/usr/share/axiom-20170501/src/algebra/ODEPACK.spad is in axiom-source 20170501-3.
This file is owned by root:root, with mode 0o644.
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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 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 | )abbrev package ODEPACK AnnaOrdinaryDifferentialEquationPackage
++ Author: Brian Dupee
++ Date Created: February 1995
++ Date Last Updated: December 1997
++ Description:
++ \axiomType{AnnaOrdinaryDifferentialEquationPackage} is a \axiom{package}
++ of functions for the \axiom{category}
++ \axiomType{OrdinaryDifferentialEquationsSolverCategory}
++ with \axiom{measure}, and \axiom{solve}.
AnnaOrdinaryDifferentialEquationPackage() : SIG == CODE where
EDF ==> Expression DoubleFloat
LDF ==> List DoubleFloat
MDF ==> Matrix DoubleFloat
DF ==> DoubleFloat
FI ==> Fraction Integer
EFI ==> Expression Fraction Integer
SOCDF ==> Segment OrderedCompletion DoubleFloat
VEDF ==> Vector Expression DoubleFloat
VEF ==> Vector Expression Float
EF ==> Expression Float
LF ==> List Float
F ==> Float
VDF ==> Vector DoubleFloat
VMF ==> Vector MachineFloat
MF ==> MachineFloat
LS ==> List Symbol
ST ==> String
LST ==> List String
INT ==> Integer
RT ==> RoutinesTable
ODEA ==> Record(xinit:DF,xend:DF,fn:VEDF,yinit:LDF,intvals:LDF,_
g:EDF,abserr:DF,relerr:DF)
IFL ==> List(Record(ifail:Integer,instruction:String))
Entry ==> Record(chapter:String, type:String, domainName: String,
defaultMin:F, measure:F, failList:IFL, explList:LST)
Measure ==> Record(measure:F,name:String, explanations:List String)
SIG ==> with
solve : (NumericalODEProblem) -> Result
++ solve(odeProblem) is a top level ANNA function to solve numerically a
++ system of ordinary differential equations equations for the
++ derivatives y[1]'..y[n]' defined in terms of x,y[1]..y[n], together
++ with starting values for x and y[1]..y[n] (called the initial
++ conditions), a final value of x, an accuracy requirement and any
++ intermediate points at which the result is required.
++
++ It iterates over the \axiom{domains} of
++ \axiomType{OrdinaryDifferentialEquationsSolverCategory}
++ to get the name and other
++ relevant information of the the (domain of the) numerical
++ routine likely to be the most appropriate,
++ have the best \axiom{measure}.
++
++ The method used to perform the numerical
++ process will be one of the routines contained in the NAG numerical
++ Library. The function predicts the likely most effective routine
++ by checking various attributes of the system of ODE's and calculating
++ a measure of compatibility of each routine to these attributes.
++
++ It then calls the resulting `best' routine.
solve : (NumericalODEProblem,RT) -> Result
++ solve(odeProblem,R) is a top level ANNA function to solve numerically a
++ system of ordinary differential equations equations for the
++ derivatives y[1]'..y[n]' defined in terms of x,y[1]..y[n], together
++ with starting values for x and y[1]..y[n] (called the initial
++ conditions), a final value of x, an accuracy requirement and any
++ intermediate points at which the result is required.
++
++ It iterates over the \axiom{domains} of
++ \axiomType{OrdinaryDifferentialEquationsSolverCategory} contained in
++ the table of routines \axiom{R} to get the name and other
++ relevant information of the the (domain of the) numerical
++ routine likely to be the most appropriate,
++ have the best \axiom{measure}.
++
++ The method used to perform the numerical
++ process will be one of the routines contained in the NAG numerical
++ Library. The function predicts the likely most effective routine
++ by checking various attributes of the system of ODE's and calculating
++ a measure of compatibility of each routine to these attributes.
++
++ It then calls the resulting `best' routine.
solve : (VEF,F,F,LF) -> Result
++ solve(f,xStart,xEnd,yInitial) is a top level ANNA function to solve
++ numerically a system of ordinary differential equations equations
++ for the derivatives y[1]'..y[n]' defined in terms of x,y[1]..y[n],
++ together with a starting value for x and y[1]..y[n] (called the initial
++ conditions) and a final value of x. A default value
++ is used for the accuracy requirement.
++
++ It iterates over the \axiom{domains} of
++ \axiomType{OrdinaryDifferentialEquationsSolverCategory} contained in
++ the table of routines \axiom{R} to get the name and other
++ relevant information of the the (domain of the) numerical
++ routine likely to be the most appropriate,
++ have the best \axiom{measure}.
++
++ The method used to perform the numerical
++ process will be one of the routines contained in the NAG numerical
++ Library. The function predicts the likely most effective routine
++ by checking various attributes of the system of ODE's and calculating
++ a measure of compatibility of each routine to these attributes.
++
++ It then calls the resulting `best' routine.
solve : (VEF,F,F,LF,F) -> Result
++ solve(f,xStart,xEnd,yInitial,tol) is a top level ANNA function to solve
++ numerically a system of ordinary differential equations, \axiom{f},
++ equations for the derivatives y[1]'..y[n]' defined in terms
++ of x,y[1]..y[n] from \axiom{xStart} to \axiom{xEnd} with the initial
++ values for y[1]..y[n] (\axiom{yInitial}) to a tolerance \axiom{tol}.
++
++ It iterates over the \axiom{domains} of
++ \axiomType{OrdinaryDifferentialEquationsSolverCategory} contained in
++ the table of routines \axiom{R} to get the name and other
++ relevant information of the the (domain of the) numerical
++ routine likely to be the most appropriate,
++ have the best \axiom{measure}.
++
++ The method used to perform the numerical
++ process will be one of the routines contained in the NAG numerical
++ Library. The function predicts the likely most effective routine
++ by checking various attributes of the system of ODE's and calculating
++ a measure of compatibility of each routine to these attributes.
++
++ It then calls the resulting `best' routine.
solve : (VEF,F,F,LF,EF,F) -> Result
++ solve(f,xStart,xEnd,yInitial,G,tol) is a top level ANNA function to
++ solve numerically a system of ordinary differential equations,
++ \axiom{f}, equations for the derivatives y[1]'..y[n]' defined in
++ terms of x,y[1]..y[n] from \axiom{xStart} to \axiom{xEnd} with the
++ initial values for y[1]..y[n] (\axiom{yInitial}) to a tolerance
++ \axiom{tol}. The calculation will stop if the function
++ G(x,y[1],..,y[n]) evaluates to zero before x = xEnd.
++
++ It iterates over the \axiom{domains} of
++ \axiomType{OrdinaryDifferentialEquationsSolverCategory} contained in
++ the table of routines \axiom{R} to get the name and other
++ relevant information of the the (domain of the) numerical
++ routine likely to be the most appropriate,
++ have the best \axiom{measure}.
++
++ The method used to perform the numerical process will be one of the
++ routines contained in the NAG numerical Library. The function
++ predicts the likely most effective routine by checking various
++ attributes of the system of ODE's and calculating a measure of
++ compatibility of each routine to these attributes.
++
++ It then calls the resulting `best' routine.
solve : (VEF,F,F,LF,LF,F) -> Result
++ solve(f,xStart,xEnd,yInitial,intVals,tol) is a top level ANNA function
++ to solve numerically a system of ordinary differential equations,
++ \axiom{f}, equations for the derivatives y[1]'..y[n]' defined in
++ terms of x,y[1]..y[n] from \axiom{xStart} to \axiom{xEnd} with the
++ initial values for y[1]..y[n] (\axiom{yInitial}) to a tolerance
++ \axiom{tol}. The values of y[1]..y[n] will be output for the values
++ of x in \axiom{intVals}.
++
++ It iterates over the \axiom{domains} of
++ \axiomType{OrdinaryDifferentialEquationsSolverCategory} contained in
++ the table of routines \axiom{R} to get the name and other
++ relevant information of the the (domain of the) numerical
++ routine likely to be the most appropriate,
++ have the best \axiom{measure}.
++
++ The method used to perform the numerical
++ process will be one of the routines contained in the NAG numerical
++ Library. The function predicts the likely most effective routine
++ by checking various attributes of the system of ODE's and calculating
++ a measure of compatibility of each routine to these attributes.
++
++ It then calls the resulting `best' routine.
solve : (VEF,F,F,LF,EF,LF,F) -> Result
++ solve(f,xStart,xEnd,yInitial,G,intVals,tol) is a top level ANNA
++ function to solve numerically a system of ordinary differential
++ equations, \axiom{f}, equations for the derivatives y[1]'..y[n]'
++ defined in terms of x,y[1]..y[n] from \axiom{xStart} to \axiom{xEnd}
++ with the initial values for y[1]..y[n] (\axiom{yInitial}) to a
++ tolerance \axiom{tol}. The values of y[1]..y[n] will be output for
++ the values of x in \axiom{intVals}. The calculation will stop if the
++ function G(x,y[1],..,y[n]) evaluates to zero before x = xEnd.
++
++ It iterates over the \axiom{domains} of
++ \axiomType{OrdinaryDifferentialEquationsSolverCategory} contained in
++ the table of routines \axiom{R} to get the name and other
++ relevant information of the the (domain of the) numerical
++ routine likely to be the most appropriate,
++ have the best \axiom{measure}.
++
++ The method used to perform the numerical
++ process will be one of the routines contained in the NAG numerical
++ Library. The function predicts the likely most effective routine
++ by checking various attributes of the system of ODE's and calculating
++ a measure of compatibility of each routine to these attributes.
++
++ It then calls the resulting `best' routine.
solve : (VEF,F,F,LF,EF,LF,F,F) -> Result
++ solve(f,xStart,xEnd,yInitial,G,intVals,epsabs,epsrel) is a top level
++ ANNA function to solve numerically a system of ordinary differential
++ equations, \axiom{f},
++ equations for the derivatives y[1]'..y[n]' defined in terms
++ of x,y[1]..y[n] from \axiom{xStart} to \axiom{xEnd} with the initial
++ values for y[1]..y[n] (\axiom{yInitial}) to an absolute error
++ requirement \axiom{epsabs} and relative error \axiom{epsrel}.
++ The values of y[1]..y[n] will be output for the values of x in
++ \axiom{intVals}. The calculation will stop if the function
++ G(x,y[1],..,y[n]) evaluates to zero before x = xEnd.
++
++ It iterates over the \axiom{domains} of
++ \axiomType{OrdinaryDifferentialEquationsSolverCategory} contained in
++ the table of routines \axiom{R} to get the name and other
++ relevant information of the the (domain of the) numerical
++ routine likely to be the most appropriate,
++ have the best \axiom{measure}.
++
++ The method used to perform the numerical
++ process will be one of the routines contained in the NAG numerical
++ Library. The function predicts the likely most effective routine
++ by checking various attributes of the system of ODE's and calculating
++ a measure of compatibility of each routine to these attributes.
++
++ It then calls the resulting `best' routine.
measure : (NumericalODEProblem) -> Measure
++ measure(prob) is a top level ANNA function for identifying the most
++ appropriate numerical routine from those in the routines table
++ provided for solving the numerical ODE
++ problem defined by \axiom{prob}.
++
++ It calls each \axiom{domain} of \axiom{category}
++ \axiomType{OrdinaryDifferentialEquationsSolverCategory} in turn to
++ calculate all measures and returns the best the name of
++ the most appropriate domain and any other relevant information.
++ It predicts the likely most effective NAG numerical
++ Library routine to solve the input set of ODEs
++ by checking various attributes of the system of ODEs and calculating
++ a measure of compatibility of each routine to these attributes.
measure : (NumericalODEProblem,RT) -> Measure
++ measure(prob,R) is a top level ANNA function for identifying the most
++ appropriate numerical routine from those in the routines table
++ provided for solving the numerical ODE
++ problem defined by \axiom{prob}.
++
++ It calls each \axiom{domain} listed in \axiom{R} of \axiom{category}
++ \axiomType{OrdinaryDifferentialEquationsSolverCategory} in turn to
++ calculate all measures and returns the best the name of
++ the most appropriate domain and any other relevant information.
++ It predicts the likely most effective NAG numerical
++ Library routine to solve the input set of ODEs
++ by checking various attributes of the system of ODEs and calculating
++ a measure of compatibility of each routine to these attributes.
CODE ==> add
import ODEA,NumericalODEProblem
f2df:F -> DF
ef2edf:EF -> EDF
preAnalysis:(ODEA,RT) -> RT
zeroMeasure:Measure -> Result
measureSpecific:(ST,RT,ODEA) -> Record(measure:F,explanations:ST)
solveSpecific:(ODEA,ST) -> Result
changeName:(Result,ST) -> Result
recoverAfterFail:(ODEA,RT,Measure,Integer,Result) -> _
Record(a:Result,b:Measure)
f2df(f:F):DF == (convert(f)@DF)$F
ef2edf(f:EF):EDF == map(f2df,f)$ExpressionFunctions2(F,DF)
preAnalysis(args:ODEA,t:RT):RT ==
rt := selectODEIVPRoutines(t)$RT
if positive?(# variables(args.g)) then
changeMeasure(rt,d02bbf@Symbol,getMeasure(rt,d02bbf@Symbol)*0.8)
if positive?(# args.intvals) then
changeMeasure(rt,d02bhf@Symbol,getMeasure(rt,d02bhf@Symbol)*0.8)
rt
zeroMeasure(m:Measure):Result ==
a := coerce(0$F)$AnyFunctions1(F)
text := coerce("Zero Measure")$AnyFunctions1(ST)
r := construct([[result@Symbol,a],[method@Symbol,text]])$Result
concat(measure2Result m,r)$ExpertSystemToolsPackage
measureSpecific(name:ST,R:RT,ode:ODEA):Record(measure:F,explanations:ST) ==
name = "d02bbfAnnaType" => measure(R,ode)$d02bbfAnnaType
name = "d02bhfAnnaType" => measure(R,ode)$d02bhfAnnaType
name = "d02cjfAnnaType" => measure(R,ode)$d02cjfAnnaType
name = "d02ejfAnnaType" => measure(R,ode)$d02ejfAnnaType
error("measureSpecific","invalid type name: " name)$ErrorFunctions
measure(Ode:NumericalODEProblem,R:RT):Measure ==
ode:ODEA := retract(Ode)$NumericalODEProblem
sofar := 0$F
best := "none" :: ST
routs := copy R
routs := preAnalysis(ode,routs)
empty?(routs)$RT =>
error("measure", "no routines found")$ErrorFunctions
rout := inspect(routs)$RT
e := retract(rout.entry)$AnyFunctions1(Entry)
meth := empty()$LST
for i in 1..# routs repeat
rout := extract!(routs)$RT
e := retract(rout.entry)$AnyFunctions1(Entry)
n := e.domainName
if e.defaultMin > sofar then
m := measureSpecific(n,R,ode)
if m.measure > sofar then
sofar := m.measure
best := n
str:LST := [string(rout.key)$Symbol "measure: "
outputMeasure(m.measure)$ExpertSystemToolsPackage " - "
m.explanations]
else
str := [string(rout.key)$Symbol " is no better than other routines"]
meth := append(meth,str)$LST
[sofar,best,meth]
measure(ode:NumericalODEProblem):Measure == measure(ode,routines()$RT)
solveSpecific(ode:ODEA,n:ST):Result ==
n = "d02bbfAnnaType" => ODESolve(ode)$d02bbfAnnaType
n = "d02bhfAnnaType" => ODESolve(ode)$d02bhfAnnaType
n = "d02cjfAnnaType" => ODESolve(ode)$d02cjfAnnaType
n = "d02ejfAnnaType" => ODESolve(ode)$d02ejfAnnaType
error("solveSpecific","invalid type name: " n)$ErrorFunctions
changeName(ans:Result,name:ST):Result ==
sy:Symbol := coerce(name "Answer")$Symbol
anyAns:Any := coerce(ans)$AnyFunctions1(Result)
construct([[sy,anyAns]])$Result
recoverAfterFail(ode:ODEA,routs:RT,m:Measure,iint:Integer,r:Result):
Record(a:Result,b:Measure) ==
while positive?(iint) repeat
routineName := m.name
s := recoverAfterFail(routs,routineName(1..6),iint)$RT
s case "failed" => iint := 0
if s = "increase tolerance" then
ode.relerr := ode.relerr*(10.0::DF)
ode.abserr := ode.abserr*(10.0::DF)
if s = "decrease tolerance" then
ode.relerr := ode.relerr/(10.0::DF)
ode.abserr := ode.abserr/(10.0::DF)
(s = "no action")@Boolean => iint := 0
fl := coerce(s)$AnyFunctions1(ST)
flrec:Record(key:Symbol,entry:Any):=[failure@Symbol,fl]
m2 := measure(ode::NumericalODEProblem,routs)
zero?(m2.measure) => iint := 0
r2:Result := solveSpecific(ode,m2.name)
m := m2
insert!(flrec,r2)$Result
r := concat(r2,changeName(r,routineName))$ExpertSystemToolsPackage
iany := search(ifail@Symbol,r2)$Result
iany case "failed" => iint := 0
iint := retract(iany)$AnyFunctions1(Integer)
[r,m]
solve(Ode:NumericalODEProblem,t:RT):Result ==
ode:ODEA := retract(Ode)$NumericalODEProblem
routs := copy(t)$RT
m := measure(Ode,routs)
zero?(m.measure) => zeroMeasure m
r := solveSpecific(ode,n := m.name)
iany := search(ifail@Symbol,r)$Result
iint := 0$Integer
if (iany case Any) then
iint := retract(iany)$AnyFunctions1(Integer)
if positive?(iint) then
tu:Record(a:Result,b:Measure) := recoverAfterFail(ode,routs,m,iint,r)
r := tu.a
m := tu.b
r := concat(measure2Result m,r)$ExpertSystemToolsPackage
expl := getExplanations(routs,n(1..6))$RoutinesTable
expla := coerce(expl)$AnyFunctions1(LST)
explaa:Record(key:Symbol,entry:Any) := ["explanations"::Symbol,expla]
r := concat(construct([explaa]),r)
iflist := showIntensityFunctions(ode)$ODEIntensityFunctionsTable
iflist case "failed" => r
concat(iflist2Result iflist, r)$ExpertSystemToolsPackage
solve(ode:NumericalODEProblem):Result == solve(ode,routines()$RT)
solve(f:VEF,xStart:F,xEnd:F,yInitial:LF,G:EF,intVals:LF,epsabs:F,epsrel:F)_
:Result ==
d:ODEA:= [f2df xStart,f2df xEnd,vector([ef2edf e for e in members f])$VEDF,
[f2df i for i in yInitial], [f2df j for j in intVals],
ef2edf G,f2df epsabs,f2df epsrel]
solve(d::NumericalODEProblem,routines()$RT)
solve(f:VEF,xStart:F,xEnd:F,yInitial:LF,G:EF,intVals:LF,tol:F):Result ==
solve(f,xStart,xEnd,yInitial,G,intVals,tol,tol)
solve(f:VEF,xStart:F,xEnd:F,yInitial:LF,intVals:LF,tol:F):Result ==
solve(f,xStart,xEnd,yInitial,1$EF,intVals,tol)
solve(f:VEF,xStart:F,xEnd:F,y:LF,G:EF,tol:F):Result ==
solve(f,xStart,xEnd,y,G,empty()$LF,tol)
solve(f:VEF,xStart:F,xEnd:F,yInitial:LF,tol:F):Result ==
solve(f,xStart,xEnd,yInitial,1$EF,empty()$LF,tol)
solve(f:VEF,xStart:F,xEnd:F,yInitial:LF):Result ==
solve(f,xStart,xEnd,yInitial,1.0e-4)
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