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|
newPackage(
"JuliaInterface",
Version => "0.1",
Date => "July 10, 2018",
Authors => {
{Name => "Tim Duff",
Email => "tduff3@gatech.edu",
HomePage => "http://people.math.gatech.edu/~tduff3/"}
},
Headline => "Interfacing Macaulay2 with Julia Homotopy Continuation",
PackageImports => {},
PackageExports => {"NumericalAlgebraicGeometry","MonodromySolver"},
DebuggingMode => true
)
export{"JuliaProcess", "solveJulia", "restartJulia","importJulia","writeJuliaFile",
-- exported options below
"IncludeTemplate","ImportList","WithImports","OnlyReal","OnlyFinite","TemplateText"
}
----------------------------------------
---GLOBAL VARIABLES / INTERFACE SETUP
----------------------------------------
importJulia = (importList,f) -> f<<concatenate apply(importList,pkg->pkg | "\n")
juliaBinary="/home/tim/julia-d55cadc350/bin/julia"
JuliaProcess=openInOut("!" |juliaBinary)
noProcessError="JuliaProcess not currently open"
importJulia({"using HomotopyContinuation","import DynamicPolynomials: PolyVar"},JuliaProcess)
---------------------
--- PACKAGE IMPORTS
---------------------
--------------
---UNEXPORTED-
--------------
numberRegex="([0-9]|| |-|\\.|e|i|m|\\+|,)*" -- potentially useful
parsePolynomial = p -> replace("ii","im",replace("p[0-9]+","0",toExternalString p))
-- the implementation here may need to change as the output of HomotopyContinuation evolves in future versions
parseSolutions = method(Options=>{OnlyReal=>false})
parseSolutions String := o -> out -> (
outLines:=select("\\*.*",out);
M:=new MutableList from {};
stride:=12;
numSols:=sub((length outLines)/stride,ZZ);
for i from 0 to numSols-1 do (
s:=first select("\\[([0-9]|| |-|\\.|e|i|m|\\+|,)*\\]",outLines#(1+i*stride));
M#i=point{apply(separate(",",replace("\\[|\\]","",replace("im","*ii",s))),x->value x)};
if match("nonsingular",outLines#(2+i*stride)) then M#i.SolutionStatus = Regular else M#i.SolutionStatus = Singular;
);
toList M
)
--todo: write exported wrapper for first two signatures
writeSys = method(Options=>{IncludeTemplate=>false,WithImports=>false,
ImportList=>{"using HomotopyContinuation",
"import DynamicPolynomials: PolyVar"},
TemplateText=>false})
writeSys (PolySystem, File) := o -> (P,f) -> (
R:=ring P;
varString:=apply(gens R,g->(toString g));
varCommas:=(P.NumberOfVariables-1):", ";
eqnCommas:=(P.NumberOfPolys-1):", ";
if o.WithImports then importJulia(o.ImportList,f);
if o.TemplateText then f << "# We declare the variables of our polynomial system\n";
f << concatenate(mingle(varString,varCommas))| " = " | "[PolyVar{true}(i) for i in [" | concatenate mingle(apply(varString,g-> "\"" | g | "\""),varCommas)|"]];\n";
if o.TemplateText then f << "# We define the polynomial system in which solutions we are interested.\n";
f <<"F = [" | concatenate mingle(
apply(equations P,e->parsePolynomial e),eqnCommas)| "];\n";
if o.TemplateText then (
f<<"# Now we can solve the system\n";
);
)
writeSys (PolySystem, String) :=o -> (P,filename) -> (
f := openOut filename;
writeSys(P,f);
close f;
)
writeSys PolySystem := o -> P -> (
if not isOpen JuliaProcess then error("JuliaProcess not open");
writeSys(P,JuliaProcess)
)
writeJuliaFile = method(Options=>{})
writeJuliaFile (PolySystem,String) := o -> (P,filename) -> (
f := openOut(filename|".jl");
f << read openIn "./jlHeader.jl";
writeSys(P,f,TemplateText=>true);
f << "result = solve(F)\n";
f << read openIn"./jlTail.jl";
close f;
)
-------------------------------------
--- EXPORTED FUNCTIONS AND METHODS---
-------------------------------------
restartJulia = () -> (
if (isOpen JuliaProcess) then close JuliaProcess;
JuliaProcess=openInOut("!" |juliaBinary);
--needsPackage("JuliaInterface",Reload=>true)
)
TEST ///
JuliaProcess
close JuliaProcess
assert(not isOpen JuliaProcess)
restartJulia()
assert(isOpen JuliaProcess)
///
-- todo: replace arbitrary variable name "f" for julia system
-- todo: remove bottom two lines from print
-- todo: parse other solutions info
-- todo: finite solutions only
-- todo: check all variables are used
solveJulia = method(Options=>{})
solveJulia PolySystem := o -> P -> (
if not isOpen JuliaProcess then error(noProcessError);
-- print "Wait for system to be solved:\n";
writeSys P;
JuliaProcess<<flush;
x:=read JuliaProcess;
JuliaProcess<<"result=solve(F);\n";
-- JuliaProcess<<"x=[s.solution for s in sols];\n";
JuliaProcess<<"show(IOContext(STDOUT, :compact=>false),[s.solution for s in result])\n";
finished:="done!!!x";
JuliaProcess<<"print(\"" | finished |"\")\n";
out:="";
cur:="";
while not match(finished,cur) do (
JuliaProcess<<flush;
cur = read JuliaProcess;
out = out | cur;
);
endIndex:=regex("Array\\{Complex",out);
parseSolutions substring(out,0,first first endIndex)
)
------------------------------------------
------------------------------------------
-- Documentation
------------------------------------------
------------------------------------------
beginDocumentation()
doc ///
Key
solveJulia
(solveJulia, PolySystem)
Headline
interface to "solve" function
Usage
sols = solve P
sols = solve L
Inputs
P:PolySystem
L:List
containing elements from a common @TO Ring @
Outputs
sols:List
each element of class @TO AbstractPoint @
Description
Text
This is the basic interface to the @HREF("https://www.juliahomotopycontinuation.org/HomotopyContinuation.jl/latest/solving.html","\"solve function")@.
Example
R=CC[x,y]
importJulia({"using HomotopyContinuation","import DynamicPolynomials: PolyVar"},JuliaProcess)
f= x^2+y
g=y^2-pi*ii
sols=solveJulia polySystem {f,g}
///
end
uninstallPackage packageName
close JuliaProcess
restart
packageName = "JuliaInterface"
path=append(path,currentDirectory())
installPackage("JuliaInterface",MakeDocumentation=>false)
R=CC[x,y]
f= x^2+y
g=y^2-pi*ii
P= polySystem {f,g}
writeJuliaFile(P,"test")
sols=solveJulia P
peek first sols
writeSys(P,"test.jl",WithImports=>true)--option not working?
needs "./ExampleSystems/jointsR6.m2"
Q=polySystem jointsR6(CC_53)
sols=solveJulia Q;
ourSols = solveSystem Q
apply(
sortSolutions ourSols,
sortSolutions sols,
(a,b) -> areEqual(a,b)
)
#sols--too many?
#ourSols
|
