/usr/share/axiom-20170501/src/algebra/D01ASFA.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 | )abbrev domain D01ASFA d01asfAnnaType
++ 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{d01asfAnnaType} is a domain of
++ \axiomType{NumericalIntegrationCategory}
++ for the NAG routine D01ASF, a numerical integration routine which can
++ handle weight functions of the form cos(\omega x) or sin(\omega x) on an
++ semi-infinite range. The
++ function \axiomFun{measure} measures the usefulness of the routine D01ASF
++ for the given problem. The function \axiomFun{numericalIntegration}
++ performs the integration by using \axiomType{NagIntegrationPackage}.
d01asfAnnaType() : 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, d01WeightsPackage, d01AgentsPackage, NagIntegrationPackage
measure(R:RT,args:NIA) ==
ext:Result := empty()$Result
Range := rangeIsFinite(args)
not(Range case upperInfinite) =>
[0.0,"d01asf is not a suitable routine for infinite integrals",ext]
weight: Union(Record(op:BOP,w:DF),"failed") :=
exprHasWeightCosWXorSinWX(args)
weight case "failed" =>
[0.0,"d01asf: A suitable weight has not been found", ext]
weight case Record(op:BOP,w:DF) =>
wany := coerce(weight)$AnyFunctions1(Record(op:BOP,w:DF))
ex:Record(key:S,entry:Any) := [d01asfextra@S,wany]
ext := insert!(ex,ext)$Result
ws:ST := string(name(weight.op)$BOP)$S "(" df2st(weight.w)
string(args.var)$S ")"
[getMeasure(R,d01asf@S)$RT,
"d01asf: A suitable weight has been found:- " ws, ext]
numericalIntegration(args:NIA,hints:Result) ==
i:INT
r:Any := coerce(search((d01asfextra@S),hints)$Result)@Any
rec:Record(op:BOP,w:DF) := retract(r)$AnyFunctions1(Record(op:BOP,w:DF))
Var := args.var :: EDF
o:BOP := rec.op
den:EDF := o((rec.w*Var)$EDF)
Argsfn:EDF := args.fn/den
if (name(o) = cos@S)@Boolean then i := 1
else i := 2
b:Float:=getButtonValue("d01asf","functionEvaluations")$AttributeButtons
fEvals:INT := wholePart exp(1.1513*(1.0/(2.0*(1.0-b))))
iw:INT := 75*fEvals
ArgsFn := map(x +-> convert(x)$DF,Argsfn)$EF2(DF,Float)
f : Union(fn:FileName,fp:Asp1(G)) := [retract(ArgsFn)$Asp1(G)]
err :=
positive?(args.abserr) => args.abserr
args.relerr
d01asf(getlo(args.range),rec.w,i,err,50,4*iw,2*iw,-1,f)
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