/usr/share/axiom-20170501/src/algebra/D01GBFA.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 | )abbrev domain D01GBFA d01gbfAnnaType
++ Author: Brian Dupee
++ Date Created: March 1994
++ Date Last Updated: December 1997
++ References:
++ Dupe95 Using Computer Algebra to Choose and Apply Numerical Routines
++ Dewa92 Using Computer Algebra to Select Numerical Algorithms
++ Description:
++ \axiomType{d01gbfAnnaType} is a domain of
++ \axiomType{NumericalIntegrationCategory}
++ for the NAG routine D01GBF, a numerical integration routine which can
++ handle multi-dimensional quadrature over a finite region. The
++ function \axiomFun{measure} measures the usefulness of the routine D01GBF
++ for the given problem. The function \axiomFun{numericalIntegration}
++ performs the integration by using \axiomType{NagIntegrationPackage}.
d01gbfAnnaType() : SIG == CODE where
EF2 ==> ExpressionFunctions2
EDF ==> Expression DoubleFloat
LDF ==> List DoubleFloat
SDF ==> Stream DoubleFloat
DF ==> DoubleFloat
FI ==> Fraction Integer
EFI ==> Expression Fraction Integer
SOCDF ==> Segment OrderedCompletion DoubleFloat
NIA ==> Record(var:Symbol,fn:EDF,range:SOCDF,abserr:DF,relerr:DF)
MDNIA ==> Record(fn:EDF,range:List SOCDF,abserr:DF,relerr:DF)
INT ==> Integer
BOP ==> BasicOperator
S ==> Symbol
ST ==> String
LST ==> List String
RT ==> RoutinesTable
SIG ==> NumericalIntegrationCategory
CODE ==> Result add
Rep:=Result
import Rep, d01AgentsPackage, NagIntegrationPackage
measure(R:RT,args:MDNIA) ==
ext:Result := empty()$Result
(rel := args.relerr) < 0.01 :: DF =>
[0.1, "d01gbf: The relative error requirement is too small",ext]
segs := args.range
vars := variables(args.fn)$EDF
for i in 1..# vars repeat
nia:NIA := [vars.i,args.fn,segs.i,args.abserr,rel]
not rangeIsFinite(nia) case finite => return
[0.0,"d01gbf is not a suitable routine for infinite integrals",ext]
[getMeasure(R,d01gbf@S)$RT, "Recommended is d01gbf", ext]
numericalIntegration(args:MDNIA,hints:Result) ==
import Integer
segs := args.range
dim:INT := # segs
low:Matrix DF := matrix([[getlo(segs.i) for i in 1..dim]])$(Matrix DF)
high:Matrix DF := matrix([[gethi(segs.i) for i in 1..dim]])$(Matrix DF)
b:Float:=getButtonValue("d01gbf","functionEvaluations")$AttributeButtons
a:Float:= exp(1.1513*(1.0/(2.0*(1.0-b))))
maxcls:INT := 1500*(dim+1)*(fEvals:INT := wholePart(a))
mincls:INT := 300*fEvals
c:Float := nthRoot((maxcls::Float)/4.0,dim)$Float
lenwrk:INT := 3*dim*(d:INT := wholePart(c))+10*dim
wrkstr:Matrix DF := matrix([[0$DF for i in 1..lenwrk]])$(Matrix DF)
ArgsFn := map(x+->convert(x)$DF,args.fn)$EF2(DF,Float)
f : Union(fn:FileName,fp:Asp4(FUNCTN)) := [retract(ArgsFn)$Asp4(FUNCTN)]
out:Result := _
d01gbf(dim,low,high,maxcls,args.relerr,lenwrk,mincls,wrkstr,-1,f)
changeName(finest@Symbol,result@Symbol,out)
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