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authordos-reis <gdr@axiomatics.org>2011-09-20 06:29:26 +0000
committerdos-reis <gdr@axiomatics.org>2011-09-20 06:29:26 +0000
commit255be06767355e3b41acd75990c6b90270b8f2bd (patch)
tree0a032d40d7cb2213e206d70beb23dc74ccf4a230 /src/algebra/c06.spad.pamphlet
parent12c856f9901ef3d6d82fb99855ecdf3e0b91484b (diff)
downloadopen-axiom-255be06767355e3b41acd75990c6b90270b8f2bd.tar.gz
* algebra/asp.spad.pamphlet: Remove.
* algebra/c02.spad.pamphlet: Likewise. * algebra/c05.spad.pamphlet: Likewise. * algebra/c06.spad.pamphlet: Likewise. * algebra/d01.spad.pamphlet: Likewise. * algebra/d02.spad.pamphlet: Likewise. * algebra/d03.spad.pamphlet: Likewise. * algebra/e01.spad.pamphlet: Likewise. * algebra/e02.spad.pamphlet: Likewise. * algebra/e04.spad.pamphlet: Likewise. * algebra/f01.spad.pamphlet: Likewise. * algebra/f02.spad.pamphlet: Likewise. * algebra/f04.spad.pamphlet: Likewise. * algebra/f07.spad.pamphlet: Likewise. * algebra/s.spad.pamphlet: Likewise. * algebra/d01Package.spad.pamphlet: Likewise. * algebra/d02Package.spad.pamphlet: Likewise. * algebra/d03Package.spad.pamphlet: Likewise. * algebra/e04Package.spad.pamphlet: Likewise. * algebra/d01agents.spad.pamphlet: Likewise. * algebra/d01routine.spad.pamphlet: Likewise. * algebra/d01transform.spad.pamphlet: Likewise. * algebra/d01weights.spad.pamphlet: Likewise. * algebra/d02agents.spad.pamphlet: Likewise. * algebra/d02routine.spad.pamphlet: Likewise. * algebra/d03agents.spad.pamphlet: Likewise. * algebra/d03routine.spad.pamphlet: Likewise. * algebra/e04agents.spad.pamphlet: Likewise. * algebra/e04routine.spad.pamphlet: Likewise.
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-\documentclass{article}
-\usepackage{open-axiom}
-\begin{document}
-\title{\$SPAD/src/algebra c06.spad}
-\author{Godfrey Nolan, Mike Dewar}
-\maketitle
-\begin{abstract}
-\end{abstract}
-\eject
-\tableofcontents
-\eject
-\section{package NAGC06 NagSeriesSummationPackage}
-<<package NAGC06 NagSeriesSummationPackage>>=
-)abbrev package NAGC06 NagSeriesSummationPackage
-++ Author: Godfrey Nolan and Mike Dewar
-++ Date Created: Jan 1994
-++ Date Last Updated: Thu May 12 17:44:30 1994
-++Description:
-++This package uses the NAG Library to calculate the discrete Fourier
-++transform of a sequence of real or complex data values, and
-++applies it to calculate convolutions and correlations.
-++See \downlink{Manual Page}{manpageXXc06}.
-
-NagSeriesSummationPackage(): Exports == Implementation where
- S ==> Symbol
- FOP ==> FortranOutputStackPackage
-
- Exports ==> with
- c06eaf : (Integer,Matrix DoubleFloat,Integer) -> Result
- ++ c06eaf(n,x,ifail)
- ++ calculates the discrete Fourier transform of a sequence of
- ++ n real data values. (No extra workspace required.)
- ++ See \downlink{Manual Page}{manpageXXc06eaf}.
- c06ebf : (Integer,Matrix DoubleFloat,Integer) -> Result
- ++ c06ebf(n,x,ifail)
- ++ calculates the discrete Fourier transform of a Hermitian
- ++ sequence of n complex data values. (No extra workspace required.)
- ++ See \downlink{Manual Page}{manpageXXc06ebf}.
- c06ecf : (Integer,Matrix DoubleFloat,Matrix DoubleFloat,Integer) -> Result
- ++ c06ecf(n,x,y,ifail)
- ++ calculates the discrete Fourier transform of a sequence of
- ++ n complex data values. (No extra workspace required.)
- ++ See \downlink{Manual Page}{manpageXXc06ecf}.
- c06ekf : (Integer,Integer,Matrix DoubleFloat,Matrix DoubleFloat,_
- Integer) -> Result
- ++ c06ekf(job,n,x,y,ifail)
- ++ calculates the circular convolution of two
- ++ real vectors of period n. No extra workspace is required.
- ++ See \downlink{Manual Page}{manpageXXc06ekf}.
- c06fpf : (Integer,Integer,String,Matrix DoubleFloat,_
- Matrix DoubleFloat,Integer) -> Result
- ++ c06fpf(m,n,init,x,trig,ifail)
- ++ computes the discrete Fourier transforms of m sequences,
- ++ each containing n real data values. This routine is designed to
- ++ be particularly efficient on vector processors.
- ++ See \downlink{Manual Page}{manpageXXc06fpf}.
- c06fqf : (Integer,Integer,String,Matrix DoubleFloat,_
- Matrix DoubleFloat,Integer) -> Result
- ++ c06fqf(m,n,init,x,trig,ifail)
- ++ computes the discrete Fourier transforms of m Hermitian
- ++ sequences, each containing n complex data values. This routine is
- ++ designed to be particularly efficient on vector processors.
- ++ See \downlink{Manual Page}{manpageXXc06fqf}.
- c06frf : (Integer,Integer,String,Matrix DoubleFloat,_
- Matrix DoubleFloat,Matrix DoubleFloat,Integer) -> Result
- ++ c06frf(m,n,init,x,y,trig,ifail)
- ++ computes the discrete Fourier transforms of m sequences,
- ++ each containing n complex data values. This routine is designed
- ++ to be particularly efficient on vector processors.
- ++ See \downlink{Manual Page}{manpageXXc06frf}.
- c06fuf : (Integer,Integer,String,Matrix DoubleFloat,_
- Matrix DoubleFloat,Matrix DoubleFloat,Matrix DoubleFloat,Integer) -> Result
- ++ c06fuf(m,n,init,x,y,trigm,trign,ifail)
- ++ computes the two-dimensional discrete Fourier transform of
- ++ a bivariate sequence of complex data values. This routine is
- ++ designed to be particularly efficient on vector processors.
- ++ See \downlink{Manual Page}{manpageXXc06fuf}.
- c06gbf : (Integer,Matrix DoubleFloat,Integer) -> Result
- ++ c06gbf(n,x,ifail)
- ++ forms the complex conjugate of n
- ++ data values.
- ++ See \downlink{Manual Page}{manpageXXc06gbf}.
- c06gcf : (Integer,Matrix DoubleFloat,Integer) -> Result
- ++ c06gcf(n,y,ifail)
- ++ forms the complex conjugate of a sequence of n data
- ++ values.
- ++ See \downlink{Manual Page}{manpageXXc06gcf}.
- c06gqf : (Integer,Integer,Matrix DoubleFloat,Integer) -> Result
- ++ c06gqf(m,n,x,ifail)
- ++ forms the complex conjugates,
- ++ each containing n data values.
- ++ See \downlink{Manual Page}{manpageXXc06gqf}.
- c06gsf : (Integer,Integer,Matrix DoubleFloat,Integer) -> Result
- ++ c06gsf(m,n,x,ifail)
- ++ takes m Hermitian sequences, each containing n data
- ++ values, and forms the real and imaginary parts of the m
- ++ corresponding complex sequences.
- ++ See \downlink{Manual Page}{manpageXXc06gsf}.
- Implementation ==> add
-
- import Lisp
- import DoubleFloat
- import Any
- import Record
- import Integer
- import Matrix DoubleFloat
- import Boolean
- import NAGLinkSupportPackage
- import AnyFunctions1(Integer)
- import AnyFunctions1(String)
- import AnyFunctions1(Matrix DoubleFloat)
-
-
- c06eaf(nArg:Integer,xArg:Matrix DoubleFloat,ifailArg:Integer): Result ==
- [(invokeNagman(NIL$Lisp,_
- "c06eaf",_
- ["n"::S,"ifail"::S,"x"::S]$Lisp,_
- []$Lisp,_
- [["double"::S,["x"::S,"n"::S]$Lisp]$Lisp_
- ,["integer"::S,"n"::S,"ifail"::S]$Lisp_
- ]$Lisp,_
- ["x"::S,"ifail"::S]$Lisp,_
- [([nArg::Any,ifailArg::Any,xArg::Any ])_
- @List Any]$Lisp)$Lisp)_
- pretend List (Record(key:Symbol,entry:Any))]$Result
-
-
- c06ebf(nArg:Integer,xArg:Matrix DoubleFloat,ifailArg:Integer): Result ==
- [(invokeNagman(NIL$Lisp,_
- "c06ebf",_
- ["n"::S,"ifail"::S,"x"::S]$Lisp,_
- []$Lisp,_
- [["double"::S,["x"::S,"n"::S]$Lisp]$Lisp_
- ,["integer"::S,"n"::S,"ifail"::S]$Lisp_
- ]$Lisp,_
- ["x"::S,"ifail"::S]$Lisp,_
- [([nArg::Any,ifailArg::Any,xArg::Any ])_
- @List Any]$Lisp)$Lisp)_
- pretend List (Record(key:Symbol,entry:Any))]$Result
-
- c06ecf(nArg:Integer,xArg:Matrix DoubleFloat,yArg:Matrix DoubleFloat,_
- ifailArg:Integer): Result ==
- [(invokeNagman(NIL$Lisp,_
- "c06ecf",_
- ["n"::S,"ifail"::S,"x"::S,"y"::S]$Lisp,_
- []$Lisp,_
- [["double"::S,["x"::S,"n"::S]$Lisp,["y"::S,"n"::S]$Lisp_
- ]$Lisp_
- ,["integer"::S,"n"::S,"ifail"::S]$Lisp_
- ]$Lisp,_
- ["x"::S,"y"::S,"ifail"::S]$Lisp,_
- [([nArg::Any,ifailArg::Any,xArg::Any,yArg::Any ])_
- @List Any]$Lisp)$Lisp)_
- pretend List (Record(key:Symbol,entry:Any))]$Result
-
- c06ekf(jobArg:Integer,nArg:Integer,xArg:Matrix DoubleFloat,_
- yArg:Matrix DoubleFloat,ifailArg:Integer): Result ==
- [(invokeNagman(NIL$Lisp,_
- "c06ekf",_
- ["job"::S,"n"::S,"ifail"::S,"x"::S,"y"::S]$Lisp,_
- []$Lisp,_
- [["double"::S,["x"::S,"n"::S]$Lisp,["y"::S,"n"::S]$Lisp_
- ]$Lisp_
- ,["integer"::S,"job"::S,"n"::S,"ifail"::S]$Lisp_
- ]$Lisp,_
- ["x"::S,"y"::S,"ifail"::S]$Lisp,_
- [([jobArg::Any,nArg::Any,ifailArg::Any,xArg::Any,yArg::Any ])_
- @List Any]$Lisp)$Lisp)_
- pretend List (Record(key:Symbol,entry:Any))]$Result
-
- c06fpf(mArg:Integer,nArg:Integer,initArg:String,_
- xArg:Matrix DoubleFloat,trigArg:Matrix DoubleFloat,ifailArg:Integer): Result ==
- [(invokeNagman(NIL$Lisp,_
- "c06fpf",_
- ["m"::S,"n"::S,"init"::S,"ifail"::S,"x"::S,"trig"::S,"work"::S]$Lisp,_
- ["work"::S]$Lisp,_
- [["double"::S,["x"::S,["*"::S,"m"::S,"n"::S]$Lisp]$Lisp_
- ,["trig"::S,["*"::S,2$Lisp,"n"::S]$Lisp]$Lisp,["work"::S,["*"::S,"m"::S,"n"::S]$Lisp]$Lisp]$Lisp_
- ,["integer"::S,"m"::S,"n"::S,"ifail"::S]$Lisp_
- ,["character"::S,"init"::S]$Lisp_
- ]$Lisp,_
- ["x"::S,"trig"::S,"ifail"::S]$Lisp,_
- [([mArg::Any,nArg::Any,initArg::Any,ifailArg::Any,xArg::Any,trigArg::Any ])_
- @List Any]$Lisp)$Lisp)_
- pretend List (Record(key:Symbol,entry:Any))]$Result
-
- c06fqf(mArg:Integer,nArg:Integer,initArg:String,_
- xArg:Matrix DoubleFloat,trigArg:Matrix DoubleFloat,ifailArg:Integer): Result ==
- [(invokeNagman(NIL$Lisp,_
- "c06fqf",_
- ["m"::S,"n"::S,"init"::S,"ifail"::S,"x"::S,"trig"::S,"work"::S]$Lisp,_
- ["work"::S]$Lisp,_
- [["double"::S,["x"::S,["*"::S,"m"::S,"n"::S]$Lisp]$Lisp_
- ,["trig"::S,["*"::S,2$Lisp,"n"::S]$Lisp]$Lisp,["work"::S,["*"::S,"m"::S,"n"::S]$Lisp]$Lisp]$Lisp_
- ,["integer"::S,"m"::S,"n"::S,"ifail"::S]$Lisp_
- ,["character"::S,"init"::S]$Lisp_
- ]$Lisp,_
- ["x"::S,"trig"::S,"ifail"::S]$Lisp,_
- [([mArg::Any,nArg::Any,initArg::Any,ifailArg::Any,xArg::Any,trigArg::Any ])_
- @List Any]$Lisp)$Lisp)_
- pretend List (Record(key:Symbol,entry:Any))]$Result
-
- c06frf(mArg:Integer,nArg:Integer,initArg:String,_
- xArg:Matrix DoubleFloat,yArg:Matrix DoubleFloat,trigArg:Matrix DoubleFloat,_
- ifailArg:Integer): Result ==
- [(invokeNagman(NIL$Lisp,_
- "c06frf",_
- ["m"::S,"n"::S,"init"::S,"ifail"::S,"x"::S,"y"::S,"trig"::S,"work"::S]$Lisp,_
- ["work"::S]$Lisp,_
- [["double"::S,["x"::S,["*"::S,"m"::S,"n"::S]$Lisp]$Lisp_
- ,["y"::S,["*"::S,"m"::S,"n"::S]$Lisp]$Lisp,["trig"::S,["*"::S,2$Lisp,"n"::S]$Lisp]$Lisp,["work"::S,["*"::S,["*"::S,2$Lisp,"m"::S]$Lisp,"n"::S]$Lisp]$Lisp_
- ]$Lisp_
- ,["integer"::S,"m"::S,"n"::S,"ifail"::S]$Lisp_
- ,["character"::S,"init"::S]$Lisp_
- ]$Lisp,_
- ["x"::S,"y"::S,"trig"::S,"ifail"::S]$Lisp,_
- [([mArg::Any,nArg::Any,initArg::Any,ifailArg::Any,xArg::Any,yArg::Any,trigArg::Any ])_
- @List Any]$Lisp)$Lisp)_
- pretend List (Record(key:Symbol,entry:Any))]$Result
-
- c06fuf(mArg:Integer,nArg:Integer,initArg:String,_
- xArg:Matrix DoubleFloat,yArg:Matrix DoubleFloat,trigmArg:Matrix DoubleFloat,_
- trignArg:Matrix DoubleFloat,ifailArg:Integer): Result ==
- [(invokeNagman(NIL$Lisp,_
- "c06fuf",_
- ["m"::S,"n"::S,"init"::S,"ifail"::S,"x"::S,"y"::S,"trigm"::S,"trign"::S,"work"::S_
- ]$Lisp,_
- ["work"::S]$Lisp,_
- [["double"::S,["x"::S,["*"::S,"m"::S,"n"::S]$Lisp]$Lisp_
- ,["y"::S,["*"::S,"m"::S,"n"::S]$Lisp]$Lisp,["trigm"::S,["*"::S,2$Lisp,"m"::S]$Lisp]$Lisp,["trign"::S,["*"::S,2$Lisp,"n"::S]$Lisp]$Lisp_
- ,["work"::S,["*"::S,["*"::S,2$Lisp,"m"::S]$Lisp,"n"::S]$Lisp]$Lisp]$Lisp_
- ,["integer"::S,"m"::S,"n"::S,"ifail"::S]$Lisp_
- ,["character"::S,"init"::S]$Lisp_
- ]$Lisp,_
- ["x"::S,"y"::S,"trigm"::S,"trign"::S,"ifail"::S]$Lisp,_
- [([mArg::Any,nArg::Any,initArg::Any,ifailArg::Any,xArg::Any,yArg::Any,trigmArg::Any,trignArg::Any ])_
- @List Any]$Lisp)$Lisp)_
- pretend List (Record(key:Symbol,entry:Any))]$Result
-
- c06gbf(nArg:Integer,xArg:Matrix DoubleFloat,ifailArg:Integer): Result ==
- [(invokeNagman(NIL$Lisp,_
- "c06gbf",_
- ["n"::S,"ifail"::S,"x"::S]$Lisp,_
- []$Lisp,_
- [["double"::S,["x"::S,"n"::S]$Lisp]$Lisp_
- ,["integer"::S,"n"::S,"ifail"::S]$Lisp_
- ]$Lisp,_
- ["x"::S,"ifail"::S]$Lisp,_
- [([nArg::Any,ifailArg::Any,xArg::Any ])_
- @List Any]$Lisp)$Lisp)_
- pretend List (Record(key:Symbol,entry:Any))]$Result
-
- c06gcf(nArg:Integer,yArg:Matrix DoubleFloat,ifailArg:Integer): Result ==
- [(invokeNagman(NIL$Lisp,_
- "c06gcf",_
- ["n"::S,"ifail"::S,"y"::S]$Lisp,_
- []$Lisp,_
- [["double"::S,["y"::S,"n"::S]$Lisp]$Lisp_
- ,["integer"::S,"n"::S,"ifail"::S]$Lisp_
- ]$Lisp,_
- ["y"::S,"ifail"::S]$Lisp,_
- [([nArg::Any,ifailArg::Any,yArg::Any ])_
- @List Any]$Lisp)$Lisp)_
- pretend List (Record(key:Symbol,entry:Any))]$Result
-
- c06gqf(mArg:Integer,nArg:Integer,xArg:Matrix DoubleFloat,_
- ifailArg:Integer): Result ==
- [(invokeNagman(NIL$Lisp,_
- "c06gqf",_
- ["m"::S,"n"::S,"ifail"::S,"x"::S]$Lisp,_
- []$Lisp,_
- [["double"::S,["x"::S,["*"::S,"m"::S,"n"::S]$Lisp]$Lisp_
- ]$Lisp_
- ,["integer"::S,"m"::S,"n"::S,"ifail"::S]$Lisp_
- ]$Lisp,_
- ["x"::S,"ifail"::S]$Lisp,_
- [([mArg::Any,nArg::Any,ifailArg::Any,xArg::Any ])_
- @List Any]$Lisp)$Lisp)_
- pretend List (Record(key:Symbol,entry:Any))]$Result
-
- c06gsf(mArg:Integer,nArg:Integer,xArg:Matrix DoubleFloat,_
- ifailArg:Integer): Result ==
- [(invokeNagman(NIL$Lisp,_
- "c06gsf",_
- ["m"::S,"n"::S,"ifail"::S,"x"::S,"u"::S,"v"::S]$Lisp,_
- ["u"::S,"v"::S]$Lisp,_
- [["double"::S,["x"::S,["*"::S,"m"::S,"n"::S]$Lisp]$Lisp_
- ,["u"::S,["*"::S,"m"::S,"n"::S]$Lisp]$Lisp,["v"::S,["*"::S,"m"::S,"n"::S]$Lisp]$Lisp]$Lisp_
- ,["integer"::S,"m"::S,"n"::S,"ifail"::S]$Lisp_
- ]$Lisp,_
- ["u"::S,"v"::S,"ifail"::S]$Lisp,_
- [([mArg::Any,nArg::Any,ifailArg::Any,xArg::Any ])_
- @List Any]$Lisp)$Lisp)_
- pretend List (Record(key:Symbol,entry:Any))]$Result
-
-@
-\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>>
-
-<<package NAGC06 NagSeriesSummationPackage>>
-@
-\eject
-\begin{thebibliography}{99}
-\bibitem{1} nothing
-\end{thebibliography}
-\end{document}