01-Jan-2023 18:05:15 quad_rule_test(): MATLAB/Octave version 4.2.2 Test quad_rule(). 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 0.5877852522924731 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 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 -0.984807753012208 0.3490658503988659 2 -0.8660254037844385 0.3490658503988659 3 -0.6427876096865394 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 0.7853981633974484 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 0.3926990816987242 3 6.123233995736766e-17 0.5235987755982988 4 0.5000000000000001 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 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 0.766044443118978 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 6.123233995736766e-17 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 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 -1.04083e-17 1.04083e-17 y 10 0.666667 0.666723 5.65402e-05 x^2 10 0.392699 0.392699 5.55112e-17 x y 10 0 -2.21177e-17 2.21177e-17 y^2 10 0.392699 0.392699 0 x^3 10 0 2.42861e-17 2.42861e-17 x^2y 10 0.133333 0.133392 5.88566e-05 x y^2 10 0 4.77049e-18 4.77049e-18 y^3 10 0.266667 0.266666 1.15821e-06 x^4 10 0.19635 0.19635 0 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 0 x^2y^4 10 0.0245437 0.0245437 3.46945e-18 y^6 10 0.122718 0.122718 2.77556e-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 -0.6234898018587335 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 0.766044443118978 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 0.2539682539682539 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 -0.6234898018587335 0.3522424237181591 4 -0.2225209339563143 0.4372084057983264 5 0.2225209339563144 0.4372084057983264 6 0.6234898018587336 0.3522424237181591 7 0.9009688679024191 0.1901410072182084 8 1.0000000000000000 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 0.7660444431189780 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 0.4444444444444444 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 0.5877852522924731 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 0.08671618072672234 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 0.5555702330196024 0.3241525190645243 7 0.8314696123025453 0.2229879330145788 8 0.9807852804032304 0.06698294569858981 9 1 -0.984807753012208 0.05273664990990675 2 -0.8660254037844387 0.1791887125220458 3 -0.6427876096865394 0.2640372225410044 4 -0.3420201433256689 0.3308451751681364 5 -1.608122649676637e-16 0.346384479717813 6 0.3420201433256686 0.3308451751681365 7 0.6427876096865391 0.2640372225410044 8 0.8660254037844386 0.1791887125220459 9 0.984807753012208 0.05273664990990676 10 1 -0.9876883405951377 0.04293911957413079 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 0.8910065241883679 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 -0.6234898018587335 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 0.1779646809620499 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 0.766044443118978 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 0.5877852522924731 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 0.6548607339452851 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 0.1338211191983219 9 0 10 0.1047295715465128 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 52.34277778455352 5 287.8852778150443 6 1871.254305797788 7 14034.40729348341 8 119292.461994609 9 1133278.388948785 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 0.0009717812450995204 2 -1.673551628767471 0.05451558281912693 3 -0.8162878828589647 0.4256072526101276 4 -0 0.8102646175568072 5 0.8162878828589647 0.4256072526101276 6 1.673551628767471 0.05451558281912693 7 2.651961356835233 0.0009717812450995204 1 -2.930637420257244 0.0001996040722113675 2 -1.981656756695843 0.01707798300741346 3 -1.15719371244678 0.2078023258148916 4 -0.3811869902073221 0.6611470125582412 5 0.3811869902073221 0.6611470125582412 6 1.15719371244678 0.2078023258148916 7 1.981656756695843 0.01707798300741346 8 2.930637420257244 0.0001996040722113675 1 -3.190993201781527 3.960697726326426e-05 2 -2.266580584531843 0.004943624275536939 3 -1.468553289216668 0.08847452739437657 4 -0.7235510187528376 0.4326515590025556 5 -0 0.7202352156060509 6 0.7235510187528376 0.4326515590025556 7 1.468553289216668 0.08847452739437657 8 2.266580584531843 0.004943624275536939 9 3.190993201781527 3.960697726326426e-05 1 -3.436159118837738 7.640432855232643e-06 2 -2.53273167423279 0.001343645746781234 3 -1.756683649299882 0.03387439445548103 4 -1.036610829789514 0.2401386110823147 5 -0.3429013272237046 0.6108626337353256 6 0.3429013272237046 0.6108626337353256 7 1.036610829789514 0.2401386110823147 8 1.756683649299882 0.03387439445548103 9 2.53273167423279 0.001343645746781234 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 ALPHA = 1.5 BETA = 0.5 N Value 0 1.570796326794896 1 -0.3926990816987241 2 0.392699081698724 3 -0.196349540849362 4 0.196349540849362 5 -0.1227184630308513 6 0.1227184630308513 7 -0.08590292412159584 8 0.08590292412159588 9 -0.0644271930911969 10 0.0644271930911969 jacobi_ss_compute_test(): jacobi_ss_compute() sets up Gauss-Jacobi quadrature; ALPHA = 1.500000 BETA = 0.500000 Index X W 1 -0.25 1.570796326794897 1 -0.6076252185107651 0.933824464862914 2 0.2742918851774317 0.6369718619319824 1 -0.760157340487268 0.5261284436611051 2 -0.1528288638647804 0.803073960008211 3 0.5379862043520485 0.2415939231255806 1 -0.8385964119177013 0.3144794551130212 2 -0.4056256275378191 0.6787436549284247 3 0.1614690409023143 0.4757517664489193 4 0.682752998553206 0.1018214503045319 1 -0.8840882653201494 0.20012525663727 2 -0.5629059317762043 0.5199632186774659 3 -0.1100274225210447 0.535689896830549 4 0.3708136309492864 0.2672477173275188 5 0.7695413220014452 0.04777023732209337 1 -0.9127717928725457 0.134305682042714 2 -0.6661693810819842 0.3902780567984852 3 -0.3028312803228947 0.4990786758998957 4 0.1144215303885478 0.3697846812371456 5 0.5134534103439397 0.1528283716957898 6 0.8253260849735087 0.02452085912086589 1 -0.9320024628657496 0.09414510038510659 2 -0.7371931739434825 0.2943041944091261 3 -0.4418817729485141 0.4309263997770967 4 -0.0859506602240642 0.4009490239804645 5 0.2825323324996325 0.2463697069136381 6 0.6138099722388772 0.09055772921029323 7 0.8631857652433007 0.01354417211917143 1 -0.9455158043974035 0.0683919092594833 2 -0.7879673764819101 0.2248513392666887 3 -0.5444273641737976 0.3606436566319116 4 -0.2412867334092741 0.3883180543539708 5 0.08860534544266938 0.3008492695347084 6 0.4095019972429186 0.1640573457854801 7 0.6866356906720188 0.05574150057933537 8 0.8900098006603341 0.007943251383318828 1 -0.9553706327691447 0.05117382374317007 2 -0.8254480244332433 0.1744634097524552 3 -0.6217762959622666 0.298474158086198 4 -0.3624524217425487 0.3552731274654828 5 -0.07051816095979099 0.3200587357332038 6 0.2280875011498078 0.2202297069828387 7 0.5068337773772098 0.1106616329196987 8 0.7409581449066008 0.03556668124983501 9 0.9096861124333758 0.004895050862014669 1 -0.962776688670377 0.03925058540055803 2 -0.8538674269792417 0.1374810592741683 3 -0.6813494824055374 0.246637984412623 4 -0.4580176529455094 0.3155655291519011 5 -0.2004353100508688 0.3157558361063396 6 0.07229409169326721 0.2531373506672515 7 0.3399439927530341 0.1603930057544804 8 0.5826653601184615 0.07598607784811141 9 0.7824610233136921 0.02344462385831621 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 -0.5773502691896258 0.9999999999999994 2 0.5773502691896258 0.9999999999999994 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 0.1806481606948574 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 0.08127438836157443 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 quad_rule_test(): Normal end of execution. 01-Jan-2023 18:05:15