/usr/share/axiom-20170501/src/algebra/D01AMFA.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 D01AMFA d01amfAnnaType
++ 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{d01amfAnnaType} is a domain of
++ \axiomType{NumericalIntegrationCategory}
++ for the NAG routine D01AMF, a general numerical integration routine which
++ can handle infinite or semi-infinite range of the input function. The
++ function \axiomFun{measure} measures the usefulness of the routine D01AMF
++ for the given problem. The function \axiomFun{numericalIntegration}
++ performs the integration by using \axiomType{NagIntegrationPackage}.
d01amfAnnaType() : 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:NIA) ==
ext:Result := empty()$Result
Range:=rangeIsFinite(args)
pp:SDF := singularitiesOf(args)
not (empty?(pp)$SDF) =>
[0.0,"d01amf: There is a possible problem at the following point(s): "
commaSeparate(sdf2lst(pp)), ext]
[getMeasure(R,d01amf@S)$RT, "d01amf is a reasonable choice if the "
"integral is infinite or semi-infinite and d01transform cannot "
"do better than using general routines",ext]
numericalIntegration(args:NIA,hints:Result) ==
r:INT
bound:DF
ArgsFn := map(x+->convert(x)$DF,args.fn)$EF2(DF,Float)
b:Float :=getButtonValue("d01amf","functionEvaluations")$AttributeButtons
fEvals:INT := wholePart exp(1.1513*(1.0/(2.0*(1.0-b))))
iw:INT := 150*fEvals
f : Union(fn:FileName,fp:Asp1(F)) := [retract(ArgsFn)$Asp1(F)]
Range:=rangeIsFinite(args)
if (Range case upperInfinite) then
bound := getlo(args.range)
r := 1
else if (Range case lowerInfinite) then
bound := gethi(args.range)
r := -1
else
bound := 0$DF
r := 2
d01amf(bound,r,args.abserr,args.relerr,4*iw,iw,-1,f)
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