02-Mar-2019 10:00:14 quadrule_test MATLAB version Test quadrule. CHEBYSHEV_SET_TEST CHEBYSHEV_SET sets a Chebyshev quadrature rule over [-1,1] Index X W 1 0 2 1 -0.5773502691896258 1 2 0.5773502691896258 1 1 -0.7071067811865475 0.6666666666666666 2 0 0.6666666666666666 3 0.7071067811865475 0.6666666666666666 1 -0.7946544722917661 0.5 2 -0.1875924740850799 0.5 3 0.1875924740850799 0.5 4 0.7946544722917661 0.5 1 -0.8324974870009819 0.4 2 -0.3745414095535811 0.4 3 0 0.4 4 0.3745414095535811 0.4 5 0.8324974870009819 0.4 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 -0.883861700758049 0.2857142857142857 2 -0.5296567752851569 0.2857142857142857 3 -0.3239118105199076 0.2857142857142857 4 0 0.2857142857142857 5 0.3239118105199076 0.2857142857142857 6 0.5296567752851569 0.2857142857142857 7 0.883861700758049 0.2857142857142857 1 -0.9115893077284345 0.2222222222222222 2 -0.601018655380238 0.2222222222222222 3 -0.52876178305788 0.2222222222222222 4 -0.1679061842148039 0.2222222222222222 5 0 0.2222222222222222 6 0.1679061842148039 0.2222222222222222 7 0.52876178305788 0.2222222222222222 8 0.601018655380238 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 6.123233995736766e-17 3.141592653589793 1 -0.7071067811865475 1.570796326794897 2 0.7071067811865476 1.570796326794897 1 -0.8660254037844387 1.047197551196598 2 6.123233995736766e-17 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 -0.587785252292473 0.6283185307179586 3 6.123233995736766e-17 0.6283185307179586 4 0.5877852522924732 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 6.123233995736766e-17 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 -0.555570233019602 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 -0.9848077530122081 0.3490658503988659 2 -0.8660254037844385 0.3490658503988659 3 -0.6427876096865393 0.3490658503988659 4 -0.3420201433256685 0.3490658503988659 5 6.123233995736766e-17 0.3490658503988659 6 0.3420201433256688 0.3490658503988659 7 0.6427876096865394 0.3490658503988659 8 0.8660254037844387 0.3490658503988659 9 0.984807753012208 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*x) dx N Value 0 3.141592653589793 1 0 2 1.570796326794897 3 0 4 1.178097245096172 5 0 6 0.9817477042468102 7 0 8 0.8590292412159591 9 0 10 0.7731263170943631 CHEBYSHEV1_SET_TEST CHEBYSHEV1_SET sets a Chebyshev Type 1 quadrature rule over [-1,1] Index X W 1 0 3.141592653589793 1 -0.7071067811865475 1.570796326794897 2 0.7071067811865476 1.570796326794897 1 -0.8660254037844387 1.047197551196598 2 0 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 -0.587785252292473 0.6283185307179586 3 0 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 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 -0.555570233019602 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 -0.984807753012208 0.3490658503988659 2 -0.8660254037844385 0.3490658503988659 3 -0.6427876096865394 0.3490658503988659 4 -0.3420201433256685 0.3490658503988659 5 0 0.3490658503988659 6 0.3420201433256688 0.3490658503988659 7 0.6427876096865394 0.3490658503988659 8 0.8660254037844387 0.3490658503988659 9 0.984807753012208 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 Chebyshev Type 2 quadrature rule over [-1,1] Index X W 1 6.123233995736766e-17 1.570796326794897 1 -0.4999999999999998 0.7853981633974486 2 0.5000000000000001 0.7853981633974481 1 -0.7071067811865475 0.3926990816987243 2 6.123233995736766e-17 0.7853981633974483 3 0.7071067811865476 0.392699081698724 1 -0.8090169943749473 0.2170787134227061 2 -0.3090169943749473 0.5683194499747424 3 0.3090169943749475 0.5683194499747423 4 0.8090169943749475 0.217078713422706 1 -0.8660254037844387 0.1308996938995747 2 -0.4999999999999998 0.3926990816987243 3 6.123233995736766e-17 0.5235987755982988 4 0.5000000000000001 0.392699081698724 5 0.8660254037844387 0.1308996938995747 1 -0.900968867902419 0.08448869089158863 2 -0.6234898018587334 0.2743330560697779 3 -0.2225209339563143 0.4265764164360819 4 0.2225209339563144 0.4265764164360819 5 0.6234898018587336 0.2743330560697778 6 0.9009688679024191 0.08448869089158857 1 -0.9238795325112867 0.05750944903191315 2 -0.7071067811865475 0.1963495408493621 3 -0.3826834323650897 0.335189632666811 4 6.123233995736766e-17 0.3926990816987241 5 0.3826834323650898 0.335189632666811 6 0.7071067811865476 0.196349540849362 7 0.9238795325112867 0.05750944903191313 1 -0.9396926207859083 0.04083294770910712 2 -0.7660444431189779 0.1442256007956728 3 -0.4999999999999998 0.2617993877991495 4 -0.1736481776669303 0.338540227093519 5 0.1736481776669304 0.338540227093519 6 0.5000000000000001 0.2617993877991494 7 0.7660444431189781 0.1442256007956727 8 0.9396926207859084 0.04083294770910708 1 -0.9510565162951535 0.02999954037160818 2 -0.8090169943749473 0.108539356711353 3 -0.587785252292473 0.2056199086476263 4 -0.3090169943749473 0.2841597249873712 5 6.123233995736766e-17 0.3141592653589793 6 0.3090169943749475 0.2841597249873711 7 0.5877852522924732 0.2056199086476263 8 0.8090169943749475 0.108539356711353 9 0.9510565162951535 0.02999954037160816 1 -0.9594929736144974 0.02266894250185883 2 -0.8412535328311811 0.08347854093418908 3 -0.654860733945285 0.1631221774548167 4 -0.4154150130018863 0.2363135602034873 5 -0.142314838273285 0.2798149423030966 6 0.1423148382732851 0.2798149423030965 7 0.4154150130018864 0.2363135602034873 8 0.6548607339452852 0.1631221774548166 9 0.8412535328311812 0.08347854093418902 10 0.9594929736144974 0.02266894250185884 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 1.5708 1.5708 2.22045e-16 x 10 0 -4.16334e-17 4.16334e-17 y 10 0.666667 0.666723 5.65402e-05 x^2 10 0.392699 0.392699 5.55112e-17 x y 10 0 -3.1225e-17 3.1225e-17 y^2 10 0.392699 0.392699 0 x^3 10 0 2.77556e-17 2.77556e-17 x^2y 10 0.133333 0.133392 5.88566e-05 x y^2 10 0 -1.50343e-17 1.50343e-17 y^3 10 0.266667 0.266666 1.15821e-06 x^4 10 0.19635 0.19635 2.77556e-17 x^2y^2 10 0.0654498 0.0654498 1.38778e-17 y^4 10 0.19635 0.19635 5.55112e-17 x^4y 10 0.0571429 0.0572043 6.13939e-05 x^2y^3 10 0.0380952 0.038094 1.26862e-06 y^5 10 0.152381 0.152381 7.361e-08 x^6 10 0.122718 0.122718 0 x^4y^2 10 0.0245437 0.0245437 3.46945e-18 x^2y^4 10 0.0245437 0.0245437 3.46945e-18 y^6 10 0.122718 0.122718 1.38778e-17 CHEBYSHEV2_INTEGRAL_TEST CHEBYSHEV2_INTEGRAL evaluates Integral ( -1 < x < +1 ) x^n * sqrt(1-x*x) dx N Value 0 1.570796326794897 1 0 2 0.3926990816987241 3 0 4 0.1963495408493621 5 0 6 0.1227184630308513 7 0 8 0.08590292412159591 9 0 10 0.06442719309119692 CHEBYSHEV2_SET_TEST CHEBYSHEV2_SET sets a Chebyshev Type 2 quadrature rule over [-1,1] Index X W 1 0 1.570796326794897 1 -0.5 0.7853981633974484 2 0.5 0.7853981633974481 1 -0.7071067811865475 0.3926990816987243 2 0 0.7853981633974483 3 0.7071067811865476 0.392699081698724 1 -0.8090169943749473 0.2170787134227061 2 -0.3090169943749473 0.5683194499747424 3 0.3090169943749475 0.5683194499747423 4 0.8090169943749475 0.217078713422706 1 -0.8660254037844387 0.1308996938995747 2 -0.5 0.3926990816987242 3 0 0.5235987755982988 4 0.5 0.392699081698724 5 0.8660254037844387 0.1308996938995747 1 -0.900968867902419 0.08448869089158863 2 -0.6234898018587335 0.2743330560697779 3 -0.2225209339563143 0.4265764164360819 4 0.2225209339563144 0.4265764164360819 5 0.6234898018587336 0.2743330560697778 6 0.9009688679024191 0.08448869089158857 1 -0.9238795325112867 0.05750944903191316 2 -0.7071067811865475 0.1963495408493621 3 -0.3826834323650897 0.335189632666811 4 0 0.3926990816987241 5 0.3826834323650898 0.335189632666811 6 0.7071067811865476 0.196349540849362 7 0.9238795325112867 0.05750944903191313 1 -0.9396926207859083 0.04083294770910712 2 -0.7660444431189779 0.1442256007956728 3 -0.5 0.2617993877991495 4 -0.1736481776669303 0.338540227093519 5 0.1736481776669304 0.338540227093519 6 0.5 0.2617993877991494 7 0.766044443118978 0.1442256007956727 8 0.9396926207859084 0.04083294770910708 1 -0.9510565162951535 0.02999954037160818 2 -0.8090169943749473 0.108539356711353 3 -0.587785252292473 0.2056199086476263 4 -0.3090169943749473 0.2841597249873712 5 0 0.3141592653589793 6 0.3090169943749475 0.2841597249873711 7 0.5877852522924731 0.2056199086476263 8 0.8090169943749475 0.108539356711353 9 0.9510565162951535 0.02999954037160816 1 -0.9594929736144974 0.02266894250185884 2 -0.8412535328311811 0.08347854093418908 3 -0.654860733945285 0.1631221774548166 4 -0.4154150130018863 0.2363135602034873 5 -0.142314838273285 0.2798149423030966 6 0.1423148382732851 0.2798149423030965 7 0.4154150130018864 0.2363135602034873 8 0.6548607339452851 0.1631221774548166 9 0.8412535328311812 0.08347854093418902 10 0.9594929736144974 0.02266894250185884 CHEBYSHEV3_COMPUTE_TEST CHEBYSHEV3_COMPUTE computes a Chebyshev Type 3 quadrature rule over [-1,1] Index X W 1 0 3.141592653589793 1 1 1.570796326794897 2 -1 1.570796326794897 1 1 0.7853981633974483 2 6.123233995736766e-17 1.570796326794897 3 -1 0.7853981633974483 1 1 0.5235987755982988 2 0.5000000000000001 1.047197551196598 3 -0.4999999999999998 1.047197551196598 4 -1 0.5235987755982988 1 1 0.3926990816987241 2 0.7071067811865476 0.7853981633974483 3 6.123233995736766e-17 0.7853981633974483 4 -0.7071067811865475 0.7853981633974483 5 -1 0.3926990816987241 1 1 0.3141592653589793 2 0.8090169943749475 0.6283185307179586 3 0.3090169943749475 0.6283185307179586 4 -0.3090169943749473 0.6283185307179586 5 -0.8090169943749473 0.6283185307179586 6 -1 0.3141592653589793 1 1 0.2617993877991494 2 0.8660254037844387 0.5235987755982988 3 0.5000000000000001 0.5235987755982988 4 6.123233995736766e-17 0.5235987755982988 5 -0.4999999999999998 0.5235987755982988 6 -0.8660254037844387 0.5235987755982988 7 -1 0.2617993877991494 1 1 0.2243994752564138 2 0.9009688679024191 0.4487989505128276 3 0.6234898018587336 0.4487989505128276 4 0.2225209339563144 0.4487989505128276 5 -0.2225209339563143 0.4487989505128276 6 -0.6234898018587334 0.4487989505128276 7 -0.900968867902419 0.4487989505128276 8 -1 0.2243994752564138 1 1 0.1963495408493621 2 0.9238795325112867 0.3926990816987241 3 0.7071067811865476 0.3926990816987241 4 0.3826834323650898 0.3926990816987241 5 6.123233995736766e-17 0.3926990816987241 6 -0.3826834323650897 0.3926990816987241 7 -0.7071067811865475 0.3926990816987241 8 -0.9238795325112867 0.3926990816987241 9 -1 0.1963495408493621 1 1 0.1745329251994329 2 0.9396926207859084 0.3490658503988659 3 0.7660444431189781 0.3490658503988659 4 0.5000000000000001 0.3490658503988659 5 0.1736481776669304 0.3490658503988659 6 -0.1736481776669303 0.3490658503988659 7 -0.4999999999999998 0.3490658503988659 8 -0.7660444431189779 0.3490658503988659 9 -0.9396926207859083 0.3490658503988659 10 -1 0.1745329251994329 CHEBYSHEV3_INTEGRAL_TEST CHEBYSHEV3_INTEGRAL evaluates Integral ( -1 < x < +1 ) x^n / sqrt(1-x*x) dx N Value 0 3.141592653589793 1 0 2 1.570796326794897 3 0 4 1.178097245096172 5 0 6 0.9817477042468102 7 0 8 0.8590292412159591 9 0 10 0.7731263170943631 CHEBYSHEV3_SET_TEST CHEBYSHEV3_SET sets a Chebyshev Type 2 quadrature rule over [-1,1]. Index X W 1 0 3.141592653589793 1 -1 1.570796326794897 2 1 1.570796326794897 1 -1 0.7853981633974483 2 0 1.570796326794897 3 1 0.7853981633974483 1 -1 0.5235987755982988 2 -0.5 1.047197551196598 3 0.5 1.047197551196598 4 1 0.5235987755982988 1 -1 0.3926990816987241 2 -0.7071067811865475 0.7853981633974483 3 0 0.7853981633974483 4 0.7071067811865476 0.7853981633974483 5 1 0.3926990816987241 1 -1 0.3141592653589793 2 -0.8090169943749473 0.6283185307179586 3 -0.3090169943749473 0.6283185307179586 4 0.3090169943749475 0.6283185307179586 5 0.8090169943749475 0.6283185307179586 6 1 0.3141592653589793 1 -1 0.2617993877991494 2 -0.8660254037844387 0.5235987755982988 3 -0.5 0.5235987755982988 4 0 0.5235987755982988 5 0.5000000000000001 0.5235987755982988 6 0.8660254037844387 0.5235987755982988 7 1 0.2617993877991494 1 -1 0.2243994752564138 2 -0.900968867902419 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 0.2243994752564138 1 -1 0.1963495408493621 2 -0.9238795325112867 0.3926990816987241 3 -0.7071067811865475 0.3926990816987241 4 -0.3826834323650897 0.3926990816987241 5 0 0.3926990816987241 6 0.3826834323650898 0.3926990816987241 7 0.7071067811865476 0.3926990816987241 8 0.9238795325112867 0.3926990816987241 9 1 0.1963495408493621 1 -1 0.1745329251994329 2 -0.9396926207859083 0.3490658503988659 3 -0.7660444431189779 0.3490658503988659 4 -0.5 0.3490658503988659 5 -0.1736481776669303 0.3490658503988659 6 0.1736481776669304 0.3490658503988659 7 0.5000000000000001 0.3490658503988659 8 0.766044443118978 0.3490658503988659 9 0.9396926207859084 0.3490658503988659 10 1 0.1745329251994329 CLENSHAW_CURTIS_COMPUTE_TEST CLENSHAW_CURTIS_COMPUTE computes a Clenshaw-Curtis quadrature rule over [-1,1] Index X W 1 0.0000000000000000 2.0000000000000000 1 -1.0000000000000000 1.0000000000000000 2 1.0000000000000000 1.0000000000000000 1 -1.0000000000000000 0.3333333333333334 2 0.0000000000000001 1.3333333333333333 3 1.0000000000000000 0.3333333333333334 1 -1.0000000000000000 0.1111111111111111 2 -0.4999999999999998 0.8888888888888892 3 0.5000000000000001 0.8888888888888888 4 1.0000000000000000 0.1111111111111111 1 -1.0000000000000000 0.0666666666666667 2 -0.7071067811865475 0.5333333333333334 3 0.0000000000000001 0.7999999999999999 4 0.7071067811865476 0.5333333333333333 5 1.0000000000000000 0.0666666666666667 1 -1.0000000000000000 0.0400000000000000 2 -0.8090169943749473 0.3607430412000113 3 -0.3090169943749473 0.5992569587999887 4 0.3090169943749475 0.5992569587999889 5 0.8090169943749475 0.3607430412000112 6 1.0000000000000000 0.0400000000000000 1 -1.0000000000000000 0.0285714285714286 2 -0.8660254037844387 0.2539682539682540 3 -0.4999999999999998 0.4571428571428573 4 0.0000000000000001 0.5206349206349206 5 0.5000000000000001 0.4571428571428571 6 0.8660254037844387 0.2539682539682539 7 1.0000000000000000 0.0285714285714286 1 -1.0000000000000000 0.0204081632653061 2 -0.9009688679024190 0.1901410072182084 3 -0.6234898018587334 0.3522424237181591 4 -0.2225209339563143 0.4372084057983264 5 0.2225209339563144 0.4372084057983264 6 0.6234898018587336 0.3522424237181591 7 0.9009688679024191 0.1901410072182084 8 1.0000000000000000 0.0204081632653061 1 -1.0000000000000000 0.0158730158730159 2 -0.9238795325112867 0.1462186492160182 3 -0.7071067811865475 0.2793650793650794 4 -0.3826834323650897 0.3617178587204898 5 0.0000000000000001 0.3936507936507936 6 0.3826834323650898 0.3617178587204897 7 0.7071067811865476 0.2793650793650794 8 0.9238795325112867 0.1462186492160181 9 1.0000000000000000 0.0158730158730159 1 -1.0000000000000000 0.0123456790123457 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 0.7660444431189781 0.2252843233381044 9 0.9396926207859084 0.1165674565720371 10 1.0000000000000000 0.0123456790123457 CLENSHAW_CURTIS_SET_TEST CLENSHAW_CURTIS_SET sets up a Clenshaw-Curtis rule; Index X W 1 0 2 1 -1 1 2 1 1 1 -1 0.3333333333333333 2 0 1.333333333333333 3 1 0.3333333333333333 1 -1 0.1111111111111111 2 -0.5 0.8888888888888888 3 0.5 0.8888888888888888 4 1 0.1111111111111111 1 -1 0.06666666666666667 2 -0.7071067811865476 0.5333333333333333 3 0 0.8 4 0.7071067811865476 0.5333333333333333 5 1 0.06666666666666667 1 -1 0.04 2 -0.8090169943749475 0.3607430412000112 3 -0.3090169943749475 0.5992569587999887 4 0.3090169943749475 0.5992569587999887 5 0.8090169943749373 0.3607430412000112 6 1 0.04 1 -1 0.02857142857142857 2 -0.8660254037844386 0.253968253968254 3 -0.5 0.4571428571428571 4 0 0.5206349206349207 5 0.5 0.4571428571428571 6 0.8660254037844386 0.253968253968254 7 1 0.02857142857142857 1 -1 0.02040816326530612 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 0.02040816326530612 1 -1 0.01587301587301587 2 -0.9238795325112867 0.1462186492160182 3 -0.7071067811865476 0.2793650793650794 4 -0.3826834323650898 0.3617178587204898 5 0 0.3936507936507936 6 0.3826834323650898 0.3617178587204898 7 0.7071067811865476 0.2793650793650794 8 0.9238795325112867 0.1462186492160182 9 1 0.01587301587301587 1 -1 0.01234567901234568 2 -0.9396926207859084 0.1165674565720371 3 -0.766044443118979 0.2252843233381044 4 -0.5 0.3019400352733686 5 -0.1736481776669304 0.3438625058041442 6 0.1736481776669304 0.3438625058041442 7 0.5 0.3019400352733686 8 0.766044443118979 0.2252843233381044 9 0.9396926207859084 0.1165674565720371 10 1 0.01234567901234568 FEJER1_COMPUTE_TEST FEJER1_COMPUTE computes the abscissas and weights of a Fejer type 1 quadrature rule. Order W X 1 1 6.123233995736766e-17 2 2 1 -0.7071067811865475 1 2 0.7071067811865476 1 3 1 -0.8660254037844387 0.4444444444444445 2 6.123233995736766e-17 1.111111111111111 3 0.8660254037844387 0.4444444444444444 4 1 -0.9238795325112867 0.2642977396044843 2 -0.3826834323650897 0.7357022603955159 3 0.3826834323650898 0.7357022603955158 4 0.9238795325112867 0.2642977396044841 5 1 -0.9510565162951535 0.1677812284666836 2 -0.587785252292473 0.5255521048666498 3 6.123233995736766e-17 0.6133333333333333 4 0.5877852522924732 0.5255521048666498 5 0.9510565162951535 0.1677812284666835 6 1 -0.9659258262890682 0.118661021381236 2 -0.7071067811865471 0.3777777777777779 3 -0.2588190451025204 0.5035612008409865 4 0.2588190451025212 0.5035612008409863 5 0.7071067811865478 0.3777777777777777 6 0.9659258262890683 0.1186610213812358 7 1 -0.9749279121818237 0.0867161807267223 2 -0.78183148246803 0.2878313947886917 3 -0.4338837391175585 0.3982415401308441 4 -1.608122649676637e-16 0.454421768707483 5 0.433883739117558 0.3982415401308442 6 0.7818314824680297 0.287831394788692 7 0.9749279121818236 0.08671618072672246 8 1 -0.9807852804032304 0.06698294569858997 2 -0.831469612302545 0.2229879330145789 3 -0.555570233019602 0.3241525190645244 4 -0.195090322016128 0.385876602222307 5 0.1950903220161285 0.385876602222307 6 0.5555702330196025 0.3241525190645243 7 0.8314696123025453 0.2229879330145788 8 0.9807852804032304 0.06698294569858981 9 1 -0.9848077530122081 0.05273664990990675 2 -0.8660254037844387 0.1791887125220459 3 -0.6427876096865393 0.2640372225410044 4 -0.3420201433256689 0.3308451751681364 5 -1.608122649676637e-16 0.346384479717813 6 0.3420201433256686 0.3308451751681365 7 0.6427876096865393 0.2640372225410044 8 0.8660254037844386 0.1791887125220459 9 0.984807753012208 0.05273664990990676 10 1 -0.9876883405951377 0.0429391195741308 2 -0.8910065241883678 0.1458749193773909 3 -0.7071067811865475 0.2203174603174603 4 -0.4539904997395467 0.2808792186638755 5 -0.1564344650402306 0.3099892820671425 6 0.1564344650402311 0.3099892820671425 7 0.453990499739547 0.2808792186638754 8 0.7071067811865477 0.2203174603174603 9 0.891006524188368 0.1458749193773908 10 0.9876883405951378 0.04293911957413078 FEJER1_SET_TEST FEJER1_SET sets the abscissas and weights of a Fejer type 1 quadrature rule. Order W X 1 2 0 2 1 -0.707107 1 0.707107 3 0.444444 -0.866025 1.11111 0 0.444444 0.866025 4 0.264298 -0.92388 0.735702 -0.382683 0.735702 0.382683 0.264298 0.92388 5 0.167781 -0.951057 0.525552 -0.587785 0.613333 0 0.525552 0.587785 0.167781 0.951057 6 0.118661 -0.965926 0.377778 -0.707107 0.503561 -0.258819 0.503561 0.258819 0.377778 0.707107 0.118661 0.965926 7 0.0867162 -0.974928 0.287831 -0.781831 0.398242 -0.433884 0.454422 0 0.398242 0.433884 0.287831 0.781831 0.0867162 0.974928 8 0.0669829 -0.980785 0.222988 -0.83147 0.324153 -0.55557 0.385877 -0.19509 0.385877 0.19509 0.324153 0.55557 0.222988 0.83147 0.0669829 0.980785 9 0.0527366 -0.984808 0.179189 -0.866025 0.264037 -0.642788 0.330845 -0.34202 0.346384 0 0.330845 0.34202 0.264037 0.642788 0.179189 0.866025 0.0527366 0.984808 10 0.0429391 -0.987688 0.145875 -0.891007 0.220317 -0.707107 0.280879 -0.45399 0.309989 -0.156434 0.309989 0.156434 0.280879 0.45399 0.220317 0.707107 0.145875 0.891007 0.0429391 0.987688 FEJER2_COMPUTE_TEST FEJER2_COMPUTE computes the abscissas and weights of a Fejer type 2 quadrature rule. Order W X 1 1 0 2 2 1 -0.5 1 2 0.5 1 3 1 -0.7071067811865475 0.6666666666666667 2 6.123233995736766e-17 0.6666666666666666 3 0.7071067811865476 0.6666666666666666 4 1 -0.8090169943749473 0.4254644007500071 2 -0.3090169943749473 0.574535599249993 3 0.3090169943749475 0.574535599249993 4 0.8090169943749475 0.425464400750007 5 1 -0.8660254037844387 0.3111111111111111 2 -0.4999999999999998 0.4000000000000001 3 6.123233995736766e-17 0.5777777777777777 4 0.5000000000000001 0.4 5 0.8660254037844387 0.3111111111111111 6 1 -0.900968867902419 0.2269152467244296 2 -0.6234898018587334 0.3267938603769863 3 -0.2225209339563143 0.4462908928985842 4 0.2225209339563144 0.4462908928985841 5 0.6234898018587336 0.3267938603769863 6 0.9009688679024191 0.2269152467244296 7 1 -0.9238795325112867 0.17796468096205 2 -0.7071067811865475 0.2476190476190477 3 -0.3826834323650897 0.3934638904665215 4 6.123233995736766e-17 0.3619047619047619 5 0.3826834323650898 0.3934638904665215 6 0.7071067811865476 0.2476190476190476 7 0.9238795325112867 0.1779646809620499 8 1 -0.9396926207859083 0.1397697435050226 2 -0.7660444431189779 0.2063696457302284 3 -0.4999999999999998 0.3142857142857144 4 -0.1736481776669303 0.3395748964790348 5 0.1736481776669304 0.3395748964790348 6 0.5000000000000001 0.3142857142857143 7 0.7660444431189781 0.2063696457302284 8 0.9396926207859084 0.1397697435050225 9 1 -0.9510565162951535 0.1147810750857218 2 -0.8090169943749473 0.1654331942222276 3 -0.587785252292473 0.2737903534857068 4 -0.3090169943749473 0.2790112502222169 5 6.123233995736766e-17 0.3339682539682539 6 0.3090169943749475 0.279011250222217 7 0.5877852522924732 0.2737903534857068 8 0.8090169943749475 0.1654331942222276 9 0.9510565162951535 0.1147810750857217 10 1 -0.9594929736144974 0.09441954173982806 2 -0.8412535328311811 0.1411354380109716 3 -0.654860733945285 0.2263866903636005 4 -0.4154150130018863 0.2530509772156453 5 -0.142314838273285 0.2850073526699546 6 0.1423148382732851 0.2850073526699544 7 0.4154150130018864 0.2530509772156453 8 0.6548607339452852 0.2263866903636005 9 0.8412535328311812 0.1411354380109716 10 0.9594929736144974 0.09441954173982806 FEJER2_SET_TEST FEJER2_SET sets the abscissas and weights of a Fejer type 2 quadrature rule. Order W X 1 2 0 2 1 -0.5 1 0.5 3 0.666667 -0.707107 0.666667 0 0.666667 0.707107 4 0.425464 -0.809017 0.574536 -0.309017 0.574536 0.309017 0.425464 0.809017 5 0.311111 -0.866025 0.4 -0.5 0.577778 0 0.4 0.5 0.311111 0.866025 6 0.226915 -0.900969 0.326794 -0.62349 0.446291 -0.222521 0.446291 0.222521 0.326794 0.62349 0.226915 0.900969 7 0.177965 -0.92388 0.247619 -0.707107 0.393464 -0.382683 0.361905 0 0.393464 0.382683 0.247619 0.707107 0.177965 0.92388 8 0.13977 -0.939693 0.20637 -0.766044 0.314286 -0.5 0.339575 -0.173648 0.339575 0.173648 0.314286 0.5 0.20637 0.766044 0.13977 0.939693 9 0.114781 -0.951057 0.165433 -0.809017 0.27379 -0.587785 0.279011 -0.309017 0.333968 0 0.279011 0.309017 0.27379 0.587785 0.165433 0.809017 0.114781 0.951057 10 0.0944195 -0.959493 0.141135 -0.841254 0.226387 -0.654861 0.253051 -0.415415 0.285007 -0.142315 0.285007 0.142315 0.253051 0.415415 0.226387 0.654861 0.141135 0.841254 0.0944195 0.959493 GEGENBAUER_INTEGRAL_TEST GEGENBAUER_INTEGRAL evaluates Integral ( -1 < x < +1 ) x^n * (1-x*x)^alpha dx N Value 0 1.748038369528081 1 0 2 0.4994395341508805 3 0 4 0.2724215640822983 5 0 6 0.1816143760548655 7 0 8 0.133821119198322 9 0 10 0.1047295715465127 GEGENBAUER_SS_COMPUTE_TEST GEGENBAUER_SS_COMPUTE computes Gauss-Gegenbauer rules; Abscissas and weights for a generalized Gauss Gegenbauer rule with ALPHA = 0.500000 1 1.570796326794897 0 1 0.7853981633974484 -0.5 2 0.7853981633974484 0.5 1 0.3926990816987239 -0.7071067811865475 2 0.7853981633974484 0 3 0.3926990816987239 0.7071067811865475 1 0.217078713422706 -0.8090169943749475 2 0.5683194499747424 -0.3090169943749475 3 0.5683194499747424 0.3090169943749474 4 0.217078713422706 0.8090169943749475 1 0.130899693899574 -0.8660254037844387 2 0.3926990816987242 -0.5 3 0.5235987755982989 0 4 0.3926990816987242 0.5 5 0.130899693899575 0.8660254037844387 1 0.08448869089158841 -0.9009688679024191 2 0.2743330560697777 -0.6234898018587335 3 0.4265764164360819 -0.2225209339563144 4 0.4265764164360819 0.2225209339563144 5 0.2743330560697777 0.6234898018587335 6 0.08448869089158884 0.900968867902419 1 0.05750944903191331 -0.9238795325112867 2 0.1963495408493619 -0.7071067811865475 3 0.3351896326668111 -0.3826834323650898 4 0.3926990816987242 0 5 0.3351896326668108 0.3826834323650898 6 0.1963495408493624 0.7071067811865476 7 0.05750944903191331 0.9238795325112867 1 0.04083294770910693 -0.9396926207859084 2 0.1442256007956728 -0.766044443118978 3 0.2617993877991495 -0.5 4 0.3385402270935191 -0.1736481776669303 5 0.3385402270935191 0.1736481776669303 6 0.2617993877991495 0.5 7 0.1442256007956728 0.766044443118978 8 0.04083294770910754 0.9396926207859084 1 0.02999954037160841 -0.9510565162951536 2 0.108539356711353 -0.8090169943749475 3 0.2056199086476264 -0.5877852522924731 4 0.2841597249873712 -0.3090169943749475 5 0.3141592653589794 0 6 0.2841597249873712 0.3090169943749475 7 0.2056199086476264 0.5877852522924731 8 0.108539356711353 0.8090169943749475 9 0.02999954037160841 0.9510565162951536 1 0.02266894250185901 -0.9594929736144974 2 0.08347854093418892 -0.8412535328311812 3 0.1631221774548165 -0.6548607339452851 4 0.2363135602034873 -0.4154150130018864 5 0.2798149423030965 -0.1423148382732851 6 0.2798149423030966 0.1423148382732851 7 0.2363135602034873 0.4154150130018864 8 0.1631221774548165 0.6548607339452851 9 0.08347854093418892 0.8412535328311812 10 0.02266894250185901 0.9594929736144974 GEN_HERMITE_EK_COMPUTE_TEST GEN_HERMITE_EK_COMPUTE computes a generalized Hermite quadrature rule using the Elhay-Kautsky algorithm. Using ALPHA = 0.5 Index X W 1 0 1.225416702465178 1 -0.8660254037844385 0.6127083512325888 2 0.8660254037844385 0.6127083512325888 1 -1.322875655532295 0.262589293385395 2 -5.116764146070064e-17 0.7002381156943873 3 1.322875655532295 0.2625892933853951 1 -1.752961966367865 0.07477218653431648 2 -0.6535475074298001 0.5379361646982723 3 0.6535475074297997 0.5379361646982722 4 1.752961966367866 0.07477218653431648 1 -2.099598150879758 0.02069085274024055 2 -1.044838554429487 0.3373854564216626 3 -3.282569029574496e-16 0.5092640841413727 4 1.044838554429487 0.3373854564216618 5 2.099598150879757 0.02069085274024059 1 -2.431196006814872 0.004758432285876828 2 -1.428264330850234 0.1432946705182552 3 -0.5471261076464521 0.4646552484284566 4 0.5471261076464519 0.4646552484284565 5 1.428264330850234 0.1432946705182554 6 2.431196006814872 0.004758432285876804 1 -2.719880088556293 0.001106289401968463 2 -1.747360778896521 0.05564733125066081 3 -0.8938582730216026 0.3522490969234104 4 -1.036026041953223e-16 0.4074112673130981 5 0.8938582730216028 0.3522490969234111 6 1.747360778896521 0.05564733125066098 7 2.719880088556293 0.00110628940196846 1 -2.999078968343316 0.0002288084584739164 2 -2.057439418477468 0.01787577463926721 3 -1.241738340943189 0.1866121206001918 4 -0.4801606747408059 0.4079916475346562 5 0.4801606747408056 0.4079916475346565 6 1.241738340943189 0.1866121206001918 7 2.057439418477468 0.01787577463926723 8 2.999078968343316 0.0002288084584739132 1 -3.251152326134132 4.824428349517108e-05 2 -2.331322119300714 0.005575754103643737 3 -1.537416408684744 0.08875797489986054 4 -0.7945417010067838 0.3467847917084952 5 -2.510890360759582e-16 0.343083172474188 6 0.794541701006784 0.3467847917084949 7 1.537416408684744 0.08875797489986068 8 2.331322119300714 0.005575754103643735 9 3.251152326134132 4.824428349517049e-05 1 -3.496605880747676 9.347334083394586e-06 2 -2.598397149544623 0.00153635644240256 3 -1.827991812365274 0.03517634314374584 4 -1.114905370566644 0.2117439807373517 5 -0.4330259998733383 0.3642423235750059 6 0.4330259998733384 0.3642423235750052 7 1.114905370566644 0.2117439807373521 8 1.827991812365275 0.03517634314374578 9 2.598397149544622 0.001536356442402556 10 3.496605880747678 9.347334083394711e-06 GEN_HERMITE_INTEGRAL_TEST GEN_HERMITE_INTEGRAL evaluates Integral ( -oo < x < +oo ) exp(-x^2) x^n |x|^alpha dx Use ALPHA = 0.5 N Value 0 1.225416702465178 1 0 2 0.9190625268488832 3 0 4 1.608359421985546 5 0 6 4.422988410460251 7 0 8 16.58620653922594 9 0 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 = 0.5 Index X W 1 1.5 0.8862269254527581 1 0.9188611699158102 0.7233630235462758 2 4.081138830084189 0.1628639019064827 1 0.6663259077023709 0.5671862778403113 2 2.800775054150256 0.305371768844547 3 7.032899038147373 0.01366887876790015 1 0.5235260767382689 0.4530087465586076 2 2.156648763269093 0.3816169601718002 3 5.137387546176711 0.05079462757224079 4 10.18243761381592 0.000806591150110032 1 0.4313988071478517 0.3704505700074587 2 1.759753698423697 0.4125843737694528 3 4.104465362828316 0.0977798200531807 4 7.746703779542557 0.005373415341171986 5 13.45767835205758 3.874628149393569e-05 1 0.3669498773083711 0.3094240968362605 2 1.488534292310453 0.417752149707022 3 3.434007968424071 0.1432858732209769 4 6.349067925680377 0.01533249102263385 5 10.54046985844834 0.0004306911960439421 6 16.82097007782838 1.623469821074069e-06 1 0.3193036339206303 0.263124514395892 2 1.290758622959153 0.409141869414102 3 2.958374458696649 0.1821177320927161 4 5.409031597244431 0.03005332430127097 5 8.804079578056783 0.001760894117540059 6 13.46853574325147 2.852947122115979e-05 7 20.24991636587088 6.166001541039125e-08 1 0.2826336481165994 0.227139361952472 2 1.139873801581615 0.3935945428036152 3 2.60152484340603 0.2129089708672277 4 4.724114537527792 0.0478774832031381 5 7.605256299231612 0.004542517474762657 6 11.41718207654583 0.0001624046001853259 7 16.49941079765582 1.642377413806098e-06 8 23.7300039959347 2.173943126630926e-09 1 0.2535325549744195 0.1985712548680197 2 1.02084427772039 0.3749207846631712 3 2.323096077022467 0.236074821000825 4 4.199350600657291 0.06709610500320433 5 6.713974316615028 0.009008508896644349 6 9.972009159539351 0.0005426607386359309 7 14.15405367127805 1.270536687910845e-05 8 19.61190281916595 8.484309239668572e-08 9 27.25123652302705 7.22864716439652e-11 1 0.2298729805186557 0.1754708150466604 2 0.9244815469866583 0.3552233888020722 3 2.099410462708799 0.2526835596756778 4 3.782880873707291 0.0863561026953325 5 6.019918027701461 0.01510977803486088 6 8.88034759799671 0.001328215628363561 7 12.47483240483621 5.418780021170328e-05 8 16.99084729354255 8.737475869187144e-07 9 22.79100289494894 4.01969988693978e-09 10 30.80640591705273 2.2922215302047e-12 GEN_LAGUERRE_INTEGRAL_TEST GEN_LAGUERRE_INTEGRAL evaluates Integral ( 0 < x < +oo ) exp(-x) x^n x^alpha dx Use ALPHA = 0.5 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 119292.461994609 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 = 0.5 Index X W 1 1.5 0.8862269254527581 1 0.9188611699158102 0.7233630235462755 2 4.08113883008419 0.1628639019064825 1 0.6663259077023709 0.5671862778403113 2 2.800775054150257 0.3053717688445466 3 7.032899038147373 0.01366887876790012 1 0.5235260767382691 0.4530087465586076 2 2.156648763269094 0.3816169601717996 3 5.137387546176711 0.05079462757224078 4 10.18243761381592 0.0008065911501100311 1 0.4313988071478514 0.3704505700074577 2 1.759753698423696 0.4125843737694528 3 4.104465362828315 0.09777982005318073 4 7.746703779542557 0.005373415341171988 5 13.45767835205758 3.874628149393578e-05 1 0.3669498773083708 0.3094240968362596 2 1.488534292310452 0.4177521497070224 3 3.434007968424071 0.1432858732209768 4 6.349067925680379 0.01533249102263384 5 10.54046985844834 0.0004306911960439413 6 16.82097007782838 1.623469821074075e-06 1 0.31930363392063 0.2631245143958917 2 1.290758622959153 0.4091418694141027 3 2.95837445869665 0.1821177320927161 4 5.409031597244433 0.03005332430127097 5 8.804079578056776 0.001760894117540062 6 13.46853574325148 2.852947122115974e-05 7 20.24991636587088 6.166001541039151e-08 1 0.2826336481165992 0.2271393619524718 2 1.139873801581614 0.3935945428036146 3 2.601524843406029 0.2129089708672283 4 4.72411453752779 0.04787748320313819 5 7.605256299231614 0.004542517474762639 6 11.41718207654583 0.0001624046001853258 7 16.49941079765582 1.642377413806097e-06 8 23.73000399593471 2.173943126630915e-09 1 0.2535325549744191 0.1985712548680198 2 1.02084427772039 0.37492078466317 3 2.323096077022466 0.2360748210008255 4 4.199350600657293 0.06709610500320429 5 6.713974316615029 0.009008508896644332 6 9.972009159539349 0.0005426607386359305 7 14.15405367127805 1.270536687910839e-05 8 19.61190281916595 8.484309239668552e-08 9 27.25123652302706 7.228647164396543e-11 1 0.2298729805186562 0.1754708150466581 2 0.9244815469866572 0.355223388802071 3 2.099410462708798 0.2526835596756779 4 3.78288087370729 0.08635610269533264 5 6.019918027701461 0.01510977803486081 6 8.880347597996709 0.001328215628363563 7 12.4748324048362 5.418780021170349e-05 8 16.99084729354255 8.737475869187144e-07 9 22.79100289494895 4.0196998869398e-09 10 30.80640591705272 2.292221530204716e-12 HERMITE_EK_COMPUTE_TEST HERMITE_EK_COMPUTE computes a Hermite quadrature rule using the Elhay-Kautsky algorithm. Index X W 1 0 1.772453850905516 1 -0.7071067811865475 0.8862269254527578 2 0.7071067811865475 0.8862269254527578 1 -1.224744871391589 0.2954089751509195 2 0 1.181635900603677 3 1.224744871391589 0.2954089751509192 1 -1.650680123885784 0.0813128354472452 2 -0.5246476232752902 0.8049140900055129 3 0.5246476232752905 0.8049140900055127 4 1.650680123885784 0.0813128354472453 1 -2.020182870456086 0.01995324205904592 2 -0.9585724646138184 0.3936193231522413 3 0 0.9453087204829423 4 0.9585724646138184 0.3936193231522407 5 2.020182870456086 0.01995324205904592 1 -2.350604973674492 0.00453000990550884 2 -1.335849074013697 0.1570673203228568 3 -0.4360774119276161 0.7246295952243927 4 0.4360774119276162 0.7246295952243929 5 1.335849074013697 0.1570673203228564 6 2.350604973674492 0.004530009905508842 1 -2.651961356835233 0.0009717812450995198 2 -1.673551628767471 0.05451558281912718 3 -0.8162878828589647 0.425607252610128 4 0 0.810264617556807 5 0.8162878828589646 0.4256072526101278 6 1.673551628767472 0.05451558281912701 7 2.651961356835232 0.0009717812450995181 1 -2.930637420257241 0.000199604072211368 2 -1.981656756695844 0.01707798300741351 3 -1.15719371244678 0.2078023258148917 4 -0.3811869902073222 0.6611470125582416 5 0.3811869902073224 0.6611470125582413 6 1.157193712446781 0.2078023258148918 7 1.981656756695843 0.0170779830074135 8 2.930637420257244 0.0001996040722113682 1 -3.190993201781527 3.960697726326435e-05 2 -2.266580584531841 0.004943624275536949 3 -1.468553289216668 0.08847452739437661 4 -0.7235510187528373 0.4326515590025557 5 0 0.7202352156060514 6 0.7235510187528374 0.4326515590025553 7 1.468553289216667 0.08847452739437671 8 2.266580584531842 0.004943624275536965 9 3.190993201781528 3.96069772632642e-05 1 -3.436159118837737 7.640432855232626e-06 2 -2.532731674232791 0.001343645746781242 3 -1.756683649299881 0.03387439445548108 4 -1.036610829789514 0.2401386110823153 5 -0.3429013272237044 0.6108626337353246 6 0.3429013272237046 0.610862633735326 7 1.036610829789513 0.2401386110823147 8 1.756683649299881 0.03387439445548109 9 2.53273167423279 0.001343645746781238 10 3.436159118837737 7.640432855232587e-06 HERMITE_INTEGRAL_TEST HERMITE_INTEGRAL evaluates Integral ( -oo < x < +oo ) exp(-x^2) x^n dx N Value 0 1.772453850905516 1 0 2 0.8862269254527579 3 0 4 1.329340388179137 5 0 6 3.323350970447842 7 0 8 11.63172839656745 9 0 10 52.34277778455352 HERMITE_SET_TEST HERMITE_SET sets a Hermite quadrature rule on (-oo,+oo); Index X W 1 0 1.772453850905516 1 -0.7071067811865476 0.8862269254527581 2 0.7071067811865476 0.8862269254527581 1 -1.224744871391589 0.2954089751509194 2 0 1.181635900603677 3 1.224744871391589 0.2954089751509194 1 -1.650680123885784 0.08131283544724517 2 -0.5246476232752904 0.8049140900055128 3 0.5246476232752904 0.8049140900055128 4 1.650680123885784 0.08131283544724517 1 -2.020182870456086 0.01995324205904591 2 -0.9585724646138185 0.3936193231522412 3 0 0.9453087204829419 4 0.9585724646138185 0.3936193231522412 5 2.020182870456086 0.01995324205904591 1 -2.350604973674492 0.004530009905508846 2 -1.335849074013697 0.1570673203228566 3 -0.4360774119276165 0.7246295952243925 4 0.4360774119276165 0.7246295952243925 5 1.335849074013697 0.1570673203228566 6 2.350604973674492 0.004530009905508846 1 -2.651961356835233 0.0009717812450995191 2 -1.673551628767471 0.05451558281912703 3 -0.8162878828589647 0.4256072526101278 4 0 0.8102646175568073 5 0.8162878828589647 0.4256072526101278 6 1.673551628767471 0.05451558281912703 7 2.651961356835233 0.0009717812450995191 1 -2.930637420257244 0.0001996040722113676 2 -1.981656756695843 0.01707798300741347 3 -1.15719371244678 0.2078023258148919 4 -0.3811869902073221 0.6611470125582413 5 0.3811869902073221 0.6611470125582413 6 1.15719371244678 0.2078023258148919 7 1.981656756695843 0.01707798300741347 8 2.930637420257244 0.0001996040722113676 1 -3.190993201781528 3.960697726326439e-05 2 -2.266580584531843 0.004943624275536947 3 -1.468553289216668 0.08847452739437657 4 -0.7235510187528376 0.4326515590025558 5 0 0.720235215606051 6 0.7235510187528376 0.4326515590025558 7 1.468553289216668 0.08847452739437657 8 2.266580584531843 0.004943624275536947 9 3.190993201781528 3.960697726326439e-05 1 -3.436159118837737 7.640432855232621e-06 2 -2.53273167423279 0.001343645746781233 3 -1.756683649299882 0.03387439445548106 4 -1.036610829789514 0.2401386110823147 5 -0.3429013272237046 0.6108626337353258 6 0.3429013272237046 0.6108626337353258 7 1.036610829789514 0.2401386110823147 8 1.756683649299882 0.03387439445548106 9 2.53273167423279 0.001343645746781233 10 3.436159118837737 7.640432855232621e-06 HERMITE_SS_COMPUTE_TEST HERMITE_SS_COMPUTE computes a Hermite quadrature rule using the Stroud-Secrest algorithm. Index X W 1 -0 1.772453850905516 1 -0.7071067811865475 0.8862269254527578 2 0.7071067811865475 0.8862269254527578 1 -1.224744871391589 0.2954089751509195 2 -0 1.181635900603677 3 1.224744871391589 0.2954089751509195 1 -1.650680123885785 0.08131283544724513 2 -0.5246476232752904 0.8049140900055128 3 0.5246476232752904 0.8049140900055128 4 1.650680123885785 0.08131283544724513 1 -2.020182870456086 0.01995324205904592 2 -0.9585724646138185 0.3936193231522412 3 -0 0.9453087204829419 4 0.9585724646138185 0.3936193231522412 5 2.020182870456086 0.01995324205904592 1 -2.350604973674492 0.004530009905508842 2 -1.335849074013697 0.1570673203228565 3 -0.4360774119276165 0.7246295952243924 4 0.4360774119276165 0.7246295952243924 5 1.335849074013697 0.1570673203228565 6 2.350604973674492 0.004530009905508842 1 -2.651961356835233 0.0009717812450995207 2 -1.673551628767471 0.05451558281912694 3 -0.8162878828589647 0.4256072526101277 4 -0 0.8102646175568073 5 0.8162878828589647 0.4256072526101277 6 1.673551628767471 0.05451558281912694 7 2.651961356835233 0.0009717812450995207 1 -2.930637420257244 0.0001996040722113675 2 -1.981656756695843 0.01707798300741346 3 -1.15719371244678 0.2078023258148916 4 -0.3811869902073221 0.6611470125582413 5 0.3811869902073221 0.6611470125582413 6 1.15719371244678 0.2078023258148916 7 1.981656756695843 0.01707798300741346 8 2.930637420257244 0.0001996040722113675 1 -3.190993201781527 3.960697726326427e-05 2 -2.266580584531843 0.00494362427553694 3 -1.468553289216668 0.08847452739437658 4 -0.7235510187528376 0.4326515590025556 5 -0 0.720235215606051 6 0.7235510187528376 0.4326515590025556 7 1.468553289216668 0.08847452739437658 8 2.266580584531843 0.00494362427553694 9 3.190993201781527 3.960697726326427e-05 1 -3.436159118837738 7.640432855232643e-06 2 -2.53273167423279 0.001343645746781235 3 -1.756683649299882 0.03387439445548104 4 -1.036610829789514 0.2401386110823147 5 -0.3429013272237046 0.6108626337353257 6 0.3429013272237046 0.6108626337353257 7 1.036610829789514 0.2401386110823147 8 1.756683649299882 0.03387439445548104 9 2.53273167423279 0.001343645746781235 10 3.436159118837738 7.640432855232643e-06 HERMITE_GK16_SET_TEST HERMITE_GK16_SET sets up a nested rule for the Hermite integration problem. Index X W 1 0 1.772453850905516 1 -1.224744871391589 0.2954089751509193 2 0 1.181635900603677 3 1.224744871391589 0.2954089751509193 1 -2.959210779063838 0.001233068065515345 2 -1.224744871391589 0.2455792853503139 3 -0.5240335474869576 0.232862517873861 4 0 0.813104108326135 5 0.5240335474869576 0.232862517873861 6 1.224744871391589 0.2455792853503139 7 2.959210779063838 0.001233068065515345 1 -2.959210779063838 0.0001670882630688235 2 -2.023230191100516 0.0141731178739791 3 -1.224744871391589 0.1681189289476777 4 -0.5240335474869576 0.4786942854911412 5 0 0.450147009753782 6 0.5240335474869576 0.4786942854911412 7 1.224744871391589 0.1681189289476777 8 2.023230191100516 0.0141731178739791 9 2.959210779063838 0.0001670882630688235 1 -4.499599398310388 3.746346994305176e-08 2 -3.667774215946338 -1.454284338706939e-06 3 -2.959210779063838 0.0001872381894927835 4 -2.023230191100516 0.01246651913280592 5 -1.835707975175187 0.00348407193468038 6 -1.224744871391589 0.1571829837665224 7 -0.8700408953529029 0.02515582570171293 8 -0.5240335474869576 0.4511980360235854 9 0 0.4731073350496539 10 0.5240335474869576 0.4511980360235854 11 0.8700408953529029 0.02515582570171293 12 1.224744871391589 0.1571829837665224 13 1.835707975175187 0.00348407193468038 14 2.023230191100516 0.01246651913280592 15 2.959210779063838 0.0001872381894927835 16 3.667774215946338 -1.454284338706939e-06 17 4.499599398310388 3.746346994305176e-08 1 -4.499599398310388 1.529571770532236e-09 2 -3.667774215946338 1.080276720662476e-06 3 -2.959210779063838 0.0001065658977285227 4 -2.266513262056788 0.005113317439088385 5 -2.023230191100516 -0.01123243848906923 6 -1.835707975175187 0.03205524309944588 7 -1.224744871391589 0.1136072989574827 8 -0.8700408953529029 0.1083886195500302 9 -0.5240335474869576 0.3692464336892085 10 0 0.5378816070051017 11 0.5240335474869576 0.3692464336892085 12 0.8700408953529029 0.1083886195500302 13 1.224744871391589 0.1136072989574827 14 1.835707975175187 0.03205524309944588 15 2.023230191100516 -0.01123243848906923 16 2.266513262056788 0.005113317439088385 17 2.959210779063838 0.0001065658977285227 18 3.667774215946338 1.080276720662476e-06 19 4.499599398310388 1.529571770532236e-09 1 -6.375939270982236 2.236564560704446e-15 2 -5.643257857885745 -2.630469645854894e-13 3 -5.036089944473094 9.067528823167982e-12 4 -4.499599398310388 1.405525202472248e-09 5 -3.667774215946338 1.088921969212812e-06 6 -2.959210779063838 0.0001054166239474666 7 -2.570558376584297 2.666515977893943e-05 8 -2.266513262056788 0.004838520820550261 9 -2.023230191100516 -0.009856627043461002 10 -1.835707975175187 0.02940942758035079 11 -1.579412134846767 0.003121021035268283 12 -1.224744871391589 0.1093932507186088 13 -0.8700408953529029 0.1159493098485312 14 -0.5240335474869576 0.3539388902958054 15 -0.1760641420820089 0.04985576189329316 16 0 0.4588883963675675 17 0.1760641420820089 0.04985576189329316 18 0.5240335474869576 0.3539388902958054 19 0.8700408953529029 0.1159493098485312 20 1.224744871391589 0.1093932507186088 21 1.579412134846767 0.003121021035268283 22 1.835707975175187 0.02940942758035079 23 2.023230191100516 -0.009856627043461002 24 2.266513262056788 0.004838520820550261 25 2.570558376584297 2.666515977893943e-05 26 2.959210779063838 0.0001054166239474666 27 3.667774215946338 1.088921969212812e-06 28 4.499599398310388 1.405525202472248e-09 29 5.036089944473094 9.067528823167982e-12 30 5.643257857885745 -2.630469645854894e-13 31 6.375939270982236 2.236564560704446e-15 1 -6.375939270982236 -1.76029328053725e-15 2 -5.643257857885745 4.721927866641769e-13 3 -5.036089944473094 -3.428157053034956e-11 4 -4.499599398310388 2.75478251389359e-09 5 -4.029220140504371 -2.390334338280351e-08 6 -3.667774215946338 1.224522096715844e-06 7 -2.959210779063838 9.871000919740917e-05 8 -2.570558376584297 0.0001475320490186277 9 -2.266513262056788 0.003758002660430479 10 -2.023230191100516 -0.004911857612387755 11 -1.835707975175187 0.0204350583591072 12 -1.579412134846767 0.01303287269902796 13 -1.224744871391589 0.09691344494458362 14 -0.8700408953529029 0.1372652119156755 15 -0.5240335474869576 0.3120865619469745 16 -0.1760641420820089 0.1841169604772579 17 0 0.2465664493282962 18 0.1760641420820089 0.1841169604772579 19 0.5240335474869576 0.3120865619469745 20 0.8700408953529029 0.1372652119156755 21 1.224744871391589 0.09691344494458362 22 1.579412134846767 0.01303287269902796 23 1.835707975175187 0.0204350583591072 24 2.023230191100516 -0.004911857612387755 25 2.266513262056788 0.003758002660430479 26 2.570558376584297 0.0001475320490186277 27 2.959210779063838 9.871000919740917e-05 28 3.667774215946338 1.224522096715844e-06 29 4.029220140504371 -2.390334338280351e-08 30 4.499599398310388 2.75478251389359e-09 31 5.036089944473094 -3.428157053034956e-11 32 5.643257857885745 4.721927866641769e-13 33 6.375939270982236 -1.76029328053725e-15 1 -6.375939270982236 1.86840148945106e-18 2 -5.643257857885745 9.659946627856324e-15 3 -5.036089944473094 5.489683694849946e-12 4 -4.499599398310388 8.15537218169169e-10 5 -4.029220140504371 3.792022239231953e-08 6 -3.667774215946338 4.373781804092699e-07 7 -3.349163953713195 4.846279973702046e-06 8 -2.959210779063838 6.332862080561789e-05 9 -2.570558376584297 0.0004878539930444377 10 -2.266513262056788 0.00145155804251559 11 -2.023230191100516 0.004096752772034405 12 -1.835707975175187 0.005592882891146918 13 -1.579412134846767 0.0277805089085351 14 -1.224744871391589 0.08024551814739089 15 -0.8700408953529029 0.163712215557358 16 -0.5240335474869576 0.2624487148878428 17 -0.1760641420820089 0.3398859558558522 18 0 0.0009126267536373792 19 0.1760641420820089 0.3398859558558522 20 0.5240335474869576 0.2624487148878428 21 0.8700408953529029 0.163712215557358 22 1.224744871391589 0.08024551814739089 23 1.579412134846767 0.0277805089085351 24 1.835707975175187 0.005592882891146918 25 2.023230191100516 0.004096752772034405 26 2.266513262056788 0.00145155804251559 27 2.570558376584297 0.0004878539930444377 28 2.959210779063838 6.332862080561789e-05 29 3.349163953713195 4.846279973702046e-06 30 3.667774215946338 4.373781804092699e-07 31 4.029220140504371 3.792022239231953e-08 32 4.499599398310388 8.15537218169169e-10 33 5.036089944473094 5.489683694849946e-12 34 5.643257857885745 9.659946627856324e-15 35 6.375939270982236 1.86840148945106e-18 HERMITE_GK18_SET_TEST HERMITE_GK18_SET sets up a nested rule for the Hermite integration problem. Index X W 1 0 1.772453850905516 1 -1.224744871391589 0.2954089751509193 2 0 1.181635900603677 3 1.224744871391589 0.2954089751509193 1 -2.959210779063838 0.0001670882630688235 2 -2.023230191100516 0.0141731178739791 3 -1.224744871391589 0.1681189289476777 4 -0.5240335474869576 0.4786942854911412 5 0 0.450147009753782 6 0.5240335474869576 0.4786942854911412 7 1.224744871391589 0.1681189289476777 8 2.023230191100516 0.0141731178739791 9 2.959210779063838 0.0001670882630688235 1 -4.499599398310388 1.529571770532236e-09 2 -3.667774215946338 1.080276720662476e-06 3 -2.959210779063838 0.0001065658977285227 4 -2.266513262056788 0.005113317439088385 5 -2.023230191100516 -0.01123243848906923 6 -1.835707975175187 0.03205524309944588 7 -1.224744871391589 0.1136072989574827 8 -0.8700408953529029 0.1083886195500302 9 -0.5240335474869576 0.3692464336892085 10 0 0.5378816070051017 11 0.5240335474869576 0.3692464336892085 12 0.8700408953529029 0.1083886195500302 13 1.224744871391589 0.1136072989574827 14 1.835707975175187 0.03205524309944588 15 2.023230191100516 -0.01123243848906923 16 2.266513262056788 0.005113317439088385 17 2.959210779063838 0.0001065658977285227 18 3.667774215946338 1.080276720662476e-06 19 4.499599398310388 1.529571770532236e-09 1 -6.853200069757519 1.90303509401305e-21 2 -6.124527854622158 1.87781893143729e-17 3 -5.52186520986835 1.822427515491294e-14 4 -4.986551454150765 4.566176367618686e-12 5 -4.499599398310388 4.22525843963111e-10 6 -4.057956316089741 1.659544880938982e-08 7 -3.667774215946338 2.959075202307441e-07 8 -3.31558461759329 3.309758709792034e-06 9 -2.959210779063838 3.226518598373974e-05 10 -2.597288631188366 0.0002349403664659752 11 -2.266513262056788 0.0009858275829964839 12 -2.023230191100516 0.001768022258182954 13 -1.835707975175187 0.004333498812272349 14 -1.561553427651873 0.01551310987485935 15 -1.224744871391589 0.04421164421898455 16 -0.870040895352903 0.09372082806552459 17 -0.524033547486958 0.1430993028968334 18 -0.214618180588171 0.1476557104026862 19 0 0.09688245529284255 20 0.214618180588171 0.1476557104026862 21 0.524033547486958 0.1430993028968334 22 0.870040895352903 0.09372082806552459 23 1.224744871391589 0.04421164421898455 24 1.561553427651873 0.01551310987485935 25 1.835707975175187 0.004333498812272349 26 2.023230191100516 0.001768022258182954 27 2.266513262056788 0.0009858275829964839 28 2.597288631188366 0.0002349403664659752 29 2.959210779063838 3.226518598373974e-05 30 3.31558461759329 3.309758709792034e-06 31 3.667774215946338 2.959075202307441e-07 32 4.057956316089741 1.659544880938982e-08 33 4.499599398310388 4.22525843963111e-10 34 4.986551454150765 4.566176367618686e-12 35 5.52186520986835 1.822427515491294e-14 36 6.124527854622158 1.87781893143729e-17 37 6.853200069757519 1.90303509401305e-21 HERMITE_GK22_SET_TEST HERMITE_GK22_SET sets up a nested rule for the Hermite integration problem. Index X W 1 0 1.772453850905516 1 -1.224744871391589 0.2954089751509193 2 0 1.181635900603677 3 1.224744871391589 0.2954089751509193 1 -2.959210779063838 0.0001670882630688235 2 -2.023230191100516 0.0141731178739791 3 -1.224744871391589 0.1681189289476777 4 -0.5240335474869576 0.4786942854911412 5 0 0.450147009753782 6 0.5240335474869576 0.4786942854911412 7 1.224744871391589 0.1681189289476777 8 2.023230191100516 0.0141731178739791 9 2.959210779063838 0.0001670882630688235 1 -4.499599398310388 1.529571770532236e-09 2 -3.667774215946338 1.080276720662476e-06 3 -2.959210779063838 0.0001065658977285227 4 -2.266513262056788 0.005113317439088385 5 -2.023230191100516 -0.01123243848906923 6 -1.835707975175187 0.03205524309944588 7 -1.224744871391589 0.1136072989574827 8 -0.8700408953529029 0.1083886195500302 9 -0.5240335474869576 0.3692464336892085 10 0 0.5378816070051017 11 0.5240335474869576 0.3692464336892085 12 0.8700408953529029 0.1083886195500302 13 1.224744871391589 0.1136072989574827 14 1.835707975175187 0.03205524309944588 15 2.023230191100516 -0.01123243848906923 16 2.266513262056788 0.005113317439088385 17 2.959210779063838 0.0001065658977285227 18 3.667774215946338 1.080276720662476e-06 19 4.499599398310388 1.529571770532236e-09 1 -7.251792998192644 6.641958938127579e-24 2 -6.54708325839754 8.604271725122073e-20 3 -5.9614610434045 1.140700785308509e-16 4 -5.437443360177798 4.08820161202506e-14 5 -4.95357434291298 5.818033931703204e-12 6 -4.499599398310388 4.007841416048347e-10 7 -4.070919267883068 1.491582104178314e-08 8 -3.667774215946338 3.153722658522649e-07 9 -3.296114596212218 3.811827917491775e-06 10 -2.959210779063838 2.889767802744787e-05 11 -2.630415236459871 0.0001890109098050979 12 -2.266513262056788 0.001406974240652468 13 -2.043834754429505 -0.01445284222069882 14 -2.023230191100516 0.01788525430336997 15 -1.835707975175187 0.0007054711101229627 16 -1.585873011819188 0.01654455267058608 17 -1.224744871391589 0.04510901033585913 18 -0.8700408953529029 0.09283382285101119 19 -0.5240335474869576 0.1459662938959264 20 -0.195324784415805 0.1656397404005296 21 0 0.05627934260432189 22 0.195324784415805 0.1656397404005296 23 0.5240335474869576 0.1459662938959264 24 0.8700408953529029 0.09283382285101119 25 1.224744871391589 0.04510901033585913 26 1.585873011819188 0.01654455267058608 27 1.835707975175187 0.0007054711101229627 28 2.023230191100516 0.01788525430336997 29 2.043834754429505 -0.01445284222069882 30 2.266513262056788 0.001406974240652468 31 2.630415236459871 0.0001890109098050979 32 2.959210779063838 2.889767802744787e-05 33 3.296114596212218 3.811827917491775e-06 34 3.667774215946338 3.153722658522649e-07 35 4.070919267883068 1.491582104178314e-08 36 4.499599398310388 4.007841416048347e-10 37 4.95357434291298 5.818033931703204e-12 38 5.437443360177798 4.08820161202506e-14 39 5.9614610434045 1.140700785308509e-16 40 6.54708325839754 8.604271725122073e-20 41 7.251792998192644 6.641958938127579e-24 HERMITE_GK24_SET_TEST HERMITE_GK24_SET sets up a nested rule for the Hermite integration problem. Index X W 1 0 1.772453850905516 1 -1.224744871391589 0.2954089751509193 2 0 1.181635900603677 3 1.224744871391589 0.2954089751509193 1 -2.959210779063838 0.0001670882630688235 2 -2.023230191100516 0.0141731178739791 3 -1.224744871391589 0.1681189289476777 4 -0.5240335474869576 0.4786942854911412 5 0 0.450147009753782 6 0.5240335474869576 0.4786942854911412 7 1.224744871391589 0.1681189289476777 8 2.023230191100516 0.0141731178739791 9 2.959210779063838 0.0001670882630688235 1 -4.499599398310388 1.529571770532236e-09 2 -3.667774215946338 1.080276720662476e-06 3 -2.959210779063838 0.0001065658977285227 4 -2.266513262056788 0.005113317439088385 5 -2.023230191100516 -0.01123243848906923 6 -1.835707975175187 0.03205524309944588 7 -1.224744871391589 0.1136072989574827 8 -0.8700408953529029 0.1083886195500302 9 -0.5240335474869576 0.3692464336892085 10 0 0.5378816070051017 11 0.5240335474869576 0.3692464336892085 12 0.8700408953529029 0.1083886195500302 13 1.224744871391589 0.1136072989574827 14 1.835707975175187 0.03205524309944588 15 2.023230191100516 -0.01123243848906923 16 2.266513262056788 0.005113317439088385 17 2.959210779063838 0.0001065658977285227 18 3.667774215946338 1.080276720662476e-06 19 4.499599398310388 1.529571770532236e-09 1 -10.16757499488187 5.461919474783181e-38 2 -7.231746029072501 8.754490987132388e-24 3 -6.535398426382995 9.926199715601491e-20 4 -5.954781975039809 1.226196149478644e-16 5 -5.434053000365068 4.21921851448196e-14 6 -4.952329763008589 5.869158852517349e-12 7 -4.499599398310388 4.000305754257769e-10 8 -4.071335874253583 1.486536435717965e-08 9 -3.667774215946338 3.160183632212892e-07 10 -3.295265921534226 3.838807619473985e-06 11 -2.959210779063838 2.868023180647778e-05 12 -2.633356763661946 0.0001847894656883574 13 -2.266513262056788 0.001509093332116388 14 -2.089340389294661 -0.003879955862387716 15 -2.023230191100516 0.00673547589010133 16 -1.835707975175187 0.001399662522915681 17 -1.583643465293944 0.01636168734938324 18 -1.224744871391589 0.0450612329041865 19 -0.8700408953529029 0.09287115844425754 20 -0.5240335474869576 0.1458632926321473 21 -0.196029453662011 0.1648809136874367 22 0 0.05795959861011811 23 0.196029453662011 0.1648809136874367 24 0.5240335474869576 0.1458632926321473 25 0.8700408953529029 0.09287115844425754 26 1.224744871391589 0.0450612329041865 27 1.583643465293944 0.01636168734938324 28 1.835707975175187 0.001399662522915681 29 2.023230191100516 0.00673547589010133 30 2.089340389294661 -0.003879955862387716 31 2.266513262056788 0.001509093332116388 32 2.633356763661946 0.0001847894656883574 33 2.959210779063838 2.868023180647778e-05 34 3.295265921534226 3.838807619473985e-06 35 3.667774215946338 3.160183632212892e-07 36 4.071335874253583 1.486536435717965e-08 37 4.499599398310388 4.000305754257769e-10 38 4.952329763008589 5.869158852517349e-12 39 5.434053000365068 4.21921851448196e-14 40 5.954781975039809 1.226196149478644e-16 41 6.535398426382995 9.926199715601491e-20 42 7.231746029072501 8.754490987132388e-24 43 10.16757499488187 5.461919474783181e-38 HERMITE_1_SET_TEST HERMITE_1_SET sets a unit density Hermite quadrature rule; The integration interval is ( -oo, +oo ). The weight is 1. Index X W 1 0 1.772453850905516 1 -0.7071067811865476 1.461141182661139 2 0.7071067811865476 1.461141182661139 1 -1.224744871391589 1.323931175213644 2 0 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 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 0.8102646175568073 5 0.8162878828589647 0.8286873032836393 6 1.673551628767471 0.8971846002251841 7 2.651961356835233 1.101330729610322 1 -2.930637420257244 1.07193014424798 2 -1.981656756695843 0.8667526065633814 3 -1.15719371244678 0.7928900483864013 4 -0.3811869902073221 0.7645441286517292 5 0.3811869902073221 0.7645441286517292 6 1.15719371244678 0.7928900483864013 7 1.981656756695843 0.8667526065633814 8 2.930637420257244 1.07193014424798 1 -3.190993201781528 1.047003580976684 2 -2.266580584531843 0.8417527014786704 3 -1.468553289216668 0.7646081250945502 4 -0.7235510187528376 0.7303024527450922 5 0 0.720235215606051 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 -2.53273167423279 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 2.53273167423279 0.8206661264048164 10 3.436159118837737 1.025451691365735 HERMITE_PROBABILIST_SET_TEST HERMITE_PROBABILIST_SET sets a Hermite quadrature rule; The integration interval is ( -oo, +oo ). The weight is exp ( - x * x / 2 ) / sqrt ( 2 * pi ). Index X W 1 0 1 1 -1 0.5 2 1 0.5 1 -1.732050807568877 0.1666666666666667 2 0 0.6666666666666666 3 1.732050807568877 0.1666666666666667 1 -2.334414218338977 0.04587585476806849 2 -0.7419637843027258 0.4541241452319315 3 0.7419637843027258 0.4541241452319315 4 2.334414218338977 0.04587585476806849 1 -2.856970013872806 0.01125741132772069 2 -1.355626179974266 0.2220759220056127 3 0 0.5333333333333333 4 1.355626179974266 0.2220759220056127 5 2.856970013872806 0.01125741132772069 1 -3.324257433552119 0.002555784402056247 2 -1.889175877753711 0.08861574604191452 3 -0.6167065901925941 0.4088284695560293 4 0.6167065901925941 0.4088284695560293 5 1.889175877753711 0.08861574604191452 6 3.324257433552119 0.002555784402056247 1 -3.750439717725742 0.0005482688559722178 2 -2.366759410734541 0.0307571239675865 3 -1.154405394739968 0.2401231786050127 4 0 0.4571428571428571 5 1.154405394739968 0.2401231786050127 6 2.366759410734541 0.0307571239675865 7 3.750439717725742 0.0005482688559722178 1 -4.144547186125894 0.0001126145383753678 2 -2.802485861287542 0.009635220120788266 3 -1.636519042435108 0.117239907661759 4 -0.5390798113513751 0.3730122576790774 5 0.5390798113513751 0.3730122576790774 6 1.636519042435108 0.117239907661759 7 2.802485861287542 0.009635220120788266 8 4.144547186125894 0.0001126145383753678 1 -4.512745863399783 2.234584400774658e-05 2 -3.20542900285647 0.002789141321231769 3 -2.07684797867783 0.04991640676521787 4 -1.023255663789133 0.2440975028949394 5 0 0.4063492063492063 6 1.023255663789133 0.2440975028949394 7 2.07684797867783 0.04991640676521787 8 3.20542900285647 0.002789141321231769 9 4.512745863399783 2.234584400774658e-05 1 -4.859462828332312 4.310652630718287e-06 2 -3.581823483551927 0.0007580709343122177 3 -2.484325841638955 0.01911158050077029 4 -1.465989094391158 0.1354837029802677 5 -0.4849357075154976 0.3446423349320191 6 0.4849357075154976 0.3446423349320191 7 1.465989094391158 0.1354837029802677 8 2.484325841638955 0.01911158050077029 9 3.581823483551927 0.0007580709343122177 10 4.859462828332312 4.310652630718287e-06 IMTQLX_TEST IMTQLX takes a symmetric tridiagonal matrix A and computes its eigenvalues LAM. It also accepts a vector Z and computes Q'*Z, where Q is the matrix that diagonalizes A. Computed eigenvalues: 1: 0.267949 2: 1 3: 2 4: 3 5: 3.73205 Exact eigenvalues: 1: 0.267949 2: 1 3: 2 4: 3 5: 3.73205 Vector Z: 1: 1 2: 1 3: 1 4: 1 5: 1 Vector Q'*Z: 1: -2.1547 2: -1.8855e-16 3: 0.57735 4: 1.66533e-16 5: -0.154701 JACOBI_EK_COMPUTE_TEST JACOBI_EK_COMPUTE sets up Gauss-Jacobi quadrature; ALPHA = 1.500000 BETA = 0.500000 Index X W 1 -0.25 1.570796326794896 1 -0.6076252185107651 0.933824464862914 2 0.2742918851774317 0.6369718619319824 1 -0.760157340487268 0.5261284436611056 2 -0.1528288638647804 0.8030739600082096 3 0.5379862043520485 0.2415939231255808 1 -0.8385964119177012 0.3144794551130207 2 -0.4056256275378191 0.678743654928424 3 0.1614690409023142 0.4757517664489192 4 0.682752998553206 0.1018214503045317 1 -0.8840882653201492 0.2001252566372697 2 -0.5629059317762043 0.5199632186774659 3 -0.1100274225210447 0.5356898968305487 4 0.3708136309492863 0.2672477173275187 5 0.7695413220014449 0.04777023732209325 1 -0.9127717928725458 0.1343056820427146 2 -0.6661693810819842 0.3902780567984853 3 -0.3028312803228947 0.499078675899895 4 0.1144215303885477 0.3697846812371453 5 0.5134534103439395 0.1528283716957896 6 0.8253260849735088 0.02452085912086582 1 -0.9320024628657495 0.09414510038510714 2 -0.7371931739434825 0.2943041944091259 3 -0.4418817729485141 0.4309263997770963 4 -0.0859506602240641 0.4009490239804647 5 0.2825323324996323 0.2463697069136382 6 0.6138099722388769 0.09055772921029319 7 0.8631857652433008 0.01354417211917143 1 -0.9455158043974037 0.06839190925948291 2 -0.7879673764819102 0.2248513392666883 3 -0.5444273641737976 0.3606436566319117 4 -0.2412867334092742 0.3883180543539711 5 0.08860534544266944 0.3008492695347081 6 0.4095019972429188 0.16405734578548 7 0.6866356906720186 0.0557415005793357 8 0.8900098006603341 0.007943251383318863 1 -0.9553706327691448 0.05117382374316969 2 -0.8254480244332432 0.1744634097524552 3 -0.6217762959622662 0.2984741580861981 4 -0.3624524217425484 0.3552731274654827 5 -0.07051816095979085 0.3200587357332041 6 0.2280875011498078 0.220229706982839 7 0.5068337773772098 0.1106616329196992 8 0.7409581449066003 0.03556668124983503 9 0.9096861124333756 0.004895050862014656 1 -0.962776688670377 0.03925058540055813 2 -0.8538674269792412 0.1374810592741681 3 -0.6813494824055374 0.2466379844126227 4 -0.4580176529455094 0.3155655291519008 5 -0.2004353100508689 0.3157558361063397 6 0.07229409169326702 0.2531373506672515 7 0.3399439927530339 0.1603930057544804 8 0.5826653601184614 0.07598607784811179 9 0.7824610233136923 0.02344462385831613 10 0.9245366386276249 0.003144274321147394 JACOBI_INTEGRAL_TEST JACOBI_INTEGRAL evaluates Integral ( -1 < x < +1 ) x^n (1-x)^alpha (1+x)^beta dx Use ALPHA = 1.5 BETA = 0.5 N Value 0 1.570796326794896 1 -0.3926990816987241 2 0.392699081698724 3 -0.1963495408493619 4 0.1963495408493619 5 -0.1227184630308513 6 0.1227184630308513 7 -0.08590292412159588 8 0.08590292412159588 9 -0.06442719309119695 10 0.06442719309119677 JACOBI_SS_COMPUTE_TEST JACOBI_SS_COMPUTE sets up Gauss-Jacobi quadrature; ALPHA = 1.500000 BETA = 0.500000 Index X W 1 -0.25 1.570796326794896 1 -0.6076252185107651 0.9338244648629137 2 0.2742918851774317 0.6369718619319822 1 -0.760157340487268 0.5261284436611049 2 -0.1528288638647804 0.8030739600082106 3 0.5379862043520485 0.2415939231255805 1 -0.8385964119177013 0.3144794551130212 2 -0.4056256275378191 0.6787436549284246 3 0.1614690409023143 0.4757517664489192 4 0.682752998553206 0.1018214503045319 1 -0.8840882653201494 0.20012525663727 2 -0.5629059317762043 0.5199632186774656 3 -0.1100274225210447 0.5356898968305488 4 0.3708136309492864 0.2672477173275187 5 0.7695413220014452 0.04777023732209335 1 -0.9127717928725457 0.134305682042714 2 -0.6661693810819842 0.3902780567984851 3 -0.3028312803228947 0.4990786758998956 4 0.1144215303885478 0.3697846812371455 5 0.5134534103439397 0.1528283716957897 6 0.8253260849735087 0.02452085912086589 1 -0.9320024628657496 0.09414510038510657 2 -0.7371931739434825 0.294304194409126 3 -0.4418817729485141 0.4309263997770965 4 -0.0859506602240642 0.4009490239804643 5 0.2825323324996325 0.246369706913638 6 0.6138099722388772 0.0905577292102932 7 0.8631857652433007 0.01354417211917143 1 -0.9455158043974035 0.06839190925948328 2 -0.7879673764819101 0.2248513392666886 3 -0.5444273641737976 0.3606436566319114 4 -0.2412867334092741 0.3883180543539708 5 0.08860534544266938 0.3008492695347083 6 0.4095019972429186 0.16405734578548 7 0.6866356906720188 0.05574150057933536 8 0.8900098006603341 0.007943251383318826 1 -0.9553706327691447 0.05117382374317006 2 -0.8254480244332433 0.1744634097524551 3 -0.6217762959622666 0.2984741580861979 4 -0.3624524217425487 0.3552731274654827 5 -0.07051816095979099 0.3200587357332037 6 0.2280875011498078 0.2202297069828386 7 0.5068337773772098 0.1106616329196987 8 0.7409581449066008 0.035566681249835 9 0.9096861124333758 0.004895050862014668 1 -0.962776688670377 0.03925058540055801 2 -0.8538674269792417 0.1374810592741682 3 -0.6813494824055374 0.2466379844126229 4 -0.4580176529455094 0.315565529151901 5 -0.2004353100508688 0.3157558361063396 6 0.07229409169326721 0.2531373506672514 7 0.3399439927530341 0.1603930057544803 8 0.5826653601184615 0.07598607784811139 9 0.7824610233136921 0.0234446238583162 10 0.9245366386276249 0.003144274321147395 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 5 0.3818300505051189 0.4058451513773972 6 0.2797053914892766 0.7415311855993945 7 0.1294849661688697 0.9491079123427585 1 0.02293532201052922 -0.9914553711208126 2 0.06309209262997854 -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 -0.207784955078985 8 0.2094821410847278 0 9 0.2044329400752989 0.207784955078985 10 0.1903505780647854 0.4058451513773972 11 0.1690047266392679 0.5860872354676911 12 0.1406532597155259 0.7415311855993943 13 0.1047900103222502 0.8648644233597691 14 0.06309209262997854 0.9491079123427585 15 0.02293532201052922 0.9914553711208126 Legendre/Kronrod quadrature pair #2 W X 1 0.06667134430868814 -0.9739065285171717 2 0.1494513491505806 -0.8650633666889845 3 0.219086362515982 -0.6794095682990244 4 0.2692667193099963 -0.4333953941292472 5 0.2955242247147529 -0.1488743389816312 6 0.2955242247147529 0.1488743389816312 7 0.2692667193099963 0.4333953941292472 8 0.219086362515982 0.6794095682990244 9 0.1494513491505806 0.8650633666889845 10 0.06667134430868814 0.9739065285171717 1 0.01169463886737187 -0.9956571630258081 2 0.03255816230796473 -0.9739065285171717 3 0.054755896574352 -0.9301574913557082 4 0.07503967481091996 -0.8650633666889845 5 0.09312545458369761 -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 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 0.09312545458369761 0.7808177265864169 18 0.07503967481091996 0.8650633666889845 19 0.054755896574352 0.9301574913557082 20 0.03255816230796473 0.9739065285171717 21 0.01169463886737187 0.9956571630258081 Legendre/Kronrod quadrature pair #3 W X 1 0.03075324199611727 -0.9879925180204854 2 0.07036604748810812 -0.937273392400706 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 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 0.07036604748810812 0.937273392400706 15 0.03075324199611727 0.9879925180204854 1 0.005377479872923349 -0.9980022986933971 2 0.01500794732931612 -0.9879925180204854 3 0.02546084732671532 -0.9677390756791391 4 0.03534636079137585 -0.937273392400706 5 0.04458975132476488 -0.8972645323440819 6 0.05348152469092809 -0.8482065834104272 7 0.06200956780067064 -0.7904185014424659 8 0.06985412131872826 -0.72441773136017 9 0.07684968075772038 -0.650996741297417 10 0.08308050282313302 -0.5709721726085388 11 0.08856444305621176 -0.4850818636402397 12 0.09312659817082532 -0.3941513470775634 13 0.09664272698362368 -0.2991800071531688 14 0.09917359872179196 -0.2011940939974345 15 0.1007698455238756 -0.1011420669187175 16 0.1013300070147915 0 17 0.1007698455238756 0.1011420669187175 18 0.09917359872179196 0.2011940939974345 19 0.09664272698362368 0.2991800071531688 20 0.09312659817082532 0.3941513470775634 21 0.08856444305621176 0.4850818636402397 22 0.08308050282313302 0.5709721726085388 23 0.07684968075772038 0.650996741297417 24 0.06985412131872826 0.72441773136017 25 0.06200956780067064 0.7904185014424659 26 0.05348152469092809 0.8482065834104272 27 0.04458975132476488 0.8972645323440819 28 0.03534636079137585 0.937273392400706 29 0.02546084732671532 0.9677390756791391 30 0.01500794732931612 0.9879925180204854 31 0.005377479872923349 0.9980022986933971 Legendre/Kronrod quadrature pair #4 W X 1 0.01761400713915212 -0.9931285991850949 2 0.04060142980038694 -0.9639719272779138 3 0.06267204833410907 -0.9122344282513259 4 0.08327674157670475 -0.8391169718222188 5 0.1019301198172404 -0.7463319064601508 6 0.1181945319615184 -0.636053680726515 7 0.1316886384491766 -0.5108670019508271 8 0.142096109318382 -0.3737060887154195 9 0.1491729864726037 -0.2277858511416451 10 0.1527533871307258 -0.07652652113349734 11 0.1527533871307258 0.07652652113349734 12 0.1491729864726037 0.2277858511416451 13 0.142096109318382 0.3737060887154195 14 0.1316886384491766 0.5108670019508271 15 0.1181945319615184 0.636053680726515 16 0.1019301198172404 0.7463319064601508 17 0.08327674157670475 0.8391169718222188 18 0.06267204833410907 0.9122344282513259 19 0.04060142980038694 0.9639719272779138 20 0.01761400713915212 0.9931285991850949 1 0.003073583718520532 -0.9988590315882777 2 0.008600269855642943 -0.9931285991850949 3 0.01462616925697125 -0.9815078774502503 4 0.02038837346126652 -0.9639719272779138 5 0.02588213360495116 -0.9408226338317548 6 0.0312873067770328 -0.9122344282513259 7 0.0366001697582008 -0.878276811252282 8 0.04166887332797369 -0.8391169718222188 9 0.04643482186749767 -0.7950414288375512 10 0.05094457392372869 -0.7463319064601508 11 0.05519510534828599 -0.6932376563347514 12 0.05911140088063957 -0.636053680726515 13 0.06265323755478117 -0.5751404468197103 14 0.06583459713361842 -0.5108670019508271 15 0.06864867292852161 -0.4435931752387251 16 0.07105442355344407 -0.3737060887154196 17 0.07303069033278667 -0.301627868114913 18 0.0745828754004992 -0.2277858511416451 19 0.07570449768455667 -0.1526054652409227 20 0.07637786767208074 -0.07652652113349732 21 0.07660071191799966 0 22 0.07637786767208074 0.07652652113349732 23 0.07570449768455667 0.1526054652409227 24 0.0745828754004992 0.2277858511416451 25 0.07303069033278667 0.301627868114913 26 0.07105442355344407 0.3737060887154196 27 0.06864867292852161 0.4435931752387251 28 0.06583459713361842 0.5108670019508271 29 0.06265323755478117 0.5751404468197103 30 0.05911140088063957 0.636053680726515 31 0.05519510534828599 0.6932376563347514 32 0.05094457392372869 0.7463319064601508 33 0.04643482186749767 0.7950414288375512 34 0.04166887332797369 0.8391169718222188 35 0.0366001697582008 0.878276811252282 36 0.0312873067770328 0.9122344282513259 37 0.02588213360495116 0.9408226338317548 38 0.02038837346126652 0.9639719272779138 39 0.01462616925697125 0.9815078774502503 40 0.008600269855642943 0.9931285991850949 41 0.003073583718520532 0.9988590315882777 LAGUERRE_EK_COMPUTE_TEST LAGUERRE_EK_COMPUTE computes a Laguerre quadrature rule using the Elhay-Kautsky algorithm. Index X W 1 1 1 1 0.5857864376269051 0.853553390593274 2 3.414213562373094 0.1464466094067262 1 0.4157745567834791 0.7110930099291731 2 2.294280360279042 0.2785177335692407 3 6.289945082937479 0.01038925650158614 1 0.3225476896193926 0.6031541043416337 2 1.745761101158347 0.3574186924377996 3 4.536620296921128 0.0388879085150054 4 9.395070912301131 0.000539294705561328 1 0.263560319718141 0.5217556105828089 2 1.413403059106517 0.3986668110831761 3 3.596425771040722 0.07594244968170767 4 7.085810005858837 0.003611758679922046 5 12.64080084427578 2.336997238577622e-05 1 0.2228466041792608 0.4589646739499636 2 1.188932101672624 0.4170008307721204 3 2.992736326059315 0.1133733820740448 4 5.775143569104511 0.01039919745314906 5 9.837467418382589 0.0002610172028149321 6 15.9828739806017 8.985479064296216e-07 1 0.1930436765603624 0.4093189517012744 2 1.026664895339192 0.4218312778617198 3 2.567876744950746 0.1471263486575055 4 4.900353084526484 0.02063351446871697 5 8.182153444562855 0.001074010143280748 6 12.73418029179781 1.586546434856422e-05 7 19.39572786226255 3.170315478995567e-08 1 0.1702796323051015 0.3691885893416387 2 0.9037017767993818 0.4187867808143421 3 2.251086629866132 0.1757949866371719 4 4.266700170287656 0.03334349226121559 5 7.045905402393467 0.002794536235225666 6 10.758516010181 9.076508773358223e-05 7 15.740678641278 8.485746716272525e-07 8 22.86313173688927 1.048001174871508e-09 1 0.1523222277318082 0.3361264217979625 2 0.8072200227422558 0.4112139804239848 3 2.005135155619348 0.1992875253708853 4 3.783473973331234 0.04746056276565157 5 6.204956777876612 0.005599626610794585 6 9.372985251687572 0.0003052497670932117 7 13.46623691109209 6.592123026075368e-06 8 18.8335977889917 4.110769330349561e-08 9 26.37407189092738 3.290874030350725e-11 1 0.1377934705404928 0.3084411157650208 2 0.729454549503172 0.4011199291552736 3 1.808342901740319 0.2180682876118088 4 3.401433697854901 0.06208745609867754 5 5.552496140063805 0.009501516975181085 6 8.330152746764496 0.0007530083885875395 7 11.84378583790006 2.825923349599567e-05 8 16.2792578313781 4.24931398496269e-07 9 21.99658581198076 1.839564823979623e-09 10 29.92069701227389 9.911827219609021e-13 LAGUERRE_INTEGRAL_TEST LAGUERRE_INTEGRAL evaluates Integral ( 0 < x < oo ) x^n * exp(-x) dx N Value 0 1 1 1 2 2 3 6 4 24 5 120 6 720 7 5040 8 40320 9 362880 10 3628800 LAGUERRE_SET_TEST LAGUERRE_SET sets a Laguerre rule. I X W 1 1 1 1 0.585786437626905 0.8535533905932737 2 3.414213562373095 0.1464466094067262 1 0.4157745567834791 0.711093009929173 2 2.294280360279042 0.2785177335692409 3 6.289945082937479 0.01038925650158613 1 0.3225476896193923 0.6031541043416336 2 1.745761101158346 0.3574186924377997 3 4.536620296921128 0.03888790851500538 4 9.395070912301133 0.0005392947055613274 1 0.2635603197181409 0.5217556105828086 2 1.413403059106517 0.3986668110831759 3 3.596425771040722 0.0759424496817076 4 7.085810005858837 0.003611758679922048 5 12.64080084427578 2.336997238577623e-05 1 0.2228466041792607 0.4589646739499636 2 1.188932101672623 0.417000830772121 3 2.992736326059314 0.113373382074045 4 5.77514356910451 0.01039919745314907 5 9.837467418382589 0.0002610172028149321 6 15.9828739806017 8.985479064296212e-07 1 0.1930436765603624 0.4093189517012739 2 1.026664895339192 0.4218312778617198 3 2.567876744950746 0.1471263486575053 4 4.900353084526484 0.02063351446871694 5 8.182153444562861 0.001074010143280746 6 12.73418029179781 1.58654643485642e-05 7 19.39572786226254 3.17031547899558e-08 1 0.170279632305101 0.3691885893416375 2 0.9037017767993799 0.418786780814343 3 2.251086629866131 0.1757949866371718 4 4.266700170287659 0.03334349226121565 5 7.045905402393466 0.002794536235225673 6 10.758516010181 9.076508773358213e-05 7 15.740678641278 8.485746716272531e-07 8 22.86313173688927 1.04800117487151e-09 1 0.1523222277318083 0.3361264217979625 2 0.8072200227422558 0.4112139804239844 3 2.005135155619347 0.1992875253708856 4 3.783473973331233 0.0474605627656516 5 6.204956777876613 0.005599626610794583 6 9.372985251687576 0.0003052497670932106 7 13.46623691109209 6.592123026075352e-06 8 18.8335977889917 4.110769330349548e-08 9 26.37407189092738 3.290874030350708e-11 1 0.1377934705404924 0.3084411157650201 2 0.7294545495031705 0.4011199291552736 3 1.808342901740316 0.2180682876118094 4 3.4014336978549 0.06208745609867775 5 5.552496140063804 0.009501516975181101 6 8.330152746764497 0.0007530083885875388 7 11.84378583790007 2.825923349599566e-05 8 16.2792578313781 4.249313984962686e-07 9 21.99658581198076 1.839564823979631e-09 10 29.92069701227389 9.911827219609008e-13 LAGUERRE_SS_COMPUTE_TEST LAGUERRE_SS_COMPUTE computes a Laguerre quadrature rule using the Stroud-Secrest algorithm. Index X W 1 1 1 1 0.585786437626905 0.8535533905932738 2 3.414213562373095 0.1464466094067263 1 0.4157745567834791 0.7110930099291736 2 2.294280360279042 0.2785177335692409 3 6.289945082937479 0.01038925650158613 1 0.3225476896193922 0.6031541043416347 2 1.745761101158347 0.3574186924377997 3 4.536620296921128 0.03888790851500539 4 9.395070912301133 0.0005392947055613274 1 0.2635603197181409 0.5217556105828079 2 1.413403059106517 0.3986668110831759 3 3.596425771040722 0.07594244968170759 4 7.085810005858837 0.003611758679922049 5 12.64080084427578 2.336997238577624e-05 1 0.2228466041792606 0.458964673949965 2 1.188932101672623 0.4170008307721219 3 2.992736326059314 0.113373382074045 4 5.775143569104511 0.01039919745314908 5 9.837467418382589 0.0002610172028149323 6 15.9828739806017 8.985479064296228e-07 1 0.1930436765603623 0.4093189517012772 2 1.026664895339192 0.42183127786172 3 2.567876744950746 0.1471263486575052 4 4.900353084526484 0.02063351446871694 5 8.182153444562861 0.001074010143280746 6 12.73418029179781 1.586546434856422e-05 7 19.39572786226254 3.170315478995584e-08 1 0.170279632305101 0.3691885893416355 2 0.9037017767993799 0.4187867808143441 3 2.251086629866131 0.1757949866371716 4 4.266700170287659 0.03334349226121566 5 7.045905402393466 0.00279453623522567 6 10.758516010181 9.076508773358207e-05 7 15.740678641278 8.48574671627254e-07 8 22.86313173688927 1.048001174871508e-09 1 0.1523222277318083 0.3361264217979637 2 0.8072200227422559 0.4112139804239832 3 2.005135155619347 0.1992875253708851 4 3.783473973331233 0.0474605627656516 5 6.204956777876613 0.005599626610794582 6 9.372985251687576 0.0003052497670932108 7 13.46623691109209 6.592123026075359e-06 8 18.8335977889917 4.110769330349552e-08 9 26.37407189092738 3.290874030350716e-11 1 0.1377934705404924 0.3084411157650176 2 0.7294545495031703 0.4011199291552729 3 1.808342901740316 0.2180682876118093 4 3.4014336978549 0.06208745609867769 5 5.552496140063804 0.009501516975181101 6 8.330152746764497 0.0007530083885875383 7 11.84378583790007 2.825923349599563e-05 8 16.2792578313781 4.249313984962677e-07 9 21.99658581198076 1.839564823979632e-09 10 29.92069701227389 9.911827219609019e-13 LAGUERRE_1_SET_TEST LAGUERRE_1_SET sets a Laguerre rule. The density function is rho(x)=1. I X W 1 1 2.718281828459045 1 0.585786437626905 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 6.48714508440766 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 5.77514356910451 3.350524582355455 5 9.837467418382589 4.886826800210821 6 15.9828739806017 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 8.40543248682831 1 0.170279632305101 0.4377234104929114 2 0.9037017767993799 1.033869347665598 3 2.251086629866131 1.669709765658776 4 4.266700170287659 2.376924701758599 5 7.045905402393466 3.208540913347926 6 10.758516010181 4.268575510825134 7 15.740678641278 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 18.8335977889917 6.212275419747135 9 26.37407189092738 9.363218237705798 1 0.1377934705404924 0.3540097386069963 2 0.7294545495031705 0.8319023010435806 3 1.808342901740316 1.330288561749328 4 3.4014336978549 1.863063903111131 5 5.552496140063804 2.450255558083011 6 8.330152746764497 3.122764155135185 7 11.84378583790007 3.934152695561524 8 16.2792578313781 4.99241487219303 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. Index X W 1 0 2 1 -0.5773502691896257 0.9999999999999998 2 0.5773502691896257 0.9999999999999998 1 -0.7745966692414833 0.5555555555555558 2 0 0.8888888888888888 3 0.7745966692414833 0.5555555555555558 1 -0.8611363115940526 0.3478548451374539 2 -0.3399810435848563 0.6521451548625462 3 0.3399810435848563 0.6521451548625462 4 0.8611363115940526 0.3478548451374539 1 -0.906179845938664 0.2369268850561891 2 -0.5384693101056831 0.4786286704993666 3 0 0.5688888888888889 4 0.5384693101056831 0.4786286704993666 5 0.906179845938664 0.2369268850561891 1 -0.9324695142031521 0.1713244923791702 2 -0.6612093864662645 0.3607615730481386 3 -0.2386191860831969 0.467913934572691 4 0.2386191860831969 0.467913934572691 5 0.6612093864662645 0.3607615730481386 6 0.9324695142031521 0.1713244923791702 1 -0.9491079123427585 0.1294849661688699 2 -0.7415311855993945 0.2797053914892767 3 -0.4058451513773972 0.3818300505051191 4 0 0.4179591836734693 5 0.4058451513773972 0.3818300505051191 6 0.7415311855993945 0.2797053914892767 7 0.9491079123427585 0.1294849661688699 1 -0.9602898564975362 0.1012285362903764 2 -0.7966664774136267 0.2223810344533745 3 -0.525532409916329 0.3137066458778873 4 -0.1834346424956498 0.3626837833783618 5 0.1834346424956498 0.3626837833783618 6 0.525532409916329 0.3137066458778873 7 0.7966664774136267 0.2223810344533745 8 0.9602898564975362 0.1012285362903764 1 -0.9681602395076261 0.08127438836157443 2 -0.8360311073266358 0.1806481606948573 3 -0.6133714327005904 0.2606106964029354 4 -0.3242534234038089 0.3123470770400029 5 0 0.3302393550012598 6 0.3242534234038089 0.3123470770400029 7 0.6133714327005904 0.2606106964029354 8 0.8360311073266358 0.1806481606948573 9 0.9681602395076261 0.08127438836157443 1 -0.9739065285171717 0.06667134430868805 2 -0.8650633666889845 0.1494513491505806 3 -0.6794095682990244 0.2190863625159821 4 -0.4333953941292472 0.2692667193099965 5 -0.1488743389816312 0.295524224714753 6 0.1488743389816312 0.295524224714753 7 0.4333953941292472 0.2692667193099965 8 0.6794095682990244 0.2190863625159821 9 0.8650633666889845 0.1494513491505806 10 0.9739065285171717 0.06667134430868805 LEGENDRE_EK_COMPUTE_TEST LEGENDRE_EK_COMPUTE computes a Legendre quadrature rule using the Elhay-Kautsky algorithm. Index X W 1 0 2 1 -0.5773502691896256 1 2 0.5773502691896256 1 1 -0.7745966692414832 0.5555555555555559 2 -6.466579952145703e-17 0.8888888888888886 3 0.7745966692414834 0.5555555555555554 1 -0.8611363115940526 0.3478548451374537 2 -0.3399810435848563 0.6521451548625463 3 0.3399810435848564 0.6521451548625459 4 0.8611363115940522 0.347854845137454 1 -0.9061798459386641 0.2369268850561892 2 -0.538469310105683 0.4786286704993667 3 -3.478412152580952e-17 0.5688888888888882 4 0.5384693101056829 0.478628670499367 5 0.9061798459386642 0.2369268850561892 1 -0.9324695142031522 0.1713244923791701 2 -0.6612093864662647 0.3607615730481389 3 -0.2386191860831971 0.4679139345726916 4 0.2386191860831969 0.4679139345726918 5 0.6612093864662648 0.3607615730481388 6 0.9324695142031524 0.1713244923791705 1 -0.9491079123427583 0.1294849661688696 2 -0.7415311855993943 0.2797053914892763 3 -0.4058451513773971 0.381830050505119 4 4.452841060583418e-17 0.4179591836734696 5 0.4058451513773971 0.3818300505051177 6 0.7415311855993941 0.2797053914892761 7 0.9491079123427584 0.1294849661688694 1 -0.9602898564975358 0.101228536290376 2 -0.7966664774136267 0.2223810344533742 3 -0.5255324099163291 0.3137066458778873 4 -0.1834346424956499 0.3626837833783611 5 0.1834346424956497 0.3626837833783627 6 0.5255324099163293 0.3137066458778878 7 0.7966664774136266 0.2223810344533745 8 0.9602898564975362 0.1012285362903759 1 -0.9681602395076263 0.08127438836157426 2 -0.836031107326636 0.1806481606948577 3 -0.6133714327005901 0.2606106964029359 4 -0.3242534234038091 0.3123470770400025 5 1.604668093316319e-16 0.3302393550012599 6 0.324253423403809 0.3123470770400033 7 0.6133714327005904 0.2606106964029349 8 0.836031107326636 0.180648160694857 9 0.9681602395076262 0.08127438836157452 1 -0.973906528517172 0.06667134430868817 2 -0.8650633666889845 0.1494513491505806 3 -0.6794095682990243 0.2190863625159822 4 -0.4333953941292472 0.2692667193099962 5 -0.1488743389816309 0.2955242247147525 6 0.148874338981631 0.2955242247147538 7 0.4333953941292469 0.2692667193099955 8 0.6794095682990243 0.2190863625159825 9 0.8650633666889844 0.14945134915058 10 0.973906528517172 0.06667134430868776 LEGENDRE_INTEGRAL_TEST LEGENDRE_INTEGRAL evaluates Integral ( -1 < x < +1 ) x^n dx N Value 0 2 1 0 2 0.6666666666666666 3 0 4 0.4 5 0 6 0.2857142857142857 7 0 8 0.2222222222222222 9 0 10 0.1818181818181818 LEGENDRE_SET_TEST LEGENDRE_SET sets a Legendre quadrature rule. I X W 1 0 2 1 -0.5773502691896257 1 2 0.5773502691896257 1 1 -0.7745966692414834 0.5555555555555556 2 0 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 -0.906179845938664 0.2369268850561891 2 -0.5384693101056831 0.4786286704993665 3 0 0.5688888888888889 4 0.5384693101056831 0.4786286704993665 5 0.906179845938664 0.2369268850561891 1 -0.9324695142031521 0.1713244923791704 2 -0.6612093864662645 0.3607615730481386 3 -0.2386191860831969 0.467913934572691 4 0.2386191860831969 0.467913934572691 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 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 -0.525532409916329 0.3137066458778873 4 -0.1834346424956498 0.362683783378362 5 0.1834346424956498 0.362683783378362 6 0.525532409916329 0.3137066458778873 7 0.7966664774136267 0.2223810344533745 8 0.9602898564975363 0.1012285362903763 1 -0.9681602395076261 0.08127438836157441 2 -0.8360311073266358 0.1806481606948574 3 -0.6133714327005904 0.2606106964029354 4 -0.3242534234038089 0.3123470770400029 5 0 0.3302393550012598 6 0.3242534234038089 0.3123470770400029 7 0.6133714327005904 0.2606106964029354 8 0.8360311073266358 0.1806481606948574 9 0.9681602395076261 0.08127438836157441 1 -0.9739065285171717 0.06667134430868814 2 -0.8650633666889845 0.1494513491505806 3 -0.6794095682990244 0.219086362515982 4 -0.4333953941292472 0.2692667193099963 5 -0.1488743389816312 0.2955242247147529 6 0.1488743389816312 0.2955242247147529 7 0.4333953941292472 0.2692667193099963 8 0.6794095682990244 0.219086362515982 9 0.8650633666889845 0.1494513491505806 10 0.9739065285171717 0.06667134430868814 LEGENDRE_SS_COMPUTE_TEST LEGENDRE_SS_COMPUTE computes a Legendre quadrature rule using the Stroud-Secrest algorithm. Index X W 1 0 2 1 -0.5773502691896257 1 2 0.5773502691896257 1 1 -0.7745966692414833 0.5555555555555551 2 0 0.8888888888888888 3 0.7745966692414834 0.5555555555555559 1 -0.8611363115940526 0.3478548451374538 2 -0.3399810435848563 0.652145154862546 3 0.3399810435848563 0.652145154862546 4 0.8611363115940526 0.3478548451374538 1 -0.906179845938664 0.236926885056189 2 -0.5384693101056831 0.4786286704993663 3 6.162975822039155e-33 0.5688888888888888 4 0.5384693101056831 0.4786286704993663 5 0.906179845938664 0.236926885056189 1 -0.9324695142031519 0.1713244923791686 2 -0.6612093864662645 0.3607615730481387 3 -0.2386191860831969 0.4679139345726911 4 0.2386191860831969 0.4679139345726909 5 0.6612093864662645 0.3607615730481383 6 0.9324695142031519 0.1713244923791676 1 -0.9491079123427585 0.1294849661688698 2 -0.7415311855993945 0.2797053914892751 3 -0.4058451513773972 0.381830050505119 4 0 0.4179591836734693 5 0.4058451513773972 0.381830050505119 6 0.7415311855993945 0.2797053914892766 7 0.9491079123427585 0.129484966168866 1 -0.9602898564975362 0.1012285362903727 2 -0.7966664774136267 0.2223810344533747 3 -0.525532409916329 0.3137066458778873 4 -0.1834346424956498 0.3626837833783619 5 0.1834346424956498 0.3626837833783619 6 0.525532409916329 0.3137066458778873 7 0.7966664774136267 0.2223810344533747 8 0.9602898564975362 0.1012285362903754 1 -0.9681602395076261 0.08127438836157465 2 -0.8360311073266358 0.1806481606948576 3 -0.6133714327005904 0.2606106964029355 4 -0.3242534234038089 0.3123470770400028 5 0 0.3302393550012597 6 0.3242534234038089 0.3123470770400028 7 0.6133714327005904 0.2606106964029355 8 0.8360311073266358 0.1806481606948576 9 0.9681602395076261 0.08127438836157465 1 -0.9739065285171717 0.0666713443086875 2 -0.8650633666889845 0.1494513491505805 3 -0.6794095682990244 0.2190863625159818 4 -0.4333953941292472 0.2692667193099962 5 -0.1488743389816312 0.2955242247147529 6 0.1488743389816312 0.2955242247147528 7 0.4333953941292472 0.2692667193099964 8 0.6794095682990244 0.2190863625159818 9 0.8650633666889845 0.1494513491505805 10 0.9739065285171717 0.0666713443086875 LOBATTO_COMPUTE_TEST LOBATTO_COMPUTE computes a Lobatto rule; I X W 1 -1 0.1666666666666667 2 -0.4472135954999579 0.8333333333333334 3 0.4472135954999579 0.8333333333333334 4 1 0.1666666666666667 1 -1 0.04761904761904762 2 -0.830223896278567 0.2768260473615659 3 -0.4688487934707142 0.4317453812098626 4 0 0.4876190476190476 5 0.4688487934707142 0.4317453812098626 6 0.830223896278567 0.2768260473615659 7 1 0.04761904761904762 1 -1 0.02222222222222222 2 -0.9195339081664587 0.1333059908510702 3 -0.7387738651055051 0.2248893420631264 4 -0.4779249498104445 0.2920426836796838 5 -0.165278957666387 0.3275397611838974 6 0.165278957666387 0.3275397611838974 7 0.4779249498104445 0.2920426836796838 8 0.7387738651055051 0.2248893420631264 9 0.9195339081664587 0.1333059908510702 10 1 0.02222222222222222 LOBATTO_SET_TEST LOBATTO_SET sets a Lobatto rule; I X W 1 -1.000000 0.166667 2 -0.447214 0.833333 3 0.447214 0.833333 4 1.000000 0.166667 1 -1.000000 0.047619 2 -0.830224 0.276826 3 -0.468849 0.431745 4 0.000000 0.487619 5 0.468849 0.431745 6 0.830224 0.276826 7 1.000000 0.047619 1 -1.000000 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 1.000000 0.022222 NC_COMPUTE_WEIGHTS_TEST NC_COMPUTE_WEIGHTS computes weights for a Newton-Cotes quadrature rule; Index X W 1 1 1 1 0 0.5 2 1 0.5 1 0 0.1666666666666666 2 0.5 0.6666666666666667 3 1 0.1666666666666666 1 0 0.125 2 0.3333333333333333 0.375 3 0.6666666666666666 0.375 4 1 0.1250000000000003 1 0 0.07777777777777839 2 0.25 0.3555555555555561 3 0.5 0.1333333333333329 4 0.75 0.3555555555555583 5 1 0.07777777777777795 1 0 0.06597222222222054 2 0.2 0.2604166666666643 3 0.4 0.1736111111111036 4 0.6000000000000001 0.1736111111110983 5 0.8 0.2604166666666812 6 1 0.06597222222222265 1 0 0.04880952380951875 2 0.1666666666666667 0.2571428571428811 3 0.3333333333333333 0.03214285714284415 4 0.5 0.3238095238094729 5 0.6666666666666666 0.03214285714285658 6 0.8333333333333333 0.2571428571428869 7 1 0.04880952380952097 1 0 0.04346064814816586 2 0.1428571428571428 0.2070023148149858 3 0.2857142857142857 0.07656250000019327 4 0.4285714285714285 0.1729745370369784 5 0.5714285714285714 0.1729745370356 6 0.7142857142857142 0.07656250000028919 7 0.8571428571428571 0.2070023148147788 8 1 0.043460648148127 1 0 0.03488536155206035 2 0.125 0.2076895943561112 3 0.25 -0.03273368606834737 4 0.375 0.3702292769000053 5 0.5 -0.1601410934754171 6 0.625 0.370229276900929 7 0.75 -0.03273368606535598 8 0.875 0.207689594355787 9 1 0.0348853615519884 1 0 0.03188616071442141 2 0.1111111111111111 0.1756808035688664 3 0.2222222222222222 0.01205357143862784 4 0.3333333333333333 0.2158928571379874 5 0.4444444444444444 0.06448660712109699 6 0.5555555555555556 0.06448660712536025 7 0.6666666666666666 0.2158928571306262 8 0.7777777777777777 0.01205357142661967 9 0.8888888888888888 0.1756808035701907 10 1 0.03188616071441192 NCC_COMPUTE_TEST NCC_COMPUTE computes a Newton-Cotes Closed quadrature rule; Index X W 1 0 2 1 -1 1 2 1 1 1 -1 0.3333333333333333 2 0 1.333333333333333 3 1 0.3333333333333333 1 -1 0.2500000000000004 2 -0.3333333333333333 0.7499999999999996 3 0.3333333333333333 0.75 4 1 0.25 1 -1 0.1555555555555557 2 -0.5 0.711111111111111 3 0 0.2666666666666666 4 0.5 0.711111111111111 5 1 0.1555555555555556 1 -1 0.1319444444444441 2 -0.6 0.5208333333333339 3 -0.2 0.3472222222222229 4 0.2 0.347222222222221 5 0.6 0.5208333333333326 6 1 0.1319444444444444 1 -1 0.09761904761904808 2 -0.6666666666666666 0.5142857142857133 3 -0.3333333333333333 0.06428571428570932 4 0 0.6476190476190524 5 0.3333333333333333 0.06428571428571317 6 0.6666666666666666 0.514285714285714 7 1 0.09761904761904755 1 -1 0.08692129629629897 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 0.08692129629629636 1 -1 0.06977072310405794 2 -0.75 0.4153791887125269 3 -0.5 -0.0654673721340393 4 -0.25 0.7404585537919086 5 0 -0.3202821869488677 6 0.25 0.740458553791866 7 0.5 -0.0654673721340393 8 0.75 0.4153791887125232 9 1 0.06977072310405667 1 -1 0.06377232142857905 2 -0.7777777777777778 0.3513616071428758 3 -0.5555555555555556 0.02410714285722957 4 -0.3333333333333333 0.4317857142858179 5 -0.1111111111111111 0.1289732142857689 6 0.1111111111111111 0.1289732142858637 7 0.3333333333333333 0.4317857142856988 8 0.5555555555555556 0.02410714285714771 9 0.7777777777777778 0.3513616071428603 10 1 0.06377232142857162 NCC_SET_TEST NCC_SET sets up a Newton-Cotes Closed quadrature rule; Index X W 1 0 2 1 -1 1 2 1 1 1 -1 0.333333 2 0 1.33333 3 1 0.333333 1 -1 0.25 2 -0.333333 0.75 3 0.333333 0.75 4 1 0.25 1 -1 0.155556 2 -0.5 0.711111 3 0 0.266667 4 0.5 0.711111 5 1 0.155556 1 -1 0.131944 2 -0.6 0.520833 3 -0.2 0.347222 4 0.2 0.347222 5 0.6 0.520833 6 1 0.131944 1 -1 0.097619 2 -0.666667 0.514286 3 -0.333333 0.0642857 4 0 0.647619 5 0.333333 0.0642857 6 0.666667 0.514286 7 1 0.097619 1 -1 0.0869213 2 -0.714286 0.414005 3 -0.428571 0.153125 4 -0.142857 0.345949 5 0.142857 0.345949 6 0.428571 0.153125 7 0.714286 0.414005 8 1 0.0869213 1 -1 0.0697707 2 -0.75 0.415379 3 -0.5 -0.0654674 4 -0.25 0.740459 5 0 -0.320282 6 0.25 0.740459 7 0.5 -0.0654674 8 0.75 0.415379 9 1 0.0697707 1 -1 0.0637723 2 -0.777778 0.351362 3 -0.555556 0.0241071 4 -0.333333 0.431786 5 -0.111111 0.128973 6 0.111111 0.128973 7 0.333333 0.431786 8 0.555556 0.0241071 9 0.777778 0.351362 10 1 0.0637723 NCO_COMPUTE_TEST NCO_COMPUTE computes a Newton-Cotes Open quadrature rule; Index X W 1 0 2 1 -0.3333333333333333 1 2 0.3333333333333333 1 1 -0.5 1.333333333333333 2 0 -0.6666666666666665 3 0.5 1.333333333333333 1 -0.6 0.9166666666666664 2 -0.2 0.08333333333333304 3 0.2 0.08333333333333304 4 0.6 0.9166666666666667 1 -0.6666666666666666 1.1 2 -0.3333333333333333 -1.4 3 0 2.6 4 0.3333333333333333 -1.4 5 0.6666666666666666 1.1 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 -0.75 0.9735449735449742 2 -0.5 -2.019047619047615 3 -0.25 4.647619047619042 4 0 -5.204232804232804 5 0.25 4.647619047619049 6 0.5 -2.019047619047616 7 0.75 0.9735449735449739 1 -0.7777777777777778 0.7977678571428612 2 -0.5555555555555556 -1.251339285714294 3 -0.3333333333333333 2.21741071428568 4 -0.1111111111111111 -0.7638392857142238 5 0.1111111111111111 -0.763839285714305 6 0.3333333333333333 2.217410714285695 7 0.5555555555555556 -1.251339285714285 8 0.7777777777777778 0.7977678571428563 1 -0.8 0.8917548500881828 2 -0.6 -2.577160493827184 3 -0.4 7.350088183421553 4 -0.2 -12.14065255731907 5 0 14.95194003527322 6 0.2 -12.14065255731914 7 0.4 7.350088183421514 8 0.6 -2.577160493827156 9 0.8 0.8917548500881831 1 -0.8181818181818182 0.7585088734567924 2 -0.6363636363636364 -1.819664627425049 3 -0.4545454545454545 4.319301146384676 4 -0.2727272727272727 -4.708337742504753 5 -0.09090909090909091 2.450192350088813 6 0.09090909090909091 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 a Newton-Cotes Open quadrature rule; Index X W 1 0 2 1 -0.333333 1 2 0.333333 1 1 -0.5 1.33333 2 0 -0.666667 3 0.5 1.33333 1 -0.6 0.916667 2 -0.2 0.0833333 3 0.2 0.0833333 4 0.6 0.916667 1 -0.666667 1.1 2 -0.333333 -1.4 3 0 2.6 4 0.333333 -1.4 5 0.666667 1.1 1 -0.714286 0.848611 2 -0.428571 -0.629167 3 -0.142857 0.780556 4 0.142857 0.780556 5 0.428571 -0.629167 6 0.714286 0.848611 1 -0.75 0.973545 2 -0.5 -2.01905 3 -0.25 4.64762 4 0 -5.20423 5 0.25 4.64762 6 0.5 -2.01905 7 0.75 0.973545 1 -0.777778 0.797768 2 -0.555556 -1.25134 3 -0.333333 2.21741 4 -0.111111 -0.763839 5 0.111111 -0.763839 6 0.333333 2.21741 7 0.555556 -1.25134 8 0.777778 0.797768 1 -0.8 0.891755 2 -0.6 -2.57716 3 -0.4 7.35009 4 -0.2 -12.1407 5 0 14.9519 6 0.2 -12.1407 7 0.4 7.35009 8 0.6 -2.57716 9 0.8 0.891755 1 -0.818182 0.758509 2 -0.636364 -1.81966 3 -0.454545 4.3193 4 -0.272727 -4.70834 5 -0.0909091 2.45019 6 0.0909091 2.45019 7 0.272727 -4.70834 8 0.454545 4.3193 9 0.636364 -1.81966 10 0.818182 0.758509 NCOH_COMPUTE_TEST NCOH_COMPUTE computes a Newton-Cotes Open Half quadrature rule; Index X W 1 0 2 1 -0.5 1 2 0.5 1 1 -0.6666666666666666 0.75 2 0 0.5 3 0.6666666666666666 0.75 1 -0.75 0.5416666666666666 2 -0.25 0.4583333333333335 3 0.25 0.4583333333333335 4 0.75 0.5416666666666666 1 -0.8 0.4774305555555558 2 -0.4 0.1736111111111107 3 0 0.697916666666667 4 0.4 0.1736111111111112 5 0.8 0.4774305555555554 1 -0.8333333333333334 0.3859375 2 -0.5 0.2171874999999994 3 -0.1666666666666667 0.3968749999999941 4 0.1666666666666667 0.3968750000000001 5 0.5 0.2171875000000004 6 0.8333333333333334 0.3859374999999999 1 -0.8571428571428571 0.3580005787037045 2 -0.5714285714285714 0.0127604166666625 3 -0.2857142857142857 0.8102864583333247 4 0 -0.3620949074074109 5 0.2857142857142857 0.8102864583333318 6 0.5714285714285714 0.01276041666666561 7 0.8571428571428571 0.3580005787037041 1 -0.875 0.3055007853835972 2 -0.625 0.07371135085978964 3 -0.375 0.4875279017857209 4 -0.125 0.1332599619708654 5 0.125 0.1332599619709007 6 0.375 0.487527901785696 7 0.625 0.07371135085978775 8 0.875 0.3055007853835978 1 -0.8888888888888888 0.2902556501116099 2 -0.6666666666666666 -0.09096261160714961 3 -0.4444444444444444 1.012537667410742 4 -0.2222222222222222 -1.12557756696433 5 0 1.82749372209814 6 0.2222222222222222 -1.125577566964292 7 0.4444444444444444 1.012537667410705 8 0.6666666666666666 -0.09096261160714395 9 0.8888888888888888 0.2902556501116076 1 -0.9 0.2557278856819025 2 -0.7 -0.02652149772308931 3 -0.5 0.6604044811645895 4 -0.3 -0.3376966473075349 5 -0.1 0.4480857781842378 6 0.1 0.4480857781845167 7 0.3 -0.3376966473076202 8 0.5 0.6604044811646075 9 0.7 -0.02652149772306411 10 0.9 0.2557278856819051 NCOH_SET_TEST NCOH_SET sets up a Newton-Cotes Open Half quadrature rule; Index X W 1 0 2 1 -0.5 1 2 0.5 1 1 -0.6666666666666666 0.75 2 0 0.5 3 0.6666666666666666 0.75 1 -0.75 0.5416666666666666 2 -0.25 0.4583333333333333 3 0.25 0.4583333333333333 4 0.75 0.5416666666666666 1 -0.8 0.4774305555555556 2 -0.4 0.1736111111111111 3 0 0.6979166666666666 4 0.4 0.1736111111111111 5 0.8 0.4774305555555556 1 -0.8333333333333334 0.3859375 2 -0.5 0.2171875 3 -0.1666666666666667 0.396875 4 0.1666666666666667 0.396875 5 0.5 0.2171875 6 0.8333333333333334 0.3859375 1 -0.8571428571428571 0.3580005787037037 2 -0.5714285714285714 0.01276041666666667 3 -0.2857142857142857 0.8102864583333333 4 0 -0.3620949074074074 5 0.2857142857142857 0.8102864583333333 6 0.5714285714285714 0.01276041666666667 7 0.8571428571428571 0.3580005787037037 1 -0.875 0.3055007853835979 2 -0.625 0.07371135085978836 3 -0.375 0.4875279017857143 4 -0.125 0.1332599619708995 5 0.125 0.1332599619708995 6 0.375 0.4875279017857143 7 0.625 0.07371135085978836 8 0.875 0.3055007853835979 1 -0.8888888888888888 0.2902556501116071 2 -0.6666666666666666 -0.09096261160714286 3 -0.4444444444444444 1.012537667410714 4 -0.2222222222222222 -1.125577566964286 5 0 1.827493722098214 6 0.2222222222222222 -1.125577566964286 7 0.4444444444444444 1.012537667410714 8 0.6666666666666666 -0.09096261160714286 9 0.8888888888888888 0.2902556501116071 1 -0.9 0.2557278856819059 2 -0.7 -0.0265214977230765 3 -0.5 0.6604044811645723 4 -0.3 -0.3376966473076499 5 -0.1 0.4480857781842482 6 0.1 0.4480857781842482 7 0.3 -0.3376966473076499 8 0.5 0.6604044811645723 9 0.7 -0.0265214977230765 10 0.9 0.2557278856819059 PATTERSON_SET_TEST PATTERSON_SET sets a Patterson quadrature rule; Index X W 1 0 2 1 -0.774597 0.555556 2 0 0.888889 3 0.774597 0.555556 1 -0.960491 0.104656 2 -0.774597 0.268488 3 -0.434244 0.401397 4 0 0.450917 5 0.434244 0.401397 6 0.774597 0.268488 7 0.960491 0.104656 1 -0.993832 0.0170017 2 -0.960491 0.0516033 3 -0.888459 0.0929272 4 -0.774597 0.134415 5 -0.621103 0.171512 6 -0.434244 0.200629 7 -0.223387 0.219157 8 0 0.22551 9 0.223387 0.219157 10 0.434244 0.200629 11 0.621103 0.171512 12 0.774597 0.134415 13 0.888459 0.0929272 14 0.960491 0.0516033 15 0.993832 0.0170017 R8_PSI_TEST: R8_PSI evaluates the Psi function. X Psi(X) Psi(X) DIFF (Tabulated) (R8_PSI) 1.00 -5.7721566490153287e-01 -5.7721566490153287e-01 0.0000e+00 1.10 -4.2375494041107681e-01 -4.2375494041107675e-01 5.5511e-17 1.20 -2.8903989659218832e-01 -2.8903989659218837e-01 5.5511e-17 1.30 -1.6919088886679970e-01 -1.6919088886679953e-01 1.6653e-16 1.40 -6.1384544585116149e-02 -6.1384544585116239e-02 9.0206e-17 1.50 3.6489973978576520e-02 3.6489973978576520e-02 0.0000e+00 1.60 1.2604745277347629e-01 1.2604745277347632e-01 2.7756e-17 1.70 2.0854787487349399e-01 2.0854787487349397e-01 2.7756e-17 1.80 2.8499143329386151e-01 2.8499143329386151e-01 0.0000e+00 1.90 3.5618416116405971e-01 3.5618416116405960e-01 1.1102e-16 2.00 4.2278433509846708e-01 4.2278433509846719e-01 1.1102e-16 RADAU_COMPUTE_TEST RADAU_COMPUTE computes a Radau rule; I X W 1 -1 0.125 2 -0.5753189235216941 0.6576886399601196 3 0.1810662711185306 0.7763869376863438 4 0.8228240809745921 0.4409244223535358 1 -1 0.04081632653061224 2 -0.8538913426394822 0.2392274892253124 3 -0.538467724060109 0.3809498736442313 4 -0.1173430375431003 0.4471098290145665 5 0.3260306194376914 0.4247037790059556 6 0.7038428006630314 0.3182042314673019 7 0.9413671456804302 0.1489884711120199 1 -1 0.02 2 -0.9274843742335811 0.1202966705574818 3 -0.7638420424200026 0.2042701318790008 4 -0.5256460303700792 0.2681948378411785 5 -0.2362344693905881 0.3058592877244227 6 0.07605919783797814 0.3135824572269384 7 0.3806648401447243 0.2906101648329185 8 0.6477666876740095 0.2391934317143795 9 0.8512252205816079 0.1643760127369217 10 0.9711751807022468 0.07361700548676069 RADAU_SET_TEST RADAU_SET sets a Radau rule. I X W 1 -1 0.125 2 -0.5753189235216941 0.6576886399601195 3 0.1810662711185306 0.7763869376863438 4 0.8228240809745921 0.4409244223535367 1 -1 0.04081632653061224 2 -0.8538913426394822 0.2392274892253124 3 -0.538467724060109 0.3809498736442312 4 -0.1173430375431003 0.4471098290145665 5 0.3260306194376914 0.4247037790059556 6 0.7038428006630314 0.3182042314673015 7 0.9413671456804302 0.1489884711120206 1 -1 0.02 2 -0.9274843742335811 0.1202966705574816 3 -0.7638420424200026 0.2042701318790007 4 -0.5256460303700792 0.2681948378411787 5 -0.236234469390588 0.3058592877244226 6 0.07605919783797813 0.3135824572269384 7 0.3806648401447243 0.2906101648329183 8 0.6477666876740095 0.2391934317143797 9 0.8512252205816079 0.1643760127369215 10 0.971175180702247 0.07361700548675849 quadrule_test Normal end of execution. 02-Mar-2019 10:00:16