 -0.4360774119276162 0.7246295952243927 0.4360774119276160 0.1570673203228566 1.335849074013696 0.4530009905508823E-02 2.350604973674493 7 0.9717812450995172E-03 -2.651961356835234 0.5451558281912706E-01 -1.673551628767471 0.4256072526101277 -0.8162878828589647 0.8102646175568082 0.000000000000000 0.4256072526101282 0.8162878828589646 0.5451558281912713E-01 1.673551628767472 0.9717812450995191E-03 2.651961356835234 8 0.1996040722113679E-03 -2.930637420257243 0.1707798300741343E-01 -1.981656756695842 0.2078023258148922 -1.157193712446780 0.6611470125582418 -0.3811869902073223 0.6611470125582410 0.3811869902073220 0.2078023258148921 1.157193712446780 0.1707798300741346E-01 1.981656756695842 0.1996040722113677E-03 2.930637420257243 9 0.3960697726326444E-04 -3.190993201781527 0.4943624275536957E-02 -2.266580584531843 0.8847452739437681E-01 -1.468553289216668 0.4326515590025557 -0.7235510187528373 0.7202352156060512 0.000000000000000 0.4326515590025563 0.7235510187528379 0.8847452739437676E-01 1.468553289216668 0.4943624275536958E-02 2.266580584531844 0.3960697726326444E-04 3.190993201781527 10 0.7640432855232631E-05 -3.436159118837738 0.1343645746781224E-02 -2.532731674232788 0.3387439445548121E-01 -1.756683649299881 0.2401386110823150 -1.036610829789514 0.6108626337353257 -0.3429013272237045 0.6108626337353257 0.3429013272237046 0.2401386110823148 1.036610829789512 0.3387439445548109E-01 1.756683649299880 0.1343645746781228E-02 2.532731674232791 0.7640432855232614E-05 3.436159118837738 HERMITE_INTEGRAL_TEST HERMITE_INTEGRAL evaluates Integral ( -oo < x < +oo ) exp(-x^2) x^n dx N Value 0 1.772453850905516 1 0.000000000000000 2 0.8862269254527579 3 0.000000000000000 4 1.329340388179137 5 0.000000000000000 6 3.323350970447842 7 0.000000000000000 8 11.63172839656745 9 0.000000000000000 10 52.34277778455352 HERMITE_SET_TEST HERMITE_SET sets a Hermite quadrature rule over (-oo,+oo). Index X W 1 0.000000000000000 1.772453850905516 1 -0.7071067811865476 0.8862269254527581 2 0.7071067811865476 0.8862269254527581 1 -1.224744871391589 0.2954089751509194 2 0.000000000000000 1.181635900603677 3 1.224744871391589 0.2954089751509194 1 -1.650680123885784 0.8131283544724517E-01 2 -0.5246476232752904 0.8049140900055128 3 0.5246476232752904 0.8049140900055128 4 1.650680123885784 0.8131283544724517E-01 1 -2.020182870456086 0.1995324205904591E-01 2 -0.9585724646138185 0.3936193231522412 3 0.000000000000000 0.9453087204829419 4 0.9585724646138185 0.3936193231522412 5 2.020182870456086 0.1995324205904591E-01 1 -2.350604973674492 0.4530009905508846E-02 2 -1.335849074013697 0.1570673203228566 3 -0.4360774119276165 0.7246295952243925 4 0.4360774119276165 0.7246295952243925 5 1.335849074013697 0.1570673203228566 6 2.350604973674492 0.4530009905508846E-02 1 -2.651961356835233 0.9717812450995191E-03 2 -1.673551628767471 0.5451558281912703E-01 3 -0.8162878828589647 0.4256072526101278 4 0.000000000000000 0.8102646175568073 5 0.8162878828589647 0.4256072526101278 6 1.673551628767471 0.5451558281912703E-01 7 2.651961356835233 0.9717812450995191E-03 1 -2.930637420257244 0.1996040722113676E-03 2 -1.981656756695843 0.1707798300741347E-01 3 -1.157193712446780 0.2078023258148919 4 -0.3811869902073221 0.6611470125582413 5 0.3811869902073221 0.6611470125582413 6 1.157193712446780 0.2078023258148919 7 1.981656756695843 0.1707798300741347E-01 8 2.930637420257244 0.1996040722113676E-03 1 -3.190993201781528 0.3960697726326439E-04 2 -2.266580584531843 0.4943624275536947E-02 3 -1.468553289216668 0.8847452739437657E-01 4 -0.7235510187528376 0.4326515590025558 5 0.000000000000000 0.7202352156060510 6 0.7235510187528376 0.4326515590025558 7 1.468553289216668 0.8847452739437657E-01 8 2.266580584531843 0.4943624275536947E-02 9 3.190993201781528 0.3960697726326439E-04 1 -3.436159118837737 0.7640432855232621E-05 2 -2.532731674232790 0.1343645746781233E-02 3 -1.756683649299882 0.3387439445548106E-01 4 -1.036610829789514 0.2401386110823147 5 -0.3429013272237046 0.6108626337353258 6 0.3429013272237046 0.6108626337353258 7 1.036610829789514 0.2401386110823147 8 1.756683649299882 0.3387439445548106E-01 9 2.532731674232790 0.1343645746781233E-02 10 3.436159118837737 0.7640432855232621E-05 HERMITE_SS_COMPUTE_TEST HERMITE_SS_COMPUTE computes a Hermite quadrature rule using the Stroud-Secrest algorithm. Order W X 1 1.772453850905516 0.000000000000000 2 0.8862269254527578 -0.7071067811865475 0.8862269254527578 0.7071067811865475 3 0.2954089751509195 -1.224744871391589 1.181635900603677 0.000000000000000 0.2954089751509195 1.224744871391589 4 0.8131283544724513E-01 -1.650680123885785 0.8049140900055128 -0.5246476232752904 0.8049140900055128 0.5246476232752904 0.8131283544724513E-01 1.650680123885785 5 0.1995324205904592E-01 -2.020182870456086 0.3936193231522412 -0.9585724646138185 0.9453087204829419 0.000000000000000 0.3936193231522412 0.9585724646138185 0.1995324205904592E-01 2.020182870456086 6 0.4530009905508842E-02 -2.350604973674492 0.1570673203228565 -1.335849074013697 0.7246295952243924 -0.4360774119276165 0.7246295952243924 0.4360774119276165 0.1570673203228565 1.335849074013697 0.4530009905508842E-02 2.350604973674492 7 0.9717812450995207E-03 -2.651961356835233 0.5451558281912694E-01 -1.673551628767471 0.4256072526101277 -0.8162878828589647 0.8102646175568073 0.000000000000000 0.4256072526101277 0.8162878828589647 0.5451558281912694E-01 1.673551628767471 0.9717812450995207E-03 2.651961356835233 8 0.1996040722113675E-03 -2.930637420257244 0.1707798300741346E-01 -1.981656756695843 0.2078023258148916 -1.157193712446780 0.6611470125582413 -0.3811869902073221 0.6611470125582413 0.3811869902073221 0.2078023258148916 1.157193712446780 0.1707798300741346E-01 1.981656756695843 0.1996040722113675E-03 2.930637420257244 9 0.3960697726326427E-04 -3.190993201781527 0.4943624275536940E-02 -2.266580584531843 0.8847452739437658E-01 -1.468553289216668 0.4326515590025556 -0.7235510187528376 0.7202352156060510 0.000000000000000 0.4326515590025556 0.7235510187528376 0.8847452739437658E-01 1.468553289216668 0.4943624275536940E-02 2.266580584531843 0.3960697726326427E-04 3.190993201781527 10 0.7640432855232643E-05 -3.436159118837738 0.1343645746781235E-02 -2.532731674232790 0.3387439445548104E-01 -1.756683649299882 0.2401386110823147 -1.036610829789514 0.6108626337353257 -0.3429013272237046 0.6108626337353257 0.3429013272237046 0.2401386110823147 1.036610829789514 0.3387439445548104E-01 1.756683649299882 0.1343645746781235E-02 2.532731674232790 0.7640432855232643E-05 3.436159118837738 HERMITE_GK16_SET_TEST HERMITE_GK16_SET sets a nested Hermite quadrature rule over (-oo,+oo). Index X W 1 0.000000000000000 1.772453850905516 1 -1.224744871391589 0.2954089751509193 2 0.000000000000000 1.181635900603677 3 1.224744871391589 0.2954089751509193 1 -2.959210779063838 0.1233068065515345E-02 2 -1.224744871391589 0.2455792853503139 3 -0.5240335474869576 0.2328625178738610 4 0.000000000000000 0.8131041083261350 5 0.5240335474869576 0.2328625178738610 6 1.224744871391589 0.2455792853503139 7 2.959210779063838 0.1233068065515345E-02 1 -2.959210779063838 0.1670882630688235E-03 2 -2.023230191100516 0.1417311787397910E-01 3 -1.224744871391589 0.1681189289476777 4 -0.5240335474869576 0.4786942854911412 5 0.000000000000000 0.4501470097537820 6 0.5240335474869576 0.4786942854911412 7 1.224744871391589 0.1681189289476777 8 2.023230191100516 0.1417311787397910E-01 9 2.959210779063838 0.1670882630688235E-03 1 -4.499599398310388 0.3746346994305176E-07 2 -3.667774215946338 -0.1454284338706939E-05 3 -2.959210779063838 0.1872381894927835E-03 4 -2.023230191100516 0.1246651913280592E-01 5 -1.835707975175187 0.3484071934680380E-02 6 -1.224744871391589 0.1571829837665224 7 -0.8700408953529029 0.2515582570171293E-01 8 -0.5240335474869576 0.4511980360235854 9 0.000000000000000 0.4731073350496539 10 0.5240335474869576 0.4511980360235854 11 0.8700408953529029 0.2515582570171293E-01 12 1.224744871391589 0.1571829837665224 13 1.835707975175187 0.3484071934680380E-02 14 2.023230191100516 0.1246651913280592E-01 15 2.959210779063838 0.1872381894927835E-03 16 3.667774215946338 -0.1454284338706939E-05 17 4.499599398310388 0.3746346994305176E-07 1 -4.499599398310388 0.1529571770532236E-08 2 -3.667774215946338 0.1080276720662476E-05 3 -2.959210779063838 0.1065658977285227E-03 4 -2.266513262056788 0.5113317439088385E-02 5 -2.023230191100516 -0.1123243848906923E-01 6 -1.835707975175187 0.3205524309944588E-01 7 -1.224744871391589 0.1136072989574827 8 -0.8700408953529029 0.1083886195500302 9 -0.5240335474869576 0.3692464336892085 10 0.000000000000000 0.5378816070051017 11 0.5240335474869576 0.3692464336892085 12 0.8700408953529029 0.1083886195500302 13 1.224744871391589 0.1136072989574827 14 1.835707975175187 0.3205524309944588E-01 15 2.023230191100516 -0.1123243848906923E-01 16 2.266513262056788 0.5113317439088385E-02 17 2.959210779063838 0.1065658977285227E-03 18 3.667774215946338 0.1080276720662476E-05 19 4.499599398310388 0.1529571770532236E-08 1 -6.375939270982236 0.2236564560704446E-14 2 -5.643257857885745 -0.2630469645854894E-12 3 -5.036089944473094 0.9067528823167982E-11 4 -4.499599398310388 0.1405525202472248E-08 5 -3.667774215946338 0.1088921969212812E-05 6 -2.959210779063838 0.1054166239474666E-03 7 -2.570558376584297 0.2666515977893943E-04 8 -2.266513262056788 0.4838520820550261E-02 9 -2.023230191100516 -0.9856627043461002E-02 10 -1.835707975175187 0.2940942758035079E-01 11 -1.579412134846767 0.3121021035268283E-02 12 -1.224744871391589 0.1093932507186088 13 -0.8700408953529029 0.1159493098485312 14 -0.5240335474869576 0.3539388902958054 15 -0.1760641420820089 0.4985576189329316E-01 16 0.000000000000000 0.4588883963675675 17 0.1760641420820089 0.4985576189329316E-01 18 0.5240335474869576 0.3539388902958054 19 0.8700408953529029 0.1159493098485312 20 1.224744871391589 0.1093932507186088 21 1.579412134846767 0.3121021035268283E-02 22 1.835707975175187 0.2940942758035079E-01 23 2.023230191100516 -0.9856627043461002E-02 24 2.266513262056788 0.4838520820550261E-02 25 2.570558376584297 0.2666515977893943E-04 26 2.959210779063838 0.1054166239474666E-03 27 3.667774215946338 0.1088921969212812E-05 28 4.499599398310388 0.1405525202472248E-08 29 5.036089944473094 0.9067528823167982E-11 30 5.643257857885745 -0.2630469645854894E-12 31 6.375939270982236 0.2236564560704446E-14 1 -6.375939270982236 -0.1760293280537250E-14 2 -5.643257857885745 0.4721927866641769E-12 3 -5.036089944473094 -0.3428157053034956E-10 4 -4.499599398310388 0.2754782513893590E-08 5 -4.029220140504371 -0.2390334338280351E-07 6 -3.667774215946338 0.1224522096715844E-05 7 -2.959210779063838 0.9871000919740917E-04 8 -2.570558376584297 0.1475320490186277E-03 9 -2.266513262056788 0.3758002660430479E-02 10 -2.023230191100516 -0.4911857612387755E-02 11 -1.835707975175187 0.2043505835910720E-01 12 -1.579412134846767 0.1303287269902796E-01 13 -1.224744871391589 0.9691344494458362E-01 14 -0.8700408953529029 0.1372652119156755 15 -0.5240335474869576 0.3120865619469745 16 -0.1760641420820089 0.1841169604772579 17 0.000000000000000 0.2465664493282962 18 0.1760641420820089 0.1841169604772579 19 0.5240335474869576 0.3120865619469745 20 0.8700408953529029 0.1372652119156755 21 1.224744871391589 0.9691344494458362E-01 22 1.579412134846767 0.1303287269902796E-01 23 1.835707975175187 0.2043505835910720E-01 24 2.023230191100516 -0.4911857612387755E-02 25 2.266513262056788 0.3758002660430479E-02 26 2.570558376584297 0.1475320490186277E-03 27 2.959210779063838 0.9871000919740917E-04 28 3.667774215946338 0.1224522096715844E-05 29 4.029220140504371 -0.2390334338280351E-07 30 4.499599398310388 0.2754782513893590E-08 31 5.036089944473094 -0.3428157053034956E-10 32 5.643257857885745 0.4721927866641769E-12 33 6.375939270982236 -0.1760293280537250E-14 1 -6.375939270982236 0.1868401489451060E-17 2 -5.643257857885745 0.9659946627856324E-14 3 -5.036089944473094 0.5489683694849946E-11 4 -4.499599398310388 0.8155372181691690E-09 5 -4.029220140504371 0.3792022239231953E-07 6 -3.667774215946338 0.4373781804092699E-06 7 -3.349163953713195 0.4846279973702046E-05 8 -2.959210779063838 0.6332862080561789E-04 9 -2.570558376584297 0.4878539930444377E-03 10 -2.266513262056788 0.1451558042515590E-02 11 -2.023230191100516 0.4096752772034405E-02 12 -1.835707975175187 0.5592882891146918E-02 13 -1.579412134846767 0.2778050890853510E-01 14 -1.224744871391589 0.8024551814739089E-01 15 -0.8700408953529029 0.1637122155573580 16 -0.5240335474869576 0.2624487148878428 17 -0.1760641420820089 0.3398859558558522 18 0.000000000000000 0.9126267536373792E-03 19 0.1760641420820089 0.3398859558558522 20 0.5240335474869576 0.2624487148878428 21 0.8700408953529029 0.1637122155573580 22 1.224744871391589 0.8024551814739089E-01 23 1.579412134846767 0.2778050890853510E-01 24 1.835707975175187 0.5592882891146918E-02 25 2.023230191100516 0.4096752772034405E-02 26 2.266513262056788 0.1451558042515590E-02 27 2.570558376584297 0.4878539930444377E-03 28 2.959210779063838 0.6332862080561789E-04 29 3.349163953713195 0.4846279973702046E-05 30 3.667774215946338 0.4373781804092699E-06 31 4.029220140504371 0.3792022239231953E-07 32 4.499599398310388 0.8155372181691690E-09 33 5.036089944473094 0.5489683694849946E-11 34 5.643257857885745 0.9659946627856324E-14 35 6.375939270982236 0.1868401489451060E-17 HERMITE_GK18_SET_TEST HERMITE_GK18_SET sets a nested Hermite quadrature rule over (-oo,+oo). Index X W 1 0.000000000000000 1.772453850905516 1 -1.224744871391589 0.2954089751509193 2 0.000000000000000 1.181635900603677 3 1.224744871391589 0.2954089751509193 1 -2.959210779063838 0.1670882630688235E-03 2 -2.023230191100516 0.1417311787397910E-01 3 -1.224744871391589 0.1681189289476777 4 -0.5240335474869576 0.4786942854911412 5 0.000000000000000 0.4501470097537820 6 0.5240335474869576 0.4786942854911412 7 1.224744871391589 0.1681189289476777 8 2.023230191100516 0.1417311787397910E-01 9 2.959210779063838 0.1670882630688235E-03 1 -4.499599398310388 0.1529571770532236E-08 2 -3.667774215946338 0.1080276720662476E-05 3 -2.959210779063838 0.1065658977285227E-03 4 -2.266513262056788 0.5113317439088385E-02 5 -2.023230191100516 -0.1123243848906923E-01 6 -1.835707975175187 0.3205524309944588E-01 7 -1.224744871391589 0.1136072989574827 8 -0.8700408953529029 0.1083886195500302 9 -0.5240335474869576 0.3692464336892085 10 0.000000000000000 0.5378816070051017 11 0.5240335474869576 0.3692464336892085 12 0.8700408953529029 0.1083886195500302 13 1.224744871391589 0.1136072989574827 14 1.835707975175187 0.3205524309944588E-01 15 2.023230191100516 -0.1123243848906923E-01 16 2.266513262056788 0.5113317439088385E-02 17 2.959210779063838 0.1065658977285227E-03 18 3.667774215946338 0.1080276720662476E-05 19 4.499599398310388 0.1529571770532236E-08 1 -6.853200069757519 0.3373041880791771E-20 2 -6.124527854622158 0.3328347396329305E-16 3 -5.521865209868350 0.3230168667828715E-13 4 -4.986551454150765 0.8093336886699500E-11 5 -4.499599398310388 0.7489075592395192E-09 6 -4.057956316089741 0.2941466714970834E-07 7 -3.667774215946338 0.5244824237448842E-06 8 -3.315584617593290 0.5866394570738962E-05 9 -2.959210779063838 0.5718855314706219E-04 10 -2.597288631188366 0.4164209572757709E-03 11 -2.266513262056788 0.1747333895810995E-02 12 -2.023230191100516 0.3133737860003044E-02 13 -1.835707975175187 0.7680926657706605E-02 14 -1.561553427651873 0.2749627133721485E-01 15 -1.224744871391589 0.7836309905080374E-01 16 -0.8700408953529030 0.1661158426147928 17 -0.5240335474869580 0.2536369104813872 18 -0.2146181805881710 0.2617129325114309 19 0.000000000000000 0.1717196809689803 20 0.2146181805881710 0.2617129325114309 21 0.5240335474869580 0.2536369104813872 22 0.8700408953529030 0.1661158426147928 23 1.224744871391589 0.7836309905080374E-01 24 1.561553427651873 0.2749627133721485E-01 25 1.835707975175187 0.7680926657706605E-02 26 2.023230191100516 0.3133737860003044E-02 27 2.266513262056788 0.1747333895810995E-02 28 2.597288631188366 0.4164209572757709E-03 29 2.959210779063838 0.5718855314706219E-04 30 3.315584617593290 0.5866394570738962E-05 31 3.667774215946338 0.5244824237448842E-06 32 4.057956316089741 0.2941466714970834E-07 33 4.499599398310388 0.7489075592395192E-09 34 4.986551454150765 0.8093336886699500E-11 35 5.521865209868350 0.3230168667828715E-13 36 6.124527854622158 0.3328347396329305E-16 37 6.853200069757519 0.3373041880791771E-20 HERMITE_GK22_SET_TEST HERMITE_GK22_SET sets a nested Hermite quadrature rule over (-oo,+oo). Index X W 1 0.000000000000000 1.772453850905516 1 -1.224744871391589 0.2954089751509193 2 0.000000000000000 1.181635900603677 3 1.224744871391589 0.2954089751509193 1 -2.959210779063838 0.1670882630688235E-03 2 -2.023230191100516 0.1417311787397910E-01 3 -1.224744871391589 0.1681189289476777 4 -0.5240335474869576 0.4786942854911412 5 0.000000000000000 0.4501470097537820 6 0.5240335474869576 0.4786942854911412 7 1.224744871391589 0.1681189289476777 8 2.023230191100516 0.1417311787397910E-01 9 2.959210779063838 0.1670882630688235E-03 1 -4.499599398310388 0.1529571770532236E-08 2 -3.667774215946338 0.1080276720662476E-05 3 -2.959210779063838 0.1065658977285227E-03 4 -2.266513262056788 0.5113317439088385E-02 5 -2.023230191100516 -0.1123243848906923E-01 6 -1.835707975175187 0.3205524309944588E-01 7 -1.224744871391589 0.1136072989574827 8 -0.8700408953529029 0.1083886195500302 9 -0.5240335474869576 0.3692464336892085 10 0.000000000000000 0.5378816070051017 11 0.5240335474869576 0.3692464336892085 12 0.8700408953529029 0.1083886195500302 13 1.224744871391589 0.1136072989574827 14 1.835707975175187 0.3205524309944588E-01 15 2.023230191100516 -0.1123243848906923E-01 16 2.266513262056788 0.5113317439088385E-02 17 2.959210779063838 0.1065658977285227E-03 18 3.667774215946338 0.1080276720662476E-05 19 4.499599398310388 0.1529571770532236E-08 1 -7.251792998192644 0.1177256569744054E-22 2 -6.547083258397540 0.1525067455343006E-18 3 -5.961461043404500 0.2021839499651013E-15 4 -5.437443360177798 0.7246148690511955E-13 5 -4.953574342912980 0.1031219664694630E-10 6 -4.499599398310388 0.7103713951693510E-09 7 -4.070919267883068 0.2643760444492605E-07 8 -3.667774215946338 0.5589827870786450E-06 9 -3.296114596212218 0.6756289071347449E-05 10 -2.959210779063838 0.5121980070197769E-04 11 -2.630415236459871 0.3350131149472009E-03 12 -2.266513262056788 0.2493796910969332E-02 13 -2.043834754429505 -0.2561699585060746E-01 14 -2.023230191100516 0.3170078786443256E-01 15 -1.835707975175187 0.1250414985840034E-02 16 -1.585873011819188 0.2932445609248943E-01 17 -1.224744871391589 0.7995363908033024E-01 18 -0.8700408953529029 0.1645436668065552 19 -0.5240335474869576 0.2587185197182411 20 -0.1953247844158050 0.2935887957359086 21 0.000000000000000 0.9975253752546119E-01 22 0.1953247844158050 0.2935887957359086 23 0.5240335474869576 0.2587185197182411 24 0.8700408953529029 0.1645436668065552 25 1.224744871391589 0.7995363908033024E-01 26 1.585873011819188 0.2932445609248943E-01 27 1.835707975175187 0.1250414985840034E-02 28 2.023230191100516 0.3170078786443256E-01 29 2.043834754429505 -0.2561699585060746E-01 30 2.266513262056788 0.2493796910969332E-02 31 2.630415236459871 0.3350131149472009E-03 32 2.959210779063838 0.5121980070197769E-04 33 3.296114596212218 0.6756289071347449E-05 34 3.667774215946338 0.5589827870786450E-06 35 4.070919267883068 0.2643760444492605E-07 36 4.499599398310388 0.7103713951693510E-09 37 4.953574342912980 0.1031219664694630E-10 38 5.437443360177798 0.7246148690511955E-13 39 5.961461043404500 0.2021839499651013E-15 40 6.547083258397540 0.1525067455343006E-18 41 7.251792998192644 0.1177256569744054E-22 HERMITE_GK24_SET_TEST HERMITE_GK24_SET sets a nested Hermite quadrature rule over (-oo,+oo). Index X W 1 0.000000000000000 1.772453850905516 1 -1.224744871391589 0.2954089751509193 2 0.000000000000000 1.181635900603677 3 1.224744871391589 0.2954089751509193 1 -2.959210779063838 0.1670882630688235E-03 2 -2.023230191100516 0.1417311787397910E-01 3 -1.224744871391589 0.1681189289476777 4 -0.5240335474869576 0.4786942854911412 5 0.000000000000000 0.4501470097537820 6 0.5240335474869576 0.4786942854911412 7 1.224744871391589 0.1681189289476777 8 2.023230191100516 0.1417311787397910E-01 9 2.959210779063838 0.1670882630688235E-03 1 -4.499599398310388 0.1529571770532236E-08 2 -3.667774215946338 0.1080276720662476E-05 3 -2.959210779063838 0.1065658977285227E-03 4 -2.266513262056788 0.5113317439088385E-02 5 -2.023230191100516 -0.1123243848906923E-01 6 -1.835707975175187 0.3205524309944588E-01 7 -1.224744871391589 0.1136072989574827 8 -0.8700408953529029 0.1083886195500302 9 -0.5240335474869576 0.3692464336892085 10 0.000000000000000 0.5378816070051017 11 0.5240335474869576 0.3692464336892085 12 0.8700408953529029 0.1083886195500302 13 1.224744871391589 0.1136072989574827 14 1.835707975175187 0.3205524309944588E-01 15 2.023230191100516 -0.1123243848906923E-01 16 2.266513262056788 0.5113317439088385E-02 17 2.959210779063838 0.1065658977285227E-03 18 3.667774215946338 0.1080276720662476E-05 19 4.499599398310388 0.1529571770532236E-08 1 -10.16757499488187 0.9681000206415281E-37 2 -7.231746029072501 0.1551693126286043E-22 3 -6.535398426382995 0.1759373091077510E-18 4 -5.954781975039809 0.2173376087108937E-15 5 -5.434053000365068 0.7478370103805401E-13 6 -4.952329763008589 0.1040281320972057E-10 7 -4.499599398310388 0.7090357338933678E-09 8 -4.071335874253583 0.2634817229999666E-07 9 -3.667774215946338 0.5601279648484322E-06 10 -3.295265921534226 0.6804109348022103E-05 11 -2.959210779063838 0.5083438731025441E-04 12 -2.633356763661946 0.3275308000661018E-03 13 -2.266513262056788 0.2674798287885530E-02 14 -2.089340389294661 -0.6877042709632538E-02 15 -2.023230191100516 0.1193832017909136E-01 16 -1.835707975175187 0.2480837228710028E-02 17 -1.583643465293944 0.2900033574972639E-01 18 -1.224744871391589 0.7986895578757570E-01 19 -0.8700408953529029 0.1646098424225806 20 -0.5240335474869576 0.2585359547316077 21 -0.1960294536620110 0.2922438104061171 22 0.000000000000000 0.1027307137534418 23 0.1960294536620110 0.2922438104061171 24 0.5240335474869576 0.2585359547316077 25 0.8700408953529029 0.1646098424225806 26 1.224744871391589 0.7986895578757570E-01 27 1.583643465293944 0.2900033574972639E-01 28 1.835707975175187 0.2480837228710028E-02 29 2.023230191100516 0.1193832017909136E-01 30 2.089340389294661 -0.6877042709632538E-02 31 2.266513262056788 0.2674798287885530E-02 32 2.633356763661946 0.3275308000661018E-03 33 2.959210779063838 0.5083438731025441E-04 34 3.295265921534226 0.6804109348022103E-05 35 3.667774215946338 0.5601279648484322E-06 36 4.071335874253583 0.2634817229999666E-07 37 4.499599398310388 0.7090357338933678E-09 38 4.952329763008589 0.1040281320972057E-10 39 5.434053000365068 0.7478370103805401E-13 40 5.954781975039809 0.2173376087108937E-15 41 6.535398426382995 0.1759373091077510E-18 42 7.231746029072501 0.1551693126286043E-22 43 10.16757499488187 0.9681000206415281E-37 HERMITE_1_SET_TEST HERMITE_1_SET sets a Hermite unit-density quadrature rule over (-oo,+oo). The weight is 1. Index X W 1 0.000000000000000 1.772453850905516 1 -0.7071067811865476 1.461141182661139 2 0.7071067811865476 1.461141182661139 1 -1.224744871391589 1.323931175213644 2 0.000000000000000 1.181635900603677 3 1.224744871391589 1.323931175213644 1 -1.650680123885784 1.240225817695815 2 -0.5246476232752904 1.059964482894969 3 0.5246476232752904 1.059964482894969 4 1.650680123885784 1.240225817695815 1 -2.020182870456086 1.181488625535987 2 -0.9585724646138185 0.9865809967514283 3 0.000000000000000 0.9453087204829419 4 0.9585724646138185 0.9865809967514283 5 2.020182870456086 1.181488625535987 1 -2.350604973674492 1.136908332674525 2 -1.335849074013697 0.9355805576311808 3 -0.4360774119276165 0.8764013344362306 4 0.4360774119276165 0.8764013344362306 5 1.335849074013697 0.9355805576311808 6 2.350604973674492 1.136908332674525 1 -2.651961356835233 1.101330729610322 2 -1.673551628767471 0.8971846002251841 3 -0.8162878828589647 0.8286873032836393 4 0.000000000000000 0.8102646175568073 5 0.8162878828589647 0.8286873032836393 6 1.673551628767471 0.8971846002251841 7 2.651961356835233 1.101330729610322 1 -2.930637420257244 1.071930144247980 2 -1.981656756695843 0.8667526065633814 3 -1.157193712446780 0.7928900483864013 4 -0.3811869902073221 0.7645441286517292 5 0.3811869902073221 0.7645441286517292 6 1.157193712446780 0.7928900483864013 7 1.981656756695843 0.8667526065633814 8 2.930637420257244 1.071930144247980 1 -3.190993201781528 1.047003580976684 2 -2.266580584531843 0.8417527014786704 3 -1.468553289216668 0.7646081250945502 4 -0.7235510187528376 0.7303024527450922 5 0.000000000000000 0.7202352156060510 6 0.7235510187528376 0.7303024527450922 7 1.468553289216668 0.7646081250945502 8 2.266580584531843 0.8417527014786704 9 3.190993201781528 1.047003580976684 1 -3.436159118837737 1.025451691365735 2 -2.532731674232790 0.8206661264048164 3 -1.756683649299882 0.7414419319435651 4 -1.036610829789514 0.7032963231049061 5 -0.3429013272237046 0.6870818539512734 6 0.3429013272237046 0.6870818539512734 7 1.036610829789514 0.7032963231049061 8 1.756683649299882 0.7414419319435651 9 2.532731674232790 0.8206661264048164 10 3.436159118837737 1.025451691365735 HERMITE_PROBABILIST_SET_TEST HERMITE_PROBABILIST_SET sets a Hermite probabilist quadrature rule over (-oo,+oo). The weight is exp ( - x * x / 2 ) / sqrt ( 2 * pi ). Index X W 1 0.000000000000000 1.000000000000000 1 -1.000000000000000 0.5000000000000000 2 1.000000000000000 0.5000000000000000 1 -1.732050807568877 0.1666666666666667 2 0.000000000000000 0.6666666666666666 3 1.732050807568877 0.1666666666666667 1 -2.334414218338977 0.4587585476806849E-01 2 -0.7419637843027258 0.4541241452319315 3 0.7419637843027258 0.4541241452319315 4 2.334414218338977 0.4587585476806849E-01 1 -2.856970013872806 0.1125741132772069E-01 2 -1.355626179974266 0.2220759220056127 3 0.000000000000000 0.5333333333333333 4 1.355626179974266 0.2220759220056127 5 2.856970013872806 0.1125741132772069E-01 1 -3.324257433552119 0.2555784402056247E-02 2 -1.889175877753711 0.8861574604191452E-01 3 -0.6167065901925941 0.4088284695560293 4 0.6167065901925941 0.4088284695560293 5 1.889175877753711 0.8861574604191452E-01 6 3.324257433552119 0.2555784402056247E-02 1 -3.750439717725742 0.5482688559722178E-03 2 -2.366759410734541 0.3075712396758650E-01 3 -1.154405394739968 0.2401231786050127 4 0.000000000000000 0.4571428571428571 5 1.154405394739968 0.2401231786050127 6 2.366759410734541 0.3075712396758650E-01 7 3.750439717725742 0.5482688559722178E-03 1 -4.144547186125894 0.1126145383753678E-03 2 -2.802485861287542 0.9635220120788266E-02 3 -1.636519042435108 0.1172399076617590 4 -0.5390798113513751 0.3730122576790774 5 0.5390798113513751 0.3730122576790774 6 1.636519042435108 0.1172399076617590 7 2.802485861287542 0.9635220120788266E-02 8 4.144547186125894 0.1126145383753678E-03 1 -4.512745863399783 0.2234584400774658E-04 2 -3.205429002856470 0.2789141321231769E-02 3 -2.076847978677830 0.4991640676521787E-01 4 -1.023255663789133 0.2440975028949394 5 0.000000000000000 0.4063492063492063 6 1.023255663789133 0.2440975028949394 7 2.076847978677830 0.4991640676521787E-01 8 3.205429002856470 0.2789141321231769E-02 9 4.512745863399783 0.2234584400774658E-04 1 -4.859462828332312 0.4310652630718287E-05 2 -3.581823483551927 0.7580709343122177E-03 3 -2.484325841638955 0.1911158050077029E-01 4 -1.465989094391158 0.1354837029802677 5 -0.4849357075154976 0.3446423349320191 6 0.4849357075154976 0.3446423349320191 7 1.465989094391158 0.1354837029802677 8 2.484325841638955 0.1911158050077029E-01 9 3.581823483551927 0.7580709343122177E-03 10 4.859462828332312 0.4310652630718287E-05 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 0.26794919 2 1.0000000 3 2.0000000 4 3.0000000 5 3.7320508 Exact eigenvalues: 1 0.26794919 2 1.0000000 3 2.0000000 4 3.0000000 5 3.7320508 Vector Z: 1 1.0000000 2 1.0000000 3 1.0000000 4 1.0000000 5 1.0000000 Vector Q'*Z: 1 -2.1547005 2 0.17113554E-15 3 0.57735027 4 0.68645097E-15 5 -0.15470054 JACOBI_EK_COMPUTE_TEST JACOBI_EK_COMPUTE computes a Gauss-Jacobi rule; ALPHA = 1.500000 BETA = 0.500000 Index X W 1 -0.2500000000000000 1.570796326794896 1 -0.6076252185107651 0.9338244648629140 2 0.2742918851774319 0.6369718619319826 1 -0.7601573404872679 0.5261284436611051 2 -0.1528288638647805 0.8030739600082103 3 0.5379862043520484 0.2415939231255808 1 -0.8385964119177013 0.3144794551130210 2 -0.4056256275378190 0.6787436549284248 3 0.1614690409023143 0.4757517664489192 4 0.6827529985532059 0.1018214503045318 1 -0.8840882653201494 0.2001252566372695 2 -0.5629059317762042 0.5199632186774659 3 -0.1100274225210447 0.5356898968305497 4 0.3708136309492865 0.2672477173275197 5 0.7695413220014453 0.4777023732209325E-01 1 -0.9127717928725460 0.1343056820427142 2 -0.6661693810819841 0.3902780567984852 3 -0.3028312803228947 0.4990786758998956 4 0.1144215303885478 0.3697846812371451 5 0.5134534103439397 0.1528283716957897 6 0.8253260849735089 0.2452085912086594E-01 1 -0.9320024628657496 0.9414510038510730E-01 2 -0.7371931739434823 0.2943041944091259 3 -0.4418817729485140 0.4309263997770960 4 -0.8595066022406408E-01 0.4009490239804637 5 0.2825323324996322 0.2463697069136380 6 0.6138099722388769 0.9055772921029343E-01 7 0.8631857652433006 0.1354417211917141E-01 1 -0.9455158043974035 0.6839190925948317E-01 2 -0.7879673764819102 0.2248513392666888 3 -0.5444273641737972 0.3606436566319109 4 -0.2412867334092745 0.3883180543539700 5 0.8860534544266949E-01 0.3008492695347091 6 0.4095019972429186 0.1640573457854803 7 0.6866356906720190 0.5574150057933543E-01 8 0.8900098006603339 0.7943251383318818E-02 1 -0.9553706327691448 0.5117382374316986E-01 2 -0.8254480244332436 0.1744634097524553 3 -0.6217762959622667 0.2984741580861980 4 -0.3624524217425486 0.3552731274654833 5 -0.7051816095979102E-01 0.3200587357332043 6 0.2280875011498076 0.2202297069828387 7 0.5068337773772099 0.1106616329196987 8 0.7409581449066013 0.3556668124983483E-01 9 0.9096861124333758 0.4895050862014709E-02 1 -0.9627766886703771 0.3925058540055813E-01 2 -0.8538674269792417 0.1374810592741681 3 -0.6813494824055376 0.2466379844126237 4 -0.4580176529455096 0.3155655291519011 5 -0.2004353100508686 0.3157558361063392 6 0.7229409169326691E-01 0.2531373506672513 7 0.3399439927530341 0.1603930057544808 8 0.5826653601184618 0.7598607784811155E-01 9 0.7824610233136919 0.2344462385831623E-01 10 0.9245366386276249 0.3144274321147428E-02 JACOBI_INTEGRAL_TEST JACOBI_INTEGRAL evaluates Integral ( -1 < x < +1 ) x^n (1-x)^alpha (1+x)^beta dx Use ALPHA = 1.50000 BETA = 0.500000 N Value 0 1.570796326794896 1 -0.3926990816987241 2 0.3926990816987240 3 -0.1963495408493619 4 0.1963495408493619 5 -0.1227184630308513 6 0.1227184630308513 7 -0.8590292412159588E-01 8 0.8590292412159588E-01 9 -0.6442719309119695E-01 10 0.6442719309119677E-01 JACOBI_SS_COMPUTE_TEST JACOBI_SS_COMPUTE computes a Gauss-Jacobi rule; ALPHA = 1.500000 BETA = 0.500000 Index X W 1 -0.2500000000000000 1.570796326794897 1 -0.6076252185107651 0.9338244648629139 2 0.2742918851774317 0.6369718619319823 1 -0.7601573404872680 0.5261284436611050 2 -0.1528288638647804 0.8030739600082109 3 0.5379862043520485 0.2415939231255806 1 -0.8385964119177013 0.3144794551130212 2 -0.4056256275378191 0.6787436549284247 3 0.1614690409023143 0.4757517664489193 4 0.6827529985532060 0.1018214503045319 1 -0.8840882653201494 0.2001252566372700 2 -0.5629059317762043 0.5199632186774658 3 -0.1100274225210447 0.5356898968305489 4 0.3708136309492864 0.2672477173275188 5 0.7695413220014452 0.4777023732209336E-01 1 -0.9127717928725457 0.1343056820427140 2 -0.6661693810819842 0.3902780567984852 3 -0.3028312803228947 0.4990786758998956 4 0.1144215303885478 0.3697846812371456 5 0.5134534103439397 0.1528283716957897 6 0.8253260849735087 0.2452085912086589E-01 1 -0.9320024628657496 0.9414510038510658E-01 2 -0.7371931739434825 0.2943041944091261 3 -0.4418817729485141 0.4309263997770966 4 -0.8595066022406420E-01 0.4009490239804644 5 0.2825323324996325 0.2463697069136380 6 0.6138099722388772 0.9055772921029322E-01 7 0.8631857652433007 0.1354417211917143E-01 1 -0.9455158043974035 0.6839190925948330E-01 2 -0.7879673764819101 0.2248513392666886 3 -0.5444273641737976 0.3606436566319115 4 -0.2412867334092741 0.3883180543539708 5 0.8860534544266938E-01 0.3008492695347084 6 0.4095019972429186 0.1640573457854800 7 0.6866356906720188 0.5574150057933536E-01 8 0.8900098006603341 0.7943251383318826E-02 1 -0.9553706327691447 0.5117382374317007E-01 2 -0.8254480244332433 0.1744634097524552 3 -0.6217762959622666 0.2984741580861980 4 -0.3624524217425487 0.3552731274654827 5 -0.7051816095979099E-01 0.3200587357332037 6 0.2280875011498078 0.2202297069828387 7 0.5068337773772098 0.1106616329196987 8 0.7409581449066008 0.3556668124983501E-01 9 0.9096861124333758 0.4895050862014669E-02 1 -0.9627766886703770 0.3925058540055802E-01 2 -0.8538674269792417 0.1374810592741683 3 -0.6813494824055374 0.2466379844126230 4 -0.4580176529455094 0.3155655291519011 5 -0.2004353100508688 0.3157558361063396 6 0.7229409169326721E-01 0.2531373506672515 7 0.3399439927530341 0.1603930057544804 8 0.5826653601184615 0.7598607784811140E-01 9 0.7824610233136921 0.2344462385831621E-01 10 0.9245366386276249 0.3144274321147395E-02 KRONROD_SET_TEST KRONROD_SET sets up a Kronrod quadrature rule; This is used following a lower order Legendre rule. Legendre/Kronrod quadrature pair #1 W X 1 0.1294849661688697 -0.9491079123427585 2 0.2797053914892766 -0.7415311855993945 3 0.3818300505051189 -0.4058451513773972 4 0.4179591836734694 0.000000000000000 5 0.3818300505051189 0.4058451513773972 6 0.2797053914892766 0.7415311855993945 7 0.1294849661688697 0.9491079123427585 1 0.2293532201052922E-01 -0.9914553711208126 2 0.6309209262997854E-01 -0.9491079123427585 3 0.1047900103222502 -0.8648644233597691 4 0.1406532597155259 -0.7415311855993943 5 0.1690047266392679 -0.5860872354676911 6 0.1903505780647854 -0.4058451513773972 7 0.2044329400752989 -0.2077849550789850 8 0.2094821410847278 0.000000000000000 9 0.2044329400752989 0.2077849550789850 10 0.1903505780647854 0.4058451513773972 11 0.1690047266392679 0.5860872354676911 12 0.1406532597155259 0.7415311855993943 13 0.1047900103222502 0.8648644233597691 14 0.6309209262997854E-01 0.9491079123427585 15 0.2293532201052922E-01 0.9914553711208126 Legendre/Kronrod quadrature pair #2 W X 1 0.6667134430868814E-01 -0.9739065285171717 2 0.1494513491505806 -0.8650633666889845 3 0.2190863625159820 -0.6794095682990244 4 0.2692667193099963 -0.4333953941292472 5 0.2955242247147529 -0.1488743389816312 6 0.2955242247147529 0.1488743389816312 7 0.2692667193099963 0.4333953941292472 8 0.2190863625159820 0.6794095682990244 9 0.1494513491505806 0.8650633666889845 10 0.6667134430868814E-01 0.9739065285171717 1 0.1169463886737187E-01 -0.9956571630258081 2 0.3255816230796473E-01 -0.9739065285171717 3 0.5475589657435200E-01 -0.9301574913557082 4 0.7503967481091996E-01 -0.8650633666889845 5 0.9312545458369761E-01 -0.7808177265864169 6 0.1093871588022976 -0.6794095682990244 7 0.1234919762620659 -0.5627571346686047 8 0.1347092173114733 -0.4333953941292472 9 0.1427759385770601 -0.2943928627014602 10 0.1477391049013385 -0.1488743389816312 11 0.1494455540029169 0.000000000000000 12 0.1477391049013385 0.1488743389816312 13 0.1427759385770601 0.2943928627014602 14 0.1347092173114733 0.4333953941292472 15 0.1234919762620659 0.5627571346686047 16 0.1093871588022976 0.6794095682990244 17 0.9312545458369761E-01 0.7808177265864169 18 0.7503967481091996E-01 0.8650633666889845 19 0.5475589657435200E-01 0.9301574913557082 20 0.3255816230796473E-01 0.9739065285171717 21 0.1169463886737187E-01 0.9956571630258081 Legendre/Kronrod quadrature pair #3 W X 1 0.3075324199611727E-01 -0.9879925180204854 2 0.7036604748810812E-01 -0.9372733924007060 3 0.1071592204671719 -0.8482065834104272 4 0.1395706779261543 -0.7244177313601701 5 0.1662692058169939 -0.5709721726085388 6 0.1861610000155622 -0.3941513470775634 7 0.1984314853271116 -0.2011940939974345 8 0.2025782419255613 0.000000000000000 9 0.1984314853271116 0.2011940939974345 10 0.1861610000155622 0.3941513470775634 11 0.1662692058169939 0.5709721726085388 12 0.1395706779261543 0.7244177313601701 13 0.1071592204671719 0.8482065834104272 14 0.7036604748810812E-01 0.9372733924007060 15 0.3075324199611727E-01 0.9879925180204854 1 0.5377479872923349E-02 -0.9980022986933971 2 0.1500794732931612E-01 -0.9879925180204854 3 0.2546084732671532E-01 -0.9677390756791391 4 0.3534636079137585E-01 -0.9372733924007060 5 0.4458975132476488E-01 -0.8972645323440819 6 0.5348152469092809E-01 -0.8482065834104272 7 0.6200956780067064E-01 -0.7904185014424659 8 0.6985412131872826E-01 -0.7244177313601700 9 0.7684968075772038E-01 -0.6509967412974170 10 0.8308050282313302E-01 -0.5709721726085388 11 0.8856444305621176E-01 -0.4850818636402397 12 0.9312659817082532E-01 -0.3941513470775634 13 0.9664272698362368E-01 -0.2991800071531688 14 0.9917359872179196E-01 -0.2011940939974345 15 0.1007698455238756 -0.1011420669187175 16 0.1013300070147915 0.000000000000000 17 0.1007698455238756 0.1011420669187175 18 0.9917359872179196E-01 0.2011940939974345 19 0.9664272698362368E-01 0.2991800071531688 20 0.9312659817082532E-01 0.3941513470775634 21 0.8856444305621176E-01 0.4850818636402397 22 0.8308050282313302E-01 0.5709721726085388 23 0.7684968075772038E-01 0.6509967412974170 24 0.6985412131872826E-01 0.7244177313601700 25 0.6200956780067064E-01 0.7904185014424659 26 0.5348152469092809E-01 0.8482065834104272 27 0.4458975132476488E-01 0.8972645323440819 28 0.3534636079137585E-01 0.9372733924007060 29 0.2546084732671532E-01 0.9677390756791391 30 0.1500794732931612E-01 0.9879925180204854 31 0.5377479872923349E-02 0.9980022986933971 Legendre/Kronrod quadrature pair #4 W X 1 0.1761400713915212E-01 -0.9931285991850949 2 0.4060142980038694E-01 -0.9639719272779138 3 0.6267204833410907E-01 -0.9122344282513259 4 0.8327674157670475E-01 -0.8391169718222188 5 0.1019301198172404 -0.7463319064601508 6 0.1181945319615184 -0.6360536807265150 7 0.1316886384491766 -0.5108670019508271 8 0.1420961093183820 -0.3737060887154195 9 0.1491729864726037 -0.2277858511416451 10 0.1527533871307258 -0.7652652113349734E-01 11 0.1527533871307258 0.7652652113349734E-01 12 0.1491729864726037 0.2277858511416451 13 0.1420961093183820 0.3737060887154195 14 0.1316886384491766 0.5108670019508271 15 0.1181945319615184 0.6360536807265150 16 0.1019301198172404 0.7463319064601508 17 0.8327674157670475E-01 0.8391169718222188 18 0.6267204833410907E-01 0.9122344282513259 19 0.4060142980038694E-01 0.9639719272779138 20 0.1761400713915212E-01 0.9931285991850949 1 0.3073583718520532E-02 -0.9988590315882777 2 0.8600269855642943E-02 -0.9931285991850949 3 0.1462616925697125E-01 -0.9815078774502503 4 0.2038837346126652E-01 -0.9639719272779138 5 0.2588213360495116E-01 -0.9408226338317548 6 0.3128730677703280E-01 -0.9122344282513259 7 0.3660016975820080E-01 -0.8782768112522820 8 0.4166887332797369E-01 -0.8391169718222188 9 0.4643482186749767E-01 -0.7950414288375512 10 0.5094457392372869E-01 -0.7463319064601508 11 0.5519510534828599E-01 -0.6932376563347514 12 0.5911140088063957E-01 -0.6360536807265150 13 0.6265323755478117E-01 -0.5751404468197103 14 0.6583459713361842E-01 -0.5108670019508271 15 0.6864867292852161E-01 -0.4435931752387251 16 0.7105442355344407E-01 -0.3737060887154196 17 0.7303069033278667E-01 -0.3016278681149130 18 0.7458287540049920E-01 -0.2277858511416451 19 0.7570449768455667E-01 -0.1526054652409227 20 0.7637786767208074E-01 -0.7652652113349732E-01 21 0.7660071191799966E-01 0.000000000000000 22 0.7637786767208074E-01 0.7652652113349732E-01 23 0.7570449768455667E-01 0.1526054652409227 24 0.7458287540049920E-01 0.2277858511416451 25 0.7303069033278667E-01 0.3016278681149130 26 0.7105442355344407E-01 0.3737060887154196 27 0.6864867292852161E-01 0.4435931752387251 28 0.6583459713361842E-01 0.5108670019508271 29 0.6265323755478117E-01 0.5751404468197103 30 0.5911140088063957E-01 0.6360536807265150 31 0.5519510534828599E-01 0.6932376563347514 32 0.5094457392372869E-01 0.7463319064601508 33 0.4643482186749767E-01 0.7950414288375512 34 0.4166887332797369E-01 0.8391169718222188 35 0.3660016975820080E-01 0.8782768112522820 36 0.3128730677703280E-01 0.9122344282513259 37 0.2588213360495116E-01 0.9408226338317548 38 0.2038837346126652E-01 0.9639719272779138 39 0.1462616925697125E-01 0.9815078774502503 40 0.8600269855642943E-02 0.9931285991850949 41 0.3073583718520532E-02 0.9988590315882777 LAGUERRE_EK_COMPUTE_TEST LAGUERRE_EK_COMPUTE computes a Laguerre quadrature rule using the Elhay-Kautsky algorithm. Order W X 1 1.000000000000000 1.000000000000000 2 0.8535533905932737 0.5857864376269051 0.1464466094067262 3.414213562373095 3 0.7110930099291729 0.4157745567834789 0.2785177335692409 2.294280360279041 0.1038925650158615E-01 6.289945082937480 4 0.6031541043416337 0.3225476896193923 0.3574186924377999 1.745761101158346 0.3888790851500538E-01 4.536620296921128 0.5392947055613278E-03 9.395070912301136 5 0.5217556105828089 0.2635603197181410 0.3986668110831760 1.413403059106517 0.7594244968170749E-01 3.596425771040721 0.3611758679922050E-02 7.085810005858835 0.2336997238577621E-04 12.64080084427578 6 0.4589646739499636 0.2228466041792610 0.4170008307721207 1.188932101672623 0.1133733820740452 2.992736326059314 0.1039919745314908E-01 5.775143569104512 0.2610172028149323E-03 9.837467418382587 0.8985479064296196E-06 15.98287398060170 7 0.4093189517012737 0.1930436765603621 0.4218312778617199 1.026664895339191 0.1471263486575055 2.567876744950745 0.2063351446871694E-01 4.900353084526484 0.1074010143280748E-02 8.182153444562859 0.1586546434856422E-04 12.73418029179781 0.3170315478995581E-07 19.39572786226254 8 0.3691885893416376 0.1702796323051008 0.4187867808143426 0.9037017767993794 0.1757949866371721 2.251086629866129 0.3334349226121563E-01 4.266700170287657 0.2794536235225677E-02 7.045905402393464 0.9076508773358235E-04 10.75851601018099 0.8485746716272511E-06 15.74067864127800 0.1048001174871507E-08 22.86313173688927 9 0.3361264217979629 0.1523222277318080 0.4112139804239849 0.8072200227422562 0.1992875253708856 2.005135155619350 0.4746056276565148E-01 3.783473973331235 0.5599626610794589E-02 6.204956777876611 0.3052497670932110E-03 9.372985251687574 0.6592123026075368E-05 13.46623691109209 0.4110769330349564E-07 18.83359778899169 0.3290874030350713E-10 26.37407189092738 10 0.3084411157650204 0.1377934705404923 0.4011199291552736 0.7294545495031706 0.2180682876118095 1.808342901740316 0.6208745609867788E-01 3.401433697854898 0.9501516975181156E-02 5.552496140063801 0.7530083885875383E-03 8.330152746764496 0.2825923349599563E-04 11.84378583790007 0.4249313984962688E-06 16.27925783137811 0.1839564823979634E-08 21.99658581198076 0.9911827219609000E-12 29.92069701227389 LAGUERRE_INTEGRAL_TEST LAGUERRE_INTEGRAL evaluates Integral ( 0 < x < oo ) x^n * exp(-x) dx N Value 0 1.000000000000000 1 1.000000000000000 2 2.000000000000000 3 6.000000000000000 4 24.00000000000000 5 120.0000000000000 6 720.0000000000000 7 5040.000000000000 8 40320.00000000000 9 362880.0000000000 10 3628800.000000000 LAGUERRE_SET_TEST LAGUERRE_SET sets a Laguerre rule from a table. I X W 1 0.3225476896193923 0.6031541043416336 2 1.745761101158346 0.3574186924377997 3 4.536620296921128 0.3888790851500538E-01 4 9.395070912301133 0.5392947055613274E-03 1 0.1930436765603624 0.4093189517012739 2 1.026664895339192 0.4218312778617198 3 2.567876744950746 0.1471263486575053 4 4.900353084526484 0.2063351446871694E-01 5 8.182153444562861 0.1074010143280746E-02 6 12.73418029179781 0.1586546434856420E-04 7 19.39572786226254 0.3170315478995580E-07 1 0.1377934705404924 0.3084411157650201 2 0.7294545495031705 0.4011199291552736 3 1.808342901740316 0.2180682876118094 4 3.401433697854900 0.6208745609867775E-01 5 5.552496140063804 0.9501516975181101E-02 6 8.330152746764497 0.7530083885875388E-03 7 11.84378583790007 0.2825923349599566E-04 8 16.27925783137810 0.4249313984962686E-06 9 21.99658581198076 0.1839564823979631E-08 10 29.92069701227389 0.9911827219609008E-12 LAGUERRE_SS_COMPUTE_TEST LAGUERRE_SS_COMPUTE computes a Laguerre quadrature rule using the Stroud-Secrest algorithm. Order W X 1 1.000000000000000 1.000000000000000 2 0.8535533905932738 0.5857864376269050 0.1464466094067263 3.414213562373095 3 0.7110930099291736 0.4157745567834791 0.2785177335692409 2.294280360279042 0.1038925650158613E-01 6.289945082937479 4 0.6031541043416347 0.3225476896193922 0.3574186924377997 1.745761101158347 0.3888790851500539E-01 4.536620296921128 0.5392947055613274E-03 9.395070912301133 5 0.5217556105828079 0.2635603197181409 0.3986668110831759 1.413403059106517 0.7594244968170759E-01 3.596425771040722 0.3611758679922049E-02 7.085810005858837 0.2336997238577624E-04 12.64080084427578 6 0.4589646739499650 0.2228466041792606 0.4170008307721219 1.188932101672623 0.1133733820740450 2.992736326059314 0.1039919745314908E-01 5.775143569104511 0.2610172028149323E-03 9.837467418382589 0.8985479064296228E-06 15.98287398060170 7 0.4093189517012772 0.1930436765603623 0.4218312778617200 1.026664895339192 0.1471263486575052 2.567876744950746 0.2063351446871694E-01 4.900353084526484 0.1074010143280746E-02 8.182153444562861 0.1586546434856422E-04 12.73418029179781 0.3170315478995584E-07 19.39572786226254 8 0.3691885893416355 0.1702796323051010 0.4187867808143441 0.9037017767993799 0.1757949866371716 2.251086629866131 0.3334349226121566E-01 4.266700170287659 0.2794536235225670E-02 7.045905402393466 0.9076508773358207E-04 10.75851601018100 0.8485746716272540E-06 15.74067864127800 0.1048001174871508E-08 22.86313173688927 9 0.3361264217979637 0.1523222277318083 0.4112139804239832 0.8072200227422559 0.1992875253708851 2.005135155619347 0.4746056276565160E-01 3.783473973331233 0.5599626610794582E-02 6.204956777876613 0.3052497670932108E-03 9.372985251687576 0.6592123026075359E-05 13.46623691109209 0.4110769330349552E-07 18.83359778899170 0.3290874030350716E-10 26.37407189092738 10 0.3084411157650176 0.1377934705404924 0.4011199291552729 0.7294545495031703 0.2180682876118093 1.808342901740316 0.6208745609867769E-01 3.401433697854900 0.9501516975181101E-02 5.552496140063804 0.7530083885875383E-03 8.330152746764497 0.2825923349599563E-04 11.84378583790007 0.4249313984962677E-06 16.27925783137810 0.1839564823979632E-08 21.99658581198076 0.9911827219609019E-12 29.92069701227389 LAGUERRE_1_SET_TEST LAGUERRE_1_SET sets a Laguerre rule from a table. The density function is rho(x)=1. I X W 1 1.000000000000000 2.718281828459045 1 0.5857864376269050 1.533326033119417 2 3.414213562373095 4.450957335054593 1 0.4157745567834791 1.077692859270921 2 2.294280360279042 2.762142961901588 3 6.289945082937479 5.601094625434427 1 0.3225476896193923 0.8327391238378892 2 1.745761101158346 2.048102438454297 3 4.536620296921128 3.631146305821517 4 9.395070912301133 6.487145084407660 1 0.2635603197181409 0.6790940422077504 2 1.413403059106517 1.638487873602747 3 3.596425771040722 2.769443242370837 4 7.085810005858837 4.315656900920894 5 12.64080084427578 7.219186354354445 1 0.2228466041792607 0.5735355074227382 2 1.188932101672623 1.369252590712305 3 2.992736326059314 2.260684593382672 4 5.775143569104510 3.350524582355455 5 9.837467418382589 4.886826800210821 6 15.98287398060170 7.849015945595828 1 0.1930436765603624 0.4964775975399723 2 1.026664895339192 1.177643060861198 3 2.567876744950746 1.918249781659806 4 4.900353084526484 2.771848636232111 5 8.182153444562861 3.841249122488515 6 12.73418029179781 5.380678207921533 7 19.39572786226254 8.405432486828310 1 0.1702796323051010 0.4377234104929114 2 0.9037017767993799 1.033869347665598 3 2.251086629866131 1.669709765658776 4 4.266700170287659 2.376924701758599 5 7.045905402393466 3.208540913347926 6 10.75851601018100 4.268575510825134 7 15.74067864127800 5.818083368671918 8 22.86313173688927 8.906226215292222 1 0.1523222277318083 0.3914311243156399 2 0.8072200227422558 0.9218050285289631 3 2.005135155619347 1.480127909942915 4 3.783473973331233 2.086770807549261 5 6.204956777876613 2.772921389711971 6 9.372985251687576 3.591626068092266 7 13.46623691109209 4.648766002140204 8 18.83359778899170 6.212275419747135 9 26.37407189092738 9.363218237705798 1 0.1377934705404924 0.3540097386069963 2 0.7294545495031705 0.8319023010435806 3 1.808342901740316 1.330288561749328 4 3.401433697854900 1.863063903111131 5 5.552496140063804 2.450255558083011 6 8.330152746764497 3.122764155135185 7 11.84378583790007 3.934152695561524 8 16.27925783137810 4.992414872193030 9 21.99658581198076 6.572202485130799 10 29.92069701227389 9.784695840374624 LEGENDRE_DR_COMPUTE_TEST LEGENDRE_DR_COMPUTE computes a Legendre quadrature rule using the Davis-Rabinowitz algorithm. Order W X 1 2.000000000000000 0.000000000000000 2 0.9999999999999996 -0.5773502691896258 0.9999999999999996 0.5773502691896258 3 0.5555555555555558 -0.7745966692414833 0.8888888888888888 0.000000000000000 0.5555555555555558 0.7745966692414833 4 0.3478548451374538 -0.8611363115940526 0.6521451548625461 -0.3399810435848563 0.6521451548625461 0.3399810435848563 0.3478548451374538 0.8611363115940526 5 0.2369268850561891 -0.9061798459386640 0.4786286704993664 -0.5384693101056831 0.5688888888888889 0.000000000000000 0.4786286704993664 0.5384693101056831 0.2369268850561891 0.9061798459386640 6 0.1713244923791702 -0.9324695142031521 0.3607615730481386 -0.6612093864662645 0.4679139345726911 -0.2386191860831969 0.4679139345726911 0.2386191860831969 0.3607615730481386 0.6612093864662645 0.1713244923791702 0.9324695142031521 7 0.1294849661688699 -0.9491079123427585 0.2797053914892767 -0.7415311855993945 0.3818300505051190 -0.4058451513773972 0.4179591836734694 0.000000000000000 0.3818300505051190 0.4058451513773972 0.2797053914892767 0.7415311855993945 0.1294849661688699 0.9491079123427585 8 0.1012285362903763 -0.9602898564975362 0.2223810344533745 -0.7966664774136267 0.3137066458778873 -0.5255324099163290 0.3626837833783619 -0.1834346424956498 0.3626837833783619 0.1834346424956498 0.3137066458778873 0.5255324099163290 0.2223810344533745 0.7966664774136267 0.1012285362903763 0.9602898564975362 9 0.8127438836157440E-01 -0.9681602395076261 0.1806481606948574 -0.8360311073266358 0.2606106964029354 -0.6133714327005904 0.3123470770400029 -0.3242534234038089 0.3302393550012598 0.000000000000000 0.3123470770400029 0.3242534234038089 0.2606106964029354 0.6133714327005904 0.1806481606948574 0.8360311073266358 0.8127438836157440E-01 0.9681602395076261 10 0.6667134430868811E-01 -0.9739065285171717 0.1494513491505806 -0.8650633666889845 0.2190863625159821 -0.6794095682990244 0.2692667193099965 -0.4333953941292472 0.2955242247147530 -0.1488743389816312 0.2955242247147530 0.1488743389816312 0.2692667193099965 0.4333953941292472 0.2190863625159821 0.6794095682990244 0.1494513491505806 0.8650633666889845 0.6667134430868811E-01 0.9739065285171717 LEGENDRE_EK_COMPUTE_TEST LEGENDRE_EK_COMPUTE computes a Legendre quadrature rule using the Elhay-Kautsky algorithm. Order W X 1 2.000000000000000 0.000000000000000 2 1.000000000000000 -0.5773502691896256 1.000000000000000 0.5773502691896256 3 0.5555555555555556 -0.7745966692414833 0.8888888888888895 0.1994931997373328E-16 0.5555555555555554 0.7745966692414832 4 0.3478548451374547 -0.8611363115940527 0.6521451548625466 -0.3399810435848563 0.6521451548625458 0.3399810435848563 0.3478548451374541 0.8611363115940526 5 0.2369268850561892 -0.9061798459386641 0.4786286704993669 -0.5384693101056830 0.5688888888888890 -0.1081853856991421E-15 0.4786286704993672 0.5384693101056831 0.2369268850561891 0.9061798459386639 6 0.1713244923791705 -0.9324695142031522 0.3607615730481384 -0.6612093864662647 0.4679139345726904 -0.2386191860831970 0.4679139345726910 0.2386191860831969 0.3607615730481382 0.6612093864662647 0.1713244923791708 0.9324695142031522 7 0.1294849661688697 -0.9491079123427585 0.2797053914892765 -0.7415311855993943 0.3818300505051193 -0.4058451513773971 0.4179591836734696 0.2944352847269754E-15 0.3818300505051192 0.4058451513773971 0.2797053914892776 0.7415311855993943 0.1294849661688697 0.9491079123427584 8 0.1012285362903760 -0.9602898564975365 0.2223810344533743 -0.7966664774136270 0.3137066458778873 -0.5255324099163290 0.3626837833783622 -0.1834346424956498 0.3626837833783619 0.1834346424956496 0.3137066458778869 0.5255324099163292 0.2223810344533742 0.7966664774136268 0.1012285362903759 0.9602898564975364 9 0.8127438836157462E-01 -0.9681602395076260 0.1806481606948576 -0.8360311073266360 0.2606106964029357 -0.6133714327005900 0.3123470770400033 -0.3242534234038094 0.3302393550012602 -0.3649533850434330E-15 0.3123470770400024 0.3242534234038092 0.2606106964029365 0.6133714327005907 0.1806481606948582 0.8360311073266359 0.8127438836157423E-01 0.9681602395076259 10 0.6667134430868846E-01 -0.9739065285171715 0.1494513491505800 -0.8650633666889844 0.2190863625159823 -0.6794095682990244 0.2692667193099961 -0.4333953941292472 0.2955242247147523 -0.1488743389816311 0.2955242247147531 0.1488743389816314 0.2692667193099947 0.4333953941292472 0.2190863625159819 0.6794095682990243 0.1494513491505811 0.8650633666889843 0.6667134430868851E-01 0.9739065285171714 LEGENDRE_GW_COMPUTE_TEST LEGENDRE_GW_COMPUTE computes a Legendre quadrature rule using the Golub-Welsch algorithm. Order W X 1 2.000000000000000 0.000000000000000 2 1.000000000000000 -0.5773502691896258 1.000000000000000 0.5773502691896258 3 0.5555555555555555 -0.7745966692414833 0.8888888888888886 -0.2419939248987646E-15 0.5555555555555559 0.7745966692414835 4 0.3478548451374535 -0.8611363115940525 0.6521451548625462 -0.3399810435848562 0.6521451548625459 0.3399810435848566 0.3478548451374545 0.8611363115940522 5 0.2369268850561893 -0.9061798459386641 0.4786286704993667 -0.5384693101056830 0.5688888888888884 -0.7110587370961332E-16 0.4786286704993669 0.5384693101056831 0.2369268850561887 0.9061798459386641 6 0.1713244923791707 -0.9324695142031519 0.3607615730481389 -0.6612093864662643 0.4679139345726904 -0.2386191860831969 0.4679139345726914 0.2386191860831968 0.3607615730481381 0.6612093864662640 0.1713244923791704 0.9324695142031524 7 0.1294849661688694 -0.9491079123427588 0.2797053914892763 -0.7415311855993948 0.3818300505051195 -0.4058451513773974 0.4179591836734692 -0.2122665808126202E-15 0.3818300505051191 0.4058451513773976 0.2797053914892768 0.7415311855993949 0.1294849661688699 0.9491079123427587 8 0.1012285362903763 -0.9602898564975361 0.2223810344533739 -0.7966664774136270 0.3137066458778873 -0.5255324099163293 0.3626837833783622 -0.1834346424956500 0.3626837833783623 0.1834346424956503 0.3137066458778876 0.5255324099163290 0.2223810344533743 0.7966664774136270 0.1012285362903761 0.9602898564975358 9 0.8127438836157459E-01 -0.9681602395076266 0.1806481606948570 -0.8360311073266357 0.2606106964029357 -0.6133714327005901 0.3123470770400034 -0.3242534234038089 0.3302393550012587 0.3041081456750698E-15 0.3123470770400036 0.3242534234038086 0.2606106964029349 0.6133714327005905 0.1806481606948572 0.8360311073266359 0.8127438836157452E-01 0.9681602395076259 10 0.6667134430868901E-01 -0.9739065285171715 0.1494513491505802 -0.8650633666889851 0.2190863625159815 -0.6794095682990239 0.2692667193099963 -0.4333953941292467 0.2955242247147528 -0.1488743389816310 0.2955242247147532 0.1488743389816307 0.2692667193099963 0.4333953941292473 0.2190863625159818 0.6794095682990243 0.1494513491505803 0.8650633666889845 0.6667134430868851E-01 0.9739065285171715 LEGENDRE_INTEGRAL_TEST LEGENDRE_INTEGRAL evaluates Integral ( -1 < x < +1 ) x^n dx N Value 0 2.000000000000000 1 0.000000000000000 2 0.6666666666666666 3 0.000000000000000 4 0.4000000000000000 5 0.000000000000000 6 0.2857142857142857 7 0.000000000000000 8 0.2222222222222222 9 0.000000000000000 10 0.1818181818181818 LEGENDRE_SET_TEST LEGENDRE_SET sets a Legendre quadrature rule. I X W 1 0.000000000000000 2.000000000000000 1 -0.5773502691896257 1.000000000000000 2 0.5773502691896257 1.000000000000000 1 -0.7745966692414834 0.5555555555555556 2 0.000000000000000 0.8888888888888888 3 0.7745966692414834 0.5555555555555556 1 -0.8611363115940526 0.3478548451374538 2 -0.3399810435848563 0.6521451548625461 3 0.3399810435848563 0.6521451548625461 4 0.8611363115940526 0.3478548451374538 1 -0.9061798459386640 0.2369268850561891 2 -0.5384693101056831 0.4786286704993665 3 0.000000000000000 0.5688888888888889 4 0.5384693101056831 0.4786286704993665 5 0.9061798459386640 0.2369268850561891 1 -0.9324695142031521 0.1713244923791704 2 -0.6612093864662645 0.3607615730481386 3 -0.2386191860831969 0.4679139345726910 4 0.2386191860831969 0.4679139345726910 5 0.6612093864662645 0.3607615730481386 6 0.9324695142031521 0.1713244923791704 1 -0.9491079123427585 0.1294849661688697 2 -0.7415311855993945 0.2797053914892766 3 -0.4058451513773972 0.3818300505051189 4 0.000000000000000 0.4179591836734694 5 0.4058451513773972 0.3818300505051189 6 0.7415311855993945 0.2797053914892766 7 0.9491079123427585 0.1294849661688697 1 -0.9602898564975363 0.1012285362903763 2 -0.7966664774136267 0.2223810344533745 3 -0.5255324099163290 0.3137066458778873 4 -0.1834346424956498 0.3626837833783620 5 0.1834346424956498 0.3626837833783620 6 0.5255324099163290 0.3137066458778873 7 0.7966664774136267 0.2223810344533745 8 0.9602898564975363 0.1012285362903763 1 -0.9681602395076261 0.8127438836157441E-01 2 -0.8360311073266358 0.1806481606948574 3 -0.6133714327005904 0.2606106964029354 4 -0.3242534234038089 0.3123470770400029 5 0.000000000000000 0.3302393550012598 6 0.3242534234038089 0.3123470770400029 7 0.6133714327005904 0.2606106964029354 8 0.8360311073266358 0.1806481606948574 9 0.9681602395076261 0.8127438836157441E-01 1 -0.9739065285171717 0.6667134430868814E-01 2 -0.8650633666889845 0.1494513491505806 3 -0.6794095682990244 0.2190863625159820 4 -0.4333953941292472 0.2692667193099963 5 -0.1488743389816312 0.2955242247147529 6 0.1488743389816312 0.2955242247147529 7 0.4333953941292472 0.2692667193099963 8 0.6794095682990244 0.2190863625159820 9 0.8650633666889845 0.1494513491505806 10 0.9739065285171717 0.6667134430868814E-01 LEGENDRE_SS_COMPUTE_TEST LEGENDRE_SS_COMPUTE computes a Legendre quadrature rule using the Stroud-Secrest algorithm. Order W X 1 2.000000000000000 0.000000000000000 2 1.000000000000000 -0.5773502691896257 1.000000000000000 0.5773502691896257 3 0.5555555555555551 -0.7745966692414833 0.8888888888888888 0.000000000000000 0.5555555555555559 0.7745966692414834 4 0.3478548451374538 -0.8611363115940526 0.6521451548625460 -0.3399810435848563 0.6521451548625460 0.3399810435848563 0.3478548451374538 0.8611363115940526 5 0.2369268850561890 -0.9061798459386640 0.4786286704993663 -0.5384693101056831 0.5688888888888888 0.6162975822039155E-32 0.4786286704993663 0.5384693101056831 0.2369268850561890 0.9061798459386640 6 0.1713244923791686 -0.9324695142031519 0.3607615730481387 -0.6612093864662645 0.4679139345726911 -0.2386191860831969 0.4679139345726909 0.2386191860831969 0.3607615730481383 0.6612093864662645 0.1713244923791676 0.9324695142031519 7 0.1294849661688698 -0.9491079123427585 0.2797053914892751 -0.7415311855993945 0.3818300505051190 -0.4058451513773972 0.4179591836734693 0.000000000000000 0.3818300505051190 0.4058451513773972 0.2797053914892766 0.7415311855993945 0.1294849661688660 0.9491079123427585 8 0.1012285362903727 -0.9602898564975362 0.2223810344533747 -0.7966664774136267 0.3137066458778873 -0.5255324099163290 0.3626837833783619 -0.1834346424956498 0.3626837833783619 0.1834346424956498 0.3137066458778873 0.5255324099163290 0.2223810344533747 0.7966664774136267 0.1012285362903754 0.9602898564975362 9 0.8127438836157465E-01 -0.9681602395076261 0.1806481606948576 -0.8360311073266358 0.2606106964029355 -0.6133714327005904 0.3123470770400028 -0.3242534234038089 0.3302393550012597 0.000000000000000 0.3123470770400028 0.3242534234038089 0.2606106964029355 0.6133714327005904 0.1806481606948576 0.8360311073266358 0.8127438836157465E-01 0.9681602395076261 10 0.6667134430868750E-01 -0.9739065285171717 0.1494513491505805 -0.8650633666889845 0.2190863625159818 -0.6794095682990244 0.2692667193099962 -0.4333953941292472 0.2955242247147529 -0.1488743389816312 0.2955242247147528 0.1488743389816312 0.2692667193099964 0.4333953941292472 0.2190863625159818 0.6794095682990244 0.1494513491505805 0.8650633666889845 0.6667134430868750E-01 0.9739065285171717 LOBATTO_COMPUTE_TEST LOBATTO_COMPUTE computes a Lobatto rule; I X W 1 -1.00000 0.166667 2 -0.447214 0.833333 3 0.447214 0.833333 4 1.00000 0.166667 1 -1.00000 0.047619 2 -0.830224 0.276826 3 -0.468849 0.431745 4 0.00000 0.487619 5 0.468849 0.431745 6 0.830224 0.276826 7 1.00000 0.047619 1 -1.00000 0.022222 2 -0.919534 0.133306 3 -0.738774 0.224889 4 -0.477925 0.292043 5 -0.165279 0.327540 6 0.165279 0.327540 7 0.477925 0.292043 8 0.738774 0.224889 9 0.919534 0.133306 10 1.00000 0.022222 LOBATTO_SET_TEST LOBATTO_SET sets a Lobatto rule; I X W 1 -1.00000 0.166667 2 -0.447214 0.833333 3 0.447214 0.833333 4 1.00000 0.166667 1 -1.00000 0.047619 2 -0.830224 0.276826 3 -0.468849 0.431745 4 0.00000 0.487619 5 0.468849 0.431745 6 0.830224 0.276826 7 1.00000 0.047619 1 -1.00000 0.022222 2 -0.919534 0.133306 3 -0.738774 0.224889 4 -0.477925 0.292043 5 -0.165279 0.327540 6 0.165279 0.327540 7 0.477925 0.292043 8 0.738774 0.224889 9 0.919534 0.133306 10 1.00000 0.022222 NC_COMPUTE_WEIGHTS_TEST NC_COMPUTE_WEIGHTS computes weights for a closed Newton-Cotes rule; Index X W 1 0.5000000000000000 1.000000000000000 1 0.000000000000000 0.5000000000000000 2 1.000000000000000 0.5000000000000000 1 0.000000000000000 0.1666666666666666 2 0.5000000000000000 0.6666666666666667 3 1.000000000000000 0.1666666666666666 1 0.000000000000000 0.1250000000000000 2 0.3333333333333333 0.3750000000000000 3 0.6666666666666666 0.3750000000000000 4 1.000000000000000 0.1250000000000003 1 0.000000000000000 0.7777777777777839E-01 2 0.2500000000000000 0.3555555555555561 3 0.5000000000000000 0.1333333333333329 4 0.7500000000000000 0.3555555555555583 5 1.000000000000000 0.7777777777777795E-01 1 0.000000000000000 0.6597222222221788E-01 2 0.2000000000000000 0.2604166666666643 3 0.4000000000000000 0.1736111111111285 4 0.6000000000000000 0.1736111111110983 5 0.8000000000000000 0.2604166666666687 6 1.000000000000000 0.6597222222222110E-01 1 0.000000000000000 0.4880952380951875E-01 2 0.1666666666666667 0.2571428571428811 3 0.3333333333333333 0.3214285714284415E-01 4 0.5000000000000000 0.3238095238095013 5 0.6666666666666666 0.3214285714278731E-01 6 0.8333333333333334 0.2571428571428838 7 1.000000000000000 0.4880952380952142E-01 1 0.000000000000000 0.4346064814816586E-01 2 0.1428571428571428 0.2070023148149858 3 0.2857142857142857 0.7656250000019327E-01 4 0.4285714285714285 0.1729745370369784 5 0.5714285714285714 0.1729745370371489 6 0.7142857142857143 0.7656250000005294E-01 7 0.8571428571428571 0.2070023148148872 8 1.000000000000000 0.4346064814818240E-01 1 0.000000000000000 0.3488536155206035E-01 2 0.1250000000000000 0.2076895943561112 3 0.2500000000000000 -0.3273368606834737E-01 4 0.3750000000000000 0.3702292769000053 5 0.5000000000000000 -0.1601410934754171 6 0.6250000000000000 0.3702292769009290 7 0.7500000000000000 -0.3273368606535598E-01 8 0.8750000000000000 0.2076895943557870 9 1.000000000000000 0.3488536155198840E-01 1 0.000000000000000 0.3188616071413897E-01 2 0.1111111111111111 0.1756808035706854 3 0.2222222222222222 0.1205357144226582E-01 4 0.3333333333333333 0.2158928571161596 5 0.4444444444444444 0.6448660712112542E-01 6 0.5555555555555556 0.6448660717715882E-01 7 0.6666666666666666 0.2158928571597940 8 0.7777777777777778 0.1205357143547303E-01 9 0.8888888888888888 0.1756808035724458 10 1.000000000000000 0.3188616071432337E-01 NCC_COMPUTE_TEST NCC_COMPUTE computes a closed Newton-Cotes rule; Index X W 1 0.000000000000000 2.000000000000000 1 -1.000000000000000 1.000000000000000 2 1.000000000000000 1.000000000000000 1 -1.000000000000000 0.3333333333333333 2 0.000000000000000 1.333333333333333 3 1.000000000000000 0.3333333333333333 1 -1.000000000000000 0.2500000000000004 2 -0.3333333333333333 0.7499999999999996 3 0.3333333333333333 0.7500000000000000 4 1.000000000000000 0.2500000000000000 1 -1.000000000000000 0.1555555555555557 2 -0.5000000000000000 0.7111111111111110 3 0.000000000000000 0.2666666666666666 4 0.5000000000000000 0.7111111111111110 5 1.000000000000000 0.1555555555555556 1 -1.000000000000000 0.1319444444444441 2 -0.6000000000000000 0.5208333333333339 3 -0.2000000000000000 0.3472222222222229 4 0.2000000000000000 0.3472222222222210 5 0.6000000000000000 0.5208333333333326 6 1.000000000000000 0.1319444444444444 1 -1.000000000000000 0.9761904761904808E-01 2 -0.6666666666666666 0.5142857142857133 3 -0.3333333333333333 0.6428571428570932E-01 4 0.000000000000000 0.6476190476190524 5 0.3333333333333333 0.6428571428571317E-01 6 0.6666666666666666 0.5142857142857140 7 1.000000000000000 0.9761904761904755E-01 1 -1.000000000000000 0.8692129629629897E-01 2 -0.7142857142857143 0.4140046296296206 3 -0.4285714285714285 0.1531249999999869 4 -0.1428571428571428 0.3459490740740891 5 0.1428571428571428 0.3459490740740738 6 0.4285714285714285 0.1531250000000043 7 0.7142857142857143 0.4140046296296293 8 1.000000000000000 0.8692129629629636E-01 1 -1.000000000000000 0.6977072310405794E-01 2 -0.7500000000000000 0.4153791887125269 3 -0.5000000000000000 -0.6546737213403930E-01 4 -0.2500000000000000 0.7404585537919086 5 0.000000000000000 -0.3202821869488677 6 0.2500000000000000 0.7404585537918660 7 0.5000000000000000 -0.6546737213403930E-01 8 0.7500000000000000 0.4153791887125232 9 1.000000000000000 0.6977072310405667E-01 1 -1.000000000000000 0.6377232142857905E-01 2 -0.7777777777777778 0.3513616071428758 3 -0.5555555555555556 0.2410714285722957E-01 4 -0.3333333333333333 0.4317857142858179 5 -0.1111111111111111 0.1289732142857689 6 0.1111111111111111 0.1289732142858637 7 0.3333333333333333 0.4317857142856988 8 0.5555555555555556 0.2410714285714771E-01 9 0.7777777777777778 0.3513616071428603 10 1.000000000000000 0.6377232142857162E-01 NCC_SET_TEST NCC_SET sets up a closed Newton-Cotes rule; Index X W 1 0.000000000000000 2.000000000000000 1 -1.000000000000000 1.000000000000000 2 1.000000000000000 1.000000000000000 1 -1.000000000000000 0.3333333333333333 2 0.000000000000000 1.333333333333333 3 1.000000000000000 0.3333333333333333 1 -1.000000000000000 0.2500000000000000 2 -0.3333333333333333 0.7500000000000000 3 0.3333333333333333 0.7500000000000000 4 1.000000000000000 0.2500000000000000 1 -1.000000000000000 0.1555555555555556 2 -0.5000000000000000 0.7111111111111111 3 0.000000000000000 0.2666666666666667 4 0.5000000000000000 0.7111111111111111 5 1.000000000000000 0.1555555555555556 1 -1.000000000000000 0.1319444444444444 2 -0.6000000000000000 0.5208333333333334 3 -0.2000000000000000 0.3472222222222222 4 0.2000000000000000 0.3472222222222222 5 0.6000000000000000 0.5208333333333334 6 1.000000000000000 0.1319444444444444 1 -1.000000000000000 0.9761904761904762E-01 2 -0.6666666666666666 0.5142857142857142 3 -0.3333333333333333 0.6428571428571428E-01 4 0.000000000000000 0.6476190476190476 5 0.3333333333333333 0.6428571428571428E-01 6 0.6666666666666666 0.5142857142857142 7 1.000000000000000 0.9761904761904762E-01 1 -1.000000000000000 0.8692129629629630E-01 2 -0.7142857142857143 0.4140046296296296 3 -0.4285714285714285 0.1531250000000000 4 -0.1428571428571428 0.3459490740740740 5 0.1428571428571428 0.3459490740740740 6 0.4285714285714285 0.1531250000000000 7 0.7142857142857143 0.4140046296296296 8 1.000000000000000 0.8692129629629630E-01 1 -1.000000000000000 0.6977072310405644E-01 2 -0.7500000000000000 0.4153791887125221 3 -0.5000000000000000 -0.6546737213403880E-01 4 -0.2500000000000000 0.7404585537918871 5 0.000000000000000 -0.3202821869488536 6 0.2500000000000000 0.7404585537918871 7 0.5000000000000000 -0.6546737213403880E-01 8 0.7500000000000000 0.4153791887125221 9 1.000000000000000 0.6977072310405644E-01 1 -1.000000000000000 0.6377232142857144E-01 2 -0.7777777777777778 0.3513616071428571 3 -0.5555555555555556 0.2410714285714286E-01 4 -0.3333333333333333 0.4317857142857143 5 -0.1111111111111111 0.1289732142857143 6 0.1111111111111111 0.1289732142857143 7 0.3333333333333333 0.4317857142857143 8 0.5555555555555556 0.2410714285714286E-01 9 0.7777777777777778 0.3513616071428571 10 1.000000000000000 0.6377232142857144E-01 NCO_COMPUTE_TEST NCO_COMPUTE computes an open Newton-Cotes rule; Index X W 1 0.000000000000000 2.000000000000000 1 -0.3333333333333333 1.000000000000000 2 0.3333333333333333 1.000000000000000 1 -0.5000000000000000 1.333333333333333 2 0.000000000000000 -0.6666666666666665 3 0.5000000000000000 1.333333333333333 1 -0.6000000000000000 0.9166666666666664 2 -0.2000000000000000 0.8333333333333304E-01 3 0.2000000000000000 0.8333333333333304E-01 4 0.6000000000000000 0.9166666666666667 1 -0.6666666666666666 1.100000000000000 2 -0.3333333333333333 -1.400000000000000 3 0.000000000000000 2.600000000000000 4 0.3333333333333333 -1.400000000000000 5 0.6666666666666666 1.100000000000000 1 -0.7142857142857143 0.8486111111111118 2 -0.4285714285714285 -0.6291666666666692 3 -0.1428571428571428 0.7805555555555526 4 0.1428571428571428 0.7805555555555541 5 0.4285714285714285 -0.6291666666666685 6 0.7142857142857143 0.8486111111111114 1 -0.7500000000000000 0.9735449735449742 2 -0.5000000000000000 -2.019047619047615 3 -0.2500000000000000 4.647619047619042 4 0.000000000000000 -5.204232804232804 5 0.2500000000000000 4.647619047619049 6 0.5000000000000000 -2.019047619047616 7 0.7500000000000000 0.9735449735449739 1 -0.7777777777777778 0.7977678571428612 2 -0.5555555555555556 -1.251339285714294 3 -0.3333333333333333 2.217410714285680 4 -0.1111111111111111 -0.7638392857142238 5 0.1111111111111111 -0.7638392857143050 6 0.3333333333333333 2.217410714285695 7 0.5555555555555556 -1.251339285714285 8 0.7777777777777778 0.7977678571428563 1 -0.8000000000000000 0.8917548500881828 2 -0.6000000000000000 -2.577160493827184 3 -0.4000000000000000 7.350088183421553 4 -0.2000000000000000 -12.14065255731907 5 0.000000000000000 14.95194003527322 6 0.2000000000000000 -12.14065255731914 7 0.4000000000000000 7.350088183421514 8 0.6000000000000000 -2.577160493827156 9 0.8000000000000000 0.8917548500881831 1 -0.8181818181818182 0.7585088734567924 2 -0.6363636363636364 -1.819664627425049 3 -0.4545454545454545 4.319301146384676 4 -0.2727272727272727 -4.708337742504753 5 -0.9090909090909091E-01 2.450192350088813 6 0.9090909090909091E-01 2.450192350087711 7 0.2727272727272727 -4.708337742504625 8 0.4545454545454545 4.319301146384526 9 0.6363636363636364 -1.819664627425028 10 0.8181818181818182 0.7585088734567896 NCO_SET_TEST NCO_SET sets up an open Newton-Cotes rule; Index X W 1 0.000000000000000 2.000000000000000 1 -0.3333333333333333 1.000000000000000 2 0.3333333333333333 1.000000000000000 1 -0.5000000000000000 1.333333333333333 2 0.000000000000000 -0.6666666666666666 3 0.5000000000000000 1.333333333333333 1 -0.6000000000000000 0.9166666666666666 2 -0.2000000000000000 0.8333333333333333E-01 3 0.2000000000000000 0.8333333333333333E-01 4 0.6000000000000000 0.9166666666666666 1 -0.6666666666666666 1.100000000000000 2 -0.3333333333333333 -1.400000000000000 3 0.000000000000000 2.600000000000000 4 0.3333333333333333 -1.400000000000000 5 0.6666666666666666 1.100000000000000 1 -0.7142857142857143 0.8486111111111111 2 -0.4285714285714285 -0.6291666666666667 3 -0.1428571428571428 0.7805555555555556 4 0.1428571428571428 0.7805555555555556 5 0.4285714285714285 -0.6291666666666667 6 0.7142857142857143 0.8486111111111111 1 -0.7500000000000000 0.9735449735449735 2 -0.5000000000000000 -2.019047619047619 3 -0.2500000000000000 4.647619047619048 4 0.000000000000000 -5.204232804232804 5 0.2500000000000000 4.647619047619048 6 0.5000000000000000 -2.019047619047619 7 0.7500000000000000 0.9735449735449735 1 -0.7777777777777778 0.7977678571428571 2 -0.5555555555555556 -1.251339285714286 3 -0.3333333333333333 2.217410714285714 4 -0.1111111111111111 -0.7638392857142857 5 0.1111111111111111 -0.7638392857142857 6 0.3333333333333333 2.217410714285714 7 0.5555555555555556 -1.251339285714286 8 0.7777777777777778 0.7977678571428571 1 -0.8000000000000000 0.8917548500881834 2 -0.6000000000000000 -2.577160493827161 3 -0.4000000000000000 7.350088183421517 4 -0.2000000000000000 -12.14065255731922 5 0.000000000000000 14.95194003527337 6 0.2000000000000000 -12.14065255731922 7 0.4000000000000000 7.350088183421517 8 0.6000000000000000 -2.577160493827161 9 0.8000000000000000 0.8917548500881834 1 -0.8181818181818182 0.7585088734567920 2 -0.6363636363636364 -1.819664627425049 3 -0.4545454545454545 4.319301146384676 4 -0.2727272727272727 -4.708337742504753 5 -0.9090909090909091E-01 2.450192350088813 6 0.9090909090909091E-01 2.450192350087711 7 0.2727272727272727 -4.708337742504625 8 0.4545454545454545 4.319301146384526 9 0.6363636363636364 -1.819664627425028 10 0.8181818181818182 0.7585088734567900 NCOH_COMPUTE_TEST NCOH_COMPUTE computes an open half Newton-Cotes rule; Index X W 1 0.000000000000000 2.000000000000000 1 -0.5000000000000000 1.000000000000000 2 0.5000000000000000 1.000000000000000 1 -0.6666666666666666 0.7500000000000000 2 0.000000000000000 0.5000000000000000 3 0.6666666666666666 0.7500000000000000 1 -0.7500000000000000 0.5416666666666666 2 -0.2500000000000000 0.4583333333333335 3 0.2500000000000000 0.4583333333333335 4 0.7500000000000000 0.5416666666666666 1 -0.8000000000000000 0.4774305555555558 2 -0.4000000000000000 0.1736111111111107 3 0.000000000000000 0.6979166666666670 4 0.4000000000000000 0.1736111111111112 5 0.8000000000000000 0.4774305555555554 1 -0.8333333333333334 0.3859375000000000 2 -0.5000000000000000 0.2171874999999994 3 -0.1666666666666667 0.3968749999999941 4 0.1666666666666667 0.3968750000000001 5 0.5000000000000000 0.2171875000000004 6 0.8333333333333334 0.3859374999999999 1 -0.8571428571428571 0.3580005787037045 2 -0.5714285714285714 0.1276041666666250E-01 3 -0.2857142857142857 0.8102864583333247 4 0.000000000000000 -0.3620949074074109 5 0.2857142857142857 0.8102864583333318 6 0.5714285714285714 0.1276041666666561E-01 7 0.8571428571428571 0.3580005787037041 1 -0.8750000000000000 0.3055007853835972 2 -0.6250000000000000 0.7371135085978964E-01 3 -0.3750000000000000 0.4875279017857209 4 -0.1250000000000000 0.1332599619708654 5 0.1250000000000000 0.1332599619709007 6 0.3750000000000000 0.4875279017856960 7 0.6250000000000000 0.7371135085978775E-01 8 0.8750000000000000 0.3055007853835978 1 -0.8888888888888888 0.2902556501116099 2 -0.6666666666666666 -0.9096261160714961E-01 3 -0.4444444444444444 1.012537667410742 4 -0.2222222222222222 -1.125577566964330 5 0.000000000000000 1.827493722098140 6 0.2222222222222222 -1.125577566964292 7 0.4444444444444444 1.012537667410705 8 0.6666666666666666 -0.9096261160714395E-01 9 0.8888888888888888 0.2902556501116076 1 -0.9000000000000000 0.2557278856819025 2 -0.7000000000000000 -0.2652149772308931E-01 3 -0.5000000000000000 0.6604044811645895 4 -0.3000000000000000 -0.3376966473075349 5 -0.1000000000000000 0.4480857781842378 6 0.1000000000000000 0.4480857781845167 7 0.3000000000000000 -0.3376966473076202 8 0.5000000000000000 0.6604044811646075 9 0.7000000000000000 -0.2652149772306411E-01 10 0.9000000000000000 0.2557278856819051 NCOH_SET_TEST NCOH_SET sets up an open half Newton-Cotes rule; Index X W 1 0.000000000000000 2.000000000000000 1 -0.5000000000000000 1.000000000000000 2 0.5000000000000000 1.000000000000000 1 -0.6666666666666666 0.7500000000000000 2 0.000000000000000 0.5000000000000000 3 0.6666666666666666 0.7500000000000000 1 -0.7500000000000000 0.5416666666666666 2 -0.2500000000000000 0.4583333333333333 3 0.2500000000000000 0.4583333333333333 4 0.7500000000000000 0.5416666666666666 1 -0.8000000000000000 0.4774305555555556 2 -0.4000000000000000 0.1736111111111111 3 0.000000000000000 0.6979166666666666 4 0.4000000000000000 0.1736111111111111 5 0.8000000000000000 0.4774305555555556 1 -0.8333333333333334 0.3859375000000000 2 -0.5000000000000000 0.2171875000000000 3 -0.1666666666666667 0.3968750000000000 4 0.1666666666666667 0.3968750000000000 5 0.5000000000000000 0.2171875000000000 6 0.8333333333333334 0.3859375000000000 1 -0.8571428571428571 0.3580005787037037 2 -0.5714285714285714 0.1276041666666667E-01 3 -0.2857142857142857 0.8102864583333333 4 0.000000000000000 -0.3620949074074074 5 0.2857142857142857 0.8102864583333333 6 0.5714285714285714 0.1276041666666667E-01 7 0.8571428571428571 0.3580005787037037 1 -0.8750000000000000 0.3055007853835979 2 -0.6250000000000000 0.7371135085978836E-01 3 -0.3750000000000000 0.4875279017857143 4 -0.1250000000000000 0.1332599619708995 5 0.1250000000000000 0.1332599619708995 6 0.3750000000000000 0.4875279017857143 7 0.6250000000000000 0.7371135085978836E-01 8 0.8750000000000000 0.3055007853835979 1 -0.8888888888888888 0.2902556501116071 2 -0.6666666666666666 -0.9096261160714286E-01 3 -0.4444444444444444 1.012537667410714 4 -0.2222222222222222 -1.125577566964286 5 0.000000000000000 1.827493722098214 6 0.2222222222222222 -1.125577566964286 7 0.4444444444444444 1.012537667410714 8 0.6666666666666666 -0.9096261160714286E-01 9 0.8888888888888888 0.2902556501116071 1 -0.9000000000000000 0.2557278856819059 2 -0.7000000000000000 -0.2652149772307650E-01 3 -0.5000000000000000 0.6604044811645723 4 -0.3000000000000000 -0.3376966473076499 5 -0.1000000000000000 0.4480857781842482 6 0.1000000000000000 0.4480857781842482 7 0.3000000000000000 -0.3376966473076499 8 0.5000000000000000 0.6604044811645723 9 0.7000000000000000 -0.2652149772307650E-01 10 0.9000000000000000 0.2557278856819059 PATTERSON_SET_TEST PATTERSON_SET sets up a Patterson quadrature rule; Index X W 1 0.000000000000000 2.000000000000000 1 -0.7745966692414834 0.5555555555555556 2 0.000000000000000 0.8888888888888888 3 0.7745966692414834 0.5555555555555556 1 -0.9604912687080203 0.1046562260264673 2 -0.7745966692414834 0.2684880898683334 3 -0.4342437493468025 0.4013974147759622 4 0.000000000000000 0.4509165386584741 5 0.4342437493468025 0.4013974147759622 6 0.7745966692414834 0.2684880898683334 7 0.9604912687080203 0.1046562260264673 1 -0.9938319632127550 0.1700171962994026E-01 2 -0.9604912687080203 0.5160328299707974E-01 3 -0.8884592328722570 0.9292719531512454E-01 4 -0.7745966692414834 0.1344152552437842 5 -0.6211029467372264 0.1715119091363914 6 -0.4342437493468025 0.2006285293769890 7 -0.2233866864289669 0.2191568584015875 8 0.000000000000000 0.2255104997982067 9 0.2233866864289669 0.2191568584015875 10 0.4342437493468025 0.2006285293769890 11 0.6211029467372264 0.1715119091363914 12 0.7745966692414834 0.1344152552437842 13 0.8884592328722570 0.9292719531512454E-01 14 0.9604912687080203 0.5160328299707974E-01 15 0.9938319632127550 0.1700171962994026E-01 R8_PSI_TEST: R8_PSI evaluates the Psi function. X Psi(X) Psi(X) DIFF (Tabulated) (R8_PSI) 1.0000 -0.5772156649015329 -0.5772156649015329 0.000 1.1000 -0.4237549404110768 -0.4237549404110768 0.5551E-16 1.2000 -0.2890398965921883 -0.2890398965921884 0.5551E-16 1.3000 -0.1691908888667997 -0.1691908888667995 0.1665E-15 1.4000 -0.6138454458511615E-01 -0.6138454458511624E-01 0.9021E-16 1.5000 0.3648997397857652E-01 0.3648997397857652E-01 0.000 1.6000 0.1260474527734763 0.1260474527734763 0.2776E-16 1.7000 0.2085478748734940 0.2085478748734940 0.2776E-16 1.8000 0.2849914332938615 0.2849914332938615 0.000 1.9000 0.3561841611640597 0.3561841611640596 0.1110E-15 2.0000 0.4227843350984671 0.4227843350984672 0.1110E-15 RADAU_COMPUTE_TEST RADAU_COMPUTE computes a Radau rule; I X W 1 -1.00000 0.125000 2 -0.575319 0.657689 3 0.181066 0.776387 4 0.822824 0.440924 1 -1.00000 0.040816 2 -0.853891 0.239227 3 -0.538468 0.380950 4 -0.117343 0.447110 5 0.326031 0.424704 6 0.703843 0.318204 7 0.941367 0.148988 1 -1.00000 0.020000 2 -0.927484 0.120297 3 -0.763842 0.204270 4 -0.525646 0.268195 5 -0.236234 0.305859 6 0.760592E-01 0.313582 7 0.380665 0.290610 8 0.647767 0.239193 9 0.851225 0.164376 10 0.971175 0.073617 RADAU_SET_TEST RADAU_SET sets a Radau rule from a table. I X W 1 -1.00000 0.125000 2 -0.575319 0.657689 3 0.181066 0.776387 4 0.822824 0.440924 1 -1.00000 0.040816 2 -0.853891 0.239227 3 -0.538468 0.380950 4 -0.117343 0.447110 5 0.326031 0.424704 6 0.703843 0.318204 7 0.941367 0.148988 1 -1.00000 0.020000 2 -0.927484 0.120297 3 -0.763842 0.204270 4 -0.525646 0.268195 5 -0.236234 0.305859 6 0.760592E-01 0.313582 7 0.380665 0.290610 8 0.647767 0.239193 9 0.851225 0.164376 10 0.971175 0.073617 QUADRULE_PRB Normal end of execution. 19 November 2015 12:31:04.691 PM