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authordos-reis <gdr@axiomatics.org>2011-09-15 18:48:07 +0000
committerdos-reis <gdr@axiomatics.org>2011-09-15 18:48:07 +0000
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tree96fc5a4bf51d9777f8d46ac1e4023c0d8e545f8a /src/algebra/nsfip.as.pamphlet
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downloadopen-axiom-12c856f9901ef3d6d82fb99855ecdf3e0b91484b.tar.gz
* algebra/axtimer.as.pamphlet: Remove.
* algebra/ffrac.as.pamphlet: Likewise. * algebra/herm.as.pamphlet: Likewise. * algebra/interval.as.pamphlet: Likewise. * algebra/invnode.as.pamphlet: Likewise. * algebra/invrender.as.pamphlet: Likewise. * algebra/invtypes.as.pamphlet: Likewise. * algebra/invutils.as.pamphlet: Likewise. * algebra/iviews.as.pamphlet: Likewise. * algebra/ndftip.as.pamphlet: Likewise. * algebra/nepip.as.pamphlet: Likewise. * algebra/noptip.as.pamphlet: Likewise. * algebra/nqip.as.pamphlet: Likewise. * algebra/nrc.as.pamphlet: Likewise. * algebra/nsfip.as.pamphlet: Likewise.
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-\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}