Analyser/Generator: support systems of non-linear algebraic equations

[agarny]

Fixes #882.

[hsorby]

In the void initialiseVariables(double *states, double *rates, double *variables); function is the rates argument ever used without the external variable argument?

[agarny]

In the void initialiseVariables(double *states, double *rates, double *variables); function is the rates argument ever used without the external variable argument?

It actually has nothing to do with external variables. The reason it was introduced is that rates[x] may now be computed using an NLA equation, in which case we need to have an initial guess for rates[x] and this is done through initialiseVariables().

[hsorby]

In the void initialiseVariables(double *states, double *rates, double *variables); function is the rates argument ever used without the external variable argument?

It actually has nothing to do with external variables. The reason it was introduced is that rates[x] may now be computed using an NLA equation, in which case we need to have an initial guess for rates[x] and this is done through initialiseVariables().

Do we have a test showing this, I couldn't see a test generating a rates argument in the initialiseVariables() without also using the externalVariable argument.

[agarny]

In the void initialiseVariables(double *states, double *rates, double *variables); function is the rates argument ever used without the external variable argument?

It actually has nothing to do with external variables. The reason it was introduced is that rates[x] may now be computed using an NLA equation, in which case we need to have an initial guess for rates[x] and this is done through initialiseVariables().

Do we have a test showing this, I couldn't see a test generating a rates argument in the initialiseVariables() without also using the externalVariable argument.

Yes:

libcellml/tests/resources/generator/hodgkin_huxley_squid_axon_model_1952/model.dae.c

Lines 489 to 517 in 842346d

	void initialiseVariables(double *states, double *rates, double *variables)
	{
	variables[0] = 0.0;
	variables[1] = 0.0;
	variables[2] = 0.0;
	variables[3] = 0.0;
	variables[4] = 1.0;
	variables[5] = 0.0;
	variables[6] = 0.0;
	variables[7] = 0.3;
	variables[8] = 0.0;
	variables[9] = 120.0;
	variables[10] = 0.0;
	variables[11] = 0.0;
	variables[12] = 0.0;
	variables[13] = 0.0;
	variables[14] = 0.0;
	variables[15] = 36.0;
	variables[16] = 0.0;
	variables[17] = 0.0;
	states[0] = 0.0;
	states[1] = 0.6;
	states[2] = 0.05;
	states[3] = 0.325;
	rates[0] = 0.0;
	rates[1] = 0.0;
	rates[2] = 0.0;
	rates[3] = 0.0;
	}

.