StrikeGoldd is a sandbox Julia package for analyzing structural identifiability of dynamical models described by ordinary differential equations (ODEs).
StrikeGoldd is (to an extent) a direct port of the MATBLAB package STRIKE-GOLDD. The package STRIKE-GOLDD is licensed under the GNU GPL Version 3.
To install StrikeGoldd, execute this command in the Julia REPL
import Pkg; Pkg.add(url="https://github.com/sumiya11/StrikeGoldd")StrikeGoldd provides two functions: find_some_identifiable_functions and find_some_symmetries.
StrikeGoldd provides the function find_some_identifiable_functions, which can be applied to polynomial ODE models to find some at least locally identifiable functions of parameters. For example, you can run in Julia:
using StrikeGoldd # load the package
ode = @ODEmodel( # create the ODE
x1'(t) = x1*x2 + a*b,
x2'(t) = x2 + a*c,
y(t) = x1
)
funcs = find_some_identifiable_functions(ode)Running this code will print:
[ Info: Searching for some (at least locally) identifiable functions
┌ Info: Constructing the observability matrix with respect to parameters:
└ Nemo.QQMPolyRingElem[a, b, c]
[ Info: The observability matrix of size (3, 3) has rank 2
┌ Info: Searching for identifiable functions of degree 2 of the form:
│ a^2*r5 + a*b*r6 + a*c*r7 + a*r2 + b^2*r8 + b*c*r9 + b*r3 + c^2*r10 + c*r4 + r1
└ where Nemo.QQMPolyRingElem[r1, r2, r3, r4, r5, r6, r7, r8, r9, r10] are the unknown coefficients.
┌ Info: Constructed the following system in Nemo.QQMPolyRingElem[r1, r2, r3, r4, r5, r6, r7, r8, r9, r10]:
└ -2*a^2*r5 - a*r2 + 2*b^2*r8 + 2*b*c*r9 + b*r3 + 2*c^2*r10 + c*r4 = 0
┌ Info: Transformed into a linear system:
│ r4 = 0
│ -2*r5 = 0
│ 2*r8 = 0
│ -r2 = 0
│ r3 = 0
│ 2*r9 = 0
└ 2*r10 = 0
┌ Info: There are 3 independent solutions
│ solutions =
│ 3-element Vector{Dict{Nemo.QQMPolyRingElem, Nemo.QQFieldElem}}:
│ Dict(r9 => 0, r10 => 0, r1 => 1, r4 => 0, r3 => 0, r2 => 0, r5 => 0, r6 => 0, r7 => 0, r8 => 0…)
│ Dict(r9 => 0, r10 => 0, r1 => 0, r4 => 0, r3 => 0, r2 => 0, r5 => 0, r6 => 1, r7 => 0, r8 => 0…)
└ Dict(r9 => 0, r10 => 0, r1 => 0, r4 => 0, r3 => 0, r2 => 0, r5 => 0, r6 => 0, r7 => 1, r8 => 0…)
[ Info: Constructing the identifiable functions, normalizing the coefficients to 1
3-element Vector{Any}:
1
a*b
a*cStrikeGoldd provides the function find_some_symmetries, which can be applied to polynomial ODE models. For example, you can run in Julia:
using StrikeGoldd # load the package
ode = @ODEmodel( # create the ODE
x1'(t) = x1(t) + p1 + p2,
y(t) = x1(t)
)
symmetries = find_some_symmetries(ode)Running this code will print, among other things, the following:
[ Info: Start searching for symmetries
[ Info: Creating the infinitesimal generator
┌ Info: ODE has 1 states and 2 parameters.
└ Creating univariate infinitesimals of degree 2.
┌ Info: Introducing 9 unknown coefficients:
└ [r10,r11,r12,r20,r21,r22,r30,r31,r32].
[ Info: Extending the infinitesimal generator
[ Info: Constructing the linear system to solve
[ Info: Constructed the linear system with 11 equations
[ Info: Solving the system
[ Info: The dimension of the right-kernel is 1.
┌ Info: Found 1 infinitesimal generators:
└ (1) (0)∂/∂x1 + (-1)∂/∂p2 + (1)∂/∂p1
[ Info: Integrating infinitesimal generator (1)
[ Info: Found 1 symmetries
[ Info: The search for symmetries concluded in 5.571 seconds
1-element Vector{Any}:
Dict{Any, Any}(p1 => p1 + ε, p2 => p2 - ε, x1 => x1)