Parsing input system

macro ODEmodel

Macro for creating an ODE from a list of equations. It also injects all variables into the global scope.

Example

Creating a simple ODE:

using StructuralIdentifiability

ode = @ODEmodel(
    x1'(t) = a * x1(t) + u(t),
    x2'(t) = b * x2(t) + c*x1(t)*x2(t),
    y(t) = x1(t)
)

Here,

• x1, x2 are state variables
• y is an output variable
• u is an input variable
• a, b, c are time-independent parameters

The main structure that represents input ODE system.

Stores information about states (x_vars), outputs (y_vars), inputs (u_vars), parameters (parameters) and the equations.

This structure is constructed via @ODEmodel macro.

set_parameter_values(ode, param_values)

Input:

• ode - an ODE as above
• param_values - values for (possibly, some of) the parameters as dictionary parameter => value

Output:

• new ode with the parameters in param_values plugged with the given numbers

linear_compartment_model(graph; inputs = [], outputs = [], leaks = [])

Input: defines a linear compartment model with nodes numbered from 1 to n by

• graph - and array of integer arrays representing the adjacency lists of the graph
• inputs - array of input nodes
• outputs - array of output nodes
• leaks - array of sink nodes

Output:

• the corresponding ODE system in a standard notation (as, e.g., in this paper)

Example: Consider a bidirected cycle with four nodes. Its adjacency list can be written as follows:

[ [2, 4], [1, 3], [2, 4], [1, 3] ]

In the list above, the i-th element is a list of vertices to which there exists an edge from the vertex i. Now we can create a linear compartment model over this graph with the output at vertex 1, input at vertex 2, and leaks at vertices 3 and 4 as follows:

julia> ode = linear_compartment_model([[2, 4], [1, 3], [2, 4], [1, 3]], outputs = [1], inputs = [2], leaks = [2, 3])
x1' = -x1*a_2_1 - x1*a_4_1 + x2*a_1_2 + x4*a_1_4
x3' = x2*a_3_2 - x3*a_2_3 - x3*a_4_3 - x3*a_0_3 + x4*a_3_4
x2' = x1*a_2_1 - x2*a_1_2 - x2*a_3_2 - x2*a_0_2 + x3*a_2_3 + u2
x4' = x1*a_4_1 + x3*a_4_3 - x4*a_1_4 - x4*a_3_4
y1 = x1

macro DDSmodel

Macro for creating a DDS (discrete dynamical system) from a list of equations. It also injects all variables into the global scope.

Example

Creating a simple DDS:

using StructuralIdentifiability

dds = @DDSmodel(
    x1(t + 1) = a * x1(t) + u(t),
    x2(t + 1) = b * x2(t) + c*x1(t)*x2(t),
    y(t) = x1(t)
)

Here,

• x1, x2 are state variables
• y is an output variable
• u is an input variable
• a, b, c are time-independent parameters