/usr/share/axiom-20170501/src/algebra/E04NAFA.spad is in axiom-source 20170501-3.
This file is owned by root:root, with mode 0o644.
The actual contents of the file can be viewed below.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 | )abbrev domain E04NAFA e04nafAnnaType
++ Author: Brian Dupee
++ Date Created: February 1996
++ Date Last Updated: February 1996
++ References:
++ Dupe95 Using Computer Algebra to Choose and Apply Numerical Routines
++ Dewa92 Using Computer Algebra to Select Numerical Algorithms
++ Description:
++ \axiomType{e04nafAnnaType} is a domain of \axiomType{NumericalOptimization}
++ for the NAG routine E04NAF, an optimization routine for Quadratic functions.
++ The function
++ \axiomFun{measure} measures the usefulness of the routine E04NAF
++ for the given problem. The function \axiomFun{numericalOptimization}
++ performs the optimization by using \axiomType{NagOptimisationPackage}.
e04nafAnnaType() : SIG == CODE where
DF ==> DoubleFloat
EF ==> Expression Float
EDF ==> Expression DoubleFloat
PDF ==> Polynomial DoubleFloat
VPDF ==> Vector Polynomial DoubleFloat
LDF ==> List DoubleFloat
LOCDF ==> List OrderedCompletion DoubleFloat
MDF ==> Matrix DoubleFloat
MPDF ==> Matrix Polynomial DoubleFloat
MF ==> Matrix Float
MEF ==> Matrix Expression Float
LEDF ==> List Expression DoubleFloat
VEF ==> Vector Expression Float
NOA ==> Record(fn:EDF, init:LDF, lb:LOCDF, cf:LEDF, ub:LOCDF)
LSA ==> Record(lfn:LEDF, init:LDF)
EF2 ==> ExpressionFunctions2
MI ==> Matrix Integer
INT ==> Integer
F ==> Float
NNI ==> NonNegativeInteger
S ==> Symbol
LS ==> List Symbol
MVCF ==> MultiVariableCalculusFunctions
ESTOOLS2 ==> ExpertSystemToolsPackage2
SDF ==> Stream DoubleFloat
LSDF ==> List Stream DoubleFloat
SOCDF ==> Segment OrderedCompletion DoubleFloat
OCDF ==> OrderedCompletion DoubleFloat
SIG ==> NumericalOptimizationCategory
CODE ==> Result add
Rep:=Result
import Rep, NagOptimisationPackage
import e04AgentsPackage,ExpertSystemToolsPackage
measure(R:RoutinesTable,args:NOA) ==
string:String := "e04naf is "
argsFn:EDF := args.fn
if not (quadratic?(argsFn) and linear?(args.cf)) then
string :=
concat(string,"for a quadratic function with linear constraints only.")
(# string) < 20 =>
string := concat(string,"recommended")
[getMeasure(R,e04naf@Symbol)$RoutinesTable, string]
[0.0,string]
numericalOptimization(args:NOA) ==
argsFn:EDF := args.fn
c := args.cf
listVars:List LS := _
concat(variables(argsFn)$EDF,[variables(z)$EDF for z in c])
n:NNI := #(v := sort(removeDuplicates(concat(listVars)$LS)$LS)$LS)
A:MDF := linearMatrix(c,n)
nclin:NNI := # linearPart(c)
nrowa:NNI := max(1,nclin)
big:DF := float(1,10,10)$DF
fea:MDF := new(1,n+nclin,float(1053,-11,10)$DF)$MDF
bl:MDF := mat(finiteBound(args.lb,float(1,21,10)$DF),n)
bu:MDF := mat(finiteBound(args.ub,float(1,21,10)$DF),n)
alin:EDF := splitLinear(argsFn)
p:PDF := retract(alin)@PDF
pl:List PDF := [coefficient(p,i,1)$PDF for i in v]
cvec:MDF := mat([pdf2df j for j in pl],n)
h1:MPDF := hessian(p,v)$MVCF(S,PDF,VPDF,LS)
hess:MDF := map(pdf2df,h1)$ESTOOLS2(PDF,DF)
h2:MEF := map(df2ef,hess)$ESTOOLS2(DF,EF)
x := mat(args.init,n)
istate:MI := zero(1,n+nclin)$MI
lwork:INT := 2*n*(n+2*nclin)+nrowa
qphess:Union(fn:FileName,fp:Asp20(QPHESS)):=[retract(h2)$Asp20(QPHESS)]
out:Result:=e04naf(20,1,n,nclin,n+nclin,nrowa,n,n,big,A,bl,bu,cvec,fea,
hess,true,false,true,2*n,lwork,x,istate,-1,qphess)
changeNameToObjf(obj@Symbol,out)
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