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+\documentclass{article}
+\usepackage{axiom}
+\begin{document}
+\title{\$SPAD/src/algebra f02.spad}
+\author{Godfrey Nolan, Mike Dewar}
+\maketitle
+\begin{abstract}
+\end{abstract}
+\eject
+\tableofcontents
+\eject
+\section{package NAGF02 NagEigenPackage}
+<<package NAGF02 NagEigenPackage>>=
+)abbrev package NAGF02 NagEigenPackage
+++ Author: Godfrey Nolan and Mike Dewar
+++ Date Created: Jan 1994
+++ Date Last Updated: Thu May 12 17:45:20 1994
+++Description:
+++This package uses the NAG Library to compute
+++\begin{items}
+++\item eigenvalues and eigenvectors of a matrix
+++\item eigenvalues and eigenvectors of generalized matrix
+++eigenvalue problems
+++\item singular values and singular vectors of a matrix.
+++\end{items}
+++See \downlink{Manual Page}{manpageXXf02}.
+
+NagEigenPackage(): Exports == Implementation where
+ S ==> Symbol
+ FOP ==> FortranOutputStackPackage
+
+ Exports ==> with
+ f02aaf : (Integer,Integer,Matrix DoubleFloat,Integer) -> Result
+ ++ f02aaf(ia,n,a,ifail)
+ ++ calculates all the eigenvalue.
+ ++ See \downlink{Manual Page}{manpageXXf02aaf}.
+ f02abf : (Matrix DoubleFloat,Integer,Integer,Integer,_
+ Integer) -> Result
+ ++ f02abf(a,ia,n,iv,ifail)
+ ++ calculates all the eigenvalues of a real
+ ++ symmetric matrix.
+ ++ See \downlink{Manual Page}{manpageXXf02abf}.
+ f02adf : (Integer,Integer,Integer,Matrix DoubleFloat,_
+ Matrix DoubleFloat,Integer) -> Result
+ ++ f02adf(ia,ib,n,a,b,ifail)
+ ++ calculates all the eigenvalues of Ax=(lambda)Bx, where A
+ ++ is a real symmetric matrix and B is a real symmetric positive-
+ ++ definite matrix.
+ ++ See \downlink{Manual Page}{manpageXXf02adf}.
+ f02aef : (Integer,Integer,Integer,Integer,_
+ Matrix DoubleFloat,Matrix DoubleFloat,Integer) -> Result
+ ++ f02aef(ia,ib,n,iv,a,b,ifail)
+ ++ calculates all the eigenvalues of
+ ++ Ax=(lambda)Bx, where A is a real symmetric matrix and B is a
+ ++ real symmetric positive-definite matrix.
+ ++ See \downlink{Manual Page}{manpageXXf02aef}.
+ f02aff : (Integer,Integer,Matrix DoubleFloat,Integer) -> Result
+ ++ f02aff(ia,n,a,ifail)
+ ++ calculates all the eigenvalues of a real unsymmetric
+ ++ matrix.
+ ++ See \downlink{Manual Page}{manpageXXf02aff}.
+ f02agf : (Integer,Integer,Integer,Integer,_
+ Matrix DoubleFloat,Integer) -> Result
+ ++ f02agf(ia,n,ivr,ivi,a,ifail)
+ ++ calculates all the eigenvalues of a real
+ ++ unsymmetric matrix.
+ ++ See \downlink{Manual Page}{manpageXXf02agf}.
+ f02ajf : (Integer,Integer,Integer,Matrix DoubleFloat,_
+ Matrix DoubleFloat,Integer) -> Result
+ ++ f02ajf(iar,iai,n,ar,ai,ifail)
+ ++ calculates all the eigenvalue.
+ ++ See \downlink{Manual Page}{manpageXXf02ajf}.
+ f02akf : (Integer,Integer,Integer,Integer,_
+ Integer,Matrix DoubleFloat,Matrix DoubleFloat,Integer) -> Result
+ ++ f02akf(iar,iai,n,ivr,ivi,ar,ai,ifail)
+ ++ calculates all the eigenvalues of a
+ ++ complex matrix.
+ ++ See \downlink{Manual Page}{manpageXXf02akf}.
+ f02awf : (Integer,Integer,Integer,Matrix DoubleFloat,_
+ Matrix DoubleFloat,Integer) -> Result
+ ++ f02awf(iar,iai,n,ar,ai,ifail)
+ ++ calculates all the eigenvalues of a complex Hermitian
+ ++ matrix.
+ ++ See \downlink{Manual Page}{manpageXXf02awf}.
+ f02axf : (Matrix DoubleFloat,Integer,Matrix DoubleFloat,Integer,_
+ Integer,Integer,Integer,Integer) -> Result
+ ++ f02axf(ar,iar,ai,iai,n,ivr,ivi,ifail)
+ ++ calculates all the eigenvalues of a
+ ++ complex Hermitian matrix.
+ ++ See \downlink{Manual Page}{manpageXXf02axf}.
+ f02bbf : (Integer,Integer,DoubleFloat,DoubleFloat,_
+ Integer,Integer,Matrix DoubleFloat,Integer) -> Result
+ ++ f02bbf(ia,n,alb,ub,m,iv,a,ifail)
+ ++ calculates selected eigenvalues of a real
+ ++ symmetric matrix by reduction to tridiagonal form, bisection and
+ ++ inverse iteration, where the selected eigenvalues lie within a
+ ++ given interval.
+ ++ See \downlink{Manual Page}{manpageXXf02bbf}.
+ f02bjf : (Integer,Integer,Integer,DoubleFloat,_
+ Boolean,Integer,Matrix DoubleFloat,Matrix DoubleFloat,Integer) -> Result
+ ++ f02bjf(n,ia,ib,eps1,matv,iv,a,b,ifail)
+ ++ calculates all the eigenvalues and, if required, all the
+ ++ eigenvectors of the generalized eigenproblem Ax=(lambda)Bx
+ ++ where A and B are real, square matrices, using the QZ algorithm.
+ ++ See \downlink{Manual Page}{manpageXXf02bjf}.
+ f02fjf : (Integer,Integer,DoubleFloat,Integer,_
+ Integer,Integer,Integer,Integer,Integer,Integer,Matrix DoubleFloat,Integer,Union(fn:FileName,fp:Asp27(DOT)),Union(fn:FileName,fp:Asp28(IMAGE))) -> Result
+ ++ f02fjf(n,k,tol,novecs,nrx,lwork,lrwork,liwork,m,noits,x,ifail,dot,image)
+ ++ finds eigenvalues of a real sparse symmetric
+ ++ or generalized symmetric eigenvalue problem.
+ ++ See \downlink{Manual Page}{manpageXXf02fjf}.
+ f02fjf : (Integer,Integer,DoubleFloat,Integer,_
+ Integer,Integer,Integer,Integer,Integer,Integer,Matrix DoubleFloat,Integer,Union(fn:FileName,fp:Asp27(DOT)),Union(fn:FileName,fp:Asp28(IMAGE)),FileName) -> Result
+ ++ f02fjf(n,k,tol,novecs,nrx,lwork,lrwork,liwork,m,noits,x,ifail,dot,image,monit)
+ ++ finds eigenvalues of a real sparse symmetric
+ ++ or generalized symmetric eigenvalue problem.
+ ++ See \downlink{Manual Page}{manpageXXf02fjf}.
+ f02wef : (Integer,Integer,Integer,Integer,_
+ Integer,Boolean,Integer,Boolean,Integer,Matrix DoubleFloat,Matrix DoubleFloat,Integer) -> Result
+ ++ f02wef(m,n,lda,ncolb,ldb,wantq,ldq,wantp,ldpt,a,b,ifail)
+ ++ returns all, or part, of the singular value decomposition
+ ++ of a general real matrix.
+ ++ See \downlink{Manual Page}{manpageXXf02wef}.
+ f02xef : (Integer,Integer,Integer,Integer,_
+ Integer,Boolean,Integer,Boolean,Integer,Matrix Complex DoubleFloat,Matrix Complex DoubleFloat,Integer) -> Result
+ ++ f02xef(m,n,lda,ncolb,ldb,wantq,ldq,wantp,ldph,a,b,ifail)
+ ++ returns all, or part, of the singular value decomposition
+ ++ of a general complex matrix.
+ ++ See \downlink{Manual Page}{manpageXXf02xef}.
+ Implementation ==> add
+
+ import Lisp
+ import DoubleFloat
+ import Any
+ import Record
+ import Integer
+ import Matrix DoubleFloat
+ import Boolean
+ import NAGLinkSupportPackage
+ import FortranPackage
+ import AnyFunctions1(Integer)
+ import AnyFunctions1(Boolean)
+ import AnyFunctions1(Matrix DoubleFloat)
+ import AnyFunctions1(Matrix Complex DoubleFloat)
+ import AnyFunctions1(DoubleFloat)
+
+
+ f02aaf(iaArg:Integer,nArg:Integer,aArg:Matrix DoubleFloat,_
+ ifailArg:Integer): Result ==
+ [(invokeNagman(NIL$Lisp,_
+ "f02aaf",_
+ ["ia"::S,"n"::S,"ifail"::S,"r"::S,"a"::S,"e"::S]$Lisp,_
+ ["r"::S,"e"::S]$Lisp,_
+ [["double"::S,["r"::S,"n"::S]$Lisp,["a"::S,"ia"::S,"n"::S]$Lisp_
+ ,["e"::S,"n"::S]$Lisp]$Lisp_
+ ,["integer"::S,"ia"::S,"n"::S,"ifail"::S]$Lisp_
+ ]$Lisp,_
+ ["r"::S,"a"::S,"ifail"::S]$Lisp,_
+ [([iaArg::Any,nArg::Any,ifailArg::Any,aArg::Any ])_
+ @List Any]$Lisp)$Lisp)_
+ pretend List (Record(key:Symbol,entry:Any))]$Result
+
+ f02abf(aArg:Matrix DoubleFloat,iaArg:Integer,nArg:Integer,_
+ ivArg:Integer,ifailArg:Integer): Result ==
+ [(invokeNagman(NIL$Lisp,_
+ "f02abf",_
+ ["ia"::S,"n"::S,"iv"::S,"ifail"::S,"a"::S,"r"::S,"v"::S,"e"::S]$Lisp,_
+ ["r"::S,"v"::S,"e"::S]$Lisp,_
+ [["double"::S,["a"::S,"ia"::S,"n"::S]$Lisp_
+ ,["r"::S,"n"::S]$Lisp,["v"::S,"iv"::S,"n"::S]$Lisp,["e"::S,"n"::S]$Lisp]$Lisp_
+ ,["integer"::S,"ia"::S,"n"::S,"iv"::S,"ifail"::S_
+ ]$Lisp_
+ ]$Lisp,_
+ ["r"::S,"v"::S,"ifail"::S]$Lisp,_
+ [([iaArg::Any,nArg::Any,ivArg::Any,ifailArg::Any,aArg::Any ])_
+ @List Any]$Lisp)$Lisp)_
+ pretend List (Record(key:Symbol,entry:Any))]$Result
+
+ f02adf(iaArg:Integer,ibArg:Integer,nArg:Integer,_
+ aArg:Matrix DoubleFloat,bArg:Matrix DoubleFloat,ifailArg:Integer): Result ==
+ [(invokeNagman(NIL$Lisp,_
+ "f02adf",_
+ ["ia"::S,"ib"::S,"n"::S,"ifail"::S,"r"::S,"a"::S,"b"::S,"de"::S]$Lisp,_
+ ["r"::S,"de"::S]$Lisp,_
+ [["double"::S,["r"::S,"n"::S]$Lisp,["a"::S,"ia"::S,"n"::S]$Lisp_
+ ,["b"::S,"ib"::S,"n"::S]$Lisp,["de"::S,"n"::S]$Lisp]$Lisp_
+ ,["integer"::S,"ia"::S,"ib"::S,"n"::S,"ifail"::S_
+ ]$Lisp_
+ ]$Lisp,_
+ ["r"::S,"a"::S,"b"::S,"ifail"::S]$Lisp,_
+ [([iaArg::Any,ibArg::Any,nArg::Any,ifailArg::Any,aArg::Any,bArg::Any ])_
+ @List Any]$Lisp)$Lisp)_
+ pretend List (Record(key:Symbol,entry:Any))]$Result
+
+ f02aef(iaArg:Integer,ibArg:Integer,nArg:Integer,_
+ ivArg:Integer,aArg:Matrix DoubleFloat,bArg:Matrix DoubleFloat,_
+ ifailArg:Integer): Result ==
+ [(invokeNagman(NIL$Lisp,_
+ "f02aef",_
+ ["ia"::S,"ib"::S,"n"::S,"iv"::S,"ifail"::S_
+ ,"r"::S,"v"::S,"a"::S,"b"::S,"dl"::S_
+ ,"e"::S]$Lisp,_
+ ["r"::S,"v"::S,"dl"::S,"e"::S]$Lisp,_
+ [["double"::S,["r"::S,"n"::S]$Lisp,["v"::S,"iv"::S,"n"::S]$Lisp_
+ ,["a"::S,"ia"::S,"n"::S]$Lisp,["b"::S,"ib"::S,"n"::S]$Lisp,["dl"::S,"n"::S]$Lisp,["e"::S,"n"::S]$Lisp_
+ ]$Lisp_
+ ,["integer"::S,"ia"::S,"ib"::S,"n"::S,"iv"::S_
+ ,"ifail"::S]$Lisp_
+ ]$Lisp,_
+ ["r"::S,"v"::S,"a"::S,"b"::S,"ifail"::S]$Lisp,_
+ [([iaArg::Any,ibArg::Any,nArg::Any,ivArg::Any,ifailArg::Any,aArg::Any,bArg::Any ])_
+ @List Any]$Lisp)$Lisp)_
+ pretend List (Record(key:Symbol,entry:Any))]$Result
+
+ f02aff(iaArg:Integer,nArg:Integer,aArg:Matrix DoubleFloat,_
+ ifailArg:Integer): Result ==
+ [(invokeNagman(NIL$Lisp,_
+ "f02aff",_
+ ["ia"::S,"n"::S,"ifail"::S,"rr"::S,"ri"::S,"intger"::S,"a"::S]$Lisp,_
+ ["rr"::S,"ri"::S,"intger"::S]$Lisp,_
+ [["double"::S,["rr"::S,"n"::S]$Lisp,["ri"::S,"n"::S]$Lisp_
+ ,["a"::S,"ia"::S,"n"::S]$Lisp]$Lisp_
+ ,["integer"::S,"ia"::S,"n"::S,["intger"::S,"n"::S]$Lisp_
+ ,"ifail"::S]$Lisp_
+ ]$Lisp,_
+ ["rr"::S,"ri"::S,"intger"::S,"a"::S,"ifail"::S]$Lisp,_
+ [([iaArg::Any,nArg::Any,ifailArg::Any,aArg::Any ])_
+ @List Any]$Lisp)$Lisp)_
+ pretend List (Record(key:Symbol,entry:Any))]$Result
+
+ f02agf(iaArg:Integer,nArg:Integer,ivrArg:Integer,_
+ iviArg:Integer,aArg:Matrix DoubleFloat,ifailArg:Integer): Result ==
+ [(invokeNagman(NIL$Lisp,_
+ "f02agf",_
+ ["ia"::S,"n"::S,"ivr"::S,"ivi"::S,"ifail"::S_
+ ,"rr"::S,"ri"::S,"vr"::S,"vi"::S,"intger"::S_
+ ,"a"::S]$Lisp,_
+ ["rr"::S,"ri"::S,"vr"::S,"vi"::S,"intger"::S]$Lisp,_
+ [["double"::S,["rr"::S,"n"::S]$Lisp,["ri"::S,"n"::S]$Lisp_
+ ,["vr"::S,"ivr"::S,"n"::S]$Lisp,["vi"::S,"ivi"::S,"n"::S]$Lisp,["a"::S,"ia"::S,"n"::S]$Lisp]$Lisp_
+ ,["integer"::S,"ia"::S,"n"::S,"ivr"::S,"ivi"::S_
+ ,["intger"::S,"n"::S]$Lisp,"ifail"::S]$Lisp_
+ ]$Lisp,_
+ ["rr"::S,"ri"::S,"vr"::S,"vi"::S,"intger"::S,"a"::S,"ifail"::S]$Lisp,_
+ [([iaArg::Any,nArg::Any,ivrArg::Any,iviArg::Any,ifailArg::Any,aArg::Any ])_
+ @List Any]$Lisp)$Lisp)_
+ pretend List (Record(key:Symbol,entry:Any))]$Result
+
+ f02ajf(iarArg:Integer,iaiArg:Integer,nArg:Integer,_
+ arArg:Matrix DoubleFloat,aiArg:Matrix DoubleFloat,ifailArg:Integer): Result ==
+ [(invokeNagman(NIL$Lisp,_
+ "f02ajf",_
+ ["iar"::S,"iai"::S,"n"::S,"ifail"::S,"rr"::S,"ri"::S,"ar"::S,"ai"::S,"intger"::S_
+ ]$Lisp,_
+ ["rr"::S,"ri"::S,"intger"::S]$Lisp,_
+ [["double"::S,["rr"::S,"n"::S]$Lisp,["ri"::S,"n"::S]$Lisp_
+ ,["ar"::S,"iar"::S,"n"::S]$Lisp,["ai"::S,"iai"::S,"n"::S]$Lisp]$Lisp_
+ ,["integer"::S,"iar"::S,"iai"::S,"n"::S,"ifail"::S_
+ ,["intger"::S,"n"::S]$Lisp]$Lisp_
+ ]$Lisp,_
+ ["rr"::S,"ri"::S,"ar"::S,"ai"::S,"ifail"::S]$Lisp,_
+ [([iarArg::Any,iaiArg::Any,nArg::Any,ifailArg::Any,arArg::Any,aiArg::Any ])_
+ @List Any]$Lisp)$Lisp)_
+ pretend List (Record(key:Symbol,entry:Any))]$Result
+
+ f02akf(iarArg:Integer,iaiArg:Integer,nArg:Integer,_
+ ivrArg:Integer,iviArg:Integer,arArg:Matrix DoubleFloat,_
+ aiArg:Matrix DoubleFloat,ifailArg:Integer): Result ==
+ [(invokeNagman(NIL$Lisp,_
+ "f02akf",_
+ ["iar"::S,"iai"::S,"n"::S,"ivr"::S,"ivi"::S_
+ ,"ifail"::S,"rr"::S,"ri"::S,"vr"::S,"vi"::S,"ar"::S_
+ ,"ai"::S,"intger"::S]$Lisp,_
+ ["rr"::S,"ri"::S,"vr"::S,"vi"::S,"intger"::S]$Lisp,_
+ [["double"::S,["rr"::S,"n"::S]$Lisp,["ri"::S,"n"::S]$Lisp_
+ ,["vr"::S,"ivr"::S,"n"::S]$Lisp,["vi"::S,"ivi"::S,"n"::S]$Lisp,["ar"::S,"iar"::S,"n"::S]$Lisp,["ai"::S,"iai"::S,"n"::S]$Lisp_
+ ]$Lisp_
+ ,["integer"::S,"iar"::S,"iai"::S,"n"::S,"ivr"::S_
+ ,"ivi"::S,"ifail"::S,["intger"::S,"n"::S]$Lisp]$Lisp_
+ ]$Lisp,_
+ ["rr"::S,"ri"::S,"vr"::S,"vi"::S,"ar"::S,"ai"::S,"ifail"::S]$Lisp,_
+ [([iarArg::Any,iaiArg::Any,nArg::Any,ivrArg::Any,iviArg::Any,ifailArg::Any,arArg::Any,aiArg::Any ])_
+ @List Any]$Lisp)$Lisp)_
+ pretend List (Record(key:Symbol,entry:Any))]$Result
+
+ f02awf(iarArg:Integer,iaiArg:Integer,nArg:Integer,_
+ arArg:Matrix DoubleFloat,aiArg:Matrix DoubleFloat,ifailArg:Integer): Result ==
+ [(invokeNagman(NIL$Lisp,_
+ "f02awf",_
+ ["iar"::S,"iai"::S,"n"::S,"ifail"::S,"r"::S,"ar"::S,"ai"::S,"wk1"::S,"wk2"::S_
+ ,"wk3"::S]$Lisp,_
+ ["r"::S,"wk1"::S,"wk2"::S,"wk3"::S]$Lisp,_
+ [["double"::S,["r"::S,"n"::S]$Lisp,["ar"::S,"iar"::S,"n"::S]$Lisp_
+ ,["ai"::S,"iai"::S,"n"::S]$Lisp,["wk1"::S,"n"::S]$Lisp,["wk2"::S,"n"::S]$Lisp,["wk3"::S,"n"::S]$Lisp_
+ ]$Lisp_
+ ,["integer"::S,"iar"::S,"iai"::S,"n"::S,"ifail"::S_
+ ]$Lisp_
+ ]$Lisp,_
+ ["r"::S,"ar"::S,"ai"::S,"ifail"::S]$Lisp,_
+ [([iarArg::Any,iaiArg::Any,nArg::Any,ifailArg::Any,arArg::Any,aiArg::Any ])_
+ @List Any]$Lisp)$Lisp)_
+ pretend List (Record(key:Symbol,entry:Any))]$Result
+
+ f02axf(arArg:Matrix DoubleFloat,iarArg:Integer,aiArg:Matrix DoubleFloat,_
+ iaiArg:Integer,nArg:Integer,ivrArg:Integer,_
+ iviArg:Integer,ifailArg:Integer): Result ==
+ [(invokeNagman(NIL$Lisp,_
+ "f02axf",_
+ ["iar"::S,"iai"::S,"n"::S,"ivr"::S,"ivi"::S_
+ ,"ifail"::S,"ar"::S,"ai"::S,"r"::S,"vr"::S,"vi"::S_
+ ,"wk1"::S,"wk2"::S,"wk3"::S]$Lisp,_
+ ["r"::S,"vr"::S,"vi"::S,"wk1"::S,"wk2"::S,"wk3"::S]$Lisp,_
+ [["double"::S,["ar"::S,"iar"::S,"n"::S]$Lisp_
+ ,["ai"::S,"iai"::S,"n"::S]$Lisp,["r"::S,"n"::S]$Lisp,["vr"::S,"ivr"::S,"n"::S]$Lisp,["vi"::S,"ivi"::S,"n"::S]$Lisp,["wk1"::S,"n"::S]$Lisp_
+ ,["wk2"::S,"n"::S]$Lisp,["wk3"::S,"n"::S]$Lisp]$Lisp_
+ ,["integer"::S,"iar"::S,"iai"::S,"n"::S,"ivr"::S_
+ ,"ivi"::S,"ifail"::S]$Lisp_
+ ]$Lisp,_
+ ["r"::S,"vr"::S,"vi"::S,"ifail"::S]$Lisp,_
+ [([iarArg::Any,iaiArg::Any,nArg::Any,ivrArg::Any,iviArg::Any,ifailArg::Any,arArg::Any,aiArg::Any ])_
+ @List Any]$Lisp)$Lisp)_
+ pretend List (Record(key:Symbol,entry:Any))]$Result
+
+ f02bbf(iaArg:Integer,nArg:Integer,albArg:DoubleFloat,_
+ ubArg:DoubleFloat,mArg:Integer,ivArg:Integer,_
+ aArg:Matrix DoubleFloat,ifailArg:Integer): Result ==
+ [(invokeNagman(NIL$Lisp,_
+ "f02bbf",_
+ ["ia"::S,"n"::S,"alb"::S,"ub"::S,"m"::S_
+ ,"iv"::S,"mm"::S,"ifail"::S,"r"::S,"v"::S,"icount"::S,"a"::S,"d"::S_
+ ,"e"::S,"e2"::S,"x"::S,"g"::S,"c"::S_
+ ]$Lisp,_
+ ["mm"::S,"r"::S,"v"::S,"icount"::S,"d"::S,"e"::S,"e2"::S,"x"::S,"g"::S,"c"::S]$Lisp,_
+ [["double"::S,"alb"::S,"ub"::S,["r"::S,"m"::S]$Lisp_
+ ,["v"::S,"iv"::S,"m"::S]$Lisp,["a"::S,"ia"::S,"n"::S]$Lisp,["d"::S,"n"::S]$Lisp,["e"::S,"n"::S]$Lisp,["e2"::S,"n"::S]$Lisp_
+ ,["x"::S,"n"::S,7$Lisp]$Lisp,["g"::S,"n"::S]$Lisp]$Lisp_
+ ,["integer"::S,"ia"::S,"n"::S,"m"::S,"iv"::S_
+ ,"mm"::S,["icount"::S,"m"::S]$Lisp,"ifail"::S]$Lisp_
+ ,["logical"::S,["c"::S,"n"::S]$Lisp]$Lisp_
+ ]$Lisp,_
+ ["mm"::S,"r"::S,"v"::S,"icount"::S,"a"::S,"ifail"::S]$Lisp,_
+ [([iaArg::Any,nArg::Any,albArg::Any,ubArg::Any,mArg::Any,ivArg::Any,ifailArg::Any,aArg::Any ])_
+ @List Any]$Lisp)$Lisp)_
+ pretend List (Record(key:Symbol,entry:Any))]$Result
+
+ f02bjf(nArg:Integer,iaArg:Integer,ibArg:Integer,_
+ eps1Arg:DoubleFloat,matvArg:Boolean,ivArg:Integer,_
+ aArg:Matrix DoubleFloat,bArg:Matrix DoubleFloat,ifailArg:Integer): Result ==
+ [(invokeNagman(NIL$Lisp,_
+ "f02bjf",_
+ ["n"::S,"ia"::S,"ib"::S,"eps1"::S,"matv"::S_
+ ,"iv"::S,"ifail"::S,"alfr"::S,"alfi"::S,"beta"::S,"v"::S,"iter"::S_
+ ,"a"::S,"b"::S]$Lisp,_
+ ["alfr"::S,"alfi"::S,"beta"::S,"v"::S,"iter"::S]$Lisp,_
+ [["double"::S,"eps1"::S,["alfr"::S,"n"::S]$Lisp_
+ ,["alfi"::S,"n"::S]$Lisp,["beta"::S,"n"::S]$Lisp,["v"::S,"iv"::S,"n"::S]$Lisp,["a"::S,"ia"::S,"n"::S]$Lisp,["b"::S,"ib"::S,"n"::S]$Lisp_
+ ]$Lisp_
+ ,["integer"::S,"n"::S,"ia"::S,"ib"::S,"iv"::S_
+ ,["iter"::S,"n"::S]$Lisp,"ifail"::S]$Lisp_
+ ,["logical"::S,"matv"::S]$Lisp_
+ ]$Lisp,_
+ ["alfr"::S,"alfi"::S,"beta"::S,"v"::S,"iter"::S,"a"::S,"b"::S,"ifail"::S]$Lisp,_
+ [([nArg::Any,iaArg::Any,ibArg::Any,eps1Arg::Any,matvArg::Any,ivArg::Any,ifailArg::Any,aArg::Any,bArg::Any ])_
+ @List Any]$Lisp)$Lisp)_
+ pretend List (Record(key:Symbol,entry:Any))]$Result
+
+ f02fjf(nArg:Integer,kArg:Integer,tolArg:DoubleFloat,_
+ novecsArg:Integer,nrxArg:Integer,lworkArg:Integer,_
+ lrworkArg:Integer,liworkArg:Integer,mArg:Integer,_
+ noitsArg:Integer,xArg:Matrix DoubleFloat,ifailArg:Integer,_
+ dotArg:Union(fn:FileName,fp:Asp27(DOT)),imageArg:Union(fn:FileName,fp:Asp28(IMAGE))): Result ==
+ pushFortranOutputStack(dotFilename := aspFilename "dot")$FOP
+ if dotArg case fn
+ then outputAsFortran(dotArg.fn)
+ else outputAsFortran(dotArg.fp)
+ popFortranOutputStack()$FOP
+ pushFortranOutputStack(imageFilename := aspFilename "image")$FOP
+ if imageArg case fn
+ then outputAsFortran(imageArg.fn)
+ else outputAsFortran(imageArg.fp)
+ popFortranOutputStack()$FOP
+ pushFortranOutputStack(monitFilename := aspFilename "monit")$FOP
+ outputAsFortran()$Asp29(MONIT)
+ popFortranOutputStack()$FOP
+ [(invokeNagman([dotFilename,imageFilename,monitFilename]$Lisp,_
+ "f02fjf",_
+ ["n"::S,"k"::S,"tol"::S,"novecs"::S,"nrx"::S_
+ ,"lwork"::S,"lrwork"::S,"liwork"::S,"m"::S,"noits"::S_
+ ,"ifail"::S,"dot"::S,"image"::S,"monit"::S,"d"::S,"x"::S,"work"::S,"rwork"::S,"iwork"::S_
+ ]$Lisp,_
+ ["d"::S,"work"::S,"rwork"::S,"iwork"::S,"dot"::S,"image"::S,"monit"::S]$Lisp,_
+ [["double"::S,"tol"::S,["d"::S,"k"::S]$Lisp_
+ ,["x"::S,"nrx"::S,"k"::S]$Lisp,["work"::S,"lwork"::S]$Lisp,["rwork"::S,"lrwork"::S]$Lisp,"dot"::S,"image"::S,"monit"::S_
+ ]$Lisp_
+ ,["integer"::S,"n"::S,"k"::S,"novecs"::S,"nrx"::S_
+ ,"lwork"::S,"lrwork"::S,"liwork"::S,"m"::S,"noits"::S,"ifail"::S,["iwork"::S,"liwork"::S]$Lisp]$Lisp_
+ ]$Lisp,_
+ ["d"::S,"m"::S,"noits"::S,"x"::S,"ifail"::S]$Lisp,_
+ [([nArg::Any,kArg::Any,tolArg::Any,novecsArg::Any,nrxArg::Any,lworkArg::Any,lrworkArg::Any,liworkArg::Any,mArg::Any,noitsArg::Any,ifailArg::Any,xArg::Any ])_
+ @List Any]$Lisp)$Lisp)_
+ pretend List (Record(key:Symbol,entry:Any))]$Result
+
+ f02fjf(nArg:Integer,kArg:Integer,tolArg:DoubleFloat,_
+ novecsArg:Integer,nrxArg:Integer,lworkArg:Integer,_
+ lrworkArg:Integer,liworkArg:Integer,mArg:Integer,_
+ noitsArg:Integer,xArg:Matrix DoubleFloat,ifailArg:Integer,_
+ dotArg:Union(fn:FileName,fp:Asp27(DOT)),imageArg:Union(fn:FileName,fp:Asp28(IMAGE)),monitArg:FileName): Result ==
+ pushFortranOutputStack(dotFilename := aspFilename "dot")$FOP
+ if dotArg case fn
+ then outputAsFortran(dotArg.fn)
+ else outputAsFortran(dotArg.fp)
+ popFortranOutputStack()$FOP
+ pushFortranOutputStack(imageFilename := aspFilename "image")$FOP
+ if imageArg case fn
+ then outputAsFortran(imageArg.fn)
+ else outputAsFortran(imageArg.fp)
+ popFortranOutputStack()$FOP
+ pushFortranOutputStack(monitFilename := aspFilename "monit")$FOP
+ outputAsFortran(monitArg)
+ [(invokeNagman([dotFilename,imageFilename,monitFilename]$Lisp,_
+ "f02fjf",_
+ ["n"::S,"k"::S,"tol"::S,"novecs"::S,"nrx"::S_
+ ,"lwork"::S,"lrwork"::S,"liwork"::S,"m"::S,"noits"::S_
+ ,"ifail"::S,"dot"::S,"image"::S,"monit"::S,"d"::S,"x"::S,"work"::S,"rwork"::S,"iwork"::S_
+ ]$Lisp,_
+ ["d"::S,"work"::S,"rwork"::S,"iwork"::S,"dot"::S,"image"::S,"monit"::S]$Lisp,_
+ [["double"::S,"tol"::S,["d"::S,"k"::S]$Lisp_
+ ,["x"::S,"nrx"::S,"k"::S]$Lisp,["work"::S,"lwork"::S]$Lisp,["rwork"::S,"lrwork"::S]$Lisp,"dot"::S,"image"::S,"monit"::S_
+ ]$Lisp_
+ ,["integer"::S,"n"::S,"k"::S,"novecs"::S,"nrx"::S_
+ ,"lwork"::S,"lrwork"::S,"liwork"::S,"m"::S,"noits"::S,"ifail"::S,["iwork"::S,"liwork"::S]$Lisp]$Lisp_
+ ]$Lisp,_
+ ["d"::S,"m"::S,"noits"::S,"x"::S,"ifail"::S]$Lisp,_
+ [([nArg::Any,kArg::Any,tolArg::Any,novecsArg::Any,nrxArg::Any,lworkArg::Any,lrworkArg::Any,liworkArg::Any,mArg::Any,noitsArg::Any,ifailArg::Any,xArg::Any ])_
+ @List Any]$Lisp)$Lisp)_
+ pretend List (Record(key:Symbol,entry:Any))]$Result
+
+ f02wef(mArg:Integer,nArg:Integer,ldaArg:Integer,_
+ ncolbArg:Integer,ldbArg:Integer,wantqArg:Boolean,_
+ ldqArg:Integer,wantpArg:Boolean,ldptArg:Integer,_
+ aArg:Matrix DoubleFloat,bArg:Matrix DoubleFloat,ifailArg:Integer): Result ==
+ workLength : Integer :=
+ mArg >= nArg =>
+ wantqArg and wantpArg =>
+ max(max(nArg**2 + 5*(nArg - 1),nArg + ncolbArg),4)
+ wantqArg =>
+ max(max(nArg**2 + 4*(nArg - 1),nArg + ncolbArg),4)
+ wantpArg =>
+ zero? ncolbArg => max(3*(nArg - 1),2)
+ max(5*(nArg - 1),2)
+ zero? ncolbArg => max(2*(nArg - 1),2)
+ max(3*(nArg - 1),2)
+ wantqArg and wantpArg =>
+ max(mArg**2 + 5*(mArg - 1),2)
+ wantqArg =>
+ max(3*(mArg - 1),1)
+ wantpArg =>
+ zero? ncolbArg => max(mArg**2+3*(mArg - 1),2)
+ max(mArg**2+5*(mArg - 1),2)
+ zero? ncolbArg => max(2*(mArg - 1),1)
+ max(3*(mArg - 1),1)
+
+ [(invokeNagman(NIL$Lisp,_
+ "f02wef",_
+ ["m"::S,"n"::S,"lda"::S,"ncolb"::S,"ldb"::S_
+ ,"wantq"::S,"ldq"::S,"wantp"::S,"ldpt"::S,"ifail"::S_
+ ,"q"::S,"sv"::S,"pt"::S,"work"::S,"a"::S_
+ ,"b"::S]$Lisp,_
+ ["q"::S,"sv"::S,"pt"::S,"work"::S]$Lisp,_
+ [["double"::S,["q"::S,"ldq"::S,"m"::S]$Lisp_
+ ,["sv"::S,"m"::S]$Lisp,["pt"::S,"ldpt"::S,"n"::S]$Lisp,["work"::S,workLength]$Lisp,["a"::S,"lda"::S,"n"::S]$Lisp,["b"::S,"ldb"::S,"ncolb"::S]$Lisp_
+ ]$Lisp_
+ ,["integer"::S,"m"::S,"n"::S,"lda"::S,"ncolb"::S_
+ ,"ldb"::S,"ldq"::S,"ldpt"::S,"ifail"::S]$Lisp_
+ ,["logical"::S,"wantq"::S,"wantp"::S]$Lisp_
+ ]$Lisp,_
+ ["q"::S,"sv"::S,"pt"::S,"work"::S,"a"::S,"b"::S,"ifail"::S]$Lisp,_
+ [([mArg::Any,nArg::Any,ldaArg::Any,ncolbArg::Any,ldbArg::Any,wantqArg::Any,ldqArg::Any,wantpArg::Any,ldptArg::Any,ifailArg::Any,aArg::Any,bArg::Any ])_
+ @List Any]$Lisp)$Lisp)_
+ pretend List (Record(key:Symbol,entry:Any))]$Result
+
+ f02xef(mArg:Integer,nArg:Integer,ldaArg:Integer,_
+ ncolbArg:Integer,ldbArg:Integer,wantqArg:Boolean,_
+ ldqArg:Integer,wantpArg:Boolean,ldphArg:Integer,_
+ aArg:Matrix Complex DoubleFloat,bArg:Matrix Complex DoubleFloat,ifailArg:Integer): Result ==
+ -- This segment added by hand, to deal with an assumed size array GDN
+ tem : Integer := (min(mArg,nArg)-1)
+ rLen : Integer :=
+ zero? ncolbArg and not wantqArg and not wantpArg => 2*tem
+ zero? ncolbArg and wantpArg and not wantqArg => 3*tem
+ not wantpArg =>
+ ncolbArg >0 or wantqArg => 3*tem
+ 5*tem
+ cLen : Integer :=
+ mArg >= nArg =>
+ wantqArg and wantpArg => 2*(nArg + max(nArg**2,ncolbArg))
+ wantqArg and not wantpArg => 2*(nArg + max(nArg**2+nArg,ncolbArg))
+ 2*(nArg + max(nArg,ncolbArg))
+ wantpArg => 2*(mArg**2 + mArg)
+ 2*mArg
+ svLength : Integer :=
+ min(mArg,nArg)
+ [(invokeNagman(NIL$Lisp,_
+ "f02xef",_
+ ["m"::S,"n"::S,"lda"::S,"ncolb"::S,"ldb"::S_
+ ,"wantq"::S,"ldq"::S,"wantp"::S,"ldph"::S,"ifail"::S_
+ ,"q"::S,"sv"::S,"ph"::S,"rwork"::S,"a"::S_
+ ,"b"::S,"cwork"::S]$Lisp,_
+ ["q"::S,"sv"::S,"ph"::S,"rwork"::S,"cwork"::S]$Lisp,_
+ [["double"::S,["sv"::S,svLength]$Lisp,["rwork"::S,rLen]$Lisp_
+ ]$Lisp_
+ ,["integer"::S,"m"::S,"n"::S,"lda"::S,"ncolb"::S_
+ ,"ldb"::S,"ldq"::S,"ldph"::S,"ifail"::S]$Lisp_
+ ,["logical"::S,"wantq"::S,"wantp"::S]$Lisp_
+ ,["double complex"::S,["q"::S,"ldq"::S,"m"::S]$Lisp,["ph"::S,"ldph"::S,"n"::S]$Lisp,["a"::S,"lda"::S,"n"::S]$Lisp,["b"::S,"ldb"::S,"ncolb"::S]$Lisp,["cwork"::S,cLen]$Lisp]$Lisp_
+ ]$Lisp,_
+ ["q"::S,"sv"::S,"ph"::S,"rwork"::S,"a"::S,"b"::S,"ifail"::S]$Lisp,_
+ [([mArg::Any,nArg::Any,ldaArg::Any,ncolbArg::Any,ldbArg::Any,wantqArg::Any,ldqArg::Any,wantpArg::Any,ldphArg::Any,ifailArg::Any,aArg::Any,bArg::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 NAGF02 NagEigenPackage>>
+@
+\eject
+\begin{thebibliography}{99}
+\bibitem{1} nothing
+\end{thebibliography}
+\end{document}
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