public static Lst <Monomial> Sum(Monomial monomial, Lst <Monomial> monomials, Style style)
{
if (monomial.IsZero())
{
return(monomials);
}
if (monomials is Cons <Monomial> cons)
{
if (cons.head.SameFactors(monomial))
{
Flow sumCoeff = OpFlow.Op(cons.head.coefficient, "+", monomial.coefficient).Normalize(style);
if (sumCoeff.IsNumber(0.0))
{
return(cons.tail);
}
else
{
return(Monomial.Cons(new Monomial(sumCoeff, monomial.factors, style), cons.tail));
}
}
else
{
return(Monomial.Cons(cons.head, Sum(monomial, cons.tail, style)));
}
}
else
{
return(Monomial.Singleton(monomial));
}
}
public Flow RateFunction(ReactionValue reaction)
{
Flow monomial = NumberFlow.numberFlowOne;
if (reaction.rate is MassActionNumericalRate)
{
double rate = ((MassActionNumericalRate)reaction.rate).Rate(this.temperature);
foreach (SpeciesValue sp in sample.stateMap.species)
{
int spStoichio = reaction.Stoichiometry(sp.symbol, reaction.reactants);
monomial = OpFlow.Op("*", monomial, OpFlow.Op("^", new SpeciesFlow(sp.symbol), new NumberFlow(spStoichio)));
}
monomial = OpFlow.Op("*", new NumberFlow(rate), monomial);
}
else if (reaction.rate is MassActionFlowRate)
{
Flow rate = (reaction.rate as MassActionFlowRate).rateFunction;
foreach (SpeciesValue sp in sample.stateMap.species)
{
int spStoichio = reaction.Stoichiometry(sp.symbol, reaction.reactants);
monomial = OpFlow.Op("*", monomial, OpFlow.Op("^", new SpeciesFlow(sp.symbol), new NumberFlow(spStoichio)));
}
monomial = OpFlow.Op("*", rate, monomial);
}
else if (reaction.rate is GeneralFlowRate)
{
monomial = (reaction.rate as GeneralFlowRate).rateFunction;
}
else
{
throw new Error("RateFunction");
}
return(monomial);
}
public static Flow ToFlow(Lst <Factor> factors, Lst <Polynomize.Equation> eqs, Style style)
{
if (factors is Cons <Factor> cons)
{
return(OpFlow.Op(cons.head.ToFlow(eqs, style), "*", ToFlow(cons.tail, eqs, style)));
}
else
{
return(Flow.one);
}
}
public static Flow ToFlow(Lst <Factor> factors)
{
if (factors is Cons <Factor> cons)
{
return(cons.tail is Nil <Factor>?cons.head.ToFlow() : OpFlow.Op(cons.head.ToFlow(), "*", ToFlow(cons.tail)));
}
else
{
return(new NumberFlow(1.0));
}
}
public static Flow ToFlow(Lst <Monomial> monomials, Lst <Polynomize.Equation> eqs, Style style)
{
if (monomials is Cons <Monomial> cons)
{
return(OpFlow.Op(cons.head.ToFlow(eqs, style), "+", ToFlow(cons.tail, eqs, style)));
}
else
{
return(Flow.zero);
}
}
public Flow ToFlow()
{
if (power == 0)
{
return(new NumberFlow(1.0));
}
if (power == 1)
{
return(variable);
}
return(OpFlow.Op(variable, "^", new NumberFlow(power)));
}
public static SampleValue MassCompileSample(Symbol outSymbol, SampleValue inSample, Netlist netlist, Style style)
{
//inSample.Consume(null, 0, null, netlist, style); // this prevents simulating a sample and its massaction version in succession
List <ReactionValue> inReactions = inSample.RelevantReactions(netlist, style);
CRN inCrn = new CRN(inSample, inReactions);
Gui.Log(Environment.NewLine + inCrn.FormatNice(style));
(Lst <Polynomize.ODE> odes, Lst <Polynomize.Equation> eqs) = Polynomize.FromCRN(inCrn);
(Lst <Polynomize.PolyODE> polyOdes, Lst <Polynomize.Equation> polyEqs) = Polynomize.PolynomizeODEs(odes, eqs.Reverse(), style);
Gui.Log("Polynomize:" + Environment.NewLine + Polynomize.PolyODE.Format(polyOdes, style)
+ "Initial:" + Environment.NewLine + Polynomize.Equation.Format(polyEqs, style));
(Lst <Polynomize.PolyODE> posOdes, Lst <Polynomize.Equation> posEqs, Dictionary <Symbol, SpeciesFlow> dict, Lst <Positivize.Subst> substs) = Positivize.PositivizeODEs(polyOdes, polyEqs, style);
Gui.Log("Positivize:" + Environment.NewLine + Polynomize.PolyODE.Format(posOdes, style)
+ "Initial:" + Environment.NewLine + Polynomize.Equation.Format(posEqs, style));
Lst <ReactionValue> outReactions = Hungarize.ToReactions(posOdes, style);
Gui.Log("Hungarize:" + Environment.NewLine + outReactions.FoldR((r, s) => { return(r.FormatNormal(style) + Environment.NewLine + s); }, "")
+ "Initial:" + Environment.NewLine + Polynomize.Equation.Format(posEqs, style));
SampleValue outSample = new SampleValue(outSymbol, new StateMap(outSymbol, new List <SpeciesValue> {
}, new State(0, lna: inSample.stateMap.state.lna)), new NumberValue(inSample.Volume()), new NumberValue(inSample.Temperature()), produced: true);
netlist.Emit(new SampleEntry(outSample));
posOdes.Each(ode => {
Flow initFlow = Polynomize.Equation.ToFlow(ode.var, posEqs, style).Normalize(style);
double init; if (initFlow is NumberFlow num)
{
init = num.value;
}
else
{
throw new Error("Cannot generate a simulatable sample because initial values contain constants (but the symbolic version has been generated assuming constants are nonnegative).");
}
if (init < 0)
{
throw new Error("Negative initial value of Polynomized ODE for: " + Polynomize.Lookup(ode.var, eqs, style).Format(style) + " = " + init + Environment.NewLine + Polynomize.Equation.Format(eqs, style));
}
outSample.stateMap.AddDimensionedSpecies(new SpeciesValue(ode.var.species, -1.0), init, 0.0, "M", outSample.Volume(), style);
});
outReactions.Each(reaction => { netlist.Emit(new ReactionEntry(reaction)); });
substs.Each(subst => { ReportEntry report = new ReportEntry(null, OpFlow.Op(subst.plus, "-", subst.minus), null, outSample); outSample.AddReport(report); });
foreach (KeyValuePair <Symbol, SpeciesFlow> keypair in dict)
{
ReportEntry report = new ReportEntry(null, keypair.Value, null, outSample); outSample.AddReport(report);
}
;
return(outSample);
}
public static Lst <ReactionValue> ToReactions(SpeciesFlow variable, Monomial monomial, Lst <ReactionValue> rest, Style style)
{
if (monomial.IsZero())
{
return(rest);
}
else
{
int decide = Polynomial.DecideNonnegative(monomial.coefficient, style);
if (decide == 1) // positive monomials
{
RateValue rate;
if (monomial.coefficient is NumberFlow num)
{
rate = new MassActionNumericalRate(num.value);
}
else
{
rate = new MassActionFlowRate(monomial.coefficient);
}
return(new Cons <ReactionValue>(
new ReactionValue(
Factor.ToList(monomial.factors),
Factor.ToList(Factor.Product(new Factor(variable, 1), monomial.factors)),
rate),
rest));
}
else if (decide == -1) // negative monomials
{
RateValue rate;
if (monomial.coefficient is NumberFlow num)
{
rate = new MassActionNumericalRate(-num.value);
}
else
{
rate = new MassActionFlowRate(OpFlow.Op("-", monomial.coefficient).Normalize(style));
}
return(new Cons <ReactionValue>(
new ReactionValue(
Factor.ToList(monomial.factors),
Factor.ToList(Factor.Quotient(monomial.factors, new Factor(variable, 1), style)),
rate),
rest));
}
else
{
throw new Error("MassActionCompiler: aborted because it cannot determine the sign of this expression: " + monomial.coefficient.Format(style));
}
}
}
public static Lst <Monomial> Product(Monomial monomial, Lst <Monomial> monomials, Style style)
{
//Gui.Log("IN Product([" + monomial.Format(style) + "], [" + Format(monomials, style) + "])");
Lst <Monomial> result;
if (monomials is Cons <Monomial> cons)
{
result = Sum(new Monomial(OpFlow.Op(cons.head.coefficient, "*", monomial.coefficient), Factor.Product(cons.head.factors, monomial.factors), style), Product(monomial, cons.tail, style), style);
}
else
{
result = Monomial.nil;
}
//Gui.Log("OUT Product([" + monomial.Format(style) + "], [" + Format(monomials, style) + "]) = [" + Format(result, style) + "]");
return(result);
}
public (SpeciesValue[] vars, Flow[] flows) MeanFlow()
{
SpeciesValue[] vars = new SpeciesValue[sample.Count()];
Flow[] flows = new Flow[sample.Count()];
for (int speciesIx = 0; speciesIx < flows.Length; speciesIx++)
{
vars[speciesIx] = sample.stateMap.species[speciesIx];
Flow polynomial = NumberFlow.numberFlowZero;
foreach (ReactionValue reaction in this.reactions)
{
int netStoichiometry = reaction.NetStoichiometry(vars[speciesIx].symbol);
Flow monomial = (netStoichiometry == 0) ? NumberFlow.numberFlowZero : OpFlow.Op("*", new NumberFlow(netStoichiometry), RateFunction(reaction));
polynomial = OpFlow.Op("+", polynomial, monomial);
}
flows[speciesIx] = polynomial;
}
return(vars, flows);
}
public Flow[,] Jacobian(Style style)
{
int speciesNo = sample.Count();
Flow[,] jacobian = new Flow[speciesNo, speciesNo];
for (int speciesI = 0; speciesI < speciesNo; speciesI++)
{
SpeciesValue variableI = sample.stateMap.species[speciesI];
for (int speciesK = 0; speciesK < speciesNo; speciesK++)
{
SpeciesValue variableK = sample.stateMap.species[speciesK];
Flow polynomial = NumberFlow.numberFlowZero;
foreach (ReactionValue reaction in this.reactions)
{
int netStoichiometryI = reaction.NetStoichiometry(variableI.symbol);
if (reaction.rate is MassActionNumericalRate)
{
int stoichiometryK = reaction.Stoichiometry(variableK.symbol, reaction.reactants);
Flow monomial = (netStoichiometryI == 0 || stoichiometryK == 0) ? NumberFlow.numberFlowZero :
OpFlow.Op("*", OpFlow.Op("*", new NumberFlow(netStoichiometryI), new NumberFlow(stoichiometryK)),
OpFlow.Op("/", RateFunction(reaction), new SpeciesFlow(variableK.symbol)));
polynomial = OpFlow.Op("+", polynomial, monomial);
}
else if (reaction.rate is GeneralFlowRate || reaction.rate is MassActionFlowRate)
{
Flow monomial = (netStoichiometryI == 0) ? NumberFlow.numberFlowZero :
OpFlow.Op("*", new NumberFlow(netStoichiometryI),
RateFunction(reaction).Differentiate(variableK.symbol, style));
polynomial = OpFlow.Op("+", polynomial, monomial);
}
else
{
throw new Error("Jacobian");
}
}
// Gui.Log("d " + variableI.Format(style) + "/d" + variableK.Format(style) + " = " + polynomial.Format(style));
jacobian[speciesI, speciesK] = polynomial;
}
}
return(jacobian);
}
public Flow[,] Drift()
{
int speciesNo = sample.Count();
int reactionsNo = reactions.Count();
Flow[,] drift = new Flow[speciesNo, speciesNo];
for (int speciesI = 0; speciesI < speciesNo; speciesI++) // rows
{
for (int speciesJ = 0; speciesJ < speciesNo; speciesJ++) // columns
{
drift[speciesI, speciesJ] = NumberFlow.numberFlowZero;
for (int reactionR = 0; reactionR < reactionsNo; reactionR++) // reactions
{
drift[speciesI, speciesJ] = OpFlow.Op("+", drift[speciesI, speciesJ],
OpFlow.Op("*", new NumberFlow(stoichio[speciesI, reactionR] * stoichio[speciesJ, reactionR]),
RateFunction(reactions[reactionR])));
}
}
}
return(drift);
}
public (SpeciesFlow[, ], Flow[, ]) CovarFlow(Style style)
{
int speciesNo = sample.Count();
SpeciesFlow[,] covar = new SpeciesFlow[speciesNo, speciesNo]; // fill it with fresh covariance variables
for (int speciesI = 0; speciesI < speciesNo; speciesI++) // rows
{
SpeciesValue variableI = sample.stateMap.species[speciesI];
for (int speciesJ = 0; speciesJ < speciesNo; speciesJ++) // columns
{
SpeciesValue variableJ = sample.stateMap.species[speciesJ];
if (style.exportTarget == ExportTarget.WolframNotebook)
{
covar[speciesI, speciesJ] = new SpeciesFlow(new Symbol(variableI.Format(style) + "_" + variableJ.Format(style)));
}
else
{
covar[speciesI, speciesJ] = (speciesI == speciesJ) ? new SpeciesFlow(new Symbol("var(" + variableI.Format(style) + ")")) : new SpeciesFlow(new Symbol("cov(" + variableI.Format(style) + "," + variableJ.Format(style) + ")"));
}
}
}
Flow[,] covarFlow = new Flow[speciesNo, speciesNo];
Flow[,] jacobian = Jacobian(style);
Flow[,] drift = Drift();
for (int speciesI = 0; speciesI < speciesNo; speciesI++) // rows
{
for (int speciesJ = 0; speciesJ < speciesNo; speciesJ++) // columns
{
covarFlow[speciesI, speciesJ] = NumberFlow.numberFlowZero;
for (int speciesK = 0; speciesK < speciesNo; speciesK++) // dot product index
{
covarFlow[speciesI, speciesJ] = OpFlow.Op("+", covarFlow[speciesI, speciesJ], OpFlow.Op("*", jacobian[speciesI, speciesK], covar[speciesK, speciesJ]));
covarFlow[speciesI, speciesJ] = OpFlow.Op("+", covarFlow[speciesI, speciesJ], OpFlow.Op("*", jacobian[speciesJ, speciesK], covar[speciesI, speciesK])); // jacobian transposed
}
covarFlow[speciesI, speciesJ] = OpFlow.Op("+", covarFlow[speciesI, speciesJ], drift[speciesI, speciesJ]);
}
}
return(covar, covarFlow);
}
public Flow ToFlow(Lst <Equation> eqs, Style style)
{
// this is a bit redundant because eventually we call Flow.Normalize, but Normalize does not handle pos, etc.
Flow result;
if (op == "id")
{
result = Monomial.ToFlow(args[0], eqs, style);
}
else if (op == "time")
{
result = Flow.zero;
}
else if (op == "poly 1/[]")
{
Flow arg0 = Monomial.ToFlow(args[0], eqs, style);
if (arg0 is NumberFlow num)
{
result = new NumberFlow(1 / num.value);
}
else
{
result = OpFlow.Op(Flow.one, "/", arg0);
}
}
else if (op == "poly []^(1/[])")
{
Flow arg0 = Monomial.ToFlow(args[0], eqs, style);
Flow arg1 = Monomial.ToFlow(args[1], eqs, style);
if (arg0 is NumberFlow num0 && arg1 is NumberFlow num1)
{
result = new NumberFlow(Math.Pow(num0.value, 1 / num1.value));
}
else
{
result = OpFlow.Op(arg0, "^", OpFlow.Op(Flow.one, "/", arg1));
}
}
// ===== Separate =====
public static (Lst <Monomial> positive, Lst <Monomial> negative) Separate(Lst <Monomial> monomials, Style style)
{
if (monomials is Cons <Monomial> cons)
{
(Lst <Monomial> positive, Lst <Monomial> negative) = Separate(cons.tail, style);
int decide = Polynomial.DecideNonnegative(cons.head.coefficient, style);
if (decide == 1)
{
return(Monomial.Cons(cons.head, positive), negative);
}
else if (decide == -1)
{
return(positive, Monomial.Cons(new Monomial(OpFlow.Op("-", cons.head.coefficient), cons.head.factors, style), negative));
}
else
{
throw new Error("MassActionCompiler: aborted because it cannot determine the sign of this expression: " + cons.head.coefficient.Format(style));
}
}
else
{
return(Monomial.nil, Monomial.nil);
}
}
public Flow ToFlow(Lst <Polynomize.Equation> eqs, Style style)
{
return(OpFlow.Op(Polynomize.Lookup(this.variable, eqs, style).ToFlow(eqs, style), "^", new NumberFlow(this.power)));
}
public Monomial Product(Flow coefficient, Style style)
{
return(new Monomial(OpFlow.Op(this.coefficient, "*", coefficient), this.factors, style));
}
public Monomial Product(Monomial other, Style style)
{
return(new Monomial(OpFlow.Op(this.coefficient, "*", other.coefficient), Factor.Product(this.factors, other.factors), style));
}
public Flow ToFlow(Lst <Polynomize.Equation> eqs, Style style)
{
return(OpFlow.Op(this.coefficient, "*", Factor.ToFlow(this.factors, eqs, style)));
}
public Monomial Power(int power, Style style)
{
return(new Monomial(OpFlow.Op(this.coefficient, "^", new NumberFlow(power)), Factor.Power(this.factors, power), style));
}