/usr/share/axiom-20170501/src/algebra/D01ALFA.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 | )abbrev domain D01ALFA d01alfAnnaType
++ 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{d01alfAnnaType} is a domain of
++ \axiomType{NumericalIntegrationCategory}
++ for the NAG routine D01ALF, a general numerical integration routine which
++ can handle a list of singularities. The
++ function \axiomFun{measure} measures the usefulness of the routine D01ALF
++ for the given problem. The function \axiomFun{numericalIntegration}
++ performs the integration by using \axiomType{NagIntegrationPackage}.
d01alfAnnaType() : 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()$Result
streamOfZeros:SDF := singularitiesOf(args)
listOfZeros:LST := removeDuplicates!(sdf2lst(streamOfZeros))
numberOfZeros:INT := # listOfZeros
(numberOfZeros > 15)@Boolean =>
[0.0,"d01alf: The list of singularities is too long", ext]
positive?(numberOfZeros) =>
l:LDF := entries(complete(streamOfZeros)$SDF)$SDF
lany:Any := coerce(l)$AnyFunctions1(LDF)
ex:Record(key:S,entry:Any) := [d01alfextra@S,lany]
ext := insert!(ex,ext)$Result
st:ST := "Recommended is d01alf with the singularities "
commaSeparate(listOfZeros)
m :=
(numberOfZeros = 1) => 0.4
getMeasure(R,d01alf@S)$RT
[m, st, ext]
[0.0, "d01alf: A list of suitable singularities has not been found", ext]
numericalIntegration(args:NIA,hints:Result) ==
la:Any := coerce(search((d01alfextra@S),hints)$Result)@Any
listOfZeros:LDF := retract(la)$AnyFunctions1(LDF)
l:= removeDuplicates(listOfZeros)$LDF
n:Integer := (#(l))$List(DF)
M:Matrix DF := matrix([l])$(Matrix DF)
b:Float :=getButtonValue("d01alf","functionEvaluations")$AttributeButtons
fEvals:INT := wholePart exp(1.1513*(1.0/(2.0*(1.0-b))))
iw:INT := 75*fEvals
ArgsFn := map(x+->convert(x)$DF,args.fn)$EF2(DF,Float)
f : Union(fn:FileName,fp:Asp1(F)) := [retract(ArgsFn)$Asp1(F)]
d01alf(getlo(args.range),gethi(args.range),n,M,_
args.abserr,args.relerr,2*n*iw,n*iw,-1,f)
|