Struct SBGraph creation from model JSON input.

[joaquinffernandez]

model rltest
  constant Integer N=10;
  Real x1[N];
  Real X2[1];
  Real a1[N];
  parameter Real R=1,C=1,L=1;
equation
  a1[1]=((10-x1[1])^3)/R;
  for i in 1:N-1 loop
    a1[i+1]=((x1[i]-x1[i+1])^3)/R;
  end for;
  for i in 1:N-1 loop
    der(x1[i])=((a1[i]-a1[i+1])^3)/C;
  end for;
  der(x1[N])=(a1[N]-x2[1])/C;
  der(x2[1])=x1[N]/L;
  ...
end rltest;

The JSON format is quite similar to the one defined here. From the variable definitions of the model, we define the following nodes:

  Real x1[N]; // Node 1, state variable.
  Real X2[1]; // Node 2, state variable.
  Real a1[N]; // Node 3, algebraic variable.

$V_1 = \{$
$\text{id} : X1$
$\text{type} = State$
$\}$

$N_1 = \{$
$\text{id} : n_1$
$\text{interval} : [1,N]$
$\text{lhs} : \{V_1\}$
$\text{rhs} : \{\}$
$\}$

$V_2 = \{$
$\text{id} : X2$
$\text{type} = State$
$\}$

$N_2 = \{$
$\text{id} : n_2$
$\text{interval} : [1,1]$
$\text{lhs} : \{V_2\}$
$\text{rhs} : \{\}$
$\}$

$V_3 = \{$
$\text{id} : a$
$\text{type} = Algebraic$
$\}$

$N_3 = \{$
$\text{id} : n_3$
$\text{interval} : [1,N]$
$\text{lhs} : \{V_3\}$
$\text{rhs} : \{\}$
$\}$

Then from the equations of the model, we can define:

• From a1[1]=((10-x1[1])^3)/R; :

  $V_4 = \{$
  $\text{id} : a1$
  $\text{exp} = (0,1) \rightarrow$ to form the expression that corresponds to $a1[1]$
  $\}$

  $V_5 = \{$
  $\text{id} : X1$
  $\text{exp} = (0,1) \rightarrow$ to form the expression that corresponds to $X1[1]$
  $\}$

  $N_4 = \{$
  $\text{id} : n_4$
  $\text{interval} : [1,1]$
  $\text{lhs} : \{V_{4}\}$
  $\text{rhs} : \{V_{5}\}$
  $\}$

• From:

  for i in 1:N-1 loop
      a1[i+1]=((x1[i]-x1[i+1])^3)/R;
  end for;
  

  $V_6 = \{$
  $\text{id} : a1$
  $\text{exp} = (1,1) \rightarrow$ to form the expression $1\times i+1$ that corresponds to $a1[i+1]$
  $\}$

  $V_7 = \{$
  $\text{id} : X1$
  $\text{exp} = (1,0) \rightarrow$ to form the expression $1\times i+0$ that corresponds to $X1[i]$
  $\}$

  $V_8 = \{$
  $\text{id} : X1$
  $\text{exp} = (1,1) \rightarrow$ to form the expression $1\times i+1$ that corresponds to $X1[i+1]$
  $\}$

  $N_5 = \{$
  $\text{id} : n_5$
  $\text{interval} : [1,N-1]$
  $\text{lhs} : \{V_{6}\}$
  $\text{rhs} : \{V_{7},V_{8}\}$
  $\}$

• From:

  for i in 1:N-1 loop
     der(x1[i])=((a1[i]-a1[i+1])^3)/C;
  end for;
  

  $V_9 = \{$
  $\text{id} : X1$
  $\text{exp} = (1,0) \rightarrow$ to form the expression $1\times i+0$ that corresponds to $a1[i]$
  $\}$

  $V_10 = \{$
  $\text{id} : a1$
  $\text{exp} = (1,0) \rightarrow$ to form the expression $1\times i+0$ that corresponds to $a1[i]$
  $\}$

  $V_11 = \{$
  $\text{id} : a1$
  $\text{exp} = (1,1) \rightarrow$ to form the expression $1\times i+1$ that corresponds to $a1[i+1]$
  $\}$

  $N_6 = \{$
  $\text{id} : n_6$
  $\text{interval} : [1,N-1]$
  $\text{lhs} : \{V_{9}\}$
  $\text{rhs} : \{V_{10},V_{11}\}$
  $\}$

• From der(x1[N])=(a1[N]-x2[1])/C; :

  $V_12 = \{$
  $\text{id} : X1$
  $\text{exp} = (0,N) \rightarrow$ to form the expression $0\times i+N$ that corresponds to $X1[N]$
  $\}$

  $V_13 = \{$
  $\text{id} : a1$
  $\text{exp} = (0,N) \rightarrow$ to form the expression $0\times i+N$ that corresponds to $a1[N]$
  $\}$

  $V_14 = \{$
  $\text{id} : X2$
  $\text{exp} = (0,1) \rightarrow$ to form the expression $1\times 0+1$ that corresponds to $X2[1]$
  $\}$

  $N_7 = \{$
  $\text{id} : n_7$
  $\text{interval} : [1,1]$
  $\text{lhs} : \{V_{12}\}$
  $\text{rhs} : \{V_{13},V_{14}\}$
  $\}$

• Finally, from der(x2[1])=x1[N]/L; :

  $V_15 = \{$
  $\text{id} : X1$
  $\text{exp} = (0,1) \rightarrow$ to form the expression $0\times i+1$ that corresponds to $X2[1]$
  $\}$

  $V_16 = \{$
  $\text{id} : X1$
  $\text{exp} = (0,N) \rightarrow$ to form the expression $0\times i+N$ that corresponds to $X1[N]$
  $\}$

  $N_8 = \{$
  $\text{id} : n_8$
  $\text{interval} : [1,1]$
  $\text{lhs} : \{V_{15}\}$
  $\text{rhs} : \{V_{16}\}$
  $\}$

An the final definition is:

$Nodes = \{N_1, N_2,N_3, N_4, N_5, N_6, N_7, N_8\}$

[joaquinffernandez]

A general JSON representation of a given Modelica model used to compute the model structural dependencies can be defined as:

$\text{Nodes} : \{$
$\text{derivatives} : \{D_1, \dots, D_m\}$ with $D_j$ of type $\text{Compute\_Node}$, the set of derivative equations defined in the model.
$\text{equations} : \{A_1, \dots, A_n\}$ with $A_j$ of type $\text{Compute\_Node}$, the set of algebraic equations defined in the model.
$\text{events} : \{E_1, \dots, E_k\}$ with $E_j$ of type $\text{Compute\_Node}$, the set of events defined in the model.
$\text{variables} : \{V_1, \dots, V_l\}$ with $V_j$ of type $\text{Variable\_Node}$, the set of variables defined in the model.
$\}$

$\text{Compute\_Node} : \{$
$\text{id} : \text{string}$
$\text{interval} : [1,\dots,M]$
$\text{type} : \{ Equation| Derivative | Event \}$
$\text{lhs} : \{ L_1, \dots, L_k \}$ where $L_i$ has type $\text{Var\_Usage}$
$\text{rhs} : \{ R_1, \dots, R_g \}$ where $R_i$ has type $\text{Var\_Usage}$
$\}$

Making use of Var_Usage records that represents the appearance of a variable in a computing node, defined as follows:

$\text{Var\_Usage} : \{$
$\text{id} : \text{string}$ where $\text{id} \in \{v_1.id, \dots, v_l.id \}$ i.e. the id must correspond to one of the Variable_Node defined in the model.
$\text{exp} : (a,b)$ where $a, b \in \mathbb{N}^0$ and they represent a constant and slope in the expression: $a * i + b$ of the usage in a given expression.
$\}$

$\text{Variable\_Node} : \{$
$\text{id} : \text{string}$
$\text{interval} : [1,\dots,M]$
$\text{type} : \{ State | Discrete | Algebraic\}$
$\}$

WIP