Examples with Equation cbit.vcell.math.Equation used on opensource projects

Example 11 with Equation

use of cbit.vcell.math.Equation in project vcell by virtualcell.

the class FiniteVolumeFileWriter method writeSimulationParamters.

/**
 * @param timeFunction
 * @param startTime
 * @param endTime
 * @param rootFinder
 * @param uniqueRootTimes
 * @param bPrintIterations
 * @throws ExpressionException
 *
 * for testing within scrapbook, see below:
 *
 * try {
 *	edu.northwestern.at.utils.math.rootfinders.MonadicFunctionRootFinder rootFinder =
 *//			new edu.northwestern.at.utils.math.rootfinders.Brent();
 *			new edu.northwestern.at.utils.math.rootfinders.Bisection();
 *//			new edu.northwestern.at.utils.math.rootfinders.NewtonRaphson();
 *//			new edu.northwestern.at.utils.math.rootfinders.Secant();
 *	cbit.vcell.parser.SimpleSymbolTable simpleSymbolTable = new cbit.vcell.parser.SimpleSymbolTable(new String[] { "t" });
 *
 *	cbit.vcell.parser.Expression exp = new cbit.vcell.parser.Expression("t-0.56");
 *
 *	exp.bindExpression(simpleSymbolTable);
 *	java.util.TreeSet<Double> rootTimes = new java.util.TreeSet<Double>();
 *	double startTime = 0.0;
 *	double endTime = 100.0;
 *	System.out.print("exp = '"+ exp.infix() + "'");
 *	long currentTimeMS = System.currentTimeMillis();
 *	cbit.vcell.solvers.FiniteVolumeFileWriter.findAllRoots(exp,startTime,endTime,rootFinder,rootTimes,false);
 *	long finalTimeMS = System.currentTimeMillis();
 *	for (double root : rootTimes){
 *		System.out.println("root = "+root);
 *	}
 *	System.out.println("elapsedTime of computation = "+(finalTimeMS-currentTimeMS)+" ms, found " + rootTimes.size() + " roots (not unique)");
 *
 *}catch (Exception e){
 *	e.printStackTrace(System.out);
 *}
 */
/*public static void findAllRoots(Expression timeFunction, double startTime, double endTime, MonadicFunctionRootFinder rootFinder, TreeSet<Double> uniqueRootTimes, boolean bPrintIterations) throws ExpressionException{
	TreeSet<Double> allRootTimes = new TreeSet<Double>();
	final Expression function_exp = new Expression(timeFunction);
	MonadicFunction valueFunction = new MonadicFunction() {
		double[] values = new double[1];
		public double f(double t) {
			values[0] = t;
			try {
				return function_exp.evaluateVector(values);
			} catch (ExpressionException e) {
				e.printStackTrace();
				throw new RuntimeException("expression exception "+e.getMessage());
			}
		}
	};
	
	final Expression derivative_exp = new Expression(timeFunction.differentiate(ReservedVariable.TIME.getName()));
	MonadicFunction derivativeFunction = new MonadicFunction() {
		double[] values = new double[1];
		public double f(double t) {
			values[0] = t;
			try {
				return derivative_exp.evaluateVector(values);
			} catch (ExpressionException e) {
				e.printStackTrace();
				throw new RuntimeException("expression exception "+e.getMessage());
			}
		}
	};
	
	RootFinderConvergenceTest convergenceTest = new StandardRootFinderConvergenceTest();
	RootFinderIterationInformation iterationInformation = null;
	if (bPrintIterations){
		iterationInformation = new RootFinderIterationInformation() {				
			public void iterationInformation(double x, double fx, double dfx, int currentIteration) {
				System.out.println(currentIteration+") x="+x+", fx="+fx+", dfx="+dfx);
			}
		};
	}
	int NUM_BRACKETS = 1000;
	double simulationTime = endTime - startTime;
	double tolerance = simulationTime/1e10;
	int maxIter = 1000;
	
	for (int i=0;i<NUM_BRACKETS-1;i++){
		double bracketMin = startTime + simulationTime*i/NUM_BRACKETS;
		double bracketMax = startTime + simulationTime*(i+1)/NUM_BRACKETS;
	
		double root = rootFinder.findRoot(bracketMin, bracketMax, tolerance, maxIter, valueFunction, derivativeFunction, convergenceTest, iterationInformation);
		if (root>startTime && root<endTime && valueFunction.f(root)<=tolerance){
			allRootTimes.add(root);
		}
	}
	double uniqueTolerance = tolerance * 100;
	double lastUniqueRoot = Double.NEGATIVE_INFINITY;
	for (double root : allRootTimes){
		if (root-lastUniqueRoot > uniqueTolerance){
			uniqueRootTimes.add(root);
		}
		lastUniqueRoot = root;
	}

}  ---------------------------------JIM's CODE COMMENTTED FOR FUTURE DEVELOPMENT*/
/**
 *# Simulation Parameters
 *SIMULATION_PARAM_BEGIN
 *SOLVER SUNDIALS_PDE_SOLVER 1.0E-7 1.0E-9
 *DISCONTINUITY_TIMES 2 1.0E-4 3.0000000000000003E-4
 *BASE_FILE_NAME c:/Vcell/users/fgao/SimID_31746636_0_
 *ENDING_TIME 4.0E-4
 *KEEP_EVERY ONE_STEP 3
 *KEEP_AT_MOST 1000
 *SIMULATION_PARAM_END
 * @throws MathException
 * @throws ExpressionException
 */
private void writeSimulationParamters() throws ExpressionException, MathException {
    Simulation simulation = simTask.getSimulation();
    SolverTaskDescription solverTaskDesc = simulation.getSolverTaskDescription();
    printWriter.println("# Simulation Parameters");
    printWriter.println(FVInputFileKeyword.SIMULATION_PARAM_BEGIN);
    if (solverTaskDesc.getSolverDescription().equals(SolverDescription.SundialsPDE)) {
        printWriter.print(FVInputFileKeyword.SOLVER + " " + FVInputFileKeyword.SUNDIALS_PDE_SOLVER + " " + solverTaskDesc.getErrorTolerance().getRelativeErrorTolerance() + " " + solverTaskDesc.getErrorTolerance().getAbsoluteErrorTolerance() + " " + solverTaskDesc.getTimeStep().getMaximumTimeStep());
        if (simulation.getMathDescription().hasVelocity()) {
            printWriter.print(" " + solverTaskDesc.getSundialsPdeSolverOptions().getMaxOrderAdvection());
        }
        printWriter.println();
        Vector<Discontinuity> discontinuities = new Vector<Discontinuity>();
        TreeSet<Double> discontinuityTimes = new TreeSet<Double>();
        MathDescription mathDesc = simulation.getMathDescription();
        Enumeration<SubDomain> enum1 = mathDesc.getSubDomains();
        while (enum1.hasMoreElements()) {
            SubDomain sd = enum1.nextElement();
            Enumeration<Equation> enum_equ = sd.getEquations();
            while (enum_equ.hasMoreElements()) {
                Equation equation = enum_equ.nextElement();
                equation.getDiscontinuities(simTask.getSimulationJob().getSimulationSymbolTable(), discontinuities);
            }
        }
        getDiscontinuityTimes(discontinuities, discontinuityTimes);
        if (discontinuityTimes.size() > 0) {
            printWriter.print(FVInputFileKeyword.DISCONTINUITY_TIMES + " " + discontinuityTimes.size());
            for (double d : discontinuityTimes) {
                printWriter.print(" " + d);
            }
            printWriter.println();
        }
    } else if (solverTaskDesc.getSolverDescription().equals(SolverDescription.Chombo)) {
        printWriter.println(FVInputFileKeyword.SOLVER + " " + FVInputFileKeyword.CHOMBO_SEMIIMPLICIT_SOLVER);
    } else if (solverTaskDesc.getSolverDescription().equals(SolverDescription.VCellPetsc)) {
        printWriter.println(FVInputFileKeyword.SOLVER + " " + FVInputFileKeyword.VCELL_PETSC_SOLVER);
    } else {
        printWriter.println(FVInputFileKeyword.SOLVER + " " + FVInputFileKeyword.FV_SOLVER + " " + solverTaskDesc.getErrorTolerance().getRelativeErrorTolerance());
    }
    printWriter.println(FVInputFileKeyword.BASE_FILE_NAME + " " + new File(workingDirectory, simTask.getSimulationJob().getSimulationJobID()).getAbsolutePath());
    if (solverTaskDesc.isParallel() && destinationDirectory != null && !destinationDirectory.equals(workingDirectory)) {
        printWriter.println(FVInputFileKeyword.PRIMARY_DATA_DIR + " " + destinationDirectory.getAbsolutePath());
    }
    printWriter.println(FVInputFileKeyword.ENDING_TIME + " " + solverTaskDesc.getTimeBounds().getEndingTime());
    OutputTimeSpec outputTimeSpec = solverTaskDesc.getOutputTimeSpec();
    if (solverTaskDesc.getSolverDescription().isChomboSolver()) {
        List<TimeInterval> timeIntervalList = solverTaskDesc.getChomboSolverSpec().getTimeIntervalList();
        printWriter.println(FVInputFileKeyword.TIME_INTERVALS + " " + timeIntervalList.size());
        for (TimeInterval ti : timeIntervalList) {
            printWriter.println(ti.getEndingTime() + " " + ti.getTimeStep() + " " + ti.getKeepEvery());
        }
    } else if (solverTaskDesc.getSolverDescription().equals(SolverDescription.SundialsPDE)) {
        if (outputTimeSpec.isDefault()) {
            DefaultOutputTimeSpec defaultOutputTimeSpec = (DefaultOutputTimeSpec) outputTimeSpec;
            printWriter.println(FVInputFileKeyword.KEEP_EVERY + " " + FVInputFileKeyword.ONE_STEP + " " + defaultOutputTimeSpec.getKeepEvery());
            printWriter.println(FVInputFileKeyword.KEEP_AT_MOST + " " + defaultOutputTimeSpec.getKeepAtMost());
        } else {
            printWriter.println(FVInputFileKeyword.TIME_STEP + " " + ((UniformOutputTimeSpec) outputTimeSpec).getOutputTimeStep());
            printWriter.println(FVInputFileKeyword.KEEP_EVERY + " 1");
        }
    } else {
        double defaultTimeStep = solverTaskDesc.getTimeStep().getDefaultTimeStep();
        printWriter.println(FVInputFileKeyword.TIME_STEP + " " + defaultTimeStep);
        int keepEvery = 1;
        if (outputTimeSpec.isDefault()) {
            keepEvery = ((DefaultOutputTimeSpec) outputTimeSpec).getKeepEvery();
        } else if (outputTimeSpec.isUniform()) {
            UniformOutputTimeSpec uots = (UniformOutputTimeSpec) outputTimeSpec;
            double ots = uots.getOutputTimeStep();
            keepEvery = (int) Math.round(ots / defaultTimeStep);
        } else {
            throw new RuntimeException("unexpected OutputTime specification type :" + outputTimeSpec.getClass().getName());
        }
        if (keepEvery <= 0) {
            throw new RuntimeException("Output KeepEvery must be a positive integer. Try to change the output option.");
        }
        printWriter.println(FVInputFileKeyword.KEEP_EVERY + " " + keepEvery);
    }
    ErrorTolerance stopAtSpatiallyUniformErrorTolerance = solverTaskDesc.getStopAtSpatiallyUniformErrorTolerance();
    if (stopAtSpatiallyUniformErrorTolerance != null) {
        printWriter.println(FVInputFileKeyword.CHECK_SPATIALLY_UNIFORM + " " + stopAtSpatiallyUniformErrorTolerance.getAbsoluteErrorTolerance() + " " + stopAtSpatiallyUniformErrorTolerance.getRelativeErrorTolerance());
    }
    printWriter.println(FVInputFileKeyword.SIMULATION_PARAM_END);
    printWriter.println();
}

Example 12 with Equation

use of cbit.vcell.math.Equation in project vcell by virtualcell.

the class ITextWriter method writeSubDomainsEquationsAsImages.

// currently not used.
protected void writeSubDomainsEquationsAsImages(Section mathDescSection, MathDescription mathDesc) {
    Enumeration<SubDomain> subDomains = mathDesc.getSubDomains();
    Expression[] expArray;
    Section volDomains = mathDescSection.addSection("Volume Domains", mathDescSection.depth() + 1);
    Section memDomains = mathDescSection.addSection("Membrane Domains", mathDescSection.depth() + 1);
    // arbitrary
    int scale = 1, height = 200;
    int viewableWidth = (int) (document.getPageSize().width() - document.leftMargin() - document.rightMargin());
    BufferedImage dummy = new BufferedImage(viewableWidth, height, BufferedImage.TYPE_3BYTE_BGR);
    while (subDomains.hasMoreElements()) {
        SubDomain subDomain = subDomains.nextElement();
        Enumeration<Equation> equationsList = subDomain.getEquations();
        ArrayList<Expression> expList = new ArrayList<Expression>();
        while (equationsList.hasMoreElements()) {
            Equation equ = equationsList.nextElement();
            try {
                Enumeration<Expression> enum_equ = equ.getTotalExpressions();
                while (enum_equ.hasMoreElements()) {
                    Expression exp = new Expression(enum_equ.nextElement());
                    expList.add(exp.flatten());
                }
            } catch (ExpressionException ee) {
                System.err.println("Unable to process the equation for subdomain: " + subDomain.getName());
                ee.printStackTrace();
                continue;
            }
        }
        expArray = (Expression[]) expList.toArray(new Expression[expList.size()]);
        Section tempSection = null;
        if (subDomain instanceof CompartmentSubDomain) {
            tempSection = volDomains.addSection(subDomain.getName(), volDomains.depth() + 1);
        } else if (subDomain instanceof MembraneSubDomain) {
            tempSection = memDomains.addSection(subDomain.getName(), memDomains.depth() + 1);
        }
        try {
            Dimension dim = ExpressionCanvas.getExpressionImageSize(expArray, (Graphics2D) dummy.getGraphics());
            System.out.println("Image dim: " + dim.width + " " + dim.height);
            BufferedImage bufferedImage = new BufferedImage((int) dim.getWidth() * scale, (int) dim.getHeight() * scale, BufferedImage.TYPE_3BYTE_BGR);
            ExpressionCanvas.getExpressionAsImage(expArray, bufferedImage, scale);
            // Table imageTable = null;;
            com.lowagie.text.Image expImage = com.lowagie.text.Image.getInstance(bufferedImage, null);
            expImage.setAlignment(com.lowagie.text.Image.LEFT);
            if (viewableWidth < expImage.scaledWidth()) {
                expImage.scaleToFit(viewableWidth, expImage.height());
                System.out.println("SubDomain expresions After scaling: " + expImage.scaledWidth());
            }
            /*Cell imageCell = new Cell();
				imageCell.add(expImage);
				if (imageTable == null) {
					imageTable = getTable(1, 100, 1, 1, 0);
				}
				imageTable.setTableFitsPage(false);
 				imageTable.setCellsFitPage(false);
				imageTable.addCell(imageCell);
				imageTable.setWidth(100);
				tempSection.add(imageTable);*/
            tempSection.add(expImage);
        } catch (Exception e) {
            System.err.println("Unable to add subdomain equation image to report.");
            e.printStackTrace();
        }
    }
    if (volDomains.isEmpty()) {
        mathDescSection.remove(volDomains);
    }
    if (memDomains.isEmpty()) {
        mathDescSection.remove(memDomains);
    }
}

Example 13 with Equation

use of cbit.vcell.math.Equation in project vcell by virtualcell.

the class ITextWriter method writeSubDomainsEquationsAsText.

protected void writeSubDomainsEquationsAsText(Section mathDescSection, MathDescription mathDesc) throws DocumentException {
    Enumeration<SubDomain> subDomains = mathDesc.getSubDomains();
    Section volDomains = mathDescSection.addSection("Volume Domains", mathDescSection.depth() + 1);
    Section memDomains = mathDescSection.addSection("Membrane Domains", mathDescSection.depth() + 1);
    Section filDomains = mathDescSection.addSection("Filament Domains", mathDescSection.depth() + 1);
    while (subDomains.hasMoreElements()) {
        Section tempSection = null;
        SubDomain subDomain = subDomains.nextElement();
        if (subDomain instanceof CompartmentSubDomain) {
            tempSection = volDomains.addSection(subDomain.getName(), volDomains.depth() + 1);
        } else if (subDomain instanceof MembraneSubDomain) {
            tempSection = memDomains.addSection(subDomain.getName(), memDomains.depth() + 1);
        } else if (subDomain instanceof FilamentSubDomain) {
            tempSection = filDomains.addSection(subDomain.getName(), filDomains.depth() + 1);
        }
        Enumeration<Equation> equationsList = subDomain.getEquations();
        while (equationsList.hasMoreElements()) {
            Equation equ = equationsList.nextElement();
            writeEquation(tempSection, equ);
        }
        if (subDomain.getFastSystem() != null) {
            writeFastSystem(tempSection, subDomain.getFastSystem());
        }
        if (subDomain instanceof MembraneSubDomain) {
            Enumeration<JumpCondition> jcList = ((MembraneSubDomain) subDomain).getJumpConditions();
            while (jcList.hasMoreElements()) {
                JumpCondition jc = jcList.nextElement();
                writeJumpCondition(tempSection, jc);
            }
        }
    }
    if (volDomains.isEmpty()) {
        mathDescSection.remove(volDomains);
    }
    if (memDomains.isEmpty()) {
        mathDescSection.remove(memDomains);
    }
    if (filDomains.isEmpty()) {
        mathDescSection.remove(filDomains);
    }
}

Example 14 with Equation

use of cbit.vcell.math.Equation in project vcell by virtualcell.

the class SimulationSymbolTable method hasTimeVaryingDiffusionOrAdvection.

public boolean hasTimeVaryingDiffusionOrAdvection(Variable variable) throws MathException, ExpressionException {
    Enumeration<SubDomain> enum1 = simulation.getMathDescription().getSubDomains();
    while (enum1.hasMoreElements()) {
        SubDomain subDomain = enum1.nextElement();
        Equation equation = subDomain.getEquation(variable);
        // 
        if (equation instanceof PdeEquation) {
            Vector<Expression> spatialExpressionList = new Vector<Expression>();
            spatialExpressionList.add(((PdeEquation) equation).getDiffusionExpression());
            if (((PdeEquation) equation).getVelocityX() != null) {
                spatialExpressionList.add(((PdeEquation) equation).getVelocityX());
            }
            if (((PdeEquation) equation).getVelocityY() != null) {
                spatialExpressionList.add(((PdeEquation) equation).getVelocityY());
            }
            if (((PdeEquation) equation).getVelocityZ() != null) {
                spatialExpressionList.add(((PdeEquation) equation).getVelocityZ());
            }
            for (int i = 0; i < spatialExpressionList.size(); i++) {
                Expression spatialExp = spatialExpressionList.elementAt(i);
                spatialExp = substituteFunctions(spatialExp);
                String[] symbols = spatialExp.getSymbols();
                if (symbols != null) {
                    for (int j = 0; j < symbols.length; j++) {
                        SymbolTableEntry entry = spatialExp.getSymbolBinding(symbols[j]);
                        if (entry instanceof ReservedVariable) {
                            if (((ReservedVariable) entry).isTIME()) {
                                return true;
                            }
                        }
                        if (entry instanceof VolVariable) {
                            return true;
                        }
                        if (entry instanceof VolumeRegionVariable) {
                            return true;
                        }
                        if (entry instanceof MemVariable || entry instanceof MembraneRegionVariable) {
                            return true;
                        }
                    }
                }
            }
        }
    }
    return false;
}

Example 15 with Equation

use of cbit.vcell.math.Equation in project vcell by virtualcell.

the class IDAFileWriter method writeEquations.

/**
 * Insert the method's description here.
 * Creation date: (3/8/00 10:31:52 PM)
 */
protected String writeEquations(HashMap<Discontinuity, String> discontinuityNameMap) throws MathException, ExpressionException {
    Simulation simulation = simTask.getSimulation();
    StringBuffer sb = new StringBuffer();
    MathDescription mathDescription = simulation.getMathDescription();
    if (mathDescription.hasFastSystems()) {
        // 
        // define vector of original variables
        // 
        SimulationSymbolTable simSymbolTable = simTask.getSimulationJob().getSimulationSymbolTable();
        CompartmentSubDomain subDomain = (CompartmentSubDomain) mathDescription.getSubDomains().nextElement();
        FastSystem fastSystem = subDomain.getFastSystem();
        FastSystemAnalyzer fs_Analyzer = new FastSystemAnalyzer(fastSystem, simSymbolTable);
        int numIndependent = fs_Analyzer.getNumIndependentVariables();
        int systemDim = mathDescription.getStateVariableNames().size();
        int numDependent = systemDim - numIndependent;
        // 
        // get all variables from fast system (dependent and independent)
        // 
        HashSet<String> fastSystemVarHash = new HashSet<String>();
        Enumeration<Variable> dependentfastSystemVarEnum = fs_Analyzer.getDependentVariables();
        while (dependentfastSystemVarEnum.hasMoreElements()) {
            fastSystemVarHash.add(dependentfastSystemVarEnum.nextElement().getName());
        }
        Enumeration<Variable> independentfastSystemVarEnum = fs_Analyzer.getIndependentVariables();
        while (independentfastSystemVarEnum.hasMoreElements()) {
            fastSystemVarHash.add(independentfastSystemVarEnum.nextElement().getName());
        }
        // 
        // get all equations including for variables that are not in the fastSystem (ode equations for "slow system")
        // 
        RationalExpMatrix origInitVector = new RationalExpMatrix(systemDim, 1);
        RationalExpMatrix origSlowRateVector = new RationalExpMatrix(systemDim, 1);
        RationalExpMatrix origVarColumnVector = new RationalExpMatrix(systemDim, 1);
        Enumeration<Equation> enumEquations = subDomain.getEquations();
        int varIndex = 0;
        while (enumEquations.hasMoreElements()) {
            Equation equation = enumEquations.nextElement();
            origVarColumnVector.set_elem(varIndex, 0, new RationalExp(equation.getVariable().getName()));
            Expression rateExpr = equation.getRateExpression();
            rateExpr.bindExpression(varsSymbolTable);
            rateExpr = MathUtilities.substituteFunctions(rateExpr, varsSymbolTable);
            origSlowRateVector.set_elem(varIndex, 0, new RationalExp("(" + rateExpr.flatten().infix() + ")"));
            Expression initExpr = new Expression(equation.getInitialExpression());
            initExpr.substituteInPlace(new Expression("t"), new Expression(0.0));
            initExpr = MathUtilities.substituteFunctions(initExpr, varsSymbolTable).flatten();
            origInitVector.set_elem(varIndex, 0, new RationalExp("(" + initExpr.flatten().infix() + ")"));
            varIndex++;
        }
        // 
        // make symbolic matrix for fast invariants (from FastSystem's fastInvariants as well as a new fast invariant for each variable not included in the fast system.
        // 
        RationalExpMatrix fastInvarianceMatrix = new RationalExpMatrix(numDependent, systemDim);
        int row = 0;
        for (int i = 0; i < origVarColumnVector.getNumRows(); i++) {
            // 
            if (!fastSystemVarHash.contains(origVarColumnVector.get(i, 0).infixString())) {
                fastInvarianceMatrix.set_elem(row, i, RationalExp.ONE);
                row++;
            }
        }
        Enumeration<FastInvariant> enumFastInvariants = fastSystem.getFastInvariants();
        while (enumFastInvariants.hasMoreElements()) {
            FastInvariant fastInvariant = enumFastInvariants.nextElement();
            Expression fastInvariantExpression = fastInvariant.getFunction();
            for (int col = 0; col < systemDim; col++) {
                Expression coeff = fastInvariantExpression.differentiate(origVarColumnVector.get(col, 0).infixString()).flatten();
                coeff = simSymbolTable.substituteFunctions(coeff);
                fastInvarianceMatrix.set_elem(row, col, RationalExpUtils.getRationalExp(coeff));
            }
            row++;
        }
        for (int i = 0; i < systemDim; i++) {
            sb.append("VAR " + origVarColumnVector.get(i, 0).infixString() + " INIT " + origInitVector.get(i, 0).infixString() + ";\n");
        }
        RationalExpMatrix fullMatrix = null;
        RationalExpMatrix inverseFullMatrix = null;
        RationalExpMatrix newSlowRateVector = null;
        try {
            RationalExpMatrix fastMat = ((RationalExpMatrix) fastInvarianceMatrix.transpose().findNullSpace());
            fullMatrix = new RationalExpMatrix(systemDim, systemDim);
            row = 0;
            for (int i = 0; i < fastInvarianceMatrix.getNumRows(); i++) {
                for (int col = 0; col < systemDim; col++) {
                    fullMatrix.set_elem(row, col, fastInvarianceMatrix.get(i, col));
                }
                row++;
            }
            for (int i = 0; i < fastMat.getNumRows(); i++) {
                for (int col = 0; col < systemDim; col++) {
                    fullMatrix.set_elem(row, col, fastMat.get(i, col));
                }
                row++;
            }
            inverseFullMatrix = new RationalExpMatrix(systemDim, systemDim);
            inverseFullMatrix.identity();
            RationalExpMatrix copyOfFullMatrix = new RationalExpMatrix(fullMatrix);
            copyOfFullMatrix.gaussianElimination(inverseFullMatrix);
            newSlowRateVector = new RationalExpMatrix(numDependent, 1);
            newSlowRateVector.matmul(fastInvarianceMatrix, origSlowRateVector);
        } catch (MatrixException ex) {
            ex.printStackTrace();
            throw new MathException(ex.getMessage());
        }
        sb.append("TRANSFORM\n");
        for (row = 0; row < systemDim; row++) {
            for (int col = 0; col < systemDim; col++) {
                sb.append(fullMatrix.get(row, col).getConstant().doubleValue() + " ");
            }
            sb.append("\n");
        }
        sb.append("INVERSETRANSFORM\n");
        for (row = 0; row < systemDim; row++) {
            for (int col = 0; col < systemDim; col++) {
                sb.append(inverseFullMatrix.get(row, col).getConstant().doubleValue() + " ");
            }
            sb.append("\n");
        }
        int numDifferential = numDependent;
        int numAlgebraic = numIndependent;
        sb.append("RHS DIFFERENTIAL " + numDifferential + " ALGEBRAIC " + numAlgebraic + "\n");
        int equationIndex = 0;
        while (equationIndex < numDependent) {
            // print row of mass matrix followed by slow rate corresponding to fast invariant
            Expression slowRateExp = new Expression(newSlowRateVector.get(equationIndex, 0).infixString()).flatten();
            slowRateExp.bindExpression(simSymbolTable);
            slowRateExp = MathUtilities.substituteFunctions(slowRateExp, varsSymbolTable).flatten();
            Vector<Discontinuity> v = slowRateExp.getDiscontinuities();
            for (Discontinuity od : v) {
                od = getSubsitutedAndFlattened(od, varsSymbolTable);
                String dname = discontinuityNameMap.get(od);
                if (dname == null) {
                    dname = ROOT_VARIABLE_PREFIX + discontinuityNameMap.size();
                    discontinuityNameMap.put(od, dname);
                }
                slowRateExp.substituteInPlace(od.getDiscontinuityExp(), new Expression("(" + dname + "==1)"));
            }
            sb.append(slowRateExp.infix() + ";\n");
            equationIndex++;
        }
        Enumeration<FastRate> enumFastRates = fastSystem.getFastRates();
        while (enumFastRates.hasMoreElements()) {
            // print the fastRate for this row
            Expression fastRateExp = new Expression(enumFastRates.nextElement().getFunction());
            fastRateExp = MathUtilities.substituteFunctions(fastRateExp, varsSymbolTable).flatten();
            Vector<Discontinuity> v = fastRateExp.getDiscontinuities();
            for (Discontinuity od : v) {
                od = getSubsitutedAndFlattened(od, varsSymbolTable);
                String dname = discontinuityNameMap.get(od);
                if (dname == null) {
                    dname = ROOT_VARIABLE_PREFIX + discontinuityNameMap.size();
                    discontinuityNameMap.put(od, dname);
                }
                fastRateExp.substituteInPlace(od.getDiscontinuityExp(), new Expression("(" + dname + "==1)"));
            }
            sb.append(fastRateExp.flatten().infix() + ";\n");
            equationIndex++;
        }
    } else {
        for (int i = 0; i < getStateVariableCount(); i++) {
            StateVariable stateVar = getStateVariable(i);
            Expression initExpr = new Expression(stateVar.getInitialRateExpression());
            initExpr = MathUtilities.substituteFunctions(initExpr, varsSymbolTable);
            initExpr.substituteInPlace(new Expression("t"), new Expression(0.0));
            sb.append("VAR " + stateVar.getVariable().getName() + " INIT " + initExpr.flatten().infix() + ";\n");
        }
        sb.append("TRANSFORM\n");
        for (int row = 0; row < getStateVariableCount(); row++) {
            for (int col = 0; col < getStateVariableCount(); col++) {
                sb.append((row == col ? 1 : 0) + " ");
            }
            sb.append("\n");
        }
        sb.append("INVERSETRANSFORM\n");
        for (int row = 0; row < getStateVariableCount(); row++) {
            for (int col = 0; col < getStateVariableCount(); col++) {
                sb.append((row == col ? 1 : 0) + " ");
            }
            sb.append("\n");
        }
        sb.append("RHS DIFFERENTIAL " + getStateVariableCount() + " ALGEBRAIC 0\n");
        for (int i = 0; i < getStateVariableCount(); i++) {
            StateVariable stateVar = getStateVariable(i);
            Expression rateExpr = new Expression(stateVar.getRateExpression());
            rateExpr = MathUtilities.substituteFunctions(rateExpr, varsSymbolTable).flatten();
            Vector<Discontinuity> v = rateExpr.getDiscontinuities();
            for (Discontinuity od : v) {
                od = getSubsitutedAndFlattened(od, varsSymbolTable);
                String dname = discontinuityNameMap.get(od);
                if (dname == null) {
                    dname = ROOT_VARIABLE_PREFIX + discontinuityNameMap.size();
                    discontinuityNameMap.put(od, dname);
                }
                rateExpr.substituteInPlace(od.getDiscontinuityExp(), new Expression("(" + dname + "==1)"));
            }
            sb.append(rateExpr.infix() + ";\n");
        }
    }
    return sb.toString();
}