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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/e01.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 e01.spad}
-\author{Godfrey Nolan, Mike Dewar}
-\maketitle
-\begin{abstract}
-\end{abstract}
-\eject
-\tableofcontents
-\eject
-\section{package NAGE01 NagInterpolationPackage}
-<<package NAGE01 NagInterpolationPackage>>=
-)abbrev package NAGE01 NagInterpolationPackage
-++ Author: Godfrey Nolan and Mike Dewar
-++ Date Created: Jan 1994
-++ Date Last Updated: Thu May 12 17:44:53 1994
-++Description:
-++This package uses the NAG Library to calculate the interpolation of a function of
-++one or two variables. When provided with the value of the
-++function (and possibly one or more of its lowest-order
-++derivatives) at each of a number of values of the variable(s),
-++the routines provide either an interpolating function or an
-++interpolated value. For some of the interpolating functions,
-++there are supporting routines to evaluate, differentiate or
-++integrate them.
-++See \downlink{Manual Page}{manpageXXe01}.
-
-
-NagInterpolationPackage(): Exports == Implementation where
- S ==> Symbol
- FOP ==> FortranOutputStackPackage
-
- Exports ==> with
- e01baf : (Integer,Matrix DoubleFloat,Matrix DoubleFloat,Integer,_
- Integer,Integer) -> Result
- ++ e01baf(m,x,y,lck,lwrk,ifail)
- ++ determines a cubic spline to a given set of
- ++ data.
- ++ See \downlink{Manual Page}{manpageXXe01baf}.
- e01bef : (Integer,Matrix DoubleFloat,Matrix DoubleFloat,Integer) -> Result
- ++ e01bef(n,x,f,ifail)
- ++ computes a monotonicity-preserving piecewise cubic Hermite
- ++ interpolant to a set of data points.
- ++ See \downlink{Manual Page}{manpageXXe01bef}.
- e01bff : (Integer,Matrix DoubleFloat,Matrix DoubleFloat,Matrix DoubleFloat,_
- Integer,Matrix DoubleFloat,Integer) -> Result
- ++ e01bff(n,x,f,d,m,px,ifail)
- ++ evaluates a piecewise cubic Hermite interpolant at a set
- ++ of points.
- ++ See \downlink{Manual Page}{manpageXXe01bff}.
- e01bgf : (Integer,Matrix DoubleFloat,Matrix DoubleFloat,Matrix DoubleFloat,_
- Integer,Matrix DoubleFloat,Integer) -> Result
- ++ e01bgf(n,x,f,d,m,px,ifail)
- ++ evaluates a piecewise cubic Hermite interpolant and its
- ++ first derivative at a set of points.
- ++ See \downlink{Manual Page}{manpageXXe01bgf}.
- e01bhf : (Integer,Matrix DoubleFloat,Matrix DoubleFloat,Matrix DoubleFloat,_
- DoubleFloat,DoubleFloat,Integer) -> Result
- ++ e01bhf(n,x,f,d,a,b,ifail)
- ++ evaluates the definite integral of a piecewise cubic
- ++ Hermite interpolant over the interval [a,b].
- ++ See \downlink{Manual Page}{manpageXXe01bhf}.
- e01daf : (Integer,Integer,Matrix DoubleFloat,Matrix DoubleFloat,_
- Matrix DoubleFloat,Integer) -> Result
- ++ e01daf(mx,my,x,y,f,ifail)
- ++ computes a bicubic spline interpolating surface through a
- ++ set of data values, given on a rectangular grid in the x-y plane.
- ++ See \downlink{Manual Page}{manpageXXe01daf}.
- e01saf : (Integer,Matrix DoubleFloat,Matrix DoubleFloat,Matrix DoubleFloat,_
- Integer) -> Result
- ++ e01saf(m,x,y,f,ifail)
- ++ generates a two-dimensional surface interpolating a set of
- ++ scattered data points, using the method of Renka and Cline.
- ++ See \downlink{Manual Page}{manpageXXe01saf}.
- e01sbf : (Integer,Matrix DoubleFloat,Matrix DoubleFloat,Matrix DoubleFloat,_
- Matrix Integer,Matrix DoubleFloat,DoubleFloat,DoubleFloat,Integer) -> Result
- ++ e01sbf(m,x,y,f,triang,grads,px,py,ifail)
- ++ evaluates at a given point the two-dimensional interpolant
- ++ function computed by E01SAF.
- ++ See \downlink{Manual Page}{manpageXXe01sbf}.
- e01sef : (Integer,Matrix DoubleFloat,Matrix DoubleFloat,Matrix DoubleFloat,_
- Integer,Integer,DoubleFloat,DoubleFloat,Integer) -> Result
- ++ e01sef(m,x,y,f,nw,nq,rnw,rnq,ifail)
- ++ generates a two-dimensional surface interpolating a set of
- ++ scattered data points, using a modified Shepard method.
- ++ See \downlink{Manual Page}{manpageXXe01sef}.
- e01sff : (Integer,Matrix DoubleFloat,Matrix DoubleFloat,Matrix DoubleFloat,_
- DoubleFloat,Matrix DoubleFloat,DoubleFloat,DoubleFloat,Integer) -> Result
- ++ e01sff(m,x,y,f,rnw,fnodes,px,py,ifail)
- ++ evaluates at a given point the two-dimensional
- ++ interpolating function computed by E01SEF.
- ++ See \downlink{Manual Page}{manpageXXe01sff}.
- Implementation ==> add
-
- import Lisp
- import DoubleFloat
- import Any
- import Record
- import Integer
- import Matrix DoubleFloat
- import Boolean
- import NAGLinkSupportPackage
- import AnyFunctions1(Integer)
- import AnyFunctions1(Matrix DoubleFloat)
- import AnyFunctions1(Matrix Integer)
- import AnyFunctions1(DoubleFloat)
-
-
- e01baf(mArg:Integer,xArg:Matrix DoubleFloat,yArg:Matrix DoubleFloat,_
- lckArg:Integer,lwrkArg:Integer,ifailArg:Integer): Result ==
- [(invokeNagman(NIL$Lisp,_
- "e01baf",_
- ["m"::S,"lck"::S,"lwrk"::S,"ifail"::S,"x"::S,"y"::S,"lamda"::S,"c"::S,"wrk"::S_
- ]$Lisp,_
- ["lamda"::S,"c"::S,"wrk"::S]$Lisp,_
- [["double"::S,["x"::S,"m"::S]$Lisp,["y"::S,"m"::S]$Lisp_
- ,["lamda"::S,"lck"::S]$Lisp,["c"::S,"lck"::S]$Lisp,["wrk"::S,"lwrk"::S]$Lisp]$Lisp_
- ,["integer"::S,"m"::S,"lck"::S,"lwrk"::S,"ifail"::S_
- ]$Lisp_
- ]$Lisp,_
- ["lamda"::S,"c"::S,"ifail"::S]$Lisp,_
- [([mArg::Any,lckArg::Any,lwrkArg::Any,ifailArg::Any,xArg::Any,yArg::Any ])_
- @List Any]$Lisp)$Lisp)_
- pretend List (Record(key:Symbol,entry:Any))]$Result
-
- e01bef(nArg:Integer,xArg:Matrix DoubleFloat,fArg:Matrix DoubleFloat,_
- ifailArg:Integer): Result ==
- [(invokeNagman(NIL$Lisp,_
- "e01bef",_
- ["n"::S,"ifail"::S,"x"::S,"f"::S,"d"::S]$Lisp,_
- ["d"::S]$Lisp,_
- [["double"::S,["x"::S,"n"::S]$Lisp,["f"::S,"n"::S]$Lisp_
- ,["d"::S,"n"::S]$Lisp]$Lisp_
- ,["integer"::S,"n"::S,"ifail"::S]$Lisp_
- ]$Lisp,_
- ["d"::S,"ifail"::S]$Lisp,_
- [([nArg::Any,ifailArg::Any,xArg::Any,fArg::Any ])_
- @List Any]$Lisp)$Lisp)_
- pretend List (Record(key:Symbol,entry:Any))]$Result
-
- e01bff(nArg:Integer,xArg:Matrix DoubleFloat,fArg:Matrix DoubleFloat,_
- dArg:Matrix DoubleFloat,mArg:Integer,pxArg:Matrix DoubleFloat,_
- ifailArg:Integer): Result ==
- [(invokeNagman(NIL$Lisp,_
- "e01bff",_
- ["n"::S,"m"::S,"ifail"::S,"x"::S,"f"::S,"d"::S,"px"::S,"pf"::S_
- ]$Lisp,_
- ["pf"::S]$Lisp,_
- [["double"::S,["x"::S,"n"::S]$Lisp,["f"::S,"n"::S]$Lisp_
- ,["d"::S,"n"::S]$Lisp,["px"::S,"m"::S]$Lisp,["pf"::S,"m"::S]$Lisp]$Lisp_
- ,["integer"::S,"n"::S,"m"::S,"ifail"::S]$Lisp_
- ]$Lisp,_
- ["pf"::S,"ifail"::S]$Lisp,_
- [([nArg::Any,mArg::Any,ifailArg::Any,xArg::Any,fArg::Any,dArg::Any,pxArg::Any ])_
- @List Any]$Lisp)$Lisp)_
- pretend List (Record(key:Symbol,entry:Any))]$Result
-
- e01bgf(nArg:Integer,xArg:Matrix DoubleFloat,fArg:Matrix DoubleFloat,_
- dArg:Matrix DoubleFloat,mArg:Integer,pxArg:Matrix DoubleFloat,_
- ifailArg:Integer): Result ==
- [(invokeNagman(NIL$Lisp,_
- "e01bgf",_
- ["n"::S,"m"::S,"ifail"::S,"x"::S,"f"::S,"d"::S,"px"::S,"pf"::S_
- ,"pd"::S]$Lisp,_
- ["pf"::S,"pd"::S]$Lisp,_
- [["double"::S,["x"::S,"n"::S]$Lisp,["f"::S,"n"::S]$Lisp_
- ,["d"::S,"n"::S]$Lisp,["px"::S,"m"::S]$Lisp,["pf"::S,"m"::S]$Lisp,["pd"::S,"m"::S]$Lisp]$Lisp_
- ,["integer"::S,"n"::S,"m"::S,"ifail"::S]$Lisp_
- ]$Lisp,_
- ["pf"::S,"pd"::S,"ifail"::S]$Lisp,_
- [([nArg::Any,mArg::Any,ifailArg::Any,xArg::Any,fArg::Any,dArg::Any,pxArg::Any ])_
- @List Any]$Lisp)$Lisp)_
- pretend List (Record(key:Symbol,entry:Any))]$Result
-
- e01bhf(nArg:Integer,xArg:Matrix DoubleFloat,fArg:Matrix DoubleFloat,_
- dArg:Matrix DoubleFloat,aArg:DoubleFloat,bArg:DoubleFloat,_
- ifailArg:Integer): Result ==
- [(invokeNagman(NIL$Lisp,_
- "e01bhf",_
- ["n"::S,"a"::S,"b"::S,"pint"::S,"ifail"::S_
- ,"x"::S,"f"::S,"d"::S]$Lisp,_
- ["pint"::S]$Lisp,_
- [["double"::S,["x"::S,"n"::S]$Lisp,["f"::S,"n"::S]$Lisp_
- ,["d"::S,"n"::S]$Lisp,"a"::S,"b"::S,"pint"::S]$Lisp_
- ,["integer"::S,"n"::S,"ifail"::S]$Lisp_
- ]$Lisp,_
- ["pint"::S,"ifail"::S]$Lisp,_
- [([nArg::Any,aArg::Any,bArg::Any,ifailArg::Any,xArg::Any,fArg::Any,dArg::Any ])_
- @List Any]$Lisp)$Lisp)_
- pretend List (Record(key:Symbol,entry:Any))]$Result
-
- e01daf(mxArg:Integer,myArg:Integer,xArg:Matrix DoubleFloat,_
- yArg:Matrix DoubleFloat,fArg:Matrix DoubleFloat,ifailArg:Integer): Result ==
- [(invokeNagman(NIL$Lisp,_
- "e01daf",_
- ["mx"::S,"my"::S,"px"::S,"py"::S,"ifail"::S_
- ,"x"::S,"y"::S,"f"::S,"lamda"::S,"mu"::S_
- ,"c"::S,"wrk"::S]$Lisp,_
- ["px"::S,"py"::S,"lamda"::S,"mu"::S,"c"::S,"wrk"::S]$Lisp,_
- [["double"::S,["x"::S,"mx"::S]$Lisp,["y"::S,"my"::S]$Lisp_
- ,["f"::S,["*"::S,"mx"::S,"my"::S]$Lisp]$Lisp,["lamda"::S,["+"::S,"mx"::S,4$Lisp]$Lisp]$Lisp,["mu"::S,["+"::S,"mx"::S,4$Lisp]$Lisp]$Lisp_
- ,["c"::S,["*"::S,"mx"::S,"my"::S]$Lisp]$Lisp,["wrk"::S,["*"::S,["+"::S,"mx"::S,6$Lisp]$Lisp,["+"::S,"my"::S,6$Lisp]$Lisp]$Lisp]$Lisp_
- ]$Lisp_
- ,["integer"::S,"mx"::S,"my"::S,"px"::S,"py"::S_
- ,"ifail"::S]$Lisp_
- ]$Lisp,_
- ["px"::S,"py"::S,"lamda"::S,"mu"::S,"c"::S,"ifail"::S]$Lisp,_
- [([mxArg::Any,myArg::Any,ifailArg::Any,xArg::Any,yArg::Any,fArg::Any ])_
- @List Any]$Lisp)$Lisp)_
- pretend List (Record(key:Symbol,entry:Any))]$Result
-
- e01saf(mArg:Integer,xArg:Matrix DoubleFloat,yArg:Matrix DoubleFloat,_
- fArg:Matrix DoubleFloat,ifailArg:Integer): Result ==
- [(invokeNagman(NIL$Lisp,_
- "e01saf",_
- ["m"::S,"ifail"::S,"x"::S,"y"::S,"f"::S,"triang"::S,"grads"::S_
- ]$Lisp,_
- ["triang"::S,"grads"::S]$Lisp,_
- [["double"::S,["x"::S,"m"::S]$Lisp,["y"::S,"m"::S]$Lisp_
- ,["f"::S,"m"::S]$Lisp,["grads"::S,2$Lisp,"m"::S]$Lisp]$Lisp_
- ,["integer"::S,"m"::S,["triang"::S,["*"::S,7$Lisp,"m"::S]$Lisp]$Lisp_
- ,"ifail"::S]$Lisp_
- ]$Lisp,_
- ["triang"::S,"grads"::S,"ifail"::S]$Lisp,_
- [([mArg::Any,ifailArg::Any,xArg::Any,yArg::Any,fArg::Any ])_
- @List Any]$Lisp)$Lisp)_
- pretend List (Record(key:Symbol,entry:Any))]$Result
-
- e01sbf(mArg:Integer,xArg:Matrix DoubleFloat,yArg:Matrix DoubleFloat,_
- fArg:Matrix DoubleFloat,triangArg:Matrix Integer,gradsArg:Matrix DoubleFloat,_
- pxArg:DoubleFloat,pyArg:DoubleFloat,ifailArg:Integer): Result ==
- [(invokeNagman(NIL$Lisp,_
- "e01sbf",_
- ["m"::S,"px"::S,"py"::S,"pf"::S,"ifail"::S_
- ,"x"::S,"y"::S,"f"::S,"triang"::S,"grads"::S_
- ]$Lisp,_
- ["pf"::S]$Lisp,_
- [["double"::S,["x"::S,"m"::S]$Lisp,["y"::S,"m"::S]$Lisp_
- ,["f"::S,"m"::S]$Lisp,["grads"::S,2$Lisp,"m"::S]$Lisp,"px"::S,"py"::S,"pf"::S]$Lisp_
- ,["integer"::S,"m"::S,["triang"::S,["*"::S,7$Lisp,"m"::S]$Lisp]$Lisp_
- ,"ifail"::S]$Lisp_
- ]$Lisp,_
- ["pf"::S,"ifail"::S]$Lisp,_
- [([mArg::Any,pxArg::Any,pyArg::Any,ifailArg::Any,xArg::Any,yArg::Any,fArg::Any,triangArg::Any,gradsArg::Any ])_
- @List Any]$Lisp)$Lisp)_
- pretend List (Record(key:Symbol,entry:Any))]$Result
-
- e01sef(mArg:Integer,xArg:Matrix DoubleFloat,yArg:Matrix DoubleFloat,_
- fArg:Matrix DoubleFloat,nwArg:Integer,nqArg:Integer,_
- rnwArg:DoubleFloat,rnqArg:DoubleFloat,ifailArg:Integer): Result ==
- [(invokeNagman(NIL$Lisp,_
- "e01sef",_
- ["m"::S,"nw"::S,"nq"::S,"minnq"::S,"rnw"::S_
- ,"rnq"::S,"ifail"::S,"x"::S,"y"::S,"f"::S,"fnodes"::S,"wrk"::S_
- ]$Lisp,_
- ["fnodes"::S,"minnq"::S,"wrk"::S]$Lisp,_
- [["double"::S,["x"::S,"m"::S]$Lisp,["y"::S,"m"::S]$Lisp_
- ,["f"::S,"m"::S]$Lisp,["fnodes"::S,["*"::S,5$Lisp,"m"::S]$Lisp]$Lisp,"rnw"::S,"rnq"::S,["wrk"::S,["*"::S,6$Lisp,"m"::S]$Lisp]$Lisp_
- ]$Lisp_
- ,["integer"::S,"m"::S,"nw"::S,"nq"::S,"minnq"::S_
- ,"ifail"::S]$Lisp_
- ]$Lisp,_
- ["fnodes"::S,"minnq"::S,"rnw"::S,"rnq"::S,"ifail"::S]$Lisp,_
- [([mArg::Any,nwArg::Any,nqArg::Any,rnwArg::Any,rnqArg::Any,ifailArg::Any,xArg::Any,yArg::Any,fArg::Any ])_
- @List Any]$Lisp)$Lisp)_
- pretend List (Record(key:Symbol,entry:Any))]$Result
-
- e01sff(mArg:Integer,xArg:Matrix DoubleFloat,yArg:Matrix DoubleFloat,_
- fArg:Matrix DoubleFloat,rnwArg:DoubleFloat,fnodesArg:Matrix DoubleFloat,_
- pxArg:DoubleFloat,pyArg:DoubleFloat,ifailArg:Integer): Result ==
- [(invokeNagman(NIL$Lisp,_
- "e01sff",_
- ["m"::S,"rnw"::S,"px"::S,"py"::S,"pf"::S_
- ,"ifail"::S,"x"::S,"y"::S,"f"::S,"fnodes"::S]$Lisp,_
- ["pf"::S]$Lisp,_
- [["double"::S,["x"::S,"m"::S]$Lisp,["y"::S,"m"::S]$Lisp_
- ,["f"::S,"m"::S]$Lisp,"rnw"::S,["fnodes"::S,["*"::S,5$Lisp,"m"::S]$Lisp]$Lisp,"px"::S,"py"::S,"pf"::S]$Lisp_
- ,["integer"::S,"m"::S,"ifail"::S]$Lisp_
- ]$Lisp,_
- ["pf"::S,"ifail"::S]$Lisp,_
- [([mArg::Any,rnwArg::Any,pxArg::Any,pyArg::Any,ifailArg::Any,xArg::Any,yArg::Any,fArg::Any,fnodesArg::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 NAGE01 NagInterpolationPackage>>
-@
-\eject
-\begin{thebibliography}{99}
-\bibitem{1} nothing
-\end{thebibliography}
-\end{document}