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diff --git a/src/algebra/nsfip.as.pamphlet b/src/algebra/nsfip.as.pamphlet deleted file mode 100644 index a0ceb8cd..00000000 --- a/src/algebra/nsfip.as.pamphlet +++ /dev/null @@ -1,1223 +0,0 @@ -\documentclass{article} -\usepackage{open-axiom} -\begin{document} -\title{\$SPAD/src/algebra nsfip.as} -\author{Michael Richardson} -\maketitle -\begin{abstract} -\end{abstract} -\eject -\tableofcontents -\eject -\section{NagSpecialFunctionsInterfacePackage} -<<NagSpecialFunctionsInterfacePackage>>= -+++ Author: M.G. Richardson -+++ Date Created: 1995 Nov. 27 -+++ Date Last Updated: -+++ Basic Functions: -+++ Related Constructors: -+++ Also See: -+++ AMS Classifications: -+++ Keywords: -+++ References: -+++ Description: -+++ This package provides Axiom-like interfaces to those of the NAG -+++ special functions in the NAGlink for which no equivalent -+++ functionality is transparently present in Axiom. - -NagSpecialFunctionsInterfacePackage: with { - - nagExpInt : DF -> DF ; - - ++ nagExpInt calculates an approximation to the exponential integral, - ++ \spad{E1}, defined by -#if saturn - ++ \[E_{1}(x) = \int_{x}^{\infty }\frac{e^{-u}}{u}\,du\] -#else - ++ \spad{E1(x) = integrate(1/u*%e^u, u=x..%infinity)} -#endif - ++ using the NAG routine S13AAF. - ++ For detailed information on the accuracy, please consult the NAG - ++ manual via the Browser page for the operation s13aaf. - - nagSinInt : DF -> DF ; - - ++ nagSinInt calculates an approximation to the sine integral, - ++ \spad{Si}, defined by -#if saturn - ++ \[{\rm Si} (x) = \int_{0}^{x}\frac{\sin u}{u}\,du\] -#else - ++ \spad{Si(x) = integrate(1/u*sin(u), u=0..x)} -#endif - ++ using the NAG routine S13ADF. - ++ For detailed information on the accuracy, please consult the NAG - ++ manual via the Browser page for the operation s13adf. - - nagCosInt : DF -> DF ; - - ++ nagCosInt calculates an approximation to the cosine integral, - ++ \spad{Ci}, defined by -#if saturn - ++ \[{\rm Ci} (x) = - ++ \gamma + \ln x+ \int_{0}^{x}\frac{\cos u- 1}{u}\,du\] -#else - ++ \spad{Ci(x) = gamma + log x + integrate(1/u*cos(u), u=0..x)} - ++ where \spad{gamma} is Euler's constant, -#endif - ++ using the NAG routine S13ACF. - ++ For detailed information on the accuracy, please consult the NAG - ++ manual via the Browser page for the operation s13acf. - - nagIncompleteGammaP : (DF, DF) -> DF ; -- to machine precision - - ++ nagIncompleteGammaP evaluates the incomplete gamma function - ++ \spad{P}, defined by -#if saturn - ++ \[P(a,x) & = & \frac{1}{\Gamma(a)}\int_{0}^{x}t^{a-1}e^{-t}\,dt\] -#else - ++ \spad{P(a,x) = 1/Gamma(a)*integrate(t^(a-1)%e^(-t),t=0..x)} -#endif - ++ to machine precision, using the NAG routine S14BAF. - - nagIncompleteGammaP : (DF, DF, DF) -> DF ; - - ++ nagIncompleteGammaP(a,x,tol) evaluates the incomplete gamma - ++ function \spad{P}, defined by -#if saturn - ++ \[P(a,x) & = & \frac{1}{\Gamma(a)}\int_{0}^{x}t^{a-1}e^{-t}\,dt\] -#else - ++ \spad{P(a,x) = 1/Gamma(a)*integrate(t^(a-1)%e^(-t),t=0..x)} -#endif - ++ to a relative accuracy \spad{tol}, using the NAG routine S14BAF. - - nagIncompleteGammaQ : (DF, DF) -> DF ; - - ++ nagIncompleteGammaQ evaluates the incomplete gamma function - ++ \spad{Q}, defined by -#if saturn - ++ \[Q(a,x)&=&\frac{1}{\Gamma(a)}\int_{x}^{\infty}t^{a-1}e^{-t}\,dt\] -#else - ++ \spad{Q(a,x) = 1/Gamma(a)*integrate(t^(a-1)%e^(-t),t=x..%infinity)} -#endif - ++ to machine precision, using the NAG routine S14BAF. - - nagIncompleteGammaQ : (DF, DF, DF) -> DF ; - - ++ nagIncompleteGammaQ(a,x,tol) evaluates the incomplete gamma - ++ function \spad{Q}, defined by -#if saturn - ++ \[Q(a,x)&=&\frac{1}{\Gamma(a)}\int_{x}^{\infty}t^{a-1}e^{-t}\,dt\] -#else - ++ \spad{Q(a,x) = 1/Gamma(a)*integrate(t^(a-1)%e^(-t),t=x..%infinity)} -#endif - ++ to a relative accuracy \spad{tol}, using the NAG routine S14BAF. - - nagErf : DF -> DF ; - - ++ nagErf calculates an approximation to the error function, - ++ \spad{erf}, defined by -#if saturn - ++ \[{\rm erf}\, x = \frac{2}{\sqrt{\pi}}\int_{0}^{x}e^{-t^{2}}\,dt\] -#else - ++ \spad{erf(x) = 2/sqrt(\%pi)*integrate(\%e^(-t^2),t=0..x)} -#endif - ++ using the NAG routine S15AEF. - ++ For detailed information on the accuracy, please consult the NAG - ++ manual via the Browser page for the operation s15aef. - - nagErfC : DF -> DF ; - - ++ nagErfC calculates an approximation to the complementary error - ++ function \spad{erfc}, defined by -#if saturn - ++ \[{\rm erfc}\,x = - ++ \frac{2} {\sqrt{\pi}}\int_{x}^{\infty}e^{-t^{2}}\,dt\] -#else - ++ \spad{erfc(x) = 2/sqrt(%pi)*integrate(%e^(-t^2),t=x..%infinity)} -#endif - ++ using the NAG routine S15ADF. - ++ For detailed information on the accuracy, please consult the NAG - ++ manual via the Browser page for the operation s15adf. - - nagDAiryAi : DF -> DF ; - - ++ nagDAiryAi calculates an approximation to \spad{Ai'}, the - ++ derivative of the Airy function \spad{Ai}, using the NAG routine - ++ S17AJF. - - nagDAiryAi : CDF -> CDF ; - - ++ nagDAiryAi calculates an approximation to \spad{Ai'}, the - ++ derivative of the Airy function \spad{Ai}, using the NAG routine - ++ S17DGF. - ++ For detailed information on the accuracy, please consult the NAG - ++ manual via the Browser page for the operation s17dgf. - - nagDAiryBi : DF -> DF ; - - ++ nagDAiryBi calculates an approximation to \spad{Bi'}, the - ++ derivative of the Airy function \spad{Bi}, using the NAG routine - ++ S17AKF. - ++ For detailed information on the accuracy, please consult the NAG - ++ manual via the Browser page for the operation s17akf. - - nagDAiryBi : CDF -> CDF ; - - ++ nagDAiryBi calculates an approximation to \spad{Bi'}, the - ++ derivative of the Airy function \spad{Bi}, using the NAG routine - ++ S17DHF. - ++ For detailed information on the accuracy, please consult the NAG - ++ manual via the Browser page for the operation s17dhf. - - nagScaledDAiryAi : CDF -> CDF ; - - ++ nagDAiryAi(z) calculates an approximation to \spad{Ai'(z)}, the - ++ derivative of the Airy function \spad{Ai(z)}, with the result - ++ scaled by a factor -#if saturn - ++ $e^{2z\sqrt{z}/ 3}$ -#else - ++ \spad{%e^(2*z*sqrt(z)/3)} -#endif - ++ using the NAG routine S17DGF. - ++ For detailed information on the accuracy, please consult the NAG - ++ manual via the Browser page for the operation s17dgf. - - nagScaledDAiryBi : CDF -> CDF ; - - ++ nagDAiryBi(z) calculates an approximation to \spad{Bi'(z)}, the - ++ derivative of the Airy function \spad{Bi(z)}, with the result - ++ scaled by a factor -#if saturn - ++ $e^{2z\sqrt{z}/ 3}$ -#else - ++ \spad{%e^(2*z*sqrt(z)/3)} -#endif - ++ using the NAG routine S17DHF. - ++ For detailed information on the accuracy, please consult the NAG - ++ manual via the Browser page for the operation s17dhf. - - nagHankelH1 : (DF, CDF, INT) -> MCDF ; - - ++ nagHankelH1(nu,z,n) calculates an approximation to a sequence of n - ++ values of the Hankel function -#if saturn - ++ $H_{\nu + k}^{(1)}(z)$ -#else - ++ \spad{H1(nu + k, z)} -#endif - ++ for non-negative nu and \spad{k = 0,1 ... n-1}, using the NAG - ++ routine S17DLF. - ++ For detailed information on the accuracy, please consult the NAG - ++ manual via the Browser page for the operation s17dlf. - - nagHankelH2 : (DF, CDF, INT) -> MCDF ; - - ++ nagHankelH2(nu,z,n) calculates an approximation to a sequence of n - ++ values of the Hankel function -#if saturn - ++ $H_{\nu + k}^{(2)}(z)$ -#else - ++ \spad{H2(nu + k, z)} -#endif - ++ for non-negative nu and \spad{k = 0,1 ... n-1}, using the NAG - ++ routine S17DLF. - ++ For detailed information on the accuracy, please consult the NAG - ++ manual via the Browser page for the operation s17dlf. - - nagScaledHankelH1 : (DF, CDF, INT) -> MCDF ; - - ++ nagHankelH1(nu,z,n) calculates an approximation to a sequence of n - ++ values of the Hankel function -#if saturn - ++ $H_{\nu + k}^{(1)}(z)$ -#else - ++ \spad{H1(nu + k, z)} -#endif - ++ for non-negative nu and \spad{k = 0,1 ... n-1}, with the result - ++ scaled by a factor -#if saturn - ++ $e^{-iz} -#else - ++ \spad{%e^(-%i*z)} -#endif - ++ using the NAG routine S17DLF. - ++ For detailed information on the accuracy, please consult the NAG - ++ manual via the Browser page for the operation s17dlf. - - nagScaledHankelH2 : (DF, CDF, INT) -> MCDF ; - - ++ nagHankelH2(nu,z,n) calculates an approximation to a sequence of n - ++ values of the Hankel function -#if saturn - ++ $H_{\nu + k}^{(2)}(z)$ -#else - ++ \spad{H2(nu + k, z)} -#endif - ++ for non-negative nu and \spad{k = 0,1 ... n-1}, with the result - ++ scaled by a factor -#if saturn - ++ $e^{iz} -#else - ++ \spad{%e^(%i*z)} -#endif - ++ using the NAG routine S17DLF. - ++ For detailed information on the accuracy, please consult the NAG - ++ manual via the Browser page for the operation s17dlf. - - nagKelvinBer : DF -> DF ; - - ++ nagKelvinBer calculates an approximation to the Kelvin function - ++ \spad{ber}, using the NAG routine S19AAF. - ++ For detailed information on the accuracy, please consult the NAG - ++ manual via the Browser page for the operation s19aaf. - - nagKelvinBei : DF -> DF ; - - ++ nagKelvinBei calculates an approximation to the Kelvin function - ++ \spad{bei}, using the NAG routine S19ABF. - ++ For detailed information on the accuracy, please consult the NAG - ++ manual via the Browser page for the operation s19abf. - - nagKelvinKer : DF -> DF ; - - ++ nagKelvinKer calculates an approximation to the Kelvin function - ++ \spad{ker}, using the NAG routine S19ACF. - ++ For detailed information on the accuracy, please consult the NAG - ++ manual via the Browser page for the operation s19acf. - - nagKelvinKei : DF -> DF ; - - ++ nagKelvinKei calculates an approximation to the Kelvin function - ++ \spad{kei}, using the NAG routine S19ADF. - ++ For detailed information on the accuracy, please consult the NAG - ++ manual via the Browser page for the operation s19adf. - - nagFresnelS : DF -> DF ; - - ++ nagFresnelS calculates an approximation to the Fresnel integral - ++ \spad{S}, defined by -#if saturn - ++ \[S(x) = \int_{0}^{x}\sin\left(\frac{\pi}{2}t^{2}\right)\,dt\] -#else - ++ \spad{S(x) = integrate(sin(%pi/2*t^2),t=0..x)} -#endif - ++ using the NAG routine S20ACF. - ++ For detailed information on the accuracy, please consult the NAG - ++ manual via the Browser page for the operation s20acf. - - nagFresnelC : DF -> DF ; - - ++ nagFresnelC calculates an approximation to the Fresnel integral - ++ \spad{C}, defined by -#if saturn - ++ \[C(x) = \int_{0}^{x}\cos\left(\frac{\pi}{2}t^{2}\right)\,dt\] -#else - ++ \spad{C(x) = integrate(cos(%pi/2*t^2),t=0..x)} -#endif - ++ using the NAG routine S20ADF. - ++ For detailed information on the accuracy, please consult the NAG - ++ manual via the Browser page for the operation s20adf. - - nagEllipticIntegralRC : (DF, DF) -> DF ; - - ++ nagEllipticIntegralRC(x,y) calculates an approximation to the - ++ elementary (degenerate symmetrised elliptic) integral -#if saturn - ++ \[R_{C}(x,y) = - ++ \frac{1}{2}\int_{0}^{\infty}\frac{dt}{\sqrt{t+x}(t+y)}\] -#else - ++ \spad{RC(x,y) = 1/2*integrate(1/(sqrt(t+x)*(t+y)),t=0..\infinity)} -#endif - ++ using the NAG routine S21BAF. - ++ For detailed information on the accuracy, please consult the NAG - ++ manual via the Browser page for the operation s21baf. - - nagEllipticIntegralRF : (DF, DF, DF) -> DF ; - - ++ nagEllipticIntegralRF(x,y,z) calculates an approximation to the - ++ symmetrised elliptic integral of the first kind, -#if saturn - ++ \[R_{F}(x, y, z) = - ++ \frac{1}{2}\int_{0}^{\infty}\frac{dt}{\sqrt{(t+x)(t+y)(t+z)}}\] -#else - ++ \spad{RF(x,y,z) = - ++ 1/2*integrate(1/sqrt((t+x)*(t+y)*(t+z)),t=0..\infinity)} -#endif - ++ using the NAG routine S21BBF. - ++ For detailed information on the accuracy, please consult the NAG - ++ manual via the Browser page for the operation s21bbf. - - nagEllipticIntegralRD : (DF, DF, DF) -> DF ; - - ++ nagEllipticIntegralRD(x,y,z) calculates an approximation to the - ++ symmetrised elliptic integral of the second kind, -#if saturn - ++ \[R_{D}(x, y, z) = - ++ \frac{3}{2}\int_{0}^{\infty}\frac{dt}{\sqrt{(t+x)(t+y)(t+z)^{3}}}\] -#else - ++ \spad{RD(x,y,z) = - ++ 1/2*integrate(1/sqrt((t+x)*(t+y)*(t+z)^3),t=0..\infinity)} -#endif - ++ using the NAG routine S21BCF. - ++ For detailed information on the accuracy, please consult the NAG - ++ manual via the Browser page for the operation s21bcf. - - nagEllipticIntegralRJ : (DF, DF, DF, DF) -> DF ; - - ++ nagEllipticIntegralRJ(x,y,z,rho) calculates an approximation to - ++ the symmetrised elliptic integral of the third kind, -#if saturn - ++ \[R_{J}(x, y, z, \rho ) = - ++ \frac{3}{2}\int_{0}^{\infty} - ++ \frac{dt}{(t+\rho)\sqrt{(t+x)(t+y)(t+z)}}\] -#else - ++ \spad{RJ(x,y,z,rho) = - ++ 3/2*integrate(1/((t+rho)*sqrt((t+x)*(t+y)*(t+z))),t=0..\infinity))u} -#endif - ++ using the NAG routine S21BDF. - ++ For detailed information on the accuracy, please consult the NAG - ++ manual via the Browser page for the operation s21bdf. - -} == add { - - import from NagSpecialFunctionsPackage ; - import from NagResultChecks ; - - local ipIfail : Integer := -1 ; - - nagExpInt(x : DF) : DF == - checkResult(s13aaf(x,ipIfail), "s13aafResult", "S13AAF") ; - - nagCosInt(x : DF) : DF == - checkResult(s13acf(x,ipIfail), "s13acfResult", "S13ACF") ; - - nagSinInt(x : DF) : DF == - checkResult(s13adf(x,ipIfail), "s13adfResult", "S13ADF") ; - - nagIncompleteGammaP(a : DF, x : DF) : DF == - checkResult(s14baf(a,x,0.0,ipIfail), "p", "S14BAF") ; - - nagIncompleteGammaP(a : DF, x : DF, tol : DF) : DF == - checkResult(s14baf(a,x,tol,ipIfail), "p", "S14BAF") ; - - nagIncompleteGammaQ(a : DF, x : DF) : DF == - checkResult(s14baf(a,x,0.0,ipIfail), "q", "S14BAF") ; - - nagIncompleteGammaQ(a : DF, x : DF, tol : DF) : DF == - checkResult(s14baf(a,x,tol,ipIfail), "q", "S14BAF") ; - - nagErfC(x : DF) : DF == - checkResult(s15adf(x,ipIfail), "s15adfResult", "S15ADF") ; - - nagErf(x : DF) : DF == - checkResult(s15aef(x,ipIfail), "s15aefResult", "S15AEF") ; - - nagDAiryAi(x : DF) : DF == - checkResult(s17ajf(x,ipIfail), "s17ajfResult", "S17AJF") ; - - nagDAiryAi(z : CDF) : CDF == - checkCxResult(s17dgf("d",z,"u",ipIfail), "ai", "S17DGF") ; - - nagDAiryBi(x : DF) : DF == - checkResult(s17akf(x,ipIfail), "s17akfResult", "S17AKF") ; - - nagDAiryBi(z : CDF) : CDF == - checkCxResult(s17dhf("d",z,"u",ipIfail), "bi", "S17DHF") ; - - nagScaledDAiryAi(z : CDF) : CDF == - checkCxResult(s17dgf("d",z,"s",ipIfail), "ai", "S17DGF") ; - - nagScaledDAiryBi(z : CDF) : CDF == - checkCxResult(s17dhf("d",z,"s",ipIfail), "bi", "S17DHF") ; - - nagHankelH1(order : DF, z : CDF, n : INT) : Matrix CDF == - checkMxCDF(s17dlf(1,order,z,n,"u",ipIfail), "cy", "S17DLF") ; - - nagHankelH2(order : DF, z : CDF, n : INT) : Matrix CDF == - checkMxCDF(s17dlf(2,order,z,n,"u",ipIfail), "cy", "S17DLF") ; - - nagScaledHankelH1(order : DF, z : CDF, n : INT) : Matrix CDF == - checkMxCDF(s17dlf(1,order,z,n,"s",ipIfail), "cy", "S17DLF") ; - - nagScaledHankelH2(order : DF, z : CDF, n : INT) : Matrix CDF == - checkMxCDF(s17dlf(2,order,z,n,"s",ipIfail), "cy", "S17DLF") ; - - nagKelvinBer(x : DF) : DF == - checkResult(s19aaf(x,ipIfail), "s19aafResult", "S19AAF") ; - - nagKelvinBei(x : DF) : DF == - checkResult(s19abf(x,ipIfail), "s19abfResult", "S19ABF") ; - - nagKelvinKer(x : DF) : DF == - checkResult(s19acf(x,ipIfail), "s19acfResult", "S19ACF") ; - - nagKelvinKei(x : DF) : DF == - checkResult(s19adf(x,ipIfail), "s19adfResult", "S19ADF") ; - - nagFresnelS(x : DF) : DF == - checkResult(s20acf(x,ipIfail), "s20acfResult", "S20ACF") ; - - nagFresnelC(x : DF) : DF == - checkResult(s20adf(x,ipIfail), "s20adfResult", "S20ADF") ; - - nagEllipticIntegralRC(x : DF, y : DF) : DF == - checkResult(s21baf(x,y,ipIfail), "s21bafResult", "S21BAF") ; - - nagEllipticIntegralRF(x : DF, y : DF, z : DF) : DF == - checkResult(s21bbf(x,y,z,ipIfail), "s21bbfResult", "S21BBF") ; - - nagEllipticIntegralRD(x : DF, y : DF, z : DF) : DF == - checkResult(s21bcf(x,y,z,ipIfail), "s21bcfResult", "S21BCF") ; - - nagEllipticIntegralRJ(x : DF, y : DF, z : DF, rho : DF) : DF == - checkResult(s21bdf(x,y,z,rho,ipIfail), "s21bdfResult", "S21BDF") ; -} - -#if NeverAssertThis - --- Note that the conversions of Results from DoubleFloat to Float --- will become unnecessary if outputGeneral is extended to apply to --- DoubleFloat quantities. - -)lib nrc -)lib nsfip - -outputGeneral 4 - --- DF here means DoubleFloat. --- Results converted to Float as outputGeneral not working on DF. - --- nagExpInt : DF -> DF ; - -nagExpInt(2) :: Float - --- 0.0489 - -nagExpInt(-1) :: Float - --- ** ABNORMAL EXIT from NAG Library routine S13AAF: IFAIL = 1 --- ** NAG soft failure - control returned --- --- Error signalled from user code: --- An error was detected when calling the NAG Library routine --- S13AAF. The error number (IFAIL value) is 1, please consult the --- NAG manual via the Browser for diagnostic information. - --- nagSinInt : DF -> DF ; - -nagSinInt(0) :: Float - --- 0.0 - -nagSinInt(0.2) :: Float - --- 0.1996 - -nagSinInt(0.4) :: Float - --- 0.3965 - -nagSinInt(0.6) :: Float - --- 0.5881 - -nagSinInt(0.8) :: Float - --- 0.7721 - -nagSinInt(1) :: Float - --- 0.9461 - --- nagCosInt : DF -> DF ; - -nagCosInt(0.2) :: Float - --- - 1.042 - -nagCosInt(0.4) :: Float - --- - 0.3788 - -nagCosInt(0.6) :: Float - --- - 0.02227 - -nagCosInt(0.8) :: Float - --- 0.1983 - -nagCosInt(1) :: Float - --- 0.3374 - --- nagIncompleteGammaP : (DF, DF) -> DF ; (to machine precision) - -nagIncompleteGammaP(2,3) :: Float - --- 0.8009 - -nagIncompleteGammaP(7,1) :: Float - --- 0.00008324 - -nagIncompleteGammaP(0.5,99) :: Float - --- 1.0 - -nagIncompleteGammaP(20,21) :: Float - --- 0.6157 - -nagIncompleteGammaP(21,20) :: Float - --- 0.4409 - --- nagIncompleteGammaP : (DF, DF, DF) -> DF ; (to specified precision) - -nagIncompleteGammaP(7,1,0.1) :: Float - --- 0.00008313 - --- nagIncompleteGammaQ : (DF, DF) -> DF ; (to machine precision) - -nagIncompleteGammaQ(2,3) :: Float - --- 0.1991 - -nagIncompleteGammaQ(7,1) :: Float - --- 0.9999 - -nagIncompleteGammaQ(0.5,99) :: Float - --- 0.5705 E -44 - -nagIncompleteGammaQ(20,21) :: Float - --- 0.3843 - -nagIncompleteGammaQ(21,20) :: Float - --- 0.5591 - -nagIncompleteGammaQ(25,14) :: Float - --- 0.995 - --- nagIncompleteGammaQ : (DF, DF, DF) -> DF ; (to specified precision) - -nagIncompleteGammaQ(25,14,0.1) :: Float - --- 0.9953 - --- nagErf : DF -> DF ; - -nagErf(-6) :: Float - --- - 1.0 - -nagErf(-4.5) :: Float - --- - 1.0 - -nagErf(-1) :: Float - --- - 0.8427 - -nagErf(1) :: Float - --- 0.8427 - -nagErf(4.5) :: Float - --- 1.0 - -nagErf(6) :: Float - --- 1.0 - --- nagErfC : DF -> DF ; - -nagErfC(-10) :: Float - --- 2.0 - -nagErfC(-1) :: Float - --- 1.843 - -nagErfC(0) :: Float - --- 1.0 - -nagErfC(1) :: Float - --- 0.1573 - -nagErfC(15) :: Float - --- 0.7213 E -99 - --- nagDAiryAi : DF -> DF ; - -nagDAiryAi(-10) :: Float - --- 0.9963 - -nagDAiryAi(-1) :: Float - --- - 0.01016 - -nagDAiryAi(0) :: Float - --- - 0.2588 - -nagDAiryAi(1) :: Float - --- - 0.1591 - -nagDAiryAi(5) :: Float - --- - 0.0002474 - -nagDAiryAi(10) :: Float - --- - 0.3521 E -9 - -nagDAiryAi(20) :: Float - --- - 0.7586 E -26 - --- nagDAiryAi : CDF -> CDF ; - -nagDAiryAi(0.3+0.4*%i) :: Complex Float - --- - 0.2612 + 0.03848 %i - --- nagDAiryBi : DF -> DF ; - -nagDAiryBi(-10) :: Float - --- 0.1194 - -nagDAiryBi(-1) :: Float - --- 0.5924 - -nagDAiryBi(0) :: Float - --- 0.4483 - -nagDAiryBi(1) :: Float - --- 0.9324 - -nagDAiryBi(5) :: Float - --- 1436.0 - -nagDAiryBi(10) :: Float - --- 0.1429 E 10 - -nagDAiryBi(20) :: Float - --- 0.9382 E 26 - --- nagDAiryBi : CDF -> CDF ; - -nagDAiryBi(0.3+0.4*%i) :: Complex Float - --- 0.4093 + 0.07966 %i - --- nagScaledDAiryAi : CDF -> CDF ; - -nagScaledDAiryAi(0.3+0.4*%i) :: Complex Float - --- - 0.2744 - 0.02356 %i - --- nagScaledDAiryBi : CDF -> CDF ; - -nagScaledDAiryBi(0.3+0.4*%i) :: Complex Float - --- 0.3924 + 0.07638 %i - --- nagHankelH1 : (DF, CDF, Int) -> List CDF ; - -nagHankelH1(0,0.3+0.4*%i,2) :: Matrix Complex Float - --- [0.3466 - 0.5588 %i - 0.7912 - 0.8178 %i] - -nagHankelH1(2.3,2,2) :: Matrix Complex Float - --- [0.2721 - 0.7398 %i 0.08902 - 1.412 %i] - -nagHankelH1(2.12,-1,2) :: Matrix Complex Float - --- [- 0.7722 - 1.693 %i 2.601 + 6.527 %i] - --- nagHankelH2 : (DF, CDF, Int) -> List CDF ; - -nagHankelH2(6,3.1-1.6*%i,2) :: Matrix Complex Float - --- [- 1.371 - 1.28 %i - 1.491 - 5.993 %i] - --- nagScaledHankelH1 : (DF, CDF, Int) -> List CDF ; - -nagScaledHankelH1(0,0.3+0.4*%i,2) :: Matrix Complex Float - --- [0.2477 - 0.9492 %i - 1.488 - 0.8166 %i] - --- nagScaledHankelH2 : (DF, CDF, Int) -> List CDF ; - -nagScaledHankelH2(6,3.1-1.6*%i,2) :: Matrix Complex Float - --- [7.05 + 6.052 %i 8.614 + 29.35 %i] - --- nagKelvinBer : DF -> DF ; - -nagKelvinBer(0.1) :: Float - --- 1.0 - -nagKelvinBer(1) :: Float - --- 0.9844 - -nagKelvinBer(2.5) :: Float - --- 0.4 - -nagKelvinBer(5) :: Float - --- - 6.23 - -nagKelvinBer(10) :: Float - --- 138.8 - -nagKelvinBer(15) :: Float - --- - 2967.0 - -nagKelvinBer(60) :: Float - --- ** ABNORMAL EXIT from NAG Library routine S19AAF: IFAIL = 1 --- ** NAG soft failure - control returned --- --- Error signalled from user code: --- An error was detected when calling the NAG Library routine --- S19AAF. The error number (IFAIL value) is 1, please consult the --- NAG manual via the Browser for diagnostic information. - -nagKelvinBer(-1) :: Float - --- 0.9844 - --- nagKelvinBei : DF -> DF ; - -nagKelvinBei(0.1) :: Float - --- 0.0025 - -nagKelvinBei(1) :: Float - --- 0.2496 - -nagKelvinBei(2.5) :: Float - --- 1.457 - -nagKelvinBei(5) :: Float - --- 0.116 - -nagKelvinBei(10) :: Float - --- 56.37 - -nagKelvinBei(15) :: Float - --- - 2953.0 - -nagKelvinBei(60) :: Float - --- ** ABNORMAL EXIT from NAG Library routine S19ABF: IFAIL = 1 --- ** NAG soft failure - control returned --- --- Error signalled from user code: --- An error was detected when calling the NAG Library routine --- S19ABF. The error number (IFAIL value) is 1, please consult the --- NAG manual via the Browser for diagnostic information. - -nagKelvinBei(-1) :: Float - --- 0.2496 - --- nagKelvinKer : DF -> DF ; - -nagKelvinKer(0) :: Float - --- ** ABNORMAL EXIT from NAG Library routine S19ACF: IFAIL = 2 --- ** NAG soft failure - control returned --- --- Error signalled from user code: --- An error was detected when calling the NAG Library routine --- S19ACF. The error number (IFAIL value) is 2, please consult the --- NAG manual via the Browser for diagnostic information. - -nagKelvinKer(0.1) :: Float - --- 2.42 - -nagKelvinKer(1) :: Float - --- 0.2867 - -nagKelvinKer(2.5) :: Float - --- - 0.06969 - -nagKelvinKer(5) :: Float - --- - 0.01151 - -nagKelvinKer(10) :: Float - --- 0.0001295 - -nagKelvinKer(15) :: Float - --- - 0.1514 E -7 - -nagKelvinKer(1100) :: Float - --- ** ABNORMAL EXIT from NAG Library routine S19ACF: IFAIL = 1 --- ** NAG soft failure - control returned --- --- Error signalled from user code: --- An error was detected when calling the NAG Library routine --- S19ACF. The error number (IFAIL value) is 1, please consult the --- NAG manual via the Browser for diagnostic information. - -nagKelvinKer(-1) :: Float - --- ** ABNORMAL EXIT from NAG Library routine S19ACF: IFAIL = 2 --- ** NAG soft failure - control returned --- --- Error signalled from user code: --- An error was detected when calling the NAG Library routine --- S19ACF. The error number (IFAIL value) is 2, please consult the --- NAG manual via the Browser for diagnostic information. - --- nagKelvinKei : DF -> DF ; - -nagKelvinKei(0) :: Float - --- - 0.7854 - -nagKelvinKei(0.1) :: Float - --- - 0.7769 - -nagKelvinKei(1) :: Float - --- - 0.495 - -nagKelvinKei(2.5) :: Float - --- - 0.1107 - -nagKelvinKei(5) :: Float - --- 0.01119 - -nagKelvinKei(10) :: Float - --- - 0.0003075 - -nagKelvinKei(15) :: Float - --- 0.000007963 - -nagKelvinKei(1100) :: Float - --- ** ABNORMAL EXIT from NAG Library routine S19ADF: IFAIL = 1 --- ** NAG soft failure - control returned --- --- Error signalled from user code: --- An error was detected when calling the NAG Library routine --- S19ADF. The error number (IFAIL value) is 1, please consult the --- NAG manual via the Browser for diagnostic information. - -nagKelvinKei(-1) :: Float - --- ** ABNORMAL EXIT from NAG Library routine S19ADF: IFAIL = 2 --- ** NAG soft failure - control returned --- --- Error signalled from user code: --- An error was detected when calling the NAG Library routine --- S19ADF. The error number (IFAIL value) is 2, please consult the --- NAG manual via the Browser for diagnostic information. - - --- nagFresnelS : DF -> DF ; - -nagFresnelS(0) :: Float - --- 0.0 - -nagFresnelS(0.5) :: Float - --- 0.06473 - -nagFresnelS(1) :: Float - --- 0.4383 - -nagFresnelS(2) :: Float - --- 0.3434 - -nagFresnelS(4) :: Float - --- 0.4205 - -nagFresnelS(5) :: Float - --- 0.4992 - -nagFresnelS(6) :: Float - --- 0.447 - -nagFresnelS(8) :: Float - --- 0.4602 - -nagFresnelS(10) :: Float - --- 0.4682 - -nagFresnelS(-1) :: Float - --- - 0.4383 - -nagFresnelS(1000) :: Float - --- 0.4997 - --- nagFresnelC : DF -> DF ; - -nagFresnelC(0) :: Float - --- 0.0 - -nagFresnelC(0.5) :: Float - --- 0.4923 - -nagFresnelC(1) :: Float - --- 0.7799 - -nagFresnelC(2) :: Float - --- 0.4883 - -nagFresnelC(4) :: Float - --- 0.4984 - -nagFresnelC(5) :: Float - --- 0.5636 - -nagFresnelC(6) :: Float - --- 0.4995 - -nagFresnelC(8) :: Float - --- 0.4998 - -nagFresnelC(10) :: Float - --- 0.4999 - -nagFresnelC(-1) :: Float - --- - 0.7799 - -nagFresnelC(1000) :: Float - --- 0.5 - --- nagEllipticIntegralRC : (DF, DF) -> DF ; - -nagEllipticIntegralRC(0.5,1) :: Float - --- 1.111 - -nagEllipticIntegralRC(1,1) :: Float - --- 1.0 - -nagEllipticIntegralRC(1.5,1) :: Float - --- 0.9312 - --- nagEllipticIntegralRD : (DF, DF, DF) -> DF ; - -nagEllipticIntegralRD(0.5,0.5,1) :: Float - --- 1.479 - -nagEllipticIntegralRD(0.5,1,1) :: Float - --- 1.211 - -nagEllipticIntegralRD(0.5,1.5,1) :: Float - --- 1.061 - -nagEllipticIntegralRD(1,1,1) :: Float - --- 1.0 - -nagEllipticIntegralRD(1,1.5,1) :: Float - --- 0.8805 - -nagEllipticIntegralRD(1.5,1.5,1) :: Float - --- 0.7775 - --- nagEllipticIntegralRF : (DF, DF, DF) -> DF ; - -nagEllipticIntegralRF(0.5,1,1.5) :: Float - --- 1.028 - -nagEllipticIntegralRF(1,1.5,2) :: Float - --- 0.826 - -nagEllipticIntegralRF(1.5,2,2.5) :: Float - --- 0.7116 - --- nagEllipticIntegralRJ : (DF, DF, DF, DF) -> DF ; - -nagEllipticIntegralRJ(0.5,0.5,0.5,2) :: Float - --- 1.118 - -nagEllipticIntegralRJ(0.5,0.5,1,2) :: Float - --- 0.9221 - -nagEllipticIntegralRJ(0.5,0.5,1.5,2) :: Float - --- 0.8115 - -nagEllipticIntegralRJ(0.5,1,1,2) :: Float - --- 0.7671 - -nagEllipticIntegralRJ(0.5,1,1.5,2) :: Float - --- 0.6784 - -nagEllipticIntegralRJ(0.5,1.5,1.5,2) :: Float - --- 0.6017 - -nagEllipticIntegralRJ(1,1,1,2) :: Float - --- 0.6438 - -nagEllipticIntegralRJ(1,1,1.5,2) :: Float - --- 0.5722 - -nagEllipticIntegralRJ(1,1.5,1.5,2) :: Float - --- 0.5101 - -nagEllipticIntegralRJ(1.5,1.5,1.5,2) :: Float - --- 0.4561 - -outputGeneral() - -output "End of tests" - -#endif - -@ -\section{License} -<<license>>= ---Copyright (c) 1991-2002, The Numerical ALgorithms Group Ltd. ---All rights reserved. --- ---Redistribution and use in source and binary forms, with or without ---modification, are permitted provided that the following conditions are ---met: --- --- - Redistributions of source code must retain the above copyright --- notice, this list of conditions and the following disclaimer. --- --- - Redistributions in binary form must reproduce the above copyright --- notice, this list of conditions and the following disclaimer in --- the documentation and/or other materials provided with the --- distribution. --- --- - Neither the name of The Numerical ALgorithms Group Ltd. nor the --- names of its contributors may be used to endorse or promote products --- derived from this software without specific prior written permission. --- ---THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS ---IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED ---TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A ---PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER ---OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, ---EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, ---PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR ---PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF ---LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING ---NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS ---SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. -@ -<<*>>= -<<license>> - --- NagSpecialFunctionsInterfacePackage - --- To test: --- sed -ne '1,/^#if NeverAssertThis/d;/#endif/d;p' < nsfip.as > nsfip.input --- axiom --- )set nag host <some machine running nagd> --- )r nsfip.input - -#unassert saturn - -#include "axiom.as" - -DF ==> DoubleFloat ; -CDF ==> Complex DoubleFloat ; -MCDF ==> Matrix Complex DoubleFloat ; -INT ==> Integer ; -RSLT ==> Result ; -SMBL ==> Symbol ; -STRG ==> String ; - -<<NagSpecialFunctionsInterfacePackage>> -@ -\eject -\begin{thebibliography}{99} -\bibitem{1} nothing -\end{thebibliography} -\end{document} |