/*
* Redberry: symbolic tensor computations.
*
* Copyright (c) 2010-2013:
* Stanislav Poslavsky <stvlpos@mail.ru>
* Bolotin Dmitriy <bolotin.dmitriy@gmail.com>
*
* This file is part of Redberry.
*
* Redberry is free software: you can redistribute it and/or modify
* it under the terms of the GNU General Public License as published by
* the Free Software Foundation, either version 3 of the License, or
* (at your option) any later version.
*
* Redberry is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
* GNU General Public License for more details.
*
* You should have received a copy of the GNU General Public License
* along with Redberry. If not, see <http://www.gnu.org/licenses/>.
*/
package cc.redberry.core.solver;
import cc.redberry.core.context.CC;
import cc.redberry.core.context.OutputFormat;
import cc.redberry.core.number.Complex;
import cc.redberry.core.tensor.Expression;
import cc.redberry.core.tensor.Product;
import cc.redberry.core.tensor.Tensor;
import cc.redberry.core.tensor.Tensors;
import cc.redberry.core.tensor.iterator.FromChildToParentIterator;
import cc.redberry.core.transformations.Transformation;
import cc.redberry.core.transformations.TransformationCollection;
import cc.redberry.core.transformations.substitutions.SubstitutionTransformation;
import cc.redberry.core.utils.THashMap;
import java.io.*;
import java.util.ArrayList;
import java.util.List;
import java.util.Map;
/**
* Tools for solving a symbolic system with external systems (Maple or Mathematica).
*
* @author Dmitry Bolotin
* @author Stanislav Poslavsky
* @since 1.1.5
*/
public class ExternalSolver {
/**
* Solves a system of symbolic equations using Maplesoft Maple installation.
*
* @param reducedSystem a system of symbolic equations
* @param keepFreeParameters if {@code true} then each solutions family will be in the most general form, otherwise
* some particular solution will be taken for each family of solutions
* @param mapleBinDir path to Maple bin directory
* @param path path to temporary directory
* @return solution of {@code reducedSystem}
* @throws IOException
* @throws InterruptedException
*/
public static Expression[][] solveSystemWithMaple(ReducedSystem reducedSystem,
boolean keepFreeParameters,
String mapleBinDir,
String path)
throws IOException, InterruptedException {
return solveSystemWithExternalProgram(MapleScriptCreator.INSTANCE, reducedSystem, keepFreeParameters, mapleBinDir, path);
}
/**
* Solves a system of symbolic equations using Wolfram Mathematica installation.
*
* @param reducedSystem a system of symbolic equations
* @param keepFreeParameters if {@code true} then each solutions family will be in the most general form, otherwise
* some particular solution will be taken for each family of solutions
* @param mathematicaBinDir path to directory with Mathematica executables
* @param path path to temporary directory
* @return solution of {@code reducedSystem}
* @throws IOException
* @throws InterruptedException
*/
public static Expression[][] solveSystemWithMathematica(ReducedSystem reducedSystem,
boolean keepFreeParameters,
String mathematicaBinDir,
String path)
throws IOException, InterruptedException {
return solveSystemWithExternalProgram(MathematicaScriptCreator.INSTANCE, reducedSystem, keepFreeParameters, mathematicaBinDir, path);
}
/**
* Solves a system of symbolic equations using external program.
*
* @param scriptCreator external engine
* @param reducedSystem a system of symbolic equations
* @param keepFreeParameters if {@code true} then each solutions family will be in the most general form, otherwise
* some particular solution will be taken for each family of solutions
* @param path path to temporary directory
* @return solution of {@code reducedSystem}
* @throws IOException
* @throws InterruptedException
*/
public static Expression[][] solveSystemWithExternalProgram(ExternalScriptCreator scriptCreator,
ReducedSystem reducedSystem,
boolean keepFreeParameters,
String programBinDir,
String path)
throws IOException, InterruptedException {
//create the general form of the inverse and system of linear equations
final Expression[] equations = reducedSystem.equations.clone();
/*in order to process equations with Maple we must to replace all tensors
with indices (they are found only in scalar combinations) with some symbols*/
//scalar tensor <-> symbol
THashMap<Tensor, Tensor> tensorSubstitutions = new THashMap<>();
//all symbols will have names scalar1,scalar2, etc.
//processing equations
int i;
for (i = 0; i < equations.length; ++i) {
Expression eq = equations[i];
//iterating over the whole equation
FromChildToParentIterator iterator = new FromChildToParentIterator(eq);
Tensor t;
while ((t = iterator.next()) != null) {
if (!(t instanceof Product) || t.getIndices().size() == 0)
continue;
//scalars content
Tensor[] scalars = ((Product) t).getContent().getScalars();
for (Tensor scalar : scalars) {
if (!tensorSubstitutions.containsKey(scalar)) {
//map does not contains rule for current scalar (e.g. k_{i}*k^{i})
//adding new rule for the scalar, e.g. k_{i}*k^{i} = scalar2
tensorSubstitutions.put(scalar, CC.generateNewSymbol());
}
}
}
}
final Expression[] scalarSubs = new Expression[tensorSubstitutions.size()];
i = -1;
for (Map.Entry<Tensor, Tensor> entry : tensorSubstitutions.entrySet())
scalarSubs[++i] = Tensors.expression(entry.getKey(), entry.getValue());
SubstitutionTransformation fullSub = new SubstitutionTransformation(scalarSubs, true);
for (i = 0; i < equations.length; ++i)
equations[i] = (Expression) fullSub.transform(equations[i]);
/*if (scalarSubs.length != 0) {
StringBuilder scalarsString = new StringBuilder().append('[');
for (Expression sub : scalarSubs)
scalarsString.append(sub).append(", ");
scalarsString.deleteCharAt(scalarsString.length() - 1).deleteCharAt(scalarsString.length() - 1).append(']');
System.out.println(scalarsString.toString());
}*/
/*System.out.println("Reduced solution: " + Arrays.toString(reducedSystem.generalSolutions));
System.out.println();*/
scriptCreator.createScript(equations, reducedSystem, path, keepFreeParameters);
//cleaning previous output
new File(path + "/equations." + scriptCreator.getScriptExtension() + "Out").delete();
//running external program
try {
Process p = Runtime.getRuntime().exec(programBinDir + "/" + scriptCreator.getScriptExecutionCommand() + " " + path + "/equations." + scriptCreator.getScriptExtension());
BufferedReader bri = new BufferedReader(new InputStreamReader(p.getInputStream()));
BufferedReader bre = new BufferedReader(new InputStreamReader(p.getErrorStream()));
String line;
while ((line = bri.readLine()) != null)
System.out.println(line);
bri.close();
while ((line = bre.readLine()) != null)
System.out.println(line);
bre.close();
p.waitFor();
} catch (IOException | InterruptedException ex) {
throw new RuntimeException(ex);
}
//reading the produced output with the solution
//allocating resulting coefficients array
Expression[] coefficientsResults = new Expression[reducedSystem.unknownCoefficients.length];
//no solutions
if (!new File(path + "/equations." + scriptCreator.getScriptExtension() + "Out").exists()) {
return new Expression[0][];
}
FileInputStream fstream = new FileInputStream(path + "/equations." + scriptCreator.getScriptExtension() + "Out");
if (fstream.available() == 0)
return null;
DataInputStream in = new DataInputStream(fstream);
BufferedReader br = new BufferedReader(new InputStreamReader(in));
String strLine;
i = -1;
List<Expression[]> solutions = new ArrayList<>();
//reading resulting solutions from file
while ((strLine = br.readLine()) != null) {
if (strLine.equals("//solution")) {
//solution parser
Expression[] solution = reducedSystem.generalSolutions.clone();
//substituting coefficients into general inverse form
List<Transformation> zeroSubs = new ArrayList<>();
for (Expression coef : coefficientsResults)
if (coef.isIdentity() && !keepFreeParameters)//if current coefficient is free parameter
{
zeroSubs.add(Tensors.expression(coef.get(0), Complex.ZERO));
} else {
for (int si = solution.length - 1; si >= 0; --si)
solution[si] = (Expression) coef.transform(solution[si]);
}
if (!keepFreeParameters)
for (int si = solution.length - 1; si >= 0; --si)
solution[si] = (Expression) new TransformationCollection(zeroSubs).transform(solution[si]);
//substituting the renamed tensors combinations
for (Expression sub : scalarSubs)
for (int si = solution.length - 1; si >= 0; --si)
solution[si] = (Expression) sub.transpose().transform(solution[si]);
solutions.add(solution);
coefficientsResults = new Expression[reducedSystem.unknownCoefficients.length];
i = -1;
} else
coefficientsResults[++i] = Tensors.parseExpression(strLine);
}
in.close();
return solutions.toArray(new Expression[solutions.size()][]);
}
public static interface ExternalScriptCreator {
void createScript(Expression[] equations, ReducedSystem reducedSystem, String path, boolean keepFreeParams) throws IOException;
String getScriptExecutionCommand();
String getScriptExtension();
}
public static final class MathematicaScriptCreator implements ExternalScriptCreator {
public static final MathematicaScriptCreator INSTANCE = new MathematicaScriptCreator();
private MathematicaScriptCreator() {
}
@Override
public void createScript(Expression[] equations, ReducedSystem reducedSystem, String path, boolean keepFreeParams) throws IOException {
//creating file with Mathematica code to solve the system of equations
FileOutputStream output = new FileOutputStream(path + "/equations.mathematica");
PrintStream file = new PrintStream(output);
file.append("$equations = {\n");
int i;
for (i = 0; ; i++) {
file.append(equations[i].toString(OutputFormat.WolframMathematica).replace("=", "=="));
if (i == equations.length - 1)
break;
file.append(",\n");
}
file.append("\n};\n");
file.append("$coefficients = {");
for (i = 0; ; i++) {
file.append(reducedSystem.unknownCoefficients[i].toString(OutputFormat.WolframMathematica));
if (i == reducedSystem.unknownCoefficients.length - 1)
break;
file.append(',');
}
file.append(" };\n");
file.append("$result = Solve[$equations,$coefficients];\n");
file.append("If[Length[$result] != 0, ");
file.append("$result = Simplify[$result];\n");
file.append("$stream = OpenWrite[\"" + path + "/equations.mathematicaOut\"];\n");
file.append("For[$solution = 1, $solution <= Length[$result], ++$solution, ");
file.append("$tempResult = $result[[$solution]];");
file.append("$found = $tempResult[[All, 1]];\n");
if (!keepFreeParams)
file.append("For[$i = 1, $i <= Length[$coefficients], ++$i,If[!MemberQ[$found, $coefficients[[$i]]], $tempResult = $tempResult/.{$coefficients[[$i]] -> 0}; AppendTo[$tempResult, $coefficients[[$i]] -> 0];]];\n");
else
file.append("For[$i = 1, $i <= Length[$coefficients], ++$i,If[!MemberQ[$found, $coefficients[[$i]]], AppendTo[$tempResult, $coefficients[[$i]] -> $coefficients[[$i]]];]];\n");
file.append("$tempResult = Simplify[$tempResult];\n");
// file.append("left = Array[Function[x,Coefficient[equations[[x, 1]], #] & /@ coefficients], Length[equations]];\n");
// file.append("right = equations[[All, 2]];\n");
// file.append("result = LinearSolve[left, right]\n");
// file.append("For[i = 1, i <= Length[coefficients], ++i, WriteString[stream, StringReplace[ToString[coefficients[[i]] == result[[i]] // InputForm], {\"==\" -> \"=\", \"^\" -> \"**\"}] <> If[i != Length[coefficients], \"\\n\", \"\"]]];\n");
file.append("For[$i = 1, $i <= Length[$coefficients], ++$i, WriteString[$stream, StringReplace[ToString[$tempResult[[$i]] // InputForm], {\"->\" -> \"=\", \"^\" -> \"**\"}] <> If[$i != Length[$coefficients], \"\\n\", \"\"]]];\n");
file.append("WriteString[$stream, \"\n//solution\n\"];");
file.append("];");
file.append("Close[$stream];");
file.append("];");
output.close();
file.close();
}
@Override
public String getScriptExecutionCommand() {
return "MathematicaScript -script";
}
@Override
public String getScriptExtension() {
return "mathematica";
}
}
public static final class MapleScriptCreator implements ExternalScriptCreator {
public static final MapleScriptCreator INSTANCE = new MapleScriptCreator();
private MapleScriptCreator() {
}
@Override
public void createScript(Expression[] equations, ReducedSystem reducedSystem, String path, boolean keepFreeParams) throws IOException {
//creating file with Maple code to solve the system of equations
FileOutputStream output = new FileOutputStream(path + "/equations.maple");
PrintStream file = new PrintStream(output);
file.append("with(StringTools):\n");
file.append("ans:=array([");
int i;
for (i = 0; i < reducedSystem.unknownCoefficients.length; ++i)
if (i == reducedSystem.unknownCoefficients.length - 1)
file.append(reducedSystem.unknownCoefficients[i].toString(OutputFormat.Maple));
else
file.append(reducedSystem.unknownCoefficients[i].toString(OutputFormat.Maple) + ",");
file.append("]):\n");
file.println("eq:=array(1.." + equations.length + "):");
for (i = 0; i < equations.length; i++)
file.println("eq[" + (i + 1) + "]:=" + equations[i].toString(OutputFormat.Maple) + ":");
file.print("Result := solve(simplify({seq(eq[i],i=1.." + equations.length + ")}),[");
for (i = 0; i < reducedSystem.unknownCoefficients.length; ++i)
if (i == reducedSystem.unknownCoefficients.length - 1)
file.append(reducedSystem.unknownCoefficients[i].toString(OutputFormat.Maple));
else
file.append(reducedSystem.unknownCoefficients[i].toString(OutputFormat.Maple) + ",");
file.append("],explicit=true):\n");
file.append("if nops(Result) <> 0 then\n");
file.append("Result:= factor(Result);\n");
file.println("file:=fopen(\"" + path + "/equations.mapleOut\",WRITE):");
file.append("for maple_positionInResult from 1 to nops(Result) do\n");
file.append("for maple_counter from 1 to " + reducedSystem.unknownCoefficients.length + " do\n");
file.append("temp1 := SubstituteAll(convert(lhs(Result[maple_positionInResult][maple_counter]), string), \"^\", \"**\");\n");
file.append("temp1 := SubstituteAll(convert(lhs(Result[maple_positionInResult][maple_counter]), string), \"(\", \"[\");\n");
file.append("temp1 := SubstituteAll(convert(lhs(Result[maple_positionInResult][maple_counter]), string), \")\", \"]\");\n");
file.append("temp2 := SubstituteAll(convert(rhs(Result[maple_positionInResult][maple_counter]), string), \"^\", \"**\");\n");
file.append("fprintf(file,\"%s=%s\\n\",temp1,temp2);\n");
file.append("od:\n");
file.append("fprintf(file,\"//solution\\n\");\n");
file.append("od:\n");
file.append("end if;\n");
file.append("fclose(file):");
output.close();
file.close();
}
@Override
public String getScriptExecutionCommand() {
return "maple";
}
@Override
public String getScriptExtension() {
return "maple";
}
}
}