/usr/share/axiom-20170501/src/algebra/D02BBFA.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 93 94 | )abbrev domain D02BBFA d02bbfAnnaType
++ Author: Brian Dupee
++ Date Created: February 1995
++ Date Last Updated: January 1996
++ References:
++ Dupe95 Using Computer Algebra to Choose and Apply Numerical Routines
++ Dewa92 Using Computer Algebra to Select Numerical Algorithms
++ Description:
++ \axiomType{d02bbfAnnaType} is a domain of
++ \axiomType{OrdinaryDifferentialEquationsInitialValueProblemSolverCategory}
++ for the NAG routine D02BBF, a ODE routine which uses an
++ Runge-Kutta method to solve a system of differential
++ equations. The function \axiomFun{measure} measures the
++ usefulness of the routine D02BBF for the given problem. The
++ function \axiomFun{ODESolve} performs the integration by using
++ \axiomType{NagOrdinaryDifferentialEquationsPackage}.
d02bbfAnnaType() : SIG == CODE where
-- Runge Kutta
EDF ==> Expression DoubleFloat
LDF ==> List DoubleFloat
MDF ==> Matrix DoubleFloat
DF ==> DoubleFloat
F ==> Float
FI ==> Fraction Integer
EFI ==> Expression Fraction Integer
SOCDF ==> Segment OrderedCompletion DoubleFloat
VEDF ==> Vector Expression DoubleFloat
VEF ==> Vector Expression Float
EF ==> Expression Float
VDF ==> Vector DoubleFloat
VMF ==> Vector MachineFloat
MF ==> MachineFloat
ODEA ==> Record(xinit:DF,xend:DF,fn:VEDF,yinit:LDF,intvals:LDF,_
g:EDF,abserr:DF,relerr:DF)
RSS ==> Record(stiffnessFactor:F,stabilityFactor:F)
INT ==> Integer
EF2 ==> ExpressionFunctions2
SIG ==> OrdinaryDifferentialEquationsSolverCategory
CODE ==> Result add
import d02AgentsPackage, NagOrdinaryDifferentialEquationsPackage
import AttributeButtons
accuracyCF(ode:ODEA):F ==
b := getButtonValue("d02bbf","accuracy")$AttributeButtons
accuracyIntensityValue := combineFeatureCompatibility(b,accuracyIF(ode))
accuracyIntensityValue > 0.999 => 0$F
0.8*exp(-((10*accuracyIntensityValue)**3)$F/266)$F
stiffnessCF(stiffnessIntensityValue:F):F ==
b := getButtonValue("d02bbf","stiffness")$AttributeButtons
0.5*exp(-(2*combineFeatureCompatibility(b,stiffnessIntensityValue))**2)$F
stabilityCF(stabilityIntensityValue:F):F ==
b := getButtonValue("d02bbf","stability")$AttributeButtons
0.5 * cos(combineFeatureCompatibility(b,stabilityIntensityValue))$F
expenseOfEvaluationCF(ode:ODEA):F ==
b := getButtonValue("d02bbf","expense")$AttributeButtons
expenseOfEvaluationIntensityValue :=
combineFeatureCompatibility(b,expenseOfEvaluationIF(ode))
0.35+0.2*exp(-(2.0*expenseOfEvaluationIntensityValue)**3)$F
measure(R:RoutinesTable,args:ODEA) ==
m := getMeasure(R,d02bbf :: Symbol)$RoutinesTable
ssf := stiffnessAndStabilityOfODEIF args
m := combineFeatureCompatibility(m,[accuracyCF(args),
stiffnessCF(ssf.stiffnessFactor),
expenseOfEvaluationCF(args),
stabilityCF(ssf.stabilityFactor)])
[m,"Runge-Kutta Merson method"]
ODESolve(ode:ODEA) ==
i:LDF := ode.intvals
M := inc(# i)$INT
irelab := 0$INT
if positive?(a := ode.abserr) then
inc(irelab)$INT
if positive?(r := ode.relerr) then
inc(irelab)$INT
if positive?(a+r) then
tol:DF := a + r
else
tol := float(1,-4,10)$DF
asp7:Union(fn:FileName,fp:Asp7(FCN)) :=
[retract(vedf2vef(ode.fn)$ExpertSystemToolsPackage)$Asp7(FCN)]
asp8:Union(fn:FileName,fp:Asp8(OUTPUT)) :=
[coerce(ldf2vmf(i)$ExpertSystemToolsPackage)$Asp8(OUTPUT)]
d02bbf(ode.xend,M,# ode.fn,irelab,ode.xinit,matrix([ode.yinit])$MDF,
tol,-1,asp7,asp8)
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